topology.algebra.order.t5
⟷
Mathlib.Topology.Algebra.Order.T5
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
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Topology.Order.Basic
-import Data.Set.Intervals.OrdConnectedComponent
+import Order.Interval.Set.OrdConnectedComponent
#align_import topology.algebra.order.t5 from "leanprover-community/mathlib"@"50832daea47b195a48b5b33b1c8b2162c48c3afc"
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -49,7 +49,7 @@ theorem compl_section_ordSeparatingSet_mem_nhdsWithin_Ici (hd : Disjoint s (clos
rcases exists_Icc_mem_subset_of_mem_nhdsWithin_Ici hmem with ⟨b, hab, hmem', hsub⟩
by_cases H : Disjoint (Icc a b) (ord_connected_section <| ord_separating_set s t)
· exact mem_of_superset hmem' (disjoint_left.1 H)
- · simp only [Set.disjoint_left, Classical.not_forall, Classical.not_not] at H
+ · simp only [Set.disjoint_left, Classical.not_forall, Classical.not_not] at H
rcases H with ⟨c, ⟨hac, hcb⟩, hc⟩
have hsub' : Icc a b ⊆ ord_connected_component (tᶜ) a :=
subset_ord_connected_component (left_mem_Icc.2 hab) hsub
mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010
@@ -49,7 +49,7 @@ theorem compl_section_ordSeparatingSet_mem_nhdsWithin_Ici (hd : Disjoint s (clos
rcases exists_Icc_mem_subset_of_mem_nhdsWithin_Ici hmem with ⟨b, hab, hmem', hsub⟩
by_cases H : Disjoint (Icc a b) (ord_connected_section <| ord_separating_set s t)
· exact mem_of_superset hmem' (disjoint_left.1 H)
- · simp only [Set.disjoint_left, not_forall, Classical.not_not] at H
+ · simp only [Set.disjoint_left, Classical.not_forall, Classical.not_not] at H
rcases H with ⟨c, ⟨hac, hcb⟩, hc⟩
have hsub' : Icc a b ⊆ ord_connected_component (tᶜ) a :=
subset_ord_connected_component (left_mem_Icc.2 hab) hsub
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
-import Mathbin.Topology.Order.Basic
-import Mathbin.Data.Set.Intervals.OrdConnectedComponent
+import Topology.Order.Basic
+import Data.Set.Intervals.OrdConnectedComponent
#align_import topology.algebra.order.t5 from "leanprover-community/mathlib"@"50832daea47b195a48b5b33b1c8b2162c48c3afc"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module topology.algebra.order.t5
-! leanprover-community/mathlib commit 50832daea47b195a48b5b33b1c8b2162c48c3afc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Topology.Order.Basic
import Mathbin.Data.Set.Intervals.OrdConnectedComponent
+#align_import topology.algebra.order.t5 from "leanprover-community/mathlib"@"50832daea47b195a48b5b33b1c8b2162c48c3afc"
+
/-!
# Linear order is a completely normal Hausdorff topological space
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -41,6 +41,7 @@ theorem ordConnectedComponent_mem_nhds : ordConnectedComponent s a ∈ 𝓝 a
#align set.ord_connected_component_mem_nhds Set.ordConnectedComponent_mem_nhds
-/
+#print Set.compl_section_ordSeparatingSet_mem_nhdsWithin_Ici /-
theorem compl_section_ordSeparatingSet_mem_nhdsWithin_Ici (hd : Disjoint s (closure t))
(ha : a ∈ s) : (ordConnectedSection <| ordSeparatingSet s t)ᶜ ∈ 𝓝[≥] a :=
by
@@ -78,7 +79,9 @@ theorem compl_section_ordSeparatingSet_mem_nhdsWithin_Ici (hd : Disjoint s (clos
have hya : y < a := not_le.1 fun hay => hsub ⟨hay, hyc.trans hcb⟩ hyt
exact hxy (Icc_subset_uIcc ⟨hya.le, hx.1⟩) ha
#align set.compl_section_ord_separating_set_mem_nhds_within_Ici Set.compl_section_ordSeparatingSet_mem_nhdsWithin_Ici
+-/
+#print Set.compl_section_ordSeparatingSet_mem_nhdsWithin_Iic /-
theorem compl_section_ordSeparatingSet_mem_nhdsWithin_Iic (hd : Disjoint s (closure t))
(ha : a ∈ s) : (ordConnectedSection <| ordSeparatingSet s t)ᶜ ∈ 𝓝[≤] a :=
by
@@ -87,7 +90,9 @@ theorem compl_section_ordSeparatingSet_mem_nhdsWithin_Iic (hd : Disjoint s (clos
simpa only [dual_ord_separating_set, dual_ord_connected_section] using
compl_section_ord_separating_set_mem_nhds_within_Ici hd' ha'
#align set.compl_section_ord_separating_set_mem_nhds_within_Iic Set.compl_section_ordSeparatingSet_mem_nhdsWithin_Iic
+-/
+#print Set.compl_section_ordSeparatingSet_mem_nhds /-
theorem compl_section_ordSeparatingSet_mem_nhds (hd : Disjoint s (closure t)) (ha : a ∈ s) :
(ordConnectedSection <| ordSeparatingSet s t)ᶜ ∈ 𝓝 a :=
by
@@ -96,13 +101,16 @@ theorem compl_section_ordSeparatingSet_mem_nhds (hd : Disjoint s (closure t)) (h
⟨compl_section_ord_separating_set_mem_nhds_within_Iic hd ha,
compl_section_ord_separating_set_mem_nhds_within_Ici hd ha⟩
#align set.compl_section_ord_separating_set_mem_nhds Set.compl_section_ordSeparatingSet_mem_nhds
+-/
+#print Set.ordT5Nhd_mem_nhdsSet /-
theorem ordT5Nhd_mem_nhdsSet (hd : Disjoint s (closure t)) : ordT5Nhd s t ∈ 𝓝ˢ s :=
bUnion_mem_nhdsSet fun x hx =>
ordConnectedComponent_mem_nhds.2 <|
inter_mem (by rw [← mem_interior_iff_mem_nhds, interior_compl]; exact disjoint_left.1 hd hx)
(compl_section_ordSeparatingSet_mem_nhds hd hx)
#align set.ord_t5_nhd_mem_nhds_set Set.ordT5Nhd_mem_nhdsSet
+-/
end Set
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -51,7 +51,7 @@ theorem compl_section_ordSeparatingSet_mem_nhdsWithin_Ici (hd : Disjoint s (clos
rcases exists_Icc_mem_subset_of_mem_nhdsWithin_Ici hmem with ⟨b, hab, hmem', hsub⟩
by_cases H : Disjoint (Icc a b) (ord_connected_section <| ord_separating_set s t)
· exact mem_of_superset hmem' (disjoint_left.1 H)
- · simp only [Set.disjoint_left, not_forall, Classical.not_not] at H
+ · simp only [Set.disjoint_left, not_forall, Classical.not_not] at H
rcases H with ⟨c, ⟨hac, hcb⟩, hc⟩
have hsub' : Icc a b ⊆ ord_connected_component (tᶜ) a :=
subset_ord_connected_component (left_mem_Icc.2 hab) hsub
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -24,7 +24,7 @@ topological space.
open Filter Set Function OrderDual
-open Topology Filter Interval
+open scoped Topology Filter Interval
variable {X : Type _} [LinearOrder X] [TopologicalSpace X] [OrderTopology X] {a b c : X}
{s t : Set X}
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -41,12 +41,6 @@ theorem ordConnectedComponent_mem_nhds : ordConnectedComponent s a ∈ 𝓝 a
#align set.ord_connected_component_mem_nhds Set.ordConnectedComponent_mem_nhds
-/
-/- warning: set.compl_section_ord_separating_set_mem_nhds_within_Ici -> Set.compl_section_ordSeparatingSet_mem_nhdsWithin_Ici is a dubious translation:
-lean 3 declaration is
- forall {X : Type.{u1}} [_inst_1 : LinearOrder.{u1} X] [_inst_2 : TopologicalSpace.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_2 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_1))))] {a : X} {s : Set.{u1} X} {t : Set.{u1} X}, (Disjoint.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.completeBooleanAlgebra.{u1} X)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} X) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} X) (Set.booleanAlgebra.{u1} X))) s (closure.{u1} X _inst_2 t)) -> (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) a s) -> (Membership.Mem.{u1, u1} (Set.{u1} X) (Filter.{u1} X) (Filter.hasMem.{u1} X) (HasCompl.compl.{u1} (Set.{u1} X) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} X) (Set.booleanAlgebra.{u1} X)) (Set.ordConnectedSection.{u1} X _inst_1 (Set.ordSeparatingSet.{u1} X _inst_1 s t))) (nhdsWithin.{u1} X _inst_2 a (Set.Ici.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_1)))) a)))
-but is expected to have type
- forall {X : Type.{u1}} [_inst_1 : LinearOrder.{u1} X] [_inst_2 : TopologicalSpace.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_2 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_1)))))] {a : X} {s : Set.{u1} X} {t : Set.{u1} X}, (Disjoint.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} X) (Preorder.toLE.{u1} (Set.{u1} X) (PartialOrder.toPreorder.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))) s (closure.{u1} X _inst_2 t)) -> (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) a s) -> (Membership.mem.{u1, u1} (Set.{u1} X) (Filter.{u1} X) (instMembershipSetFilter.{u1} X) (HasCompl.compl.{u1} (Set.{u1} X) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} X) (Set.instBooleanAlgebraSet.{u1} X)) (Set.ordConnectedSection.{u1} X _inst_1 (Set.ordSeparatingSet.{u1} X _inst_1 s t))) (nhdsWithin.{u1} X _inst_2 a (Set.Ici.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_1))))) a)))
-Case conversion may be inaccurate. Consider using '#align set.compl_section_ord_separating_set_mem_nhds_within_Ici Set.compl_section_ordSeparatingSet_mem_nhdsWithin_Iciₓ'. -/
theorem compl_section_ordSeparatingSet_mem_nhdsWithin_Ici (hd : Disjoint s (closure t))
(ha : a ∈ s) : (ordConnectedSection <| ordSeparatingSet s t)ᶜ ∈ 𝓝[≥] a :=
by
@@ -85,12 +79,6 @@ theorem compl_section_ordSeparatingSet_mem_nhdsWithin_Ici (hd : Disjoint s (clos
exact hxy (Icc_subset_uIcc ⟨hya.le, hx.1⟩) ha
#align set.compl_section_ord_separating_set_mem_nhds_within_Ici Set.compl_section_ordSeparatingSet_mem_nhdsWithin_Ici
-/- warning: set.compl_section_ord_separating_set_mem_nhds_within_Iic -> Set.compl_section_ordSeparatingSet_mem_nhdsWithin_Iic is a dubious translation:
-lean 3 declaration is
- forall {X : Type.{u1}} [_inst_1 : LinearOrder.{u1} X] [_inst_2 : TopologicalSpace.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_2 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_1))))] {a : X} {s : Set.{u1} X} {t : Set.{u1} X}, (Disjoint.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.completeBooleanAlgebra.{u1} X)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} X) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} X) (Set.booleanAlgebra.{u1} X))) s (closure.{u1} X _inst_2 t)) -> (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) a s) -> (Membership.Mem.{u1, u1} (Set.{u1} X) (Filter.{u1} X) (Filter.hasMem.{u1} X) (HasCompl.compl.{u1} (Set.{u1} X) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} X) (Set.booleanAlgebra.{u1} X)) (Set.ordConnectedSection.{u1} X _inst_1 (Set.ordSeparatingSet.{u1} X _inst_1 s t))) (nhdsWithin.{u1} X _inst_2 a (Set.Iic.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_1)))) a)))
-but is expected to have type
- forall {X : Type.{u1}} [_inst_1 : LinearOrder.{u1} X] [_inst_2 : TopologicalSpace.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_2 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_1)))))] {a : X} {s : Set.{u1} X} {t : Set.{u1} X}, (Disjoint.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} X) (Preorder.toLE.{u1} (Set.{u1} X) (PartialOrder.toPreorder.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))) s (closure.{u1} X _inst_2 t)) -> (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) a s) -> (Membership.mem.{u1, u1} (Set.{u1} X) (Filter.{u1} X) (instMembershipSetFilter.{u1} X) (HasCompl.compl.{u1} (Set.{u1} X) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} X) (Set.instBooleanAlgebraSet.{u1} X)) (Set.ordConnectedSection.{u1} X _inst_1 (Set.ordSeparatingSet.{u1} X _inst_1 s t))) (nhdsWithin.{u1} X _inst_2 a (Set.Iic.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_1))))) a)))
-Case conversion may be inaccurate. Consider using '#align set.compl_section_ord_separating_set_mem_nhds_within_Iic Set.compl_section_ordSeparatingSet_mem_nhdsWithin_Iicₓ'. -/
theorem compl_section_ordSeparatingSet_mem_nhdsWithin_Iic (hd : Disjoint s (closure t))
(ha : a ∈ s) : (ordConnectedSection <| ordSeparatingSet s t)ᶜ ∈ 𝓝[≤] a :=
by
@@ -100,12 +88,6 @@ theorem compl_section_ordSeparatingSet_mem_nhdsWithin_Iic (hd : Disjoint s (clos
compl_section_ord_separating_set_mem_nhds_within_Ici hd' ha'
#align set.compl_section_ord_separating_set_mem_nhds_within_Iic Set.compl_section_ordSeparatingSet_mem_nhdsWithin_Iic
-/- warning: set.compl_section_ord_separating_set_mem_nhds -> Set.compl_section_ordSeparatingSet_mem_nhds is a dubious translation:
-lean 3 declaration is
- forall {X : Type.{u1}} [_inst_1 : LinearOrder.{u1} X] [_inst_2 : TopologicalSpace.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_2 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_1))))] {a : X} {s : Set.{u1} X} {t : Set.{u1} X}, (Disjoint.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.completeBooleanAlgebra.{u1} X)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} X) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} X) (Set.booleanAlgebra.{u1} X))) s (closure.{u1} X _inst_2 t)) -> (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) a s) -> (Membership.Mem.{u1, u1} (Set.{u1} X) (Filter.{u1} X) (Filter.hasMem.{u1} X) (HasCompl.compl.{u1} (Set.{u1} X) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} X) (Set.booleanAlgebra.{u1} X)) (Set.ordConnectedSection.{u1} X _inst_1 (Set.ordSeparatingSet.{u1} X _inst_1 s t))) (nhds.{u1} X _inst_2 a))
-but is expected to have type
- forall {X : Type.{u1}} [_inst_1 : LinearOrder.{u1} X] [_inst_2 : TopologicalSpace.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_2 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_1)))))] {a : X} {s : Set.{u1} X} {t : Set.{u1} X}, (Disjoint.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} X) (Preorder.toLE.{u1} (Set.{u1} X) (PartialOrder.toPreorder.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))) s (closure.{u1} X _inst_2 t)) -> (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) a s) -> (Membership.mem.{u1, u1} (Set.{u1} X) (Filter.{u1} X) (instMembershipSetFilter.{u1} X) (HasCompl.compl.{u1} (Set.{u1} X) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} X) (Set.instBooleanAlgebraSet.{u1} X)) (Set.ordConnectedSection.{u1} X _inst_1 (Set.ordSeparatingSet.{u1} X _inst_1 s t))) (nhds.{u1} X _inst_2 a))
-Case conversion may be inaccurate. Consider using '#align set.compl_section_ord_separating_set_mem_nhds Set.compl_section_ordSeparatingSet_mem_nhdsₓ'. -/
theorem compl_section_ordSeparatingSet_mem_nhds (hd : Disjoint s (closure t)) (ha : a ∈ s) :
(ordConnectedSection <| ordSeparatingSet s t)ᶜ ∈ 𝓝 a :=
by
@@ -115,12 +97,6 @@ theorem compl_section_ordSeparatingSet_mem_nhds (hd : Disjoint s (closure t)) (h
compl_section_ord_separating_set_mem_nhds_within_Ici hd ha⟩
#align set.compl_section_ord_separating_set_mem_nhds Set.compl_section_ordSeparatingSet_mem_nhds
-/- warning: set.ord_t5_nhd_mem_nhds_set -> Set.ordT5Nhd_mem_nhdsSet is a dubious translation:
-lean 3 declaration is
- forall {X : Type.{u1}} [_inst_1 : LinearOrder.{u1} X] [_inst_2 : TopologicalSpace.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_2 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_1))))] {s : Set.{u1} X} {t : Set.{u1} X}, (Disjoint.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.completeBooleanAlgebra.{u1} X)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} X) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} X) (Set.booleanAlgebra.{u1} X))) s (closure.{u1} X _inst_2 t)) -> (Membership.Mem.{u1, u1} (Set.{u1} X) (Filter.{u1} X) (Filter.hasMem.{u1} X) (Set.ordT5Nhd.{u1} X _inst_1 s t) (nhdsSet.{u1} X _inst_2 s))
-but is expected to have type
- forall {X : Type.{u1}} [_inst_1 : LinearOrder.{u1} X] [_inst_2 : TopologicalSpace.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_2 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_1)))))] {s : Set.{u1} X} {t : Set.{u1} X}, (Disjoint.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} X) (Preorder.toLE.{u1} (Set.{u1} X) (PartialOrder.toPreorder.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))) s (closure.{u1} X _inst_2 t)) -> (Membership.mem.{u1, u1} (Set.{u1} X) (Filter.{u1} X) (instMembershipSetFilter.{u1} X) (Set.ordT5Nhd.{u1} X _inst_1 s t) (nhdsSet.{u1} X _inst_2 s))
-Case conversion may be inaccurate. Consider using '#align set.ord_t5_nhd_mem_nhds_set Set.ordT5Nhd_mem_nhdsSetₓ'. -/
theorem ordT5Nhd_mem_nhdsSet (hd : Disjoint s (closure t)) : ordT5Nhd s t ∈ 𝓝ˢ s :=
bUnion_mem_nhdsSet fun x hx =>
ordConnectedComponent_mem_nhds.2 <|
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -124,10 +124,7 @@ Case conversion may be inaccurate. Consider using '#align set.ord_t5_nhd_mem_nhd
theorem ordT5Nhd_mem_nhdsSet (hd : Disjoint s (closure t)) : ordT5Nhd s t ∈ 𝓝ˢ s :=
bUnion_mem_nhdsSet fun x hx =>
ordConnectedComponent_mem_nhds.2 <|
- inter_mem
- (by
- rw [← mem_interior_iff_mem_nhds, interior_compl]
- exact disjoint_left.1 hd hx)
+ inter_mem (by rw [← mem_interior_iff_mem_nhds, interior_compl]; exact disjoint_left.1 hd hx)
(compl_section_ordSeparatingSet_mem_nhds hd hx)
#align set.ord_t5_nhd_mem_nhds_set Set.ordT5Nhd_mem_nhdsSet
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Move Set.Ixx
, Finset.Ixx
, Multiset.Ixx
together under two different folders:
Order.Interval
for their definition and basic propertiesAlgebra.Order.Interval
for their algebraic propertiesMove the definitions of Multiset.Ixx
to what is now Order.Interval.Multiset
. I believe we could just delete this file in a later PR as nothing uses it (and I already had doubts when defining Multiset.Ixx
three years ago).
Move the algebraic results out of what is now Order.Interval.Finset.Basic
to a new file Algebra.Order.Interval.Finset.Basic
.
@@ -3,7 +3,7 @@ Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
-import Mathlib.Data.Set.Intervals.OrdConnectedComponent
+import Mathlib.Order.Interval.Set.OrdConnectedComponent
import Mathlib.Topology.Order.Basic
#align_import topology.algebra.order.t5 from "leanprover-community/mathlib"@"4c19a16e4b705bf135cf9a80ac18fcc99c438514"
Move files from Topology.Algebra.Order
to Topology.Order
when they do not contain any algebra. Also move Topology.LocalExtr
to Topology.Order.LocalExtr
.
According to git, the moves are:
Mathlib/Topology/{Algebra => }/Order/ExtendFrom.lean
Mathlib/Topology/{Algebra => }/Order/ExtrClosure.lean
Mathlib/Topology/{Algebra => }/Order/Filter.lean
Mathlib/Topology/{Algebra => }/Order/IntermediateValue.lean
Mathlib/Topology/{Algebra => }/Order/LeftRight.lean
Mathlib/Topology/{Algebra => }/Order/LeftRightLim.lean
Mathlib/Topology/{Algebra => }/Order/MonotoneContinuity.lean
Mathlib/Topology/{Algebra => }/Order/MonotoneConvergence.lean
Mathlib/Topology/{Algebra => }/Order/ProjIcc.lean
Mathlib/Topology/{Algebra => }/Order/T5.lean
Mathlib/Topology/{ => Order}/LocalExtr.lean
@@ -3,8 +3,8 @@ Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
-import Mathlib.Topology.Order.Basic
import Mathlib.Data.Set.Intervals.OrdConnectedComponent
+import Mathlib.Topology.Order.Basic
#align_import topology.algebra.order.t5 from "leanprover-community/mathlib"@"4c19a16e4b705bf135cf9a80ac18fcc99c438514"
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -18,7 +18,7 @@ topological space.
open Filter Set Function OrderDual Topology Interval
-variable {X : Type _} [LinearOrder X] [TopologicalSpace X] [OrderTopology X] {a b c : X}
+variable {X : Type*} [LinearOrder X] [TopologicalSpace X] [OrderTopology X] {a b c : X}
{s t : Set X}
namespace Set
@@ -2,15 +2,12 @@
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module topology.algebra.order.t5
-! leanprover-community/mathlib commit 4c19a16e4b705bf135cf9a80ac18fcc99c438514
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Topology.Order.Basic
import Mathlib.Data.Set.Intervals.OrdConnectedComponent
+#align_import topology.algebra.order.t5 from "leanprover-community/mathlib"@"4c19a16e4b705bf135cf9a80ac18fcc99c438514"
+
/-!
# Linear order is a completely normal Hausdorff topological space
@@ -44,7 +44,7 @@ theorem compl_section_ordSeparatingSet_mem_nhdsWithin_Ici (hd : Disjoint s (clos
· exact mem_of_superset hmem' (disjoint_left.1 H)
· simp only [Set.disjoint_left, not_forall, Classical.not_not] at H
rcases H with ⟨c, ⟨hac, hcb⟩, hc⟩
- have hsub' : Icc a b ⊆ ordConnectedComponent (tᶜ) a :=
+ have hsub' : Icc a b ⊆ ordConnectedComponent tᶜ a :=
subset_ordConnectedComponent (left_mem_Icc.2 hab) hsub
have hd : Disjoint s (ordConnectedSection (ordSeparatingSet s t)) :=
disjoint_left_ordSeparatingSet.mono_right ordConnectedSection_subset
sSup
/iSup
(#3938)
As discussed on Zulip
supₛ
→ sSup
infₛ
→ sInf
supᵢ
→ iSup
infᵢ
→ iInf
bsupₛ
→ bsSup
binfₛ
→ bsInf
bsupᵢ
→ biSup
binfᵢ
→ biInf
csupₛ
→ csSup
cinfₛ
→ csInf
csupᵢ
→ ciSup
cinfᵢ
→ ciInf
unionₛ
→ sUnion
interₛ
→ sInter
unionᵢ
→ iUnion
interᵢ
→ iInter
bunionₛ
→ bsUnion
binterₛ
→ bsInter
bunionᵢ
→ biUnion
binterᵢ
→ biInter
Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>
@@ -52,11 +52,11 @@ theorem compl_section_ordSeparatingSet_mem_nhdsWithin_Ici (hd : Disjoint s (clos
disjoint_left.1 hd ha
refine' mem_of_superset (Ico_mem_nhdsWithin_Ici (left_mem_Ico.2 hac)) fun x hx hx' => _
refine' hx.2.ne (eq_of_mem_ordConnectedSection_of_uIcc_subset hx' hc _)
- refine' subset_inter (subset_unionᵢ₂_of_subset a ha _) _
+ refine' subset_inter (subset_iUnion₂_of_subset a ha _) _
· exact OrdConnected.uIcc_subset inferInstance (hsub' ⟨hx.1, hx.2.le.trans hcb⟩)
(hsub' ⟨hac.le, hcb⟩)
- · rcases mem_unionᵢ₂.1 (ordConnectedSection_subset hx').2 with ⟨y, hyt, hxy⟩
- refine' subset_unionᵢ₂_of_subset y hyt (OrdConnected.uIcc_subset inferInstance hxy _)
+ · rcases mem_iUnion₂.1 (ordConnectedSection_subset hx').2 with ⟨y, hyt, hxy⟩
+ refine' subset_iUnion₂_of_subset y hyt (OrdConnected.uIcc_subset inferInstance hxy _)
refine' subset_ordConnectedComponent left_mem_uIcc hxy _
suffices c < y by
rw [uIcc_of_ge (hx.2.trans this).le]
The unported dependencies are