topology.sets.order
⟷
Mathlib.Topology.Sets.Order
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -45,10 +45,10 @@ theorem upper (s : ClopenUpperSet α) : IsUpperSet (s : Set α) :=
#align clopen_upper_set.upper ClopenUpperSet.upper
-/
-#print ClopenUpperSet.clopen /-
-theorem clopen (s : ClopenUpperSet α) : IsClopen (s : Set α) :=
+#print ClopenUpperSet.isClopen /-
+theorem isClopen (s : ClopenUpperSet α) : IsClopen (s : Set α) :=
s.clopen'
-#align clopen_upper_set.clopen ClopenUpperSet.clopen
+#align clopen_upper_set.clopen ClopenUpperSet.isClopen
-/
#print ClopenUpperSet.toUpperSet /-
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
-import Mathbin.Order.UpperLower.Basic
-import Mathbin.Topology.Sets.Closeds
+import Order.UpperLower.Basic
+import Topology.Sets.Closeds
#align_import topology.sets.order from "leanprover-community/mathlib"@"ac34df03f74e6f797efd6991df2e3b7f7d8d33e0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-
-! This file was ported from Lean 3 source module topology.sets.order
-! leanprover-community/mathlib commit ac34df03f74e6f797efd6991df2e3b7f7d8d33e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Order.UpperLower.Basic
import Mathbin.Topology.Sets.Closeds
+#align_import topology.sets.order from "leanprover-community/mathlib"@"ac34df03f74e6f797efd6991df2e3b7f7d8d33e0"
+
/-!
# Clopen upper sets
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -94,25 +94,33 @@ instance : Lattice (ClopenUpperSet α) :=
instance : BoundedOrder (ClopenUpperSet α) :=
BoundedOrder.lift (coe : _ → Set α) (fun _ _ => id) rfl rfl
+#print ClopenUpperSet.coe_sup /-
@[simp]
theorem coe_sup (s t : ClopenUpperSet α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
rfl
#align clopen_upper_set.coe_sup ClopenUpperSet.coe_sup
+-/
+#print ClopenUpperSet.coe_inf /-
@[simp]
theorem coe_inf (s t : ClopenUpperSet α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
rfl
#align clopen_upper_set.coe_inf ClopenUpperSet.coe_inf
+-/
+#print ClopenUpperSet.coe_top /-
@[simp]
theorem coe_top : (↑(⊤ : ClopenUpperSet α) : Set α) = univ :=
rfl
#align clopen_upper_set.coe_top ClopenUpperSet.coe_top
+-/
+#print ClopenUpperSet.coe_bot /-
@[simp]
theorem coe_bot : (↑(⊥ : ClopenUpperSet α) : Set α) = ∅ :=
rfl
#align clopen_upper_set.coe_bot ClopenUpperSet.coe_bot
+-/
instance : Inhabited (ClopenUpperSet α) :=
⟨⊥⟩
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -94,45 +94,21 @@ instance : Lattice (ClopenUpperSet α) :=
instance : BoundedOrder (ClopenUpperSet α) :=
BoundedOrder.lift (coe : _ → Set α) (fun _ _ => id) rfl rfl
-/- warning: clopen_upper_set.coe_sup -> ClopenUpperSet.coe_sup is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LE.{u1} α] (s : ClopenUpperSet.{u1} α _inst_1 _inst_2) (t : ClopenUpperSet.{u1} α _inst_1 _inst_2), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.setLike.{u1} α _inst_1 _inst_2)))) (Sup.sup.{u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (ClopenUpperSet.hasSup.{u1} α _inst_1 _inst_2) 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) (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.setLike.{u1} α _inst_1 _inst_2)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.setLike.{u1} α _inst_1 _inst_2)))) t))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LE.{u1} α] (s : ClopenUpperSet.{u1} α _inst_1 _inst_2) (t : ClopenUpperSet.{u1} α _inst_1 _inst_2), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.instSetLikeClopenUpperSet.{u1} α _inst_1 _inst_2) (Sup.sup.{u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (ClopenUpperSet.instSupClopenUpperSet.{u1} α _inst_1 _inst_2) s t)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SetLike.coe.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.instSetLikeClopenUpperSet.{u1} α _inst_1 _inst_2) s) (SetLike.coe.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.instSetLikeClopenUpperSet.{u1} α _inst_1 _inst_2) t))
-Case conversion may be inaccurate. Consider using '#align clopen_upper_set.coe_sup ClopenUpperSet.coe_supₓ'. -/
@[simp]
theorem coe_sup (s t : ClopenUpperSet α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
rfl
#align clopen_upper_set.coe_sup ClopenUpperSet.coe_sup
-/- warning: clopen_upper_set.coe_inf -> ClopenUpperSet.coe_inf is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align clopen_upper_set.coe_inf ClopenUpperSet.coe_infₓ'. -/
@[simp]
theorem coe_inf (s t : ClopenUpperSet α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
rfl
#align clopen_upper_set.coe_inf ClopenUpperSet.coe_inf
-/- warning: clopen_upper_set.coe_top -> ClopenUpperSet.coe_top is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align clopen_upper_set.coe_top ClopenUpperSet.coe_topₓ'. -/
@[simp]
theorem coe_top : (↑(⊤ : ClopenUpperSet α) : Set α) = univ :=
rfl
#align clopen_upper_set.coe_top ClopenUpperSet.coe_top
-/- warning: clopen_upper_set.coe_bot -> ClopenUpperSet.coe_bot is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align clopen_upper_set.coe_bot ClopenUpperSet.coe_botₓ'. -/
@[simp]
theorem coe_bot : (↑(⊥ : ClopenUpperSet α) : Set α) = ∅ :=
rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -40,10 +40,7 @@ namespace ClopenUpperSet
instance : SetLike (ClopenUpperSet 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 ClopenUpperSet.upper /-
theorem upper (s : ClopenUpperSet α) : IsUpperSet (s : Set α) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -79,10 +79,10 @@ theorem coe_mk (s : Clopens α) (h) : (mk s h : Set α) = s :=
#align clopen_upper_set.coe_mk ClopenUpperSet.coe_mk
-/
-instance : HasSup (ClopenUpperSet α) :=
+instance : Sup (ClopenUpperSet α) :=
⟨fun s t => ⟨s.toClopens ⊔ t.toClopens, s.upper.union t.upper⟩⟩
-instance : HasInf (ClopenUpperSet α) :=
+instance : Inf (ClopenUpperSet α) :=
⟨fun s t => ⟨s.toClopens ⊓ t.toClopens, s.upper.inter t.upper⟩⟩
instance : Top (ClopenUpperSet α) :=
@@ -99,9 +99,9 @@ instance : BoundedOrder (ClopenUpperSet α) :=
/- warning: clopen_upper_set.coe_sup -> ClopenUpperSet.coe_sup is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LE.{u1} α] (s : ClopenUpperSet.{u1} α _inst_1 _inst_2) (t : ClopenUpperSet.{u1} α _inst_1 _inst_2), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.setLike.{u1} α _inst_1 _inst_2)))) (Sup.sup.{u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (ClopenUpperSet.hasSup.{u1} α _inst_1 _inst_2) 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) (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.setLike.{u1} α _inst_1 _inst_2)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.setLike.{u1} α _inst_1 _inst_2)))) t))
but is expected to have type
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+ forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LE.{u1} α] (s : ClopenUpperSet.{u1} α _inst_1 _inst_2) (t : ClopenUpperSet.{u1} α _inst_1 _inst_2), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.instSetLikeClopenUpperSet.{u1} α _inst_1 _inst_2) (Sup.sup.{u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (ClopenUpperSet.instSupClopenUpperSet.{u1} α _inst_1 _inst_2) s t)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SetLike.coe.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.instSetLikeClopenUpperSet.{u1} α _inst_1 _inst_2) s) (SetLike.coe.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.instSetLikeClopenUpperSet.{u1} α _inst_1 _inst_2) t))
Case conversion may be inaccurate. Consider using '#align clopen_upper_set.coe_sup ClopenUpperSet.coe_supₓ'. -/
@[simp]
theorem coe_sup (s t : ClopenUpperSet α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
@@ -110,9 +110,9 @@ theorem coe_sup (s t : ClopenUpperSet α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
/- warning: clopen_upper_set.coe_inf -> ClopenUpperSet.coe_inf is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LE.{u1} α] (s : ClopenUpperSet.{u1} α _inst_1 _inst_2) (t : ClopenUpperSet.{u1} α _inst_1 _inst_2), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.setLike.{u1} α _inst_1 _inst_2)))) (Inf.inf.{u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (ClopenUpperSet.hasInf.{u1} α _inst_1 _inst_2) 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) (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.setLike.{u1} α _inst_1 _inst_2)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.setLike.{u1} α _inst_1 _inst_2)))) t))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LE.{u1} α] (s : ClopenUpperSet.{u1} α _inst_1 _inst_2) (t : ClopenUpperSet.{u1} α _inst_1 _inst_2), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.instSetLikeClopenUpperSet.{u1} α _inst_1 _inst_2) (HasInf.inf.{u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (ClopenUpperSet.instHasInfClopenUpperSet.{u1} α _inst_1 _inst_2) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.instSetLikeClopenUpperSet.{u1} α _inst_1 _inst_2) s) (SetLike.coe.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.instSetLikeClopenUpperSet.{u1} α _inst_1 _inst_2) t))
+ forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LE.{u1} α] (s : ClopenUpperSet.{u1} α _inst_1 _inst_2) (t : ClopenUpperSet.{u1} α _inst_1 _inst_2), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.instSetLikeClopenUpperSet.{u1} α _inst_1 _inst_2) (Inf.inf.{u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) (ClopenUpperSet.instInfClopenUpperSet.{u1} α _inst_1 _inst_2) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.instSetLikeClopenUpperSet.{u1} α _inst_1 _inst_2) s) (SetLike.coe.{u1, u1} (ClopenUpperSet.{u1} α _inst_1 _inst_2) α (ClopenUpperSet.instSetLikeClopenUpperSet.{u1} α _inst_1 _inst_2) t))
Case conversion may be inaccurate. Consider using '#align clopen_upper_set.coe_inf ClopenUpperSet.coe_infₓ'. -/
@[simp]
theorem coe_inf (s t : ClopenUpperSet α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
This PR renames the field Clopens.clopen' -> Clopens.isClopen', and the lemmas
as well as: ClopenUpperSet.clopen -> ClopenUpperSet.isClopen connectedComponent_eq_iInter_clopen -> connectedComponent_eq_iInter_isClopen connectedComponent_subset_iInter_clopen -> connectedComponent_subset_iInter_isClopen continuous_boolIndicator_iff_clopen -> continuous_boolIndicator_iff_isClopen continuousOn_boolIndicator_iff_clopen -> continuousOn_boolIndicator_iff_isClopen DiscreteQuotient.ofClopen -> DiscreteQuotient.ofIsClopen disjoint_or_subset_of_clopen -> disjoint_or_subset_of_isClopen exists_clopen_{lower,upper}of_not_le -> exists_isClopen{lower,upper}_of_not_le exists_clopen_of_cofiltered -> exists_isClopen_of_cofiltered exists_clopen_of_totally_separated -> exists_isClopen_of_totally_separated exists_clopen_upper_or_lower_of_ne -> exists_isClopen_upper_or_lower_of_ne IsPreconnected.subset_clopen -> IsPreconnected.subset_isClopen isTotallyDisconnected_of_clopen_set -> isTotallyDisconnected_of_isClopen_set LocallyConstant.ofClopen_fiber_one -> LocallyConstant.ofIsClopen_fiber_one LocallyConstant.ofClopen_fiber_zero -> LocallyConstant.ofIsClopen_fiber_zero LocallyConstant.ofClopen -> LocallyConstant.ofIsClopen preimage_clopen_of_clopen -> preimage_isClopen_of_isClopen TopologicalSpace.Clopens.clopen -> TopologicalSpace.Clopens.isClopen
@@ -45,9 +45,9 @@ theorem upper (s : ClopenUpperSet α) : IsUpperSet (s : Set α) :=
s.upper'
#align clopen_upper_set.upper ClopenUpperSet.upper
-theorem clopen (s : ClopenUpperSet α) : IsClopen (s : Set α) :=
- s.clopen'
-#align clopen_upper_set.clopen ClopenUpperSet.clopen
+theorem isClopen (s : ClopenUpperSet α) : IsClopen (s : Set α) :=
+ s.isClopen'
+#align clopen_upper_set.clopen ClopenUpperSet.isClopen
/-- Reinterpret an upper clopen as an upper set. -/
@[simps]
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -17,13 +17,13 @@ In this file we define the type of clopen upper sets.
open Set TopologicalSpace
-variable {α β : Type _} [TopologicalSpace α] [LE α] [TopologicalSpace β] [LE β]
+variable {α β : Type*} [TopologicalSpace α] [LE α] [TopologicalSpace β] [LE β]
/-! ### Compact open sets -/
/-- The type of clopen upper sets of a topological space. -/
-structure ClopenUpperSet (α : Type _) [TopologicalSpace α] [LE α] extends Clopens α where
+structure ClopenUpperSet (α : Type*) [TopologicalSpace α] [LE α] extends Clopens α where
upper' : IsUpperSet carrier
#align clopen_upper_set ClopenUpperSet
@@ -2,15 +2,12 @@
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-
-! This file was ported from Lean 3 source module topology.sets.order
-! leanprover-community/mathlib commit dc6c365e751e34d100e80fe6e314c3c3e0fd2988
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Order.UpperLower.Basic
import Mathlib.Topology.Sets.Closeds
+#align_import topology.sets.order from "leanprover-community/mathlib"@"dc6c365e751e34d100e80fe6e314c3c3e0fd2988"
+
/-!
# Clopen upper sets
@@ -52,7 +52,7 @@ theorem clopen (s : ClopenUpperSet α) : IsClopen (s : Set α) :=
s.clopen'
#align clopen_upper_set.clopen ClopenUpperSet.clopen
-/-- Reinterpret a upper clopen as an upper set. -/
+/-- Reinterpret an upper clopen as an upper set. -/
@[simps]
def toUpperSet (s : ClopenUpperSet α) : UpperSet α :=
⟨s, s.upper⟩
@@ -42,7 +42,7 @@ instance : SetLike (ClopenUpperSet α) α where
/-- See Note [custom simps projection]. -/
def Simps.coe (s : ClopenUpperSet α) : Set α := s
-initialize_simps_projections ClopenUpperSet (toClopens_carrier → coe)
+initialize_simps_projections ClopenUpperSet (carrier → coe)
theorem upper (s : ClopenUpperSet α) : IsUpperSet (s : Set α) :=
s.upper'
@@ -68,10 +68,10 @@ theorem coe_mk (s : Clopens α) (h) : (mk s h : Set α) = s :=
rfl
#align clopen_upper_set.coe_mk ClopenUpperSet.coe_mk
-instance : HasSup (ClopenUpperSet α) :=
+instance : Sup (ClopenUpperSet α) :=
⟨fun s t => ⟨s.toClopens ⊔ t.toClopens, s.upper.union t.upper⟩⟩
-instance : HasInf (ClopenUpperSet α) :=
+instance : Inf (ClopenUpperSet α) :=
⟨fun s t => ⟨s.toClopens ⊓ t.toClopens, s.upper.inter t.upper⟩⟩
instance : Top (ClopenUpperSet α) :=
@@ -110,4 +110,3 @@ instance : Inhabited (ClopenUpperSet α) :=
⟨⊥⟩
end ClopenUpperSet
-
The unported dependencies are