topology.category.Profinite.cofiltered_limit ⟷ Mathlib.Topology.Category.Profinite.CofilteredLimit

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

@@ -6,8 +6,8 @@ Authors: Adam Topaz
 import Topology.Category.Profinite.Basic
 import Topology.LocallyConstant.Basic
 import Topology.DiscreteQuotient
-import Topology.Category.Top.Limits.Cofiltered
-import Topology.Category.Top.Limits.Konig
+import Topology.Category.TopCat.Limits.Cofiltered
+import Topology.Category.TopCat.Limits.Konig
 
 #align_import topology.category.Profinite.cofiltered_limit from "leanprover-community/mathlib"@"fd4551cfe4b7484b81c2c9ba3405edae27659676"
 

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

@@ -107,13 +107,13 @@ theorem exists_isClopen_of_cofiltered {U : Set C.pt} (hU : IsClopen U) :
       dsimp only [W] at hh ⊢
       rwa [dif_pos hs, ← Set.preimage_comp, ← Profinite.coe_comp, C.w]
     · intro hx
-      simp_rw [Set.preimage_iUnion, Set.mem_iUnion] at hx 
+      simp_rw [Set.preimage_iUnion, Set.mem_iUnion] at hx
       obtain ⟨s, hs, hx⟩ := hx
       rw [h]
       refine' ⟨s.1, s.2, _⟩
       rw [(hV s).2]
-      dsimp only [W] at hx 
-      rwa [dif_pos hs, ← Set.preimage_comp, ← Profinite.coe_comp, C.w] at hx 
+      dsimp only [W] at hx
+      rwa [dif_pos hs, ← Set.preimage_comp, ← Profinite.coe_comp, C.w] at hx
 #align Profinite.exists_clopen_of_cofiltered Profinite.exists_isClopen_of_cofiltered
 -/
 
@@ -197,10 +197,10 @@ theorem exists_locallyConstant_finite_nonempty {α : Type _} [Finite α] [Nonemp
   · rw [h2.some_spec]
     exact h1
   · intro a b hh
-    apply_fun fun e => e a at hh 
-    dsimp [ι] at hh 
-    rw [if_pos rfl] at hh 
-    split_ifs at hh  with hh1 hh1
+    apply_fun fun e => e a at hh
+    dsimp [ι] at hh
+    rw [if_pos rfl] at hh
+    split_ifs at hh with hh1 hh1
     · exact hh1.symm
     · exact False.elim (bot_ne_top hh)
 #align Profinite.exists_locally_constant_finite_nonempty Profinite.exists_locallyConstant_finite_nonempty
@@ -239,7 +239,7 @@ theorem exists_locallyConstant {α : Type _} (f : LocallyConstant C.pt α) :
     obtain ⟨j, g', hj⟩ := exists_locally_constant_finite_nonempty _ hC f'
     refine' ⟨j, ⟨ff ∘ g', g'.is_locally_constant.comp _⟩, _⟩
     ext1 t
-    apply_fun fun e => e t at hj 
+    apply_fun fun e => e t at hj
     rw [LocallyConstant.coe_comap _ _ (C.π.app j).Continuous] at hj ⊢
     dsimp at hj ⊢
     rw [← hj]

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

@@ -57,7 +57,7 @@ theorem exists_isClopen_of_cofiltered {U : Set C.pt} (hU : IsClopen U) :
   rotate_left
   · intro i
     change TopologicalSpace.IsTopologicalBasis {W : Set (F.obj i) | IsClopen W}
-    apply isTopologicalBasis_clopen
+    apply isTopologicalBasis_isClopen
   · rintro i j f V (hV : IsClopen _)
     refine' ⟨hV.1.preimage _, hV.2.preimage _⟩ <;> continuity
   -- Using this, since `U` is open, we can write `U` as a union of clopen sets all of which

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

@@ -41,11 +41,11 @@ universe u
 variable {J : Type u} [SmallCategory J] [IsCofiltered J] {F : J ⥤ Profinite.{u}} (C : Cone F)
   (hC : IsLimit C)
 
-#print Profinite.exists_clopen_of_cofiltered /-
+#print Profinite.exists_isClopen_of_cofiltered /-
 /-- If `X` is a cofiltered limit of profinite sets, then any clopen subset of `X` arises from
 a clopen set in one of the terms in the limit.
 -/
-theorem exists_clopen_of_cofiltered {U : Set C.pt} (hU : IsClopen U) :
+theorem exists_isClopen_of_cofiltered {U : Set C.pt} (hU : IsClopen U) :
     ∃ (j : J) (V : Set (F.obj j)) (hV : IsClopen V), U = C.π.app j ⁻¹' V :=
   by
   -- First, we have the topological basis of the cofiltered limit obtained by pulling back
@@ -114,7 +114,7 @@ theorem exists_clopen_of_cofiltered {U : Set C.pt} (hU : IsClopen U) :
       rw [(hV s).2]
       dsimp only [W] at hx 
       rwa [dif_pos hs, ← Set.preimage_comp, ← Profinite.coe_comp, C.w] at hx 
-#align Profinite.exists_clopen_of_cofiltered Profinite.exists_clopen_of_cofiltered
+#align Profinite.exists_clopen_of_cofiltered Profinite.exists_isClopen_of_cofiltered
 -/
 
 #print Profinite.exists_locallyConstant_fin_two /-
@@ -124,11 +124,11 @@ theorem exists_locallyConstant_fin_two (f : LocallyConstant C.pt (Fin 2)) :
   let U := f ⁻¹' {0}
   have hU : IsClopen U := f.is_locally_constant.is_clopen_fiber _
   obtain ⟨j, V, hV, h⟩ := exists_clopen_of_cofiltered C hC hU
-  use j, LocallyConstant.ofClopen hV
+  use j, LocallyConstant.ofIsClopen hV
   apply LocallyConstant.locallyConstant_eq_of_fiber_zero_eq
   rw [LocallyConstant.coe_comap _ _ (C.π.app j).Continuous]
   conv_rhs => rw [Set.preimage_comp]
-  rw [LocallyConstant.ofClopen_fiber_zero hV, ← h]
+  rw [LocallyConstant.ofIsClopen_fiber_zero hV, ← h]
 #align Profinite.exists_locally_constant_fin_two Profinite.exists_locallyConstant_fin_two
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

@@ -222,7 +222,7 @@ theorem exists_locallyConstant {α : Type _} (f : LocallyConstant C.pt α) :
         exact @Set.eq_empty_of_isEmpty _ hj _
       · ext x
         exact hj.elim' (C.π.app j x)
-    simp only [← not_nonempty_iff, ← not_forall]
+    simp only [← not_nonempty_iff, ← Classical.not_forall]
     intro h
     haveI : ∀ j : J, Nonempty ((F ⋙ Profinite.toTopCat).obj j) := h
     haveI : ∀ j : J, T2Space ((F ⋙ Profinite.toTopCat).obj j) := fun j =>

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

@@ -3,11 +3,11 @@ Copyright (c) 2021 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 -/
-import Mathbin.Topology.Category.Profinite.Basic
-import Mathbin.Topology.LocallyConstant.Basic
-import Mathbin.Topology.DiscreteQuotient
-import Mathbin.Topology.Category.Top.Limits.Cofiltered
-import Mathbin.Topology.Category.Top.Limits.Konig
+import Topology.Category.Profinite.Basic
+import Topology.LocallyConstant.Basic
+import Topology.DiscreteQuotient
+import Topology.Category.Top.Limits.Cofiltered
+import Topology.Category.Top.Limits.Konig
 
 #align_import topology.category.Profinite.cofiltered_limit from "leanprover-community/mathlib"@"fd4551cfe4b7484b81c2c9ba3405edae27659676"
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
-
-! This file was ported from Lean 3 source module topology.category.Profinite.cofiltered_limit
-! leanprover-community/mathlib commit fd4551cfe4b7484b81c2c9ba3405edae27659676
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Category.Profinite.Basic
 import Mathbin.Topology.LocallyConstant.Basic
@@ -14,6 +9,8 @@ import Mathbin.Topology.DiscreteQuotient
 import Mathbin.Topology.Category.Top.Limits.Cofiltered
 import Mathbin.Topology.Category.Top.Limits.Konig
 
+#align_import topology.category.Profinite.cofiltered_limit from "leanprover-community/mathlib"@"fd4551cfe4b7484b81c2c9ba3405edae27659676"
+
 /-!
 # Cofiltered limits of profinite sets.
 

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

@@ -44,8 +44,7 @@ universe u
 variable {J : Type u} [SmallCategory J] [IsCofiltered J] {F : J ⥤ Profinite.{u}} (C : Cone F)
   (hC : IsLimit C)
 
-include hC
-
+#print Profinite.exists_clopen_of_cofiltered /-
 /-- If `X` is a cofiltered limit of profinite sets, then any clopen subset of `X` arises from
 a clopen set in one of the terms in the limit.
 -/
@@ -119,7 +118,9 @@ theorem exists_clopen_of_cofiltered {U : Set C.pt} (hU : IsClopen U) :
       dsimp only [W] at hx 
       rwa [dif_pos hs, ← Set.preimage_comp, ← Profinite.coe_comp, C.w] at hx 
 #align Profinite.exists_clopen_of_cofiltered Profinite.exists_clopen_of_cofiltered
+-/
 
+#print Profinite.exists_locallyConstant_fin_two /-
 theorem exists_locallyConstant_fin_two (f : LocallyConstant C.pt (Fin 2)) :
     ∃ (j : J) (g : LocallyConstant (F.obj j) (Fin 2)), f = g.comap (C.π.app _) :=
   by
@@ -132,7 +133,9 @@ theorem exists_locallyConstant_fin_two (f : LocallyConstant C.pt (Fin 2)) :
   conv_rhs => rw [Set.preimage_comp]
   rw [LocallyConstant.ofClopen_fiber_zero hV, ← h]
 #align Profinite.exists_locally_constant_fin_two Profinite.exists_locallyConstant_fin_two
+-/
 
+#print Profinite.exists_locallyConstant_finite_aux /-
 theorem exists_locallyConstant_finite_aux {α : Type _} [Finite α] (f : LocallyConstant C.pt α) :
     ∃ (j : J) (g : LocallyConstant (F.obj j) (α → Fin 2)),
       (f.map fun a b => if a = b then (0 : Fin 2) else 1) = g.comap (C.π.app _) :=
@@ -172,7 +175,9 @@ theorem exists_locallyConstant_finite_aux {α : Type _} [Finite α] (f : Locally
     rw [C.w]
   all_goals continuity
 #align Profinite.exists_locally_constant_finite_aux Profinite.exists_locallyConstant_finite_aux
+-/
 
+#print Profinite.exists_locallyConstant_finite_nonempty /-
 theorem exists_locallyConstant_finite_nonempty {α : Type _} [Finite α] [Nonempty α]
     (f : LocallyConstant C.pt α) :
     ∃ (j : J) (g : LocallyConstant (F.obj j) α), f = g.comap (C.π.app _) :=
@@ -202,7 +207,9 @@ theorem exists_locallyConstant_finite_nonempty {α : Type _} [Finite α] [Nonemp
     · exact hh1.symm
     · exact False.elim (bot_ne_top hh)
 #align Profinite.exists_locally_constant_finite_nonempty Profinite.exists_locallyConstant_finite_nonempty
+-/
 
+#print Profinite.exists_locallyConstant /-
 /-- Any locally constant function from a cofiltered limit of profinite sets factors through
 one of the components. -/
 theorem exists_locallyConstant {α : Type _} (f : LocallyConstant C.pt α) :
@@ -241,6 +248,7 @@ theorem exists_locallyConstant {α : Type _} (f : LocallyConstant C.pt α) :
     rw [← hj]
     rfl
 #align Profinite.exists_locally_constant Profinite.exists_locallyConstant
+-/
 
 end Profinite
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/c471da714c044131b90c133701e51b877c246677

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 
 ! This file was ported from Lean 3 source module topology.category.Profinite.cofiltered_limit
-! leanprover-community/mathlib commit 178a32653e369dce2da68dc6b2694e385d484ef1
+! leanprover-community/mathlib commit fd4551cfe4b7484b81c2c9ba3405edae27659676
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.Topology.Category.Top.Limits.Konig
 /-!
 # Cofiltered limits of profinite sets.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains some theorems about cofiltered limits of profinite sets.
 
 ## Main Results

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

@@ -53,11 +53,11 @@ theorem exists_clopen_of_cofiltered {U : Set C.pt} (hU : IsClopen U) :
   -- clopen sets from the factors in the limit. By continuity, all such sets are again clopen.
   have hB :=
     TopCat.isTopologicalBasis_cofiltered_limit.{u} (F ⋙ Profinite.toTopCat)
-      (Profinite.to_Top.map_cone C) (is_limit_of_preserves _ hC) (fun j => { W | IsClopen W }) _
+      (Profinite.to_Top.map_cone C) (is_limit_of_preserves _ hC) (fun j => {W | IsClopen W}) _
       (fun i => isClopen_univ) (fun i U1 U2 hU1 hU2 => hU1.inter hU2) _
   rotate_left
   · intro i
-    change TopologicalSpace.IsTopologicalBasis { W : Set (F.obj i) | IsClopen W }
+    change TopologicalSpace.IsTopologicalBasis {W : Set (F.obj i) | IsClopen W}
     apply isTopologicalBasis_clopen
   · rintro i j f V (hV : IsClopen _)
     refine' ⟨hV.1.preimage _, hV.2.preimage _⟩ <;> continuity
@@ -192,10 +192,10 @@ theorem exists_locallyConstant_finite_nonempty {α : Type _} [Finite α] [Nonemp
   · rw [h2.some_spec]
     exact h1
   · intro a b hh
-    apply_fun fun e => e a  at hh 
+    apply_fun fun e => e a at hh 
     dsimp [ι] at hh 
     rw [if_pos rfl] at hh 
-    split_ifs  at hh  with hh1 hh1
+    split_ifs at hh  with hh1 hh1
     · exact hh1.symm
     · exact False.elim (bot_ne_top hh)
 #align Profinite.exists_locally_constant_finite_nonempty Profinite.exists_locallyConstant_finite_nonempty
@@ -232,7 +232,7 @@ theorem exists_locallyConstant {α : Type _} (f : LocallyConstant C.pt α) :
     obtain ⟨j, g', hj⟩ := exists_locally_constant_finite_nonempty _ hC f'
     refine' ⟨j, ⟨ff ∘ g', g'.is_locally_constant.comp _⟩, _⟩
     ext1 t
-    apply_fun fun e => e t  at hj 
+    apply_fun fun e => e t at hj 
     rw [LocallyConstant.coe_comap _ _ (C.π.app j).Continuous] at hj ⊢
     dsimp at hj ⊢
     rw [← hj]

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

@@ -47,7 +47,7 @@ include hC
 a clopen set in one of the terms in the limit.
 -/
 theorem exists_clopen_of_cofiltered {U : Set C.pt} (hU : IsClopen U) :
-    ∃ (j : J)(V : Set (F.obj j))(hV : IsClopen V), U = C.π.app j ⁻¹' V :=
+    ∃ (j : J) (V : Set (F.obj j)) (hV : IsClopen V), U = C.π.app j ⁻¹' V :=
   by
   -- First, we have the topological basis of the cofiltered limit obtained by pulling back
   -- clopen sets from the factors in the limit. By continuity, all such sets are again clopen.
@@ -105,20 +105,20 @@ theorem exists_clopen_of_cofiltered {U : Set C.pt} (hU : IsClopen U) :
       simp_rw [Set.preimage_iUnion, Set.mem_iUnion]
       obtain ⟨_, ⟨s, rfl⟩, _, ⟨hs, rfl⟩, hh⟩ := hG hx
       refine' ⟨s, hs, _⟩
-      dsimp only [W] at hh⊢
+      dsimp only [W] at hh ⊢
       rwa [dif_pos hs, ← Set.preimage_comp, ← Profinite.coe_comp, C.w]
     · intro hx
-      simp_rw [Set.preimage_iUnion, Set.mem_iUnion] at hx
+      simp_rw [Set.preimage_iUnion, Set.mem_iUnion] at hx 
       obtain ⟨s, hs, hx⟩ := hx
       rw [h]
       refine' ⟨s.1, s.2, _⟩
       rw [(hV s).2]
-      dsimp only [W] at hx
-      rwa [dif_pos hs, ← Set.preimage_comp, ← Profinite.coe_comp, C.w] at hx
+      dsimp only [W] at hx 
+      rwa [dif_pos hs, ← Set.preimage_comp, ← Profinite.coe_comp, C.w] at hx 
 #align Profinite.exists_clopen_of_cofiltered Profinite.exists_clopen_of_cofiltered
 
 theorem exists_locallyConstant_fin_two (f : LocallyConstant C.pt (Fin 2)) :
-    ∃ (j : J)(g : LocallyConstant (F.obj j) (Fin 2)), f = g.comap (C.π.app _) :=
+    ∃ (j : J) (g : LocallyConstant (F.obj j) (Fin 2)), f = g.comap (C.π.app _) :=
   by
   let U := f ⁻¹' {0}
   have hU : IsClopen U := f.is_locally_constant.is_clopen_fiber _
@@ -131,7 +131,7 @@ theorem exists_locallyConstant_fin_two (f : LocallyConstant C.pt (Fin 2)) :
 #align Profinite.exists_locally_constant_fin_two Profinite.exists_locallyConstant_fin_two
 
 theorem exists_locallyConstant_finite_aux {α : Type _} [Finite α] (f : LocallyConstant C.pt α) :
-    ∃ (j : J)(g : LocallyConstant (F.obj j) (α → Fin 2)),
+    ∃ (j : J) (g : LocallyConstant (F.obj j) (α → Fin 2)),
       (f.map fun a b => if a = b then (0 : Fin 2) else 1) = g.comap (C.π.app _) :=
   by
   cases nonempty_fintype α
@@ -172,7 +172,7 @@ theorem exists_locallyConstant_finite_aux {α : Type _} [Finite α] (f : Locally
 
 theorem exists_locallyConstant_finite_nonempty {α : Type _} [Finite α] [Nonempty α]
     (f : LocallyConstant C.pt α) :
-    ∃ (j : J)(g : LocallyConstant (F.obj j) α), f = g.comap (C.π.app _) :=
+    ∃ (j : J) (g : LocallyConstant (F.obj j) α), f = g.comap (C.π.app _) :=
   by
   inhabit α
   obtain ⟨j, gg, h⟩ := exists_locally_constant_finite_aux _ hC f
@@ -192,10 +192,10 @@ theorem exists_locallyConstant_finite_nonempty {α : Type _} [Finite α] [Nonemp
   · rw [h2.some_spec]
     exact h1
   · intro a b hh
-    apply_fun fun e => e a  at hh
-    dsimp [ι] at hh
-    rw [if_pos rfl] at hh
-    split_ifs  at hh with hh1 hh1
+    apply_fun fun e => e a  at hh 
+    dsimp [ι] at hh 
+    rw [if_pos rfl] at hh 
+    split_ifs  at hh  with hh1 hh1
     · exact hh1.symm
     · exact False.elim (bot_ne_top hh)
 #align Profinite.exists_locally_constant_finite_nonempty Profinite.exists_locallyConstant_finite_nonempty
@@ -203,7 +203,7 @@ theorem exists_locallyConstant_finite_nonempty {α : Type _} [Finite α] [Nonemp
 /-- Any locally constant function from a cofiltered limit of profinite sets factors through
 one of the components. -/
 theorem exists_locallyConstant {α : Type _} (f : LocallyConstant C.pt α) :
-    ∃ (j : J)(g : LocallyConstant (F.obj j) α), f = g.comap (C.π.app _) :=
+    ∃ (j : J) (g : LocallyConstant (F.obj j) α), f = g.comap (C.π.app _) :=
   by
   let S := f.discrete_quotient
   let ff : S → α := f.lift
@@ -232,9 +232,9 @@ theorem exists_locallyConstant {α : Type _} (f : LocallyConstant C.pt α) :
     obtain ⟨j, g', hj⟩ := exists_locally_constant_finite_nonempty _ hC f'
     refine' ⟨j, ⟨ff ∘ g', g'.is_locally_constant.comp _⟩, _⟩
     ext1 t
-    apply_fun fun e => e t  at hj
-    rw [LocallyConstant.coe_comap _ _ (C.π.app j).Continuous] at hj⊢
-    dsimp at hj⊢
+    apply_fun fun e => e t  at hj 
+    rw [LocallyConstant.coe_comap _ _ (C.π.app j).Continuous] at hj ⊢
+    dsimp at hj ⊢
     rw [← hj]
     rfl
 #align Profinite.exists_locally_constant Profinite.exists_locallyConstant

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

@@ -30,7 +30,7 @@ This file contains some theorems about cofiltered limits of profinite sets.
 
 namespace Profinite
 
-open Classical
+open scoped Classical
 
 open CategoryTheory
 

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

@@ -149,14 +149,12 @@ theorem exists_locallyConstant_finite_aux {α : Type _} [Finite α] (f : Locally
   let ggg := LocallyConstant.unflip gg
   refine' ⟨j0, ggg, _⟩
   have : f.map ι = LocallyConstant.unflip (f.map ι).flip := by simp
-  rw [this]
-  clear this
+  rw [this]; clear this
   have :
     LocallyConstant.comap (C.π.app j0) ggg =
       LocallyConstant.unflip (LocallyConstant.comap (C.π.app j0) ggg).flip :=
     by simp
-  rw [this]
-  clear this
+  rw [this]; clear this
   congr 1
   ext1 a
   change ff a = _
@@ -225,8 +223,7 @@ theorem exists_locallyConstant {α : Type _} (f : LocallyConstant C.pt α) :
     haveI : ∀ j : J, CompactSpace ((F ⋙ Profinite.toTopCat).obj j) := fun j =>
       (inferInstance : CompactSpace (F.obj j))
     have cond := TopCat.nonempty_limitCone_of_compact_t2_cofiltered_system (F ⋙ Profinite.toTopCat)
-    suffices : Nonempty C.X
-    exact IsEmpty.false (S.proj this.some)
+    suffices : Nonempty C.X; exact IsEmpty.false (S.proj this.some)
     let D := Profinite.to_Top.map_cone C
     have hD : is_limit D := is_limit_of_preserves Profinite.toTopCat hC
     have CD := (hD.cone_point_unique_up_to_iso (TopCat.limitConeIsLimit.{u} _)).inv

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

@@ -94,7 +94,7 @@ theorem exists_clopen_of_cofiltered {U : Set C.pt} (hU : IsClopen U) :
   let W : S → Set (F.obj j0) := fun s => if hs : s ∈ G then F.map (f s hs) ⁻¹' V s else Set.univ
   -- Conclude, using the `j0` and the clopen set of `F.obj j0` obtained above.
   refine' ⟨j0, ⋃ (s : S) (hs : s ∈ G), W s, _, _⟩
-  · apply isClopen_bunionᵢ_finset
+  · apply isClopen_biUnion_finset
     intro s hs
     dsimp only [W]
     rw [dif_pos hs]
@@ -102,13 +102,13 @@ theorem exists_clopen_of_cofiltered {U : Set C.pt} (hU : IsClopen U) :
   · ext x
     constructor
     · intro hx
-      simp_rw [Set.preimage_unionᵢ, Set.mem_unionᵢ]
+      simp_rw [Set.preimage_iUnion, Set.mem_iUnion]
       obtain ⟨_, ⟨s, rfl⟩, _, ⟨hs, rfl⟩, hh⟩ := hG hx
       refine' ⟨s, hs, _⟩
       dsimp only [W] at hh⊢
       rwa [dif_pos hs, ← Set.preimage_comp, ← Profinite.coe_comp, C.w]
     · intro hx
-      simp_rw [Set.preimage_unionᵢ, Set.mem_unionᵢ] at hx
+      simp_rw [Set.preimage_iUnion, Set.mem_iUnion] at hx
       obtain ⟨s, hs, hx⟩ := hx
       rw [h]
       refine' ⟨s.1, s.2, _⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b8ba04e2f326f3f7cf24ad129beda58531ada61

@@ -52,7 +52,7 @@ theorem exists_clopen_of_cofiltered {U : Set C.pt} (hU : IsClopen U) :
   -- First, we have the topological basis of the cofiltered limit obtained by pulling back
   -- clopen sets from the factors in the limit. By continuity, all such sets are again clopen.
   have hB :=
-    TopCat.isTopologicalBasis_cofiltered_limit.{u} (F ⋙ Profinite.toTop)
+    TopCat.isTopologicalBasis_cofiltered_limit.{u} (F ⋙ Profinite.toTopCat)
       (Profinite.to_Top.map_cone C) (is_limit_of_preserves _ hC) (fun j => { W | IsClopen W }) _
       (fun i => isClopen_univ) (fun i U1 U2 hU1 hU2 => hU1.inter hU2) _
   rotate_left
@@ -219,16 +219,16 @@ theorem exists_locallyConstant {α : Type _} (f : LocallyConstant C.pt α) :
         exact hj.elim' (C.π.app j x)
     simp only [← not_nonempty_iff, ← not_forall]
     intro h
-    haveI : ∀ j : J, Nonempty ((F ⋙ Profinite.toTop).obj j) := h
-    haveI : ∀ j : J, T2Space ((F ⋙ Profinite.toTop).obj j) := fun j =>
+    haveI : ∀ j : J, Nonempty ((F ⋙ Profinite.toTopCat).obj j) := h
+    haveI : ∀ j : J, T2Space ((F ⋙ Profinite.toTopCat).obj j) := fun j =>
       (inferInstance : T2Space (F.obj j))
-    haveI : ∀ j : J, CompactSpace ((F ⋙ Profinite.toTop).obj j) := fun j =>
+    haveI : ∀ j : J, CompactSpace ((F ⋙ Profinite.toTopCat).obj j) := fun j =>
       (inferInstance : CompactSpace (F.obj j))
-    have cond := TopCat.nonempty_limitCone_of_compact_t2_cofiltered_system (F ⋙ Profinite.toTop)
+    have cond := TopCat.nonempty_limitCone_of_compact_t2_cofiltered_system (F ⋙ Profinite.toTopCat)
     suffices : Nonempty C.X
     exact IsEmpty.false (S.proj this.some)
     let D := Profinite.to_Top.map_cone C
-    have hD : is_limit D := is_limit_of_preserves Profinite.toTop hC
+    have hD : is_limit D := is_limit_of_preserves Profinite.toTopCat hC
     have CD := (hD.cone_point_unique_up_to_iso (TopCat.limitConeIsLimit.{u} _)).inv
     exact cond.map CD
   · let f' : LocallyConstant C.X S := ⟨S.proj, S.proj_is_locally_constant⟩

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

@@ -4,13 +4,15 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 
 ! This file was ported from Lean 3 source module topology.category.Profinite.cofiltered_limit
-! leanprover-community/mathlib commit 829895f162a1f29d0133f4b3538f4cd1fb5bffd3
+! leanprover-community/mathlib commit 178a32653e369dce2da68dc6b2694e385d484ef1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Category.Profinite.Basic
 import Mathbin.Topology.LocallyConstant.Basic
 import Mathbin.Topology.DiscreteQuotient
+import Mathbin.Topology.Category.Top.Limits.Cofiltered
+import Mathbin.Topology.Category.Top.Limits.Konig
 
 /-!
 # Cofiltered limits of profinite sets.

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

@@ -44,7 +44,7 @@ include hC
 /-- If `X` is a cofiltered limit of profinite sets, then any clopen subset of `X` arises from
 a clopen set in one of the terms in the limit.
 -/
-theorem exists_clopen_of_cofiltered {U : Set C.x} (hU : IsClopen U) :
+theorem exists_clopen_of_cofiltered {U : Set C.pt} (hU : IsClopen U) :
     ∃ (j : J)(V : Set (F.obj j))(hV : IsClopen V), U = C.π.app j ⁻¹' V :=
   by
   -- First, we have the topological basis of the cofiltered limit obtained by pulling back
@@ -115,7 +115,7 @@ theorem exists_clopen_of_cofiltered {U : Set C.x} (hU : IsClopen U) :
       rwa [dif_pos hs, ← Set.preimage_comp, ← Profinite.coe_comp, C.w] at hx
 #align Profinite.exists_clopen_of_cofiltered Profinite.exists_clopen_of_cofiltered
 
-theorem exists_locallyConstant_fin_two (f : LocallyConstant C.x (Fin 2)) :
+theorem exists_locallyConstant_fin_two (f : LocallyConstant C.pt (Fin 2)) :
     ∃ (j : J)(g : LocallyConstant (F.obj j) (Fin 2)), f = g.comap (C.π.app _) :=
   by
   let U := f ⁻¹' {0}
@@ -128,7 +128,7 @@ theorem exists_locallyConstant_fin_two (f : LocallyConstant C.x (Fin 2)) :
   rw [LocallyConstant.ofClopen_fiber_zero hV, ← h]
 #align Profinite.exists_locally_constant_fin_two Profinite.exists_locallyConstant_fin_two
 
-theorem exists_locallyConstant_finite_aux {α : Type _} [Finite α] (f : LocallyConstant C.x α) :
+theorem exists_locallyConstant_finite_aux {α : Type _} [Finite α] (f : LocallyConstant C.pt α) :
     ∃ (j : J)(g : LocallyConstant (F.obj j) (α → Fin 2)),
       (f.map fun a b => if a = b then (0 : Fin 2) else 1) = g.comap (C.π.app _) :=
   by
@@ -171,7 +171,7 @@ theorem exists_locallyConstant_finite_aux {α : Type _} [Finite α] (f : Locally
 #align Profinite.exists_locally_constant_finite_aux Profinite.exists_locallyConstant_finite_aux
 
 theorem exists_locallyConstant_finite_nonempty {α : Type _} [Finite α] [Nonempty α]
-    (f : LocallyConstant C.x α) :
+    (f : LocallyConstant C.pt α) :
     ∃ (j : J)(g : LocallyConstant (F.obj j) α), f = g.comap (C.π.app _) :=
   by
   inhabit α
@@ -202,7 +202,7 @@ theorem exists_locallyConstant_finite_nonempty {α : Type _} [Finite α] [Nonemp
 
 /-- Any locally constant function from a cofiltered limit of profinite sets factors through
 one of the components. -/
-theorem exists_locallyConstant {α : Type _} (f : LocallyConstant C.x α) :
+theorem exists_locallyConstant {α : Type _} (f : LocallyConstant C.pt α) :
     ∃ (j : J)(g : LocallyConstant (F.obj j) α), f = g.comap (C.π.app _) :=
   by
   let S := f.discrete_quotient

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

Changes the definition of LocallyConstant.comap so that it takes an argument of the form C(X, Y) instead of X → Y. There was no example of a non-continuous argument in mathlib, and this definition generally makes proofs easier.

@@ -117,11 +117,10 @@ theorem exists_locallyConstant_fin_two (hC : IsLimit C) (f : LocallyConstant C.p
   obtain ⟨j, V, hV, h⟩ := exists_isClopen_of_cofiltered C hC hU
   use j, LocallyConstant.ofIsClopen hV
   apply LocallyConstant.locallyConstant_eq_of_fiber_zero_eq
+  simp only [Fin.isValue, Functor.const_obj_obj, LocallyConstant.coe_comap, Set.preimage_comp,
+    LocallyConstant.ofIsClopen_fiber_zero]
   -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
-  conv_rhs => rw [Set.preimage_comp]
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [LocallyConstant.ofIsClopen_fiber_zero hV, ← h]
+  erw [← h]
 set_option linter.uppercaseLean3 false in
 #align Profinite.exists_locally_constant_fin_two Profinite.exists_locallyConstant_fin_two
 
@@ -155,20 +154,8 @@ theorem exists_locallyConstant_finite_aux {α : Type*} [Finite α] (hC : IsLimit
   rw [h]
   dsimp
   ext1 x
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [LocallyConstant.coe_comap _ _ (C.π.app (j a)).continuous]
-  dsimp [ggg, LocallyConstant.flip, LocallyConstant.unflip]
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [LocallyConstant.coe_comap _ _ (C.π.app j0).continuous]
-  dsimp
-  rw [LocallyConstant.coe_comap _ _ _]
-  -- Porting note: `repeat' rw [LocallyConstant.coe_comap]` didn't work
-  -- so I did all three rewrites manually
-  · dsimp
-    congr! 1
-    change _ = (C.π.app j0 ≫ F.map (fs a)) x
-    rw [C.w]; rfl
-  · exact (F.map _).continuous
+  change _ = (g a) ((C.π.app j0 ≫ F.map (fs a)) x)
+  rw [C.w]; rfl
 set_option linter.uppercaseLean3 false in
 #align Profinite.exists_locally_constant_finite_aux Profinite.exists_locallyConstant_finite_aux
 
@@ -181,13 +168,13 @@ theorem exists_locallyConstant_finite_nonempty {α : Type*} [Finite α] [Nonempt
   let σ : (α → Fin 2) → α := fun f => if h : ∃ a : α, ι a = f then h.choose else default
   refine' ⟨j, gg.map σ, _⟩
   ext x
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
+  simp only [Functor.const_obj_obj, LocallyConstant.coe_comap, LocallyConstant.map_apply,
+    Function.comp_apply]
   dsimp [σ]
   have h1 : ι (f x) = gg (C.π.app j x) := by
     change f.map (fun a b => if a = b then (0 : Fin 2) else 1) x = _
     -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-    erw [h, LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
+    erw [h]
     rfl
   have h2 : ∃ a : α, ι a = gg (C.π.app j x) := ⟨f x, h1⟩
   -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
@@ -240,8 +227,6 @@ theorem exists_locallyConstant {α : Type*} (hC : IsLimit C) (f : LocallyConstan
     refine' ⟨j, ⟨ff ∘ g', g'.isLocallyConstant.comp _⟩, _⟩
     ext1 t
     apply_fun fun e => e t at hj
-    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-    erw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous] at hj ⊢
     dsimp at hj ⊢
     rw [← hj]
     rfl

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

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

@@ -90,18 +90,18 @@ theorem exists_isClopen_of_cofiltered {U : Set C.pt} (hC : IsLimit C) (hU : IsCl
   refine' ⟨j0, ⋃ (s : S) (_ : s ∈ G), W s, _, _⟩
   · apply isClopen_biUnion_finset
     intro s hs
-    dsimp
+    dsimp [W]
     rw [dif_pos hs]
     exact ⟨(hV s).1.1.preimage (F.map _).continuous, (hV s).1.2.preimage (F.map _).continuous⟩
   · ext x
     constructor
     · intro hx
-      simp_rw [Set.preimage_iUnion, Set.mem_iUnion]
+      simp_rw [W, Set.preimage_iUnion, Set.mem_iUnion]
       obtain ⟨_, ⟨s, rfl⟩, _, ⟨hs, rfl⟩, hh⟩ := hG hx
       refine' ⟨s, hs, _⟩
       rwa [dif_pos hs, ← Set.preimage_comp, ← Profinite.coe_comp, ← Functor.map_comp, C.w]
     · intro hx
-      simp_rw [Set.preimage_iUnion, Set.mem_iUnion] at hx
+      simp_rw [W, Set.preimage_iUnion, Set.mem_iUnion] at hx
       obtain ⟨s, hs, hx⟩ := hx
       rw [h]
       refine' ⟨s.1, s.2, _⟩
@@ -157,7 +157,7 @@ theorem exists_locallyConstant_finite_aux {α : Type*} [Finite α] (hC : IsLimit
   ext1 x
   -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
   erw [LocallyConstant.coe_comap _ _ (C.π.app (j a)).continuous]
-  dsimp [LocallyConstant.flip, LocallyConstant.unflip]
+  dsimp [ggg, LocallyConstant.flip, LocallyConstant.unflip]
   -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
   erw [LocallyConstant.coe_comap _ _ (C.π.app j0).continuous]
   dsimp
@@ -183,7 +183,7 @@ theorem exists_locallyConstant_finite_nonempty {α : Type*} [Finite α] [Nonempt
   ext x
   -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
   erw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
-  dsimp
+  dsimp [σ]
   have h1 : ι (f x) = gg (C.π.app j x) := by
     change f.map (fun a b => if a = b then (0 : Fin 2) else 1) x = _
     -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
@@ -197,7 +197,7 @@ theorem exists_locallyConstant_finite_nonempty {α : Type*} [Finite α] [Nonempt
     exact h1
   · intro a b hh
     have hhh := congr_fun hh a
-    dsimp at hhh
+    dsimp [ι] at hhh
     rw [if_pos rfl] at hhh
     split_ifs at hhh with hh1
     · exact hh1.symm

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

This follows on from #6964.

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

@@ -65,11 +65,11 @@ theorem exists_isClopen_of_cofiltered {U : Set C.pt} (hC : IsLimit C) (hU : IsCl
 
   -- Since `U` is also closed, hence compact, it is covered by finitely many of the
   -- clopens constructed in the previous step.
-  have hUo : ∀ (i : ↑S), IsOpen ((fun s ↦ (forget Profinite).map (C.π.app (j s)) ⁻¹' V s) i)
-  · intro s
+  have hUo : ∀ (i : ↑S), IsOpen ((fun s ↦ (forget Profinite).map (C.π.app (j s)) ⁻¹' V s) i) := by
+    intro s
     exact (hV s).1.2.preimage (C.π.app (j s)).continuous
-  have hsU : U ⊆ ⋃ (i : ↑S), (fun s ↦ (forget Profinite).map (C.π.app (j s)) ⁻¹' V s) i
-  · dsimp only
+  have hsU : U ⊆ ⋃ (i : ↑S), (fun s ↦ (forget Profinite).map (C.π.app (j s)) ⁻¹' V s) i := by
+    dsimp only
     rw [h]
     rintro x ⟨T, hT, hx⟩
     refine' ⟨_, ⟨⟨T, hT⟩, rfl⟩, _⟩
@@ -215,8 +215,8 @@ theorem exists_locallyConstant {α : Type*} (hC : IsLimit C) (f : LocallyConstan
   · suffices ∃ j, IsEmpty (F.obj j) by
       refine' this.imp fun j hj => _
       refine' ⟨⟨hj.elim, fun A => _⟩, _⟩
-      · suffices : (fun a ↦ IsEmpty.elim hj a) ⁻¹' A = ∅
-        · rw [this]
+      · suffices (fun a ↦ IsEmpty.elim hj a) ⁻¹' A = ∅ by
+          rw [this]
           exact isOpen_empty
         exact @Set.eq_empty_of_isEmpty _ hj _
       · ext x
@@ -230,7 +230,7 @@ theorem exists_locallyConstant {α : Type*} (hC : IsLimit C) (f : LocallyConstan
       (inferInstance : CompactSpace (F.obj j))
     have cond := TopCat.nonempty_limitCone_of_compact_t2_cofiltered_system.{u}
       (F ⋙ Profinite.toTopCat)
-    suffices : Nonempty C.pt; exact IsEmpty.false (S.proj this.some)
+    suffices Nonempty C.pt from IsEmpty.false (S.proj this.some)
     let D := Profinite.toTopCat.mapCone C
     have hD : IsLimit D := isLimitOfPreserves Profinite.toTopCat hC
     have CD := (hD.conePointUniqueUpToIso (TopCat.limitConeIsLimit.{v, max u v} _)).inv

This one was added by myself and not removed in #10503.

@@ -36,9 +36,6 @@ universe u v
 
 variable {J : Type v} [SmallCategory J] [IsCofiltered J] {F : J ⥤ ProfiniteMax.{u, v}} (C : Cone F)
 
--- include hC
--- Porting note: I just add `(hC : IsLimit C)` explicitly as a hypothesis to all the theorems
-
 /-- If `X` is a cofiltered limit of profinite sets, then any clopen subset of `X` arises from
 a clopen set in one of the terms in the limit.
 -/

This PR adds PreservesColimits/PreservesLimits instances for adjoint functors.

Co-authored-by: Markus Himmel <markus@himmel-villmar.de>

@@ -36,11 +36,6 @@ universe u v
 
 variable {J : Type v} [SmallCategory J] [IsCofiltered J] {F : J ⥤ ProfiniteMax.{u, v}} (C : Cone F)
 
-noncomputable
-instance preserves_smaller_limits_toTopCat :
-    PreservesLimitsOfSize.{v, v} (toTopCat : ProfiniteMax.{v, u} ⥤ TopCatMax.{v, u}) :=
-  Limits.preservesLimitsOfSizeShrink.{v, max u v, v, max u v} _
-
 -- include hC
 -- Porting note: I just add `(hC : IsLimit C)` explicitly as a hypothesis to all the theorems
 
@@ -49,7 +44,6 @@ a clopen set in one of the terms in the limit.
 -/
 theorem exists_isClopen_of_cofiltered {U : Set C.pt} (hC : IsLimit C) (hU : IsClopen U) :
     ∃ (j : J) (V : Set (F.obj j)), IsClopen V ∧ U = C.π.app j ⁻¹' V := by
-  have := preserves_smaller_limits_toTopCat.{u, v}
   -- First, we have the topological basis of the cofiltered limit obtained by pulling back
   -- clopen sets from the factors in the limit. By continuity, all such sets are again clopen.
   have hB := TopCat.isTopologicalBasis_cofiltered_limit.{u, v} (F ⋙ Profinite.toTopCat)
@@ -218,7 +212,6 @@ set_option linter.uppercaseLean3 false in
 one of the components. -/
 theorem exists_locallyConstant {α : Type*} (hC : IsLimit C) (f : LocallyConstant C.pt α) :
     ∃ (j : J) (g : LocallyConstant (F.obj j) α), f = g.comap (C.π.app _) := by
-  have := preserves_smaller_limits_toTopCat.{u, v}
   let S := f.discreteQuotient
   let ff : S → α := f.lift
   cases isEmpty_or_nonempty S

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

@@ -65,7 +65,7 @@ theorem exists_isClopen_of_cofiltered {U : Set C.pt} (hC : IsLimit C) (hU : IsCl
     -- Porting note: `<;> continuity` fails
   -- Using this, since `U` is open, we can write `U` as a union of clopen sets all of which
   -- are preimages of clopens from the factors in the limit.
-  obtain ⟨S, hS, h⟩ := hB.open_eq_sUnion hU.1
+  obtain ⟨S, hS, h⟩ := hB.open_eq_sUnion hU.2
   clear hB
   let j : S → J := fun s => (hS s.2).choose
   let V : ∀ s : S, Set (F.obj (j s)) := fun s => (hS s.2).choose_spec.choose
@@ -76,7 +76,7 @@ theorem exists_isClopen_of_cofiltered {U : Set C.pt} (hC : IsLimit C) (hU : IsCl
   -- clopens constructed in the previous step.
   have hUo : ∀ (i : ↑S), IsOpen ((fun s ↦ (forget Profinite).map (C.π.app (j s)) ⁻¹' V s) i)
   · intro s
-    exact (hV s).1.1.preimage (C.π.app (j s)).continuous
+    exact (hV s).1.2.preimage (C.π.app (j s)).continuous
   have hsU : U ⊆ ⋃ (i : ↑S), (fun s ↦ (forget Profinite).map (C.π.app (j s)) ⁻¹' V s) i
   · dsimp only
     rw [h]
@@ -84,7 +84,7 @@ theorem exists_isClopen_of_cofiltered {U : Set C.pt} (hC : IsLimit C) (hU : IsCl
     refine' ⟨_, ⟨⟨T, hT⟩, rfl⟩, _⟩
     dsimp only [forget_map_eq_coe]
     rwa [← (hV ⟨T, hT⟩).2]
-  have := hU.2.isCompact.elim_finite_subcover (fun s : S => C.π.app (j s) ⁻¹' V s) hUo hsU
+  have := hU.1.isCompact.elim_finite_subcover (fun s : S => C.π.app (j s) ⁻¹' V s) hUo hsU
   -- Porting note: same remark as after `hB`
   -- We thus obtain a finite set `G : Finset J` and a clopen set of `F.obj j` for each
   -- `j ∈ G` such that `U` is the union of the preimages of these clopen sets.

Search for [∀∃].*(_ and manually replace some occurrences with more readable versions. In case of ∀, the new expressions are defeq to the old ones. In case of ∃, they differ by exists_prop.

In some rare cases, golf proofs that needed fixing.

@@ -48,7 +48,7 @@ instance preserves_smaller_limits_toTopCat :
 a clopen set in one of the terms in the limit.
 -/
 theorem exists_isClopen_of_cofiltered {U : Set C.pt} (hC : IsLimit C) (hU : IsClopen U) :
-    ∃ (j : J) (V : Set (F.obj j)) (_ : IsClopen V), U = C.π.app j ⁻¹' V := by
+    ∃ (j : J) (V : Set (F.obj j)), IsClopen V ∧ U = C.π.app j ⁻¹' V := by
   have := preserves_smaller_limits_toTopCat.{u, v}
   -- First, we have the topological basis of the cofiltered limit obtained by pulling back
   -- clopen sets from the factors in the limit. By continuity, all such sets are again clopen.
@@ -93,8 +93,7 @@ theorem exists_isClopen_of_cofiltered {U : Set C.pt} (hC : IsLimit C) (hU : IsCl
   -- Pulling back all of the sets from the previous step to `F.obj j0` and taking a union,
   -- we obtain a clopen set in `F.obj j0` which works.
   obtain ⟨j0, hj0⟩ := IsCofiltered.inf_objs_exists (G.image j)
-  let f : ∀ (s : S) (_ : s ∈ G), j0 ⟶ j s := fun s hs =>
-    (hj0 (Finset.mem_image.mpr ⟨s, hs, rfl⟩)).some
+  let f : ∀ s ∈ G, j0 ⟶ j s := fun s hs => (hj0 (Finset.mem_image.mpr ⟨s, hs, rfl⟩)).some
   let W : S → Set (F.obj j0) := fun s => if hs : s ∈ G then F.map (f s hs) ⁻¹' V s else Set.univ
   -- Conclude, using the `j0` and the clopen set of `F.obj j0` obtained above.
   refine' ⟨j0, ⋃ (s : S) (_ : s ∈ G), W s, _, _⟩

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

@@ -58,7 +58,7 @@ theorem exists_isClopen_of_cofiltered {U : Set C.pt} (hC : IsLimit C) (hU : IsCl
   rotate_left
   · intro i
     change TopologicalSpace.IsTopologicalBasis {W : Set (F.obj i) | IsClopen W}
-    apply isTopologicalBasis_clopen
+    apply isTopologicalBasis_isClopen
   · rintro i j f V (hV : IsClopen _)
     exact ⟨hV.1.preimage ((F ⋙ toTopCat).map f).continuous,
       hV.2.preimage ((F ⋙ toTopCat).map f).continuous⟩

This PR renames the field Clopens.clopen' -> Clopens.isClopen', and the lemmas

• preimage_closed_of_closed -> ContinuousOn.preimage_isClosed_of_isClosed

as well as: ClopenUpperSet.clopen -> ClopenUpperSet.isClopen connectedComponent_eq_iInter_clopen -> connectedComponent_eq_iInter_isClopen connectedComponent_subset_iInter_clopen -> connectedComponent_subset_iInter_isClopen continuous_boolIndicator_iff_clopen -> continuous_boolIndicator_iff_isClopen continuousOn_boolIndicator_iff_clopen -> continuousOn_boolIndicator_iff_isClopen DiscreteQuotient.ofClopen -> DiscreteQuotient.ofIsClopen disjoint_or_subset_of_clopen -> disjoint_or_subset_of_isClopen exists_clopen_{lower,upper}of_not_le -> exists_isClopen{lower,upper}_of_not_le exists_clopen_of_cofiltered -> exists_isClopen_of_cofiltered exists_clopen_of_totally_separated -> exists_isClopen_of_totally_separated exists_clopen_upper_or_lower_of_ne -> exists_isClopen_upper_or_lower_of_ne IsPreconnected.subset_clopen -> IsPreconnected.subset_isClopen isTotallyDisconnected_of_clopen_set -> isTotallyDisconnected_of_isClopen_set LocallyConstant.ofClopen_fiber_one -> LocallyConstant.ofIsClopen_fiber_one LocallyConstant.ofClopen_fiber_zero -> LocallyConstant.ofIsClopen_fiber_zero LocallyConstant.ofClopen -> LocallyConstant.ofIsClopen preimage_clopen_of_clopen -> preimage_isClopen_of_isClopen TopologicalSpace.Clopens.clopen -> TopologicalSpace.Clopens.isClopen

@@ -18,7 +18,7 @@ This file contains some theorems about cofiltered limits of profinite sets.
 
 ## Main Results
 
-- `exists_clopen_of_cofiltered` shows that any clopen set in a cofiltered limit of profinite
+- `exists_isClopen_of_cofiltered` shows that any clopen set in a cofiltered limit of profinite
   sets is the pullback of a clopen set from one of the factors in the limit.
 - `exists_locally_constant` shows that any locally constant function from a cofiltered limit
   of profinite sets factors through one of the components.
@@ -47,7 +47,7 @@ instance preserves_smaller_limits_toTopCat :
 /-- If `X` is a cofiltered limit of profinite sets, then any clopen subset of `X` arises from
 a clopen set in one of the terms in the limit.
 -/
-theorem exists_clopen_of_cofiltered {U : Set C.pt} (hC : IsLimit C) (hU : IsClopen U) :
+theorem exists_isClopen_of_cofiltered {U : Set C.pt} (hC : IsLimit C) (hU : IsClopen U) :
     ∃ (j : J) (V : Set (F.obj j)) (_ : IsClopen V), U = C.π.app j ⁻¹' V := by
   have := preserves_smaller_limits_toTopCat.{u, v}
   -- First, we have the topological basis of the cofiltered limit obtained by pulling back
@@ -118,20 +118,20 @@ theorem exists_clopen_of_cofiltered {U : Set C.pt} (hC : IsLimit C) (hU : IsClop
       rw [(hV s).2]
       rwa [dif_pos hs, ← Set.preimage_comp, ← Profinite.coe_comp, ← Functor.map_comp, C.w] at hx
 set_option linter.uppercaseLean3 false in
-#align Profinite.exists_clopen_of_cofiltered Profinite.exists_clopen_of_cofiltered
+#align Profinite.exists_clopen_of_cofiltered Profinite.exists_isClopen_of_cofiltered
 
 theorem exists_locallyConstant_fin_two (hC : IsLimit C) (f : LocallyConstant C.pt (Fin 2)) :
     ∃ (j : J) (g : LocallyConstant (F.obj j) (Fin 2)), f = g.comap (C.π.app _) := by
   let U := f ⁻¹' {0}
   have hU : IsClopen U := f.isLocallyConstant.isClopen_fiber _
-  obtain ⟨j, V, hV, h⟩ := exists_clopen_of_cofiltered C hC hU
-  use j, LocallyConstant.ofClopen hV
+  obtain ⟨j, V, hV, h⟩ := exists_isClopen_of_cofiltered C hC hU
+  use j, LocallyConstant.ofIsClopen hV
   apply LocallyConstant.locallyConstant_eq_of_fiber_zero_eq
   -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
   erw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
   conv_rhs => rw [Set.preimage_comp]
   -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [LocallyConstant.ofClopen_fiber_zero hV, ← h]
+  erw [LocallyConstant.ofIsClopen_fiber_zero hV, ← h]
 set_option linter.uppercaseLean3 false in
 #align Profinite.exists_locally_constant_fin_two Profinite.exists_locallyConstant_fin_two
 

We allow the indexing category for the cofiltered limit in the result Profinite.exists_locallyConstant to live in a smaller universe than our profinite sets.

@@ -24,7 +24,6 @@ This file contains some theorems about cofiltered limits of profinite sets.
   of profinite sets factors through one of the components.
 -/
 
-
 namespace Profinite
 
 open scoped Classical
@@ -33,9 +32,14 @@ open CategoryTheory
 
 open CategoryTheory.Limits
 
-universe u
+universe u v
+
+variable {J : Type v} [SmallCategory J] [IsCofiltered J] {F : J ⥤ ProfiniteMax.{u, v}} (C : Cone F)
 
-variable {J : Type u} [SmallCategory J] [IsCofiltered J] {F : J ⥤ Profinite.{u}} (C : Cone F)
+noncomputable
+instance preserves_smaller_limits_toTopCat :
+    PreservesLimitsOfSize.{v, v} (toTopCat : ProfiniteMax.{v, u} ⥤ TopCatMax.{v, u}) :=
+  Limits.preservesLimitsOfSizeShrink.{v, max u v, v, max u v} _
 
 -- include hC
 -- Porting note: I just add `(hC : IsLimit C)` explicitly as a hypothesis to all the theorems
@@ -45,9 +49,10 @@ a clopen set in one of the terms in the limit.
 -/
 theorem exists_clopen_of_cofiltered {U : Set C.pt} (hC : IsLimit C) (hU : IsClopen U) :
     ∃ (j : J) (V : Set (F.obj j)) (_ : IsClopen V), U = C.π.app j ⁻¹' V := by
+  have := preserves_smaller_limits_toTopCat.{u, v}
   -- First, we have the topological basis of the cofiltered limit obtained by pulling back
   -- clopen sets from the factors in the limit. By continuity, all such sets are again clopen.
-  have hB := TopCat.isTopologicalBasis_cofiltered_limit.{u, u} (F ⋙ Profinite.toTopCat)
+  have hB := TopCat.isTopologicalBasis_cofiltered_limit.{u, v} (F ⋙ Profinite.toTopCat)
       (Profinite.toTopCat.mapCone C) (isLimitOfPreserves _ hC) (fun j => {W | IsClopen W}) ?_
       (fun i => isClopen_univ) (fun i U1 U2 hU1 hU2 => hU1.inter hU2) ?_
   rotate_left
@@ -214,6 +219,7 @@ set_option linter.uppercaseLean3 false in
 one of the components. -/
 theorem exists_locallyConstant {α : Type*} (hC : IsLimit C) (f : LocallyConstant C.pt α) :
     ∃ (j : J) (g : LocallyConstant (F.obj j) α), f = g.comap (C.π.app _) := by
+  have := preserves_smaller_limits_toTopCat.{u, v}
   let S := f.discreteQuotient
   let ff : S → α := f.lift
   cases isEmpty_or_nonempty S
@@ -238,7 +244,7 @@ theorem exists_locallyConstant {α : Type*} (hC : IsLimit C) (f : LocallyConstan
     suffices : Nonempty C.pt; exact IsEmpty.false (S.proj this.some)
     let D := Profinite.toTopCat.mapCone C
     have hD : IsLimit D := isLimitOfPreserves Profinite.toTopCat hC
-    have CD := (hD.conePointUniqueUpToIso (TopCat.limitConeIsLimit.{u, u} _)).inv
+    have CD := (hD.conePointUniqueUpToIso (TopCat.limitConeIsLimit.{v, max u v} _)).inv
     exact cond.map CD
   · let f' : LocallyConstant C.pt S := ⟨S.proj, S.proj_isLocallyConstant⟩
     obtain ⟨j, g', hj⟩ := exists_locallyConstant_finite_nonempty _ hC f'

This reverts commit f3695eb2.

@@ -122,9 +122,11 @@ theorem exists_locallyConstant_fin_two (hC : IsLimit C) (f : LocallyConstant C.p
   obtain ⟨j, V, hV, h⟩ := exists_clopen_of_cofiltered C hC hU
   use j, LocallyConstant.ofClopen hV
   apply LocallyConstant.locallyConstant_eq_of_fiber_zero_eq
-  rw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
   conv_rhs => rw [Set.preimage_comp]
-  rw [LocallyConstant.ofClopen_fiber_zero hV, ← h]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [LocallyConstant.ofClopen_fiber_zero hV, ← h]
 set_option linter.uppercaseLean3 false in
 #align Profinite.exists_locally_constant_fin_two Profinite.exists_locallyConstant_fin_two
 
@@ -158,9 +160,11 @@ theorem exists_locallyConstant_finite_aux {α : Type*} [Finite α] (hC : IsLimit
   rw [h]
   dsimp
   ext1 x
-  rw [LocallyConstant.coe_comap _ _ (C.π.app (j a)).continuous]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [LocallyConstant.coe_comap _ _ (C.π.app (j a)).continuous]
   dsimp [LocallyConstant.flip, LocallyConstant.unflip]
-  rw [LocallyConstant.coe_comap _ _ (C.π.app j0).continuous]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [LocallyConstant.coe_comap _ _ (C.π.app j0).continuous]
   dsimp
   rw [LocallyConstant.coe_comap _ _ _]
   -- Porting note: `repeat' rw [LocallyConstant.coe_comap]` didn't work
@@ -168,7 +172,7 @@ theorem exists_locallyConstant_finite_aux {α : Type*} [Finite α] (hC : IsLimit
   · dsimp
     congr! 1
     change _ = (C.π.app j0 ≫ F.map (fs a)) x
-    rw [C.w]
+    rw [C.w]; rfl
   · exact (F.map _).continuous
 set_option linter.uppercaseLean3 false in
 #align Profinite.exists_locally_constant_finite_aux Profinite.exists_locallyConstant_finite_aux
@@ -182,14 +186,17 @@ theorem exists_locallyConstant_finite_nonempty {α : Type*} [Finite α] [Nonempt
   let σ : (α → Fin 2) → α := fun f => if h : ∃ a : α, ι a = f then h.choose else default
   refine' ⟨j, gg.map σ, _⟩
   ext x
-  rw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
   dsimp
   have h1 : ι (f x) = gg (C.π.app j x) := by
     change f.map (fun a b => if a = b then (0 : Fin 2) else 1) x = _
-    rw [h, LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
+    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+    erw [h, LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
     rfl
   have h2 : ∃ a : α, ι a = gg (C.π.app j x) := ⟨f x, h1⟩
-  rw [dif_pos h2]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [dif_pos h2]
   apply_fun ι
   · rw [h2.choose_spec]
     exact h1
@@ -238,7 +245,8 @@ theorem exists_locallyConstant {α : Type*} (hC : IsLimit C) (f : LocallyConstan
     refine' ⟨j, ⟨ff ∘ g', g'.isLocallyConstant.comp _⟩, _⟩
     ext1 t
     apply_fun fun e => e t at hj
-    rw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous] at hj ⊢
+    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+    erw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous] at hj ⊢
     dsimp at hj ⊢
     rw [← hj]
     rfl

This reverts commit 26eb2b0a.

@@ -122,11 +122,9 @@ theorem exists_locallyConstant_fin_two (hC : IsLimit C) (f : LocallyConstant C.p
   obtain ⟨j, V, hV, h⟩ := exists_clopen_of_cofiltered C hC hU
   use j, LocallyConstant.ofClopen hV
   apply LocallyConstant.locallyConstant_eq_of_fiber_zero_eq
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
+  rw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
   conv_rhs => rw [Set.preimage_comp]
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [LocallyConstant.ofClopen_fiber_zero hV, ← h]
+  rw [LocallyConstant.ofClopen_fiber_zero hV, ← h]
 set_option linter.uppercaseLean3 false in
 #align Profinite.exists_locally_constant_fin_two Profinite.exists_locallyConstant_fin_two
 
@@ -160,11 +158,9 @@ theorem exists_locallyConstant_finite_aux {α : Type*} [Finite α] (hC : IsLimit
   rw [h]
   dsimp
   ext1 x
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [LocallyConstant.coe_comap _ _ (C.π.app (j a)).continuous]
+  rw [LocallyConstant.coe_comap _ _ (C.π.app (j a)).continuous]
   dsimp [LocallyConstant.flip, LocallyConstant.unflip]
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [LocallyConstant.coe_comap _ _ (C.π.app j0).continuous]
+  rw [LocallyConstant.coe_comap _ _ (C.π.app j0).continuous]
   dsimp
   rw [LocallyConstant.coe_comap _ _ _]
   -- Porting note: `repeat' rw [LocallyConstant.coe_comap]` didn't work
@@ -172,7 +168,7 @@ theorem exists_locallyConstant_finite_aux {α : Type*} [Finite α] (hC : IsLimit
   · dsimp
     congr! 1
     change _ = (C.π.app j0 ≫ F.map (fs a)) x
-    rw [C.w]; rfl
+    rw [C.w]
   · exact (F.map _).continuous
 set_option linter.uppercaseLean3 false in
 #align Profinite.exists_locally_constant_finite_aux Profinite.exists_locallyConstant_finite_aux
@@ -186,17 +182,14 @@ theorem exists_locallyConstant_finite_nonempty {α : Type*} [Finite α] [Nonempt
   let σ : (α → Fin 2) → α := fun f => if h : ∃ a : α, ι a = f then h.choose else default
   refine' ⟨j, gg.map σ, _⟩
   ext x
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
+  rw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
   dsimp
   have h1 : ι (f x) = gg (C.π.app j x) := by
     change f.map (fun a b => if a = b then (0 : Fin 2) else 1) x = _
-    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-    erw [h, LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
+    rw [h, LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
     rfl
   have h2 : ∃ a : α, ι a = gg (C.π.app j x) := ⟨f x, h1⟩
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [dif_pos h2]
+  rw [dif_pos h2]
   apply_fun ι
   · rw [h2.choose_spec]
     exact h1
@@ -245,8 +238,7 @@ theorem exists_locallyConstant {α : Type*} (hC : IsLimit C) (f : LocallyConstan
     refine' ⟨j, ⟨ff ∘ g', g'.isLocallyConstant.comp _⟩, _⟩
     ext1 t
     apply_fun fun e => e t at hj
-    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-    erw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous] at hj ⊢
+    rw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous] at hj ⊢
     dsimp at hj ⊢
     rw [← hj]
     rfl

This includes all the changes from #7606.

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

@@ -122,9 +122,11 @@ theorem exists_locallyConstant_fin_two (hC : IsLimit C) (f : LocallyConstant C.p
   obtain ⟨j, V, hV, h⟩ := exists_clopen_of_cofiltered C hC hU
   use j, LocallyConstant.ofClopen hV
   apply LocallyConstant.locallyConstant_eq_of_fiber_zero_eq
-  rw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
   conv_rhs => rw [Set.preimage_comp]
-  rw [LocallyConstant.ofClopen_fiber_zero hV, ← h]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [LocallyConstant.ofClopen_fiber_zero hV, ← h]
 set_option linter.uppercaseLean3 false in
 #align Profinite.exists_locally_constant_fin_two Profinite.exists_locallyConstant_fin_two
 
@@ -158,9 +160,11 @@ theorem exists_locallyConstant_finite_aux {α : Type*} [Finite α] (hC : IsLimit
   rw [h]
   dsimp
   ext1 x
-  rw [LocallyConstant.coe_comap _ _ (C.π.app (j a)).continuous]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [LocallyConstant.coe_comap _ _ (C.π.app (j a)).continuous]
   dsimp [LocallyConstant.flip, LocallyConstant.unflip]
-  rw [LocallyConstant.coe_comap _ _ (C.π.app j0).continuous]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [LocallyConstant.coe_comap _ _ (C.π.app j0).continuous]
   dsimp
   rw [LocallyConstant.coe_comap _ _ _]
   -- Porting note: `repeat' rw [LocallyConstant.coe_comap]` didn't work
@@ -168,7 +172,7 @@ theorem exists_locallyConstant_finite_aux {α : Type*} [Finite α] (hC : IsLimit
   · dsimp
     congr! 1
     change _ = (C.π.app j0 ≫ F.map (fs a)) x
-    rw [C.w]
+    rw [C.w]; rfl
   · exact (F.map _).continuous
 set_option linter.uppercaseLean3 false in
 #align Profinite.exists_locally_constant_finite_aux Profinite.exists_locallyConstant_finite_aux
@@ -182,14 +186,17 @@ theorem exists_locallyConstant_finite_nonempty {α : Type*} [Finite α] [Nonempt
   let σ : (α → Fin 2) → α := fun f => if h : ∃ a : α, ι a = f then h.choose else default
   refine' ⟨j, gg.map σ, _⟩
   ext x
-  rw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
   dsimp
   have h1 : ι (f x) = gg (C.π.app j x) := by
     change f.map (fun a b => if a = b then (0 : Fin 2) else 1) x = _
-    rw [h, LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
+    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+    erw [h, LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
     rfl
   have h2 : ∃ a : α, ι a = gg (C.π.app j x) := ⟨f x, h1⟩
-  rw [dif_pos h2]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [dif_pos h2]
   apply_fun ι
   · rw [h2.choose_spec]
     exact h1
@@ -238,7 +245,8 @@ theorem exists_locallyConstant {α : Type*} (hC : IsLimit C) (f : LocallyConstan
     refine' ⟨j, ⟨ff ∘ g', g'.isLocallyConstant.comp _⟩, _⟩
     ext1 t
     apply_fun fun e => e t at hj
-    rw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous] at hj ⊢
+    -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+    erw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous] at hj ⊢
     dsimp at hj ⊢
     rw [← hj]
     rfl

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

This has nice performance benefits.

@@ -128,7 +128,7 @@ theorem exists_locallyConstant_fin_two (hC : IsLimit C) (f : LocallyConstant C.p
 set_option linter.uppercaseLean3 false in
 #align Profinite.exists_locally_constant_fin_two Profinite.exists_locallyConstant_fin_two
 
-theorem exists_locallyConstant_finite_aux {α : Type _} [Finite α] (hC : IsLimit C)
+theorem exists_locallyConstant_finite_aux {α : Type*} [Finite α] (hC : IsLimit C)
     (f : LocallyConstant C.pt α) : ∃ (j : J) (g : LocallyConstant (F.obj j) (α → Fin 2)),
       (f.map fun a b => if a = b then (0 : Fin 2) else 1) = g.comap (C.π.app _) := by
   cases nonempty_fintype α
@@ -173,7 +173,7 @@ theorem exists_locallyConstant_finite_aux {α : Type _} [Finite α] (hC : IsLimi
 set_option linter.uppercaseLean3 false in
 #align Profinite.exists_locally_constant_finite_aux Profinite.exists_locallyConstant_finite_aux
 
-theorem exists_locallyConstant_finite_nonempty {α : Type _} [Finite α] [Nonempty α]
+theorem exists_locallyConstant_finite_nonempty {α : Type*} [Finite α] [Nonempty α]
     (hC : IsLimit C) (f : LocallyConstant C.pt α) :
     ∃ (j : J) (g : LocallyConstant (F.obj j) α), f = g.comap (C.π.app _) := by
   inhabit α
@@ -205,7 +205,7 @@ set_option linter.uppercaseLean3 false in
 
 /-- Any locally constant function from a cofiltered limit of profinite sets factors through
 one of the components. -/
-theorem exists_locallyConstant {α : Type _} (hC : IsLimit C) (f : LocallyConstant C.pt α) :
+theorem exists_locallyConstant {α : Type*} (hC : IsLimit C) (f : LocallyConstant C.pt α) :
     ∃ (j : J) (g : LocallyConstant (F.obj j) α), f = g.comap (C.π.app _) := by
   let S := f.discreteQuotient
   let ff : S → α := f.lift

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
-
-! This file was ported from Lean 3 source module topology.category.Profinite.cofiltered_limit
-! leanprover-community/mathlib commit 178a32653e369dce2da68dc6b2694e385d484ef1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Category.Profinite.Basic
 import Mathlib.Topology.LocallyConstant.Basic
@@ -14,6 +9,8 @@ import Mathlib.Topology.DiscreteQuotient
 import Mathlib.Topology.Category.TopCat.Limits.Cofiltered
 import Mathlib.Topology.Category.TopCat.Limits.Konig
 
+#align_import topology.category.Profinite.cofiltered_limit from "leanprover-community/mathlib"@"178a32653e369dce2da68dc6b2694e385d484ef1"
+
 /-!
 # Cofiltered limits of profinite sets.
 

This was caught up in a simultaneous split and port, and wasn't quite done correctly as a result

Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -229,7 +229,7 @@ theorem exists_locallyConstant {α : Type _} (hC : IsLimit C) (f : LocallyConsta
       (inferInstance : T2Space (F.obj j))
     haveI : ∀ j : J, CompactSpace ((F ⋙ Profinite.toTopCat).obj j) := fun j =>
       (inferInstance : CompactSpace (F.obj j))
-    have cond := TopCat.nonempty_limitCone_of_compact_t2_cofiltered_system.{u, u}
+    have cond := TopCat.nonempty_limitCone_of_compact_t2_cofiltered_system.{u}
       (F ⋙ Profinite.toTopCat)
     suffices : Nonempty C.pt; exact IsEmpty.false (S.proj this.some)
     let D := Profinite.toTopCat.mapCone C

@@ -38,8 +38,6 @@ open CategoryTheory.Limits
 
 universe u
 
-set_option autoImplicit false -- **TODO** delete this later
-
 variable {J : Type u} [SmallCategory J] [IsCofiltered J] {F : J ⥤ Profinite.{u}} (C : Cone F)
 
 -- include hC
@@ -86,7 +84,7 @@ theorem exists_clopen_of_cofiltered {U : Set C.pt} (hC : IsLimit C) (hU : IsClop
     rwa [← (hV ⟨T, hT⟩).2]
   have := hU.2.isCompact.elim_finite_subcover (fun s : S => C.π.app (j s) ⁻¹' V s) hUo hsU
   -- Porting note: same remark as after `hB`
-  -- We thus obtain a finite set `G : finset J` and a clopen set of `F.obj j` for each
+  -- We thus obtain a finite set `G : Finset J` and a clopen set of `F.obj j` for each
   -- `j ∈ G` such that `U` is the union of the preimages of these clopen sets.
   obtain ⟨G, hG⟩ := this
   -- Since `J` is cofiltered, we can find a single `j0` dominating all the `j ∈ G`.

To create new goals from have you need to use ?_, rather than _.

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

@@ -52,22 +52,17 @@ theorem exists_clopen_of_cofiltered {U : Set C.pt} (hC : IsLimit C) (hU : IsClop
     ∃ (j : J) (V : Set (F.obj j)) (_ : IsClopen V), U = C.π.app j ⁻¹' V := by
   -- First, we have the topological basis of the cofiltered limit obtained by pulling back
   -- clopen sets from the factors in the limit. By continuity, all such sets are again clopen.
-  have hT : ∀ (j : J), TopologicalSpace.IsTopologicalBasis
-      ((fun j ↦ {W : Set (F.obj j)| IsClopen W}) j)
+  have hB := TopCat.isTopologicalBasis_cofiltered_limit.{u, u} (F ⋙ Profinite.toTopCat)
+      (Profinite.toTopCat.mapCone C) (isLimitOfPreserves _ hC) (fun j => {W | IsClopen W}) ?_
+      (fun i => isClopen_univ) (fun i U1 U2 hU1 hU2 => hU1.inter hU2) ?_
+  rotate_left
   · intro i
     change TopologicalSpace.IsTopologicalBasis {W : Set (F.obj i) | IsClopen W}
     apply isTopologicalBasis_clopen
-  have compat : ∀ (i j : J) (f : i ⟶ j) (V : Set ↑((F ⋙ toTopCat).obj j)),
-      V ∈ (fun j ↦ {W | IsClopen W}) j → (forget TopCat).map ((F ⋙ toTopCat).map f) ⁻¹' V ∈
-      (fun j ↦ {W | IsClopen W}) i
   · rintro i j f V (hV : IsClopen _)
     exact ⟨hV.1.preimage ((F ⋙ toTopCat).map f).continuous,
       hV.2.preimage ((F ⋙ toTopCat).map f).continuous⟩
     -- Porting note: `<;> continuity` fails
-  have hB := TopCat.isTopologicalBasis_cofiltered_limit.{u, u} (F ⋙ Profinite.toTopCat)
-      (Profinite.toTopCat.mapCone C) (isLimitOfPreserves _ hC) (fun j => {W | IsClopen W}) hT
-      (fun i => isClopen_univ) (fun i U1 U2 hU1 hU2 => hU1.inter hU2) compat
-  -- Porting note: before, `hT` and `compat` were blank and created new goals proved afterwards.
   -- Using this, since `U` is open, we can write `U` as a union of clopen sets all of which
   -- are preimages of clopens from the factors in the limit.
   obtain ⟨S, hS, h⟩ := hB.open_eq_sUnion hU.1

@@ -87,7 +87,7 @@ theorem exists_clopen_of_cofiltered {U : Set C.pt} (hC : IsLimit C) (hU : IsClop
     rw [h]
     rintro x ⟨T, hT, hx⟩
     refine' ⟨_, ⟨⟨T, hT⟩, rfl⟩, _⟩
-    dsimp only
+    dsimp only [forget_map_eq_coe]
     rwa [← (hV ⟨T, hT⟩).2]
   have := hU.2.isCompact.elim_finite_subcover (fun s : S => C.π.app (j s) ⁻¹' V s) hUo hsU
   -- Porting note: same remark as after `hB`
@@ -132,7 +132,7 @@ theorem exists_locallyConstant_fin_two (hC : IsLimit C) (f : LocallyConstant C.p
   obtain ⟨j, V, hV, h⟩ := exists_clopen_of_cofiltered C hC hU
   use j, LocallyConstant.ofClopen hV
   apply LocallyConstant.locallyConstant_eq_of_fiber_zero_eq
-  rw [LocallyConstant.coe_comap ((forget Profinite).map _) _ (C.π.app j).continuous]
+  rw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
   conv_rhs => rw [Set.preimage_comp]
   rw [LocallyConstant.ofClopen_fiber_zero hV, ← h]
 set_option linter.uppercaseLean3 false in
@@ -168,11 +168,11 @@ theorem exists_locallyConstant_finite_aux {α : Type _} [Finite α] (hC : IsLimi
   rw [h]
   dsimp
   ext1 x
-  rw [LocallyConstant.coe_comap ((forget Profinite).map _) _ (C.π.app (j a)).continuous]
+  rw [LocallyConstant.coe_comap _ _ (C.π.app (j a)).continuous]
   dsimp [LocallyConstant.flip, LocallyConstant.unflip]
-  rw [LocallyConstant.coe_comap ((forget Profinite).map _) _ (C.π.app j0).continuous]
+  rw [LocallyConstant.coe_comap _ _ (C.π.app j0).continuous]
   dsimp
-  rw [LocallyConstant.coe_comap ((forget Profinite).map _) _ _]
+  rw [LocallyConstant.coe_comap _ _ _]
   -- Porting note: `repeat' rw [LocallyConstant.coe_comap]` didn't work
   -- so I did all three rewrites manually
   · dsimp
@@ -192,11 +192,11 @@ theorem exists_locallyConstant_finite_nonempty {α : Type _} [Finite α] [Nonemp
   let σ : (α → Fin 2) → α := fun f => if h : ∃ a : α, ι a = f then h.choose else default
   refine' ⟨j, gg.map σ, _⟩
   ext x
-  rw [LocallyConstant.coe_comap ((forget Profinite).map _) _ (C.π.app j).continuous]
+  rw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
   dsimp
   have h1 : ι (f x) = gg (C.π.app j x) := by
     change f.map (fun a b => if a = b then (0 : Fin 2) else 1) x = _
-    rw [h, LocallyConstant.coe_comap ((forget Profinite).map _) _ (C.π.app j).continuous]
+    rw [h, LocallyConstant.coe_comap _ _ (C.π.app j).continuous]
     rfl
   have h2 : ∃ a : α, ι a = gg (C.π.app j x) := ⟨f x, h1⟩
   rw [dif_pos h2]
@@ -248,7 +248,7 @@ theorem exists_locallyConstant {α : Type _} (hC : IsLimit C) (f : LocallyConsta
     refine' ⟨j, ⟨ff ∘ g', g'.isLocallyConstant.comp _⟩, _⟩
     ext1 t
     apply_fun fun e => e t at hj
-    rw [LocallyConstant.coe_comap ((forget Profinite).map _) _ (C.π.app j).continuous] at hj ⊢
+    rw [LocallyConstant.coe_comap _ _ (C.π.app j).continuous] at hj ⊢
     dsimp at hj ⊢
     rw [← hj]
     rfl