topology.sets.closeds ⟷ Mathlib.Topology.Sets.Closeds

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

@@ -302,7 +302,7 @@ theorem Closeds.isAtom_iff [T1Space α] {s : Closeds α} : IsAtom s ↔ ∃ x, s
     refine' closeds.gi.is_atom_iff' rfl (fun t ht => _) s
     obtain ⟨x, rfl⟩ := t.is_atom_iff.mp ht
     exact closure_singleton
-  simpa only [← this, (s : Set α).isAtom_iff, SetLike.ext_iff, Set.ext_iff]
+  simpa only [← this, (s : Set α).isAtom_iff_le_of_ge, SetLike.ext_iff, Set.ext_iff]
 #align topological_space.closeds.is_atom_iff TopologicalSpace.Closeds.isAtom_iff
 -/
 
@@ -315,7 +315,7 @@ theorem Opens.isCoatom_iff [T1Space α] {s : Opens α} :
   by
   rw [← s.compl_compl, ← isAtom_dual_iff_isCoatom]
   change IsAtom (closeds.compl_order_iso α s.compl) ↔ _
-  rw [(closeds.compl_order_iso α).isAtom_iff, closeds.is_atom_iff]
+  rw [(closeds.compl_order_iso α).isAtom_iff_le_of_ge, closeds.is_atom_iff]
   trace
     "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr∃ , »((x), _)]]"
   exact closeds.compl_bijective.injective.eq_iff.symm

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

@@ -339,17 +339,17 @@ instance : SetLike (Clopens α) α where
   coe s := s.carrier
   coe_injective' s t h := by cases s; cases t; congr
 
-#print TopologicalSpace.Clopens.clopen /-
-theorem clopen (s : Clopens α) : IsClopen (s : Set α) :=
+#print TopologicalSpace.Clopens.isClopen /-
+theorem isClopen (s : Clopens α) : IsClopen (s : Set α) :=
   s.clopen'
-#align topological_space.clopens.clopen TopologicalSpace.Clopens.clopen
+#align topological_space.clopens.clopen TopologicalSpace.Clopens.isClopen
 -/
 
 #print TopologicalSpace.Clopens.toOpens /-
 /-- Reinterpret a compact open as an open. -/
 @[simps]
 def toOpens (s : Clopens α) : Opens α :=
-  ⟨s, s.clopen.IsOpen⟩
+  ⟨s, s.isClopen.IsOpen⟩
 #align topological_space.clopens.to_opens TopologicalSpace.Clopens.toOpens
 -/
 
@@ -368,10 +368,10 @@ theorem coe_mk (s : Set α) (h) : (mk s h : Set α) = s :=
 -/
 
 instance : Sup (Clopens α) :=
-  ⟨fun s t => ⟨s ∪ t, s.clopen.union t.clopen⟩⟩
+  ⟨fun s t => ⟨s ∪ t, s.isClopen.union t.isClopen⟩⟩
 
 instance : Inf (Clopens α) :=
-  ⟨fun s t => ⟨s ∩ t, s.clopen.inter t.clopen⟩⟩
+  ⟨fun s t => ⟨s ∩ t, s.isClopen.inter t.isClopen⟩⟩
 
 instance : Top (Clopens α) :=
   ⟨⟨⊤, isClopen_univ⟩⟩
@@ -380,10 +380,10 @@ instance : Bot (Clopens α) :=
   ⟨⟨⊥, isClopen_empty⟩⟩
 
 instance : SDiff (Clopens α) :=
-  ⟨fun s t => ⟨s \ t, s.clopen.diffₓ t.clopen⟩⟩
+  ⟨fun s t => ⟨s \ t, s.isClopen.diffₓ t.isClopen⟩⟩
 
 instance : HasCompl (Clopens α) :=
-  ⟨fun s => ⟨sᶜ, s.clopen.compl⟩⟩
+  ⟨fun s => ⟨sᶜ, s.isClopen.compl⟩⟩
 
 instance : BooleanAlgebra (Clopens α) :=
   SetLike.coe_injective.BooleanAlgebra _ (fun _ _ => rfl) (fun _ _ => rfl) rfl rfl (fun _ => rfl)

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

@@ -3,7 +3,7 @@ Copyright (c) 2020 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Yaël Dillies
 -/
-import Mathbin.Topology.Sets.Opens
+import Topology.Sets.Opens
 
 #align_import topology.sets.closeds from "leanprover-community/mathlib"@"34ee86e6a59d911a8e4f89b68793ee7577ae79c7"
 

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

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Yaël Dillies
-
-! This file was ported from Lean 3 source module topology.sets.closeds
-! leanprover-community/mathlib commit 34ee86e6a59d911a8e4f89b68793ee7577ae79c7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Sets.Opens
 
+#align_import topology.sets.closeds from "leanprover-community/mathlib"@"34ee86e6a59d911a8e4f89b68793ee7577ae79c7"
+
 /-!
 # Closed sets
 

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

@@ -78,10 +78,13 @@ protected def closure (s : Set α) : Closeds α :=
 #align topological_space.closeds.closure TopologicalSpace.Closeds.closure
 -/
 
+#print TopologicalSpace.Closeds.gc /-
 theorem gc : GaloisConnection Closeds.closure (coe : Closeds α → Set α) := fun s U =>
   ⟨subset_closure.trans, fun h => closure_minimal h U.closed⟩
 #align topological_space.closeds.gc TopologicalSpace.Closeds.gc
+-/
 
+#print TopologicalSpace.Closeds.gi /-
 /-- The galois coinsertion between sets and opens. -/
 def gi : GaloisInsertion (@Closeds.closure α _) coe
     where
@@ -90,6 +93,7 @@ def gi : GaloisInsertion (@Closeds.closure α _) coe
   le_l_u _ := subset_closure
   choice_eq s hs := SetLike.coe_injective <| subset_closure.antisymm hs
 #align topological_space.closeds.gi TopologicalSpace.Closeds.gi
+-/
 
 instance : CompleteLattice (Closeds α) :=
   CompleteLattice.copy
@@ -116,67 +120,91 @@ instance : CompleteLattice (Closeds α) :=
 instance : Inhabited (Closeds α) :=
   ⟨⊥⟩
 
+#print TopologicalSpace.Closeds.coe_sup /-
 @[simp, norm_cast]
 theorem coe_sup (s t : Closeds α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
   rfl
 #align topological_space.closeds.coe_sup TopologicalSpace.Closeds.coe_sup
+-/
 
+#print TopologicalSpace.Closeds.coe_inf /-
 @[simp, norm_cast]
 theorem coe_inf (s t : Closeds α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
   rfl
 #align topological_space.closeds.coe_inf TopologicalSpace.Closeds.coe_inf
+-/
 
+#print TopologicalSpace.Closeds.coe_top /-
 @[simp, norm_cast]
 theorem coe_top : (↑(⊤ : Closeds α) : Set α) = univ :=
   rfl
 #align topological_space.closeds.coe_top TopologicalSpace.Closeds.coe_top
+-/
 
+#print TopologicalSpace.Closeds.coe_bot /-
 @[simp, norm_cast]
 theorem coe_bot : (↑(⊥ : Closeds α) : Set α) = ∅ :=
   rfl
 #align topological_space.closeds.coe_bot TopologicalSpace.Closeds.coe_bot
+-/
 
+#print TopologicalSpace.Closeds.coe_sInf /-
 @[simp, norm_cast]
 theorem coe_sInf {S : Set (Closeds α)} : (↑(sInf S) : Set α) = ⋂ i ∈ S, ↑i :=
   rfl
 #align topological_space.closeds.coe_Inf TopologicalSpace.Closeds.coe_sInf
+-/
 
+#print TopologicalSpace.Closeds.coe_finset_sup /-
 @[simp, norm_cast]
 theorem coe_finset_sup (f : ι → Closeds α) (s : Finset ι) :
     (↑(s.sup f) : Set α) = s.sup (coe ∘ f) :=
   map_finset_sup (⟨⟨coe, coe_sup⟩, coe_bot⟩ : SupBotHom (Closeds α) (Set α)) _ _
 #align topological_space.closeds.coe_finset_sup TopologicalSpace.Closeds.coe_finset_sup
+-/
 
+#print TopologicalSpace.Closeds.coe_finset_inf /-
 @[simp, norm_cast]
 theorem coe_finset_inf (f : ι → Closeds α) (s : Finset ι) :
     (↑(s.inf f) : Set α) = s.inf (coe ∘ f) :=
   map_finset_inf (⟨⟨coe, coe_inf⟩, coe_top⟩ : InfTopHom (Closeds α) (Set α)) _ _
 #align topological_space.closeds.coe_finset_inf TopologicalSpace.Closeds.coe_finset_inf
+-/
 
+#print TopologicalSpace.Closeds.iInf_def /-
 theorem iInf_def {ι} (s : ι → Closeds α) :
     (⨅ i, s i) = ⟨⋂ i, s i, isClosed_iInter fun i => (s i).2⟩ := by ext;
   simp only [iInf, coe_Inf, bInter_range]; rfl
 #align topological_space.closeds.infi_def TopologicalSpace.Closeds.iInf_def
+-/
 
+#print TopologicalSpace.Closeds.iInf_mk /-
 @[simp]
 theorem iInf_mk {ι} (s : ι → Set α) (h : ∀ i, IsClosed (s i)) :
     (⨅ i, ⟨s i, h i⟩ : Closeds α) = ⟨⋂ i, s i, isClosed_iInter h⟩ := by simp [infi_def]
 #align topological_space.closeds.infi_mk TopologicalSpace.Closeds.iInf_mk
+-/
 
+#print TopologicalSpace.Closeds.coe_iInf /-
 @[simp, norm_cast]
 theorem coe_iInf {ι} (s : ι → Closeds α) : ((⨅ i, s i : Closeds α) : Set α) = ⋂ i, s i := by
   simp [infi_def]
 #align topological_space.closeds.coe_infi TopologicalSpace.Closeds.coe_iInf
+-/
 
+#print TopologicalSpace.Closeds.mem_iInf /-
 @[simp]
 theorem mem_iInf {ι} {x : α} {s : ι → Closeds α} : x ∈ iInf s ↔ ∀ i, x ∈ s i := by
   simp [← SetLike.mem_coe]
 #align topological_space.closeds.mem_infi TopologicalSpace.Closeds.mem_iInf
+-/
 
+#print TopologicalSpace.Closeds.mem_sInf /-
 @[simp]
 theorem mem_sInf {S : Set (Closeds α)} {x : α} : x ∈ sInf S ↔ ∀ s ∈ S, x ∈ s := by
   simp_rw [sInf_eq_iInf, mem_infi]
 #align topological_space.closeds.mem_Inf TopologicalSpace.Closeds.mem_sInf
+-/
 
 instance : Coframe (Closeds α) :=
   { Closeds.completeLattice with
@@ -236,6 +264,7 @@ theorem Opens.compl_bijective : Function.Bijective (@Opens.compl α _) :=
 
 variable (α)
 
+#print TopologicalSpace.Closeds.complOrderIso /-
 /-- `closeds.compl` as an `order_iso` to the order dual of `opens α`. -/
 @[simps]
 def Closeds.complOrderIso : Closeds α ≃o (Opens α)ᵒᵈ
@@ -248,7 +277,9 @@ def Closeds.complOrderIso : Closeds α ≃o (Opens α)ᵒᵈ
     simpa only [Equiv.coe_fn_mk, Function.comp_apply, OrderDual.toDual_le_toDual] using
       compl_subset_compl
 #align topological_space.closeds.compl_order_iso TopologicalSpace.Closeds.complOrderIso
+-/
 
+#print TopologicalSpace.Opens.complOrderIso /-
 /-- `opens.compl` as an `order_iso` to the order dual of `closeds α`. -/
 @[simps]
 def Opens.complOrderIso : Opens α ≃o (Closeds α)ᵒᵈ
@@ -261,9 +292,11 @@ def Opens.complOrderIso : Opens α ≃o (Closeds α)ᵒᵈ
     simpa only [Equiv.coe_fn_mk, Function.comp_apply, OrderDual.toDual_le_toDual] using
       compl_subset_compl
 #align topological_space.opens.compl_order_iso TopologicalSpace.Opens.complOrderIso
+-/
 
 variable {α}
 
+#print TopologicalSpace.Closeds.isAtom_iff /-
 /-- in a `t1_space`, atoms of `closeds α` are precisely the `closeds.singleton`s. -/
 theorem Closeds.isAtom_iff [T1Space α] {s : Closeds α} : IsAtom s ↔ ∃ x, s = Closeds.singleton x :=
   by
@@ -274,8 +307,10 @@ theorem Closeds.isAtom_iff [T1Space α] {s : Closeds α} : IsAtom s ↔ ∃ x, s
     exact closure_singleton
   simpa only [← this, (s : Set α).isAtom_iff, SetLike.ext_iff, Set.ext_iff]
 #align topological_space.closeds.is_atom_iff TopologicalSpace.Closeds.isAtom_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr∃ , »((x), _)]] -/
+#print TopologicalSpace.Opens.isCoatom_iff /-
 /-- in a `t1_space`, coatoms of `opens α` are precisely complements of singletons:
 `(closeds.singleton x).compl`. -/
 theorem Opens.isCoatom_iff [T1Space α] {s : Opens α} :
@@ -288,6 +323,7 @@ theorem Opens.isCoatom_iff [T1Space α] {s : Opens α} :
     "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr∃ , »((x), _)]]"
   exact closeds.compl_bijective.injective.eq_iff.symm
 #align topological_space.opens.is_coatom_iff TopologicalSpace.Opens.isCoatom_iff
+-/
 
 /-! ### Clopen sets -/
 
@@ -356,35 +392,47 @@ instance : BooleanAlgebra (Clopens α) :=
   SetLike.coe_injective.BooleanAlgebra _ (fun _ _ => rfl) (fun _ _ => rfl) rfl rfl (fun _ => rfl)
     fun _ _ => rfl
 
+#print TopologicalSpace.Clopens.coe_sup /-
 @[simp]
 theorem coe_sup (s t : Clopens α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
   rfl
 #align topological_space.clopens.coe_sup TopologicalSpace.Clopens.coe_sup
+-/
 
+#print TopologicalSpace.Clopens.coe_inf /-
 @[simp]
 theorem coe_inf (s t : Clopens α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
   rfl
 #align topological_space.clopens.coe_inf TopologicalSpace.Clopens.coe_inf
+-/
 
+#print TopologicalSpace.Clopens.coe_top /-
 @[simp]
 theorem coe_top : (↑(⊤ : Clopens α) : Set α) = univ :=
   rfl
 #align topological_space.clopens.coe_top TopologicalSpace.Clopens.coe_top
+-/
 
+#print TopologicalSpace.Clopens.coe_bot /-
 @[simp]
 theorem coe_bot : (↑(⊥ : Clopens α) : Set α) = ∅ :=
   rfl
 #align topological_space.clopens.coe_bot TopologicalSpace.Clopens.coe_bot
+-/
 
+#print TopologicalSpace.Clopens.coe_sdiff /-
 @[simp]
 theorem coe_sdiff (s t : Clopens α) : (↑(s \ t) : Set α) = s \ t :=
   rfl
 #align topological_space.clopens.coe_sdiff TopologicalSpace.Clopens.coe_sdiff
+-/
 
+#print TopologicalSpace.Clopens.coe_compl /-
 @[simp]
 theorem coe_compl (s : Clopens α) : (↑(sᶜ) : Set α) = sᶜ :=
   rfl
 #align topological_space.clopens.coe_compl TopologicalSpace.Clopens.coe_compl
+-/
 
 instance : Inhabited (Clopens α) :=
   ⟨⊥⟩

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

@@ -78,22 +78,10 @@ protected def closure (s : Set α) : Closeds α :=
 #align topological_space.closeds.closure TopologicalSpace.Closeds.closure
 -/
 
-/- warning: topological_space.closeds.gc -> TopologicalSpace.Closeds.gc is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α], GaloisConnection.{u1, u1} (Set.{u1} α) (TopologicalSpace.Closeds.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α))))))) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1))) (TopologicalSpace.Closeds.closure.{u1} α _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α], GaloisConnection.{u1, u1} (Set.{u1} α) (TopologicalSpace.Closeds.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.instPartialOrder.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1))) (TopologicalSpace.Closeds.closure.{u1} α _inst_1) (SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align topological_space.closeds.gc TopologicalSpace.Closeds.gcₓ'. -/
 theorem gc : GaloisConnection Closeds.closure (coe : Closeds α → Set α) := fun s U =>
   ⟨subset_closure.trans, fun h => closure_minimal h U.closed⟩
 #align topological_space.closeds.gc TopologicalSpace.Closeds.gc
 
-/- warning: topological_space.closeds.gi -> TopologicalSpace.Closeds.gi is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α], GaloisInsertion.{u1, u1} (Set.{u1} α) (TopologicalSpace.Closeds.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α))))))) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1))) (TopologicalSpace.Closeds.closure.{u1} α _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α], GaloisInsertion.{u1, u1} (Set.{u1} α) (TopologicalSpace.Closeds.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.instPartialOrder.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1))) (TopologicalSpace.Closeds.closure.{u1} α _inst_1) (SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align topological_space.closeds.gi TopologicalSpace.Closeds.giₓ'. -/
 /-- The galois coinsertion between sets and opens. -/
 def gi : GaloisInsertion (@Closeds.closure α _) coe
     where
@@ -128,135 +116,63 @@ instance : CompleteLattice (Closeds α) :=
 instance : Inhabited (Closeds α) :=
   ⟨⊥⟩
 
-/- warning: topological_space.closeds.coe_sup -> TopologicalSpace.Closeds.coe_sup is a dubious translation:
-lean 3 declaration is
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 @[simp, norm_cast]
 theorem coe_sup (s t : Closeds α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
   rfl
 #align topological_space.closeds.coe_sup TopologicalSpace.Closeds.coe_sup
 
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 @[simp, norm_cast]
 theorem coe_inf (s t : Closeds α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
   rfl
 #align topological_space.closeds.coe_inf TopologicalSpace.Closeds.coe_inf
 
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 @[simp, norm_cast]
 theorem coe_top : (↑(⊤ : Closeds α) : Set α) = univ :=
   rfl
 #align topological_space.closeds.coe_top TopologicalSpace.Closeds.coe_top
 
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 @[simp, norm_cast]
 theorem coe_bot : (↑(⊥ : Closeds α) : Set α) = ∅ :=
   rfl
 #align topological_space.closeds.coe_bot TopologicalSpace.Closeds.coe_bot
 
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 @[simp, norm_cast]
 theorem coe_sInf {S : Set (Closeds α)} : (↑(sInf S) : Set α) = ⋂ i ∈ S, ↑i :=
   rfl
 #align topological_space.closeds.coe_Inf TopologicalSpace.Closeds.coe_sInf
 
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 @[simp, norm_cast]
 theorem coe_finset_sup (f : ι → Closeds α) (s : Finset ι) :
     (↑(s.sup f) : Set α) = s.sup (coe ∘ f) :=
   map_finset_sup (⟨⟨coe, coe_sup⟩, coe_bot⟩ : SupBotHom (Closeds α) (Set α)) _ _
 #align topological_space.closeds.coe_finset_sup TopologicalSpace.Closeds.coe_finset_sup
 
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 @[simp, norm_cast]
 theorem coe_finset_inf (f : ι → Closeds α) (s : Finset ι) :
     (↑(s.inf f) : Set α) = s.inf (coe ∘ f) :=
   map_finset_inf (⟨⟨coe, coe_inf⟩, coe_top⟩ : InfTopHom (Closeds α) (Set α)) _ _
 #align topological_space.closeds.coe_finset_inf TopologicalSpace.Closeds.coe_finset_inf
 
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 theorem iInf_def {ι} (s : ι → Closeds α) :
     (⨅ i, s i) = ⟨⋂ i, s i, isClosed_iInter fun i => (s i).2⟩ := by ext;
   simp only [iInf, coe_Inf, bInter_range]; rfl
 #align topological_space.closeds.infi_def TopologicalSpace.Closeds.iInf_def
 
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 @[simp]
 theorem iInf_mk {ι} (s : ι → Set α) (h : ∀ i, IsClosed (s i)) :
     (⨅ i, ⟨s i, h i⟩ : Closeds α) = ⟨⋂ i, s i, isClosed_iInter h⟩ := by simp [infi_def]
 #align topological_space.closeds.infi_mk TopologicalSpace.Closeds.iInf_mk
 
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-Case conversion may be inaccurate. Consider using '#align topological_space.closeds.coe_infi TopologicalSpace.Closeds.coe_iInfₓ'. -/
 @[simp, norm_cast]
 theorem coe_iInf {ι} (s : ι → Closeds α) : ((⨅ i, s i : Closeds α) : Set α) = ⋂ i, s i := by
   simp [infi_def]
 #align topological_space.closeds.coe_infi TopologicalSpace.Closeds.coe_iInf
 
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-Case conversion may be inaccurate. Consider using '#align topological_space.closeds.mem_infi TopologicalSpace.Closeds.mem_iInfₓ'. -/
 @[simp]
 theorem mem_iInf {ι} {x : α} {s : ι → Closeds α} : x ∈ iInf s ↔ ∀ i, x ∈ s i := by
   simp [← SetLike.mem_coe]
 #align topological_space.closeds.mem_infi TopologicalSpace.Closeds.mem_iInf
 
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-Case conversion may be inaccurate. Consider using '#align topological_space.closeds.mem_Inf TopologicalSpace.Closeds.mem_sInfₓ'. -/
 @[simp]
 theorem mem_sInf {S : Set (Closeds α)} {x : α} : x ∈ sInf S ↔ ∀ s ∈ S, x ∈ s := by
   simp_rw [sInf_eq_iInf, mem_infi]
@@ -320,12 +236,6 @@ theorem Opens.compl_bijective : Function.Bijective (@Opens.compl α _) :=
 
 variable (α)
 
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-Case conversion may be inaccurate. Consider using '#align topological_space.closeds.compl_order_iso TopologicalSpace.Closeds.complOrderIsoₓ'. -/
 /-- `closeds.compl` as an `order_iso` to the order dual of `opens α`. -/
 @[simps]
 def Closeds.complOrderIso : Closeds α ≃o (Opens α)ᵒᵈ
@@ -339,12 +249,6 @@ def Closeds.complOrderIso : Closeds α ≃o (Opens α)ᵒᵈ
       compl_subset_compl
 #align topological_space.closeds.compl_order_iso TopologicalSpace.Closeds.complOrderIso
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align topological_space.opens.compl_order_iso TopologicalSpace.Opens.complOrderIsoₓ'. -/
 /-- `opens.compl` as an `order_iso` to the order dual of `closeds α`. -/
 @[simps]
 def Opens.complOrderIso : Opens α ≃o (Closeds α)ᵒᵈ
@@ -360,12 +264,6 @@ def Opens.complOrderIso : Opens α ≃o (Closeds α)ᵒᵈ
 
 variable {α}
 
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-Case conversion may be inaccurate. Consider using '#align topological_space.closeds.is_atom_iff TopologicalSpace.Closeds.isAtom_iffₓ'. -/
 /-- in a `t1_space`, atoms of `closeds α` are precisely the `closeds.singleton`s. -/
 theorem Closeds.isAtom_iff [T1Space α] {s : Closeds α} : IsAtom s ↔ ∃ x, s = Closeds.singleton x :=
   by
@@ -377,12 +275,6 @@ theorem Closeds.isAtom_iff [T1Space α] {s : Closeds α} : IsAtom s ↔ ∃ x, s
   simpa only [← this, (s : Set α).isAtom_iff, SetLike.ext_iff, Set.ext_iff]
 #align topological_space.closeds.is_atom_iff TopologicalSpace.Closeds.isAtom_iff
 
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-Case conversion may be inaccurate. Consider using '#align topological_space.opens.is_coatom_iff TopologicalSpace.Opens.isCoatom_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr∃ , »((x), _)]] -/
 /-- in a `t1_space`, coatoms of `opens α` are precisely complements of singletons:
 `(closeds.singleton x).compl`. -/
@@ -464,67 +356,31 @@ instance : BooleanAlgebra (Clopens α) :=
   SetLike.coe_injective.BooleanAlgebra _ (fun _ _ => rfl) (fun _ _ => rfl) rfl rfl (fun _ => rfl)
     fun _ _ => rfl
 
-/- warning: topological_space.clopens.coe_sup -> TopologicalSpace.Clopens.coe_sup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align topological_space.clopens.coe_sup TopologicalSpace.Clopens.coe_supₓ'. -/
 @[simp]
 theorem coe_sup (s t : Clopens α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
   rfl
 #align topological_space.clopens.coe_sup TopologicalSpace.Clopens.coe_sup
 
-/- warning: topological_space.clopens.coe_inf -> TopologicalSpace.Clopens.coe_inf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align topological_space.clopens.coe_inf TopologicalSpace.Clopens.coe_infₓ'. -/
 @[simp]
 theorem coe_inf (s t : Clopens α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
   rfl
 #align topological_space.clopens.coe_inf TopologicalSpace.Clopens.coe_inf
 
-/- warning: topological_space.clopens.coe_top -> TopologicalSpace.Clopens.coe_top is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α], Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.setLike.{u1} α _inst_1)))) (Top.top.{u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (TopologicalSpace.Clopens.hasTop.{u1} α _inst_1))) (Set.univ.{u1} α)
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-Case conversion may be inaccurate. Consider using '#align topological_space.clopens.coe_top TopologicalSpace.Clopens.coe_topₓ'. -/
 @[simp]
 theorem coe_top : (↑(⊤ : Clopens α) : Set α) = univ :=
   rfl
 #align topological_space.clopens.coe_top TopologicalSpace.Clopens.coe_top
 
-/- warning: topological_space.clopens.coe_bot -> TopologicalSpace.Clopens.coe_bot is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align topological_space.clopens.coe_bot TopologicalSpace.Clopens.coe_botₓ'. -/
 @[simp]
 theorem coe_bot : (↑(⊥ : Clopens α) : Set α) = ∅ :=
   rfl
 #align topological_space.clopens.coe_bot TopologicalSpace.Clopens.coe_bot
 
-/- warning: topological_space.clopens.coe_sdiff -> TopologicalSpace.Clopens.coe_sdiff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Clopens.{u1} α _inst_1) (t : TopologicalSpace.Clopens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.setLike.{u1} α _inst_1)))) (SDiff.sdiff.{u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (TopologicalSpace.Clopens.hasSdiff.{u1} α _inst_1) s t)) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.setLike.{u1} α _inst_1)))) t))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Clopens.{u1} α _inst_1) (t : TopologicalSpace.Clopens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.instSetLikeClopens.{u1} α _inst_1) (SDiff.sdiff.{u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (TopologicalSpace.Clopens.instSDiffClopens.{u1} α _inst_1) s t)) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.instSetLikeClopens.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.instSetLikeClopens.{u1} α _inst_1) t))
-Case conversion may be inaccurate. Consider using '#align topological_space.clopens.coe_sdiff TopologicalSpace.Clopens.coe_sdiffₓ'. -/
 @[simp]
 theorem coe_sdiff (s t : Clopens α) : (↑(s \ t) : Set α) = s \ t :=
   rfl
 #align topological_space.clopens.coe_sdiff TopologicalSpace.Clopens.coe_sdiff
 
-/- warning: topological_space.clopens.coe_compl -> TopologicalSpace.Clopens.coe_compl is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Clopens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.setLike.{u1} α _inst_1)))) (HasCompl.compl.{u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (TopologicalSpace.Clopens.hasCompl.{u1} α _inst_1) s)) (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.setLike.{u1} α _inst_1)))) s))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Clopens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.instSetLikeClopens.{u1} α _inst_1) (HasCompl.compl.{u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (TopologicalSpace.Clopens.instHasComplClopens.{u1} α _inst_1) s)) (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)) (SetLike.coe.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.instSetLikeClopens.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align topological_space.clopens.coe_compl TopologicalSpace.Clopens.coe_complₓ'. -/
 @[simp]
 theorem coe_compl (s : Clopens α) : (↑(sᶜ) : Set α) = sᶜ :=
   rfl

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

@@ -49,10 +49,7 @@ variable {α}
 
 instance : SetLike (Closeds α) α where
   coe := Closeds.carrier
-  coe_injective' s t h := by
-    cases s
-    cases t
-    congr
+  coe_injective' s t h := by cases s; cases t; congr
 
 #print TopologicalSpace.Closeds.closed /-
 theorem closed (s : Closeds α) : IsClosed (s : Set α) :=
@@ -217,11 +214,8 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} (s : ι -> (TopologicalSpace.Closeds.{u1} α _inst_1)), Eq.{succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (iInf.{u1, u2} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toInfSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))) ι (fun (i : ι) => s i)) (TopologicalSpace.Closeds.mk.{u1} α _inst_1 (Set.iInter.{u1, u2} α ι (fun (i : ι) => SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) (s i))) (isClosed_iInter.{u1, u2} α ι _inst_1 (fun (i : ι) => SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) (s i)) (fun (i : ι) => TopologicalSpace.Closeds.closed'.{u1} α _inst_1 (s i))))
 Case conversion may be inaccurate. Consider using '#align topological_space.closeds.infi_def TopologicalSpace.Closeds.iInf_defₓ'. -/
 theorem iInf_def {ι} (s : ι → Closeds α) :
-    (⨅ i, s i) = ⟨⋂ i, s i, isClosed_iInter fun i => (s i).2⟩ :=
-  by
-  ext
-  simp only [iInf, coe_Inf, bInter_range]
-  rfl
+    (⨅ i, s i) = ⟨⋂ i, s i, isClosed_iInter fun i => (s i).2⟩ := by ext;
+  simp only [iInf, coe_Inf, bInter_range]; rfl
 #align topological_space.closeds.infi_def TopologicalSpace.Closeds.iInf_def
 
 /- warning: topological_space.closeds.infi_mk -> TopologicalSpace.Closeds.iInf_mk is a dubious translation:
@@ -418,10 +412,7 @@ namespace Clopens
 
 instance : SetLike (Clopens α) α where
   coe s := s.carrier
-  coe_injective' s t h := by
-    cases s
-    cases t
-    congr
+  coe_injective' s t h := by cases s; cases t; congr
 
 #print TopologicalSpace.Clopens.clopen /-
 theorem clopen (s : Clopens α) : IsClopen (s : Set α) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -188,7 +188,7 @@ theorem coe_sInf {S : Set (Closeds α)} : (↑(sInf S) : Set α) = ⋂ i ∈ S,
 
 /- warning: topological_space.closeds.coe_finset_sup -> TopologicalSpace.Closeds.coe_finset_sup is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] (f : ι -> (TopologicalSpace.Closeds.{u2} α _inst_1)) (s : Finset.{u1} ι), Eq.{succ u2} (Set.{u2} α) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (HasLiftT.mk.{succ u2, succ u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (CoeTCₓ.coe.{succ u2, succ u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (SetLike.Set.hasCoeT.{u2, u2} (TopologicalSpace.Closeds.{u2} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u2} α _inst_1)))) (Finset.sup.{u2, u1} (TopologicalSpace.Closeds.{u2} α _inst_1) ι (Lattice.toSemilatticeSup.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u2} α _inst_1)))) (BoundedOrder.toOrderBot.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Preorder.toLE.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (PartialOrder.toPreorder.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (SemilatticeSup.toPartialOrder.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Lattice.toSemilatticeSup.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u2} α _inst_1))))))) (CompleteLattice.toBoundedOrder.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u2} α _inst_1))) s f)) (Finset.sup.{u2, u1} (Set.{u2} α) ι (Lattice.toSemilatticeSup.{u2} (Set.{u2} α) (ConditionallyCompleteLattice.toLattice.{u2} (Set.{u2} α) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.completeBooleanAlgebra.{u2} α))))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} α) (Set.booleanAlgebra.{u2} α))) s (Function.comp.{succ u1, succ u2, succ u2} ι (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (HasLiftT.mk.{succ u2, succ u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (CoeTCₓ.coe.{succ u2, succ u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (SetLike.Set.hasCoeT.{u2, u2} (TopologicalSpace.Closeds.{u2} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u2} α _inst_1))))) f))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] (f : ι -> (TopologicalSpace.Closeds.{u2} α _inst_1)) (s : Finset.{u1} ι), Eq.{succ u2} (Set.{u2} α) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (HasLiftT.mk.{succ u2, succ u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (CoeTCₓ.coe.{succ u2, succ u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (SetLike.Set.hasCoeT.{u2, u2} (TopologicalSpace.Closeds.{u2} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u2} α _inst_1)))) (Finset.sup.{u2, u1} (TopologicalSpace.Closeds.{u2} α _inst_1) ι (Lattice.toSemilatticeSup.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u2} α _inst_1)))) (BoundedOrder.toOrderBot.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Preorder.toHasLe.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (PartialOrder.toPreorder.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (SemilatticeSup.toPartialOrder.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Lattice.toSemilatticeSup.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u2} α _inst_1))))))) (CompleteLattice.toBoundedOrder.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u2} α _inst_1))) s f)) (Finset.sup.{u2, u1} (Set.{u2} α) ι (Lattice.toSemilatticeSup.{u2} (Set.{u2} α) (ConditionallyCompleteLattice.toLattice.{u2} (Set.{u2} α) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.completeBooleanAlgebra.{u2} α))))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} α) (Set.booleanAlgebra.{u2} α))) s (Function.comp.{succ u1, succ u2, succ u2} ι (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (HasLiftT.mk.{succ u2, succ u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (CoeTCₓ.coe.{succ u2, succ u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (SetLike.Set.hasCoeT.{u2, u2} (TopologicalSpace.Closeds.{u2} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u2} α _inst_1))))) f))
 but is expected to have type
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] (f : ι -> (TopologicalSpace.Closeds.{u2} α _inst_1)) (s : Finset.{u1} ι), Eq.{succ u2} (Set.{u2} α) (SetLike.coe.{u2, u2} (TopologicalSpace.Closeds.{u2} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u2} α _inst_1) (Finset.sup.{u2, u1} (TopologicalSpace.Closeds.{u2} α _inst_1) ι (Lattice.toSemilatticeSup.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u2} α _inst_1)))) (BoundedOrder.toOrderBot.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Preorder.toLE.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (PartialOrder.toPreorder.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (SemilatticeSup.toPartialOrder.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Lattice.toSemilatticeSup.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u2} α _inst_1))))))) (CompleteLattice.toBoundedOrder.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u2} α _inst_1))) s f)) (Finset.sup.{u2, u1} (Set.{u2} α) ι (Lattice.toSemilatticeSup.{u2} (Set.{u2} α) (ConditionallyCompleteLattice.toLattice.{u2} (Set.{u2} α) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α))))))) (BoundedOrder.toOrderBot.{u2} (Set.{u2} α) (Preorder.toLE.{u2} (Set.{u2} α) (PartialOrder.toPreorder.{u2} (Set.{u2} α) (SemilatticeSup.toPartialOrder.{u2} (Set.{u2} α) (Lattice.toSemilatticeSup.{u2} (Set.{u2} α) (ConditionallyCompleteLattice.toLattice.{u2} (Set.{u2} α) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))))))) (CompleteLattice.toBoundedOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) s (Function.comp.{succ u1, succ u2, succ u2} ι (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (SetLike.coe.{u2, u2} (TopologicalSpace.Closeds.{u2} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u2} α _inst_1)) f))
 Case conversion may be inaccurate. Consider using '#align topological_space.closeds.coe_finset_sup TopologicalSpace.Closeds.coe_finset_supₓ'. -/
@@ -200,7 +200,7 @@ theorem coe_finset_sup (f : ι → Closeds α) (s : Finset ι) :
 
 /- warning: topological_space.closeds.coe_finset_inf -> TopologicalSpace.Closeds.coe_finset_inf is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] (f : ι -> (TopologicalSpace.Closeds.{u2} α _inst_1)) (s : Finset.{u1} ι), Eq.{succ u2} (Set.{u2} α) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (HasLiftT.mk.{succ u2, succ u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (CoeTCₓ.coe.{succ u2, succ u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (SetLike.Set.hasCoeT.{u2, u2} (TopologicalSpace.Closeds.{u2} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u2} α _inst_1)))) (Finset.inf.{u2, u1} (TopologicalSpace.Closeds.{u2} α _inst_1) ι (Lattice.toSemilatticeInf.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u2} α _inst_1)))) (BoundedOrder.toOrderTop.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Preorder.toLE.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (PartialOrder.toPreorder.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (SemilatticeInf.toPartialOrder.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Lattice.toSemilatticeInf.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u2} α _inst_1))))))) (CompleteLattice.toBoundedOrder.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u2} α _inst_1))) s f)) (Finset.inf.{u2, u1} (Set.{u2} α) ι (Lattice.toSemilatticeInf.{u2} (Set.{u2} α) (ConditionallyCompleteLattice.toLattice.{u2} (Set.{u2} α) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.completeBooleanAlgebra.{u2} α))))))) (Set.orderTop.{u2} α) s (Function.comp.{succ u1, succ u2, succ u2} ι (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (HasLiftT.mk.{succ u2, succ u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (CoeTCₓ.coe.{succ u2, succ u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (SetLike.Set.hasCoeT.{u2, u2} (TopologicalSpace.Closeds.{u2} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u2} α _inst_1))))) f))
+  forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] (f : ι -> (TopologicalSpace.Closeds.{u2} α _inst_1)) (s : Finset.{u1} ι), Eq.{succ u2} (Set.{u2} α) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (HasLiftT.mk.{succ u2, succ u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (CoeTCₓ.coe.{succ u2, succ u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (SetLike.Set.hasCoeT.{u2, u2} (TopologicalSpace.Closeds.{u2} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u2} α _inst_1)))) (Finset.inf.{u2, u1} (TopologicalSpace.Closeds.{u2} α _inst_1) ι (Lattice.toSemilatticeInf.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u2} α _inst_1)))) (BoundedOrder.toOrderTop.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Preorder.toHasLe.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (PartialOrder.toPreorder.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (SemilatticeInf.toPartialOrder.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Lattice.toSemilatticeInf.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u2} α _inst_1))))))) (CompleteLattice.toBoundedOrder.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u2} α _inst_1))) s f)) (Finset.inf.{u2, u1} (Set.{u2} α) ι (Lattice.toSemilatticeInf.{u2} (Set.{u2} α) (ConditionallyCompleteLattice.toLattice.{u2} (Set.{u2} α) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.completeBooleanAlgebra.{u2} α))))))) (Set.orderTop.{u2} α) s (Function.comp.{succ u1, succ u2, succ u2} ι (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (HasLiftT.mk.{succ u2, succ u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (CoeTCₓ.coe.{succ u2, succ u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (SetLike.Set.hasCoeT.{u2, u2} (TopologicalSpace.Closeds.{u2} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u2} α _inst_1))))) f))
 but is expected to have type
   forall {ι : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] (f : ι -> (TopologicalSpace.Closeds.{u2} α _inst_1)) (s : Finset.{u1} ι), Eq.{succ u2} (Set.{u2} α) (SetLike.coe.{u2, u2} (TopologicalSpace.Closeds.{u2} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u2} α _inst_1) (Finset.inf.{u2, u1} (TopologicalSpace.Closeds.{u2} α _inst_1) ι (Lattice.toSemilatticeInf.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u2} α _inst_1)))) (BoundedOrder.toOrderTop.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Preorder.toLE.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (PartialOrder.toPreorder.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (SemilatticeInf.toPartialOrder.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (Lattice.toSemilatticeInf.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u2} α _inst_1))))))) (CompleteLattice.toBoundedOrder.{u2} (TopologicalSpace.Closeds.{u2} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u2} α _inst_1))) s f)) (Finset.inf.{u2, u1} (Set.{u2} α) ι (Lattice.toSemilatticeInf.{u2} (Set.{u2} α) (ConditionallyCompleteLattice.toLattice.{u2} (Set.{u2} α) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α))))))) (Set.instOrderTopSetInstLESet.{u2} α) s (Function.comp.{succ u1, succ u2, succ u2} ι (TopologicalSpace.Closeds.{u2} α _inst_1) (Set.{u2} α) (SetLike.coe.{u2, u2} (TopologicalSpace.Closeds.{u2} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u2} α _inst_1)) f))
 Case conversion may be inaccurate. Consider using '#align topological_space.closeds.coe_finset_inf TopologicalSpace.Closeds.coe_finset_infₓ'. -/
@@ -328,7 +328,7 @@ variable (α)
 
 /- warning: topological_space.closeds.compl_order_iso -> TopologicalSpace.Closeds.complOrderIso is a dubious translation:
 lean 3 declaration is
-  forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α], OrderIso.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (OrderDual.{u1} (TopologicalSpace.Opens.{u1} α _inst_1)) (Preorder.toLE.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) (OrderDual.hasLe.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} α _inst_1) α (TopologicalSpace.Opens.setLike.{u1} α _inst_1)))))
+  forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α], OrderIso.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (OrderDual.{u1} (TopologicalSpace.Opens.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) (OrderDual.hasLe.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (Preorder.toHasLe.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} α _inst_1) α (TopologicalSpace.Opens.setLike.{u1} α _inst_1)))))
 but is expected to have type
   forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α], OrderIso.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (OrderDual.{u1} (TopologicalSpace.Opens.{u1} α _inst_1)) (Preorder.toLE.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))))) (OrderDual.instLEOrderDual.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} α _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align topological_space.closeds.compl_order_iso TopologicalSpace.Closeds.complOrderIsoₓ'. -/
@@ -347,7 +347,7 @@ def Closeds.complOrderIso : Closeds α ≃o (Opens α)ᵒᵈ
 
 /- warning: topological_space.opens.compl_order_iso -> TopologicalSpace.Opens.complOrderIso is a dubious translation:
 lean 3 declaration is
-  forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α], OrderIso.{u1, u1} (TopologicalSpace.Opens.{u1} α _inst_1) (OrderDual.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} α _inst_1) α (TopologicalSpace.Opens.setLike.{u1} α _inst_1)))) (OrderDual.hasLe.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Preorder.toLE.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))))
+  forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α], OrderIso.{u1, u1} (TopologicalSpace.Opens.{u1} α _inst_1) (OrderDual.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} α _inst_1) α (TopologicalSpace.Opens.setLike.{u1} α _inst_1)))) (OrderDual.hasLe.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Preorder.toHasLe.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))))
 but is expected to have type
   forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α], OrderIso.{u1, u1} (TopologicalSpace.Opens.{u1} α _inst_1) (OrderDual.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} α _inst_1))))) (OrderDual.instLEOrderDual.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Preorder.toLE.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align topological_space.opens.compl_order_iso TopologicalSpace.Opens.complOrderIsoₓ'. -/
@@ -368,7 +368,7 @@ variable {α}
 
 /- warning: topological_space.closeds.is_atom_iff -> TopologicalSpace.Closeds.isAtom_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T1Space.{u1} α _inst_1] {s : TopologicalSpace.Closeds.{u1} α _inst_1}, Iff (IsAtom.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Preorder.toLE.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u1} α _inst_1))) s) (Exists.{succ u1} α (fun (x : α) => Eq.{succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) s (TopologicalSpace.Closeds.singleton.{u1} α _inst_1 _inst_3 x)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T1Space.{u1} α _inst_1] {s : TopologicalSpace.Closeds.{u1} α _inst_1}, Iff (IsAtom.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1))) (BoundedOrder.toOrderBot.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Preorder.toHasLe.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u1} α _inst_1))) s) (Exists.{succ u1} α (fun (x : α) => Eq.{succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) s (TopologicalSpace.Closeds.singleton.{u1} α _inst_1 _inst_3 x)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T1Space.{u1} α _inst_1] {s : TopologicalSpace.Closeds.{u1} α _inst_1}, Iff (IsAtom.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1)))) (BoundedOrder.toOrderBot.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Preorder.toLE.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))))) (CompleteLattice.toBoundedOrder.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))) s) (Exists.{succ u1} α (fun (x : α) => Eq.{succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) s (TopologicalSpace.Closeds.singleton.{u1} α _inst_1 _inst_3 x)))
 Case conversion may be inaccurate. Consider using '#align topological_space.closeds.is_atom_iff TopologicalSpace.Closeds.isAtom_iffₓ'. -/
@@ -385,7 +385,7 @@ theorem Closeds.isAtom_iff [T1Space α] {s : Closeds α} : IsAtom s ↔ ∃ x, s
 
 /- warning: topological_space.opens.is_coatom_iff -> TopologicalSpace.Opens.isCoatom_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T1Space.{u1} α _inst_1] {s : TopologicalSpace.Opens.{u1} α _inst_1}, Iff (IsCoatom.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} α _inst_1) α (TopologicalSpace.Opens.setLike.{u1} α _inst_1))) (BoundedOrder.toOrderTop.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} α _inst_1) α (TopologicalSpace.Opens.setLike.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (TopologicalSpace.Opens.completeLattice.{u1} α _inst_1))) s) (Exists.{succ u1} α (fun (x : α) => Eq.{succ u1} (TopologicalSpace.Opens.{u1} α _inst_1) s (TopologicalSpace.Closeds.compl.{u1} α _inst_1 (TopologicalSpace.Closeds.singleton.{u1} α _inst_1 _inst_3 x))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T1Space.{u1} α _inst_1] {s : TopologicalSpace.Opens.{u1} α _inst_1}, Iff (IsCoatom.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} α _inst_1) α (TopologicalSpace.Opens.setLike.{u1} α _inst_1))) (BoundedOrder.toOrderTop.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (Preorder.toHasLe.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (SetLike.partialOrder.{u1, u1} (TopologicalSpace.Opens.{u1} α _inst_1) α (TopologicalSpace.Opens.setLike.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (TopologicalSpace.Opens.completeLattice.{u1} α _inst_1))) s) (Exists.{succ u1} α (fun (x : α) => Eq.{succ u1} (TopologicalSpace.Opens.{u1} α _inst_1) s (TopologicalSpace.Closeds.compl.{u1} α _inst_1 (TopologicalSpace.Closeds.singleton.{u1} α _inst_1 _inst_3 x))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T1Space.{u1} α _inst_1] {s : TopologicalSpace.Opens.{u1} α _inst_1}, Iff (IsCoatom.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} α _inst_1)))) (BoundedOrder.toOrderTop.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} α _inst_1))))) (CompleteLattice.toBoundedOrder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} α _inst_1))) s) (Exists.{succ u1} α (fun (x : α) => Eq.{succ u1} (TopologicalSpace.Opens.{u1} α _inst_1) s (TopologicalSpace.Closeds.compl.{u1} α _inst_1 (TopologicalSpace.Closeds.singleton.{u1} α _inst_1 _inst_3 x))))
 Case conversion may be inaccurate. Consider using '#align topological_space.opens.is_coatom_iff TopologicalSpace.Opens.isCoatom_iffₓ'. -/

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

@@ -124,8 +124,8 @@ instance : CompleteLattice (Closeds α) :=
     _
     rfl
     (-- Inf
-    fun S => ⟨⋂ s ∈ S, ↑s, isClosed_binterᵢ fun s _ => s.2⟩)
-    (funext fun S => SetLike.coe_injective infₛ_image.symm)
+    fun S => ⟨⋂ s ∈ S, ↑s, isClosed_biInter fun s _ => s.2⟩)
+    (funext fun S => SetLike.coe_injective sInf_image.symm)
 
 /-- The type of closed sets is inhabited, with default element the empty set. -/
 instance : Inhabited (Closeds α) :=
@@ -175,16 +175,16 @@ theorem coe_bot : (↑(⊥ : Closeds α) : Set α) = ∅ :=
   rfl
 #align topological_space.closeds.coe_bot TopologicalSpace.Closeds.coe_bot
 
-/- warning: topological_space.closeds.coe_Inf -> TopologicalSpace.Closeds.coe_infₛ is a dubious translation:
+/- warning: topological_space.closeds.coe_Inf -> TopologicalSpace.Closeds.coe_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {S : Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)}, Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) (InfSet.infₛ.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toHasInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u1} α _inst_1))) S)) (Set.interᵢ.{u1, succ u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (fun (i : TopologicalSpace.Closeds.{u1} α _inst_1) => Set.interᵢ.{u1, 0} α (Membership.Mem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) (Set.hasMem.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) i S) (fun (H : Membership.Mem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) (Set.hasMem.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) i S) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) i)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {S : Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)}, Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) (InfSet.sInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toHasInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u1} α _inst_1))) S)) (Set.iInter.{u1, succ u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (fun (i : TopologicalSpace.Closeds.{u1} α _inst_1) => Set.iInter.{u1, 0} α (Membership.Mem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) (Set.hasMem.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) i S) (fun (H : Membership.Mem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) (Set.hasMem.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) i S) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) i)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {S : Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)}, Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) (InfSet.infₛ.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toInfSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))) S)) (Set.interᵢ.{u1, succ u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (fun (i : TopologicalSpace.Closeds.{u1} α _inst_1) => Set.interᵢ.{u1, 0} α (Membership.mem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) i S) (fun (H : Membership.mem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) i S) => SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) i)))
-Case conversion may be inaccurate. Consider using '#align topological_space.closeds.coe_Inf TopologicalSpace.Closeds.coe_infₛₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {S : Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)}, Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) (InfSet.sInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toInfSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))) S)) (Set.iInter.{u1, succ u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (fun (i : TopologicalSpace.Closeds.{u1} α _inst_1) => Set.iInter.{u1, 0} α (Membership.mem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) i S) (fun (H : Membership.mem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) i S) => SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) i)))
+Case conversion may be inaccurate. Consider using '#align topological_space.closeds.coe_Inf TopologicalSpace.Closeds.coe_sInfₓ'. -/
 @[simp, norm_cast]
-theorem coe_infₛ {S : Set (Closeds α)} : (↑(infₛ S) : Set α) = ⋂ i ∈ S, ↑i :=
+theorem coe_sInf {S : Set (Closeds α)} : (↑(sInf S) : Set α) = ⋂ i ∈ S, ↑i :=
   rfl
-#align topological_space.closeds.coe_Inf TopologicalSpace.Closeds.coe_infₛ
+#align topological_space.closeds.coe_Inf TopologicalSpace.Closeds.coe_sInf
 
 /- warning: topological_space.closeds.coe_finset_sup -> TopologicalSpace.Closeds.coe_finset_sup is a dubious translation:
 lean 3 declaration is
@@ -210,69 +210,69 @@ theorem coe_finset_inf (f : ι → Closeds α) (s : Finset ι) :
   map_finset_inf (⟨⟨coe, coe_inf⟩, coe_top⟩ : InfTopHom (Closeds α) (Set α)) _ _
 #align topological_space.closeds.coe_finset_inf TopologicalSpace.Closeds.coe_finset_inf
 
-/- warning: topological_space.closeds.infi_def -> TopologicalSpace.Closeds.infᵢ_def is a dubious translation:
+/- warning: topological_space.closeds.infi_def -> TopologicalSpace.Closeds.iInf_def is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} (s : ι -> (TopologicalSpace.Closeds.{u1} α _inst_1)), Eq.{succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (infᵢ.{u1, u2} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toHasInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u1} α _inst_1))) ι (fun (i : ι) => s i)) (TopologicalSpace.Closeds.mk.{u1} α _inst_1 (Set.interᵢ.{u1, u2} α ι (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) (s i))) (isClosed_interᵢ.{u1, u2} α ι _inst_1 (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) (s i)) (fun (i : ι) => TopologicalSpace.Closeds.closed'.{u1} α _inst_1 (s i))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} (s : ι -> (TopologicalSpace.Closeds.{u1} α _inst_1)), Eq.{succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (iInf.{u1, u2} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toHasInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u1} α _inst_1))) ι (fun (i : ι) => s i)) (TopologicalSpace.Closeds.mk.{u1} α _inst_1 (Set.iInter.{u1, u2} α ι (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) (s i))) (isClosed_iInter.{u1, u2} α ι _inst_1 (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) (s i)) (fun (i : ι) => TopologicalSpace.Closeds.closed'.{u1} α _inst_1 (s i))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} (s : ι -> (TopologicalSpace.Closeds.{u1} α _inst_1)), Eq.{succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (infᵢ.{u1, u2} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toInfSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))) ι (fun (i : ι) => s i)) (TopologicalSpace.Closeds.mk.{u1} α _inst_1 (Set.interᵢ.{u1, u2} α ι (fun (i : ι) => SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) (s i))) (isClosed_interᵢ.{u1, u2} α ι _inst_1 (fun (i : ι) => SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) (s i)) (fun (i : ι) => TopologicalSpace.Closeds.closed'.{u1} α _inst_1 (s i))))
-Case conversion may be inaccurate. Consider using '#align topological_space.closeds.infi_def TopologicalSpace.Closeds.infᵢ_defₓ'. -/
-theorem infᵢ_def {ι} (s : ι → Closeds α) :
-    (⨅ i, s i) = ⟨⋂ i, s i, isClosed_interᵢ fun i => (s i).2⟩ :=
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} (s : ι -> (TopologicalSpace.Closeds.{u1} α _inst_1)), Eq.{succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (iInf.{u1, u2} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toInfSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))) ι (fun (i : ι) => s i)) (TopologicalSpace.Closeds.mk.{u1} α _inst_1 (Set.iInter.{u1, u2} α ι (fun (i : ι) => SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) (s i))) (isClosed_iInter.{u1, u2} α ι _inst_1 (fun (i : ι) => SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) (s i)) (fun (i : ι) => TopologicalSpace.Closeds.closed'.{u1} α _inst_1 (s i))))
+Case conversion may be inaccurate. Consider using '#align topological_space.closeds.infi_def TopologicalSpace.Closeds.iInf_defₓ'. -/
+theorem iInf_def {ι} (s : ι → Closeds α) :
+    (⨅ i, s i) = ⟨⋂ i, s i, isClosed_iInter fun i => (s i).2⟩ :=
   by
   ext
-  simp only [infᵢ, coe_Inf, bInter_range]
+  simp only [iInf, coe_Inf, bInter_range]
   rfl
-#align topological_space.closeds.infi_def TopologicalSpace.Closeds.infᵢ_def
+#align topological_space.closeds.infi_def TopologicalSpace.Closeds.iInf_def
 
-/- warning: topological_space.closeds.infi_mk -> TopologicalSpace.Closeds.infᵢ_mk is a dubious translation:
+/- warning: topological_space.closeds.infi_mk -> TopologicalSpace.Closeds.iInf_mk is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} (s : ι -> (Set.{u1} α)) (h : forall (i : ι), IsClosed.{u1} α _inst_1 (s i)), Eq.{succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (infᵢ.{u1, u2} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toHasInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u1} α _inst_1))) ι (fun (i : ι) => TopologicalSpace.Closeds.mk.{u1} α _inst_1 (s i) (h i))) (TopologicalSpace.Closeds.mk.{u1} α _inst_1 (Set.interᵢ.{u1, u2} α ι (fun (i : ι) => s i)) (isClosed_interᵢ.{u1, u2} α ι _inst_1 (fun (i : ι) => s i) h))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} (s : ι -> (Set.{u1} α)) (h : forall (i : ι), IsClosed.{u1} α _inst_1 (s i)), Eq.{succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (iInf.{u1, u2} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toHasInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u1} α _inst_1))) ι (fun (i : ι) => TopologicalSpace.Closeds.mk.{u1} α _inst_1 (s i) (h i))) (TopologicalSpace.Closeds.mk.{u1} α _inst_1 (Set.iInter.{u1, u2} α ι (fun (i : ι) => s i)) (isClosed_iInter.{u1, u2} α ι _inst_1 (fun (i : ι) => s i) h))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} (s : ι -> (Set.{u1} α)) (h : forall (i : ι), IsClosed.{u1} α _inst_1 (s i)), Eq.{succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (infᵢ.{u1, u2} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toInfSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))) ι (fun (i : ι) => TopologicalSpace.Closeds.mk.{u1} α _inst_1 (s i) (h i))) (TopologicalSpace.Closeds.mk.{u1} α _inst_1 (Set.interᵢ.{u1, u2} α ι (fun (i : ι) => s i)) (isClosed_interᵢ.{u1, u2} α ι _inst_1 (fun (i : ι) => s i) h))
-Case conversion may be inaccurate. Consider using '#align topological_space.closeds.infi_mk TopologicalSpace.Closeds.infᵢ_mkₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} (s : ι -> (Set.{u1} α)) (h : forall (i : ι), IsClosed.{u1} α _inst_1 (s i)), Eq.{succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (iInf.{u1, u2} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toInfSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))) ι (fun (i : ι) => TopologicalSpace.Closeds.mk.{u1} α _inst_1 (s i) (h i))) (TopologicalSpace.Closeds.mk.{u1} α _inst_1 (Set.iInter.{u1, u2} α ι (fun (i : ι) => s i)) (isClosed_iInter.{u1, u2} α ι _inst_1 (fun (i : ι) => s i) h))
+Case conversion may be inaccurate. Consider using '#align topological_space.closeds.infi_mk TopologicalSpace.Closeds.iInf_mkₓ'. -/
 @[simp]
-theorem infᵢ_mk {ι} (s : ι → Set α) (h : ∀ i, IsClosed (s i)) :
-    (⨅ i, ⟨s i, h i⟩ : Closeds α) = ⟨⋂ i, s i, isClosed_interᵢ h⟩ := by simp [infi_def]
-#align topological_space.closeds.infi_mk TopologicalSpace.Closeds.infᵢ_mk
+theorem iInf_mk {ι} (s : ι → Set α) (h : ∀ i, IsClosed (s i)) :
+    (⨅ i, ⟨s i, h i⟩ : Closeds α) = ⟨⋂ i, s i, isClosed_iInter h⟩ := by simp [infi_def]
+#align topological_space.closeds.infi_mk TopologicalSpace.Closeds.iInf_mk
 
-/- warning: topological_space.closeds.coe_infi -> TopologicalSpace.Closeds.coe_infᵢ is a dubious translation:
+/- warning: topological_space.closeds.coe_infi -> TopologicalSpace.Closeds.coe_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} (s : ι -> (TopologicalSpace.Closeds.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) (infᵢ.{u1, u2} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toHasInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u1} α _inst_1))) ι (fun (i : ι) => s i))) (Set.interᵢ.{u1, u2} α ι (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) (s i)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} (s : ι -> (TopologicalSpace.Closeds.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) (iInf.{u1, u2} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toHasInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u1} α _inst_1))) ι (fun (i : ι) => s i))) (Set.iInter.{u1, u2} α ι (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) (s i)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} (s : ι -> (TopologicalSpace.Closeds.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) (infᵢ.{u1, u2} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toInfSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))) ι (fun (i : ι) => s i))) (Set.interᵢ.{u1, u2} α ι (fun (i : ι) => SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) (s i)))
-Case conversion may be inaccurate. Consider using '#align topological_space.closeds.coe_infi TopologicalSpace.Closeds.coe_infᵢₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} (s : ι -> (TopologicalSpace.Closeds.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) (iInf.{u1, u2} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toInfSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))) ι (fun (i : ι) => s i))) (Set.iInter.{u1, u2} α ι (fun (i : ι) => SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) (s i)))
+Case conversion may be inaccurate. Consider using '#align topological_space.closeds.coe_infi TopologicalSpace.Closeds.coe_iInfₓ'. -/
 @[simp, norm_cast]
-theorem coe_infᵢ {ι} (s : ι → Closeds α) : ((⨅ i, s i : Closeds α) : Set α) = ⋂ i, s i := by
+theorem coe_iInf {ι} (s : ι → Closeds α) : ((⨅ i, s i : Closeds α) : Set α) = ⋂ i, s i := by
   simp [infi_def]
-#align topological_space.closeds.coe_infi TopologicalSpace.Closeds.coe_infᵢ
+#align topological_space.closeds.coe_infi TopologicalSpace.Closeds.coe_iInf
 
-/- warning: topological_space.closeds.mem_infi -> TopologicalSpace.Closeds.mem_infᵢ is a dubious translation:
+/- warning: topological_space.closeds.mem_infi -> TopologicalSpace.Closeds.mem_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {x : α} {s : ι -> (TopologicalSpace.Closeds.{u1} α _inst_1)}, Iff (Membership.Mem.{u1, u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)) x (infᵢ.{u1, u2} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toHasInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u1} α _inst_1))) ι s)) (forall (i : ι), Membership.Mem.{u1, u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)) x (s i))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {x : α} {s : ι -> (TopologicalSpace.Closeds.{u1} α _inst_1)}, Iff (Membership.Mem.{u1, u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)) x (iInf.{u1, u2} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toHasInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u1} α _inst_1))) ι s)) (forall (i : ι), Membership.Mem.{u1, u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)) x (s i))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {x : α} {s : ι -> (TopologicalSpace.Closeds.{u1} α _inst_1)}, Iff (Membership.mem.{u1, u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1)) x (infᵢ.{u1, u2} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toInfSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))) ι s)) (forall (i : ι), Membership.mem.{u1, u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1)) x (s i))
-Case conversion may be inaccurate. Consider using '#align topological_space.closeds.mem_infi TopologicalSpace.Closeds.mem_infᵢₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {x : α} {s : ι -> (TopologicalSpace.Closeds.{u1} α _inst_1)}, Iff (Membership.mem.{u1, u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1)) x (iInf.{u1, u2} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toInfSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))) ι s)) (forall (i : ι), Membership.mem.{u1, u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1)) x (s i))
+Case conversion may be inaccurate. Consider using '#align topological_space.closeds.mem_infi TopologicalSpace.Closeds.mem_iInfₓ'. -/
 @[simp]
-theorem mem_infᵢ {ι} {x : α} {s : ι → Closeds α} : x ∈ infᵢ s ↔ ∀ i, x ∈ s i := by
+theorem mem_iInf {ι} {x : α} {s : ι → Closeds α} : x ∈ iInf s ↔ ∀ i, x ∈ s i := by
   simp [← SetLike.mem_coe]
-#align topological_space.closeds.mem_infi TopologicalSpace.Closeds.mem_infᵢ
+#align topological_space.closeds.mem_infi TopologicalSpace.Closeds.mem_iInf
 
-/- warning: topological_space.closeds.mem_Inf -> TopologicalSpace.Closeds.mem_infₛ is a dubious translation:
+/- warning: topological_space.closeds.mem_Inf -> TopologicalSpace.Closeds.mem_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {S : Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)} {x : α}, Iff (Membership.Mem.{u1, u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)) x (InfSet.infₛ.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toHasInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u1} α _inst_1))) S)) (forall (s : TopologicalSpace.Closeds.{u1} α _inst_1), (Membership.Mem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) (Set.hasMem.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) s S) -> (Membership.Mem.{u1, u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)) x s))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {S : Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)} {x : α}, Iff (Membership.Mem.{u1, u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)) x (InfSet.sInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toHasInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u1} α _inst_1))) S)) (forall (s : TopologicalSpace.Closeds.{u1} α _inst_1), (Membership.Mem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) (Set.hasMem.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) s S) -> (Membership.Mem.{u1, u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)) x s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {S : Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)} {x : α}, Iff (Membership.mem.{u1, u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1)) x (InfSet.infₛ.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toInfSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))) S)) (forall (s : TopologicalSpace.Closeds.{u1} α _inst_1), (Membership.mem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) s S) -> (Membership.mem.{u1, u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1)) x s))
-Case conversion may be inaccurate. Consider using '#align topological_space.closeds.mem_Inf TopologicalSpace.Closeds.mem_infₛₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {S : Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)} {x : α}, Iff (Membership.mem.{u1, u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1)) x (InfSet.sInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toInfSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))) S)) (forall (s : TopologicalSpace.Closeds.{u1} α _inst_1), (Membership.mem.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1)) s S) -> (Membership.mem.{u1, u1} α (TopologicalSpace.Closeds.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1)) x s))
+Case conversion may be inaccurate. Consider using '#align topological_space.closeds.mem_Inf TopologicalSpace.Closeds.mem_sInfₓ'. -/
 @[simp]
-theorem mem_infₛ {S : Set (Closeds α)} {x : α} : x ∈ infₛ S ↔ ∀ s ∈ S, x ∈ s := by
-  simp_rw [infₛ_eq_infᵢ, mem_infi]
-#align topological_space.closeds.mem_Inf TopologicalSpace.Closeds.mem_infₛ
+theorem mem_sInf {S : Set (Closeds α)} {x : α} : x ∈ sInf S ↔ ∀ s ∈ S, x ∈ s := by
+  simp_rw [sInf_eq_iInf, mem_infi]
+#align topological_space.closeds.mem_Inf TopologicalSpace.Closeds.mem_sInf
 
 instance : Coframe (Closeds α) :=
   { Closeds.completeLattice with
-    infₛ := infₛ
-    infᵢ_sup_le_sup_inf := fun a s =>
-      (SetLike.coe_injective <| by simp only [coe_sup, coe_infi, coe_Inf, Set.union_interᵢ₂]).le }
+    sInf := sInf
+    iInf_sup_le_sup_inf := fun a s =>
+      (SetLike.coe_injective <| by simp only [coe_sup, coe_infi, coe_Inf, Set.union_iInter₂]).le }
 
 #print TopologicalSpace.Closeds.singleton /-
 /-- The term of `closeds α` corresponding to a singleton. -/

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

@@ -389,7 +389,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T1Space.{u1} α _inst_1] {s : TopologicalSpace.Opens.{u1} α _inst_1}, Iff (IsCoatom.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} α _inst_1)))) (BoundedOrder.toOrderTop.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} α _inst_1))))) (CompleteLattice.toBoundedOrder.{u1} (TopologicalSpace.Opens.{u1} α _inst_1) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} α _inst_1))) s) (Exists.{succ u1} α (fun (x : α) => Eq.{succ u1} (TopologicalSpace.Opens.{u1} α _inst_1) s (TopologicalSpace.Closeds.compl.{u1} α _inst_1 (TopologicalSpace.Closeds.singleton.{u1} α _inst_1 _inst_3 x))))
 Case conversion may be inaccurate. Consider using '#align topological_space.opens.is_coatom_iff TopologicalSpace.Opens.isCoatom_iffₓ'. -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr «expr∃ , »((x), _)]] -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr∃ , »((x), _)]] -/
 /-- in a `t1_space`, coatoms of `opens α` are precisely complements of singletons:
 `(closeds.singleton x).compl`. -/
 theorem Opens.isCoatom_iff [T1Space α] {s : Opens α} :
@@ -399,7 +399,7 @@ theorem Opens.isCoatom_iff [T1Space α] {s : Opens α} :
   change IsAtom (closeds.compl_order_iso α s.compl) ↔ _
   rw [(closeds.compl_order_iso α).isAtom_iff, closeds.is_atom_iff]
   trace
-    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr «expr∃ , »((x), _)]]"
+    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr «expr∃ , »((x), _)]]"
   exact closeds.compl_bijective.injective.eq_iff.symm
 #align topological_space.opens.is_coatom_iff TopologicalSpace.Opens.isCoatom_iff
 

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

@@ -133,9 +133,9 @@ instance : Inhabited (Closeds α) :=
 
 /- warning: topological_space.closeds.coe_sup -> TopologicalSpace.Closeds.coe_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Closeds.{u1} α _inst_1) (t : TopologicalSpace.Closeds.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) (HasSup.sup.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (SemilatticeSup.toHasSup.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Lattice.toSemilatticeSup.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u1} α _inst_1))))) s t)) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Closeds.{u1} α _inst_1) (t : TopologicalSpace.Closeds.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) (Sup.sup.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (SemilatticeSup.toHasSup.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Lattice.toSemilatticeSup.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u1} α _inst_1))))) s t)) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Closeds.{u1} α _inst_1) (t : TopologicalSpace.Closeds.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) (HasSup.sup.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (SemilatticeSup.toHasSup.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Lattice.toSemilatticeSup.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))))) s t)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Closeds.{u1} α _inst_1) (t : TopologicalSpace.Closeds.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) (Sup.sup.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (SemilatticeSup.toSup.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Lattice.toSemilatticeSup.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1))))) s t)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align topological_space.closeds.coe_sup TopologicalSpace.Closeds.coe_supₓ'. -/
 @[simp, norm_cast]
 theorem coe_sup (s t : Closeds α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
@@ -144,9 +144,9 @@ theorem coe_sup (s t : Closeds α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
 
 /- warning: topological_space.closeds.coe_inf -> TopologicalSpace.Closeds.coe_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Closeds.{u1} α _inst_1) (t : TopologicalSpace.Closeds.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) (HasInf.inf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (SemilatticeInf.toHasInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Lattice.toSemilatticeInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u1} α _inst_1))))) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Closeds.{u1} α _inst_1) (t : TopologicalSpace.Closeds.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) (Inf.inf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (SemilatticeInf.toHasInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Lattice.toSemilatticeInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.completeLattice.{u1} α _inst_1))))) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.setLike.{u1} α _inst_1)))) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Closeds.{u1} α _inst_1) (t : TopologicalSpace.Closeds.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) (HasInf.inf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Lattice.toHasInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1)))) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Closeds.{u1} α _inst_1) (t : TopologicalSpace.Closeds.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) (Inf.inf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (Lattice.toInf.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (ConditionallyCompleteLattice.toLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Closeds.{u1} α _inst_1) (TopologicalSpace.Closeds.instCompleteLatticeCloseds.{u1} α _inst_1)))) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.Closeds.{u1} α _inst_1) α (TopologicalSpace.Closeds.instSetLikeCloseds.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align topological_space.closeds.coe_inf TopologicalSpace.Closeds.coe_infₓ'. -/
 @[simp, norm_cast]
 theorem coe_inf (s t : Closeds α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
@@ -451,10 +451,10 @@ theorem coe_mk (s : Set α) (h) : (mk s h : Set α) = s :=
 #align topological_space.clopens.coe_mk TopologicalSpace.Clopens.coe_mk
 -/
 
-instance : HasSup (Clopens α) :=
+instance : Sup (Clopens α) :=
   ⟨fun s t => ⟨s ∪ t, s.clopen.union t.clopen⟩⟩
 
-instance : HasInf (Clopens α) :=
+instance : Inf (Clopens α) :=
   ⟨fun s t => ⟨s ∩ t, s.clopen.inter t.clopen⟩⟩
 
 instance : Top (Clopens α) :=
@@ -475,9 +475,9 @@ instance : BooleanAlgebra (Clopens α) :=
 
 /- warning: topological_space.clopens.coe_sup -> TopologicalSpace.Clopens.coe_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Clopens.{u1} α _inst_1) (t : TopologicalSpace.Clopens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.setLike.{u1} α _inst_1)))) (HasSup.sup.{u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (TopologicalSpace.Clopens.hasSup.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.setLike.{u1} α _inst_1)))) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Clopens.{u1} α _inst_1) (t : TopologicalSpace.Clopens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.setLike.{u1} α _inst_1)))) (Sup.sup.{u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (TopologicalSpace.Clopens.hasSup.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.setLike.{u1} α _inst_1)))) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Clopens.{u1} α _inst_1) (t : TopologicalSpace.Clopens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.instSetLikeClopens.{u1} α _inst_1) (HasSup.sup.{u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (TopologicalSpace.Clopens.instHasSupClopens.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.instSetLikeClopens.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.instSetLikeClopens.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Clopens.{u1} α _inst_1) (t : TopologicalSpace.Clopens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.instSetLikeClopens.{u1} α _inst_1) (Sup.sup.{u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (TopologicalSpace.Clopens.instSupClopens.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.instSetLikeClopens.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.instSetLikeClopens.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align topological_space.clopens.coe_sup TopologicalSpace.Clopens.coe_supₓ'. -/
 @[simp]
 theorem coe_sup (s t : Clopens α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
@@ -486,9 +486,9 @@ theorem coe_sup (s t : Clopens α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
 
 /- warning: topological_space.clopens.coe_inf -> TopologicalSpace.Clopens.coe_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Clopens.{u1} α _inst_1) (t : TopologicalSpace.Clopens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.setLike.{u1} α _inst_1)))) (HasInf.inf.{u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (TopologicalSpace.Clopens.hasInf.{u1} α _inst_1) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.setLike.{u1} α _inst_1)))) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Clopens.{u1} α _inst_1) (t : TopologicalSpace.Clopens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.setLike.{u1} α _inst_1)))) (Inf.inf.{u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (TopologicalSpace.Clopens.hasInf.{u1} α _inst_1) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.setLike.{u1} α _inst_1)))) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Clopens.{u1} α _inst_1) (t : TopologicalSpace.Clopens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.instSetLikeClopens.{u1} α _inst_1) (HasInf.inf.{u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (TopologicalSpace.Clopens.instHasInfClopens.{u1} α _inst_1) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.instSetLikeClopens.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.instSetLikeClopens.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Clopens.{u1} α _inst_1) (t : TopologicalSpace.Clopens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.instSetLikeClopens.{u1} α _inst_1) (Inf.inf.{u1} (TopologicalSpace.Clopens.{u1} α _inst_1) (TopologicalSpace.Clopens.instInfClopens.{u1} α _inst_1) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.instSetLikeClopens.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.Clopens.{u1} α _inst_1) α (TopologicalSpace.Clopens.instSetLikeClopens.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align topological_space.clopens.coe_inf TopologicalSpace.Clopens.coe_infₓ'. -/
 @[simp]
 theorem coe_inf (s t : Clopens α) : (↑(s ⊓ t) : Set α) = s ∩ t :=

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

Classifies by adding issue number #10756 to porting notes claiming anything equivalent to:

• "added theorem"
• "added theorems"
• "new theorem"
• "new theorems"
• "added lemma"
• "new lemma"
• "new lemmas"

@@ -120,7 +120,7 @@ theorem coe_top : (↑(⊤ : Closeds α) : Set α) = univ :=
   rfl
 #align topological_space.closeds.coe_top TopologicalSpace.Closeds.coe_top
 
-@[simp, norm_cast] -- Porting note: new
+@[simp, norm_cast] -- Porting note (#10756): new theorem
 theorem coe_eq_univ {s : Closeds α} : (s : Set α) = univ ↔ s = ⊤ :=
   SetLike.coe_injective.eq_iff' rfl
 
@@ -129,7 +129,7 @@ theorem coe_bot : (↑(⊥ : Closeds α) : Set α) = ∅ :=
   rfl
 #align topological_space.closeds.coe_bot TopologicalSpace.Closeds.coe_bot
 
-@[simp, norm_cast] -- Porting note: new
+@[simp, norm_cast] -- Porting note (#10756): new theorem
 theorem coe_eq_empty {s : Closeds α} : (s : Set α) = ∅ ↔ s = ⊥ :=
   SetLike.coe_injective.eq_iff' rfl
 

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".

@@ -120,7 +120,7 @@ theorem coe_top : (↑(⊤ : Closeds α) : Set α) = univ :=
   rfl
 #align topological_space.closeds.coe_top TopologicalSpace.Closeds.coe_top
 
-@[simp, norm_cast] -- porting note: new
+@[simp, norm_cast] -- Porting note: new
 theorem coe_eq_univ {s : Closeds α} : (s : Set α) = univ ↔ s = ⊤ :=
   SetLike.coe_injective.eq_iff' rfl
 
@@ -129,7 +129,7 @@ theorem coe_bot : (↑(⊥ : Closeds α) : Set α) = ∅ :=
   rfl
 #align topological_space.closeds.coe_bot TopologicalSpace.Closeds.coe_bot
 
-@[simp, norm_cast] -- porting note: new
+@[simp, norm_cast] -- Porting note: new
 theorem coe_eq_empty {s : Closeds α} : (s : Set α) = ∅ ↔ s = ⊥ :=
   SetLike.coe_injective.eq_iff' rfl
 
@@ -157,7 +157,7 @@ theorem coe_finset_inf (f : ι → Closeds α) (s : Finset ι) :
   map_finset_inf (⟨⟨(↑), coe_inf⟩, coe_top⟩ : InfTopHom (Closeds α) (Set α)) _ _
 #align topological_space.closeds.coe_finset_inf TopologicalSpace.Closeds.coe_finset_inf
 
--- porting note: Lean 3 proofs didn't work as expected, so I reordered lemmas to fix&golf the proofs
+-- Porting note: Lean 3 proofs didn't work as expected, so I reordered lemmas to fix&golf the proofs
 
 @[simp]
 theorem mem_sInf {S : Set (Closeds α)} {x : α} : x ∈ sInf S ↔ ∀ s ∈ S, x ∈ s := mem_iInter₂

• Rename (and generalize and move)

Int.units_ne_neg_self -> units_ne_neg_self
Int.neg_units_ne_self -> neg_units_ne_self

• Change the simps config for Closeds
• Add some gcongr-lemmas (currently is a bit picky about the exact statement of lemmas tagged with gcongr, so I had to add some variants that I could tag).

@@ -51,7 +51,7 @@ theorem closed (s : Closeds α) : IsClosed (s : Set α) :=
 /-- See Note [custom simps projection]. -/
 def Simps.coe (s : Closeds α) : Set α := s
 
-initialize_simps_projections Closeds (carrier → coe)
+initialize_simps_projections Closeds (carrier → coe, as_prefix coe)
 
 @[ext]
 protected theorem ext {s t : Closeds α} (h : (s : Set α) = t) : s = t :=
@@ -64,6 +64,7 @@ theorem coe_mk (s : Set α) (h) : (mk s h : Set α) = s :=
 #align topological_space.closeds.coe_mk TopologicalSpace.Closeds.coe_mk
 
 /-- The closure of a set, as an element of `TopologicalSpace.Closeds`. -/
+@[simps]
 protected def closure (s : Set α) : Closeds α :=
   ⟨closure s, isClosed_closure⟩
 #align topological_space.closeds.closure TopologicalSpace.Closeds.closure
@@ -80,7 +81,7 @@ def gi : GaloisInsertion (@Closeds.closure α _) (↑) where
   choice_eq _s hs := SetLike.coe_injective <| subset_closure.antisymm hs
 #align topological_space.closeds.gi TopologicalSpace.Closeds.gi
 
-instance : CompleteLattice (Closeds α) :=
+instance completeLattice : CompleteLattice (Closeds α) :=
   CompleteLattice.copy
     (GaloisInsertion.liftCompleteLattice gi)
     -- le
@@ -105,7 +106,7 @@ instance : Inhabited (Closeds α) :=
   ⟨⊥⟩
 
 @[simp, norm_cast]
-theorem coe_sup (s t : Closeds α) : (↑(s ⊔ t) : Set α) = ↑s ∪ ↑t :=
+theorem coe_sup (s t : Closeds α) : (↑(s ⊔ t) : Set α) = ↑s ∪ ↑t := by
   rfl
 #align topological_space.closeds.coe_sup TopologicalSpace.Closeds.coe_sup
 
@@ -140,6 +141,10 @@ theorem coe_sInf {S : Set (Closeds α)} : (↑(sInf S) : Set α) = ⋂ i ∈ S,
   rfl
 #align topological_space.closeds.coe_Inf TopologicalSpace.Closeds.coe_sInf
 
+@[simp]
+lemma coe_sSup {S : Set (Closeds α)} : ((sSup S : Closeds α) : Set α) =
+    closure (⋃₀ ((↑) '' S)) := by rfl
+
 @[simp, norm_cast]
 theorem coe_finset_sup (f : ι → Closeds α) (s : Finset ι) :
     (↑(s.sup f) : Set α) = s.sup ((↑) ∘ f) :=

See Zulip thread for the discussion.

@@ -251,7 +251,7 @@ lemma Closeds.coe_eq_singleton_of_isAtom [T0Space α] {s : Closeds α} (hs : IsA
     ∃ a, (s : Set α) = {a} := by
   refine minimal_nonempty_closed_eq_singleton s.2 (coe_nonempty.2 hs.1) fun t hts ht ht' ↦ ?_
   lift t to Closeds α using ht'
-  exact SetLike.coe_injective.eq_iff.2 $ (hs.le_iff_eq $ coe_nonempty.1 ht).1 hts
+  exact SetLike.coe_injective.eq_iff.2 <| (hs.le_iff_eq <| coe_nonempty.1 ht).1 hts
 
 @[simp, norm_cast] lemma Closeds.isAtom_coe [T1Space α] {s : Closeds α} :
     IsAtom (s : Set α) ↔ IsAtom s :=

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

@@ -315,6 +315,8 @@ theorem coe_mk (s : Set α) (h) : (mk s h : Set α) = s :=
   rfl
 #align topological_space.clopens.coe_mk TopologicalSpace.Clopens.coe_mk
 
+@[simp] lemma mem_mk {s : Set α} {x h} : x ∈ mk s h ↔ x ∈ s := .rfl
+
 instance : Sup (Clopens α) := ⟨fun s t => ⟨s ∪ t, s.isClopen.union t.isClopen⟩⟩
 instance : Inf (Clopens α) := ⟨fun s t => ⟨s ∩ t, s.isClopen.inter t.isClopen⟩⟩
 instance : Top (Clopens α) := ⟨⟨⊤, isClopen_univ⟩⟩
@@ -346,6 +348,15 @@ instance : BooleanAlgebra (Clopens α) :=
 
 instance : Inhabited (Clopens α) := ⟨⊥⟩
 
+variable [TopologicalSpace β]
+
+instance : SProd (Clopens α) (Clopens β) (Clopens (α × β)) where
+  sprod s t := ⟨s ×ˢ t, s.2.prod t.2⟩
+
+@[simp]
+protected lemma mem_prod {s : Clopens α} {t : Clopens β} {x : α × β} :
+    x ∈ s ×ˢ t ↔ x.1 ∈ s ∧ x.2 ∈ t := .rfl
+
 end Clopens
 
 end TopologicalSpace

Characterise IsAtom, IsCoatom, Covby in Set α, Multiset α, Finset α and deduce that Multiset α, Finset α are graded orders.

Note I am moving some existing characterisations to here because it makes sense thematically, but I could be convinced otherwise.

@@ -189,6 +189,8 @@ def singleton [T1Space α] (x : α) : Closeds α :=
   ⟨{x}, isClosed_singleton⟩
 #align topological_space.closeds.singleton TopologicalSpace.Closeds.singleton
 
+@[simp] lemma mem_singleton [T1Space α] {a b : α} : a ∈ singleton b ↔ a = b := Iff.rfl
+
 end Closeds
 
 /-- The complement of a closed set as an open set. -/
@@ -245,18 +247,22 @@ def Opens.complOrderIso : Opens α ≃o (Closeds α)ᵒᵈ where
 
 variable {α}
 
-/-- in a `T1Space`, atoms of `TopologicalSpace.Closeds α` are precisely the
-`TopologicalSpace.Closeds.singleton`s.
+lemma Closeds.coe_eq_singleton_of_isAtom [T0Space α] {s : Closeds α} (hs : IsAtom s) :
+    ∃ a, (s : Set α) = {a} := by
+  refine minimal_nonempty_closed_eq_singleton s.2 (coe_nonempty.2 hs.1) fun t hts ht ht' ↦ ?_
+  lift t to Closeds α using ht'
+  exact SetLike.coe_injective.eq_iff.2 $ (hs.le_iff_eq $ coe_nonempty.1 ht).1 hts
 
-TODO: use `minimal_nonempty_closed_eq_singleton` to show that an atom in `TopologicalSpace.Closeds`
-in a T₀ space is a singleton. -/
+@[simp, norm_cast] lemma Closeds.isAtom_coe [T1Space α] {s : Closeds α} :
+    IsAtom (s : Set α) ↔ IsAtom s :=
+  Closeds.gi.isAtom_iff' rfl
+    (fun t ht ↦ by obtain ⟨x, rfl⟩ := Set.isAtom_iff.1 ht; exact closure_singleton) s
+
+/-- in a `T1Space`, atoms of `TopologicalSpace.Closeds α` are precisely the
+`TopologicalSpace.Closeds.singleton`s. -/
 theorem Closeds.isAtom_iff [T1Space α] {s : Closeds α} :
     IsAtom s ↔ ∃ x, s = Closeds.singleton x := by
-  have : IsAtom (s : Set α) ↔ IsAtom s := by
-    refine' Closeds.gi.isAtom_iff' rfl (fun t ht => _) s
-    obtain ⟨x, rfl⟩ := t.isAtom_iff.mp ht
-    exact closure_singleton
-  simp only [← this, (s : Set α).isAtom_iff, SetLike.ext'_iff, Closeds.singleton_coe]
+  simp [← Closeds.isAtom_coe, Set.isAtom_iff, SetLike.ext_iff, Set.ext_iff]
 #align topological_space.closeds.is_atom_iff TopologicalSpace.Closeds.isAtom_iff
 
 /-- in a `T1Space`, coatoms of `TopologicalSpace.Opens α` are precisely complements of singletons:

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

@@ -275,7 +275,7 @@ theorem Opens.isCoatom_iff [T1Space α] {s : Opens α} :
 /-- The type of clopen sets of a topological space. -/
 structure Clopens (α : Type*) [TopologicalSpace α] where
   carrier : Set α
-  clopen' : IsClopen carrier
+  isClopen' : IsClopen carrier
 #align topological_space.clopens TopologicalSpace.Clopens
 
 namespace Clopens
@@ -284,9 +284,9 @@ instance : SetLike (Clopens α) α where
   coe s := s.carrier
   coe_injective' s t h := by cases s; cases t; congr
 
-theorem clopen (s : Clopens α) : IsClopen (s : Set α) :=
-  s.clopen'
-#align topological_space.clopens.clopen TopologicalSpace.Clopens.clopen
+theorem isClopen (s : Clopens α) : IsClopen (s : Set α) :=
+  s.isClopen'
+#align topological_space.clopens.clopen TopologicalSpace.Clopens.isClopen
 
 /-- See Note [custom simps projection]. -/
 def Simps.coe (s : Clopens α) : Set α := s
@@ -296,7 +296,7 @@ initialize_simps_projections Clopens (carrier → coe)
 /-- Reinterpret a clopen as an open. -/
 @[simps]
 def toOpens (s : Clopens α) : Opens α :=
-  ⟨s, s.clopen.isOpen⟩
+  ⟨s, s.isClopen.isOpen⟩
 #align topological_space.clopens.to_opens TopologicalSpace.Clopens.toOpens
 
 @[ext]
@@ -309,12 +309,12 @@ theorem coe_mk (s : Set α) (h) : (mk s h : Set α) = s :=
   rfl
 #align topological_space.clopens.coe_mk TopologicalSpace.Clopens.coe_mk
 
-instance : Sup (Clopens α) := ⟨fun s t => ⟨s ∪ t, s.clopen.union t.clopen⟩⟩
-instance : Inf (Clopens α) := ⟨fun s t => ⟨s ∩ t, s.clopen.inter t.clopen⟩⟩
+instance : Sup (Clopens α) := ⟨fun s t => ⟨s ∪ t, s.isClopen.union t.isClopen⟩⟩
+instance : Inf (Clopens α) := ⟨fun s t => ⟨s ∩ t, s.isClopen.inter t.isClopen⟩⟩
 instance : Top (Clopens α) := ⟨⟨⊤, isClopen_univ⟩⟩
 instance : Bot (Clopens α) := ⟨⟨⊥, isClopen_empty⟩⟩
-instance : SDiff (Clopens α) := ⟨fun s t => ⟨s \ t, s.clopen.diff t.clopen⟩⟩
-instance : HasCompl (Clopens α) := ⟨fun s => ⟨sᶜ, s.clopen.compl⟩⟩
+instance : SDiff (Clopens α) := ⟨fun s t => ⟨s \ t, s.isClopen.diff t.isClopen⟩⟩
+instance : HasCompl (Clopens α) := ⟨fun s => ⟨sᶜ, s.isClopen.compl⟩⟩
 
 instance : BooleanAlgebra (Clopens α) :=
   SetLike.coe_injective.booleanAlgebra _ (fun _ _ => rfl) (fun _ _ => rfl) rfl rfl (fun _ => rfl)

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

This has nice performance benefits.

@@ -22,7 +22,7 @@ For a topological space `α`,
 
 open Order OrderDual Set
 
-variable {ι α β : Type _} [TopologicalSpace α] [TopologicalSpace β]
+variable {ι α β : Type*} [TopologicalSpace α] [TopologicalSpace β]
 
 namespace TopologicalSpace
 
@@ -30,7 +30,7 @@ namespace TopologicalSpace
 
 
 /-- The type of closed subsets of a topological space. -/
-structure Closeds (α : Type _) [TopologicalSpace α] where
+structure Closeds (α : Type*) [TopologicalSpace α] where
   carrier : Set α
   closed' : IsClosed carrier
 #align topological_space.closeds TopologicalSpace.Closeds
@@ -273,7 +273,7 @@ theorem Opens.isCoatom_iff [T1Space α] {s : Opens α} :
 
 
 /-- The type of clopen sets of a topological space. -/
-structure Clopens (α : Type _) [TopologicalSpace α] where
+structure Clopens (α : Type*) [TopologicalSpace α] where
   carrier : Set α
   clopen' : IsClopen carrier
 #align topological_space.clopens TopologicalSpace.Clopens

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn, Yaël Dillies
-
-! This file was ported from Lean 3 source module topology.sets.closeds
-! leanprover-community/mathlib commit dc6c365e751e34d100e80fe6e314c3c3e0fd2988
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Sets.Opens
 
+#align_import topology.sets.closeds from "leanprover-community/mathlib"@"dc6c365e751e34d100e80fe6e314c3c3e0fd2988"
+
 /-!
 # Closed sets
 

@@ -171,7 +171,7 @@ theorem coe_iInf {ι} (s : ι → Closeds α) : ((⨅ i, s i : Closeds α) : Set
 #align topological_space.closeds.coe_infi TopologicalSpace.Closeds.coe_iInf
 
 theorem iInf_def {ι} (s : ι → Closeds α) :
-    (⨅ i, s i) = ⟨⋂ i, s i, isClosed_iInter fun i => (s i).2⟩ := by ext1; simp
+    ⨅ i, s i = ⟨⋂ i, s i, isClosed_iInter fun i => (s i).2⟩ := by ext1; simp
 #align topological_space.closeds.infi_def TopologicalSpace.Closeds.iInf_def
 
 @[simp]

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

@@ -338,7 +338,7 @@ instance : BooleanAlgebra (Clopens α) :=
 @[simp] theorem coe_sdiff (s t : Clopens α) : (↑(s \ t) : Set α) = ↑s \ ↑t := rfl
 #align topological_space.clopens.coe_sdiff TopologicalSpace.Clopens.coe_sdiff
 
-@[simp] theorem coe_compl (s : Clopens α) : (↑(sᶜ) : Set α) = ↑sᶜ := rfl
+@[simp] theorem coe_compl (s : Clopens α) : (↑sᶜ : Set α) = (↑s)ᶜ := rfl
 #align topological_space.clopens.coe_compl TopologicalSpace.Clopens.coe_compl
 
 instance : Inhabited (Clopens α) := ⟨⊥⟩

As discussed on Zulip

Renames

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

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

@@ -97,11 +97,11 @@ instance : CompleteLattice (Closeds α) :=
     (funext fun s => funext fun t => SetLike.coe_injective (s.2.union t.2).closure_eq.symm)
     -- inf
     (fun s t => ⟨s ∩ t, s.2.inter t.2⟩) rfl
-    -- supₛ
+    -- sSup
     _ rfl
-    -- infₛ
-    (fun S => ⟨⋂ s ∈ S, ↑s, isClosed_binterᵢ fun s _ => s.2⟩)
-    (funext fun _ => SetLike.coe_injective infₛ_image.symm)
+    -- sInf
+    (fun S => ⟨⋂ s ∈ S, ↑s, isClosed_biInter fun s _ => s.2⟩)
+    (funext fun _ => SetLike.coe_injective sInf_image.symm)
 
 /-- The type of closed sets is inhabited, with default element the empty set. -/
 instance : Inhabited (Closeds α) :=
@@ -139,9 +139,9 @@ theorem coe_nonempty {s : Closeds α} : (s : Set α).Nonempty ↔ s ≠ ⊥ :=
   nonempty_iff_ne_empty.trans coe_eq_empty.not
 
 @[simp, norm_cast]
-theorem coe_infₛ {S : Set (Closeds α)} : (↑(infₛ S) : Set α) = ⋂ i ∈ S, ↑i :=
+theorem coe_sInf {S : Set (Closeds α)} : (↑(sInf S) : Set α) = ⋂ i ∈ S, ↑i :=
   rfl
-#align topological_space.closeds.coe_Inf TopologicalSpace.Closeds.coe_infₛ
+#align topological_space.closeds.coe_Inf TopologicalSpace.Closeds.coe_sInf
 
 @[simp, norm_cast]
 theorem coe_finset_sup (f : ι → Closeds α) (s : Finset ι) :
@@ -158,33 +158,33 @@ theorem coe_finset_inf (f : ι → Closeds α) (s : Finset ι) :
 -- porting note: Lean 3 proofs didn't work as expected, so I reordered lemmas to fix&golf the proofs
 
 @[simp]
-theorem mem_infₛ {S : Set (Closeds α)} {x : α} : x ∈ infₛ S ↔ ∀ s ∈ S, x ∈ s := mem_interᵢ₂
-#align topological_space.closeds.mem_Inf TopologicalSpace.Closeds.mem_infₛ
+theorem mem_sInf {S : Set (Closeds α)} {x : α} : x ∈ sInf S ↔ ∀ s ∈ S, x ∈ s := mem_iInter₂
+#align topological_space.closeds.mem_Inf TopologicalSpace.Closeds.mem_sInf
 
 @[simp]
-theorem mem_infᵢ {ι} {x : α} {s : ι → Closeds α} : x ∈ infᵢ s ↔ ∀ i, x ∈ s i := by simp [infᵢ]
-#align topological_space.closeds.mem_infi TopologicalSpace.Closeds.mem_infᵢ
+theorem mem_iInf {ι} {x : α} {s : ι → Closeds α} : x ∈ iInf s ↔ ∀ i, x ∈ s i := by simp [iInf]
+#align topological_space.closeds.mem_infi TopologicalSpace.Closeds.mem_iInf
 
 @[simp, norm_cast]
-theorem coe_infᵢ {ι} (s : ι → Closeds α) : ((⨅ i, s i : Closeds α) : Set α) = ⋂ i, s i := by
+theorem coe_iInf {ι} (s : ι → Closeds α) : ((⨅ i, s i : Closeds α) : Set α) = ⋂ i, s i := by
   ext; simp
-#align topological_space.closeds.coe_infi TopologicalSpace.Closeds.coe_infᵢ
+#align topological_space.closeds.coe_infi TopologicalSpace.Closeds.coe_iInf
 
-theorem infᵢ_def {ι} (s : ι → Closeds α) :
-    (⨅ i, s i) = ⟨⋂ i, s i, isClosed_interᵢ fun i => (s i).2⟩ := by ext1; simp
-#align topological_space.closeds.infi_def TopologicalSpace.Closeds.infᵢ_def
+theorem iInf_def {ι} (s : ι → Closeds α) :
+    (⨅ i, s i) = ⟨⋂ i, s i, isClosed_iInter fun i => (s i).2⟩ := by ext1; simp
+#align topological_space.closeds.infi_def TopologicalSpace.Closeds.iInf_def
 
 @[simp]
-theorem infᵢ_mk {ι} (s : ι → Set α) (h : ∀ i, IsClosed (s i)) :
-    (⨅ i, ⟨s i, h i⟩ : Closeds α) = ⟨⋂ i, s i, isClosed_interᵢ h⟩ :=
-  infᵢ_def _
-#align topological_space.closeds.infi_mk TopologicalSpace.Closeds.infᵢ_mk
+theorem iInf_mk {ι} (s : ι → Set α) (h : ∀ i, IsClosed (s i)) :
+    (⨅ i, ⟨s i, h i⟩ : Closeds α) = ⟨⋂ i, s i, isClosed_iInter h⟩ :=
+  iInf_def _
+#align topological_space.closeds.infi_mk TopologicalSpace.Closeds.iInf_mk
 
 instance : Coframe (Closeds α) :=
   { inferInstanceAs (CompleteLattice (Closeds α)) with
-    infₛ := infₛ
-    infᵢ_sup_le_sup_infₛ := fun a s =>
-      (SetLike.coe_injective <| by simp only [coe_sup, coe_infᵢ, coe_infₛ, Set.union_interᵢ₂]).le }
+    sInf := sInf
+    iInf_sup_le_sup_sInf := fun a s =>
+      (SetLike.coe_injective <| by simp only [coe_sup, coe_iInf, coe_sInf, Set.union_iInter₂]).le }
 
 /-- The term of `TopologicalSpace.Closeds α` corresponding to a singleton. -/
 @[simps]

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

@@ -312,8 +312,8 @@ theorem coe_mk (s : Set α) (h) : (mk s h : Set α) = s :=
   rfl
 #align topological_space.clopens.coe_mk TopologicalSpace.Clopens.coe_mk
 
-instance : HasSup (Clopens α) := ⟨fun s t => ⟨s ∪ t, s.clopen.union t.clopen⟩⟩
-instance : HasInf (Clopens α) := ⟨fun s t => ⟨s ∩ t, s.clopen.inter t.clopen⟩⟩
+instance : Sup (Clopens α) := ⟨fun s t => ⟨s ∪ t, s.clopen.union t.clopen⟩⟩
+instance : Inf (Clopens α) := ⟨fun s t => ⟨s ∩ t, s.clopen.inter t.clopen⟩⟩
 instance : Top (Clopens α) := ⟨⟨⊤, isClopen_univ⟩⟩
 instance : Bot (Clopens α) := ⟨⟨⊥, isClopen_empty⟩⟩
 instance : SDiff (Clopens α) := ⟨fun s t => ⟨s \ t, s.clopen.diff t.clopen⟩⟩

@@ -97,9 +97,9 @@ instance : CompleteLattice (Closeds α) :=
     (funext fun s => funext fun t => SetLike.coe_injective (s.2.union t.2).closure_eq.symm)
     -- inf
     (fun s t => ⟨s ∩ t, s.2.inter t.2⟩) rfl
-    -- Sup
+    -- supₛ
     _ rfl
-    -- Inf
+    -- infₛ
     (fun S => ⟨⋂ s ∈ S, ↑s, isClosed_binterᵢ fun s _ => s.2⟩)
     (funext fun _ => SetLike.coe_injective infₛ_image.symm)
 

@@ -44,6 +44,9 @@ instance : SetLike (Closeds α) α where
   coe := Closeds.carrier
   coe_injective' s t h := by cases s; cases t; congr
 
+instance : CanLift (Set α) (Closeds α) (↑) IsClosed where
+  prf s hs := ⟨⟨s, hs⟩, rfl⟩
+
 theorem closed (s : Closeds α) : IsClosed (s : Set α) :=
   s.closed'
 #align topological_space.closeds.closed TopologicalSpace.Closeds.closed