topology.sets.compacts | Mathlib porting status

(last sync)

feat(topology/sets/compacts): add positive_compacts.map (#18872)

Also adds some missing functorial lemmas about map.

Diff

@@ -26,7 +26,7 @@ For a topological space `α`,
 
 open set
 
-variables {α β : Type*} [topological_space α] [topological_space β]
+variables {α β γ : Type*} [topological_space α] [topological_space β] [topological_space γ]
 
 namespace topological_space
 
@@ -93,20 +93,35 @@ end
 protected def map (f : α → β) (hf : continuous f) (K : compacts α) : compacts β :=
 ⟨f '' K.1, K.2.image hf⟩
 
-@[simp] lemma coe_map {f : α → β} (hf : continuous f) (s : compacts α) :
+@[simp, norm_cast] lemma coe_map {f : α → β} (hf : continuous f) (s : compacts α) :
   (s.map f hf : set β) = f '' s := rfl
 
+@[simp] lemma map_id (K : compacts α) : K.map id continuous_id = K := compacts.ext $ set.image_id _
+
+lemma map_comp (f : β → γ) (g : α → β) (hf : continuous f) (hg : continuous g) (K : compacts α) :
+  K.map (f ∘ g) (hf.comp hg) = (K.map g hg).map f hf := compacts.ext $ set.image_comp _ _ _
+
 /-- A homeomorphism induces an equivalence on compact sets, by taking the image. -/
-@[simp] protected def equiv (f : α ≃ₜ β) : compacts α ≃ compacts β :=
+@[simps] protected def equiv (f : α ≃ₜ β) : compacts α ≃ compacts β :=
 { to_fun := compacts.map f f.continuous,
   inv_fun := compacts.map _ f.symm.continuous,
   left_inv := λ s, by { ext1, simp only [coe_map, ← image_comp, f.symm_comp_self, image_id] },
   right_inv := λ s, by { ext1, simp only [coe_map, ← image_comp, f.self_comp_symm, image_id] } }
 
+@[simp] lemma equiv_refl : compacts.equiv (homeomorph.refl α) = equiv.refl _ :=
+equiv.ext map_id
+
+@[simp] lemma equiv_trans (f : α ≃ₜ β) (g : β ≃ₜ γ) :
+  compacts.equiv (f.trans g) = (compacts.equiv f).trans (compacts.equiv g) :=
+equiv.ext $ map_comp _ _ _ _
+
+@[simp] lemma equiv_symm (f : α ≃ₜ β) : compacts.equiv f.symm = (compacts.equiv f).symm :=
+rfl
+
 /-- The image of a compact set under a homeomorphism can also be expressed as a preimage. -/
-lemma equiv_to_fun_val (f : α ≃ₜ β) (K : compacts α) :
-  (compacts.equiv f K).1 = f.symm ⁻¹' K.1 :=
-congr_fun (image_eq_preimage_of_inverse f.left_inv f.right_inv) K.1
+lemma coe_equiv_apply_eq_preimage (f : α ≃ₜ β) (K : compacts α) :
+  (compacts.equiv f K : set β) = f.symm ⁻¹' (K : set α) :=
+f.to_equiv.image_eq_preimage K
 
 /-- The product of two `compacts`, as a `compacts` in the product space. -/
 protected def prod (K : compacts α) (L : compacts β) : compacts (α × β) :=
@@ -225,6 +240,26 @@ order_top.lift (coe : _ → set α) (λ _ _, id) rfl
 @[simp] lemma coe_top [compact_space α] [nonempty α] :
   (↑(⊤ : positive_compacts α) : set α) = univ := rfl
 
+/-- The image of a positive compact set under a continuous open map. -/
+protected def map (f : α → β) (hf : continuous f) (hf' : is_open_map f) (K : positive_compacts α) :
+  positive_compacts β :=
+{ interior_nonempty' :=
+    (K.interior_nonempty'.image _).mono (hf'.image_interior_subset K.to_compacts),
+  ..K.map f hf }
+
+@[simp, norm_cast] lemma coe_map {f : α → β} (hf : continuous f) (hf' : is_open_map f)
+  (s : positive_compacts α) :
+  (s.map f hf hf' : set β) = f '' s := rfl
+
+@[simp] lemma map_id (K : positive_compacts α) : K.map id continuous_id is_open_map.id = K :=
+positive_compacts.ext $ set.image_id _
+
+lemma map_comp (f : β → γ) (g : α → β) (hf : continuous f) (hg : continuous g)
+  (hf' : is_open_map f) (hg' : is_open_map g)
+  (K : positive_compacts α) :
+  K.map (f ∘ g) (hf.comp hg) (hf'.comp hg') = (K.map g hg hg').map f hf hf' :=
+positive_compacts.ext $ set.image_comp _ _ _
+
 lemma _root_.exists_positive_compacts_subset [locally_compact_space α] {U : set α} (ho : is_open U)
   (hn : U.nonempty) : ∃ K : positive_compacts α, ↑K ⊆ U :=
 let ⟨x, hx⟩ := hn, ⟨K, hKc, hxK, hKU⟩ := exists_compact_subset ho hx in ⟨⟨⟨K, hKc⟩, ⟨x, hxK⟩⟩, hKU⟩
@@ -322,8 +357,17 @@ instance : inhabited (compact_opens α) := ⟨⊥⟩
   compact_opens β :=
 ⟨s.to_compacts.map f hf, hf' _ s.is_open⟩
 
-@[simp] lemma coe_map {f : α → β} (hf : continuous f) (hf' : is_open_map f) (s : compact_opens α) :
-  (s.map f hf hf' : set β) = f '' s := rfl
+@[simp, norm_cast] lemma coe_map {f : α → β} (hf : continuous f) (hf' : is_open_map f)
+  (s : compact_opens α) : (s.map f hf hf' : set β) = f '' s := rfl
+
+@[simp] lemma map_id (K : compact_opens α) : K.map id continuous_id is_open_map.id = K :=
+compact_opens.ext $ set.image_id _
+
+lemma map_comp (f : β → γ) (g : α → β) (hf : continuous f) (hg : continuous g)
+  (hf' : is_open_map f) (hg' : is_open_map g)
+  (K : compact_opens α) :
+  K.map (f ∘ g) (hf.comp hg) (hf'.comp hg') = (K.map g hg hg').map f hf hf' :=
+compact_opens.ext $ set.image_comp _ _ _
 
 /-- The product of two `compact_opens`, as a `compact_opens` in the product space. -/
 protected def prod (K : compact_opens α) (L : compact_opens β) :

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -143,7 +143,11 @@ theorem coe_bot : (↑(⊥ : Compacts α) : Set α) = ∅ :=
 #print TopologicalSpace.Compacts.coe_finset_sup /-
 @[simp]
 theorem coe_finset_sup {ι : Type _} {s : Finset ι} {f : ι → Compacts α} :
-    (↑(s.sup f) : Set α) = s.sup fun i => f i := by classical
+    (↑(s.sup f) : Set α) = s.sup fun i => f i := by
+  classical
+  refine' Finset.induction_on s rfl fun a s _ h => _
+  simp_rw [Finset.sup_insert, coe_sup, sup_eq_union]
+  congr
 #align topological_space.compacts.coe_finset_sup TopologicalSpace.Compacts.coe_finset_sup
 -/

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -143,11 +143,7 @@ theorem coe_bot : (↑(⊥ : Compacts α) : Set α) = ∅ :=
 #print TopologicalSpace.Compacts.coe_finset_sup /-
 @[simp]
 theorem coe_finset_sup {ι : Type _} {s : Finset ι} {f : ι → Compacts α} :
-    (↑(s.sup f) : Set α) = s.sup fun i => f i := by
-  classical
-  refine' Finset.induction_on s rfl fun a s _ h => _
-  simp_rw [Finset.sup_insert, coe_sup, sup_eq_union]
-  congr
+    (↑(s.sup f) : Set α) = s.sup fun i => f i := by classical
 #align topological_space.compacts.coe_finset_sup TopologicalSpace.Compacts.coe_finset_sup
 -/

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ 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.Closeds
-import Mathbin.Topology.QuasiSeparated
+import Topology.Sets.Closeds
+import Topology.QuasiSeparated
 
 #align_import topology.sets.compacts from "leanprover-community/mathlib"@"8c1b484d6a214e059531e22f1be9898ed6c1fd47"

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 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.compacts
-! leanprover-community/mathlib commit 8c1b484d6a214e059531e22f1be9898ed6c1fd47
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Sets.Closeds
 import Mathbin.Topology.QuasiSeparated
 
+#align_import topology.sets.compacts from "leanprover-community/mathlib"@"8c1b484d6a214e059531e22f1be9898ed6c1fd47"
+
 /-!
 # Compact sets

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -115,15 +115,19 @@ instance [CompactSpace α] : BoundedOrder (Compacts α) :=
 instance : Inhabited (Compacts α) :=
   ⟨⊥⟩
 
+#print TopologicalSpace.Compacts.coe_sup /-
 @[simp]
 theorem coe_sup (s t : Compacts α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
   rfl
 #align topological_space.compacts.coe_sup TopologicalSpace.Compacts.coe_sup
+-/
 
+#print TopologicalSpace.Compacts.coe_inf /-
 @[simp]
 theorem coe_inf [T2Space α] (s t : Compacts α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
   rfl
 #align topological_space.compacts.coe_inf TopologicalSpace.Compacts.coe_inf
+-/
 
 #print TopologicalSpace.Compacts.coe_top /-
 @[simp]
@@ -139,6 +143,7 @@ theorem coe_bot : (↑(⊥ : Compacts α) : Set α) = ∅ :=
 #align topological_space.compacts.coe_bot TopologicalSpace.Compacts.coe_bot
 -/
 
+#print TopologicalSpace.Compacts.coe_finset_sup /-
 @[simp]
 theorem coe_finset_sup {ι : Type _} {s : Finset ι} {f : ι → Compacts α} :
     (↑(s.sup f) : Set α) = s.sup fun i => f i := by
@@ -147,6 +152,7 @@ theorem coe_finset_sup {ι : Type _} {s : Finset ι} {f : ι → Compacts α} :
   simp_rw [Finset.sup_insert, coe_sup, sup_eq_union]
   congr
 #align topological_space.compacts.coe_finset_sup TopologicalSpace.Compacts.coe_finset_sup
+-/
 
 #print TopologicalSpace.Compacts.map /-
 /-- The image of a compact set under a continuous function. -/
@@ -155,10 +161,12 @@ protected def map (f : α → β) (hf : Continuous f) (K : Compacts α) : Compac
 #align topological_space.compacts.map TopologicalSpace.Compacts.map
 -/
 
+#print TopologicalSpace.Compacts.coe_map /-
 @[simp, norm_cast]
 theorem coe_map {f : α → β} (hf : Continuous f) (s : Compacts α) : (s.map f hf : Set β) = f '' s :=
   rfl
 #align topological_space.compacts.coe_map TopologicalSpace.Compacts.coe_map
+-/
 
 #print TopologicalSpace.Compacts.map_id /-
 @[simp]
@@ -167,10 +175,12 @@ theorem map_id (K : Compacts α) : K.map id continuous_id = K :=
 #align topological_space.compacts.map_id TopologicalSpace.Compacts.map_id
 -/
 
+#print TopologicalSpace.Compacts.map_comp /-
 theorem map_comp (f : β → γ) (g : α → β) (hf : Continuous f) (hg : Continuous g) (K : Compacts α) :
     K.map (f ∘ g) (hf.comp hg) = (K.map g hg).map f hf :=
   Compacts.ext <| Set.image_comp _ _ _
 #align topological_space.compacts.map_comp TopologicalSpace.Compacts.map_comp
+-/
 
 #print TopologicalSpace.Compacts.equiv /-
 /-- A homeomorphism induces an equivalence on compact sets, by taking the image. -/
@@ -191,36 +201,46 @@ theorem equiv_refl : Compacts.equiv (Homeomorph.refl α) = Equiv.refl _ :=
 #align topological_space.compacts.equiv_refl TopologicalSpace.Compacts.equiv_refl
 -/
 
+#print TopologicalSpace.Compacts.equiv_trans /-
 @[simp]
 theorem equiv_trans (f : α ≃ₜ β) (g : β ≃ₜ γ) :
     Compacts.equiv (f.trans g) = (Compacts.equiv f).trans (Compacts.equiv g) :=
   Equiv.ext <| map_comp _ _ _ _
 #align topological_space.compacts.equiv_trans TopologicalSpace.Compacts.equiv_trans
+-/
 
+#print TopologicalSpace.Compacts.equiv_symm /-
 @[simp]
 theorem equiv_symm (f : α ≃ₜ β) : Compacts.equiv f.symm = (Compacts.equiv f).symm :=
   rfl
 #align topological_space.compacts.equiv_symm TopologicalSpace.Compacts.equiv_symm
+-/
 
+#print TopologicalSpace.Compacts.coe_equiv_apply_eq_preimage /-
 /-- The image of a compact set under a homeomorphism can also be expressed as a preimage. -/
 theorem coe_equiv_apply_eq_preimage (f : α ≃ₜ β) (K : Compacts α) :
     (Compacts.equiv f K : Set β) = f.symm ⁻¹' (K : Set α) :=
   f.toEquiv.image_eq_preimage K
 #align topological_space.compacts.coe_equiv_apply_eq_preimage TopologicalSpace.Compacts.coe_equiv_apply_eq_preimage
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print TopologicalSpace.Compacts.prod /-
 /-- The product of two `compacts`, as a `compacts` in the product space. -/
 protected def prod (K : Compacts α) (L : Compacts β) : Compacts (α × β)
     where
   carrier := K ×ˢ L
   is_compact' := IsCompact.prod K.2 L.2
 #align topological_space.compacts.prod TopologicalSpace.Compacts.prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print TopologicalSpace.Compacts.coe_prod /-
 @[simp]
 theorem coe_prod (K : Compacts α) (L : Compacts β) : (K.Prod L : Set (α × β)) = K ×ˢ L :=
   rfl
 #align topological_space.compacts.coe_prod TopologicalSpace.Compacts.coe_prod
+-/
 
 end Compacts
 
@@ -293,10 +313,12 @@ instance : SemilatticeSup (NonemptyCompacts α) :=
 instance [CompactSpace α] [Nonempty α] : OrderTop (NonemptyCompacts α) :=
   OrderTop.lift (coe : _ → Set α) (fun _ _ => id) rfl
 
+#print TopologicalSpace.NonemptyCompacts.coe_sup /-
 @[simp]
 theorem coe_sup (s t : NonemptyCompacts α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
   rfl
 #align topological_space.nonempty_compacts.coe_sup TopologicalSpace.NonemptyCompacts.coe_sup
+-/
 
 #print TopologicalSpace.NonemptyCompacts.coe_top /-
 @[simp]
@@ -324,17 +346,21 @@ instance toNonempty {s : NonemptyCompacts α} : Nonempty s :=
 #align topological_space.nonempty_compacts.to_nonempty TopologicalSpace.NonemptyCompacts.toNonempty
 -/
 
+#print TopologicalSpace.NonemptyCompacts.prod /-
 /-- The product of two `nonempty_compacts`, as a `nonempty_compacts` in the product space. -/
 protected def prod (K : NonemptyCompacts α) (L : NonemptyCompacts β) : NonemptyCompacts (α × β) :=
   { K.toCompacts.Prod L.toCompacts with nonempty' := K.Nonempty.Prod L.Nonempty }
 #align topological_space.nonempty_compacts.prod TopologicalSpace.NonemptyCompacts.prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print TopologicalSpace.NonemptyCompacts.coe_prod /-
 @[simp]
 theorem coe_prod (K : NonemptyCompacts α) (L : NonemptyCompacts β) :
     (K.Prod L : Set (α × β)) = K ×ˢ L :=
   rfl
 #align topological_space.nonempty_compacts.coe_prod TopologicalSpace.NonemptyCompacts.coe_prod
+-/
 
 end NonemptyCompacts
 
@@ -416,10 +442,12 @@ instance : SemilatticeSup (PositiveCompacts α) :=
 instance [CompactSpace α] [Nonempty α] : OrderTop (PositiveCompacts α) :=
   OrderTop.lift (coe : _ → Set α) (fun _ _ => id) rfl
 
+#print TopologicalSpace.PositiveCompacts.coe_sup /-
 @[simp]
 theorem coe_sup (s t : PositiveCompacts α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
   rfl
 #align topological_space.positive_compacts.coe_sup TopologicalSpace.PositiveCompacts.coe_sup
+-/
 
 #print TopologicalSpace.PositiveCompacts.coe_top /-
 @[simp]
@@ -438,11 +466,13 @@ protected def map (f : α → β) (hf : Continuous f) (hf' : IsOpenMap f) (K : P
 #align topological_space.positive_compacts.map TopologicalSpace.PositiveCompacts.map
 -/
 
+#print TopologicalSpace.PositiveCompacts.coe_map /-
 @[simp, norm_cast]
 theorem coe_map {f : α → β} (hf : Continuous f) (hf' : IsOpenMap f) (s : PositiveCompacts α) :
     (s.map f hf hf' : Set β) = f '' s :=
   rfl
 #align topological_space.positive_compacts.coe_map TopologicalSpace.PositiveCompacts.coe_map
+-/
 
 #print TopologicalSpace.PositiveCompacts.map_id /-
 @[simp]
@@ -451,11 +481,13 @@ theorem map_id (K : PositiveCompacts α) : K.map id continuous_id IsOpenMap.id =
 #align topological_space.positive_compacts.map_id TopologicalSpace.PositiveCompacts.map_id
 -/
 
+#print TopologicalSpace.PositiveCompacts.map_comp /-
 theorem map_comp (f : β → γ) (g : α → β) (hf : Continuous f) (hg : Continuous g) (hf' : IsOpenMap f)
     (hg' : IsOpenMap g) (K : PositiveCompacts α) :
     K.map (f ∘ g) (hf.comp hg) (hf'.comp hg') = (K.map g hg hg').map f hf hf' :=
   PositiveCompacts.ext <| Set.image_comp _ _ _
 #align topological_space.positive_compacts.map_comp TopologicalSpace.PositiveCompacts.map_comp
+-/
 
 #print exists_positiveCompacts_subset /-
 theorem exists_positiveCompacts_subset [LocallyCompactSpace α] {U : Set α} (ho : IsOpen U)
@@ -476,6 +508,7 @@ instance nonempty' [LocallyCompactSpace α] [Nonempty α] : Nonempty (PositiveCo
 #align topological_space.positive_compacts.nonempty' TopologicalSpace.PositiveCompacts.nonempty'
 -/
 
+#print TopologicalSpace.PositiveCompacts.prod /-
 /-- The product of two `positive_compacts`, as a `positive_compacts` in the product space. -/
 protected def prod (K : PositiveCompacts α) (L : PositiveCompacts β) : PositiveCompacts (α × β) :=
   { K.toCompacts.Prod L.toCompacts with
@@ -484,13 +517,16 @@ protected def prod (K : PositiveCompacts α) (L : PositiveCompacts β) : Positiv
       simp only [compacts.carrier_eq_coe, compacts.coe_prod, interior_prod_eq]
       exact K.interior_nonempty.prod L.interior_nonempty }
 #align topological_space.positive_compacts.prod TopologicalSpace.PositiveCompacts.prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print TopologicalSpace.PositiveCompacts.coe_prod /-
 @[simp]
 theorem coe_prod (K : PositiveCompacts α) (L : PositiveCompacts β) :
     (K.Prod L : Set (α × β)) = K ×ˢ L :=
   rfl
 #align topological_space.positive_compacts.coe_prod TopologicalSpace.PositiveCompacts.coe_prod
+-/
 
 end PositiveCompacts
 
@@ -595,15 +631,19 @@ instance [T2Space α] [CompactSpace α] : BooleanAlgebra (CompactOpens α) :=
   SetLike.coe_injective.BooleanAlgebra _ (fun _ _ => rfl) (fun _ _ => rfl) rfl rfl (fun _ => rfl)
     fun _ _ => rfl
 
+#print TopologicalSpace.CompactOpens.coe_sup /-
 @[simp]
 theorem coe_sup (s t : CompactOpens α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
   rfl
 #align topological_space.compact_opens.coe_sup TopologicalSpace.CompactOpens.coe_sup
+-/
 
+#print TopologicalSpace.CompactOpens.coe_inf /-
 @[simp]
 theorem coe_inf [T2Space α] (s t : CompactOpens α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
   rfl
 #align topological_space.compact_opens.coe_inf TopologicalSpace.CompactOpens.coe_inf
+-/
 
 #print TopologicalSpace.CompactOpens.coe_top /-
 @[simp]
@@ -619,15 +659,19 @@ theorem coe_bot : (↑(⊥ : CompactOpens α) : Set α) = ∅ :=
 #align topological_space.compact_opens.coe_bot TopologicalSpace.CompactOpens.coe_bot
 -/
 
+#print TopologicalSpace.CompactOpens.coe_sdiff /-
 @[simp]
 theorem coe_sdiff [T2Space α] (s t : CompactOpens α) : (↑(s \ t) : Set α) = s \ t :=
   rfl
 #align topological_space.compact_opens.coe_sdiff TopologicalSpace.CompactOpens.coe_sdiff
+-/
 
+#print TopologicalSpace.CompactOpens.coe_compl /-
 @[simp]
 theorem coe_compl [T2Space α] [CompactSpace α] (s : CompactOpens α) : (↑(sᶜ) : Set α) = sᶜ :=
   rfl
 #align topological_space.compact_opens.coe_compl TopologicalSpace.CompactOpens.coe_compl
+-/
 
 instance : Inhabited (CompactOpens α) :=
   ⟨⊥⟩
@@ -640,11 +684,13 @@ def map (f : α → β) (hf : Continuous f) (hf' : IsOpenMap f) (s : CompactOpen
 #align topological_space.compact_opens.map TopologicalSpace.CompactOpens.map
 -/
 
+#print TopologicalSpace.CompactOpens.coe_map /-
 @[simp, norm_cast]
 theorem coe_map {f : α → β} (hf : Continuous f) (hf' : IsOpenMap f) (s : CompactOpens α) :
     (s.map f hf hf' : Set β) = f '' s :=
   rfl
 #align topological_space.compact_opens.coe_map TopologicalSpace.CompactOpens.coe_map
+-/
 
 #print TopologicalSpace.CompactOpens.map_id /-
 @[simp]
@@ -653,22 +699,28 @@ theorem map_id (K : CompactOpens α) : K.map id continuous_id IsOpenMap.id = K :
 #align topological_space.compact_opens.map_id TopologicalSpace.CompactOpens.map_id
 -/
 
+#print TopologicalSpace.CompactOpens.map_comp /-
 theorem map_comp (f : β → γ) (g : α → β) (hf : Continuous f) (hg : Continuous g) (hf' : IsOpenMap f)
     (hg' : IsOpenMap g) (K : CompactOpens α) :
     K.map (f ∘ g) (hf.comp hg) (hf'.comp hg') = (K.map g hg hg').map f hf hf' :=
   CompactOpens.ext <| Set.image_comp _ _ _
 #align topological_space.compact_opens.map_comp TopologicalSpace.CompactOpens.map_comp
+-/
 
+#print TopologicalSpace.CompactOpens.prod /-
 /-- The product of two `compact_opens`, as a `compact_opens` in the product space. -/
 protected def prod (K : CompactOpens α) (L : CompactOpens β) : CompactOpens (α × β) :=
   { K.toCompacts.Prod L.toCompacts with is_open' := K.IsOpen.Prod L.IsOpen }
 #align topological_space.compact_opens.prod TopologicalSpace.CompactOpens.prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print TopologicalSpace.CompactOpens.coe_prod /-
 @[simp]
 theorem coe_prod (K : CompactOpens α) (L : CompactOpens β) : (K.Prod L : Set (α × β)) = K ×ˢ L :=
   rfl
 #align topological_space.compact_opens.coe_prod TopologicalSpace.CompactOpens.coe_prod
+-/
 
 end CompactOpens

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -143,9 +143,9 @@ theorem coe_bot : (↑(⊥ : Compacts α) : Set α) = ∅ :=
 theorem coe_finset_sup {ι : Type _} {s : Finset ι} {f : ι → Compacts α} :
     (↑(s.sup f) : Set α) = s.sup fun i => f i := by
   classical
-    refine' Finset.induction_on s rfl fun a s _ h => _
-    simp_rw [Finset.sup_insert, coe_sup, sup_eq_union]
-    congr
+  refine' Finset.induction_on s rfl fun a s _ h => _
+  simp_rw [Finset.sup_insert, coe_sup, sup_eq_union]
+  congr
 #align topological_space.compacts.coe_finset_sup TopologicalSpace.Compacts.coe_finset_sup
 
 #print TopologicalSpace.Compacts.map /-

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -115,23 +115,11 @@ instance [CompactSpace α] : BoundedOrder (Compacts α) :=
 instance : Inhabited (Compacts α) :=
   ⟨⊥⟩
 
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 @[simp]
 theorem coe_sup (s t : Compacts α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
   rfl
 #align topological_space.compacts.coe_sup TopologicalSpace.Compacts.coe_sup
 
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 @[simp]
 theorem coe_inf [T2Space α] (s t : Compacts α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
   rfl
@@ -151,12 +139,6 @@ theorem coe_bot : (↑(⊥ : Compacts α) : Set α) = ∅ :=
 #align topological_space.compacts.coe_bot TopologicalSpace.Compacts.coe_bot
 -/
 
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 @[simp]
 theorem coe_finset_sup {ι : Type _} {s : Finset ι} {f : ι → Compacts α} :
     (↑(s.sup f) : Set α) = s.sup fun i => f i := by
@@ -173,12 +155,6 @@ protected def map (f : α → β) (hf : Continuous f) (K : Compacts α) : Compac
 #align topological_space.compacts.map TopologicalSpace.Compacts.map
 -/
 
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 @[simp, norm_cast]
 theorem coe_map {f : α → β} (hf : Continuous f) (s : Compacts α) : (s.map f hf : Set β) = f '' s :=
   rfl
@@ -191,12 +167,6 @@ theorem map_id (K : Compacts α) : K.map id continuous_id = K :=
 #align topological_space.compacts.map_id TopologicalSpace.Compacts.map_id
 -/
 
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 theorem map_comp (f : β → γ) (g : α → β) (hf : Continuous f) (hg : Continuous g) (K : Compacts α) :
     K.map (f ∘ g) (hf.comp hg) = (K.map g hg).map f hf :=
   Compacts.ext <| Set.image_comp _ _ _
@@ -221,47 +191,23 @@ theorem equiv_refl : Compacts.equiv (Homeomorph.refl α) = Equiv.refl _ :=
 #align topological_space.compacts.equiv_refl TopologicalSpace.Compacts.equiv_refl
 -/
 
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 @[simp]
 theorem equiv_trans (f : α ≃ₜ β) (g : β ≃ₜ γ) :
     Compacts.equiv (f.trans g) = (Compacts.equiv f).trans (Compacts.equiv g) :=
   Equiv.ext <| map_comp _ _ _ _
 #align topological_space.compacts.equiv_trans TopologicalSpace.Compacts.equiv_trans
 
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 @[simp]
 theorem equiv_symm (f : α ≃ₜ β) : Compacts.equiv f.symm = (Compacts.equiv f).symm :=
   rfl
 #align topological_space.compacts.equiv_symm TopologicalSpace.Compacts.equiv_symm
 
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 /-- The image of a compact set under a homeomorphism can also be expressed as a preimage. -/
 theorem coe_equiv_apply_eq_preimage (f : α ≃ₜ β) (K : Compacts α) :
     (Compacts.equiv f K : Set β) = f.symm ⁻¹' (K : Set α) :=
   f.toEquiv.image_eq_preimage K
 #align topological_space.compacts.coe_equiv_apply_eq_preimage TopologicalSpace.Compacts.coe_equiv_apply_eq_preimage
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The product of two `compacts`, as a `compacts` in the product space. -/
 protected def prod (K : Compacts α) (L : Compacts β) : Compacts (α × β)
@@ -270,12 +216,6 @@ protected def prod (K : Compacts α) (L : Compacts β) : Compacts (α × β)
   is_compact' := IsCompact.prod K.2 L.2
 #align topological_space.compacts.prod TopologicalSpace.Compacts.prod
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
 theorem coe_prod (K : Compacts α) (L : Compacts β) : (K.Prod L : Set (α × β)) = K ×ˢ L :=
@@ -353,12 +293,6 @@ instance : SemilatticeSup (NonemptyCompacts α) :=
 instance [CompactSpace α] [Nonempty α] : OrderTop (NonemptyCompacts α) :=
   OrderTop.lift (coe : _ → Set α) (fun _ _ => id) rfl
 
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 @[simp]
 theorem coe_sup (s t : NonemptyCompacts α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
   rfl
@@ -390,23 +324,11 @@ instance toNonempty {s : NonemptyCompacts α} : Nonempty s :=
 #align topological_space.nonempty_compacts.to_nonempty TopologicalSpace.NonemptyCompacts.toNonempty
 -/
 
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 /-- The product of two `nonempty_compacts`, as a `nonempty_compacts` in the product space. -/
 protected def prod (K : NonemptyCompacts α) (L : NonemptyCompacts β) : NonemptyCompacts (α × β) :=
   { K.toCompacts.Prod L.toCompacts with nonempty' := K.Nonempty.Prod L.Nonempty }
 #align topological_space.nonempty_compacts.prod TopologicalSpace.NonemptyCompacts.prod
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
 theorem coe_prod (K : NonemptyCompacts α) (L : NonemptyCompacts β) :
@@ -494,12 +416,6 @@ instance : SemilatticeSup (PositiveCompacts α) :=
 instance [CompactSpace α] [Nonempty α] : OrderTop (PositiveCompacts α) :=
   OrderTop.lift (coe : _ → Set α) (fun _ _ => id) rfl
 
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 @[simp]
 theorem coe_sup (s t : PositiveCompacts α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
   rfl
@@ -522,12 +438,6 @@ protected def map (f : α → β) (hf : Continuous f) (hf' : IsOpenMap f) (K : P
 #align topological_space.positive_compacts.map TopologicalSpace.PositiveCompacts.map
 -/
 
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 @[simp, norm_cast]
 theorem coe_map {f : α → β} (hf : Continuous f) (hf' : IsOpenMap f) (s : PositiveCompacts α) :
     (s.map f hf hf' : Set β) = f '' s :=
@@ -541,12 +451,6 @@ theorem map_id (K : PositiveCompacts α) : K.map id continuous_id IsOpenMap.id =
 #align topological_space.positive_compacts.map_id TopologicalSpace.PositiveCompacts.map_id
 -/
 
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 theorem map_comp (f : β → γ) (g : α → β) (hf : Continuous f) (hg : Continuous g) (hf' : IsOpenMap f)
     (hg' : IsOpenMap g) (K : PositiveCompacts α) :
     K.map (f ∘ g) (hf.comp hg) (hf'.comp hg') = (K.map g hg hg').map f hf hf' :=
@@ -572,12 +476,6 @@ instance nonempty' [LocallyCompactSpace α] [Nonempty α] : Nonempty (PositiveCo
 #align topological_space.positive_compacts.nonempty' TopologicalSpace.PositiveCompacts.nonempty'
 -/
 
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 /-- The product of two `positive_compacts`, as a `positive_compacts` in the product space. -/
 protected def prod (K : PositiveCompacts α) (L : PositiveCompacts β) : PositiveCompacts (α × β) :=
   { K.toCompacts.Prod L.toCompacts with
@@ -587,12 +485,6 @@ protected def prod (K : PositiveCompacts α) (L : PositiveCompacts β) : Positiv
       exact K.interior_nonempty.prod L.interior_nonempty }
 #align topological_space.positive_compacts.prod TopologicalSpace.PositiveCompacts.prod
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
 theorem coe_prod (K : PositiveCompacts α) (L : PositiveCompacts β) :
@@ -703,23 +595,11 @@ instance [T2Space α] [CompactSpace α] : BooleanAlgebra (CompactOpens α) :=
   SetLike.coe_injective.BooleanAlgebra _ (fun _ _ => rfl) (fun _ _ => rfl) rfl rfl (fun _ => rfl)
     fun _ _ => rfl
 
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 @[simp]
 theorem coe_sup (s t : CompactOpens α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
   rfl
 #align topological_space.compact_opens.coe_sup TopologicalSpace.CompactOpens.coe_sup
 
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 @[simp]
 theorem coe_inf [T2Space α] (s t : CompactOpens α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
   rfl
@@ -739,23 +619,11 @@ theorem coe_bot : (↑(⊥ : CompactOpens α) : Set α) = ∅ :=
 #align topological_space.compact_opens.coe_bot TopologicalSpace.CompactOpens.coe_bot
 -/
 
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 @[simp]
 theorem coe_sdiff [T2Space α] (s t : CompactOpens α) : (↑(s \ t) : Set α) = s \ t :=
   rfl
 #align topological_space.compact_opens.coe_sdiff TopologicalSpace.CompactOpens.coe_sdiff
 
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 @[simp]
 theorem coe_compl [T2Space α] [CompactSpace α] (s : CompactOpens α) : (↑(sᶜ) : Set α) = sᶜ :=
   rfl
@@ -772,12 +640,6 @@ def map (f : α → β) (hf : Continuous f) (hf' : IsOpenMap f) (s : CompactOpen
 #align topological_space.compact_opens.map TopologicalSpace.CompactOpens.map
 -/
 
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 @[simp, norm_cast]
 theorem coe_map {f : α → β} (hf : Continuous f) (hf' : IsOpenMap f) (s : CompactOpens α) :
     (s.map f hf hf' : Set β) = f '' s :=
@@ -791,35 +653,17 @@ theorem map_id (K : CompactOpens α) : K.map id continuous_id IsOpenMap.id = K :
 #align topological_space.compact_opens.map_id TopologicalSpace.CompactOpens.map_id
 -/
 
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 theorem map_comp (f : β → γ) (g : α → β) (hf : Continuous f) (hg : Continuous g) (hf' : IsOpenMap f)
     (hg' : IsOpenMap g) (K : CompactOpens α) :
     K.map (f ∘ g) (hf.comp hg) (hf'.comp hg') = (K.map g hg hg').map f hf hf' :=
   CompactOpens.ext <| Set.image_comp _ _ _
 #align topological_space.compact_opens.map_comp TopologicalSpace.CompactOpens.map_comp
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align topological_space.compact_opens.prod TopologicalSpace.CompactOpens.prodₓ'. -/
 /-- The product of two `compact_opens`, as a `compact_opens` in the product space. -/
 protected def prod (K : CompactOpens α) (L : CompactOpens β) : CompactOpens (α × β) :=
   { K.toCompacts.Prod L.toCompacts with is_open' := K.IsOpen.Prod L.IsOpen }
 #align topological_space.compact_opens.prod TopologicalSpace.CompactOpens.prod
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
 theorem coe_prod (K : CompactOpens α) (L : CompactOpens β) : (K.Prod L : Set (α × β)) = K ×ˢ L :=

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -53,10 +53,7 @@ variable {α}
 
 instance : SetLike (Compacts α) α where
   coe := Compacts.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.Compacts.isCompact /-
 protected theorem isCompact (s : Compacts α) : IsCompact (s : Set α) :=
@@ -212,12 +209,8 @@ protected def equiv (f : α ≃ₜ β) : Compacts α ≃ Compacts β
     where
   toFun := Compacts.map f f.Continuous
   invFun := Compacts.map _ f.symm.Continuous
-  left_inv s := by
-    ext1
-    simp only [coe_map, ← image_comp, f.symm_comp_self, image_id]
-  right_inv s := by
-    ext1
-    simp only [coe_map, ← image_comp, f.self_comp_symm, image_id]
+  left_inv s := by ext1; simp only [coe_map, ← image_comp, f.symm_comp_self, image_id]
+  right_inv s := by ext1; simp only [coe_map, ← image_comp, f.self_comp_symm, image_id]
 #align topological_space.compacts.equiv TopologicalSpace.Compacts.equiv
 -/
 
@@ -306,10 +299,7 @@ namespace NonemptyCompacts
 instance : SetLike (NonemptyCompacts α) α
     where
   coe s := s.carrier
-  coe_injective' s t h := by
-    obtain ⟨⟨_, _⟩, _⟩ := s
-    obtain ⟨⟨_, _⟩, _⟩ := t
-    congr
+  coe_injective' s t h := by obtain ⟨⟨_, _⟩, _⟩ := s; obtain ⟨⟨_, _⟩, _⟩ := t; congr
 
 #print TopologicalSpace.NonemptyCompacts.isCompact /-
 protected theorem isCompact (s : NonemptyCompacts α) : IsCompact (s : Set α) :=
@@ -442,10 +432,7 @@ namespace PositiveCompacts
 instance : SetLike (PositiveCompacts α) α
     where
   coe s := s.carrier
-  coe_injective' s t h := by
-    obtain ⟨⟨_, _⟩, _⟩ := s
-    obtain ⟨⟨_, _⟩, _⟩ := t
-    congr
+  coe_injective' s t h := by obtain ⟨⟨_, _⟩, _⟩ := s; obtain ⟨⟨_, _⟩, _⟩ := t; congr
 
 #print TopologicalSpace.PositiveCompacts.isCompact /-
 protected theorem isCompact (s : PositiveCompacts α) : IsCompact (s : Set α) :=
@@ -631,10 +618,7 @@ namespace CompactOpens
 instance : SetLike (CompactOpens α) α
     where
   coe s := s.carrier
-  coe_injective' s t h := by
-    obtain ⟨⟨_, _⟩, _⟩ := s
-    obtain ⟨⟨_, _⟩, _⟩ := t
-    congr
+  coe_injective' s t h := by obtain ⟨⟨_, _⟩, _⟩ := s; obtain ⟨⟨_, _⟩, _⟩ := t; congr
 
 #print TopologicalSpace.CompactOpens.isCompact /-
 protected theorem isCompact (s : CompactOpens α) : IsCompact (s : Set α) :=

bump to nightly-2023-05-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

ed98987c

Diff

@@ -187,11 +187,19 @@ theorem coe_map {f : α → β} (hf : Continuous f) (s : Compacts α) : (s.map f
   rfl
 #align topological_space.compacts.coe_map TopologicalSpace.Compacts.coe_map
 
+#print TopologicalSpace.Compacts.map_id /-
 @[simp]
 theorem map_id (K : Compacts α) : K.map id continuous_id = K :=
   Compacts.ext <| Set.image_id _
 #align topological_space.compacts.map_id TopologicalSpace.Compacts.map_id
+-/
 
+/- warning: topological_space.compacts.map_comp -> TopologicalSpace.Compacts.map_comp is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align topological_space.compacts.map_comp TopologicalSpace.Compacts.map_compₓ'. -/
 theorem map_comp (f : β → γ) (g : α → β) (hf : Continuous f) (hg : Continuous g) (K : Compacts α) :
     K.map (f ∘ g) (hf.comp hg) = (K.map g hg).map f hf :=
   Compacts.ext <| Set.image_comp _ _ _
@@ -213,22 +221,42 @@ protected def equiv (f : α ≃ₜ β) : Compacts α ≃ Compacts β
 #align topological_space.compacts.equiv TopologicalSpace.Compacts.equiv
 -/
 
+#print TopologicalSpace.Compacts.equiv_refl /-
 @[simp]
 theorem equiv_refl : Compacts.equiv (Homeomorph.refl α) = Equiv.refl _ :=
   Equiv.ext map_id
 #align topological_space.compacts.equiv_refl TopologicalSpace.Compacts.equiv_refl
+-/
 
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 @[simp]
 theorem equiv_trans (f : α ≃ₜ β) (g : β ≃ₜ γ) :
     Compacts.equiv (f.trans g) = (Compacts.equiv f).trans (Compacts.equiv g) :=
   Equiv.ext <| map_comp _ _ _ _
 #align topological_space.compacts.equiv_trans TopologicalSpace.Compacts.equiv_trans
 
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 @[simp]
 theorem equiv_symm (f : α ≃ₜ β) : Compacts.equiv f.symm = (Compacts.equiv f).symm :=
   rfl
 #align topological_space.compacts.equiv_symm TopologicalSpace.Compacts.equiv_symm
 
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+Case conversion may be inaccurate. Consider using '#align topological_space.compacts.coe_equiv_apply_eq_preimage TopologicalSpace.Compacts.coe_equiv_apply_eq_preimageₓ'. -/
 /-- The image of a compact set under a homeomorphism can also be expressed as a preimage. -/
 theorem coe_equiv_apply_eq_preimage (f : α ≃ₜ β) (K : Compacts α) :
     (Compacts.equiv f K : Set β) = f.symm ⁻¹' (K : Set α) :=
@@ -497,6 +525,7 @@ theorem coe_top [CompactSpace α] [Nonempty α] : (↑(⊤ : PositiveCompacts α
 #align topological_space.positive_compacts.coe_top TopologicalSpace.PositiveCompacts.coe_top
 -/
 
+#print TopologicalSpace.PositiveCompacts.map /-
 /-- The image of a positive compact set under a continuous open map. -/
 protected def map (f : α → β) (hf : Continuous f) (hf' : IsOpenMap f) (K : PositiveCompacts α) :
     PositiveCompacts β :=
@@ -504,18 +533,33 @@ protected def map (f : α → β) (hf : Continuous f) (hf' : IsOpenMap f) (K : P
     interior_nonempty' :=
       (K.interior_nonempty'.image _).mono (hf'.image_interior_subset K.toCompacts) }
 #align topological_space.positive_compacts.map TopologicalSpace.PositiveCompacts.map
+-/
 
+/- warning: topological_space.positive_compacts.coe_map -> TopologicalSpace.PositiveCompacts.coe_map is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] {f : α -> β} (hf : Continuous.{u1, u2} α β _inst_1 _inst_2 f) (hf' : IsOpenMap.{u1, u2} α β _inst_1 _inst_2 f) (s : TopologicalSpace.PositiveCompacts.{u1} α _inst_1), Eq.{succ u2} (Set.{u2} β) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (TopologicalSpace.PositiveCompacts.{u2} β _inst_2) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (TopologicalSpace.PositiveCompacts.{u2} β _inst_2) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (TopologicalSpace.PositiveCompacts.{u2} β _inst_2) (Set.{u2} β) (SetLike.Set.hasCoeT.{u2, u2} (TopologicalSpace.PositiveCompacts.{u2} β _inst_2) β (TopologicalSpace.PositiveCompacts.setLike.{u2} β _inst_2)))) (TopologicalSpace.PositiveCompacts.map.{u1, u2} α β _inst_1 _inst_2 f hf hf' s)) (Set.image.{u1, u2} α β f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) α (TopologicalSpace.PositiveCompacts.setLike.{u1} α _inst_1)))) s))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : TopologicalSpace.{u1} β] {f : α -> β} (hf : Continuous.{u2, u1} α β _inst_1 _inst_2 f) (hf' : IsOpenMap.{u2, u1} α β _inst_1 _inst_2 f) (s : TopologicalSpace.PositiveCompacts.{u2} α _inst_1), Eq.{succ u1} (Set.{u1} β) (SetLike.coe.{u1, u1} (TopologicalSpace.PositiveCompacts.{u1} β _inst_2) β (TopologicalSpace.PositiveCompacts.instSetLikePositiveCompacts.{u1} β _inst_2) (TopologicalSpace.PositiveCompacts.map.{u2, u1} α β _inst_1 _inst_2 f hf hf' s)) (Set.image.{u2, u1} α β f (SetLike.coe.{u2, u2} (TopologicalSpace.PositiveCompacts.{u2} α _inst_1) α (TopologicalSpace.PositiveCompacts.instSetLikePositiveCompacts.{u2} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align topological_space.positive_compacts.coe_map TopologicalSpace.PositiveCompacts.coe_mapₓ'. -/
 @[simp, norm_cast]
 theorem coe_map {f : α → β} (hf : Continuous f) (hf' : IsOpenMap f) (s : PositiveCompacts α) :
     (s.map f hf hf' : Set β) = f '' s :=
   rfl
 #align topological_space.positive_compacts.coe_map TopologicalSpace.PositiveCompacts.coe_map
 
+#print TopologicalSpace.PositiveCompacts.map_id /-
 @[simp]
 theorem map_id (K : PositiveCompacts α) : K.map id continuous_id IsOpenMap.id = K :=
   PositiveCompacts.ext <| Set.image_id _
 #align topological_space.positive_compacts.map_id TopologicalSpace.PositiveCompacts.map_id
+-/
 
+/- warning: topological_space.positive_compacts.map_comp -> TopologicalSpace.PositiveCompacts.map_comp is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] [_inst_3 : TopologicalSpace.{u3} γ] (f : β -> γ) (g : α -> β) (hf : Continuous.{u2, u3} β γ _inst_2 _inst_3 f) (hg : Continuous.{u1, u2} α β _inst_1 _inst_2 g) (hf' : IsOpenMap.{u2, u3} β γ _inst_2 _inst_3 f) (hg' : IsOpenMap.{u1, u2} α β _inst_1 _inst_2 g) (K : TopologicalSpace.PositiveCompacts.{u1} α _inst_1), Eq.{succ u3} (TopologicalSpace.PositiveCompacts.{u3} γ _inst_3) (TopologicalSpace.PositiveCompacts.map.{u1, u3} α γ _inst_1 _inst_3 (Function.comp.{succ u1, succ u2, succ u3} α β γ f g) (Continuous.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 f g hf hg) (IsOpenMap.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 f g hf' hg') K) (TopologicalSpace.PositiveCompacts.map.{u2, u3} β γ _inst_2 _inst_3 f hf hf' (TopologicalSpace.PositiveCompacts.map.{u1, u2} α β _inst_1 _inst_2 g hg hg' K))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u3} β] [_inst_3 : TopologicalSpace.{u2} γ] (f : β -> γ) (g : α -> β) (hf : Continuous.{u3, u2} β γ _inst_2 _inst_3 f) (hg : Continuous.{u1, u3} α β _inst_1 _inst_2 g) (hf' : IsOpenMap.{u3, u2} β γ _inst_2 _inst_3 f) (hg' : IsOpenMap.{u1, u3} α β _inst_1 _inst_2 g) (K : TopologicalSpace.PositiveCompacts.{u1} α _inst_1), Eq.{succ u2} (TopologicalSpace.PositiveCompacts.{u2} γ _inst_3) (TopologicalSpace.PositiveCompacts.map.{u1, u2} α γ _inst_1 _inst_3 (Function.comp.{succ u1, succ u3, succ u2} α β γ f g) (Continuous.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 f g hf hg) (IsOpenMap.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 f g hf' hg') K) (TopologicalSpace.PositiveCompacts.map.{u3, u2} β γ _inst_2 _inst_3 f hf hf' (TopologicalSpace.PositiveCompacts.map.{u1, u3} α β _inst_1 _inst_2 g hg hg' K))
+Case conversion may be inaccurate. Consider using '#align topological_space.positive_compacts.map_comp TopologicalSpace.PositiveCompacts.map_compₓ'. -/
 theorem map_comp (f : β → γ) (g : α → β) (hf : Continuous f) (hg : Continuous g) (hf' : IsOpenMap f)
     (hg' : IsOpenMap g) (K : PositiveCompacts α) :
     K.map (f ∘ g) (hf.comp hg) (hf'.comp hg') = (K.map g hg hg').map f hf hf' :=
@@ -756,11 +800,19 @@ theorem coe_map {f : α → β} (hf : Continuous f) (hf' : IsOpenMap f) (s : Com
   rfl
 #align topological_space.compact_opens.coe_map TopologicalSpace.CompactOpens.coe_map
 
+#print TopologicalSpace.CompactOpens.map_id /-
 @[simp]
 theorem map_id (K : CompactOpens α) : K.map id continuous_id IsOpenMap.id = K :=
   CompactOpens.ext <| Set.image_id _
 #align topological_space.compact_opens.map_id TopologicalSpace.CompactOpens.map_id
+-/
 
+/- warning: topological_space.compact_opens.map_comp -> TopologicalSpace.CompactOpens.map_comp is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] [_inst_3 : TopologicalSpace.{u3} γ] (f : β -> γ) (g : α -> β) (hf : Continuous.{u2, u3} β γ _inst_2 _inst_3 f) (hg : Continuous.{u1, u2} α β _inst_1 _inst_2 g) (hf' : IsOpenMap.{u2, u3} β γ _inst_2 _inst_3 f) (hg' : IsOpenMap.{u1, u2} α β _inst_1 _inst_2 g) (K : TopologicalSpace.CompactOpens.{u1} α _inst_1), Eq.{succ u3} (TopologicalSpace.CompactOpens.{u3} γ _inst_3) (TopologicalSpace.CompactOpens.map.{u1, u3} α γ _inst_1 _inst_3 (Function.comp.{succ u1, succ u2, succ u3} α β γ f g) (Continuous.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 f g hf hg) (IsOpenMap.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 f g hf' hg') K) (TopologicalSpace.CompactOpens.map.{u2, u3} β γ _inst_2 _inst_3 f hf hf' (TopologicalSpace.CompactOpens.map.{u1, u2} α β _inst_1 _inst_2 g hg hg' K))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u3} β] [_inst_3 : TopologicalSpace.{u2} γ] (f : β -> γ) (g : α -> β) (hf : Continuous.{u3, u2} β γ _inst_2 _inst_3 f) (hg : Continuous.{u1, u3} α β _inst_1 _inst_2 g) (hf' : IsOpenMap.{u3, u2} β γ _inst_2 _inst_3 f) (hg' : IsOpenMap.{u1, u3} α β _inst_1 _inst_2 g) (K : TopologicalSpace.CompactOpens.{u1} α _inst_1), Eq.{succ u2} (TopologicalSpace.CompactOpens.{u2} γ _inst_3) (TopologicalSpace.CompactOpens.map.{u1, u2} α γ _inst_1 _inst_3 (Function.comp.{succ u1, succ u3, succ u2} α β γ f g) (Continuous.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 f g hf hg) (IsOpenMap.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 f g hf' hg') K) (TopologicalSpace.CompactOpens.map.{u3, u2} β γ _inst_2 _inst_3 f hf hf' (TopologicalSpace.CompactOpens.map.{u1, u3} α β _inst_1 _inst_2 g hg hg' K))
+Case conversion may be inaccurate. Consider using '#align topological_space.compact_opens.map_comp TopologicalSpace.CompactOpens.map_compₓ'. -/
 theorem map_comp (f : β → γ) (g : α → β) (hf : Continuous f) (hg : Continuous g) (hf' : IsOpenMap f)
     (hg' : IsOpenMap g) (K : CompactOpens α) :
     K.map (f ∘ g) (hf.comp hg) (hf'.comp hg') = (K.map g hg hg').map f hf hf' :=

bump to nightly-2023-05-13-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/403190b5419b3f03f1a2893ad9352ca7f7d8bff6

d312d6d5

Diff

@@ -4,7 +4,7 @@ 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.compacts
-! leanprover-community/mathlib commit 1ead22342e1a078bd44744ace999f85756555d35
+! leanprover-community/mathlib commit 8c1b484d6a214e059531e22f1be9898ed6c1fd47
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -32,7 +32,7 @@ For a topological space `α`,
 
 open Set
 
-variable {α β : Type _} [TopologicalSpace α] [TopologicalSpace β]
+variable {α β γ : Type _} [TopologicalSpace α] [TopologicalSpace β] [TopologicalSpace γ]
 
 namespace TopologicalSpace
 
@@ -131,9 +131,9 @@ theorem coe_sup (s t : Compacts α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
 
 /- warning: topological_space.compacts.coe_inf -> TopologicalSpace.Compacts.coe_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T2Space.{u1} α _inst_1] (s : TopologicalSpace.Compacts.{u1} α _inst_1) (t : TopologicalSpace.Compacts.{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.Compacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.setLike.{u1} α _inst_1)))) (Inf.inf.{u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.hasInf.{u1} α _inst_1 _inst_3) 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.Compacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.setLike.{u1} α _inst_1)))) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_4 : T2Space.{u1} α _inst_1] (s : TopologicalSpace.Compacts.{u1} α _inst_1) (t : TopologicalSpace.Compacts.{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.Compacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.setLike.{u1} α _inst_1)))) (Inf.inf.{u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.hasInf.{u1} α _inst_1 _inst_4) 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.Compacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.setLike.{u1} α _inst_1)))) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T2Space.{u1} α _inst_1] (s : TopologicalSpace.Compacts.{u1} α _inst_1) (t : TopologicalSpace.Compacts.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} α _inst_1) (Inf.inf.{u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.instInfCompacts.{u1} α _inst_1 _inst_3) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_4 : T2Space.{u1} α _inst_1] (s : TopologicalSpace.Compacts.{u1} α _inst_1) (t : TopologicalSpace.Compacts.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} α _inst_1) (Inf.inf.{u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.instInfCompacts.{u1} α _inst_1 _inst_4) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align topological_space.compacts.coe_inf TopologicalSpace.Compacts.coe_infₓ'. -/
 @[simp]
 theorem coe_inf [T2Space α] (s t : Compacts α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
@@ -182,14 +182,24 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : TopologicalSpace.{u1} β] {f : α -> β} (hf : Continuous.{u2, u1} α β _inst_1 _inst_2 f) (s : TopologicalSpace.Compacts.{u2} α _inst_1), Eq.{succ u1} (Set.{u1} β) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} β _inst_2) β (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} β _inst_2) (TopologicalSpace.Compacts.map.{u2, u1} α β _inst_1 _inst_2 f hf s)) (Set.image.{u2, u1} α β f (SetLike.coe.{u2, u2} (TopologicalSpace.Compacts.{u2} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u2} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align topological_space.compacts.coe_map TopologicalSpace.Compacts.coe_mapₓ'. -/
-@[simp]
+@[simp, norm_cast]
 theorem coe_map {f : α → β} (hf : Continuous f) (s : Compacts α) : (s.map f hf : Set β) = f '' s :=
   rfl
 #align topological_space.compacts.coe_map TopologicalSpace.Compacts.coe_map
 
+@[simp]
+theorem map_id (K : Compacts α) : K.map id continuous_id = K :=
+  Compacts.ext <| Set.image_id _
+#align topological_space.compacts.map_id TopologicalSpace.Compacts.map_id
+
+theorem map_comp (f : β → γ) (g : α → β) (hf : Continuous f) (hg : Continuous g) (K : Compacts α) :
+    K.map (f ∘ g) (hf.comp hg) = (K.map g hg).map f hf :=
+  Compacts.ext <| Set.image_comp _ _ _
+#align topological_space.compacts.map_comp TopologicalSpace.Compacts.map_comp
+
 #print TopologicalSpace.Compacts.equiv /-
 /-- A homeomorphism induces an equivalence on compact sets, by taking the image. -/
-@[simp]
+@[simps]
 protected def equiv (f : α ≃ₜ β) : Compacts α ≃ Compacts β
     where
   toFun := Compacts.map f f.Continuous
@@ -203,16 +213,27 @@ protected def equiv (f : α ≃ₜ β) : Compacts α ≃ Compacts β
 #align topological_space.compacts.equiv TopologicalSpace.Compacts.equiv
 -/
 
-/- warning: topological_space.compacts.equiv_to_fun_val -> TopologicalSpace.Compacts.equiv_to_fun_val is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] (f : Homeomorph.{u1, u2} α β _inst_1 _inst_2) (K : TopologicalSpace.Compacts.{u1} α _inst_1), Eq.{succ u2} (Set.{u2} β) (TopologicalSpace.Compacts.carrier.{u2} β _inst_2 (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.{u2} β _inst_2)) (fun (_x : Equiv.{succ u1, succ u2} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.{u2} β _inst_2)) => (TopologicalSpace.Compacts.{u1} α _inst_1) -> (TopologicalSpace.Compacts.{u2} β _inst_2)) (Equiv.hasCoeToFun.{succ u1, succ u2} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.{u2} β _inst_2)) (TopologicalSpace.Compacts.equiv.{u1, u2} α β _inst_1 _inst_2 f) K)) (Set.preimage.{u2, u1} β α (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Homeomorph.{u2, u1} β α _inst_2 _inst_1) (fun (_x : Homeomorph.{u2, u1} β α _inst_2 _inst_1) => β -> α) (Homeomorph.hasCoeToFun.{u2, u1} β α _inst_2 _inst_1) (Homeomorph.symm.{u1, u2} α β _inst_1 _inst_2 f)) (TopologicalSpace.Compacts.carrier.{u1} α _inst_1 K))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align topological_space.compacts.equiv_to_fun_val TopologicalSpace.Compacts.equiv_to_fun_valₓ'. -/
+@[simp]
+theorem equiv_refl : Compacts.equiv (Homeomorph.refl α) = Equiv.refl _ :=
+  Equiv.ext map_id
+#align topological_space.compacts.equiv_refl TopologicalSpace.Compacts.equiv_refl
+
+@[simp]
+theorem equiv_trans (f : α ≃ₜ β) (g : β ≃ₜ γ) :
+    Compacts.equiv (f.trans g) = (Compacts.equiv f).trans (Compacts.equiv g) :=
+  Equiv.ext <| map_comp _ _ _ _
+#align topological_space.compacts.equiv_trans TopologicalSpace.Compacts.equiv_trans
+
+@[simp]
+theorem equiv_symm (f : α ≃ₜ β) : Compacts.equiv f.symm = (Compacts.equiv f).symm :=
+  rfl
+#align topological_space.compacts.equiv_symm TopologicalSpace.Compacts.equiv_symm
+
 /-- The image of a compact set under a homeomorphism can also be expressed as a preimage. -/
-theorem equiv_to_fun_val (f : α ≃ₜ β) (K : Compacts α) : (Compacts.equiv f K).1 = f.symm ⁻¹' K.1 :=
-  congr_fun (image_eq_preimage_of_inverse f.left_inv f.right_inv) K.1
-#align topological_space.compacts.equiv_to_fun_val TopologicalSpace.Compacts.equiv_to_fun_val
+theorem coe_equiv_apply_eq_preimage (f : α ≃ₜ β) (K : Compacts α) :
+    (Compacts.equiv f K : Set β) = f.symm ⁻¹' (K : Set α) :=
+  f.toEquiv.image_eq_preimage K
+#align topological_space.compacts.coe_equiv_apply_eq_preimage TopologicalSpace.Compacts.coe_equiv_apply_eq_preimage
 
 /- warning: topological_space.compacts.prod -> TopologicalSpace.Compacts.prod is a dubious translation:
 lean 3 declaration is
@@ -476,6 +497,31 @@ theorem coe_top [CompactSpace α] [Nonempty α] : (↑(⊤ : PositiveCompacts α
 #align topological_space.positive_compacts.coe_top TopologicalSpace.PositiveCompacts.coe_top
 -/
 
+/-- The image of a positive compact set under a continuous open map. -/
+protected def map (f : α → β) (hf : Continuous f) (hf' : IsOpenMap f) (K : PositiveCompacts α) :
+    PositiveCompacts β :=
+  { K.map f hf with
+    interior_nonempty' :=
+      (K.interior_nonempty'.image _).mono (hf'.image_interior_subset K.toCompacts) }
+#align topological_space.positive_compacts.map TopologicalSpace.PositiveCompacts.map
+
+@[simp, norm_cast]
+theorem coe_map {f : α → β} (hf : Continuous f) (hf' : IsOpenMap f) (s : PositiveCompacts α) :
+    (s.map f hf hf' : Set β) = f '' s :=
+  rfl
+#align topological_space.positive_compacts.coe_map TopologicalSpace.PositiveCompacts.coe_map
+
+@[simp]
+theorem map_id (K : PositiveCompacts α) : K.map id continuous_id IsOpenMap.id = K :=
+  PositiveCompacts.ext <| Set.image_id _
+#align topological_space.positive_compacts.map_id TopologicalSpace.PositiveCompacts.map_id
+
+theorem map_comp (f : β → γ) (g : α → β) (hf : Continuous f) (hg : Continuous g) (hf' : IsOpenMap f)
+    (hg' : IsOpenMap g) (K : PositiveCompacts α) :
+    K.map (f ∘ g) (hf.comp hg) (hf'.comp hg') = (K.map g hg hg').map f hf hf' :=
+  PositiveCompacts.ext <| Set.image_comp _ _ _
+#align topological_space.positive_compacts.map_comp TopologicalSpace.PositiveCompacts.map_comp
+
 #print exists_positiveCompacts_subset /-
 theorem exists_positiveCompacts_subset [LocallyCompactSpace α] {U : Set α} (ho : IsOpen U)
     (hn : U.Nonempty) : ∃ K : PositiveCompacts α, ↑K ⊆ U :=
@@ -642,9 +688,9 @@ theorem coe_sup (s t : CompactOpens α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
 
 /- warning: topological_space.compact_opens.coe_inf -> TopologicalSpace.CompactOpens.coe_inf is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_4 : T2Space.{u1} α _inst_1] (s : TopologicalSpace.CompactOpens.{u1} α _inst_1) (t : TopologicalSpace.CompactOpens.{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.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) (Inf.inf.{u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (TopologicalSpace.CompactOpens.hasInf.{u1} α _inst_1 (T2Space.to_quasiSeparatedSpace.{u1} α _inst_1 _inst_4)) 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.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) t))
 but is expected to have type
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+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_4 : T2Space.{u1} α _inst_1] (s : TopologicalSpace.CompactOpens.{u1} α _inst_1) (t : TopologicalSpace.CompactOpens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) (Inf.inf.{u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (TopologicalSpace.CompactOpens.instInfCompactOpens.{u1} α _inst_1 (T2Space.to_quasiSeparatedSpace.{u1} α _inst_1 _inst_4)) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align topological_space.compact_opens.coe_inf TopologicalSpace.CompactOpens.coe_infₓ'. -/
 @[simp]
 theorem coe_inf [T2Space α] (s t : CompactOpens α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
@@ -667,9 +713,9 @@ theorem coe_bot : (↑(⊥ : CompactOpens α) : Set α) = ∅ :=
 
 /- warning: topological_space.compact_opens.coe_sdiff -> TopologicalSpace.CompactOpens.coe_sdiff is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T2Space.{u1} α _inst_1] (s : TopologicalSpace.CompactOpens.{u1} α _inst_1) (t : TopologicalSpace.CompactOpens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) (SDiff.sdiff.{u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (TopologicalSpace.CompactOpens.instSDiffCompactOpens.{u1} α _inst_1 _inst_3) s t)) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_4 : T2Space.{u1} α _inst_1] (s : TopologicalSpace.CompactOpens.{u1} α _inst_1) (t : TopologicalSpace.CompactOpens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) (SDiff.sdiff.{u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (TopologicalSpace.CompactOpens.instSDiffCompactOpens.{u1} α _inst_1 _inst_4) s t)) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align topological_space.compact_opens.coe_sdiff TopologicalSpace.CompactOpens.coe_sdiffₓ'. -/
 @[simp]
 theorem coe_sdiff [T2Space α] (s t : CompactOpens α) : (↑(s \ t) : Set α) = s \ t :=
@@ -678,9 +724,9 @@ theorem coe_sdiff [T2Space α] (s t : CompactOpens α) : (↑(s \ t) : Set α) =
 
 /- warning: topological_space.compact_opens.coe_compl -> TopologicalSpace.CompactOpens.coe_compl is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T2Space.{u1} α _inst_1] [_inst_4 : CompactSpace.{u1} α _inst_1] (s : TopologicalSpace.CompactOpens.{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.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) (HasCompl.compl.{u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (TopologicalSpace.CompactOpens.hasCompl.{u1} α _inst_1 _inst_3 _inst_4) 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.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) s))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_4 : T2Space.{u1} α _inst_1] [_inst_5 : CompactSpace.{u1} α _inst_1] (s : TopologicalSpace.CompactOpens.{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.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) (HasCompl.compl.{u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (TopologicalSpace.CompactOpens.hasCompl.{u1} α _inst_1 _inst_4 _inst_5) 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.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T2Space.{u1} α _inst_1] [_inst_4 : CompactSpace.{u1} α _inst_1] (s : TopologicalSpace.CompactOpens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) (HasCompl.compl.{u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (TopologicalSpace.CompactOpens.instHasComplCompactOpens.{u1} α _inst_1 _inst_3 _inst_4) s)) (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_4 : T2Space.{u1} α _inst_1] [_inst_5 : CompactSpace.{u1} α _inst_1] (s : TopologicalSpace.CompactOpens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) (HasCompl.compl.{u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (TopologicalSpace.CompactOpens.instHasComplCompactOpens.{u1} α _inst_1 _inst_4 _inst_5) s)) (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align topological_space.compact_opens.coe_compl TopologicalSpace.CompactOpens.coe_complₓ'. -/
 @[simp]
 theorem coe_compl [T2Space α] [CompactSpace α] (s : CompactOpens α) : (↑(sᶜ) : Set α) = sᶜ :=
@@ -704,12 +750,23 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : TopologicalSpace.{u1} β] {f : α -> β} (hf : Continuous.{u2, u1} α β _inst_1 _inst_2 f) (hf' : IsOpenMap.{u2, u1} α β _inst_1 _inst_2 f) (s : TopologicalSpace.CompactOpens.{u2} α _inst_1), Eq.{succ u1} (Set.{u1} β) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} β _inst_2) β (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} β _inst_2) (TopologicalSpace.CompactOpens.map.{u2, u1} α β _inst_1 _inst_2 f hf hf' s)) (Set.image.{u2, u1} α β f (SetLike.coe.{u2, u2} (TopologicalSpace.CompactOpens.{u2} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u2} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align topological_space.compact_opens.coe_map TopologicalSpace.CompactOpens.coe_mapₓ'. -/
-@[simp]
+@[simp, norm_cast]
 theorem coe_map {f : α → β} (hf : Continuous f) (hf' : IsOpenMap f) (s : CompactOpens α) :
     (s.map f hf hf' : Set β) = f '' s :=
   rfl
 #align topological_space.compact_opens.coe_map TopologicalSpace.CompactOpens.coe_map
 
+@[simp]
+theorem map_id (K : CompactOpens α) : K.map id continuous_id IsOpenMap.id = K :=
+  CompactOpens.ext <| Set.image_id _
+#align topological_space.compact_opens.map_id TopologicalSpace.CompactOpens.map_id
+
+theorem map_comp (f : β → γ) (g : α → β) (hf : Continuous f) (hg : Continuous g) (hf' : IsOpenMap f)
+    (hg' : IsOpenMap g) (K : CompactOpens α) :
+    K.map (f ∘ g) (hf.comp hg) (hf'.comp hg') = (K.map g hg hg').map f hf hf' :=
+  CompactOpens.ext <| Set.image_comp _ _ _
+#align topological_space.compact_opens.map_comp TopologicalSpace.CompactOpens.map_comp
+
 /- warning: topological_space.compact_opens.prod -> TopologicalSpace.CompactOpens.prod is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β], (TopologicalSpace.CompactOpens.{u1} α _inst_1) -> (TopologicalSpace.CompactOpens.{u2} β _inst_2) -> (TopologicalSpace.CompactOpens.{max u1 u2} (Prod.{u1, u2} α β) (Prod.topologicalSpace.{u1, u2} α β _inst_1 _inst_2))

bump to nightly-2023-03-16-13

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

d225db81

Diff

@@ -207,7 +207,7 @@ protected def equiv (f : α ≃ₜ β) : Compacts α ≃ Compacts β
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] (f : Homeomorph.{u1, u2} α β _inst_1 _inst_2) (K : TopologicalSpace.Compacts.{u1} α _inst_1), Eq.{succ u2} (Set.{u2} β) (TopologicalSpace.Compacts.carrier.{u2} β _inst_2 (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.{u2} β _inst_2)) (fun (_x : Equiv.{succ u1, succ u2} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.{u2} β _inst_2)) => (TopologicalSpace.Compacts.{u1} α _inst_1) -> (TopologicalSpace.Compacts.{u2} β _inst_2)) (Equiv.hasCoeToFun.{succ u1, succ u2} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.{u2} β _inst_2)) (TopologicalSpace.Compacts.equiv.{u1, u2} α β _inst_1 _inst_2 f) K)) (Set.preimage.{u2, u1} β α (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Homeomorph.{u2, u1} β α _inst_2 _inst_1) (fun (_x : Homeomorph.{u2, u1} β α _inst_2 _inst_1) => β -> α) (Homeomorph.hasCoeToFun.{u2, u1} β α _inst_2 _inst_1) (Homeomorph.symm.{u1, u2} α β _inst_1 _inst_2 f)) (TopologicalSpace.Compacts.carrier.{u1} α _inst_1 K))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : TopologicalSpace.{u1} β] (f : Homeomorph.{u2, u1} α β _inst_1 _inst_2) (K : TopologicalSpace.Compacts.{u2} α _inst_1), Eq.{succ u1} (Set.{u1} β) (TopologicalSpace.Compacts.carrier.{u1} β _inst_2 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} (TopologicalSpace.Compacts.{u2} α _inst_1) (TopologicalSpace.Compacts.{u1} β _inst_2)) (TopologicalSpace.Compacts.{u2} α _inst_1) (fun (_x : TopologicalSpace.Compacts.{u2} α _inst_1) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : TopologicalSpace.Compacts.{u2} α _inst_1) => TopologicalSpace.Compacts.{u1} β _inst_2) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} (TopologicalSpace.Compacts.{u2} α _inst_1) (TopologicalSpace.Compacts.{u1} β _inst_2)) (TopologicalSpace.Compacts.equiv.{u2, u1} α β _inst_1 _inst_2 f) K)) (Set.preimage.{u1, u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Homeomorph.{u1, u2} β α _inst_2 _inst_1) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u1, succ u2} (Homeomorph.{u1, u2} β α _inst_2 _inst_1) β α (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u1, succ u2} (Homeomorph.{u1, u2} β α _inst_2 _inst_1) β α (Homeomorph.instEquivLikeHomeomorph.{u1, u2} β α _inst_2 _inst_1))) (Homeomorph.symm.{u2, u1} α β _inst_1 _inst_2 f)) (TopologicalSpace.Compacts.carrier.{u2} α _inst_1 K))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : TopologicalSpace.{u1} β] (f : Homeomorph.{u2, u1} α β _inst_1 _inst_2) (K : TopologicalSpace.Compacts.{u2} α _inst_1), Eq.{succ u1} (Set.{u1} β) (TopologicalSpace.Compacts.carrier.{u1} β _inst_2 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} (TopologicalSpace.Compacts.{u2} α _inst_1) (TopologicalSpace.Compacts.{u1} β _inst_2)) (TopologicalSpace.Compacts.{u2} α _inst_1) (fun (_x : TopologicalSpace.Compacts.{u2} α _inst_1) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : TopologicalSpace.Compacts.{u2} α _inst_1) => TopologicalSpace.Compacts.{u1} β _inst_2) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} (TopologicalSpace.Compacts.{u2} α _inst_1) (TopologicalSpace.Compacts.{u1} β _inst_2)) (TopologicalSpace.Compacts.equiv.{u2, u1} α β _inst_1 _inst_2 f) K)) (Set.preimage.{u1, u2} β α (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Homeomorph.{u1, u2} β α _inst_2 _inst_1) β (fun (_x : β) => α) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u1, succ u2} (Homeomorph.{u1, u2} β α _inst_2 _inst_1) β α (EquivLike.toEmbeddingLike.{max (succ u1) (succ u2), succ u1, succ u2} (Homeomorph.{u1, u2} β α _inst_2 _inst_1) β α (Homeomorph.instEquivLikeHomeomorph.{u1, u2} β α _inst_2 _inst_1))) (Homeomorph.symm.{u2, u1} α β _inst_1 _inst_2 f)) (TopologicalSpace.Compacts.carrier.{u2} α _inst_1 K))
 Case conversion may be inaccurate. Consider using '#align topological_space.compacts.equiv_to_fun_val TopologicalSpace.Compacts.equiv_to_fun_valₓ'. -/
 /-- The image of a compact set under a homeomorphism can also be expressed as a preimage. -/
 theorem equiv_to_fun_val (f : α ≃ₜ β) (K : Compacts α) : (Compacts.equiv f K).1 = f.symm ⁻¹' K.1 :=

bump to nightly-2023-03-11-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

a8ee822f

Diff

@@ -207,7 +207,7 @@ protected def equiv (f : α ≃ₜ β) : Compacts α ≃ Compacts β
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] (f : Homeomorph.{u1, u2} α β _inst_1 _inst_2) (K : TopologicalSpace.Compacts.{u1} α _inst_1), Eq.{succ u2} (Set.{u2} β) (TopologicalSpace.Compacts.carrier.{u2} β _inst_2 (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.{u2} β _inst_2)) (fun (_x : Equiv.{succ u1, succ u2} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.{u2} β _inst_2)) => (TopologicalSpace.Compacts.{u1} α _inst_1) -> (TopologicalSpace.Compacts.{u2} β _inst_2)) (Equiv.hasCoeToFun.{succ u1, succ u2} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.{u2} β _inst_2)) (TopologicalSpace.Compacts.equiv.{u1, u2} α β _inst_1 _inst_2 f) K)) (Set.preimage.{u2, u1} β α (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Homeomorph.{u2, u1} β α _inst_2 _inst_1) (fun (_x : Homeomorph.{u2, u1} β α _inst_2 _inst_1) => β -> α) (Homeomorph.hasCoeToFun.{u2, u1} β α _inst_2 _inst_1) (Homeomorph.symm.{u1, u2} α β _inst_1 _inst_2 f)) (TopologicalSpace.Compacts.carrier.{u1} α _inst_1 K))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : TopologicalSpace.{u1} β] (f : Homeomorph.{u2, u1} α β _inst_1 _inst_2) (K : TopologicalSpace.Compacts.{u2} α _inst_1), Eq.{succ u1} (Set.{u1} β) (TopologicalSpace.Compacts.carrier.{u1} β _inst_2 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} (TopologicalSpace.Compacts.{u2} α _inst_1) (TopologicalSpace.Compacts.{u1} β _inst_2)) (TopologicalSpace.Compacts.{u2} α _inst_1) (fun (_x : TopologicalSpace.Compacts.{u2} α _inst_1) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : TopologicalSpace.Compacts.{u2} α _inst_1) => TopologicalSpace.Compacts.{u1} β _inst_2) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} (TopologicalSpace.Compacts.{u2} α _inst_1) (TopologicalSpace.Compacts.{u1} β _inst_2)) (TopologicalSpace.Compacts.equiv.{u2, u1} α β _inst_1 _inst_2 f) K)) (Set.preimage.{u1, u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Homeomorph.{u1, u2} β α _inst_2 _inst_1) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u1, succ u2} (Homeomorph.{u1, u2} β α _inst_2 _inst_1) β α (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u1, succ u2} (Homeomorph.{u1, u2} β α _inst_2 _inst_1) β α (Homeomorph.instEquivLikeHomeomorph.{u1, u2} β α _inst_2 _inst_1))) (Homeomorph.symm.{u2, u1} α β _inst_1 _inst_2 f)) (TopologicalSpace.Compacts.carrier.{u2} α _inst_1 K))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : TopologicalSpace.{u1} β] (f : Homeomorph.{u2, u1} α β _inst_1 _inst_2) (K : TopologicalSpace.Compacts.{u2} α _inst_1), Eq.{succ u1} (Set.{u1} β) (TopologicalSpace.Compacts.carrier.{u1} β _inst_2 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} (TopologicalSpace.Compacts.{u2} α _inst_1) (TopologicalSpace.Compacts.{u1} β _inst_2)) (TopologicalSpace.Compacts.{u2} α _inst_1) (fun (_x : TopologicalSpace.Compacts.{u2} α _inst_1) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : TopologicalSpace.Compacts.{u2} α _inst_1) => TopologicalSpace.Compacts.{u1} β _inst_2) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} (TopologicalSpace.Compacts.{u2} α _inst_1) (TopologicalSpace.Compacts.{u1} β _inst_2)) (TopologicalSpace.Compacts.equiv.{u2, u1} α β _inst_1 _inst_2 f) K)) (Set.preimage.{u1, u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Homeomorph.{u1, u2} β α _inst_2 _inst_1) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u1, succ u2} (Homeomorph.{u1, u2} β α _inst_2 _inst_1) β α (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u1, succ u2} (Homeomorph.{u1, u2} β α _inst_2 _inst_1) β α (Homeomorph.instEquivLikeHomeomorph.{u1, u2} β α _inst_2 _inst_1))) (Homeomorph.symm.{u2, u1} α β _inst_1 _inst_2 f)) (TopologicalSpace.Compacts.carrier.{u2} α _inst_1 K))
 Case conversion may be inaccurate. Consider using '#align topological_space.compacts.equiv_to_fun_val TopologicalSpace.Compacts.equiv_to_fun_valₓ'. -/
 /-- The image of a compact set under a homeomorphism can also be expressed as a preimage. -/
 theorem equiv_to_fun_val (f : α ≃ₜ β) (K : Compacts α) : (Compacts.equiv f K).1 = f.symm ⁻¹' K.1 :=

bump to nightly-2023-02-28-04

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

2097f8af

Diff

@@ -90,10 +90,10 @@ theorem carrier_eq_coe (s : Compacts α) : s.carrier = s :=
 #align topological_space.compacts.carrier_eq_coe TopologicalSpace.Compacts.carrier_eq_coe
 -/
 
-instance : HasSup (Compacts α) :=
+instance : Sup (Compacts α) :=
   ⟨fun s t => ⟨s ∪ t, s.IsCompact.union t.IsCompact⟩⟩
 
-instance [T2Space α] : HasInf (Compacts α) :=
+instance [T2Space α] : Inf (Compacts α) :=
   ⟨fun s t => ⟨s ∩ t, s.IsCompact.inter t.IsCompact⟩⟩
 
 instance [CompactSpace α] : Top (Compacts α) :=
@@ -120,9 +120,9 @@ instance : Inhabited (Compacts α) :=
 
 /- warning: topological_space.compacts.coe_sup -> TopologicalSpace.Compacts.coe_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Compacts.{u1} α _inst_1) (t : TopologicalSpace.Compacts.{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.Compacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.setLike.{u1} α _inst_1)))) (HasSup.sup.{u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.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.Compacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.setLike.{u1} α _inst_1)))) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Compacts.{u1} α _inst_1) (t : TopologicalSpace.Compacts.{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.Compacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.setLike.{u1} α _inst_1)))) (Sup.sup.{u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.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.Compacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.setLike.{u1} α _inst_1)))) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Compacts.{u1} α _inst_1) (t : TopologicalSpace.Compacts.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} α _inst_1) (HasSup.sup.{u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.instHasSupCompacts.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.Compacts.{u1} α _inst_1) (t : TopologicalSpace.Compacts.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} α _inst_1) (Sup.sup.{u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.instSupCompacts.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align topological_space.compacts.coe_sup TopologicalSpace.Compacts.coe_supₓ'. -/
 @[simp]
 theorem coe_sup (s t : Compacts α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
@@ -131,9 +131,9 @@ theorem coe_sup (s t : Compacts α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
 
 /- warning: topological_space.compacts.coe_inf -> TopologicalSpace.Compacts.coe_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T2Space.{u1} α _inst_1] (s : TopologicalSpace.Compacts.{u1} α _inst_1) (t : TopologicalSpace.Compacts.{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.Compacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.setLike.{u1} α _inst_1)))) (HasInf.inf.{u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.hasInf.{u1} α _inst_1 _inst_3) 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.Compacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.setLike.{u1} α _inst_1)))) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T2Space.{u1} α _inst_1] (s : TopologicalSpace.Compacts.{u1} α _inst_1) (t : TopologicalSpace.Compacts.{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.Compacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.setLike.{u1} α _inst_1)))) (Inf.inf.{u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.hasInf.{u1} α _inst_1 _inst_3) 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.Compacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.setLike.{u1} α _inst_1)))) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T2Space.{u1} α _inst_1] (s : TopologicalSpace.Compacts.{u1} α _inst_1) (t : TopologicalSpace.Compacts.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} α _inst_1) (HasInf.inf.{u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.instHasInfCompacts.{u1} α _inst_1 _inst_3) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T2Space.{u1} α _inst_1] (s : TopologicalSpace.Compacts.{u1} α _inst_1) (t : TopologicalSpace.Compacts.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} α _inst_1) (Inf.inf.{u1} (TopologicalSpace.Compacts.{u1} α _inst_1) (TopologicalSpace.Compacts.instInfCompacts.{u1} α _inst_1 _inst_3) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.Compacts.{u1} α _inst_1) α (TopologicalSpace.Compacts.instSetLikeCompacts.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align topological_space.compacts.coe_inf TopologicalSpace.Compacts.coe_infₓ'. -/
 @[simp]
 theorem coe_inf [T2Space α] (s t : Compacts α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
@@ -302,7 +302,7 @@ theorem carrier_eq_coe (s : NonemptyCompacts α) : s.carrier = s :=
 #align topological_space.nonempty_compacts.carrier_eq_coe TopologicalSpace.NonemptyCompacts.carrier_eq_coe
 -/
 
-instance : HasSup (NonemptyCompacts α) :=
+instance : Sup (NonemptyCompacts α) :=
   ⟨fun s t => ⟨s.toCompacts ⊔ t.toCompacts, s.Nonempty.mono <| subset_union_left _ _⟩⟩
 
 instance [CompactSpace α] [Nonempty α] : Top (NonemptyCompacts α) :=
@@ -316,9 +316,9 @@ instance [CompactSpace α] [Nonempty α] : OrderTop (NonemptyCompacts α) :=
 
 /- warning: topological_space.nonempty_compacts.coe_sup -> TopologicalSpace.NonemptyCompacts.coe_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (t : TopologicalSpace.NonemptyCompacts.{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.NonemptyCompacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) α (TopologicalSpace.NonemptyCompacts.setLike.{u1} α _inst_1)))) (HasSup.sup.{u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (TopologicalSpace.NonemptyCompacts.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.NonemptyCompacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) α (TopologicalSpace.NonemptyCompacts.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) α (TopologicalSpace.NonemptyCompacts.setLike.{u1} α _inst_1)))) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (t : TopologicalSpace.NonemptyCompacts.{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.NonemptyCompacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) α (TopologicalSpace.NonemptyCompacts.setLike.{u1} α _inst_1)))) (Sup.sup.{u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (TopologicalSpace.NonemptyCompacts.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.NonemptyCompacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) α (TopologicalSpace.NonemptyCompacts.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) α (TopologicalSpace.NonemptyCompacts.setLike.{u1} α _inst_1)))) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (t : TopologicalSpace.NonemptyCompacts.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) α (TopologicalSpace.NonemptyCompacts.instSetLikeNonemptyCompacts.{u1} α _inst_1) (HasSup.sup.{u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (TopologicalSpace.NonemptyCompacts.instHasSupNonemptyCompacts.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) α (TopologicalSpace.NonemptyCompacts.instSetLikeNonemptyCompacts.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) α (TopologicalSpace.NonemptyCompacts.instSetLikeNonemptyCompacts.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (t : TopologicalSpace.NonemptyCompacts.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) α (TopologicalSpace.NonemptyCompacts.instSetLikeNonemptyCompacts.{u1} α _inst_1) (Sup.sup.{u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) (TopologicalSpace.NonemptyCompacts.instSupNonemptyCompacts.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) α (TopologicalSpace.NonemptyCompacts.instSetLikeNonemptyCompacts.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.NonemptyCompacts.{u1} α _inst_1) α (TopologicalSpace.NonemptyCompacts.instSetLikeNonemptyCompacts.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align topological_space.nonempty_compacts.coe_sup TopologicalSpace.NonemptyCompacts.coe_supₓ'. -/
 @[simp]
 theorem coe_sup (s t : NonemptyCompacts α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
@@ -444,7 +444,7 @@ theorem carrier_eq_coe (s : PositiveCompacts α) : s.carrier = s :=
 #align topological_space.positive_compacts.carrier_eq_coe TopologicalSpace.PositiveCompacts.carrier_eq_coe
 -/
 
-instance : HasSup (PositiveCompacts α) :=
+instance : Sup (PositiveCompacts α) :=
   ⟨fun s t =>
     ⟨s.toCompacts ⊔ t.toCompacts,
       s.interior_nonempty.mono <| interior_mono <| subset_union_left _ _⟩⟩
@@ -460,9 +460,9 @@ instance [CompactSpace α] [Nonempty α] : OrderTop (PositiveCompacts α) :=
 
 /- warning: topological_space.positive_compacts.coe_sup -> TopologicalSpace.PositiveCompacts.coe_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (t : TopologicalSpace.PositiveCompacts.{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.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) α (TopologicalSpace.PositiveCompacts.setLike.{u1} α _inst_1)))) (HasSup.sup.{u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (TopologicalSpace.PositiveCompacts.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.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) α (TopologicalSpace.PositiveCompacts.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) α (TopologicalSpace.PositiveCompacts.setLike.{u1} α _inst_1)))) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (t : TopologicalSpace.PositiveCompacts.{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.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) α (TopologicalSpace.PositiveCompacts.setLike.{u1} α _inst_1)))) (Sup.sup.{u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (TopologicalSpace.PositiveCompacts.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.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) α (TopologicalSpace.PositiveCompacts.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) α (TopologicalSpace.PositiveCompacts.setLike.{u1} α _inst_1)))) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (t : TopologicalSpace.PositiveCompacts.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) α (TopologicalSpace.PositiveCompacts.instSetLikePositiveCompacts.{u1} α _inst_1) (HasSup.sup.{u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (TopologicalSpace.PositiveCompacts.instHasSupPositiveCompacts.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) α (TopologicalSpace.PositiveCompacts.instSetLikePositiveCompacts.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) α (TopologicalSpace.PositiveCompacts.instSetLikePositiveCompacts.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (t : TopologicalSpace.PositiveCompacts.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) α (TopologicalSpace.PositiveCompacts.instSetLikePositiveCompacts.{u1} α _inst_1) (Sup.sup.{u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) (TopologicalSpace.PositiveCompacts.instSupPositiveCompacts.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) α (TopologicalSpace.PositiveCompacts.instSetLikePositiveCompacts.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.PositiveCompacts.{u1} α _inst_1) α (TopologicalSpace.PositiveCompacts.instSetLikePositiveCompacts.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align topological_space.positive_compacts.coe_sup TopologicalSpace.PositiveCompacts.coe_supₓ'. -/
 @[simp]
 theorem coe_sup (s t : PositiveCompacts α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
@@ -588,10 +588,10 @@ theorem coe_mk (s : Compacts α) (h) : (mk s h : Set α) = s :=
 #align topological_space.compact_opens.coe_mk TopologicalSpace.CompactOpens.coe_mk
 -/
 
-instance : HasSup (CompactOpens α) :=
+instance : Sup (CompactOpens α) :=
   ⟨fun s t => ⟨s.toCompacts ⊔ t.toCompacts, s.IsOpen.union t.IsOpen⟩⟩
 
-instance [QuasiSeparatedSpace α] : HasInf (CompactOpens α) :=
+instance [QuasiSeparatedSpace α] : Inf (CompactOpens α) :=
   ⟨fun U V =>
     ⟨⟨(U : Set α) ∩ (V : Set α),
         QuasiSeparatedSpace.inter_isCompact U.1.1 V.1.1 U.2 U.1.2 V.2 V.1.2⟩,
@@ -631,9 +631,9 @@ instance [T2Space α] [CompactSpace α] : BooleanAlgebra (CompactOpens α) :=
 
 /- warning: topological_space.compact_opens.coe_sup -> TopologicalSpace.CompactOpens.coe_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.CompactOpens.{u1} α _inst_1) (t : TopologicalSpace.CompactOpens.{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.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) (HasSup.sup.{u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (TopologicalSpace.CompactOpens.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.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.CompactOpens.{u1} α _inst_1) (t : TopologicalSpace.CompactOpens.{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.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) (Sup.sup.{u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (TopologicalSpace.CompactOpens.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.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.CompactOpens.{u1} α _inst_1) (t : TopologicalSpace.CompactOpens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) (HasSup.sup.{u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (TopologicalSpace.CompactOpens.instHasSupCompactOpens.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] (s : TopologicalSpace.CompactOpens.{u1} α _inst_1) (t : TopologicalSpace.CompactOpens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) (Sup.sup.{u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (TopologicalSpace.CompactOpens.instSupCompactOpens.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align topological_space.compact_opens.coe_sup TopologicalSpace.CompactOpens.coe_supₓ'. -/
 @[simp]
 theorem coe_sup (s t : CompactOpens α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
@@ -642,9 +642,9 @@ theorem coe_sup (s t : CompactOpens α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
 
 /- warning: topological_space.compact_opens.coe_inf -> TopologicalSpace.CompactOpens.coe_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T2Space.{u1} α _inst_1] (s : TopologicalSpace.CompactOpens.{u1} α _inst_1) (t : TopologicalSpace.CompactOpens.{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.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) (HasInf.inf.{u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (TopologicalSpace.CompactOpens.hasInf.{u1} α _inst_1 (T2Space.to_quasiSeparatedSpace.{u1} α _inst_1 _inst_3)) 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.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T2Space.{u1} α _inst_1] (s : TopologicalSpace.CompactOpens.{u1} α _inst_1) (t : TopologicalSpace.CompactOpens.{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.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) (Inf.inf.{u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (TopologicalSpace.CompactOpens.hasInf.{u1} α _inst_1 (T2Space.to_quasiSeparatedSpace.{u1} α _inst_1 _inst_3)) 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.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.setLike.{u1} α _inst_1)))) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T2Space.{u1} α _inst_1] (s : TopologicalSpace.CompactOpens.{u1} α _inst_1) (t : TopologicalSpace.CompactOpens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) (HasInf.inf.{u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (TopologicalSpace.CompactOpens.instHasInfCompactOpens.{u1} α _inst_1 (T2Space.to_quasiSeparatedSpace.{u1} α _inst_1 _inst_3)) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : T2Space.{u1} α _inst_1] (s : TopologicalSpace.CompactOpens.{u1} α _inst_1) (t : TopologicalSpace.CompactOpens.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) (Inf.inf.{u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) (TopologicalSpace.CompactOpens.instInfCompactOpens.{u1} α _inst_1 (T2Space.to_quasiSeparatedSpace.{u1} α _inst_1 _inst_3)) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (TopologicalSpace.CompactOpens.{u1} α _inst_1) α (TopologicalSpace.CompactOpens.instSetLikeCompactOpens.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align topological_space.compact_opens.coe_inf TopologicalSpace.CompactOpens.coe_infₓ'. -/
 @[simp]
 theorem coe_inf [T2Space α] (s t : CompactOpens α) : (↑(s ⊓ t) : Set α) = s ∩ t :=

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore: classify new lemma porting notes (#11217)

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

"new lemma"
"added lemma"

68df7d0d

Diff

@@ -250,7 +250,7 @@ theorem carrier_eq_coe (s : NonemptyCompacts α) : s.carrier = s :=
   rfl
 #align topological_space.nonempty_compacts.carrier_eq_coe TopologicalSpace.NonemptyCompacts.carrier_eq_coe
 
-@[simp] -- Porting note: new lemma
+@[simp] -- Porting note (#10756): new lemma
 theorem coe_toCompacts (s : NonemptyCompacts α) : (s.toCompacts : Set α) = s := rfl
 
 instance : Sup (NonemptyCompacts α) :=

style: homogenise porting notes (#11145)

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".

8be0b69c

Diff

@@ -169,7 +169,7 @@ theorem equiv_refl : Compacts.equiv (Homeomorph.refl α) = Equiv.refl _ :=
 @[simp]
 theorem equiv_trans (f : α ≃ₜ β) (g : β ≃ₜ γ) :
     Compacts.equiv (f.trans g) = (Compacts.equiv f).trans (Compacts.equiv g) :=
-  -- porting note: can no longer write `map_comp _ _ _ _` and unify
+  -- Porting note: can no longer write `map_comp _ _ _ _` and unify
   Equiv.ext <| map_comp g f g.continuous f.continuous
 #align topological_space.compacts.equiv_trans TopologicalSpace.Compacts.equiv_trans
 
@@ -245,12 +245,12 @@ theorem coe_mk (s : Compacts α) (h) : (mk s h : Set α) = s :=
   rfl
 #align topological_space.nonempty_compacts.coe_mk TopologicalSpace.NonemptyCompacts.coe_mk
 
--- porting note: `@[simp]` moved to `coe_toCompacts`
+-- Porting note: `@[simp]` moved to `coe_toCompacts`
 theorem carrier_eq_coe (s : NonemptyCompacts α) : s.carrier = s :=
   rfl
 #align topological_space.nonempty_compacts.carrier_eq_coe TopologicalSpace.NonemptyCompacts.carrier_eq_coe
 
-@[simp] -- porting note: new lemma
+@[simp] -- Porting note: new lemma
 theorem coe_toCompacts (s : NonemptyCompacts α) : (s.toCompacts : Set α) = s := rfl
 
 instance : Sup (NonemptyCompacts α) :=
@@ -353,7 +353,7 @@ theorem coe_mk (s : Compacts α) (h) : (mk s h : Set α) = s :=
   rfl
 #align topological_space.positive_compacts.coe_mk TopologicalSpace.PositiveCompacts.coe_mk
 
--- porting note: `@[simp]` moved to a new lemma
+-- Porting note: `@[simp]` moved to a new lemma
 theorem carrier_eq_coe (s : PositiveCompacts α) : s.carrier = s :=
   rfl
 #align topological_space.positive_compacts.carrier_eq_coe TopologicalSpace.PositiveCompacts.carrier_eq_coe

chore(MetricSpace/Baire): fix Encodable/Countable (#10249)

Assume {ι : Sort*} [Countable ι] instead of {ι : Type*} [Encodable ι].
Generalize 2nd Baire theorem from T₂ spaces to R₁ spaces.
Rename type variables.

d27890e8

Diff

@@ -418,6 +418,11 @@ theorem _root_.exists_positiveCompacts_subset [LocallyCompactSpace α] {U : Set
   ⟨⟨⟨K, hKc⟩, ⟨x, hxK⟩⟩, hKU⟩
 #align exists_positive_compacts_subset exists_positiveCompacts_subset
 
+theorem _root_.IsOpen.exists_positiveCompacts_closure_subset [R1Space α] [LocallyCompactSpace α]
+    {U : Set α} (ho : IsOpen U) (hn : U.Nonempty) : ∃ K : PositiveCompacts α, closure ↑K ⊆ U :=
+  let ⟨K, hKU⟩ := exists_positiveCompacts_subset ho hn
+  ⟨K, K.isCompact.closure_subset_of_isOpen ho hKU⟩
+
 instance [CompactSpace α] [Nonempty α] : Inhabited (PositiveCompacts α) :=
   ⟨⊤⟩

refactor(Topology/Clopen): order of open and closed (#9957)

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

79a9e0eb

Diff

@@ -484,7 +484,7 @@ def toOpens (s : CompactOpens α) : Opens α := ⟨s, s.isOpen⟩
 /-- Reinterpret a compact open as a clopen. -/
 @[simps]
 def toClopens [T2Space α] (s : CompactOpens α) : Clopens α :=
-  ⟨s, s.isOpen, s.isCompact.isClosed⟩
+  ⟨s, s.isCompact.isClosed, s.isOpen⟩
 #align topological_space.compact_opens.to_clopens TopologicalSpace.CompactOpens.toClopens
 
 @[ext]

feat: define weakly locally compact spaces (#6770)

8c47c403

Diff

@@ -422,8 +422,10 @@ instance [CompactSpace α] [Nonempty α] : Inhabited (PositiveCompacts α) :=
   ⟨⊤⟩
 
 /-- In a nonempty locally compact space, there exists a compact set with nonempty interior. -/
-instance nonempty' [LocallyCompactSpace α] [Nonempty α] : Nonempty (PositiveCompacts α) :=
-  nonempty_of_exists <| exists_positiveCompacts_subset isOpen_univ univ_nonempty
+instance nonempty' [WeaklyLocallyCompactSpace α] [Nonempty α] : Nonempty (PositiveCompacts α) := by
+  inhabit α
+  rcases exists_compact_mem_nhds (default : α) with ⟨K, hKc, hK⟩
+  exact ⟨⟨K, hKc⟩, _, mem_interior_iff_mem_nhds.2 hK⟩
 #align topological_space.positive_compacts.nonempty' TopologicalSpace.PositiveCompacts.nonempty'
 
 /-- The product of two `TopologicalSpace.PositiveCompacts`, as a `TopologicalSpace.PositiveCompacts`

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -26,14 +26,14 @@ For a topological space `α`,
 
 open Set
 
-variable {α β γ : Type _} [TopologicalSpace α] [TopologicalSpace β] [TopologicalSpace γ]
+variable {α β γ : Type*} [TopologicalSpace α] [TopologicalSpace β] [TopologicalSpace γ]
 
 namespace TopologicalSpace
 
 /-! ### Compact sets -/
 
 /-- The type of compact sets of a topological space. -/
-structure Compacts (α : Type _) [TopologicalSpace α] where
+structure Compacts (α : Type*) [TopologicalSpace α] where
   carrier : Set α
   isCompact' : IsCompact carrier
 #align topological_space.compacts TopologicalSpace.Compacts
@@ -121,7 +121,7 @@ theorem coe_bot : (↑(⊥ : Compacts α) : Set α) = ∅ :=
 #align topological_space.compacts.coe_bot TopologicalSpace.Compacts.coe_bot
 
 @[simp]
-theorem coe_finset_sup {ι : Type _} {s : Finset ι} {f : ι → Compacts α} :
+theorem coe_finset_sup {ι : Type*} {s : Finset ι} {f : ι → Compacts α} :
     (↑(s.sup f) : Set α) = s.sup fun i => ↑(f i) := by
   refine Finset.cons_induction_on s rfl fun a s _ h => ?_
   simp_rw [Finset.sup_cons, coe_sup, sup_eq_union]
@@ -204,7 +204,7 @@ end Compacts
 /-! ### Nonempty compact sets -/
 
 /-- The type of nonempty compact sets of a topological space. -/
-structure NonemptyCompacts (α : Type _) [TopologicalSpace α] extends Compacts α where
+structure NonemptyCompacts (α : Type*) [TopologicalSpace α] extends Compacts α where
   nonempty' : carrier.Nonempty
 #align topological_space.nonempty_compacts TopologicalSpace.NonemptyCompacts
 
@@ -308,7 +308,7 @@ end NonemptyCompacts
 
 /-- The type of compact sets with nonempty interior of a topological space.
 See also `TopologicalSpace.Compacts` and `TopologicalSpace.NonemptyCompacts`. -/
-structure PositiveCompacts (α : Type _) [TopologicalSpace α] extends Compacts α where
+structure PositiveCompacts (α : Type*) [TopologicalSpace α] extends Compacts α where
   interior_nonempty' : (interior carrier).Nonempty
 #align topological_space.positive_compacts TopologicalSpace.PositiveCompacts
 
@@ -448,7 +448,7 @@ end PositiveCompacts
 
 /-- The type of compact open sets of a topological space. This is useful in non Hausdorff contexts,
 in particular spectral spaces. -/
-structure CompactOpens (α : Type _) [TopologicalSpace α] extends Compacts α where
+structure CompactOpens (α : Type*) [TopologicalSpace α] extends Compacts α where
   isOpen' : IsOpen carrier
 #align topological_space.compact_opens TopologicalSpace.CompactOpens

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 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.compacts
-! leanprover-community/mathlib commit 8c1b484d6a214e059531e22f1be9898ed6c1fd47
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Sets.Closeds
 import Mathlib.Topology.QuasiSeparated
 
+#align_import topology.sets.compacts from "leanprover-community/mathlib"@"8c1b484d6a214e059531e22f1be9898ed6c1fd47"
+
 /-!
 # Compact sets

fix: change compl precedence (#5586)

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

4d4f0f25

Diff

@@ -565,7 +565,7 @@ theorem coe_sdiff [T2Space α] (s t : CompactOpens α) : (↑(s \ t) : Set α) =
 #align topological_space.compact_opens.coe_sdiff TopologicalSpace.CompactOpens.coe_sdiff
 
 @[simp]
-theorem coe_compl [T2Space α] [CompactSpace α] (s : CompactOpens α) : (↑(sᶜ) : Set α) = ↑sᶜ :=
+theorem coe_compl [T2Space α] [CompactSpace α] (s : CompactOpens α) : (↑sᶜ : Set α) = (↑s)ᶜ :=
   rfl
 #align topological_space.compact_opens.coe_compl TopologicalSpace.CompactOpens.coe_compl

refactor: use the typeclass SProd to implement overloaded notation · ×ˢ · (#4200)

Currently, the following notations are changed from · ×ˢ · because Lean 4 can't deal with ambiguous notations. | Definition | Notation | | :

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com>

6c01dc6e

Diff

@@ -195,7 +195,8 @@ protected def prod (K : Compacts α) (L : Compacts β) : Compacts (α × β) whe
 #align topological_space.compacts.prod TopologicalSpace.Compacts.prod
 
 @[simp]
-theorem coe_prod (K : Compacts α) (L : Compacts β) : (K.prod L : Set (α × β)) = K ×ˢ L :=
+theorem coe_prod (K : Compacts α) (L : Compacts β) :
+    (K.prod L : Set (α × β)) = (K : Set α) ×ˢ (L : Set β) :=
   rfl
 #align topological_space.compacts.coe_prod TopologicalSpace.Compacts.coe_prod
 
@@ -300,7 +301,7 @@ protected def prod (K : NonemptyCompacts α) (L : NonemptyCompacts β) : Nonempt
 
 @[simp]
 theorem coe_prod (K : NonemptyCompacts α) (L : NonemptyCompacts β) :
-    (K.prod L : Set (α × β)) = K ×ˢ L :=
+    (K.prod L : Set (α × β)) = (K : Set α) ×ˢ (L : Set β) :=
   rfl
 #align topological_space.nonempty_compacts.coe_prod TopologicalSpace.NonemptyCompacts.coe_prod
 
@@ -440,7 +441,7 @@ protected def prod (K : PositiveCompacts α) (L : PositiveCompacts β) :
 
 @[simp]
 theorem coe_prod (K : PositiveCompacts α) (L : PositiveCompacts β) :
-    (K.prod L : Set (α × β)) = K ×ˢ L :=
+    (K.prod L : Set (α × β)) = (K : Set α) ×ˢ (L : Set β) :=
   rfl
 #align topological_space.positive_compacts.coe_prod TopologicalSpace.PositiveCompacts.coe_prod
 
@@ -601,7 +602,8 @@ protected def prod (K : CompactOpens α) (L : CompactOpens β) : CompactOpens (
 #align topological_space.compact_opens.prod TopologicalSpace.CompactOpens.prod
 
 @[simp]
-theorem coe_prod (K : CompactOpens α) (L : CompactOpens β) : (K.prod L : Set (α × β)) = K ×ˢ L :=
+theorem coe_prod (K : CompactOpens α) (L : CompactOpens β) :
+    (K.prod L : Set (α × β)) = (K : Set α) ×ˢ (L : Set β) :=
   rfl
 #align topological_space.compact_opens.coe_prod TopologicalSpace.CompactOpens.coe_prod

chore: forward-port leanprover-community/mathlib#18872 (#3958)

2f771251

Diff

@@ -4,7 +4,7 @@ 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.compacts
-! leanprover-community/mathlib commit dc6c365e751e34d100e80fe6e314c3c3e0fd2988
+! leanprover-community/mathlib commit 8c1b484d6a214e059531e22f1be9898ed6c1fd47
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -29,7 +29,7 @@ For a topological space `α`,
 
 open Set
 
-variable {α β : Type _} [TopologicalSpace α] [TopologicalSpace β]
+variable {α β γ : Type _} [TopologicalSpace α] [TopologicalSpace β] [TopologicalSpace γ]
 
 namespace TopologicalSpace
 
@@ -136,13 +136,23 @@ protected def map (f : α → β) (hf : Continuous f) (K : Compacts α) : Compac
   ⟨f '' K.1, K.2.image hf⟩
 #align topological_space.compacts.map TopologicalSpace.Compacts.map
 
-@[simp]
+@[simp, norm_cast]
 theorem coe_map {f : α → β} (hf : Continuous f) (s : Compacts α) : (s.map f hf : Set β) = f '' s :=
   rfl
 #align topological_space.compacts.coe_map TopologicalSpace.Compacts.coe_map
 
-/-- A homeomorphism induces an equivalence on compact sets, by taking the image. -/
 @[simp]
+theorem map_id (K : Compacts α) : K.map id continuous_id = K :=
+  Compacts.ext <| Set.image_id _
+#align topological_space.compacts.map_id TopologicalSpace.Compacts.map_id
+
+theorem map_comp (f : β → γ) (g : α → β) (hf : Continuous f) (hg : Continuous g) (K : Compacts α) :
+    K.map (f ∘ g) (hf.comp hg) = (K.map g hg).map f hf :=
+  Compacts.ext <| Set.image_comp _ _ _
+#align topological_space.compacts.map_comp TopologicalSpace.Compacts.map_comp
+
+/-- A homeomorphism induces an equivalence on compact sets, by taking the image. -/
+@[simps]
 protected def equiv (f : α ≃ₜ β) : Compacts α ≃ Compacts β where
   toFun := Compacts.map f f.continuous
   invFun := Compacts.map _ f.symm.continuous
@@ -154,10 +164,28 @@ protected def equiv (f : α ≃ₜ β) : Compacts α ≃ Compacts β where
     simp only [coe_map, ← image_comp, f.self_comp_symm, image_id]
 #align topological_space.compacts.equiv TopologicalSpace.Compacts.equiv
 
+@[simp]
+theorem equiv_refl : Compacts.equiv (Homeomorph.refl α) = Equiv.refl _ :=
+  Equiv.ext map_id
+#align topological_space.compacts.equiv_refl TopologicalSpace.Compacts.equiv_refl
+
+@[simp]
+theorem equiv_trans (f : α ≃ₜ β) (g : β ≃ₜ γ) :
+    Compacts.equiv (f.trans g) = (Compacts.equiv f).trans (Compacts.equiv g) :=
+  -- porting note: can no longer write `map_comp _ _ _ _` and unify
+  Equiv.ext <| map_comp g f g.continuous f.continuous
+#align topological_space.compacts.equiv_trans TopologicalSpace.Compacts.equiv_trans
+
+@[simp]
+theorem equiv_symm (f : α ≃ₜ β) : Compacts.equiv f.symm = (Compacts.equiv f).symm :=
+  rfl
+#align topological_space.compacts.equiv_symm TopologicalSpace.Compacts.equiv_symm
+
 /-- The image of a compact set under a homeomorphism can also be expressed as a preimage. -/
-theorem equiv_to_fun_val (f : α ≃ₜ β) (K : Compacts α) : (Compacts.equiv f K).1 = f.symm ⁻¹' K.1 :=
-  congr_fun (image_eq_preimage_of_inverse f.left_inv f.right_inv) K.1
-#align topological_space.compacts.equiv_to_fun_val TopologicalSpace.Compacts.equiv_to_fun_val
+theorem coe_equiv_apply_eq_preimage (f : α ≃ₜ β) (K : Compacts α) :
+    (Compacts.equiv f K : Set β) = f.symm ⁻¹' (K : Set α) :=
+  f.toEquiv.image_eq_preimage K
+#align topological_space.compacts.coe_equiv_apply_eq_preimage TopologicalSpace.Compacts.coe_equiv_apply_eq_preimage
 
 /-- The product of two `TopologicalSpace.Compacts`, as a `TopologicalSpace.Compacts` in the product
 space. -/
@@ -360,6 +388,31 @@ theorem coe_top [CompactSpace α] [Nonempty α] : (↑(⊤ : PositiveCompacts α
   rfl
 #align topological_space.positive_compacts.coe_top TopologicalSpace.PositiveCompacts.coe_top
 
+/-- The image of a positive compact set under a continuous open map. -/
+protected def map (f : α → β) (hf : Continuous f) (hf' : IsOpenMap f) (K : PositiveCompacts α) :
+    PositiveCompacts β :=
+  { Compacts.map f hf K.toCompacts with
+    interior_nonempty' :=
+      (K.interior_nonempty'.image _).mono (hf'.image_interior_subset K.toCompacts) }
+#align topological_space.positive_compacts.map TopologicalSpace.PositiveCompacts.map
+
+@[simp, norm_cast]
+theorem coe_map {f : α → β} (hf : Continuous f) (hf' : IsOpenMap f) (s : PositiveCompacts α) :
+    (s.map f hf hf' : Set β) = f '' s :=
+  rfl
+#align topological_space.positive_compacts.coe_map TopologicalSpace.PositiveCompacts.coe_map
+
+@[simp]
+theorem map_id (K : PositiveCompacts α) : K.map id continuous_id IsOpenMap.id = K :=
+  PositiveCompacts.ext <| Set.image_id _
+#align topological_space.positive_compacts.map_id TopologicalSpace.PositiveCompacts.map_id
+
+theorem map_comp (f : β → γ) (g : α → β) (hf : Continuous f) (hg : Continuous g) (hf' : IsOpenMap f)
+    (hg' : IsOpenMap g) (K : PositiveCompacts α) :
+    K.map (f ∘ g) (hf.comp hg) (hf'.comp hg') = (K.map g hg hg').map f hf hf' :=
+  PositiveCompacts.ext <| Set.image_comp _ _ _
+#align topological_space.positive_compacts.map_comp TopologicalSpace.PositiveCompacts.map_comp
+
 theorem _root_.exists_positiveCompacts_subset [LocallyCompactSpace α] {U : Set α} (ho : IsOpen U)
     (hn : U.Nonempty) : ∃ K : PositiveCompacts α, ↑K ⊆ U :=
   let ⟨x, hx⟩ := hn
@@ -524,12 +577,23 @@ def map (f : α → β) (hf : Continuous f) (hf' : IsOpenMap f) (s : CompactOpen
   ⟨s.toCompacts.map f hf, hf' _ s.isOpen⟩
 #align topological_space.compact_opens.map TopologicalSpace.CompactOpens.map
 
-@[simp]
+@[simp, norm_cast]
 theorem coe_map {f : α → β} (hf : Continuous f) (hf' : IsOpenMap f) (s : CompactOpens α) :
     (s.map f hf hf' : Set β) = f '' s :=
   rfl
 #align topological_space.compact_opens.coe_map TopologicalSpace.CompactOpens.coe_map
 
+@[simp]
+theorem map_id (K : CompactOpens α) : K.map id continuous_id IsOpenMap.id = K :=
+  CompactOpens.ext <| Set.image_id _
+#align topological_space.compact_opens.map_id TopologicalSpace.CompactOpens.map_id
+
+theorem map_comp (f : β → γ) (g : α → β) (hf : Continuous f) (hg : Continuous g) (hf' : IsOpenMap f)
+    (hg' : IsOpenMap g) (K : CompactOpens α) :
+    K.map (f ∘ g) (hf.comp hg) (hf'.comp hg') = (K.map g hg hg').map f hf hf' :=
+  CompactOpens.ext <| Set.image_comp _ _ _
+#align topological_space.compact_opens.map_comp TopologicalSpace.CompactOpens.map_comp
+
 /-- The product of two `TopologicalSpace.CompactOpens`, as a `TopologicalSpace.CompactOpens` in the
 product space. -/
 protected def prod (K : CompactOpens α) (L : CompactOpens β) : CompactOpens (α × β) :=

Fix: some initialize_simps_projections configurations (#2561)

Some of the older ones do exactly the same as the shorter new ones
Also update doc (some remarks are only true after #2045 is merged)

2b503331

Diff

@@ -194,7 +194,7 @@ instance : SetLike (NonemptyCompacts α) α where
 /-- See Note [custom simps projection]. -/
 def Simps.coe (s : NonemptyCompacts α) : Set α := s
 
-initialize_simps_projections NonemptyCompacts (toCompacts_carrier → coe)
+initialize_simps_projections NonemptyCompacts (carrier → coe)
 
 protected theorem isCompact (s : NonemptyCompacts α) : IsCompact (s : Set α) :=
   s.isCompact'
@@ -298,7 +298,7 @@ instance : SetLike (PositiveCompacts α) α where
 /-- See Note [custom simps projection]. -/
 def Simps.coe (s : PositiveCompacts α) : Set α := s
 
-initialize_simps_projections PositiveCompacts (toCompacts_carrier → coe)
+initialize_simps_projections PositiveCompacts (carrier → coe)
 
 protected theorem isCompact (s : PositiveCompacts α) : IsCompact (s : Set α) :=
   s.isCompact'
@@ -413,7 +413,7 @@ instance : SetLike (CompactOpens α) α where
 /-- See Note [custom simps projection]. -/
 def Simps.coe (s : CompactOpens α) : Set α := s
 
-initialize_simps_projections CompactOpens (toCompacts_carrier → coe)
+initialize_simps_projections CompactOpens (carrier → coe)
 
 protected theorem isCompact (s : CompactOpens α) : IsCompact (s : Set α) :=
   s.isCompact'

refactor: rename HasSup/HasInf to Sup/Inf (#2475)

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

294082ef

Diff

@@ -76,10 +76,10 @@ theorem carrier_eq_coe (s : Compacts α) : s.carrier = s :=
   rfl
 #align topological_space.compacts.carrier_eq_coe TopologicalSpace.Compacts.carrier_eq_coe
 
-instance : HasSup (Compacts α) :=
+instance : Sup (Compacts α) :=
   ⟨fun s t => ⟨s ∪ t, s.isCompact.union t.isCompact⟩⟩
 
-instance [T2Space α] : HasInf (Compacts α) :=
+instance [T2Space α] : Inf (Compacts α) :=
   ⟨fun s t => ⟨s ∩ t, s.isCompact.inter t.isCompact⟩⟩
 
 instance [CompactSpace α] : Top (Compacts α) :=
@@ -227,7 +227,7 @@ theorem carrier_eq_coe (s : NonemptyCompacts α) : s.carrier = s :=
 @[simp] -- porting note: new lemma
 theorem coe_toCompacts (s : NonemptyCompacts α) : (s.toCompacts : Set α) = s := rfl
 
-instance : HasSup (NonemptyCompacts α) :=
+instance : Sup (NonemptyCompacts α) :=
   ⟨fun s t => ⟨s.toCompacts ⊔ t.toCompacts, s.nonempty.mono <| subset_union_left _ _⟩⟩
 
 instance [CompactSpace α] [Nonempty α] : Top (NonemptyCompacts α) :=
@@ -336,7 +336,7 @@ theorem carrier_eq_coe (s : PositiveCompacts α) : s.carrier = s :=
 theorem coe_toCompacts (s : PositiveCompacts α) : (s.toCompacts : Set α) = s :=
   rfl
 
-instance : HasSup (PositiveCompacts α) :=
+instance : Sup (PositiveCompacts α) :=
   ⟨fun s t =>
     ⟨s.toCompacts ⊔ t.toCompacts,
       s.interior_nonempty.mono <| interior_mono <| subset_union_left _ _⟩⟩
@@ -444,10 +444,10 @@ theorem coe_mk (s : Compacts α) (h) : (mk s h : Set α) = s :=
   rfl
 #align topological_space.compact_opens.coe_mk TopologicalSpace.CompactOpens.coe_mk
 
-instance : HasSup (CompactOpens α) :=
+instance : Sup (CompactOpens α) :=
   ⟨fun s t => ⟨s.toCompacts ⊔ t.toCompacts, s.isOpen.union t.isOpen⟩⟩
 
-instance [QuasiSeparatedSpace α] : HasInf (CompactOpens α) :=
+instance [QuasiSeparatedSpace α] : Inf (CompactOpens α) :=
   ⟨fun U V =>
     ⟨⟨(U : Set α) ∩ (V : Set α),
         QuasiSeparatedSpace.inter_isCompact U.1.1 V.1.1 U.2 U.1.2 V.2 V.1.2⟩,