order.upper_lower.hom
⟷
Mathlib.Order.UpperLower.Hom
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
@@ -3,8 +3,8 @@ Copyright (c) 2022 Yaël Dillies, Sara Rousta. 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.Order.Hom.CompleteLattice
+import Order.UpperLower.Basic
+import Order.Hom.CompleteLattice
#align_import order.upper_lower.hom from "leanprover-community/mathlib"@"b6da1a0b3e7cd83b1f744c49ce48ef8c6307d2f6"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2022 Yaël Dillies, Sara Rousta. 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 order.upper_lower.hom
-! leanprover-community/mathlib commit b6da1a0b3e7cd83b1f744c49ce48ef8c6307d2f6
-! 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.Order.Hom.CompleteLattice
+#align_import order.upper_lower.hom from "leanprover-community/mathlib"@"b6da1a0b3e7cd83b1f744c49ce48ef8c6307d2f6"
+
/-!
# `upper_set.Ici` etc as `sup`/`Sup`/`inf`/`Inf`-homomorphisms
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -32,10 +32,12 @@ section SemilatticeSup
variable [SemilatticeSup α]
+#print UpperSet.iciSupHom /-
/-- `upper_set.Ici` as a `sup_hom`. -/
def iciSupHom : SupHom α (UpperSet α) :=
⟨Ici, Ici_sup⟩
#align upper_set.Ici_sup_hom UpperSet.iciSupHom
+-/
#print UpperSet.coe_iciSupHom /-
@[simp]
@@ -78,10 +80,12 @@ section SemilatticeInf
variable [SemilatticeInf α]
+#print LowerSet.iicInfHom /-
/-- `lower_set.Iic` as an `inf_hom`. -/
def iicInfHom : InfHom α (LowerSet α) :=
⟨Iic, Iic_inf⟩
#align lower_set.Iic_inf_hom LowerSet.iicInfHom
+-/
#print LowerSet.coe_iicInfHom /-
@[simp]
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -37,15 +37,19 @@ def iciSupHom : SupHom α (UpperSet α) :=
⟨Ici, Ici_sup⟩
#align upper_set.Ici_sup_hom UpperSet.iciSupHom
+#print UpperSet.coe_iciSupHom /-
@[simp]
theorem coe_iciSupHom : (iciSupHom : α → UpperSet α) = Ici :=
rfl
#align upper_set.coe_Ici_sup_hom UpperSet.coe_iciSupHom
+-/
+#print UpperSet.iciSupHom_apply /-
@[simp]
theorem iciSupHom_apply (a : α) : iciSupHom a = Ici a :=
rfl
#align upper_set.Ici_sup_hom_apply UpperSet.iciSupHom_apply
+-/
end SemilatticeSup
@@ -79,15 +83,19 @@ def iicInfHom : InfHom α (LowerSet α) :=
⟨Iic, Iic_inf⟩
#align lower_set.Iic_inf_hom LowerSet.iicInfHom
+#print LowerSet.coe_iicInfHom /-
@[simp]
theorem coe_iicInfHom : (iicInfHom : α → LowerSet α) = Iic :=
rfl
#align lower_set.coe_Iic_inf_hom LowerSet.coe_iicInfHom
+-/
+#print LowerSet.iicInfHom_apply /-
@[simp]
theorem iicInfHom_apply (a : α) : iicInfHom a = Iic a :=
rfl
#align lower_set.Iic_inf_hom_apply LowerSet.iicInfHom_apply
+-/
end SemilatticeInf
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -32,34 +32,16 @@ section SemilatticeSup
variable [SemilatticeSup α]
-/- warning: upper_set.Ici_sup_hom -> UpperSet.iciSupHom is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α], SupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α _inst_1) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α], SupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α _inst_1) (UpperSet.instSupUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align upper_set.Ici_sup_hom UpperSet.iciSupHomₓ'. -/
/-- `upper_set.Ici` as a `sup_hom`. -/
def iciSupHom : SupHom α (UpperSet α) :=
⟨Ici, Ici_sup⟩
#align upper_set.Ici_sup_hom UpperSet.iciSupHom
-/- warning: upper_set.coe_Ici_sup_hom -> UpperSet.coe_iciSupHom is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α], Eq.{succ u1} ((fun (_x : SupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α _inst_1) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) => α -> (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) (UpperSet.iciSupHom.{u1} α _inst_1)) (coeFn.{succ u1, succ u1} (SupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α _inst_1) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) (fun (_x : SupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α _inst_1) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) => α -> (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) (SupHom.hasCoeToFun.{u1, u1} α (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α _inst_1) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) (UpperSet.iciSupHom.{u1} α _inst_1)) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align upper_set.coe_Ici_sup_hom UpperSet.coe_iciSupHomₓ'. -/
@[simp]
theorem coe_iciSupHom : (iciSupHom : α → UpperSet α) = Ici :=
rfl
#align upper_set.coe_Ici_sup_hom UpperSet.coe_iciSupHom
-/- warning: upper_set.Ici_sup_hom_apply -> UpperSet.iciSupHom_apply is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align upper_set.Ici_sup_hom_apply UpperSet.iciSupHom_applyₓ'. -/
@[simp]
theorem iciSupHom_apply (a : α) : iciSupHom a = Ici a :=
rfl
@@ -92,34 +74,16 @@ section SemilatticeInf
variable [SemilatticeInf α]
-/- warning: lower_set.Iic_inf_hom -> LowerSet.iicInfHom is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α], InfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toHasInf.{u1} α _inst_1) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α], InfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toInf.{u1} α _inst_1) (LowerSet.instInfLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align lower_set.Iic_inf_hom LowerSet.iicInfHomₓ'. -/
/-- `lower_set.Iic` as an `inf_hom`. -/
def iicInfHom : InfHom α (LowerSet α) :=
⟨Iic, Iic_inf⟩
#align lower_set.Iic_inf_hom LowerSet.iicInfHom
-/- warning: lower_set.coe_Iic_inf_hom -> LowerSet.coe_iicInfHom is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align lower_set.coe_Iic_inf_hom LowerSet.coe_iicInfHomₓ'. -/
@[simp]
theorem coe_iicInfHom : (iicInfHom : α → LowerSet α) = Iic :=
rfl
#align lower_set.coe_Iic_inf_hom LowerSet.coe_iicInfHom
-/- warning: lower_set.Iic_inf_hom_apply -> LowerSet.iicInfHom_apply is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] (a : α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (InfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toHasInf.{u1} α _inst_1) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))) (fun (_x : InfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toHasInf.{u1} α _inst_1) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))) => α -> (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))) (InfHom.hasCoeToFun.{u1, u1} α (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toHasInf.{u1} α _inst_1) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))) (LowerSet.iicInfHom.{u1} α _inst_1) a) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) a)
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-Case conversion may be inaccurate. Consider using '#align lower_set.Iic_inf_hom_apply LowerSet.iicInfHom_applyₓ'. -/
@[simp]
theorem iicInfHom_apply (a : α) : iicInfHom a = Iic a :=
rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -34,7 +34,7 @@ variable [SemilatticeSup α]
/- warning: upper_set.Ici_sup_hom -> UpperSet.iciSupHom is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α], SupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α _inst_1) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α], SupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α _inst_1) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α], SupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α _inst_1) (UpperSet.instSupUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align upper_set.Ici_sup_hom UpperSet.iciSupHomₓ'. -/
@@ -43,19 +43,27 @@ def iciSupHom : SupHom α (UpperSet α) :=
⟨Ici, Ici_sup⟩
#align upper_set.Ici_sup_hom UpperSet.iciSupHom
-#print UpperSet.coe_iciSupHom /-
+/- warning: upper_set.coe_Ici_sup_hom -> UpperSet.coe_iciSupHom is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α], Eq.{succ u1} ((fun (_x : SupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α _inst_1) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) => α -> (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) (UpperSet.iciSupHom.{u1} α _inst_1)) (coeFn.{succ u1, succ u1} (SupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α _inst_1) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) (fun (_x : SupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α _inst_1) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) => α -> (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) (SupHom.hasCoeToFun.{u1, u1} α (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α _inst_1) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) (UpperSet.iciSupHom.{u1} α _inst_1)) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α], Eq.{succ u1} (forall (a : α), (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.2625 : α) => UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (SupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α _inst_1) (UpperSet.instSupUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.2625 : α) => UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _x) (SupHom.instFunLikeSupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α _inst_1) (UpperSet.instSupUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) (UpperSet.iciSupHom.{u1} α _inst_1)) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align upper_set.coe_Ici_sup_hom UpperSet.coe_iciSupHomₓ'. -/
@[simp]
theorem coe_iciSupHom : (iciSupHom : α → UpperSet α) = Ici :=
rfl
#align upper_set.coe_Ici_sup_hom UpperSet.coe_iciSupHom
--/
-#print UpperSet.iciSupHom_apply /-
+/- warning: upper_set.Ici_sup_hom_apply -> UpperSet.iciSupHom_apply is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α] (a : α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (SupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α _inst_1) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) (fun (_x : SupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α _inst_1) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) => α -> (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) (SupHom.hasCoeToFun.{u1, u1} α (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α _inst_1) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) (UpperSet.iciSupHom.{u1} α _inst_1) a) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) a)
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α] (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Order.Hom.Lattice._hyg.2625 : α) => UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (SupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α _inst_1) (UpperSet.instSupUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.2625 : α) => UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _x) (SupHom.instFunLikeSupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α _inst_1) (UpperSet.instSupUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))) (UpperSet.iciSupHom.{u1} α _inst_1) a) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) a)
+Case conversion may be inaccurate. Consider using '#align upper_set.Ici_sup_hom_apply UpperSet.iciSupHom_applyₓ'. -/
@[simp]
theorem iciSupHom_apply (a : α) : iciSupHom a = Ici a :=
rfl
#align upper_set.Ici_sup_hom_apply UpperSet.iciSupHom_apply
--/
end SemilatticeSup
@@ -86,7 +94,7 @@ variable [SemilatticeInf α]
/- warning: lower_set.Iic_inf_hom -> LowerSet.iicInfHom is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α], InfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toHasInf.{u1} α _inst_1) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α], InfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toHasInf.{u1} α _inst_1) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α], InfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toInf.{u1} α _inst_1) (LowerSet.instInfLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align lower_set.Iic_inf_hom LowerSet.iicInfHomₓ'. -/
@@ -95,19 +103,27 @@ def iicInfHom : InfHom α (LowerSet α) :=
⟨Iic, Iic_inf⟩
#align lower_set.Iic_inf_hom LowerSet.iicInfHom
-#print LowerSet.coe_iicInfHom /-
+/- warning: lower_set.coe_Iic_inf_hom -> LowerSet.coe_iicInfHom is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α], Eq.{succ u1} ((fun (_x : InfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toHasInf.{u1} α _inst_1) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))) => α -> (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))) (LowerSet.iicInfHom.{u1} α _inst_1)) (coeFn.{succ u1, succ u1} (InfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toHasInf.{u1} α _inst_1) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))) (fun (_x : InfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toHasInf.{u1} α _inst_1) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))) => α -> (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))) (InfHom.hasCoeToFun.{u1, u1} α (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toHasInf.{u1} α _inst_1) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))) (LowerSet.iicInfHom.{u1} α _inst_1)) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α], Eq.{succ u1} (forall (a : α), (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.4234 : α) => LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (InfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toInf.{u1} α _inst_1) (LowerSet.instInfLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.4234 : α) => LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) _x) (InfHom.instFunLikeInfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toInf.{u1} α _inst_1) (LowerSet.instInfLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))) (LowerSet.iicInfHom.{u1} α _inst_1)) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align lower_set.coe_Iic_inf_hom LowerSet.coe_iicInfHomₓ'. -/
@[simp]
theorem coe_iicInfHom : (iicInfHom : α → LowerSet α) = Iic :=
rfl
#align lower_set.coe_Iic_inf_hom LowerSet.coe_iicInfHom
--/
-#print LowerSet.iicInfHom_apply /-
+/- warning: lower_set.Iic_inf_hom_apply -> LowerSet.iicInfHom_apply is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] (a : α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (coeFn.{succ u1, succ u1} (InfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toHasInf.{u1} α _inst_1) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))) (fun (_x : InfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toHasInf.{u1} α _inst_1) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))) => α -> (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))) (InfHom.hasCoeToFun.{u1, u1} α (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toHasInf.{u1} α _inst_1) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))) (LowerSet.iicInfHom.{u1} α _inst_1) a) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) a)
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Order.Hom.Lattice._hyg.4234 : α) => LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) a) (FunLike.coe.{succ u1, succ u1, succ u1} (InfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toInf.{u1} α _inst_1) (LowerSet.instInfLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.4234 : α) => LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) _x) (InfHom.instFunLikeInfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toInf.{u1} α _inst_1) (LowerSet.instInfLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))) (LowerSet.iicInfHom.{u1} α _inst_1) a) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) a)
+Case conversion may be inaccurate. Consider using '#align lower_set.Iic_inf_hom_apply LowerSet.iicInfHom_applyₓ'. -/
@[simp]
theorem iicInfHom_apply (a : α) : iicInfHom a = Iic a :=
rfl
#align lower_set.Iic_inf_hom_apply LowerSet.iicInfHom_apply
--/
end SemilatticeInf
mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee
@@ -62,19 +62,19 @@ end SemilatticeSup
variable [CompleteLattice α]
/-- `upper_set.Ici` as a `Sup_hom`. -/
-def iciSupₛHom : SupₛHom α (UpperSet α) :=
- ⟨Ici, fun s => (Ici_supₛ s).trans supₛ_image.symm⟩
-#align upper_set.Ici_Sup_hom UpperSet.iciSupₛHomₓ
+def icisSupHom : sSupHom α (UpperSet α) :=
+ ⟨Ici, fun s => (Ici_sSup s).trans sSup_image.symm⟩
+#align upper_set.Ici_Sup_hom UpperSet.icisSupHomₓ
@[simp]
-theorem coe_iciSupₛHom : (iciSupₛHom : α → UpperSet α) = Ici :=
+theorem coe_icisSupHom : (icisSupHom : α → UpperSet α) = Ici :=
rfl
-#align upper_set.coe_Ici_Sup_hom UpperSet.coe_iciSupₛHomₓ
+#align upper_set.coe_Ici_Sup_hom UpperSet.coe_icisSupHomₓ
@[simp]
-theorem iciSupₛHom_apply (a : α) : iciSupₛHom a = Ici a :=
+theorem icisSupHom_apply (a : α) : icisSupHom a = Ici a :=
rfl
-#align upper_set.Ici_Sup_hom_apply UpperSet.iciSupₛHom_applyₓ
+#align upper_set.Ici_Sup_hom_apply UpperSet.icisSupHom_applyₓ
end UpperSet
@@ -114,19 +114,19 @@ end SemilatticeInf
variable [CompleteLattice α]
/-- `lower_set.Iic` as an `Inf_hom`. -/
-def iicInfₛHom : InfₛHom α (LowerSet α) :=
- ⟨Iic, fun s => (Iic_infₛ s).trans infₛ_image.symm⟩
-#align lower_set.Iic_Inf_hom LowerSet.iicInfₛHomₓ
+def iicsInfHom : sInfHom α (LowerSet α) :=
+ ⟨Iic, fun s => (Iic_sInf s).trans sInf_image.symm⟩
+#align lower_set.Iic_Inf_hom LowerSet.iicsInfHomₓ
@[simp]
-theorem coe_iicInfₛHom : (iicInfₛHom : α → LowerSet α) = Iic :=
+theorem coe_iicsInfHom : (iicsInfHom : α → LowerSet α) = Iic :=
rfl
-#align lower_set.coe_Iic_Inf_hom LowerSet.coe_iicInfₛHomₓ
+#align lower_set.coe_Iic_Inf_hom LowerSet.coe_iicsInfHomₓ
@[simp]
-theorem iicInfₛHom_apply (a : α) : iicInfₛHom a = Iic a :=
+theorem iicsInfHom_apply (a : α) : iicsInfHom a = Iic a :=
rfl
-#align lower_set.Iic_Inf_hom_apply LowerSet.iicInfₛHom_applyₓ
+#align lower_set.Iic_Inf_hom_apply LowerSet.iicsInfHom_applyₓ
end LowerSet
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -36,7 +36,7 @@ variable [SemilatticeSup α]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α], SupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α _inst_1) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α], SupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α _inst_1) (UpperSet.instHasSupUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α], SupHom.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α _inst_1) (UpperSet.instSupUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align upper_set.Ici_sup_hom UpperSet.iciSupHomₓ'. -/
/-- `upper_set.Ici` as a `sup_hom`. -/
def iciSupHom : SupHom α (UpperSet α) :=
@@ -88,7 +88,7 @@ variable [SemilatticeInf α]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α], InfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toHasInf.{u1} α _inst_1) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α], InfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toHasInf.{u1} α _inst_1) (LowerSet.instHasInfLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α], InfHom.{u1, u1} α (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (SemilatticeInf.toInf.{u1} α _inst_1) (LowerSet.instInfLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align lower_set.Iic_inf_hom LowerSet.iicInfHomₓ'. -/
/-- `lower_set.Iic` as an `inf_hom`. -/
def iicInfHom : InfHom α (LowerSet α) :=
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.
@@ -16,7 +16,7 @@ In this file we define `UpperSet.iciSupHom` etc. These functions are `UpperSet.I
-/
-variable {α : Type _}
+variable {α : Type*}
open OrderDual
@@ -2,15 +2,12 @@
Copyright (c) 2022 Yaël Dillies, Sara Rousta. 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 order.upper_lower.hom
-! leanprover-community/mathlib commit 0a0ec35061ed9960bf0e7ffb0335f44447b58977
-! 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.Order.Hom.CompleteLattice
+#align_import order.upper_lower.hom from "leanprover-community/mathlib"@"0a0ec35061ed9960bf0e7ffb0335f44447b58977"
+
/-!
# `UpperSet.Ici` etc as `Sup`/`sSup`/`Inf`/`sInf`-homomorphisms
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>
@@ -12,10 +12,10 @@ import Mathlib.Order.UpperLower.Basic
import Mathlib.Order.Hom.CompleteLattice
/-!
-# `UpperSet.Ici` etc as `Sup`/`Supₛ`/`Inf`/`Infₛ`-homomorphisms
+# `UpperSet.Ici` etc as `Sup`/`sSup`/`Inf`/`sInf`-homomorphisms
In this file we define `UpperSet.iciSupHom` etc. These functions are `UpperSet.Ici` and
-`LowerSet.Iic` bundled as `SupHom`s, `InfHom`s, `SupₛHom`s, or `InfₛHom`s.
+`LowerSet.Iic` bundled as `SupHom`s, `InfHom`s, `sSupHom`s, or `sInfHom`s.
-/
@@ -48,23 +48,23 @@ end SemilatticeSup
variable [CompleteLattice α]
-/-- `UpperSet.Ici` as a `SupₛHom`. -/
-def iciSupₛHom : SupₛHom α (UpperSet α) :=
- ⟨Ici, fun s => (Ici_supₛ s).trans supₛ_image.symm⟩
+/-- `UpperSet.Ici` as a `sSupHom`. -/
+def icisSupHom : sSupHom α (UpperSet α) :=
+ ⟨Ici, fun s => (Ici_sSup s).trans sSup_image.symm⟩
-- Porting note: `ₓ` because typeclass assumption changed
-#align upper_set.Ici_Sup_hom UpperSet.iciSupₛHomₓ
+#align upper_set.Ici_Sup_hom UpperSet.icisSupHomₓ
@[simp]
-theorem coe_iciSupₛHom : (iciSupₛHom : α → UpperSet α) = Ici :=
+theorem coe_icisSupHom : (icisSupHom : α → UpperSet α) = Ici :=
rfl
-- Porting note: `ₓ` because typeclass assumption changed
-#align upper_set.coe_Ici_Sup_hom UpperSet.coe_iciSupₛHomₓ
+#align upper_set.coe_Ici_Sup_hom UpperSet.coe_icisSupHomₓ
@[simp]
-theorem iciSupₛHom_apply (a : α) : iciSupₛHom a = Ici a :=
+theorem icisSupHom_apply (a : α) : icisSupHom a = Ici a :=
rfl
-- Porting note: `ₓ` because typeclass assumption changed
-#align upper_set.Ici_Sup_hom_apply UpperSet.iciSupₛHom_applyₓ
+#align upper_set.Ici_Sup_hom_apply UpperSet.icisSupHom_applyₓ
end UpperSet
@@ -93,22 +93,22 @@ end SemilatticeInf
variable [CompleteLattice α]
-/-- `LowerSet.Iic` as an `InfₛHom`. -/
-def iicInfₛHom : InfₛHom α (LowerSet α) :=
- ⟨Iic, fun s => (Iic_infₛ s).trans infₛ_image.symm⟩
+/-- `LowerSet.Iic` as an `sInfHom`. -/
+def iicsInfHom : sInfHom α (LowerSet α) :=
+ ⟨Iic, fun s => (Iic_sInf s).trans sInf_image.symm⟩
-- Porting note: `ₓ` because typeclass assumption changed
-#align lower_set.Iic_Inf_hom LowerSet.iicInfₛHomₓ
+#align lower_set.Iic_Inf_hom LowerSet.iicsInfHomₓ
@[simp]
-theorem coe_iicInfₛHom : (iicInfₛHom : α → LowerSet α) = Iic :=
+theorem coe_iicsInfHom : (iicsInfHom : α → LowerSet α) = Iic :=
rfl
-- Porting note: `ₓ` because typeclass assumption changed
-#align lower_set.coe_Iic_Inf_hom LowerSet.coe_iicInfₛHomₓ
+#align lower_set.coe_Iic_Inf_hom LowerSet.coe_iicsInfHomₓ
@[simp]
-theorem iicInfₛHom_apply (a : α) : iicInfₛHom a = Iic a :=
+theorem iicsInfHom_apply (a : α) : iicsInfHom a = Iic a :=
rfl
-- Porting note: `ₓ` because typeclass assumption changed
-#align lower_set.Iic_Inf_hom_apply LowerSet.iicInfₛHom_applyₓ
+#align lower_set.Iic_Inf_hom_apply LowerSet.iicsInfHom_applyₓ
end LowerSet
All dependencies are ported!