order.rel_iso.set
⟷
Mathlib.Order.RelIso.Set
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
@@ -34,7 +34,7 @@ variable {F : Type _}
theorem map_inf [SemilatticeInf α] [LinearOrder β]
[RelHomClass F ((· < ·) : β → β → Prop) ((· < ·) : α → α → Prop)] (a : F) (m n : β) :
a (m ⊓ n) = a m ⊓ a n :=
- (StrictMono.monotone fun x y => map_rel a).map_inf m n
+ (StrictMono.monotone fun x y => mapRel a).map_inf m n
#align rel_hom_class.map_inf RelHomClass.map_inf
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
-import Mathbin.Order.RelIso.Basic
-import Mathbin.Logic.Embedding.Set
+import Order.RelIso.Basic
+import Logic.Embedding.Set
#align_import order.rel_iso.set from "leanprover-community/mathlib"@"448144f7ae193a8990cb7473c9e9a01990f64ac7"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-
-! This file was ported from Lean 3 source module order.rel_iso.set
-! leanprover-community/mathlib commit 448144f7ae193a8990cb7473c9e9a01990f64ac7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Order.RelIso.Basic
import Mathbin.Logic.Embedding.Set
+#align_import order.rel_iso.set from "leanprover-community/mathlib"@"448144f7ae193a8990cb7473c9e9a01990f64ac7"
+
/-!
# Interactions between relation homomorphisms and sets
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -33,26 +33,32 @@ namespace RelHomClass
variable {F : Type _}
+#print RelHomClass.map_inf /-
theorem map_inf [SemilatticeInf α] [LinearOrder β]
[RelHomClass F ((· < ·) : β → β → Prop) ((· < ·) : α → α → Prop)] (a : F) (m n : β) :
a (m ⊓ n) = a m ⊓ a n :=
(StrictMono.monotone fun x y => map_rel a).map_inf m n
#align rel_hom_class.map_inf RelHomClass.map_inf
+-/
+#print RelHomClass.map_sup /-
theorem map_sup [SemilatticeSup α] [LinearOrder β]
[RelHomClass F ((· > ·) : β → β → Prop) ((· > ·) : α → α → Prop)] (a : F) (m n : β) :
a (m ⊔ n) = a m ⊔ a n :=
@map_inf αᵒᵈ βᵒᵈ _ _ _ _ _ _ _
#align rel_hom_class.map_sup RelHomClass.map_sup
+-/
end RelHomClass
namespace RelIso
+#print RelIso.range_eq /-
@[simp]
theorem range_eq (e : r ≃r s) : Set.range e = Set.univ :=
e.Surjective.range_eq
#align rel_iso.range_eq RelIso.range_eq
+-/
end RelIso
@@ -79,10 +85,12 @@ protected def relEmbedding (r : α → α → Prop) (p : Set α) : Subrel r p
#align subrel.rel_embedding Subrel.relEmbedding
-/
+#print Subrel.relEmbedding_apply /-
@[simp]
theorem relEmbedding_apply (r : α → α → Prop) (p a) : Subrel.relEmbedding r p a = a.1 :=
rfl
#align subrel.rel_embedding_apply Subrel.relEmbedding_apply
+-/
instance (r : α → α → Prop) [IsWellOrder α r] (p : Set α) : IsWellOrder p (Subrel r p) :=
RelEmbedding.isWellOrder (Subrel.relEmbedding r p)
@@ -101,14 +109,18 @@ instance (r : α → α → Prop) [IsIrrefl α r] (p : Set α) : IsIrrefl p (Sub
end Subrel
+#print RelEmbedding.codRestrict /-
/-- Restrict the codomain of a relation embedding. -/
def RelEmbedding.codRestrict (p : Set β) (f : r ↪r s) (H : ∀ a, f a ∈ p) : r ↪r Subrel s p :=
⟨f.toEmbedding.codRestrict p H, fun _ _ => f.map_rel_iff'⟩
#align rel_embedding.cod_restrict RelEmbedding.codRestrict
+-/
+#print RelEmbedding.codRestrict_apply /-
@[simp]
theorem RelEmbedding.codRestrict_apply (p) (f : r ↪r s) (H a) :
RelEmbedding.codRestrict p f H a = ⟨f a, H a⟩ :=
rfl
#align rel_embedding.cod_restrict_apply RelEmbedding.codRestrict_apply
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -33,24 +33,12 @@ namespace RelHomClass
variable {F : Type _}
-/- warning: rel_hom_class.map_inf -> RelHomClass.map_inf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align rel_hom_class.map_inf RelHomClass.map_infₓ'. -/
theorem map_inf [SemilatticeInf α] [LinearOrder β]
[RelHomClass F ((· < ·) : β → β → Prop) ((· < ·) : α → α → Prop)] (a : F) (m n : β) :
a (m ⊓ n) = a m ⊓ a n :=
(StrictMono.monotone fun x y => map_rel a).map_inf m n
#align rel_hom_class.map_inf RelHomClass.map_inf
-/- warning: rel_hom_class.map_sup -> RelHomClass.map_sup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align rel_hom_class.map_sup RelHomClass.map_supₓ'. -/
theorem map_sup [SemilatticeSup α] [LinearOrder β]
[RelHomClass F ((· > ·) : β → β → Prop) ((· > ·) : α → α → Prop)] (a : F) (m n : β) :
a (m ⊔ n) = a m ⊔ a n :=
@@ -61,12 +49,6 @@ end RelHomClass
namespace RelIso
-/- warning: rel_iso.range_eq -> RelIso.range_eq is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align rel_iso.range_eq RelIso.range_eqₓ'. -/
@[simp]
theorem range_eq (e : r ≃r s) : Set.range e = Set.univ :=
e.Surjective.range_eq
@@ -97,12 +79,6 @@ protected def relEmbedding (r : α → α → Prop) (p : Set α) : Subrel r p
#align subrel.rel_embedding Subrel.relEmbedding
-/
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@[simp]
theorem relEmbedding_apply (r : α → α → Prop) (p a) : Subrel.relEmbedding r p a = a.1 :=
rfl
@@ -125,23 +101,11 @@ instance (r : α → α → Prop) [IsIrrefl α r] (p : Set α) : IsIrrefl p (Sub
end Subrel
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/-- Restrict the codomain of a relation embedding. -/
def RelEmbedding.codRestrict (p : Set β) (f : r ↪r s) (H : ∀ a, f a ∈ p) : r ↪r Subrel s p :=
⟨f.toEmbedding.codRestrict p H, fun _ _ => f.map_rel_iff'⟩
#align rel_embedding.cod_restrict RelEmbedding.codRestrict
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@[simp]
theorem RelEmbedding.codRestrict_apply (p) (f : r ↪r s) (H a) :
RelEmbedding.codRestrict p f H a = ⟨f a, H a⟩ :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4
@@ -37,7 +37,7 @@ variable {F : Type _}
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but is expected to have type
- forall {α : Type.{u3}} {β : Type.{u2}} {F : Type.{u1}} [_inst_1 : SemilatticeInf.{u3} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (x._@.Mathlib.Order.RelIso.Set._hyg.133 : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) x._@.Mathlib.Order.RelIso.Set._hyg.133 x._@.Mathlib.Order.RelIso.Set._hyg.135)] (a : F) (m : β) (n : β), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Inf.inf.{u2} β (Lattice.toInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2))) m n)) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.135) _inst_3) a (Inf.inf.{u2} β (Lattice.toInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2))) m n)) (Inf.inf.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) (SemilatticeInf.toInf.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) _inst_1) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.135) _inst_3) a m) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.135) _inst_3) a n))
+ forall {α : Type.{u3}} {β : Type.{u2}} {F : Type.{u1}} [_inst_1 : SemilatticeInf.{u3} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (x._@.Mathlib.Order.RelIso.Set._hyg.133 : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) x._@.Mathlib.Order.RelIso.Set._hyg.133 x._@.Mathlib.Order.RelIso.Set._hyg.135)] (a : F) (m : β) (n : β), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) (Inf.inf.{u2} β (Lattice.toInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2))) m n)) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.135) _inst_3) a (Inf.inf.{u2} β (Lattice.toInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2))) m n)) (Inf.inf.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) m) (SemilatticeInf.toInf.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) m) _inst_1) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.135) _inst_3) a m) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.135) _inst_3) a n))
Case conversion may be inaccurate. Consider using '#align rel_hom_class.map_inf RelHomClass.map_infₓ'. -/
theorem map_inf [SemilatticeInf α] [LinearOrder β]
[RelHomClass F ((· < ·) : β → β → Prop) ((· < ·) : α → α → Prop)] (a : F) (m n : β) :
@@ -49,7 +49,7 @@ theorem map_inf [SemilatticeInf α] [LinearOrder β]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {F : Type.{u3}} [_inst_1 : SemilatticeSup.{u1} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))] (a : F) (m : β) (n : β), Eq.{succ u1} α (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a (Sup.sup.{u2} β (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))) m n)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a m) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a n))
but is expected to have type
- forall {α : Type.{u3}} {β : Type.{u2}} {F : Type.{u1}} [_inst_1 : SemilatticeSup.{u3} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.228 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.230 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.228 x._@.Mathlib.Order.RelIso.Set._hyg.230) (fun (x._@.Mathlib.Order.RelIso.Set._hyg.250 : α) (x._@.Mathlib.Order.RelIso.Set._hyg.252 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) x._@.Mathlib.Order.RelIso.Set._hyg.250 x._@.Mathlib.Order.RelIso.Set._hyg.252)] (a : F) (m : β) (n : β), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Sup.sup.{u2} β (SemilatticeSup.toSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))) m n)) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.228 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.230 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.228 x._@.Mathlib.Order.RelIso.Set._hyg.230) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.252 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.252) _inst_3) a (Sup.sup.{u2} β (SemilatticeSup.toSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))) m n)) (Sup.sup.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) (SemilatticeSup.toSup.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) _inst_1) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.228 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.230 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.228 x._@.Mathlib.Order.RelIso.Set._hyg.230) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.252 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.252) _inst_3) a m) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.228 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.230 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.228 x._@.Mathlib.Order.RelIso.Set._hyg.230) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.252 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.252) _inst_3) a n))
+ forall {α : Type.{u3}} {β : Type.{u2}} {F : Type.{u1}} [_inst_1 : SemilatticeSup.{u3} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.228 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.230 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.228 x._@.Mathlib.Order.RelIso.Set._hyg.230) (fun (x._@.Mathlib.Order.RelIso.Set._hyg.250 : α) (x._@.Mathlib.Order.RelIso.Set._hyg.252 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) x._@.Mathlib.Order.RelIso.Set._hyg.250 x._@.Mathlib.Order.RelIso.Set._hyg.252)] (a : F) (m : β) (n : β), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) (Sup.sup.{u2} β (SemilatticeSup.toSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))) m n)) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.228 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.230 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.228 x._@.Mathlib.Order.RelIso.Set._hyg.230) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.252 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.252) _inst_3) a (Sup.sup.{u2} β (SemilatticeSup.toSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))) m n)) (Sup.sup.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) m) (SemilatticeSup.toSup.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) m) _inst_1) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.228 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.230 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.228 x._@.Mathlib.Order.RelIso.Set._hyg.230) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.252 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.252) _inst_3) a m) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.228 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.230 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.228 x._@.Mathlib.Order.RelIso.Set._hyg.230) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.252 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.252) _inst_3) a n))
Case conversion may be inaccurate. Consider using '#align rel_hom_class.map_sup RelHomClass.map_supₓ'. -/
theorem map_sup [SemilatticeSup α] [LinearOrder β]
[RelHomClass F ((· > ·) : β → β → Prop) ((· > ·) : α → α → Prop)] (a : F) (m n : β) :
@@ -101,7 +101,7 @@ protected def relEmbedding (r : α → α → Prop) (p : Set α) : Subrel r p
lean 3 declaration is
forall {α : Type.{u1}} (r : α -> α -> Prop) (p : Set.{u1} α) (a : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) p), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (RelEmbedding.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) p) α (Subrel.{u1} α r p) r) (fun (_x : RelEmbedding.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) p) α (Subrel.{u1} α r p) r) => (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) p) -> α) (RelEmbedding.hasCoeToFun.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) p) α (Subrel.{u1} α r p) r) (Subrel.relEmbedding.{u1} α r p) a) (Subtype.val.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x p) a)
but is expected to have type
- forall {α : Type.{u1}} (r : α -> α -> Prop) (p : Set.{u1} α) (a : Set.Elem.{u1} α p), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Set.Elem.{u1} α p) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (RelEmbedding.{u1, u1} (Set.Elem.{u1} α p) α (Subrel.{u1} α r p) r) (Set.Elem.{u1} α p) (fun (_x : Set.Elem.{u1} α p) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Set.Elem.{u1} α p) => α) _x) (RelHomClass.toFunLike.{u1, u1, u1} (RelEmbedding.{u1, u1} (Set.Elem.{u1} α p) α (Subrel.{u1} α r p) r) (Set.Elem.{u1} α p) α (Subrel.{u1} α r p) r (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Set.Elem.{u1} α p) α (Subrel.{u1} α r p) r)) (Subrel.relEmbedding.{u1} α r p) a) (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x p) a)
+ forall {α : Type.{u1}} (r : α -> α -> Prop) (p : Set.{u1} α) (a : Set.Elem.{u1} α p), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Set.Elem.{u1} α p) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (RelEmbedding.{u1, u1} (Set.Elem.{u1} α p) α (Subrel.{u1} α r p) r) (Set.Elem.{u1} α p) (fun (_x : Set.Elem.{u1} α p) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Set.Elem.{u1} α p) => α) _x) (RelHomClass.toFunLike.{u1, u1, u1} (RelEmbedding.{u1, u1} (Set.Elem.{u1} α p) α (Subrel.{u1} α r p) r) (Set.Elem.{u1} α p) α (Subrel.{u1} α r p) r (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Set.Elem.{u1} α p) α (Subrel.{u1} α r p) r)) (Subrel.relEmbedding.{u1} α r p) a) (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x p) a)
Case conversion may be inaccurate. Consider using '#align subrel.rel_embedding_apply Subrel.relEmbedding_applyₓ'. -/
@[simp]
theorem relEmbedding_apply (r : α → α → Prop) (p a) : Subrel.relEmbedding r p a = a.1 :=
@@ -129,7 +129,7 @@ end Subrel
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {s : β -> β -> Prop} (p : Set.{u2} β) (f : RelEmbedding.{u1, u2} α β r s), (forall (a : α), Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RelEmbedding.{u1, u2} α β r s) (fun (_x : RelEmbedding.{u1, u2} α β r s) => α -> β) (RelEmbedding.hasCoeToFun.{u1, u2} α β r s) f a) p) -> (RelEmbedding.{u1, u2} α (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) p) r (Subrel.{u2} β s p))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {s : β -> β -> Prop} (p : Set.{u2} β) (f : RelEmbedding.{u1, u2} α β r s), (forall (a : α), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => β) a) (Set.{u2} β) (Set.instMembershipSet.{u2} β) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelEmbedding.{u1, u2} α β r s) α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => β) _x) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelEmbedding.{u1, u2} α β r s) α β r s (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} α β r s)) f a) p) -> (RelEmbedding.{u1, u2} α (Set.Elem.{u2} β p) r (Subrel.{u2} β s p))
+ forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {s : β -> β -> Prop} (p : Set.{u2} β) (f : RelEmbedding.{u1, u2} α β r s), (forall (a : α), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : α) => β) a) (Set.{u2} β) (Set.instMembershipSet.{u2} β) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelEmbedding.{u1, u2} α β r s) α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : α) => β) _x) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelEmbedding.{u1, u2} α β r s) α β r s (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} α β r s)) f a) p) -> (RelEmbedding.{u1, u2} α (Set.Elem.{u2} β p) r (Subrel.{u2} β s p))
Case conversion may be inaccurate. Consider using '#align rel_embedding.cod_restrict RelEmbedding.codRestrictₓ'. -/
/-- Restrict the codomain of a relation embedding. -/
def RelEmbedding.codRestrict (p : Set β) (f : r ↪r s) (H : ∀ a, f a ∈ p) : r ↪r Subrel s p :=
@@ -140,7 +140,7 @@ def RelEmbedding.codRestrict (p : Set β) (f : r ↪r s) (H : ∀ a, f a ∈ p)
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {s : β -> β -> Prop} (p : Set.{u2} β) (f : RelEmbedding.{u1, u2} α β r s) (H : forall (a : α), Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RelEmbedding.{u1, u2} α β r s) (fun (_x : RelEmbedding.{u1, u2} α β r s) => α -> β) (RelEmbedding.hasCoeToFun.{u1, u2} α β r s) f a) p) (a : α), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) p) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RelEmbedding.{u1, u2} α (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) p) r (Subrel.{u2} β s p)) (fun (_x : RelEmbedding.{u1, u2} α (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) p) r (Subrel.{u2} β s p)) => α -> (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) p)) (RelEmbedding.hasCoeToFun.{u1, u2} α (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) p) r (Subrel.{u2} β s p)) (RelEmbedding.codRestrict.{u1, u2} α β r s p f H) a) (Subtype.mk.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x p) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RelEmbedding.{u1, u2} α β r s) (fun (_x : RelEmbedding.{u1, u2} α β r s) => α -> β) (RelEmbedding.hasCoeToFun.{u1, u2} α β r s) f a) (H a))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {s : β -> β -> Prop} (p : Set.{u2} β) (f : RelEmbedding.{u1, u2} α β r s) (H : forall (a : α), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => β) a) (Set.{u2} β) (Set.instMembershipSet.{u2} β) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelEmbedding.{u1, u2} α β r s) α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => β) _x) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelEmbedding.{u1, u2} α β r s) α β r s (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} α β r s)) f a) p) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => Set.Elem.{u2} β p) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelEmbedding.{u1, u2} α (Set.Elem.{u2} β p) r (Subrel.{u2} β s p)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => Set.Elem.{u2} β p) _x) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelEmbedding.{u1, u2} α (Set.Elem.{u2} β p) r (Subrel.{u2} β s p)) α (Set.Elem.{u2} β p) r (Subrel.{u2} β s p) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} α (Set.Elem.{u2} β p) r (Subrel.{u2} β s p))) (RelEmbedding.codRestrict.{u1, u2} α β r s p f H) a) (Subtype.mk.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x p) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelEmbedding.{u1, u2} α β r s) α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => β) _x) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelEmbedding.{u1, u2} α β r s) α β r s (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} α β r s)) f a) (H a))
+ forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {s : β -> β -> Prop} (p : Set.{u2} β) (f : RelEmbedding.{u1, u2} α β r s) (H : forall (a : α), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : α) => β) a) (Set.{u2} β) (Set.instMembershipSet.{u2} β) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelEmbedding.{u1, u2} α β r s) α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : α) => β) _x) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelEmbedding.{u1, u2} α β r s) α β r s (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} α β r s)) f a) p) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : α) => Set.Elem.{u2} β p) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelEmbedding.{u1, u2} α (Set.Elem.{u2} β p) r (Subrel.{u2} β s p)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : α) => Set.Elem.{u2} β p) _x) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelEmbedding.{u1, u2} α (Set.Elem.{u2} β p) r (Subrel.{u2} β s p)) α (Set.Elem.{u2} β p) r (Subrel.{u2} β s p) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} α (Set.Elem.{u2} β p) r (Subrel.{u2} β s p))) (RelEmbedding.codRestrict.{u1, u2} α β r s p f H) a) (Subtype.mk.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x p) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelEmbedding.{u1, u2} α β r s) α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : α) => β) _x) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelEmbedding.{u1, u2} α β r s) α β r s (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} α β r s)) f a) (H a))
Case conversion may be inaccurate. Consider using '#align rel_embedding.cod_restrict_apply RelEmbedding.codRestrict_applyₓ'. -/
@[simp]
theorem RelEmbedding.codRestrict_apply (p) (f : r ↪r s) (H a) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -35,7 +35,7 @@ variable {F : Type _}
/- warning: rel_hom_class.map_inf -> RelHomClass.map_inf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {F : Type.{u3}} [_inst_1 : SemilatticeInf.{u1} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u3, u2, u1} F β α (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))] (a : F) (m : β) (n : β), Eq.{succ u1} α (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a (Inf.inf.{u2} β (SemilatticeInf.toHasInf.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))) m n)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a m) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a n))
+ forall {α : Type.{u1}} {β : Type.{u2}} {F : Type.{u3}} [_inst_1 : SemilatticeInf.{u1} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u3, u2, u1} F β α (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))] (a : F) (m : β) (n : β), Eq.{succ u1} α (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a (Inf.inf.{u2} β (SemilatticeInf.toHasInf.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))) m n)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a m) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a n))
but is expected to have type
forall {α : Type.{u3}} {β : Type.{u2}} {F : Type.{u1}} [_inst_1 : SemilatticeInf.{u3} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (x._@.Mathlib.Order.RelIso.Set._hyg.133 : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) x._@.Mathlib.Order.RelIso.Set._hyg.133 x._@.Mathlib.Order.RelIso.Set._hyg.135)] (a : F) (m : β) (n : β), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Inf.inf.{u2} β (Lattice.toInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2))) m n)) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.135) _inst_3) a (Inf.inf.{u2} β (Lattice.toInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2))) m n)) (Inf.inf.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) (SemilatticeInf.toInf.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) _inst_1) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.135) _inst_3) a m) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.135) _inst_3) a n))
Case conversion may be inaccurate. Consider using '#align rel_hom_class.map_inf RelHomClass.map_infₓ'. -/
@@ -47,7 +47,7 @@ theorem map_inf [SemilatticeInf α] [LinearOrder β]
/- warning: rel_hom_class.map_sup -> RelHomClass.map_sup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {F : Type.{u3}} [_inst_1 : SemilatticeSup.{u1} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))] (a : F) (m : β) (n : β), Eq.{succ u1} α (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a (Sup.sup.{u2} β (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))) m n)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a m) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a n))
+ forall {α : Type.{u1}} {β : Type.{u2}} {F : Type.{u3}} [_inst_1 : SemilatticeSup.{u1} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))] (a : F) (m : β) (n : β), Eq.{succ u1} α (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a (Sup.sup.{u2} β (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))) m n)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a m) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a n))
but is expected to have type
forall {α : Type.{u3}} {β : Type.{u2}} {F : Type.{u1}} [_inst_1 : SemilatticeSup.{u3} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.228 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.230 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.228 x._@.Mathlib.Order.RelIso.Set._hyg.230) (fun (x._@.Mathlib.Order.RelIso.Set._hyg.250 : α) (x._@.Mathlib.Order.RelIso.Set._hyg.252 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) x._@.Mathlib.Order.RelIso.Set._hyg.250 x._@.Mathlib.Order.RelIso.Set._hyg.252)] (a : F) (m : β) (n : β), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Sup.sup.{u2} β (SemilatticeSup.toSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))) m n)) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.228 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.230 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.228 x._@.Mathlib.Order.RelIso.Set._hyg.230) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.252 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.252) _inst_3) a (Sup.sup.{u2} β (SemilatticeSup.toSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))) m n)) (Sup.sup.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) (SemilatticeSup.toSup.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) _inst_1) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.228 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.230 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.228 x._@.Mathlib.Order.RelIso.Set._hyg.230) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.252 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.252) _inst_3) a m) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.228 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.230 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.228 x._@.Mathlib.Order.RelIso.Set._hyg.230) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.252 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.252) _inst_3) a n))
Case conversion may be inaccurate. Consider using '#align rel_hom_class.map_sup RelHomClass.map_supₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba
@@ -65,7 +65,7 @@ namespace RelIso
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {s : β -> β -> Prop} (e : RelIso.{u1, u2} α β r s), Eq.{succ u2} (Set.{u2} β) (Set.range.{u2, succ u1} β α (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RelIso.{u1, u2} α β r s) (fun (_x : RelIso.{u1, u2} α β r s) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β r s) e)) (Set.univ.{u2} β)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} (e : RelIso.{u2, u1} α β r s), Eq.{succ u1} (Set.{u1} β) (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) (RelEmbedding.toEmbedding.{u2, u1} α β r s (RelIso.toRelEmbedding.{u2, u1} α β r s e)))) (Set.univ.{u1} β)
+ forall {α : Type.{u2}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} (e : RelIso.{u2, u1} α β r s), Eq.{succ u1} (Set.{u1} β) (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β r s) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β r s) α β r s (RelIso.instRelHomClassRelIso.{u2, u1} α β r s)) e)) (Set.univ.{u1} β)
Case conversion may be inaccurate. Consider using '#align rel_iso.range_eq RelIso.range_eqₓ'. -/
@[simp]
theorem range_eq (e : r ≃r s) : Set.range e = Set.univ :=
@@ -101,7 +101,7 @@ protected def relEmbedding (r : α → α → Prop) (p : Set α) : Subrel r p
lean 3 declaration is
forall {α : Type.{u1}} (r : α -> α -> Prop) (p : Set.{u1} α) (a : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) p), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (RelEmbedding.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) p) α (Subrel.{u1} α r p) r) (fun (_x : RelEmbedding.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) p) α (Subrel.{u1} α r p) r) => (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) p) -> α) (RelEmbedding.hasCoeToFun.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) p) α (Subrel.{u1} α r p) r) (Subrel.relEmbedding.{u1} α r p) a) (Subtype.val.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x p) a)
but is expected to have type
- forall {α : Type.{u1}} (r : α -> α -> Prop) (p : Set.{u1} α) (a : Set.Elem.{u1} α p), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u1} α p) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Set.Elem.{u1} α p) α) (Set.Elem.{u1} α p) (fun (_x : Set.Elem.{u1} α p) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u1} α p) => α) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Set.Elem.{u1} α p) α) (Set.Elem.{u1} α p) α (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (Set.Elem.{u1} α p) α)) (RelEmbedding.toEmbedding.{u1, u1} (Set.Elem.{u1} α p) α (Subrel.{u1} α r p) r (Subrel.relEmbedding.{u1} α r p)) a) (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x p) a)
+ forall {α : Type.{u1}} (r : α -> α -> Prop) (p : Set.{u1} α) (a : Set.Elem.{u1} α p), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Set.Elem.{u1} α p) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (RelEmbedding.{u1, u1} (Set.Elem.{u1} α p) α (Subrel.{u1} α r p) r) (Set.Elem.{u1} α p) (fun (_x : Set.Elem.{u1} α p) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Set.Elem.{u1} α p) => α) _x) (RelHomClass.toFunLike.{u1, u1, u1} (RelEmbedding.{u1, u1} (Set.Elem.{u1} α p) α (Subrel.{u1} α r p) r) (Set.Elem.{u1} α p) α (Subrel.{u1} α r p) r (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Set.Elem.{u1} α p) α (Subrel.{u1} α r p) r)) (Subrel.relEmbedding.{u1} α r p) a) (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x p) a)
Case conversion may be inaccurate. Consider using '#align subrel.rel_embedding_apply Subrel.relEmbedding_applyₓ'. -/
@[simp]
theorem relEmbedding_apply (r : α → α → Prop) (p a) : Subrel.relEmbedding r p a = a.1 :=
@@ -129,7 +129,7 @@ end Subrel
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {s : β -> β -> Prop} (p : Set.{u2} β) (f : RelEmbedding.{u1, u2} α β r s), (forall (a : α), Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RelEmbedding.{u1, u2} α β r s) (fun (_x : RelEmbedding.{u1, u2} α β r s) => α -> β) (RelEmbedding.hasCoeToFun.{u1, u2} α β r s) f a) p) -> (RelEmbedding.{u1, u2} α (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) p) r (Subrel.{u2} β s p))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {s : β -> β -> Prop} (p : Set.{u2} β) (f : RelEmbedding.{u1, u2} α β r s), (forall (a : α), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (Set.{u2} β) (Set.instMembershipSet.{u2} β) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u1, succ u2} α β)) (RelEmbedding.toEmbedding.{u1, u2} α β r s f) a) p) -> (RelEmbedding.{u1, u2} α (Set.Elem.{u2} β p) r (Subrel.{u2} β s p))
+ forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {s : β -> β -> Prop} (p : Set.{u2} β) (f : RelEmbedding.{u1, u2} α β r s), (forall (a : α), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => β) a) (Set.{u2} β) (Set.instMembershipSet.{u2} β) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelEmbedding.{u1, u2} α β r s) α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => β) _x) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelEmbedding.{u1, u2} α β r s) α β r s (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} α β r s)) f a) p) -> (RelEmbedding.{u1, u2} α (Set.Elem.{u2} β p) r (Subrel.{u2} β s p))
Case conversion may be inaccurate. Consider using '#align rel_embedding.cod_restrict RelEmbedding.codRestrictₓ'. -/
/-- Restrict the codomain of a relation embedding. -/
def RelEmbedding.codRestrict (p : Set β) (f : r ↪r s) (H : ∀ a, f a ∈ p) : r ↪r Subrel s p :=
@@ -140,7 +140,7 @@ def RelEmbedding.codRestrict (p : Set β) (f : r ↪r s) (H : ∀ a, f a ∈ p)
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {s : β -> β -> Prop} (p : Set.{u2} β) (f : RelEmbedding.{u1, u2} α β r s) (H : forall (a : α), Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RelEmbedding.{u1, u2} α β r s) (fun (_x : RelEmbedding.{u1, u2} α β r s) => α -> β) (RelEmbedding.hasCoeToFun.{u1, u2} α β r s) f a) p) (a : α), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) p) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RelEmbedding.{u1, u2} α (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) p) r (Subrel.{u2} β s p)) (fun (_x : RelEmbedding.{u1, u2} α (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) p) r (Subrel.{u2} β s p)) => α -> (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) p)) (RelEmbedding.hasCoeToFun.{u1, u2} α (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) p) r (Subrel.{u2} β s p)) (RelEmbedding.codRestrict.{u1, u2} α β r s p f H) a) (Subtype.mk.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x p) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RelEmbedding.{u1, u2} α β r s) (fun (_x : RelEmbedding.{u1, u2} α β r s) => α -> β) (RelEmbedding.hasCoeToFun.{u1, u2} α β r s) f a) (H a))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {s : β -> β -> Prop} (p : Set.{u2} β) (f : RelEmbedding.{u1, u2} α β r s) (H : forall (a : α), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (Set.{u2} β) (Set.instMembershipSet.{u2} β) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u1, succ u2} α β)) (RelEmbedding.toEmbedding.{u1, u2} α β r s f) a) p) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => Set.Elem.{u2} β p) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} α (Set.Elem.{u2} β p)) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => Set.Elem.{u2} β p) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} α (Set.Elem.{u2} β p)) α (Set.Elem.{u2} β p) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u2} α (Set.Elem.{u2} β p))) (RelEmbedding.toEmbedding.{u1, u2} α (Set.Elem.{u2} β p) r (Subrel.{u2} β s p) (RelEmbedding.codRestrict.{u1, u2} α β r s p f H)) a) (Subtype.mk.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x p) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u1, succ u2} α β)) (RelEmbedding.toEmbedding.{u1, u2} α β r s f) a) (H a))
+ forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {s : β -> β -> Prop} (p : Set.{u2} β) (f : RelEmbedding.{u1, u2} α β r s) (H : forall (a : α), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => β) a) (Set.{u2} β) (Set.instMembershipSet.{u2} β) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelEmbedding.{u1, u2} α β r s) α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => β) _x) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelEmbedding.{u1, u2} α β r s) α β r s (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} α β r s)) f a) p) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => Set.Elem.{u2} β p) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelEmbedding.{u1, u2} α (Set.Elem.{u2} β p) r (Subrel.{u2} β s p)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => Set.Elem.{u2} β p) _x) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelEmbedding.{u1, u2} α (Set.Elem.{u2} β p) r (Subrel.{u2} β s p)) α (Set.Elem.{u2} β p) r (Subrel.{u2} β s p) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} α (Set.Elem.{u2} β p) r (Subrel.{u2} β s p))) (RelEmbedding.codRestrict.{u1, u2} α β r s p f H) a) (Subtype.mk.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x p) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelEmbedding.{u1, u2} α β r s) α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => β) _x) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelEmbedding.{u1, u2} α β r s) α β r s (RelEmbedding.instRelHomClassRelEmbedding.{u1, u2} α β r s)) f a) (H a))
Case conversion may be inaccurate. Consider using '#align rel_embedding.cod_restrict_apply RelEmbedding.codRestrict_applyₓ'. -/
@[simp]
theorem RelEmbedding.codRestrict_apply (p) (f : r ↪r s) (H a) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212
@@ -49,7 +49,7 @@ theorem map_inf [SemilatticeInf α] [LinearOrder β]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {F : Type.{u3}} [_inst_1 : SemilatticeSup.{u1} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))] (a : F) (m : β) (n : β), Eq.{succ u1} α (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a (Sup.sup.{u2} β (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))) m n)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a m) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a n))
but is expected to have type
- forall {α : Type.{u3}} {β : Type.{u2}} {F : Type.{u1}} [_inst_1 : SemilatticeSup.{u3} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.225 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.227 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.225 x._@.Mathlib.Order.RelIso.Set._hyg.227) (fun (x._@.Mathlib.Order.RelIso.Set._hyg.247 : α) (x._@.Mathlib.Order.RelIso.Set._hyg.249 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) x._@.Mathlib.Order.RelIso.Set._hyg.247 x._@.Mathlib.Order.RelIso.Set._hyg.249)] (a : F) (m : β) (n : β), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Sup.sup.{u2} β (SemilatticeSup.toSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))) m n)) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.225 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.227 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.225 x._@.Mathlib.Order.RelIso.Set._hyg.227) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.249 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.249) _inst_3) a (Sup.sup.{u2} β (SemilatticeSup.toSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))) m n)) (Sup.sup.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) (SemilatticeSup.toSup.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) _inst_1) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.225 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.227 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.225 x._@.Mathlib.Order.RelIso.Set._hyg.227) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.249 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.249) _inst_3) a m) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.225 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.227 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.225 x._@.Mathlib.Order.RelIso.Set._hyg.227) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.249 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.249) _inst_3) a n))
+ forall {α : Type.{u3}} {β : Type.{u2}} {F : Type.{u1}} [_inst_1 : SemilatticeSup.{u3} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.228 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.230 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.228 x._@.Mathlib.Order.RelIso.Set._hyg.230) (fun (x._@.Mathlib.Order.RelIso.Set._hyg.250 : α) (x._@.Mathlib.Order.RelIso.Set._hyg.252 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) x._@.Mathlib.Order.RelIso.Set._hyg.250 x._@.Mathlib.Order.RelIso.Set._hyg.252)] (a : F) (m : β) (n : β), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Sup.sup.{u2} β (SemilatticeSup.toSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))) m n)) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.228 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.230 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.228 x._@.Mathlib.Order.RelIso.Set._hyg.230) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.252 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.252) _inst_3) a (Sup.sup.{u2} β (SemilatticeSup.toSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))) m n)) (Sup.sup.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) (SemilatticeSup.toSup.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) _inst_1) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.228 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.230 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.228 x._@.Mathlib.Order.RelIso.Set._hyg.230) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.252 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.252) _inst_3) a m) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.228 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.230 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.228 x._@.Mathlib.Order.RelIso.Set._hyg.230) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.252 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.252) _inst_3) a n))
Case conversion may be inaccurate. Consider using '#align rel_hom_class.map_sup RelHomClass.map_supₓ'. -/
theorem map_sup [SemilatticeSup α] [LinearOrder β]
[RelHomClass F ((· > ·) : β → β → Prop) ((· > ·) : α → α → Prop)] (a : F) (m n : β) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -35,9 +35,9 @@ variable {F : Type _}
/- warning: rel_hom_class.map_inf -> RelHomClass.map_inf is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {F : Type.{u3}} [_inst_1 : SemilatticeInf.{u1} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u3, u2, u1} F β α (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))] (a : F) (m : β) (n : β), Eq.{succ u1} α (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a (HasInf.inf.{u2} β (SemilatticeInf.toHasInf.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))) m n)) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a m) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a n))
+ forall {α : Type.{u1}} {β : Type.{u2}} {F : Type.{u3}} [_inst_1 : SemilatticeInf.{u1} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u3, u2, u1} F β α (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1))))] (a : F) (m : β) (n : β), Eq.{succ u1} α (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a (Inf.inf.{u2} β (SemilatticeInf.toHasInf.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))) m n)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a m) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a n))
but is expected to have type
- forall {α : Type.{u3}} {β : Type.{u2}} {F : Type.{u1}} [_inst_1 : SemilatticeInf.{u3} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (x._@.Mathlib.Order.RelIso.Set._hyg.133 : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) x._@.Mathlib.Order.RelIso.Set._hyg.133 x._@.Mathlib.Order.RelIso.Set._hyg.135)] (a : F) (m : β) (n : β), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (HasInf.inf.{u2} β (Lattice.toHasInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2))) m n)) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.135) _inst_3) a (HasInf.inf.{u2} β (Lattice.toHasInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2))) m n)) (HasInf.inf.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) (SemilatticeInf.toHasInf.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) _inst_1) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.135) _inst_3) a m) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.135) _inst_3) a n))
+ forall {α : Type.{u3}} {β : Type.{u2}} {F : Type.{u1}} [_inst_1 : SemilatticeInf.{u3} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (x._@.Mathlib.Order.RelIso.Set._hyg.133 : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) x._@.Mathlib.Order.RelIso.Set._hyg.133 x._@.Mathlib.Order.RelIso.Set._hyg.135)] (a : F) (m : β) (n : β), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Inf.inf.{u2} β (Lattice.toInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2))) m n)) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.135) _inst_3) a (Inf.inf.{u2} β (Lattice.toInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2))) m n)) (Inf.inf.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) (SemilatticeInf.toInf.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) _inst_1) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.135) _inst_3) a m) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.111 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.113 : β) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.111 x._@.Mathlib.Order.RelIso.Set._hyg.113) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.135 : α) => LT.lt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.135) _inst_3) a n))
Case conversion may be inaccurate. Consider using '#align rel_hom_class.map_inf RelHomClass.map_infₓ'. -/
theorem map_inf [SemilatticeInf α] [LinearOrder β]
[RelHomClass F ((· < ·) : β → β → Prop) ((· < ·) : α → α → Prop)] (a : F) (m n : β) :
@@ -47,9 +47,9 @@ theorem map_inf [SemilatticeInf α] [LinearOrder β]
/- warning: rel_hom_class.map_sup -> RelHomClass.map_sup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {F : Type.{u3}} [_inst_1 : SemilatticeSup.{u1} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))] (a : F) (m : β) (n : β), Eq.{succ u1} α (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a (HasSup.sup.{u2} β (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))) m n)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a m) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a n))
+ forall {α : Type.{u1}} {β : Type.{u2}} {F : Type.{u3}} [_inst_1 : SemilatticeSup.{u1} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1))))] (a : F) (m : β) (n : β), Eq.{succ u1} α (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a (Sup.sup.{u2} β (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (LinearOrder.toLattice.{u2} β _inst_2))) m n)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a m) (coeFn.{succ u3, max (succ u2) (succ u1)} F (fun (_x : F) => β -> α) (FunLike.hasCoeToFun.{succ u3, succ u2, succ u1} F β (fun (_x : β) => α) (RelHomClass.toFunLike.{u3, u2, u1} F β α (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_2)))))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) _inst_3)) a n))
but is expected to have type
- forall {α : Type.{u3}} {β : Type.{u2}} {F : Type.{u1}} [_inst_1 : SemilatticeSup.{u3} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.225 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.227 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.225 x._@.Mathlib.Order.RelIso.Set._hyg.227) (fun (x._@.Mathlib.Order.RelIso.Set._hyg.247 : α) (x._@.Mathlib.Order.RelIso.Set._hyg.249 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) x._@.Mathlib.Order.RelIso.Set._hyg.247 x._@.Mathlib.Order.RelIso.Set._hyg.249)] (a : F) (m : β) (n : β), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (HasSup.sup.{u2} β (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))) m n)) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.225 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.227 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.225 x._@.Mathlib.Order.RelIso.Set._hyg.227) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.249 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.249) _inst_3) a (HasSup.sup.{u2} β (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))) m n)) (HasSup.sup.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) (SemilatticeSup.toHasSup.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) _inst_1) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.225 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.227 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.225 x._@.Mathlib.Order.RelIso.Set._hyg.227) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.249 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.249) _inst_3) a m) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.225 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.227 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.225 x._@.Mathlib.Order.RelIso.Set._hyg.227) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.249 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.249) _inst_3) a n))
+ forall {α : Type.{u3}} {β : Type.{u2}} {F : Type.{u1}} [_inst_1 : SemilatticeSup.{u3} α] [_inst_2 : LinearOrder.{u2} β] [_inst_3 : RelHomClass.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.225 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.227 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.225 x._@.Mathlib.Order.RelIso.Set._hyg.227) (fun (x._@.Mathlib.Order.RelIso.Set._hyg.247 : α) (x._@.Mathlib.Order.RelIso.Set._hyg.249 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) x._@.Mathlib.Order.RelIso.Set._hyg.247 x._@.Mathlib.Order.RelIso.Set._hyg.249)] (a : F) (m : β) (n : β), Eq.{succ u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) (Sup.sup.{u2} β (SemilatticeSup.toSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))) m n)) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.225 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.227 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.225 x._@.Mathlib.Order.RelIso.Set._hyg.227) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.249 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.249) _inst_3) a (Sup.sup.{u2} β (SemilatticeSup.toSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))) m n)) (Sup.sup.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) (SemilatticeSup.toSup.{u3} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) m) _inst_1) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.225 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.227 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.225 x._@.Mathlib.Order.RelIso.Set._hyg.227) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.249 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.249) _inst_3) a m) (FunLike.coe.{succ u1, succ u2, succ u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : β) => α) _x) (RelHomClass.toFunLike.{u1, u2, u3} F β α (fun (x._@.Mathlib.Order.RelIso.Set._hyg.225 : β) (x._@.Mathlib.Order.RelIso.Set._hyg.227 : β) => GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_2)))))) x._@.Mathlib.Order.RelIso.Set._hyg.225 x._@.Mathlib.Order.RelIso.Set._hyg.227) (fun (_x : α) (x._@.Mathlib.Order.RelIso.Set._hyg.249 : α) => GT.gt.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeSup.toPartialOrder.{u3} α _inst_1))) _x x._@.Mathlib.Order.RelIso.Set._hyg.249) _inst_3) a n))
Case conversion may be inaccurate. Consider using '#align rel_hom_class.map_sup RelHomClass.map_supₓ'. -/
theorem map_sup [SemilatticeSup α] [LinearOrder β]
[RelHomClass F ((· > ·) : β → β → Prop) ((· > ·) : α → α → Prop)] (a : F) (m n : β) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun
instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike
is EquivLike
, since that has a custom coe_injective'
field that is easier to implement. All other classes should take FunLike
or EquivLike
as a parameter.
Previously, morphism classes would be Type
-valued and extend FunLike
:
/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))
After this PR, they should be Prop
-valued and take FunLike
as a parameter:
/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
[FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))
(Note that A B
stay marked as outParam
even though they are not purely required to be so due to the FunLike
parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam
is slightly faster.)
Similarly, MyEquivClass
should take EquivLike
as a parameter.
As a result, every mention of [MyHomClass F A B]
should become [FunLike F A B] [MyHomClass F A B]
.
While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul
is more expensive. This is due to suboptimal processing of arguments. For example:
variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)
theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y
example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _
Before this PR, applying map_mul f
gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]
. Since M
and N
are out_param
s, [MulHomClass F ?M ?N]
is synthesized first, supplies values for ?M
and ?N
and then the Mul M
and Mul N
instances can be found.
After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]
. Now [FunLike F ?M ?N]
is synthesized first, supplies values for ?M
and ?N
and then the Mul M
and Mul N
instances can be found, before trying MulHomClass F M N
which fails. Since the Mul
hierarchy is very big, this can be slow to fail, especially when there is no such Mul
instance.
A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul
to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N]
because MulHomClass
fails or succeeds much faster than the others.
As a consequence, the simpNF
linter is much slower since by design it tries and fails to apply many map_
lemmas. The same issue occurs a few times in existing calls to simp [map_mul]
, where map_mul
is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.
simp
not firing sometimesThis affects map_smulₛₗ
and related definitions. For simp
lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw
can find every argument to map_smulₛₗ
successfully but simp
can't: leanprover/lean4#3701.
Especially in the category theory library, we might sometimes have a type A
which is also accessible as a synonym (Bundled A hA).1
. Instance synthesis doesn't always work if we have f : A →* B
but x * y : (Bundled A hA).1
or vice versa. This seems to be mostly fixed by keeping A B
as outParam
s in MulHomClass F A B
. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1
instead of using the syntax in the discrimination tree.)
The timeouts can be worked around for now by specifying which map_mul
we mean, either as map_mul f
for some explicit f
, or as e.g. MonoidHomClass.map_mul
.
map_smulₛₗ
not firing as simp
lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ
a simp
lemma instead of the generic map_smulₛₗ
. Writing simp [map_smulₛₗ _]
also works.
Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
@@ -27,16 +27,16 @@ namespace RelHomClass
variable {F : Type*}
-theorem map_inf [SemilatticeInf α] [LinearOrder β]
- [RelHomClass F ((· < ·) : β → β → Prop) ((· < ·) : α → α → Prop)] (a : F) (m n : β) :
+theorem map_inf [SemilatticeInf α] [LinearOrder β] [FunLike F β α]
+ [RelHomClass F (· < ·) (· < ·)] (a : F) (m n : β) :
a (m ⊓ n) = a m ⊓ a n :=
(StrictMono.monotone fun _ _ => map_rel a).map_inf m n
#align rel_hom_class.map_inf RelHomClass.map_inf
-theorem map_sup [SemilatticeSup α] [LinearOrder β]
- [RelHomClass F ((· > ·) : β → β → Prop) ((· > ·) : α → α → Prop)] (a : F) (m n : β) :
+theorem map_sup [SemilatticeSup α] [LinearOrder β] [FunLike F β α]
+ [RelHomClass F (· > ·) (· > ·)] (a : F) (m n : β) :
a (m ⊔ n) = a m ⊔ a n :=
- @map_inf αᵒᵈ βᵒᵈ _ _ _ _ _ _ _
+ map_inf (α := αᵒᵈ) (β := βᵒᵈ) _ _ _
#align rel_hom_class.map_sup RelHomClass.map_sup
end RelHomClass
@@ -45,7 +45,7 @@ namespace RelIso
@[simp]
theorem range_eq (e : r ≃r s) : Set.range e = Set.univ :=
- Function.Surjective.range_eq e.surjective
+ e.surjective.range_eq
#align rel_iso.range_eq RelIso.range_eq
end RelIso
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -20,12 +20,12 @@ open Function
universe u v w
-variable {α β γ δ : Type _} {r : α → α → Prop} {s : β → β → Prop} {t : γ → γ → Prop}
+variable {α β γ δ : Type*} {r : α → α → Prop} {s : β → β → Prop} {t : γ → γ → Prop}
{u : δ → δ → Prop}
namespace RelHomClass
-variable {F : Type _}
+variable {F : Type*}
theorem map_inf [SemilatticeInf α] [LinearOrder β]
[RelHomClass F ((· < ·) : β → β → Prop) ((· < ·) : α → α → Prop)] (a : F) (m n : β) :
@@ -2,15 +2,12 @@
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-
-! This file was ported from Lean 3 source module order.rel_iso.set
-! leanprover-community/mathlib commit ee0c179cd3c8a45aa5bffbf1b41d8dbede452865
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Order.RelIso.Basic
import Mathlib.Logic.Embedding.Set
+#align_import order.rel_iso.set from "leanprover-community/mathlib"@"ee0c179cd3c8a45aa5bffbf1b41d8dbede452865"
+
/-!
# Interactions between relation homomorphisms and sets
fix-comments.py
on all files.@@ -53,7 +53,7 @@ theorem range_eq (e : r ≃r s) : Set.range e = Set.univ :=
end RelIso
-/-- `subrel r p` is the inherited relation on a subset. -/
+/-- `Subrel r p` is the inherited relation on a subset. -/
def Subrel (r : α → α → Prop) (p : Set α) : p → p → Prop :=
(Subtype.val : p → α) ⁻¹'o r
#align subrel Subrel
The script used to do this is included. The yaml file was obtained from https://raw.githubusercontent.com/wiki/leanprover-community/mathlib/mathlib4-port-status.md
@@ -2,6 +2,11 @@
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
+
+! This file was ported from Lean 3 source module order.rel_iso.set
+! leanprover-community/mathlib commit ee0c179cd3c8a45aa5bffbf1b41d8dbede452865
+! Please do not edit these lines, except to modify the commit id
+! if you have ported upstream changes.
-/
import Mathlib.Order.RelIso.Basic
import Mathlib.Logic.Embedding.Set
All dependencies are ported!