order.lattice_intervals
⟷
Mathlib.Order.LatticeIntervals
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/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
-import Mathbin.Order.Bounds.Basic
+import Order.Bounds.Basic
#align_import order.lattice_intervals from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-
-! This file was ported from Lean 3 source module order.lattice_intervals
-! leanprover-community/mathlib commit c3291da49cfa65f0d43b094750541c0731edc932
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Order.Bounds.Basic
+#align_import order.lattice_intervals from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
+
/-!
# Intervals in Lattices
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -98,20 +98,24 @@ instance [Preorder α] {a : α} : OrderTop (Iic a)
top := ⟨a, le_refl a⟩
le_top x := x.Prop
+#print Set.Iic.coe_top /-
@[simp]
theorem coe_top [Preorder α] {a : α} : ↑(⊤ : Iic a) = a :=
rfl
#align set.Iic.coe_top Set.Iic.coe_top
+-/
instance [Preorder α] [OrderBot α] {a : α} : OrderBot (Iic a)
where
bot := ⟨⊥, bot_le⟩
bot_le := fun ⟨_, _⟩ => Subtype.mk_le_mk.2 bot_le
+#print Set.Iic.coe_bot /-
@[simp]
theorem coe_bot [Preorder α] [OrderBot α] {a : α} : ↑(⊥ : Iic a) = (⊥ : α) :=
rfl
#align set.Iic.coe_bot Set.Iic.coe_bot
+-/
instance [Preorder α] [OrderBot α] {a : α} : BoundedOrder (Iic a) :=
{ Iic.orderTop, Iic.orderBot with }
@@ -137,20 +141,24 @@ instance [Preorder α] {a : α} : OrderBot (Ici a)
bot := ⟨a, le_refl a⟩
bot_le x := x.Prop
+#print Set.Ici.coe_bot /-
@[simp]
theorem coe_bot [Preorder α] {a : α} : ↑(⊥ : Ici a) = a :=
rfl
#align set.Ici.coe_bot Set.Ici.coe_bot
+-/
instance [Preorder α] [OrderTop α] {a : α} : OrderTop (Ici a)
where
top := ⟨⊤, le_top⟩
le_top := fun ⟨_, _⟩ => Subtype.mk_le_mk.2 le_top
+#print Set.Ici.coe_top /-
@[simp]
theorem coe_top [Preorder α] [OrderTop α] {a : α} : ↑(⊤ : Ici a) = (⊤ : α) :=
rfl
#align set.Ici.coe_top Set.Ici.coe_top
+-/
instance [Preorder α] [OrderTop α] {a : α} : BoundedOrder (Ici a) :=
{ Ici.orderTop, Ici.orderBot with }
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -43,11 +43,13 @@ namespace Ico
instance [SemilatticeInf α] {a b : α} : SemilatticeInf (Ico a b) :=
Subtype.semilatticeInf fun x y hx hy => ⟨le_inf hx.1 hy.1, lt_of_le_of_lt inf_le_left hx.2⟩
+#print Set.Ico.orderBot /-
/-- `Ico a b` has a bottom element whenever `a < b`. -/
@[reducible]
protected def orderBot [PartialOrder α] {a b : α} (h : a < b) : OrderBot (Ico a b) :=
(isLeast_Ico h).OrderBot
#align set.Ico.order_bot Set.Ico.orderBot
+-/
end Ico
@@ -63,11 +65,13 @@ namespace Ioc
instance [SemilatticeSup α] {a b : α} : SemilatticeSup (Ioc a b) :=
Subtype.semilatticeSup fun x y hx hy => ⟨lt_of_lt_of_le hx.1 le_sup_left, sup_le hx.2 hy.2⟩
+#print Set.Ioc.orderTop /-
/-- `Ioc a b` has a top element whenever `a < b`. -/
@[reducible]
protected def orderTop [PartialOrder α] {a b : α} (h : a < b) : OrderTop (Ioc a b) :=
(isGreatest_Ioc h).OrderTop
#align set.Ioc.order_top Set.Ioc.orderTop
+-/
end Ioc
@@ -164,23 +168,29 @@ instance [SemilatticeSup α] {a b : α} : SemilatticeSup (Icc a b) :=
instance [Lattice α] {a b : α} : Lattice (Icc a b) :=
{ Icc.semilatticeInf, Icc.semilatticeSup with }
+#print Set.Icc.orderBot /-
/-- `Icc a b` has a bottom element whenever `a ≤ b`. -/
@[reducible]
protected def orderBot [Preorder α] {a b : α} (h : a ≤ b) : OrderBot (Icc a b) :=
(isLeast_Icc h).OrderBot
#align set.Icc.order_bot Set.Icc.orderBot
+-/
+#print Set.Icc.orderTop /-
/-- `Icc a b` has a top element whenever `a ≤ b`. -/
@[reducible]
protected def orderTop [Preorder α] {a b : α} (h : a ≤ b) : OrderTop (Icc a b) :=
(isGreatest_Icc h).OrderTop
#align set.Icc.order_top Set.Icc.orderTop
+-/
+#print Set.Icc.boundedOrder /-
/-- `Icc a b` is a `bounded_order` whenever `a ≤ b`. -/
@[reducible]
protected def boundedOrder [Preorder α] {a b : α} (h : a ≤ b) : BoundedOrder (Icc a b) :=
{ Icc.orderTop h, Icc.orderBot h with }
#align set.Icc.bounded_order Set.Icc.boundedOrder
+-/
end Icc
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -43,12 +43,6 @@ namespace Ico
instance [SemilatticeInf α] {a b : α} : SemilatticeInf (Ico a b) :=
Subtype.semilatticeInf fun x y hx hy => ⟨le_inf hx.1 hy.1, lt_of_le_of_lt inf_le_left hx.2⟩
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/-- `Ico a b` has a bottom element whenever `a < b`. -/
@[reducible]
protected def orderBot [PartialOrder α] {a b : α} (h : a < b) : OrderBot (Ico a b) :=
@@ -69,12 +63,6 @@ namespace Ioc
instance [SemilatticeSup α] {a b : α} : SemilatticeSup (Ioc a b) :=
Subtype.semilatticeSup fun x y hx hy => ⟨lt_of_lt_of_le hx.1 le_sup_left, sup_le hx.2 hy.2⟩
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/-- `Ioc a b` has a top element whenever `a < b`. -/
@[reducible]
protected def orderTop [PartialOrder α] {a b : α} (h : a < b) : OrderTop (Ioc a b) :=
@@ -106,12 +94,6 @@ instance [Preorder α] {a : α} : OrderTop (Iic a)
top := ⟨a, le_refl a⟩
le_top x := x.Prop
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@[simp]
theorem coe_top [Preorder α] {a : α} : ↑(⊤ : Iic a) = a :=
rfl
@@ -122,12 +104,6 @@ instance [Preorder α] [OrderBot α] {a : α} : OrderBot (Iic a)
bot := ⟨⊥, bot_le⟩
bot_le := fun ⟨_, _⟩ => Subtype.mk_le_mk.2 bot_le
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@[simp]
theorem coe_bot [Preorder α] [OrderBot α] {a : α} : ↑(⊥ : Iic a) = (⊥ : α) :=
rfl
@@ -157,12 +133,6 @@ instance [Preorder α] {a : α} : OrderBot (Ici a)
bot := ⟨a, le_refl a⟩
bot_le x := x.Prop
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@[simp]
theorem coe_bot [Preorder α] {a : α} : ↑(⊥ : Ici a) = a :=
rfl
@@ -173,12 +143,6 @@ instance [Preorder α] [OrderTop α] {a : α} : OrderTop (Ici a)
top := ⟨⊤, le_top⟩
le_top := fun ⟨_, _⟩ => Subtype.mk_le_mk.2 le_top
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@[simp]
theorem coe_top [Preorder α] [OrderTop α] {a : α} : ↑(⊤ : Ici a) = (⊤ : α) :=
rfl
@@ -200,36 +164,18 @@ instance [SemilatticeSup α] {a b : α} : SemilatticeSup (Icc a b) :=
instance [Lattice α] {a b : α} : Lattice (Icc a b) :=
{ Icc.semilatticeInf, Icc.semilatticeSup with }
-/- warning: set.Icc.order_bot -> Set.Icc.orderBot is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.Icc.order_bot Set.Icc.orderBotₓ'. -/
/-- `Icc a b` has a bottom element whenever `a ≤ b`. -/
@[reducible]
protected def orderBot [Preorder α] {a b : α} (h : a ≤ b) : OrderBot (Icc a b) :=
(isLeast_Icc h).OrderBot
#align set.Icc.order_bot Set.Icc.orderBot
-/- warning: set.Icc.order_top -> Set.Icc.orderTop is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.Icc.order_top Set.Icc.orderTopₓ'. -/
/-- `Icc a b` has a top element whenever `a ≤ b`. -/
@[reducible]
protected def orderTop [Preorder α] {a b : α} (h : a ≤ b) : OrderTop (Icc a b) :=
(isGreatest_Icc h).OrderTop
#align set.Icc.order_top Set.Icc.orderTop
-/- warning: set.Icc.bounded_order -> Set.Icc.boundedOrder is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.Icc.bounded_order Set.Icc.boundedOrderₓ'. -/
/-- `Icc a b` is a `bounded_order` whenever `a ≤ b`. -/
@[reducible]
protected def boundedOrder [Preorder α] {a b : α} (h : a ≤ b) : BoundedOrder (Icc a b) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -43,13 +43,17 @@ namespace Ico
instance [SemilatticeInf α] {a b : α} : SemilatticeInf (Ico a b) :=
Subtype.semilatticeInf fun x y hx hy => ⟨le_inf hx.1 hy.1, lt_of_le_of_lt inf_le_left hx.2⟩
-#print Set.Ico.orderBot /-
+/- warning: set.Ico.order_bot -> Set.Ico.orderBot is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a b) -> (OrderBot.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a b)) (Subtype.hasLe.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a b))))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a b) -> (OrderBot.{u1} (Set.Elem.{u1} α (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a b)) (Subtype.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a b))))
+Case conversion may be inaccurate. Consider using '#align set.Ico.order_bot Set.Ico.orderBotₓ'. -/
/-- `Ico a b` has a bottom element whenever `a < b`. -/
@[reducible]
protected def orderBot [PartialOrder α] {a b : α} (h : a < b) : OrderBot (Ico a b) :=
(isLeast_Ico h).OrderBot
#align set.Ico.order_bot Set.Ico.orderBot
--/
end Ico
@@ -65,13 +69,17 @@ namespace Ioc
instance [SemilatticeSup α] {a b : α} : SemilatticeSup (Ioc a b) :=
Subtype.semilatticeSup fun x y hx hy => ⟨lt_of_lt_of_le hx.1 le_sup_left, sup_le hx.2 hy.2⟩
-#print Set.Ioc.orderTop /-
+/- warning: set.Ioc.order_top -> Set.Ioc.orderTop is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a b) -> (OrderTop.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a b)) (Subtype.hasLe.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a b))))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a b) -> (OrderTop.{u1} (Set.Elem.{u1} α (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a b)) (Subtype.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a b))))
+Case conversion may be inaccurate. Consider using '#align set.Ioc.order_top Set.Ioc.orderTopₓ'. -/
/-- `Ioc a b` has a top element whenever `a < b`. -/
@[reducible]
protected def orderTop [PartialOrder α] {a b : α} (h : a < b) : OrderTop (Ioc a b) :=
(isGreatest_Ioc h).OrderTop
#align set.Ioc.order_top Set.Ioc.orderTop
--/
end Ioc
@@ -100,7 +108,7 @@ instance [Preorder α] {a : α} : OrderTop (Iic a)
/- warning: set.Iic.coe_top -> Set.Iic.coe_top is a dubious translation:
lean 3 declaration is
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but is expected to have type
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Case conversion may be inaccurate. Consider using '#align set.Iic.coe_top Set.Iic.coe_topₓ'. -/
@@ -116,7 +124,7 @@ instance [Preorder α] [OrderBot α] {a : α} : OrderBot (Iic a)
/- warning: set.Iic.coe_bot -> Set.Iic.coe_bot is a dubious translation:
lean 3 declaration is
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but is expected to have type
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Case conversion may be inaccurate. Consider using '#align set.Iic.coe_bot Set.Iic.coe_botₓ'. -/
@@ -151,7 +159,7 @@ instance [Preorder α] {a : α} : OrderBot (Ici a)
/- warning: set.Ici.coe_bot -> Set.Ici.coe_bot is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {a : α}, Eq.{succ u1} α ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ici.{u1} α _inst_1 a)))))) (Bot.bot.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) (OrderBot.toHasBot.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) (Subtype.hasLe.{u1} α (Preorder.toLE.{u1} α _inst_1) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ici.{u1} α _inst_1 a))) (Set.Ici.orderBot.{u1} α _inst_1 a)))) a
+ forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {a : α}, Eq.{succ u1} α ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ici.{u1} α _inst_1 a)))))) (Bot.bot.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) (OrderBot.toHasBot.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) (Subtype.hasLe.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ici.{u1} α _inst_1 a))) (Set.Ici.orderBot.{u1} α _inst_1 a)))) a
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {a : α}, Eq.{succ u1} α (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ici.{u1} α _inst_1 a)) (Bot.bot.{u1} (Set.Elem.{u1} α (Set.Ici.{u1} α _inst_1 a)) (OrderBot.toBot.{u1} (Set.Elem.{u1} α (Set.Ici.{u1} α _inst_1 a)) (Subtype.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ici.{u1} α _inst_1 a))) (Set.Ici.orderBot.{u1} α _inst_1 a)))) a
Case conversion may be inaccurate. Consider using '#align set.Ici.coe_bot Set.Ici.coe_botₓ'. -/
@@ -167,7 +175,7 @@ instance [Preorder α] [OrderTop α] {a : α} : OrderTop (Ici a)
/- warning: set.Ici.coe_top -> Set.Ici.coe_top is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, Eq.{succ u1} α ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ici.{u1} α _inst_1 a)))))) (Top.top.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) (OrderTop.toHasTop.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) (Subtype.hasLe.{u1} α (Preorder.toLE.{u1} α _inst_1) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ici.{u1} α _inst_1 a))) (Set.Ici.orderTop.{u1} α _inst_1 _inst_2 a)))) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2))
+ forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] {a : α}, Eq.{succ u1} α ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ici.{u1} α _inst_1 a)))))) (Top.top.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) (OrderTop.toHasTop.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ici.{u1} α _inst_1 a)) (Subtype.hasLe.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ici.{u1} α _inst_1 a))) (Set.Ici.orderTop.{u1} α _inst_1 _inst_2 a)))) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_2))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)] {a : α}, Eq.{succ u1} α (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ici.{u1} α _inst_1 a)) (Top.top.{u1} (Set.Elem.{u1} α (Set.Ici.{u1} α _inst_1 a)) (OrderTop.toTop.{u1} (Set.Elem.{u1} α (Set.Ici.{u1} α _inst_1 a)) (Subtype.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ici.{u1} α _inst_1 a))) (Set.Ici.orderTop.{u1} α _inst_1 _inst_2 a)))) (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2))
Case conversion may be inaccurate. Consider using '#align set.Ici.coe_top Set.Ici.coe_topₓ'. -/
@@ -192,29 +200,41 @@ instance [SemilatticeSup α] {a b : α} : SemilatticeSup (Icc a b) :=
instance [Lattice α] {a b : α} : Lattice (Icc a b) :=
{ Icc.semilatticeInf, Icc.semilatticeSup with }
-#print Set.Icc.orderBot /-
+/- warning: set.Icc.order_bot -> Set.Icc.orderBot is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1) a b) -> (OrderBot.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α _inst_1 a b)) (Subtype.hasLe.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α _inst_1 a b))))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) a b) -> (OrderBot.{u1} (Set.Elem.{u1} α (Set.Icc.{u1} α _inst_1 a b)) (Subtype.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Icc.{u1} α _inst_1 a b))))
+Case conversion may be inaccurate. Consider using '#align set.Icc.order_bot Set.Icc.orderBotₓ'. -/
/-- `Icc a b` has a bottom element whenever `a ≤ b`. -/
@[reducible]
protected def orderBot [Preorder α] {a b : α} (h : a ≤ b) : OrderBot (Icc a b) :=
(isLeast_Icc h).OrderBot
#align set.Icc.order_bot Set.Icc.orderBot
--/
-#print Set.Icc.orderTop /-
+/- warning: set.Icc.order_top -> Set.Icc.orderTop is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1) a b) -> (OrderTop.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α _inst_1 a b)) (Subtype.hasLe.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α _inst_1 a b))))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) a b) -> (OrderTop.{u1} (Set.Elem.{u1} α (Set.Icc.{u1} α _inst_1 a b)) (Subtype.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Icc.{u1} α _inst_1 a b))))
+Case conversion may be inaccurate. Consider using '#align set.Icc.order_top Set.Icc.orderTopₓ'. -/
/-- `Icc a b` has a top element whenever `a ≤ b`. -/
@[reducible]
protected def orderTop [Preorder α] {a b : α} (h : a ≤ b) : OrderTop (Icc a b) :=
(isGreatest_Icc h).OrderTop
#align set.Icc.order_top Set.Icc.orderTop
--/
-#print Set.Icc.boundedOrder /-
+/- warning: set.Icc.bounded_order -> Set.Icc.boundedOrder is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1) a b) -> (BoundedOrder.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Icc.{u1} α _inst_1 a b)) (Subtype.hasLe.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Icc.{u1} α _inst_1 a b))))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) a b) -> (BoundedOrder.{u1} (Set.Elem.{u1} α (Set.Icc.{u1} α _inst_1 a b)) (Subtype.le.{u1} α (Preorder.toLE.{u1} α _inst_1) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Icc.{u1} α _inst_1 a b))))
+Case conversion may be inaccurate. Consider using '#align set.Icc.bounded_order Set.Icc.boundedOrderₓ'. -/
/-- `Icc a b` is a `bounded_order` whenever `a ≤ b`. -/
@[reducible]
protected def boundedOrder [Preorder α] {a b : α} (h : a ≤ b) : BoundedOrder (Icc a b) :=
{ Icc.orderTop h, Icc.orderBot h with }
#align set.Icc.bounded_order Set.Icc.boundedOrder
--/
end Icc
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -28,7 +28,7 @@ In the following, `*` can represent either `c`, `o`, or `i`.
-/
-variable {α : Type _}
+variable {α : Type*}
namespace Set
@@ -2,13 +2,11 @@
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-! This file was ported from Lean 3 source module order.lattice_intervals
-! leanprover-community/mathlib commit d012cd09a9b256d870751284dd6a29882b0be105
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Order.Bounds.Basic
+#align_import order.lattice_intervals from "leanprover-community/mathlib"@"d012cd09a9b256d870751284dd6a29882b0be105"
+
/-!
# Intervals in Lattices
fix-comments.py
on all files.@@ -172,7 +172,7 @@ protected def orderTop [Preorder α] {a b : α} (h : a ≤ b) : OrderTop (Icc a
(isGreatest_Icc h).orderTop
#align set.Icc.order_top Set.Icc.orderTop
-/-- `Icc a b` is a `bounded_order` whenever `a ≤ b`. -/
+/-- `Icc a b` is a `BoundedOrder` whenever `a ≤ b`. -/
@[reducible]
protected def boundedOrder [Preorder α] {a b : α} (h : a ≤ b) : BoundedOrder (Icc a b) :=
{ Icc.orderTop h, Icc.orderBot h with }
@@ -20,13 +20,13 @@ intervals, but more can be added easily along the same lines when needed.
## Main definitions
In the following, `*` can represent either `c`, `o`, or `i`.
- * `Set.Ic*.order_bot`
- * `Set.Ii*.semillatice_inf`
- * `Set.I*c.order_top`
- * `Set.I*c.semillatice_inf`
+ * `Set.Ic*.orderBot`
+ * `Set.Ii*.semillaticeInf`
+ * `Set.I*c.orderTop`
+ * `Set.I*c.semillaticeInf`
* `Set.I**.lattice`
- * `Set.Iic.bounded_order`, within an `order_bot`
- * `Set.Ici.bounded_order`, within an `order_top`
+ * `Set.Iic.boundedOrder`, within an `OrderBot`
+ * `Set.Ici.boundedOrder`, within an `OrderTop`
-/
All dependencies are ported!