order.hom.bounded
⟷
Mathlib.Order.Hom.Bounded
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
@@ -679,7 +679,7 @@ instance : BoundedOrderHomClass (BoundedOrderHom α β) α β
where
coe f := f.toFun
coe_injective' f g h := by obtain ⟨⟨_, _⟩, _⟩ := f <;> obtain ⟨⟨_, _⟩, _⟩ := g <;> congr
- map_rel f := f.monotone'
+ mapRel f := f.monotone'
map_top f := f.map_top'
map_bot f := f.map_bot'
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -69,7 +69,7 @@ section
You should extend this class when you extend `top_hom`. -/
class TopHomClass (F : Type _) (α β : outParam <| Type _) [Top α] [Top β] extends
- FunLike F α fun _ => β where
+ DFunLike F α fun _ => β where
map_top (f : F) : f ⊤ = ⊤
#align top_hom_class TopHomClass
-/
@@ -79,7 +79,7 @@ class TopHomClass (F : Type _) (α β : outParam <| Type _) [Top α] [Top β] ex
You should extend this class when you extend `bot_hom`. -/
class BotHomClass (F : Type _) (α β : outParam <| Type _) [Bot α] [Bot β] extends
- FunLike F α fun _ => β where
+ DFunLike F α fun _ => β where
map_bot (f : F) : f ⊥ = ⊥
#align bot_hom_class BotHomClass
-/
@@ -195,7 +195,7 @@ instance : TopHomClass (TopHom α β) α β
/-- Helper instance for when there's too many metavariables to apply `fun_like.has_coe_to_fun`
directly. -/
instance : CoeFun (TopHom α β) fun _ => α → β :=
- FunLike.hasCoeToFun
+ DFunLike.hasCoeToFun
@[simp]
theorem toFun_eq_coe {f : TopHom α β} : f.toFun = (f : α → β) :=
@@ -208,7 +208,7 @@ initialize_simps_projections TopHom (toFun → apply)
#print TopHom.ext /-
@[ext]
theorem ext {f g : TopHom α β} (h : ∀ a, f a = g a) : f = g :=
- FunLike.ext f g h
+ DFunLike.ext f g h
#align top_hom.ext TopHom.ext
-/
@@ -231,7 +231,7 @@ theorem coe_copy (f : TopHom α β) (f' : α → β) (h : f' = f) : ⇑(f.copy f
#print TopHom.copy_eq /-
theorem copy_eq (f : TopHom α β) (f' : α → β) (h : f' = f) : f.copy f' h = f :=
- FunLike.ext' h
+ DFunLike.ext' h
#align top_hom.copy_eq TopHom.copy_eq
-/
@@ -311,7 +311,7 @@ theorem id_comp (f : TopHom α β) : (TopHom.id β).comp f = f :=
#print TopHom.cancel_right /-
theorem cancel_right {g₁ g₂ : TopHom β γ} {f : TopHom α β} (hf : Surjective f) :
g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
- ⟨fun h => TopHom.ext <| hf.forall.2 <| FunLike.ext_iff.1 h, congr_arg _⟩
+ ⟨fun h => TopHom.ext <| hf.forall.2 <| DFunLike.ext_iff.1 h, congr_arg _⟩
#align top_hom.cancel_right TopHom.cancel_right
-/
@@ -329,7 +329,7 @@ instance [Preorder β] [Top β] : Preorder (TopHom α β) :=
Preorder.lift (coeFn : TopHom α β → α → β)
instance [PartialOrder β] [Top β] : PartialOrder (TopHom α β) :=
- PartialOrder.lift _ FunLike.coe_injective
+ PartialOrder.lift _ DFunLike.coe_injective
section OrderTop
@@ -362,7 +362,7 @@ instance : Inf (TopHom α β) :=
⟨fun f g => ⟨f ⊓ g, by rw [Pi.inf_apply, map_top, map_top, inf_top_eq]⟩⟩
instance : SemilatticeInf (TopHom α β) :=
- FunLike.coe_injective.SemilatticeInf _ fun _ _ => rfl
+ DFunLike.coe_injective.SemilatticeInf _ fun _ _ => rfl
#print TopHom.coe_inf /-
@[simp]
@@ -388,7 +388,7 @@ instance : Sup (TopHom α β) :=
⟨fun f g => ⟨f ⊔ g, by rw [Pi.sup_apply, map_top, map_top, sup_top_eq]⟩⟩
instance : SemilatticeSup (TopHom α β) :=
- FunLike.coe_injective.SemilatticeSup _ fun _ _ => rfl
+ DFunLike.coe_injective.SemilatticeSup _ fun _ _ => rfl
#print TopHom.coe_sup /-
@[simp]
@@ -407,10 +407,10 @@ theorem sup_apply (a : α) : (f ⊔ g) a = f a ⊔ g a :=
end SemilatticeSup
instance [Lattice β] [OrderTop β] : Lattice (TopHom α β) :=
- FunLike.coe_injective.Lattice _ (fun _ _ => rfl) fun _ _ => rfl
+ DFunLike.coe_injective.Lattice _ (fun _ _ => rfl) fun _ _ => rfl
instance [DistribLattice β] [OrderTop β] : DistribLattice (TopHom α β) :=
- FunLike.coe_injective.DistribLattice _ (fun _ _ => rfl) fun _ _ => rfl
+ DFunLike.coe_injective.DistribLattice _ (fun _ _ => rfl) fun _ _ => rfl
end TopHom
@@ -434,7 +434,7 @@ instance : BotHomClass (BotHom α β) α β
/-- Helper instance for when there's too many metavariables to apply `fun_like.has_coe_to_fun`
directly. -/
instance : CoeFun (BotHom α β) fun _ => α → β :=
- FunLike.hasCoeToFun
+ DFunLike.hasCoeToFun
@[simp]
theorem toFun_eq_coe {f : BotHom α β} : f.toFun = (f : α → β) :=
@@ -447,7 +447,7 @@ initialize_simps_projections BotHom (toFun → apply)
#print BotHom.ext /-
@[ext]
theorem ext {f g : BotHom α β} (h : ∀ a, f a = g a) : f = g :=
- FunLike.ext f g h
+ DFunLike.ext f g h
#align bot_hom.ext BotHom.ext
-/
@@ -470,7 +470,7 @@ theorem coe_copy (f : BotHom α β) (f' : α → β) (h : f' = f) : ⇑(f.copy f
#print BotHom.copy_eq /-
theorem copy_eq (f : BotHom α β) (f' : α → β) (h : f' = f) : f.copy f' h = f :=
- FunLike.ext' h
+ DFunLike.ext' h
#align bot_hom.copy_eq BotHom.copy_eq
-/
@@ -550,7 +550,7 @@ theorem id_comp (f : BotHom α β) : (BotHom.id β).comp f = f :=
#print BotHom.cancel_right /-
theorem cancel_right {g₁ g₂ : BotHom β γ} {f : BotHom α β} (hf : Surjective f) :
g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
- ⟨fun h => BotHom.ext <| hf.forall.2 <| FunLike.ext_iff.1 h, congr_arg _⟩
+ ⟨fun h => BotHom.ext <| hf.forall.2 <| DFunLike.ext_iff.1 h, congr_arg _⟩
#align bot_hom.cancel_right BotHom.cancel_right
-/
@@ -568,7 +568,7 @@ instance [Preorder β] [Bot β] : Preorder (BotHom α β) :=
Preorder.lift (coeFn : BotHom α β → α → β)
instance [PartialOrder β] [Bot β] : PartialOrder (BotHom α β) :=
- PartialOrder.lift _ FunLike.coe_injective
+ PartialOrder.lift _ DFunLike.coe_injective
section OrderBot
@@ -601,7 +601,7 @@ instance : Inf (BotHom α β) :=
⟨fun f g => ⟨f ⊓ g, by rw [Pi.inf_apply, map_bot, map_bot, inf_bot_eq]⟩⟩
instance : SemilatticeInf (BotHom α β) :=
- FunLike.coe_injective.SemilatticeInf _ fun _ _ => rfl
+ DFunLike.coe_injective.SemilatticeInf _ fun _ _ => rfl
#print BotHom.coe_inf /-
@[simp]
@@ -627,7 +627,7 @@ instance : Sup (BotHom α β) :=
⟨fun f g => ⟨f ⊔ g, by rw [Pi.sup_apply, map_bot, map_bot, sup_bot_eq]⟩⟩
instance : SemilatticeSup (BotHom α β) :=
- FunLike.coe_injective.SemilatticeSup _ fun _ _ => rfl
+ DFunLike.coe_injective.SemilatticeSup _ fun _ _ => rfl
#print BotHom.coe_sup /-
@[simp]
@@ -646,10 +646,10 @@ theorem sup_apply (a : α) : (f ⊔ g) a = f a ⊔ g a :=
end SemilatticeSup
instance [Lattice β] [OrderBot β] : Lattice (BotHom α β) :=
- FunLike.coe_injective.Lattice _ (fun _ _ => rfl) fun _ _ => rfl
+ DFunLike.coe_injective.Lattice _ (fun _ _ => rfl) fun _ _ => rfl
instance [DistribLattice β] [OrderBot β] : DistribLattice (BotHom α β) :=
- FunLike.coe_injective.DistribLattice _ (fun _ _ => rfl) fun _ _ => rfl
+ DFunLike.coe_injective.DistribLattice _ (fun _ _ => rfl) fun _ _ => rfl
end BotHom
@@ -686,7 +686,7 @@ instance : BoundedOrderHomClass (BoundedOrderHom α β) α β
/-- Helper instance for when there's too many metavariables to apply `fun_like.has_coe_to_fun`
directly. -/
instance : CoeFun (BoundedOrderHom α β) fun _ => α → β :=
- FunLike.hasCoeToFun
+ DFunLike.hasCoeToFun
@[simp]
theorem toFun_eq_coe {f : BoundedOrderHom α β} : f.toFun = (f : α → β) :=
@@ -696,7 +696,7 @@ theorem toFun_eq_coe {f : BoundedOrderHom α β} : f.toFun = (f : α → β) :=
#print BoundedOrderHom.ext /-
@[ext]
theorem ext {f g : BoundedOrderHom α β} (h : ∀ a, f a = g a) : f = g :=
- FunLike.ext f g h
+ DFunLike.ext f g h
#align bounded_order_hom.ext BoundedOrderHom.ext
-/
@@ -717,7 +717,7 @@ theorem coe_copy (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : ⇑
#print BoundedOrderHom.copy_eq /-
theorem copy_eq (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : f.copy f' h = f :=
- FunLike.ext' h
+ DFunLike.ext' h
#align bounded_order_hom.copy_eq BoundedOrderHom.copy_eq
-/
@@ -820,7 +820,7 @@ theorem id_comp (f : BoundedOrderHom α β) : (BoundedOrderHom.id β).comp f = f
#print BoundedOrderHom.cancel_right /-
theorem cancel_right {g₁ g₂ : BoundedOrderHom β γ} {f : BoundedOrderHom α β} (hf : Surjective f) :
g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
- ⟨fun h => BoundedOrderHom.ext <| hf.forall.2 <| FunLike.ext_iff.1 h, congr_arg _⟩
+ ⟨fun h => BoundedOrderHom.ext <| hf.forall.2 <| DFunLike.ext_iff.1 h, congr_arg _⟩
#align bounded_order_hom.cancel_right BoundedOrderHom.cancel_right
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
-import Mathbin.Order.Hom.Basic
-import Mathbin.Order.BoundedOrder
+import Order.Hom.Basic
+import Order.BoundedOrder
#align_import order.hom.bounded from "leanprover-community/mathlib"@"cc70d9141824ea8982d1562ce009952f2c3ece30"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-
-! This file was ported from Lean 3 source module order.hom.bounded
-! leanprover-community/mathlib commit cc70d9141824ea8982d1562ce009952f2c3ece30
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Order.Hom.Basic
import Mathbin.Order.BoundedOrder
+#align_import order.hom.bounded from "leanprover-community/mathlib"@"cc70d9141824ea8982d1562ce009952f2c3ece30"
+
/-!
# Bounded order homomorphisms
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -106,25 +106,32 @@ export BotHomClass (map_bot)
attribute [simp] map_top map_bot
+#print BoundedOrderHomClass.toTopHomClass /-
-- See note [lower instance priority]
instance (priority := 100) BoundedOrderHomClass.toTopHomClass [LE α] [LE β] [BoundedOrder α]
[BoundedOrder β] [BoundedOrderHomClass F α β] : TopHomClass F α β :=
{ ‹BoundedOrderHomClass F α β› with }
#align bounded_order_hom_class.to_top_hom_class BoundedOrderHomClass.toTopHomClass
+-/
+#print BoundedOrderHomClass.toBotHomClass /-
-- See note [lower instance priority]
instance (priority := 100) BoundedOrderHomClass.toBotHomClass [LE α] [LE β] [BoundedOrder α]
[BoundedOrder β] [BoundedOrderHomClass F α β] : BotHomClass F α β :=
{ ‹BoundedOrderHomClass F α β› with }
#align bounded_order_hom_class.to_bot_hom_class BoundedOrderHomClass.toBotHomClass
+-/
+#print OrderIsoClass.toTopHomClass /-
-- See note [lower instance priority]
instance (priority := 100) OrderIsoClass.toTopHomClass [LE α] [OrderTop α] [PartialOrder β]
[OrderTop β] [OrderIsoClass F α β] : TopHomClass F α β :=
{ show OrderHomClass F α β from inferInstance with
map_top := fun f => top_le_iff.1 <| (map_inv_le_iff f).1 le_top }
#align order_iso_class.to_top_hom_class OrderIsoClass.toTopHomClass
+-/
+#print OrderIsoClass.toBotHomClass /-
-- See note [lower instance priority]
instance (priority := 100) OrderIsoClass.toBotHomClass [LE α] [OrderBot α] [PartialOrder β]
[OrderBot β] [OrderIsoClass F α β] : BotHomClass F α β :=
@@ -132,6 +139,7 @@ instance (priority := 100) OrderIsoClass.toBotHomClass [LE α] [OrderBot α] [Pa
show OrderHomClass F α β from inferInstance with
map_bot := fun f => le_bot_iff.1 <| (le_map_inv_iff f).1 bot_le }
#align order_iso_class.to_bot_hom_class OrderIsoClass.toBotHomClass
+-/
#print OrderIsoClass.toBoundedOrderHomClass /-
-- See note [lower instance priority]
@@ -142,15 +150,19 @@ instance (priority := 100) OrderIsoClass.toBoundedOrderHomClass [LE α] [Bounded
#align order_iso_class.to_bounded_order_hom_class OrderIsoClass.toBoundedOrderHomClass
-/
+#print map_eq_top_iff /-
@[simp]
theorem map_eq_top_iff [LE α] [OrderTop α] [PartialOrder β] [OrderTop β] [OrderIsoClass F α β]
(f : F) {a : α} : f a = ⊤ ↔ a = ⊤ := by rw [← map_top f, (EquivLike.injective f).eq_iff]
#align map_eq_top_iff map_eq_top_iff
+-/
+#print map_eq_bot_iff /-
@[simp]
theorem map_eq_bot_iff [LE α] [OrderBot α] [PartialOrder β] [OrderBot β] [OrderIsoClass F α β]
(f : F) {a : α} : f a = ⊥ ↔ a = ⊥ := by rw [← map_bot f, (EquivLike.injective f).eq_iff]
#align map_eq_bot_iff map_eq_bot_iff
+-/
instance [Top α] [Top β] [TopHomClass F α β] : CoeTC F (TopHom α β) :=
⟨fun f => ⟨f, map_top f⟩⟩
@@ -196,11 +208,14 @@ theorem toFun_eq_coe {f : TopHom α β} : f.toFun = (f : α → β) :=
-- this must come after the coe_to_fun definition
initialize_simps_projections TopHom (toFun → apply)
+#print TopHom.ext /-
@[ext]
theorem ext {f g : TopHom α β} (h : ∀ a, f a = g a) : f = g :=
FunLike.ext f g h
#align top_hom.ext TopHom.ext
+-/
+#print TopHom.copy /-
/-- Copy of a `top_hom` with a new `to_fun` equal to the old one. Useful to fix definitional
equalities. -/
protected def copy (f : TopHom α β) (f' : α → β) (h : f' = f) : TopHom α β
@@ -208,15 +223,20 @@ protected def copy (f : TopHom α β) (f' : α → β) (h : f' = f) : TopHom α
toFun := f'
map_top' := h.symm ▸ f.map_top'
#align top_hom.copy TopHom.copy
+-/
+#print TopHom.coe_copy /-
@[simp]
theorem coe_copy (f : TopHom α β) (f' : α → β) (h : f' = f) : ⇑(f.copy f' h) = f' :=
rfl
#align top_hom.coe_copy TopHom.coe_copy
+-/
+#print TopHom.copy_eq /-
theorem copy_eq (f : TopHom α β) (f' : α → β) (h : f' = f) : f.copy f' h = f :=
FunLike.ext' h
#align top_hom.copy_eq TopHom.copy_eq
+-/
instance : Inhabited (TopHom α β) :=
⟨⟨fun _ => ⊤, rfl⟩⟩
@@ -230,17 +250,21 @@ protected def id : TopHom α α :=
#align top_hom.id TopHom.id
-/
+#print TopHom.coe_id /-
@[simp]
theorem coe_id : ⇑(TopHom.id α) = id :=
rfl
#align top_hom.coe_id TopHom.coe_id
+-/
variable {α}
+#print TopHom.id_apply /-
@[simp]
theorem id_apply (a : α) : TopHom.id α a = a :=
rfl
#align top_hom.id_apply TopHom.id_apply
+-/
#print TopHom.comp /-
/-- Composition of `top_hom`s as a `top_hom`. -/
@@ -251,42 +275,56 @@ def comp (f : TopHom β γ) (g : TopHom α β) : TopHom α γ
#align top_hom.comp TopHom.comp
-/
+#print TopHom.coe_comp /-
@[simp]
theorem coe_comp (f : TopHom β γ) (g : TopHom α β) : (f.comp g : α → γ) = f ∘ g :=
rfl
#align top_hom.coe_comp TopHom.coe_comp
+-/
+#print TopHom.comp_apply /-
@[simp]
theorem comp_apply (f : TopHom β γ) (g : TopHom α β) (a : α) : (f.comp g) a = f (g a) :=
rfl
#align top_hom.comp_apply TopHom.comp_apply
+-/
+#print TopHom.comp_assoc /-
@[simp]
theorem comp_assoc (f : TopHom γ δ) (g : TopHom β γ) (h : TopHom α β) :
(f.comp g).comp h = f.comp (g.comp h) :=
rfl
#align top_hom.comp_assoc TopHom.comp_assoc
+-/
+#print TopHom.comp_id /-
@[simp]
theorem comp_id (f : TopHom α β) : f.comp (TopHom.id α) = f :=
TopHom.ext fun a => rfl
#align top_hom.comp_id TopHom.comp_id
+-/
+#print TopHom.id_comp /-
@[simp]
theorem id_comp (f : TopHom α β) : (TopHom.id β).comp f = f :=
TopHom.ext fun a => rfl
#align top_hom.id_comp TopHom.id_comp
+-/
+#print TopHom.cancel_right /-
theorem cancel_right {g₁ g₂ : TopHom β γ} {f : TopHom α β} (hf : Surjective f) :
g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
⟨fun h => TopHom.ext <| hf.forall.2 <| FunLike.ext_iff.1 h, congr_arg _⟩
#align top_hom.cancel_right TopHom.cancel_right
+-/
+#print TopHom.cancel_left /-
theorem cancel_left {g : TopHom β γ} {f₁ f₂ : TopHom α β} (hg : Injective g) :
g.comp f₁ = g.comp f₂ ↔ f₁ = f₂ :=
⟨fun h => TopHom.ext fun a => hg <| by rw [← TopHom.comp_apply, h, TopHom.comp_apply],
congr_arg _⟩
#align top_hom.cancel_left TopHom.cancel_left
+-/
end Top
@@ -303,15 +341,19 @@ variable [Preorder β] [OrderTop β]
instance : OrderTop (TopHom α β) :=
⟨⟨⊤, rfl⟩, fun _ => le_top⟩
+#print TopHom.coe_top /-
@[simp]
theorem coe_top : ⇑(⊤ : TopHom α β) = ⊤ :=
rfl
#align top_hom.coe_top TopHom.coe_top
+-/
+#print TopHom.top_apply /-
@[simp]
theorem top_apply (a : α) : (⊤ : TopHom α β) a = ⊤ :=
rfl
#align top_hom.top_apply TopHom.top_apply
+-/
end OrderTop
@@ -325,15 +367,19 @@ instance : Inf (TopHom α β) :=
instance : SemilatticeInf (TopHom α β) :=
FunLike.coe_injective.SemilatticeInf _ fun _ _ => rfl
+#print TopHom.coe_inf /-
@[simp]
theorem coe_inf : ⇑(f ⊓ g) = f ⊓ g :=
rfl
#align top_hom.coe_inf TopHom.coe_inf
+-/
+#print TopHom.inf_apply /-
@[simp]
theorem inf_apply (a : α) : (f ⊓ g) a = f a ⊓ g a :=
rfl
#align top_hom.inf_apply TopHom.inf_apply
+-/
end SemilatticeInf
@@ -347,15 +393,19 @@ instance : Sup (TopHom α β) :=
instance : SemilatticeSup (TopHom α β) :=
FunLike.coe_injective.SemilatticeSup _ fun _ _ => rfl
+#print TopHom.coe_sup /-
@[simp]
theorem coe_sup : ⇑(f ⊔ g) = f ⊔ g :=
rfl
#align top_hom.coe_sup TopHom.coe_sup
+-/
+#print TopHom.sup_apply /-
@[simp]
theorem sup_apply (a : α) : (f ⊔ g) a = f a ⊔ g a :=
rfl
#align top_hom.sup_apply TopHom.sup_apply
+-/
end SemilatticeSup
@@ -397,11 +447,14 @@ theorem toFun_eq_coe {f : BotHom α β} : f.toFun = (f : α → β) :=
-- this must come after the coe_to_fun definition
initialize_simps_projections BotHom (toFun → apply)
+#print BotHom.ext /-
@[ext]
theorem ext {f g : BotHom α β} (h : ∀ a, f a = g a) : f = g :=
FunLike.ext f g h
#align bot_hom.ext BotHom.ext
+-/
+#print BotHom.copy /-
/-- Copy of a `bot_hom` with a new `to_fun` equal to the old one. Useful to fix definitional
equalities. -/
protected def copy (f : BotHom α β) (f' : α → β) (h : f' = f) : BotHom α β
@@ -409,15 +462,20 @@ protected def copy (f : BotHom α β) (f' : α → β) (h : f' = f) : BotHom α
toFun := f'
map_bot' := h.symm ▸ f.map_bot'
#align bot_hom.copy BotHom.copy
+-/
+#print BotHom.coe_copy /-
@[simp]
theorem coe_copy (f : BotHom α β) (f' : α → β) (h : f' = f) : ⇑(f.copy f' h) = f' :=
rfl
#align bot_hom.coe_copy BotHom.coe_copy
+-/
+#print BotHom.copy_eq /-
theorem copy_eq (f : BotHom α β) (f' : α → β) (h : f' = f) : f.copy f' h = f :=
FunLike.ext' h
#align bot_hom.copy_eq BotHom.copy_eq
+-/
instance : Inhabited (BotHom α β) :=
⟨⟨fun _ => ⊥, rfl⟩⟩
@@ -431,17 +489,21 @@ protected def id : BotHom α α :=
#align bot_hom.id BotHom.id
-/
+#print BotHom.coe_id /-
@[simp]
theorem coe_id : ⇑(BotHom.id α) = id :=
rfl
#align bot_hom.coe_id BotHom.coe_id
+-/
variable {α}
+#print BotHom.id_apply /-
@[simp]
theorem id_apply (a : α) : BotHom.id α a = a :=
rfl
#align bot_hom.id_apply BotHom.id_apply
+-/
#print BotHom.comp /-
/-- Composition of `bot_hom`s as a `bot_hom`. -/
@@ -452,42 +514,56 @@ def comp (f : BotHom β γ) (g : BotHom α β) : BotHom α γ
#align bot_hom.comp BotHom.comp
-/
+#print BotHom.coe_comp /-
@[simp]
theorem coe_comp (f : BotHom β γ) (g : BotHom α β) : (f.comp g : α → γ) = f ∘ g :=
rfl
#align bot_hom.coe_comp BotHom.coe_comp
+-/
+#print BotHom.comp_apply /-
@[simp]
theorem comp_apply (f : BotHom β γ) (g : BotHom α β) (a : α) : (f.comp g) a = f (g a) :=
rfl
#align bot_hom.comp_apply BotHom.comp_apply
+-/
+#print BotHom.comp_assoc /-
@[simp]
theorem comp_assoc (f : BotHom γ δ) (g : BotHom β γ) (h : BotHom α β) :
(f.comp g).comp h = f.comp (g.comp h) :=
rfl
#align bot_hom.comp_assoc BotHom.comp_assoc
+-/
+#print BotHom.comp_id /-
@[simp]
theorem comp_id (f : BotHom α β) : f.comp (BotHom.id α) = f :=
BotHom.ext fun a => rfl
#align bot_hom.comp_id BotHom.comp_id
+-/
+#print BotHom.id_comp /-
@[simp]
theorem id_comp (f : BotHom α β) : (BotHom.id β).comp f = f :=
BotHom.ext fun a => rfl
#align bot_hom.id_comp BotHom.id_comp
+-/
+#print BotHom.cancel_right /-
theorem cancel_right {g₁ g₂ : BotHom β γ} {f : BotHom α β} (hf : Surjective f) :
g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
⟨fun h => BotHom.ext <| hf.forall.2 <| FunLike.ext_iff.1 h, congr_arg _⟩
#align bot_hom.cancel_right BotHom.cancel_right
+-/
+#print BotHom.cancel_left /-
theorem cancel_left {g : BotHom β γ} {f₁ f₂ : BotHom α β} (hg : Injective g) :
g.comp f₁ = g.comp f₂ ↔ f₁ = f₂ :=
⟨fun h => BotHom.ext fun a => hg <| by rw [← BotHom.comp_apply, h, BotHom.comp_apply],
congr_arg _⟩
#align bot_hom.cancel_left BotHom.cancel_left
+-/
end Bot
@@ -504,15 +580,19 @@ variable [Preorder β] [OrderBot β]
instance : OrderBot (BotHom α β) :=
⟨⟨⊥, rfl⟩, fun _ => bot_le⟩
+#print BotHom.coe_bot /-
@[simp]
theorem coe_bot : ⇑(⊥ : BotHom α β) = ⊥ :=
rfl
#align bot_hom.coe_bot BotHom.coe_bot
+-/
+#print BotHom.bot_apply /-
@[simp]
theorem bot_apply (a : α) : (⊥ : BotHom α β) a = ⊥ :=
rfl
#align bot_hom.bot_apply BotHom.bot_apply
+-/
end OrderBot
@@ -526,15 +606,19 @@ instance : Inf (BotHom α β) :=
instance : SemilatticeInf (BotHom α β) :=
FunLike.coe_injective.SemilatticeInf _ fun _ _ => rfl
+#print BotHom.coe_inf /-
@[simp]
theorem coe_inf : ⇑(f ⊓ g) = f ⊓ g :=
rfl
#align bot_hom.coe_inf BotHom.coe_inf
+-/
+#print BotHom.inf_apply /-
@[simp]
theorem inf_apply (a : α) : (f ⊓ g) a = f a ⊓ g a :=
rfl
#align bot_hom.inf_apply BotHom.inf_apply
+-/
end SemilatticeInf
@@ -548,15 +632,19 @@ instance : Sup (BotHom α β) :=
instance : SemilatticeSup (BotHom α β) :=
FunLike.coe_injective.SemilatticeSup _ fun _ _ => rfl
+#print BotHom.coe_sup /-
@[simp]
theorem coe_sup : ⇑(f ⊔ g) = f ⊔ g :=
rfl
#align bot_hom.coe_sup BotHom.coe_sup
+-/
+#print BotHom.sup_apply /-
@[simp]
theorem sup_apply (a : α) : (f ⊔ g) a = f a ⊔ g a :=
rfl
#align bot_hom.sup_apply BotHom.sup_apply
+-/
end SemilatticeSup
@@ -576,15 +664,19 @@ namespace BoundedOrderHom
variable [Preorder α] [Preorder β] [Preorder γ] [Preorder δ] [BoundedOrder α] [BoundedOrder β]
[BoundedOrder γ] [BoundedOrder δ]
+#print BoundedOrderHom.toTopHom /-
/-- Reinterpret a `bounded_order_hom` as a `top_hom`. -/
def toTopHom (f : BoundedOrderHom α β) : TopHom α β :=
{ f with }
#align bounded_order_hom.to_top_hom BoundedOrderHom.toTopHom
+-/
+#print BoundedOrderHom.toBotHom /-
/-- Reinterpret a `bounded_order_hom` as a `bot_hom`. -/
def toBotHom (f : BoundedOrderHom α β) : BotHom α β :=
{ f with }
#align bounded_order_hom.to_bot_hom BoundedOrderHom.toBotHom
+-/
instance : BoundedOrderHomClass (BoundedOrderHom α β) α β
where
@@ -604,25 +696,33 @@ theorem toFun_eq_coe {f : BoundedOrderHom α β} : f.toFun = (f : α → β) :=
rfl
#align bounded_order_hom.to_fun_eq_coe BoundedOrderHom.toFun_eq_coe
+#print BoundedOrderHom.ext /-
@[ext]
theorem ext {f g : BoundedOrderHom α β} (h : ∀ a, f a = g a) : f = g :=
FunLike.ext f g h
#align bounded_order_hom.ext BoundedOrderHom.ext
+-/
+#print BoundedOrderHom.copy /-
/-- Copy of a `bounded_order_hom` with a new `to_fun` equal to the old one. Useful to fix
definitional equalities. -/
protected def copy (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : BoundedOrderHom α β :=
{ f.toOrderHom.copy f' h, f.toTopHom.copy f' h, f.toBotHom.copy f' h with }
#align bounded_order_hom.copy BoundedOrderHom.copy
+-/
+#print BoundedOrderHom.coe_copy /-
@[simp]
theorem coe_copy (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : ⇑(f.copy f' h) = f' :=
rfl
#align bounded_order_hom.coe_copy BoundedOrderHom.coe_copy
+-/
+#print BoundedOrderHom.copy_eq /-
theorem copy_eq (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : f.copy f' h = f :=
FunLike.ext' h
#align bounded_order_hom.copy_eq BoundedOrderHom.copy_eq
+-/
variable (α)
@@ -636,17 +736,21 @@ protected def id : BoundedOrderHom α α :=
instance : Inhabited (BoundedOrderHom α α) :=
⟨BoundedOrderHom.id α⟩
+#print BoundedOrderHom.coe_id /-
@[simp]
theorem coe_id : ⇑(BoundedOrderHom.id α) = id :=
rfl
#align bounded_order_hom.coe_id BoundedOrderHom.coe_id
+-/
variable {α}
+#print BoundedOrderHom.id_apply /-
@[simp]
theorem id_apply (a : α) : BoundedOrderHom.id α a = a :=
rfl
#align bounded_order_hom.id_apply BoundedOrderHom.id_apply
+-/
#print BoundedOrderHom.comp /-
/-- Composition of `bounded_order_hom`s as a `bounded_order_hom`. -/
@@ -655,56 +759,75 @@ def comp (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) : BoundedOrderH
#align bounded_order_hom.comp BoundedOrderHom.comp
-/
+#print BoundedOrderHom.coe_comp /-
@[simp]
theorem coe_comp (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) : (f.comp g : α → γ) = f ∘ g :=
rfl
#align bounded_order_hom.coe_comp BoundedOrderHom.coe_comp
+-/
+#print BoundedOrderHom.comp_apply /-
@[simp]
theorem comp_apply (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) (a : α) :
(f.comp g) a = f (g a) :=
rfl
#align bounded_order_hom.comp_apply BoundedOrderHom.comp_apply
+-/
+#print BoundedOrderHom.coe_comp_orderHom /-
@[simp]
theorem coe_comp_orderHom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) :
(f.comp g : OrderHom α γ) = (f : OrderHom β γ).comp g :=
rfl
#align bounded_order_hom.coe_comp_order_hom BoundedOrderHom.coe_comp_orderHom
+-/
+#print BoundedOrderHom.coe_comp_topHom /-
@[simp]
theorem coe_comp_topHom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) :
(f.comp g : TopHom α γ) = (f : TopHom β γ).comp g :=
rfl
#align bounded_order_hom.coe_comp_top_hom BoundedOrderHom.coe_comp_topHom
+-/
+#print BoundedOrderHom.coe_comp_botHom /-
@[simp]
theorem coe_comp_botHom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) :
(f.comp g : BotHom α γ) = (f : BotHom β γ).comp g :=
rfl
#align bounded_order_hom.coe_comp_bot_hom BoundedOrderHom.coe_comp_botHom
+-/
+#print BoundedOrderHom.comp_assoc /-
@[simp]
theorem comp_assoc (f : BoundedOrderHom γ δ) (g : BoundedOrderHom β γ) (h : BoundedOrderHom α β) :
(f.comp g).comp h = f.comp (g.comp h) :=
rfl
#align bounded_order_hom.comp_assoc BoundedOrderHom.comp_assoc
+-/
+#print BoundedOrderHom.comp_id /-
@[simp]
theorem comp_id (f : BoundedOrderHom α β) : f.comp (BoundedOrderHom.id α) = f :=
BoundedOrderHom.ext fun a => rfl
#align bounded_order_hom.comp_id BoundedOrderHom.comp_id
+-/
+#print BoundedOrderHom.id_comp /-
@[simp]
theorem id_comp (f : BoundedOrderHom α β) : (BoundedOrderHom.id β).comp f = f :=
BoundedOrderHom.ext fun a => rfl
#align bounded_order_hom.id_comp BoundedOrderHom.id_comp
+-/
+#print BoundedOrderHom.cancel_right /-
theorem cancel_right {g₁ g₂ : BoundedOrderHom β γ} {f : BoundedOrderHom α β} (hf : Surjective f) :
g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
⟨fun h => BoundedOrderHom.ext <| hf.forall.2 <| FunLike.ext_iff.1 h, congr_arg _⟩
#align bounded_order_hom.cancel_right BoundedOrderHom.cancel_right
+-/
+#print BoundedOrderHom.cancel_left /-
theorem cancel_left {g : BoundedOrderHom β γ} {f₁ f₂ : BoundedOrderHom α β} (hg : Injective g) :
g.comp f₁ = g.comp f₂ ↔ f₁ = f₂ :=
⟨fun h =>
@@ -712,6 +835,7 @@ theorem cancel_left {g : BoundedOrderHom β γ} {f₁ f₂ : BoundedOrderHom α
hg <| by rw [← BoundedOrderHom.comp_apply, h, BoundedOrderHom.comp_apply],
congr_arg _⟩
#align bounded_order_hom.cancel_left BoundedOrderHom.cancel_left
+-/
end BoundedOrderHom
@@ -722,6 +846,7 @@ namespace TopHom
variable [LE α] [OrderTop α] [LE β] [OrderTop β] [LE γ] [OrderTop γ]
+#print TopHom.dual /-
/-- Reinterpret a top homomorphism as a bot homomorphism between the dual lattices. -/
@[simps]
protected def dual : TopHom α β ≃ BotHom αᵒᵈ βᵒᵈ
@@ -731,27 +856,36 @@ protected def dual : TopHom α β ≃ BotHom αᵒᵈ βᵒᵈ
left_inv f := TopHom.ext fun _ => rfl
right_inv f := BotHom.ext fun _ => rfl
#align top_hom.dual TopHom.dual
+-/
+#print TopHom.dual_id /-
@[simp]
theorem dual_id : (TopHom.id α).dual = BotHom.id _ :=
rfl
#align top_hom.dual_id TopHom.dual_id
+-/
+#print TopHom.dual_comp /-
@[simp]
theorem dual_comp (g : TopHom β γ) (f : TopHom α β) : (g.comp f).dual = g.dual.comp f.dual :=
rfl
#align top_hom.dual_comp TopHom.dual_comp
+-/
+#print TopHom.symm_dual_id /-
@[simp]
theorem symm_dual_id : TopHom.dual.symm (BotHom.id _) = TopHom.id α :=
rfl
#align top_hom.symm_dual_id TopHom.symm_dual_id
+-/
+#print TopHom.symm_dual_comp /-
@[simp]
theorem symm_dual_comp (g : BotHom βᵒᵈ γᵒᵈ) (f : BotHom αᵒᵈ βᵒᵈ) :
TopHom.dual.symm (g.comp f) = (TopHom.dual.symm g).comp (TopHom.dual.symm f) :=
rfl
#align top_hom.symm_dual_comp TopHom.symm_dual_comp
+-/
end TopHom
@@ -759,6 +893,7 @@ namespace BotHom
variable [LE α] [OrderBot α] [LE β] [OrderBot β] [LE γ] [OrderBot γ]
+#print BotHom.dual /-
/-- Reinterpret a bot homomorphism as a top homomorphism between the dual lattices. -/
@[simps]
protected def dual : BotHom α β ≃ TopHom αᵒᵈ βᵒᵈ
@@ -768,27 +903,36 @@ protected def dual : BotHom α β ≃ TopHom αᵒᵈ βᵒᵈ
left_inv f := BotHom.ext fun _ => rfl
right_inv f := TopHom.ext fun _ => rfl
#align bot_hom.dual BotHom.dual
+-/
+#print BotHom.dual_id /-
@[simp]
theorem dual_id : (BotHom.id α).dual = TopHom.id _ :=
rfl
#align bot_hom.dual_id BotHom.dual_id
+-/
+#print BotHom.dual_comp /-
@[simp]
theorem dual_comp (g : BotHom β γ) (f : BotHom α β) : (g.comp f).dual = g.dual.comp f.dual :=
rfl
#align bot_hom.dual_comp BotHom.dual_comp
+-/
+#print BotHom.symm_dual_id /-
@[simp]
theorem symm_dual_id : BotHom.dual.symm (TopHom.id _) = BotHom.id α :=
rfl
#align bot_hom.symm_dual_id BotHom.symm_dual_id
+-/
+#print BotHom.symm_dual_comp /-
@[simp]
theorem symm_dual_comp (g : TopHom βᵒᵈ γᵒᵈ) (f : TopHom αᵒᵈ βᵒᵈ) :
BotHom.dual.symm (g.comp f) = (BotHom.dual.symm g).comp (BotHom.dual.symm f) :=
rfl
#align bot_hom.symm_dual_comp BotHom.symm_dual_comp
+-/
end BotHom
@@ -816,11 +960,13 @@ theorem dual_id : (BoundedOrderHom.id α).dual = BoundedOrderHom.id _ :=
#align bounded_order_hom.dual_id BoundedOrderHom.dual_id
-/
+#print BoundedOrderHom.dual_comp /-
@[simp]
theorem dual_comp (g : BoundedOrderHom β γ) (f : BoundedOrderHom α β) :
(g.comp f).dual = g.dual.comp f.dual :=
rfl
#align bounded_order_hom.dual_comp BoundedOrderHom.dual_comp
+-/
#print BoundedOrderHom.symm_dual_id /-
@[simp]
@@ -829,12 +975,14 @@ theorem symm_dual_id : BoundedOrderHom.dual.symm (BoundedOrderHom.id _) = Bounde
#align bounded_order_hom.symm_dual_id BoundedOrderHom.symm_dual_id
-/
+#print BoundedOrderHom.symm_dual_comp /-
@[simp]
theorem symm_dual_comp (g : BoundedOrderHom βᵒᵈ γᵒᵈ) (f : BoundedOrderHom αᵒᵈ βᵒᵈ) :
BoundedOrderHom.dual.symm (g.comp f) =
(BoundedOrderHom.dual.symm g).comp (BoundedOrderHom.dual.symm f) :=
rfl
#align bounded_order_hom.symm_dual_comp BoundedOrderHom.symm_dual_comp
+-/
end BoundedOrderHom
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -59,7 +59,7 @@ structure BotHom (α β : Type _) [Bot α] [Bot β] where
#print BoundedOrderHom /-
/-- The type of bounded order homomorphisms from `α` to `β`. -/
structure BoundedOrderHom (α β : Type _) [Preorder α] [Preorder β] [BoundedOrder α]
- [BoundedOrder β] extends OrderHom α β where
+ [BoundedOrder β] extends OrderHom α β where
map_top' : to_fun ⊤ = ⊤
map_bot' : to_fun ⊥ = ⊥
#align bounded_order_hom BoundedOrderHom
@@ -72,7 +72,7 @@ section
You should extend this class when you extend `top_hom`. -/
class TopHomClass (F : Type _) (α β : outParam <| Type _) [Top α] [Top β] extends
- FunLike F α fun _ => β where
+ FunLike F α fun _ => β where
map_top (f : F) : f ⊤ = ⊤
#align top_hom_class TopHomClass
-/
@@ -82,7 +82,7 @@ class TopHomClass (F : Type _) (α β : outParam <| Type _) [Top α] [Top β] ex
You should extend this class when you extend `bot_hom`. -/
class BotHomClass (F : Type _) (α β : outParam <| Type _) [Bot α] [Bot β] extends
- FunLike F α fun _ => β where
+ FunLike F α fun _ => β where
map_bot (f : F) : f ⊥ = ⊥
#align bot_hom_class BotHomClass
-/
@@ -92,7 +92,7 @@ class BotHomClass (F : Type _) (α β : outParam <| Type _) [Bot α] [Bot β] ex
You should extend this class when you extend `bounded_order_hom`. -/
class BoundedOrderHomClass (F : Type _) (α β : outParam <| Type _) [LE α] [LE β] [BoundedOrder α]
- [BoundedOrder β] extends RelHomClass F ((· ≤ ·) : α → α → Prop) ((· ≤ ·) : β → β → Prop) where
+ [BoundedOrder β] extends RelHomClass F ((· ≤ ·) : α → α → Prop) ((· ≤ ·) : β → β → Prop) where
map_top (f : F) : f ⊤ = ⊤
map_bot (f : F) : f ⊥ = ⊥
#align bounded_order_hom_class BoundedOrderHomClass
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -188,12 +188,10 @@ directly. -/
instance : CoeFun (TopHom α β) fun _ => α → β :=
FunLike.hasCoeToFun
-/- warning: top_hom.to_fun_eq_coe clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align top_hom.to_fun_eq_coe [anonymous]ₓ'. -/
@[simp]
-theorem [anonymous] {f : TopHom α β} : f.toFun = (f : α → β) :=
+theorem toFun_eq_coe {f : TopHom α β} : f.toFun = (f : α → β) :=
rfl
-#align top_hom.to_fun_eq_coe [anonymous]
+#align top_hom.to_fun_eq_coe TopHom.toFun_eq_coe
-- this must come after the coe_to_fun definition
initialize_simps_projections TopHom (toFun → apply)
@@ -391,12 +389,10 @@ directly. -/
instance : CoeFun (BotHom α β) fun _ => α → β :=
FunLike.hasCoeToFun
-/- warning: bot_hom.to_fun_eq_coe clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align bot_hom.to_fun_eq_coe [anonymous]ₓ'. -/
@[simp]
-theorem [anonymous] {f : BotHom α β} : f.toFun = (f : α → β) :=
+theorem toFun_eq_coe {f : BotHom α β} : f.toFun = (f : α → β) :=
rfl
-#align bot_hom.to_fun_eq_coe [anonymous]
+#align bot_hom.to_fun_eq_coe BotHom.toFun_eq_coe
-- this must come after the coe_to_fun definition
initialize_simps_projections BotHom (toFun → apply)
@@ -603,12 +599,10 @@ directly. -/
instance : CoeFun (BoundedOrderHom α β) fun _ => α → β :=
FunLike.hasCoeToFun
-/- warning: bounded_order_hom.to_fun_eq_coe clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align bounded_order_hom.to_fun_eq_coe [anonymous]ₓ'. -/
@[simp]
-theorem [anonymous] {f : BoundedOrderHom α β} : f.toFun = (f : α → β) :=
+theorem toFun_eq_coe {f : BoundedOrderHom α β} : f.toFun = (f : α → β) :=
rfl
-#align bounded_order_hom.to_fun_eq_coe [anonymous]
+#align bounded_order_hom.to_fun_eq_coe BoundedOrderHom.toFun_eq_coe
@[ext]
theorem ext {f g : BoundedOrderHom α β} (h : ∀ a, f a = g a) : f = g :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -56,12 +56,14 @@ structure BotHom (α β : Type _) [Bot α] [Bot β] where
#align bot_hom BotHom
-/
+#print BoundedOrderHom /-
/-- The type of bounded order homomorphisms from `α` to `β`. -/
structure BoundedOrderHom (α β : Type _) [Preorder α] [Preorder β] [BoundedOrder α]
[BoundedOrder β] extends OrderHom α β where
map_top' : to_fun ⊤ = ⊤
map_bot' : to_fun ⊥ = ⊥
#align bounded_order_hom BoundedOrderHom
+-/
section
@@ -131,12 +133,14 @@ instance (priority := 100) OrderIsoClass.toBotHomClass [LE α] [OrderBot α] [Pa
map_bot := fun f => le_bot_iff.1 <| (le_map_inv_iff f).1 bot_le }
#align order_iso_class.to_bot_hom_class OrderIsoClass.toBotHomClass
+#print OrderIsoClass.toBoundedOrderHomClass /-
-- See note [lower instance priority]
instance (priority := 100) OrderIsoClass.toBoundedOrderHomClass [LE α] [BoundedOrder α]
[PartialOrder β] [BoundedOrder β] [OrderIsoClass F α β] : BoundedOrderHomClass F α β :=
{ show OrderHomClass F α β from inferInstance, OrderIsoClass.toTopHomClass,
OrderIsoClass.toBotHomClass with }
#align order_iso_class.to_bounded_order_hom_class OrderIsoClass.toBoundedOrderHomClass
+-/
@[simp]
theorem map_eq_top_iff [LE α] [OrderTop α] [PartialOrder β] [OrderTop β] [OrderIsoClass F α β]
@@ -628,10 +632,12 @@ theorem copy_eq (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : f.co
variable (α)
+#print BoundedOrderHom.id /-
/-- `id` as a `bounded_order_hom`. -/
protected def id : BoundedOrderHom α α :=
{ OrderHom.id, TopHom.id α, BotHom.id α with }
#align bounded_order_hom.id BoundedOrderHom.id
+-/
instance : Inhabited (BoundedOrderHom α α) :=
⟨BoundedOrderHom.id α⟩
@@ -648,10 +654,12 @@ theorem id_apply (a : α) : BoundedOrderHom.id α a = a :=
rfl
#align bounded_order_hom.id_apply BoundedOrderHom.id_apply
+#print BoundedOrderHom.comp /-
/-- Composition of `bounded_order_hom`s as a `bounded_order_hom`. -/
def comp (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) : BoundedOrderHom α γ :=
{ f.toOrderHom.comp g.toOrderHom, f.toTopHom.comp g.toTopHom, f.toBotHom.comp g.toBotHom with }
#align bounded_order_hom.comp BoundedOrderHom.comp
+-/
@[simp]
theorem coe_comp (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) : (f.comp g : α → γ) = f ∘ g :=
@@ -794,6 +802,7 @@ namespace BoundedOrderHom
variable [Preorder α] [BoundedOrder α] [Preorder β] [BoundedOrder β] [Preorder γ] [BoundedOrder γ]
+#print BoundedOrderHom.dual /-
/-- Reinterpret a bounded order homomorphism as a bounded order homomorphism between the dual
orders. -/
@[simps]
@@ -804,11 +813,14 @@ protected def dual : BoundedOrderHom α β ≃ BoundedOrderHom αᵒᵈ βᵒᵈ
left_inv f := ext fun a => rfl
right_inv f := ext fun a => rfl
#align bounded_order_hom.dual BoundedOrderHom.dual
+-/
+#print BoundedOrderHom.dual_id /-
@[simp]
theorem dual_id : (BoundedOrderHom.id α).dual = BoundedOrderHom.id _ :=
rfl
#align bounded_order_hom.dual_id BoundedOrderHom.dual_id
+-/
@[simp]
theorem dual_comp (g : BoundedOrderHom β γ) (f : BoundedOrderHom α β) :
@@ -816,10 +828,12 @@ theorem dual_comp (g : BoundedOrderHom β γ) (f : BoundedOrderHom α β) :
rfl
#align bounded_order_hom.dual_comp BoundedOrderHom.dual_comp
+#print BoundedOrderHom.symm_dual_id /-
@[simp]
theorem symm_dual_id : BoundedOrderHom.dual.symm (BoundedOrderHom.id _) = BoundedOrderHom.id α :=
rfl
#align bounded_order_hom.symm_dual_id BoundedOrderHom.symm_dual_id
+-/
@[simp]
theorem symm_dual_comp (g : BoundedOrderHom βᵒᵈ γᵒᵈ) (f : BoundedOrderHom αᵒᵈ βᵒᵈ) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -56,12 +56,6 @@ structure BotHom (α β : Type _) [Bot α] [Bot β] where
#align bot_hom BotHom
-/
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-Case conversion may be inaccurate. Consider using '#align bounded_order_hom BoundedOrderHomₓ'. -/
/-- The type of bounded order homomorphisms from `α` to `β`. -/
structure BoundedOrderHom (α β : Type _) [Preorder α] [Preorder β] [BoundedOrder α]
[BoundedOrder β] extends OrderHom α β where
@@ -110,36 +104,18 @@ export BotHomClass (map_bot)
attribute [simp] map_top map_bot
-/- warning: bounded_order_hom_class.to_top_hom_class -> BoundedOrderHomClass.toTopHomClass is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align bounded_order_hom_class.to_top_hom_class BoundedOrderHomClass.toTopHomClassₓ'. -/
-- See note [lower instance priority]
instance (priority := 100) BoundedOrderHomClass.toTopHomClass [LE α] [LE β] [BoundedOrder α]
[BoundedOrder β] [BoundedOrderHomClass F α β] : TopHomClass F α β :=
{ ‹BoundedOrderHomClass F α β› with }
#align bounded_order_hom_class.to_top_hom_class BoundedOrderHomClass.toTopHomClass
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-- See note [lower instance priority]
instance (priority := 100) BoundedOrderHomClass.toBotHomClass [LE α] [LE β] [BoundedOrder α]
[BoundedOrder β] [BoundedOrderHomClass F α β] : BotHomClass F α β :=
{ ‹BoundedOrderHomClass F α β› with }
#align bounded_order_hom_class.to_bot_hom_class BoundedOrderHomClass.toBotHomClass
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-Case conversion may be inaccurate. Consider using '#align order_iso_class.to_top_hom_class OrderIsoClass.toTopHomClassₓ'. -/
-- See note [lower instance priority]
instance (priority := 100) OrderIsoClass.toTopHomClass [LE α] [OrderTop α] [PartialOrder β]
[OrderTop β] [OrderIsoClass F α β] : TopHomClass F α β :=
@@ -147,12 +123,6 @@ instance (priority := 100) OrderIsoClass.toTopHomClass [LE α] [OrderTop α] [Pa
map_top := fun f => top_le_iff.1 <| (map_inv_le_iff f).1 le_top }
#align order_iso_class.to_top_hom_class OrderIsoClass.toTopHomClass
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-- See note [lower instance priority]
instance (priority := 100) OrderIsoClass.toBotHomClass [LE α] [OrderBot α] [PartialOrder β]
[OrderBot β] [OrderIsoClass F α β] : BotHomClass F α β :=
@@ -161,12 +131,6 @@ instance (priority := 100) OrderIsoClass.toBotHomClass [LE α] [OrderBot α] [Pa
map_bot := fun f => le_bot_iff.1 <| (le_map_inv_iff f).1 bot_le }
#align order_iso_class.to_bot_hom_class OrderIsoClass.toBotHomClass
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-Case conversion may be inaccurate. Consider using '#align order_iso_class.to_bounded_order_hom_class OrderIsoClass.toBoundedOrderHomClassₓ'. -/
-- See note [lower instance priority]
instance (priority := 100) OrderIsoClass.toBoundedOrderHomClass [LE α] [BoundedOrder α]
[PartialOrder β] [BoundedOrder β] [OrderIsoClass F α β] : BoundedOrderHomClass F α β :=
@@ -174,23 +138,11 @@ instance (priority := 100) OrderIsoClass.toBoundedOrderHomClass [LE α] [Bounded
OrderIsoClass.toBotHomClass with }
#align order_iso_class.to_bounded_order_hom_class OrderIsoClass.toBoundedOrderHomClass
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@[simp]
theorem map_eq_top_iff [LE α] [OrderTop α] [PartialOrder β] [OrderTop β] [OrderIsoClass F α β]
(f : F) {a : α} : f a = ⊤ ↔ a = ⊤ := by rw [← map_top f, (EquivLike.injective f).eq_iff]
#align map_eq_top_iff map_eq_top_iff
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@[simp]
theorem map_eq_bot_iff [LE α] [OrderBot α] [PartialOrder β] [OrderBot β] [OrderIsoClass F α β]
(f : F) {a : α} : f a = ⊥ ↔ a = ⊥ := by rw [← map_bot f, (EquivLike.injective f).eq_iff]
@@ -233,11 +185,6 @@ instance : CoeFun (TopHom α β) fun _ => α → β :=
FunLike.hasCoeToFun
/- warning: top_hom.to_fun_eq_coe clashes with [anonymous] -> [anonymous]
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@[simp]
theorem [anonymous] {f : TopHom α β} : f.toFun = (f : α → β) :=
@@ -247,23 +194,11 @@ theorem [anonymous] {f : TopHom α β} : f.toFun = (f : α → β) :=
-- this must come after the coe_to_fun definition
initialize_simps_projections TopHom (toFun → apply)
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@[ext]
theorem ext {f g : TopHom α β} (h : ∀ a, f a = g a) : f = g :=
FunLike.ext f g h
#align top_hom.ext TopHom.ext
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/-- Copy of a `top_hom` with a new `to_fun` equal to the old one. Useful to fix definitional
equalities. -/
protected def copy (f : TopHom α β) (f' : α → β) (h : f' = f) : TopHom α β
@@ -272,23 +207,11 @@ protected def copy (f : TopHom α β) (f' : α → β) (h : f' = f) : TopHom α
map_top' := h.symm ▸ f.map_top'
#align top_hom.copy TopHom.copy
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@[simp]
theorem coe_copy (f : TopHom α β) (f' : α → β) (h : f' = f) : ⇑(f.copy f' h) = f' :=
rfl
#align top_hom.coe_copy TopHom.coe_copy
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theorem copy_eq (f : TopHom α β) (f' : α → β) (h : f' = f) : f.copy f' h = f :=
FunLike.ext' h
#align top_hom.copy_eq TopHom.copy_eq
@@ -305,12 +228,6 @@ protected def id : TopHom α α :=
#align top_hom.id TopHom.id
-/
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@[simp]
theorem coe_id : ⇑(TopHom.id α) = id :=
rfl
@@ -318,12 +235,6 @@ theorem coe_id : ⇑(TopHom.id α) = id :=
variable {α}
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@[simp]
theorem id_apply (a : α) : TopHom.id α a = a :=
rfl
@@ -338,79 +249,37 @@ def comp (f : TopHom β γ) (g : TopHom α β) : TopHom α γ
#align top_hom.comp TopHom.comp
-/
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@[simp]
theorem coe_comp (f : TopHom β γ) (g : TopHom α β) : (f.comp g : α → γ) = f ∘ g :=
rfl
#align top_hom.coe_comp TopHom.coe_comp
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@[simp]
theorem comp_apply (f : TopHom β γ) (g : TopHom α β) (a : α) : (f.comp g) a = f (g a) :=
rfl
#align top_hom.comp_apply TopHom.comp_apply
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@[simp]
theorem comp_assoc (f : TopHom γ δ) (g : TopHom β γ) (h : TopHom α β) :
(f.comp g).comp h = f.comp (g.comp h) :=
rfl
#align top_hom.comp_assoc TopHom.comp_assoc
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@[simp]
theorem comp_id (f : TopHom α β) : f.comp (TopHom.id α) = f :=
TopHom.ext fun a => rfl
#align top_hom.comp_id TopHom.comp_id
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@[simp]
theorem id_comp (f : TopHom α β) : (TopHom.id β).comp f = f :=
TopHom.ext fun a => rfl
#align top_hom.id_comp TopHom.id_comp
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theorem cancel_right {g₁ g₂ : TopHom β γ} {f : TopHom α β} (hf : Surjective f) :
g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
⟨fun h => TopHom.ext <| hf.forall.2 <| FunLike.ext_iff.1 h, congr_arg _⟩
#align top_hom.cancel_right TopHom.cancel_right
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theorem cancel_left {g : TopHom β γ} {f₁ f₂ : TopHom α β} (hg : Injective g) :
g.comp f₁ = g.comp f₂ ↔ f₁ = f₂ :=
⟨fun h => TopHom.ext fun a => hg <| by rw [← TopHom.comp_apply, h, TopHom.comp_apply],
@@ -432,23 +301,11 @@ variable [Preorder β] [OrderTop β]
instance : OrderTop (TopHom α β) :=
⟨⟨⊤, rfl⟩, fun _ => le_top⟩
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@[simp]
theorem coe_top : ⇑(⊤ : TopHom α β) = ⊤ :=
rfl
#align top_hom.coe_top TopHom.coe_top
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@[simp]
theorem top_apply (a : α) : (⊤ : TopHom α β) a = ⊤ :=
rfl
@@ -466,23 +323,11 @@ instance : Inf (TopHom α β) :=
instance : SemilatticeInf (TopHom α β) :=
FunLike.coe_injective.SemilatticeInf _ fun _ _ => rfl
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@[simp]
theorem coe_inf : ⇑(f ⊓ g) = f ⊓ g :=
rfl
#align top_hom.coe_inf TopHom.coe_inf
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@[simp]
theorem inf_apply (a : α) : (f ⊓ g) a = f a ⊓ g a :=
rfl
@@ -500,23 +345,11 @@ instance : Sup (TopHom α β) :=
instance : SemilatticeSup (TopHom α β) :=
FunLike.coe_injective.SemilatticeSup _ fun _ _ => rfl
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@[simp]
theorem coe_sup : ⇑(f ⊔ g) = f ⊔ g :=
rfl
#align top_hom.coe_sup TopHom.coe_sup
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@[simp]
theorem sup_apply (a : α) : (f ⊔ g) a = f a ⊔ g a :=
rfl
@@ -555,11 +388,6 @@ instance : CoeFun (BotHom α β) fun _ => α → β :=
FunLike.hasCoeToFun
/- warning: bot_hom.to_fun_eq_coe clashes with [anonymous] -> [anonymous]
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Case conversion may be inaccurate. Consider using '#align bot_hom.to_fun_eq_coe [anonymous]ₓ'. -/
@[simp]
theorem [anonymous] {f : BotHom α β} : f.toFun = (f : α → β) :=
@@ -569,23 +397,11 @@ theorem [anonymous] {f : BotHom α β} : f.toFun = (f : α → β) :=
-- this must come after the coe_to_fun definition
initialize_simps_projections BotHom (toFun → apply)
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@[ext]
theorem ext {f g : BotHom α β} (h : ∀ a, f a = g a) : f = g :=
FunLike.ext f g h
#align bot_hom.ext BotHom.ext
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/-- Copy of a `bot_hom` with a new `to_fun` equal to the old one. Useful to fix definitional
equalities. -/
protected def copy (f : BotHom α β) (f' : α → β) (h : f' = f) : BotHom α β
@@ -594,23 +410,11 @@ protected def copy (f : BotHom α β) (f' : α → β) (h : f' = f) : BotHom α
map_bot' := h.symm ▸ f.map_bot'
#align bot_hom.copy BotHom.copy
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@[simp]
theorem coe_copy (f : BotHom α β) (f' : α → β) (h : f' = f) : ⇑(f.copy f' h) = f' :=
rfl
#align bot_hom.coe_copy BotHom.coe_copy
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theorem copy_eq (f : BotHom α β) (f' : α → β) (h : f' = f) : f.copy f' h = f :=
FunLike.ext' h
#align bot_hom.copy_eq BotHom.copy_eq
@@ -627,12 +431,6 @@ protected def id : BotHom α α :=
#align bot_hom.id BotHom.id
-/
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@[simp]
theorem coe_id : ⇑(BotHom.id α) = id :=
rfl
@@ -640,12 +438,6 @@ theorem coe_id : ⇑(BotHom.id α) = id :=
variable {α}
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@[simp]
theorem id_apply (a : α) : BotHom.id α a = a :=
rfl
@@ -660,79 +452,37 @@ def comp (f : BotHom β γ) (g : BotHom α β) : BotHom α γ
#align bot_hom.comp BotHom.comp
-/
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@[simp]
theorem coe_comp (f : BotHom β γ) (g : BotHom α β) : (f.comp g : α → γ) = f ∘ g :=
rfl
#align bot_hom.coe_comp BotHom.coe_comp
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@[simp]
theorem comp_apply (f : BotHom β γ) (g : BotHom α β) (a : α) : (f.comp g) a = f (g a) :=
rfl
#align bot_hom.comp_apply BotHom.comp_apply
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@[simp]
theorem comp_assoc (f : BotHom γ δ) (g : BotHom β γ) (h : BotHom α β) :
(f.comp g).comp h = f.comp (g.comp h) :=
rfl
#align bot_hom.comp_assoc BotHom.comp_assoc
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@[simp]
theorem comp_id (f : BotHom α β) : f.comp (BotHom.id α) = f :=
BotHom.ext fun a => rfl
#align bot_hom.comp_id BotHom.comp_id
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@[simp]
theorem id_comp (f : BotHom α β) : (BotHom.id β).comp f = f :=
BotHom.ext fun a => rfl
#align bot_hom.id_comp BotHom.id_comp
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theorem cancel_right {g₁ g₂ : BotHom β γ} {f : BotHom α β} (hf : Surjective f) :
g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
⟨fun h => BotHom.ext <| hf.forall.2 <| FunLike.ext_iff.1 h, congr_arg _⟩
#align bot_hom.cancel_right BotHom.cancel_right
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theorem cancel_left {g : BotHom β γ} {f₁ f₂ : BotHom α β} (hg : Injective g) :
g.comp f₁ = g.comp f₂ ↔ f₁ = f₂ :=
⟨fun h => BotHom.ext fun a => hg <| by rw [← BotHom.comp_apply, h, BotHom.comp_apply],
@@ -754,23 +504,11 @@ variable [Preorder β] [OrderBot β]
instance : OrderBot (BotHom α β) :=
⟨⟨⊥, rfl⟩, fun _ => bot_le⟩
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@[simp]
theorem coe_bot : ⇑(⊥ : BotHom α β) = ⊥ :=
rfl
#align bot_hom.coe_bot BotHom.coe_bot
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@[simp]
theorem bot_apply (a : α) : (⊥ : BotHom α β) a = ⊥ :=
rfl
@@ -788,23 +526,11 @@ instance : Inf (BotHom α β) :=
instance : SemilatticeInf (BotHom α β) :=
FunLike.coe_injective.SemilatticeInf _ fun _ _ => rfl
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@[simp]
theorem coe_inf : ⇑(f ⊓ g) = f ⊓ g :=
rfl
#align bot_hom.coe_inf BotHom.coe_inf
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@[simp]
theorem inf_apply (a : α) : (f ⊓ g) a = f a ⊓ g a :=
rfl
@@ -822,23 +548,11 @@ instance : Sup (BotHom α β) :=
instance : SemilatticeSup (BotHom α β) :=
FunLike.coe_injective.SemilatticeSup _ fun _ _ => rfl
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@[simp]
theorem coe_sup : ⇑(f ⊔ g) = f ⊔ g :=
rfl
#align bot_hom.coe_sup BotHom.coe_sup
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@[simp]
theorem sup_apply (a : α) : (f ⊔ g) a = f a ⊔ g a :=
rfl
@@ -862,23 +576,11 @@ namespace BoundedOrderHom
variable [Preorder α] [Preorder β] [Preorder γ] [Preorder δ] [BoundedOrder α] [BoundedOrder β]
[BoundedOrder γ] [BoundedOrder δ]
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/-- Reinterpret a `bounded_order_hom` as a `top_hom`. -/
def toTopHom (f : BoundedOrderHom α β) : TopHom α β :=
{ f with }
#align bounded_order_hom.to_top_hom BoundedOrderHom.toTopHom
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/-- Reinterpret a `bounded_order_hom` as a `bot_hom`. -/
def toBotHom (f : BoundedOrderHom α β) : BotHom α β :=
{ f with }
@@ -898,69 +600,34 @@ instance : CoeFun (BoundedOrderHom α β) fun _ => α → β :=
FunLike.hasCoeToFun
/- warning: bounded_order_hom.to_fun_eq_coe clashes with [anonymous] -> [anonymous]
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@[simp]
theorem [anonymous] {f : BoundedOrderHom α β} : f.toFun = (f : α → β) :=
rfl
#align bounded_order_hom.to_fun_eq_coe [anonymous]
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@[ext]
theorem ext {f g : BoundedOrderHom α β} (h : ∀ a, f a = g a) : f = g :=
FunLike.ext f g h
#align bounded_order_hom.ext BoundedOrderHom.ext
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/-- Copy of a `bounded_order_hom` with a new `to_fun` equal to the old one. Useful to fix
definitional equalities. -/
protected def copy (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : BoundedOrderHom α β :=
{ f.toOrderHom.copy f' h, f.toTopHom.copy f' h, f.toBotHom.copy f' h with }
#align bounded_order_hom.copy BoundedOrderHom.copy
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@[simp]
theorem coe_copy (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : ⇑(f.copy f' h) = f' :=
rfl
#align bounded_order_hom.coe_copy BoundedOrderHom.coe_copy
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theorem copy_eq (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : f.copy f' h = f :=
FunLike.ext' h
#align bounded_order_hom.copy_eq BoundedOrderHom.copy_eq
variable (α)
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/-- `id` as a `bounded_order_hom`. -/
protected def id : BoundedOrderHom α α :=
{ OrderHom.id, TopHom.id α, BotHom.id α with }
@@ -969,12 +636,6 @@ protected def id : BoundedOrderHom α α :=
instance : Inhabited (BoundedOrderHom α α) :=
⟨BoundedOrderHom.id α⟩
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@[simp]
theorem coe_id : ⇑(BoundedOrderHom.id α) = id :=
rfl
@@ -982,117 +643,66 @@ theorem coe_id : ⇑(BoundedOrderHom.id α) = id :=
variable {α}
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@[simp]
theorem id_apply (a : α) : BoundedOrderHom.id α a = a :=
rfl
#align bounded_order_hom.id_apply BoundedOrderHom.id_apply
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/-- Composition of `bounded_order_hom`s as a `bounded_order_hom`. -/
def comp (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) : BoundedOrderHom α γ :=
{ f.toOrderHom.comp g.toOrderHom, f.toTopHom.comp g.toTopHom, f.toBotHom.comp g.toBotHom with }
#align bounded_order_hom.comp BoundedOrderHom.comp
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@[simp]
theorem coe_comp (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) : (f.comp g : α → γ) = f ∘ g :=
rfl
#align bounded_order_hom.coe_comp BoundedOrderHom.coe_comp
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@[simp]
theorem comp_apply (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) (a : α) :
(f.comp g) a = f (g a) :=
rfl
#align bounded_order_hom.comp_apply BoundedOrderHom.comp_apply
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@[simp]
theorem coe_comp_orderHom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) :
(f.comp g : OrderHom α γ) = (f : OrderHom β γ).comp g :=
rfl
#align bounded_order_hom.coe_comp_order_hom BoundedOrderHom.coe_comp_orderHom
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@[simp]
theorem coe_comp_topHom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) :
(f.comp g : TopHom α γ) = (f : TopHom β γ).comp g :=
rfl
#align bounded_order_hom.coe_comp_top_hom BoundedOrderHom.coe_comp_topHom
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@[simp]
theorem coe_comp_botHom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) :
(f.comp g : BotHom α γ) = (f : BotHom β γ).comp g :=
rfl
#align bounded_order_hom.coe_comp_bot_hom BoundedOrderHom.coe_comp_botHom
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@[simp]
theorem comp_assoc (f : BoundedOrderHom γ δ) (g : BoundedOrderHom β γ) (h : BoundedOrderHom α β) :
(f.comp g).comp h = f.comp (g.comp h) :=
rfl
#align bounded_order_hom.comp_assoc BoundedOrderHom.comp_assoc
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@[simp]
theorem comp_id (f : BoundedOrderHom α β) : f.comp (BoundedOrderHom.id α) = f :=
BoundedOrderHom.ext fun a => rfl
#align bounded_order_hom.comp_id BoundedOrderHom.comp_id
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@[simp]
theorem id_comp (f : BoundedOrderHom α β) : (BoundedOrderHom.id β).comp f = f :=
BoundedOrderHom.ext fun a => rfl
#align bounded_order_hom.id_comp BoundedOrderHom.id_comp
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theorem cancel_right {g₁ g₂ : BoundedOrderHom β γ} {f : BoundedOrderHom α β} (hf : Surjective f) :
g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
⟨fun h => BoundedOrderHom.ext <| hf.forall.2 <| FunLike.ext_iff.1 h, congr_arg _⟩
#align bounded_order_hom.cancel_right BoundedOrderHom.cancel_right
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theorem cancel_left {g : BoundedOrderHom β γ} {f₁ f₂ : BoundedOrderHom α β} (hg : Injective g) :
g.comp f₁ = g.comp f₂ ↔ f₁ = f₂ :=
⟨fun h =>
@@ -1110,12 +720,6 @@ namespace TopHom
variable [LE α] [OrderTop α] [LE β] [OrderTop β] [LE γ] [OrderTop γ]
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/-- Reinterpret a top homomorphism as a bot homomorphism between the dual lattices. -/
@[simps]
protected def dual : TopHom α β ≃ BotHom αᵒᵈ βᵒᵈ
@@ -1126,39 +730,21 @@ protected def dual : TopHom α β ≃ BotHom αᵒᵈ βᵒᵈ
right_inv f := BotHom.ext fun _ => rfl
#align top_hom.dual TopHom.dual
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@[simp]
theorem dual_id : (TopHom.id α).dual = BotHom.id _ :=
rfl
#align top_hom.dual_id TopHom.dual_id
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@[simp]
theorem dual_comp (g : TopHom β γ) (f : TopHom α β) : (g.comp f).dual = g.dual.comp f.dual :=
rfl
#align top_hom.dual_comp TopHom.dual_comp
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@[simp]
theorem symm_dual_id : TopHom.dual.symm (BotHom.id _) = TopHom.id α :=
rfl
#align top_hom.symm_dual_id TopHom.symm_dual_id
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@[simp]
theorem symm_dual_comp (g : BotHom βᵒᵈ γᵒᵈ) (f : BotHom αᵒᵈ βᵒᵈ) :
TopHom.dual.symm (g.comp f) = (TopHom.dual.symm g).comp (TopHom.dual.symm f) :=
@@ -1171,12 +757,6 @@ namespace BotHom
variable [LE α] [OrderBot α] [LE β] [OrderBot β] [LE γ] [OrderBot γ]
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/-- Reinterpret a bot homomorphism as a top homomorphism between the dual lattices. -/
@[simps]
protected def dual : BotHom α β ≃ TopHom αᵒᵈ βᵒᵈ
@@ -1187,39 +767,21 @@ protected def dual : BotHom α β ≃ TopHom αᵒᵈ βᵒᵈ
right_inv f := TopHom.ext fun _ => rfl
#align bot_hom.dual BotHom.dual
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@[simp]
theorem dual_id : (BotHom.id α).dual = TopHom.id _ :=
rfl
#align bot_hom.dual_id BotHom.dual_id
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@[simp]
theorem dual_comp (g : BotHom β γ) (f : BotHom α β) : (g.comp f).dual = g.dual.comp f.dual :=
rfl
#align bot_hom.dual_comp BotHom.dual_comp
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@[simp]
theorem symm_dual_id : BotHom.dual.symm (TopHom.id _) = BotHom.id α :=
rfl
#align bot_hom.symm_dual_id BotHom.symm_dual_id
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@[simp]
theorem symm_dual_comp (g : TopHom βᵒᵈ γᵒᵈ) (f : TopHom αᵒᵈ βᵒᵈ) :
BotHom.dual.symm (g.comp f) = (BotHom.dual.symm g).comp (BotHom.dual.symm f) :=
@@ -1232,12 +794,6 @@ namespace BoundedOrderHom
variable [Preorder α] [BoundedOrder α] [Preorder β] [BoundedOrder β] [Preorder γ] [BoundedOrder γ]
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/-- Reinterpret a bounded order homomorphism as a bounded order homomorphism between the dual
orders. -/
@[simps]
@@ -1249,40 +805,22 @@ protected def dual : BoundedOrderHom α β ≃ BoundedOrderHom αᵒᵈ βᵒᵈ
right_inv f := ext fun a => rfl
#align bounded_order_hom.dual BoundedOrderHom.dual
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@[simp]
theorem dual_id : (BoundedOrderHom.id α).dual = BoundedOrderHom.id _ :=
rfl
#align bounded_order_hom.dual_id BoundedOrderHom.dual_id
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@[simp]
theorem dual_comp (g : BoundedOrderHom β γ) (f : BoundedOrderHom α β) :
(g.comp f).dual = g.dual.comp f.dual :=
rfl
#align bounded_order_hom.dual_comp BoundedOrderHom.dual_comp
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@[simp]
theorem symm_dual_id : BoundedOrderHom.dual.symm (BoundedOrderHom.id _) = BoundedOrderHom.id α :=
rfl
#align bounded_order_hom.symm_dual_id BoundedOrderHom.symm_dual_id
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@[simp]
theorem symm_dual_comp (g : BoundedOrderHom βᵒᵈ γᵒᵈ) (f : BoundedOrderHom αᵒᵈ βᵒᵈ) :
BoundedOrderHom.dual.symm (g.comp f) =
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -1005,10 +1005,7 @@ def comp (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) : BoundedOrderH
#align bounded_order_hom.comp BoundedOrderHom.comp
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@[simp]
theorem coe_comp (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) : (f.comp g : α → γ) = f ∘ g :=
@@ -1016,10 +1013,7 @@ theorem coe_comp (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) : (f.co
#align bounded_order_hom.coe_comp BoundedOrderHom.coe_comp
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Case conversion may be inaccurate. Consider using '#align bounded_order_hom.comp_apply BoundedOrderHom.comp_applyₓ'. -/
@[simp]
theorem comp_apply (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) (a : α) :
@@ -1028,10 +1022,7 @@ theorem comp_apply (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) (a :
#align bounded_order_hom.comp_apply BoundedOrderHom.comp_apply
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Case conversion may be inaccurate. Consider using '#align bounded_order_hom.coe_comp_order_hom BoundedOrderHom.coe_comp_orderHomₓ'. -/
@[simp]
theorem coe_comp_orderHom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) :
@@ -1040,10 +1031,7 @@ theorem coe_comp_orderHom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β
#align bounded_order_hom.coe_comp_order_hom BoundedOrderHom.coe_comp_orderHom
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Case conversion may be inaccurate. Consider using '#align bounded_order_hom.coe_comp_top_hom BoundedOrderHom.coe_comp_topHomₓ'. -/
@[simp]
theorem coe_comp_topHom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) :
@@ -1052,10 +1040,7 @@ theorem coe_comp_topHom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β)
#align bounded_order_hom.coe_comp_top_hom BoundedOrderHom.coe_comp_topHom
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Case conversion may be inaccurate. Consider using '#align bounded_order_hom.coe_comp_bot_hom BoundedOrderHom.coe_comp_botHomₓ'. -/
@[simp]
theorem coe_comp_botHom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) :
@@ -1098,10 +1083,7 @@ theorem id_comp (f : BoundedOrderHom α β) : (BoundedOrderHom.id β).comp f = f
#align bounded_order_hom.id_comp BoundedOrderHom.id_comp
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Case conversion may be inaccurate. Consider using '#align bounded_order_hom.cancel_right BoundedOrderHom.cancel_rightₓ'. -/
theorem cancel_right {g₁ g₂ : BoundedOrderHom β γ} {f : BoundedOrderHom α β} (hf : Surjective f) :
g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
@@ -1109,10 +1091,7 @@ theorem cancel_right {g₁ g₂ : BoundedOrderHom β γ} {f : BoundedOrderHom α
#align bounded_order_hom.cancel_right BoundedOrderHom.cancel_right
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Case conversion may be inaccurate. Consider using '#align bounded_order_hom.cancel_left BoundedOrderHom.cancel_leftₓ'. -/
theorem cancel_left {g : BoundedOrderHom β γ} {f₁ f₂ : BoundedOrderHom α β} (hg : Injective g) :
g.comp f₁ = g.comp f₂ ↔ f₁ = f₂ :=
@@ -1159,10 +1138,7 @@ theorem dual_id : (TopHom.id α).dual = BotHom.id _ :=
#align top_hom.dual_id TopHom.dual_id
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@[simp]
theorem dual_comp (g : TopHom β γ) (f : TopHom α β) : (g.comp f).dual = g.dual.comp f.dual :=
@@ -1181,10 +1157,7 @@ theorem symm_dual_id : TopHom.dual.symm (BotHom.id _) = TopHom.id α :=
#align top_hom.symm_dual_id TopHom.symm_dual_id
/- warning: top_hom.symm_dual_comp -> TopHom.symm_dual_comp is a dubious translation:
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@[simp]
theorem symm_dual_comp (g : BotHom βᵒᵈ γᵒᵈ) (f : BotHom αᵒᵈ βᵒᵈ) :
@@ -1226,10 +1199,7 @@ theorem dual_id : (BotHom.id α).dual = TopHom.id _ :=
#align bot_hom.dual_id BotHom.dual_id
/- warning: bot_hom.dual_comp -> BotHom.dual_comp is a dubious translation:
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@[simp]
theorem dual_comp (g : BotHom β γ) (f : BotHom α β) : (g.comp f).dual = g.dual.comp f.dual :=
@@ -1248,10 +1218,7 @@ theorem symm_dual_id : BotHom.dual.symm (TopHom.id _) = BotHom.id α :=
#align bot_hom.symm_dual_id BotHom.symm_dual_id
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@[simp]
theorem symm_dual_comp (g : TopHom βᵒᵈ γᵒᵈ) (f : TopHom αᵒᵈ βᵒᵈ) :
@@ -1294,10 +1261,7 @@ theorem dual_id : (BoundedOrderHom.id α).dual = BoundedOrderHom.id _ :=
#align bounded_order_hom.dual_id BoundedOrderHom.dual_id
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@[simp]
theorem dual_comp (g : BoundedOrderHom β γ) (f : BoundedOrderHom α β) :
@@ -1317,10 +1281,7 @@ theorem symm_dual_id : BoundedOrderHom.dual.symm (BoundedOrderHom.id _) = Bounde
#align bounded_order_hom.symm_dual_id BoundedOrderHom.symm_dual_id
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Case conversion may be inaccurate. Consider using '#align bounded_order_hom.symm_dual_comp BoundedOrderHom.symm_dual_compₓ'. -/
@[simp]
theorem symm_dual_comp (g : BoundedOrderHom βᵒᵈ γᵒᵈ) (f : BoundedOrderHom αᵒᵈ βᵒᵈ) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4
@@ -1151,7 +1151,7 @@ protected def dual : TopHom α β ≃ BotHom αᵒᵈ βᵒᵈ
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Case conversion may be inaccurate. Consider using '#align top_hom.dual_id TopHom.dual_idₓ'. -/
@[simp]
theorem dual_id : (TopHom.id α).dual = BotHom.id _ :=
@@ -1162,7 +1162,7 @@ theorem dual_id : (TopHom.id α).dual = BotHom.id _ :=
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@[simp]
theorem dual_comp (g : TopHom β γ) (f : TopHom α β) : (g.comp f).dual = g.dual.comp f.dual :=
@@ -1173,7 +1173,7 @@ theorem dual_comp (g : TopHom β γ) (f : TopHom α β) : (g.comp f).dual = g.du
lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align top_hom.symm_dual_id TopHom.symm_dual_idₓ'. -/
@[simp]
theorem symm_dual_id : TopHom.dual.symm (BotHom.id _) = TopHom.id α :=
@@ -1184,7 +1184,7 @@ theorem symm_dual_id : TopHom.dual.symm (BotHom.id _) = TopHom.id α :=
lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align top_hom.symm_dual_comp TopHom.symm_dual_compₓ'. -/
@[simp]
theorem symm_dual_comp (g : BotHom βᵒᵈ γᵒᵈ) (f : BotHom αᵒᵈ βᵒᵈ) :
@@ -1218,7 +1218,7 @@ protected def dual : BotHom α β ≃ TopHom αᵒᵈ βᵒᵈ
lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align bot_hom.dual_id BotHom.dual_idₓ'. -/
@[simp]
theorem dual_id : (BotHom.id α).dual = TopHom.id _ :=
@@ -1229,7 +1229,7 @@ theorem dual_id : (BotHom.id α).dual = TopHom.id _ :=
lean 3 declaration is
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@[simp]
theorem dual_comp (g : BotHom β γ) (f : BotHom α β) : (g.comp f).dual = g.dual.comp f.dual :=
@@ -1240,7 +1240,7 @@ theorem dual_comp (g : BotHom β γ) (f : BotHom α β) : (g.comp f).dual = g.du
lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align bot_hom.symm_dual_id BotHom.symm_dual_idₓ'. -/
@[simp]
theorem symm_dual_id : BotHom.dual.symm (TopHom.id _) = BotHom.id α :=
@@ -1251,7 +1251,7 @@ theorem symm_dual_id : BotHom.dual.symm (TopHom.id _) = BotHom.id α :=
lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align bot_hom.symm_dual_comp BotHom.symm_dual_compₓ'. -/
@[simp]
theorem symm_dual_comp (g : TopHom βᵒᵈ γᵒᵈ) (f : TopHom αᵒᵈ βᵒᵈ) :
@@ -1286,7 +1286,7 @@ protected def dual : BoundedOrderHom α β ≃ BoundedOrderHom αᵒᵈ βᵒᵈ
lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align bounded_order_hom.dual_id BoundedOrderHom.dual_idₓ'. -/
@[simp]
theorem dual_id : (BoundedOrderHom.id α).dual = BoundedOrderHom.id _ :=
@@ -1297,7 +1297,7 @@ theorem dual_id : (BoundedOrderHom.id α).dual = BoundedOrderHom.id _ :=
lean 3 declaration is
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@[simp]
theorem dual_comp (g : BoundedOrderHom β γ) (f : BoundedOrderHom α β) :
@@ -1309,7 +1309,7 @@ theorem dual_comp (g : BoundedOrderHom β γ) (f : BoundedOrderHom α β) :
lean 3 declaration is
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but is expected to have type
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Case conversion may be inaccurate. Consider using '#align bounded_order_hom.symm_dual_id BoundedOrderHom.symm_dual_idₓ'. -/
@[simp]
theorem symm_dual_id : BoundedOrderHom.dual.symm (BoundedOrderHom.id _) = BoundedOrderHom.id α :=
@@ -1320,7 +1320,7 @@ theorem symm_dual_id : BoundedOrderHom.dual.symm (BoundedOrderHom.id _) = Bounde
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@[simp]
theorem symm_dual_comp (g : BoundedOrderHom βᵒᵈ γᵒᵈ) (f : BoundedOrderHom αᵒᵈ βᵒᵈ) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -56,14 +56,18 @@ structure BotHom (α β : Type _) [Bot α] [Bot β] where
#align bot_hom BotHom
-/
-#print BoundedOrderHom /-
+/- warning: bounded_order_hom -> BoundedOrderHom is a dubious translation:
+lean 3 declaration is
+ forall (α : Type.{u1}) (β : Type.{u2}) [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] [_inst_4 : BoundedOrder.{u2} β (Preorder.toHasLe.{u2} β _inst_2)], Sort.{max (succ u1) (succ u2)}
+but is expected to have type
+ forall (α : Type.{u1}) (β : Type.{u2}) [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_4 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β _inst_2)], Sort.{max (succ u1) (succ u2)}
+Case conversion may be inaccurate. Consider using '#align bounded_order_hom BoundedOrderHomₓ'. -/
/-- The type of bounded order homomorphisms from `α` to `β`. -/
structure BoundedOrderHom (α β : Type _) [Preorder α] [Preorder β] [BoundedOrder α]
[BoundedOrder β] extends OrderHom α β where
map_top' : to_fun ⊤ = ⊤
map_bot' : to_fun ⊥ = ⊥
#align bounded_order_hom BoundedOrderHom
--/
section
@@ -132,7 +136,7 @@ instance (priority := 100) BoundedOrderHomClass.toBotHomClass [LE α] [LE β] [B
/- warning: order_iso_class.to_top_hom_class -> OrderIsoClass.toTopHomClass is a dubious translation:
lean 3 declaration is
- forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : OrderTop.{u2} α _inst_1] [_inst_3 : PartialOrder.{u3} β] [_inst_4 : OrderTop.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))], TopHomClass.{u1, u2, u3} F α β (OrderTop.toHasTop.{u2} α _inst_1 _inst_2) (OrderTop.toHasTop.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4)
+ forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : OrderTop.{u2} α _inst_1] [_inst_3 : PartialOrder.{u3} β] [_inst_4 : OrderTop.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))], TopHomClass.{u1, u2, u3} F α β (OrderTop.toHasTop.{u2} α _inst_1 _inst_2) (OrderTop.toHasTop.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4)
but is expected to have type
forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : OrderTop.{u2} α _inst_1] [_inst_3 : PartialOrder.{u3} β] [_inst_4 : OrderTop.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))], TopHomClass.{u1, u2, u3} F α β (OrderTop.toTop.{u2} α _inst_1 _inst_2) (OrderTop.toTop.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4)
Case conversion may be inaccurate. Consider using '#align order_iso_class.to_top_hom_class OrderIsoClass.toTopHomClassₓ'. -/
@@ -145,7 +149,7 @@ instance (priority := 100) OrderIsoClass.toTopHomClass [LE α] [OrderTop α] [Pa
/- warning: order_iso_class.to_bot_hom_class -> OrderIsoClass.toBotHomClass is a dubious translation:
lean 3 declaration is
- forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : OrderBot.{u2} α _inst_1] [_inst_3 : PartialOrder.{u3} β] [_inst_4 : OrderBot.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))], BotHomClass.{u1, u2, u3} F α β (OrderBot.toHasBot.{u2} α _inst_1 _inst_2) (OrderBot.toHasBot.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4)
+ forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : OrderBot.{u2} α _inst_1] [_inst_3 : PartialOrder.{u3} β] [_inst_4 : OrderBot.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))], BotHomClass.{u1, u2, u3} F α β (OrderBot.toHasBot.{u2} α _inst_1 _inst_2) (OrderBot.toHasBot.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4)
but is expected to have type
forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : OrderBot.{u2} α _inst_1] [_inst_3 : PartialOrder.{u3} β] [_inst_4 : OrderBot.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))], BotHomClass.{u1, u2, u3} F α β (OrderBot.toBot.{u2} α _inst_1 _inst_2) (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4)
Case conversion may be inaccurate. Consider using '#align order_iso_class.to_bot_hom_class OrderIsoClass.toBotHomClassₓ'. -/
@@ -157,18 +161,22 @@ instance (priority := 100) OrderIsoClass.toBotHomClass [LE α] [OrderBot α] [Pa
map_bot := fun f => le_bot_iff.1 <| (le_map_inv_iff f).1 bot_le }
#align order_iso_class.to_bot_hom_class OrderIsoClass.toBotHomClass
-#print OrderIsoClass.toBoundedOrderHomClass /-
+/- warning: order_iso_class.to_bounded_order_hom_class -> OrderIsoClass.toBoundedOrderHomClass is a dubious translation:
+lean 3 declaration is
+ forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : BoundedOrder.{u2} α _inst_1] [_inst_3 : PartialOrder.{u3} β] [_inst_4 : BoundedOrder.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))], BoundedOrderHomClass.{u1, u2, u3} F α β _inst_1 (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_2 _inst_4
+but is expected to have type
+ forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : BoundedOrder.{u2} α _inst_1] [_inst_3 : PartialOrder.{u3} β] [_inst_4 : BoundedOrder.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))], BoundedOrderHomClass.{u1, u2, u3} F α β _inst_1 (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_2 _inst_4
+Case conversion may be inaccurate. Consider using '#align order_iso_class.to_bounded_order_hom_class OrderIsoClass.toBoundedOrderHomClassₓ'. -/
-- See note [lower instance priority]
instance (priority := 100) OrderIsoClass.toBoundedOrderHomClass [LE α] [BoundedOrder α]
[PartialOrder β] [BoundedOrder β] [OrderIsoClass F α β] : BoundedOrderHomClass F α β :=
{ show OrderHomClass F α β from inferInstance, OrderIsoClass.toTopHomClass,
OrderIsoClass.toBotHomClass with }
#align order_iso_class.to_bounded_order_hom_class OrderIsoClass.toBoundedOrderHomClass
--/
/- warning: map_eq_top_iff -> map_eq_top_iff is a dubious translation:
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+ forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : OrderTop.{u2} α _inst_1] [_inst_3 : PartialOrder.{u3} β] [_inst_4 : OrderTop.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] (f : F) {a : α}, Iff (Eq.{succ u3} β (coeFn.{succ u1, max (succ u2) (succ u3)} F (fun (_x : F) => α -> β) (FunLike.hasCoeToFun.{succ u1, succ u2, succ u3} F α (fun (_x : α) => β) (TopHomClass.toFunLike.{u1, u2, u3} F α β (OrderTop.toHasTop.{u2} α _inst_1 _inst_2) (OrderTop.toHasTop.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4) (OrderIsoClass.toTopHomClass.{u1, u2, u3} F α β _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) f a) (Top.top.{u3} β (OrderTop.toHasTop.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4))) (Eq.{succ u2} α a (Top.top.{u2} α (OrderTop.toHasTop.{u2} α _inst_1 _inst_2)))
but is expected to have type
forall {F : Type.{u1}} {α : Type.{u3}} {β : Type.{u2}} [_inst_1 : LE.{u3} α] [_inst_2 : OrderTop.{u3} α _inst_1] [_inst_3 : PartialOrder.{u2} β] [_inst_4 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u3, u2} F α β _inst_1 (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_3))] (f : F) {a : α}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (FunLike.coe.{succ u1, succ u3, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{u1, u3, u2} F α β (OrderTop.toTop.{u3} α _inst_1 _inst_2) (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_3)) _inst_4) (OrderIsoClass.toTopHomClass.{u1, u3, u2} F α β _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) f a) (Top.top.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (OrderTop.toTop.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) _inst_3)) _inst_4))) (Eq.{succ u3} α a (Top.top.{u3} α (OrderTop.toTop.{u3} α _inst_1 _inst_2)))
Case conversion may be inaccurate. Consider using '#align map_eq_top_iff map_eq_top_iffₓ'. -/
@@ -179,7 +187,7 @@ theorem map_eq_top_iff [LE α] [OrderTop α] [PartialOrder β] [OrderTop β] [Or
/- warning: map_eq_bot_iff -> map_eq_bot_iff is a dubious translation:
lean 3 declaration is
- forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : OrderBot.{u2} α _inst_1] [_inst_3 : PartialOrder.{u3} β] [_inst_4 : OrderBot.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] (f : F) {a : α}, Iff (Eq.{succ u3} β (coeFn.{succ u1, max (succ u2) (succ u3)} F (fun (_x : F) => α -> β) (FunLike.hasCoeToFun.{succ u1, succ u2, succ u3} F α (fun (_x : α) => β) (BotHomClass.toFunLike.{u1, u2, u3} F α β (OrderBot.toHasBot.{u2} α _inst_1 _inst_2) (OrderBot.toHasBot.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4) (OrderIsoClass.toBotHomClass.{u1, u2, u3} F α β _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) f a) (Bot.bot.{u3} β (OrderBot.toHasBot.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4))) (Eq.{succ u2} α a (Bot.bot.{u2} α (OrderBot.toHasBot.{u2} α _inst_1 _inst_2)))
+ forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : OrderBot.{u2} α _inst_1] [_inst_3 : PartialOrder.{u3} β] [_inst_4 : OrderBot.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] (f : F) {a : α}, Iff (Eq.{succ u3} β (coeFn.{succ u1, max (succ u2) (succ u3)} F (fun (_x : F) => α -> β) (FunLike.hasCoeToFun.{succ u1, succ u2, succ u3} F α (fun (_x : α) => β) (BotHomClass.toFunLike.{u1, u2, u3} F α β (OrderBot.toHasBot.{u2} α _inst_1 _inst_2) (OrderBot.toHasBot.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4) (OrderIsoClass.toBotHomClass.{u1, u2, u3} F α β _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) f a) (Bot.bot.{u3} β (OrderBot.toHasBot.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4))) (Eq.{succ u2} α a (Bot.bot.{u2} α (OrderBot.toHasBot.{u2} α _inst_1 _inst_2)))
but is expected to have type
forall {F : Type.{u1}} {α : Type.{u3}} {β : Type.{u2}} [_inst_1 : LE.{u3} α] [_inst_2 : OrderBot.{u3} α _inst_1] [_inst_3 : PartialOrder.{u2} β] [_inst_4 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u3, u2} F α β _inst_1 (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_3))] (f : F) {a : α}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (FunLike.coe.{succ u1, succ u3, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{u1, u3, u2} F α β (OrderBot.toBot.{u3} α _inst_1 _inst_2) (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_3)) _inst_4) (OrderIsoClass.toBotHomClass.{u1, u3, u2} F α β _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) f a) (Bot.bot.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (OrderBot.toBot.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) _inst_3)) _inst_4))) (Eq.{succ u3} α a (Bot.bot.{u3} α (OrderBot.toBot.{u3} α _inst_1 _inst_2)))
Case conversion may be inaccurate. Consider using '#align map_eq_bot_iff map_eq_bot_iffₓ'. -/
@@ -426,7 +434,7 @@ instance : OrderTop (TopHom α β) :=
/- warning: top_hom.coe_top -> TopHom.coe_top is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Top.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β _inst_2)], Eq.{succ (max u1 u2)} (α -> β) (coeFn.{max (succ u1) (succ u2), succ (max u1 u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (Top.top.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (OrderTop.toHasTop.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (Preorder.toLE.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (TopHom.preorder.{u1, u2} α β _inst_1 _inst_2 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))) (TopHom.orderTop.{u1, u2} α β _inst_1 _inst_2 _inst_3)))) (Top.top.{max u1 u2} (α -> β) (Pi.hasTop.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Top.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2)], Eq.{succ (max u1 u2)} (α -> β) (coeFn.{max (succ u1) (succ u2), succ (max u1 u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (Top.top.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (OrderTop.toHasTop.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (Preorder.toHasLe.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (TopHom.preorder.{u1, u2} α β _inst_1 _inst_2 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3))) (TopHom.orderTop.{u1, u2} α β _inst_1 _inst_2 _inst_3)))) (Top.top.{max u1 u2} (α -> β) (Pi.hasTop.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Top.{u2} α] [_inst_2 : Preorder.{u1} β] [_inst_3 : OrderTop.{u1} β (Preorder.toLE.{u1} β _inst_2)], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u2 u1, u2, u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3) (TopHom.instTopHomClassTopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3))) (Top.top.{max u2 u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) (OrderTop.toTop.{max u2 u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) (Preorder.toLE.{max u2 u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) (TopHom.instPreorderTopHom.{u2, u1} α β _inst_1 _inst_2 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3))) (TopHom.instOrderTopTopHomToTopToLEToLEInstPreorderTopHom.{u2, u1} α β _inst_1 _inst_2 _inst_3)))) (Top.top.{max u2 u1} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) ᾰ) (Pi.instTopForAll.{u2, u1} α (fun (ᾰ : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) ᾰ) (fun (i : α) => OrderTop.toTop.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) i) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) i) _inst_2) _inst_3)))
Case conversion may be inaccurate. Consider using '#align top_hom.coe_top TopHom.coe_topₓ'. -/
@@ -437,7 +445,7 @@ theorem coe_top : ⇑(⊤ : TopHom α β) = ⊤ :=
/- warning: top_hom.top_apply -> TopHom.top_apply is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Top.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β _inst_2)] (a : α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (Top.top.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (OrderTop.toHasTop.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (Preorder.toLE.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (TopHom.preorder.{u1, u2} α β _inst_1 _inst_2 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))) (TopHom.orderTop.{u1, u2} α β _inst_1 _inst_2 _inst_3))) a) (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Top.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2)] (a : α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (Top.top.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (OrderTop.toHasTop.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (Preorder.toHasLe.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (TopHom.preorder.{u1, u2} α β _inst_1 _inst_2 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3))) (TopHom.orderTop.{u1, u2} α β _inst_1 _inst_2 _inst_3))) a) (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3))
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Top.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β _inst_2)] (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u1 u2, u1, u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3) (TopHom.instTopHomClassTopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))) (Top.top.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (OrderTop.toTop.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (Preorder.toLE.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (TopHom.instPreorderTopHom.{u1, u2} α β _inst_1 _inst_2 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))) (TopHom.instOrderTopTopHomToTopToLEToLEInstPreorderTopHom.{u1, u2} α β _inst_1 _inst_2 _inst_3))) a) (Top.top.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (OrderTop.toTop.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) _inst_2) _inst_3))
Case conversion may be inaccurate. Consider using '#align top_hom.top_apply TopHom.top_applyₓ'. -/
@@ -460,7 +468,7 @@ instance : SemilatticeInf (TopHom α β) :=
/- warning: top_hom.coe_inf -> TopHom.coe_inf is a dubious translation:
lean 3 declaration is
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but is expected to have type
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Case conversion may be inaccurate. Consider using '#align top_hom.coe_inf TopHom.coe_infₓ'. -/
@@ -471,7 +479,7 @@ theorem coe_inf : ⇑(f ⊓ g) = f ⊓ g :=
/- warning: top_hom.inf_apply -> TopHom.inf_apply is a dubious translation:
lean 3 declaration is
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but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Top.{u1} α] [_inst_2 : SemilatticeInf.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2)))] (f : TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u1 u2, u1, u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) (Inf.inf.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (TopHom.instInfTopHomToTopToLEToPreorderToPartialOrder.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Inf.inf.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (SemilatticeInf.toInf.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u1 u2, u1, u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) f a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u1 u2, u1, u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) g a))
Case conversion may be inaccurate. Consider using '#align top_hom.inf_apply TopHom.inf_applyₓ'. -/
@@ -494,7 +502,7 @@ instance : SemilatticeSup (TopHom α β) :=
/- warning: top_hom.coe_sup -> TopHom.coe_sup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Top.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)))] (f : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)), Eq.{succ (max u1 u2)} (α -> β) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (Sup.sup.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (TopHom.hasSup.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g)) (Sup.sup.{max u1 u2} (α -> β) (Pi.hasSup.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => SemilatticeSup.toHasSup.{u2} β _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) f) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) g))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Top.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)))] (f : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)), Eq.{succ (max u1 u2)} (α -> β) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (Sup.sup.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (TopHom.hasSup.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g)) (Sup.sup.{max u1 u2} (α -> β) (Pi.hasSup.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => SemilatticeSup.toHasSup.{u2} β _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) f) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) g))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Top.{u2} α] [_inst_2 : SemilatticeSup.{u1} β] [_inst_3 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2)))] (f : TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) (g : TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u2 u1, u2, u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3))) (Sup.sup.{max u2 u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) (TopHom.instSupTopHomToTopToLEToPreorderToPartialOrder.{u2, u1} α β _inst_1 _inst_2 _inst_3) f g)) (Sup.sup.{max u2 u1} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) ᾰ) (Pi.instSupForAll.{u2, u1} α (fun (ᾰ : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) ᾰ) (fun (i : α) => SemilatticeSup.toSup.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) i) _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u2 u1, u2, u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u2 u1, u2, u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3))) g))
Case conversion may be inaccurate. Consider using '#align top_hom.coe_sup TopHom.coe_supₓ'. -/
@@ -505,7 +513,7 @@ theorem coe_sup : ⇑(f ⊔ g) = f ⊔ g :=
/- warning: top_hom.sup_apply -> TopHom.sup_apply is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Top.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)))] (f : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (Sup.sup.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (TopHom.hasSup.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Sup.sup.{u2} β (SemilatticeSup.toHasSup.{u2} β _inst_2) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) f a) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) g a))
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Top.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)))] (f : TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u1 u2, u1, u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) (Sup.sup.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (TopHom.instSupTopHomToTopToLEToPreorderToPartialOrder.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Sup.sup.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (SemilatticeSup.toSup.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u1 u2, u1, u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) f a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u1 u2, u1, u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) g a))
Case conversion may be inaccurate. Consider using '#align top_hom.sup_apply TopHom.sup_applyₓ'. -/
@@ -748,7 +756,7 @@ instance : OrderBot (BotHom α β) :=
/- warning: bot_hom.coe_bot -> BotHom.coe_bot is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2)], Eq.{succ (max u1 u2)} (α -> β) (coeFn.{max (succ u1) (succ u2), succ (max u1 u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (Bot.bot.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (OrderBot.toHasBot.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (Preorder.toLE.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (BotHom.preorder.{u1, u2} α β _inst_1 _inst_2 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))) (BotHom.orderBot.{u1, u2} α β _inst_1 _inst_2 _inst_3)))) (Bot.bot.{max u1 u2} (α -> β) (Pi.hasBot.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2)], Eq.{succ (max u1 u2)} (α -> β) (coeFn.{max (succ u1) (succ u2), succ (max u1 u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (Bot.bot.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (OrderBot.toHasBot.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (Preorder.toHasLe.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (BotHom.preorder.{u1, u2} α β _inst_1 _inst_2 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3))) (BotHom.orderBot.{u1, u2} α β _inst_1 _inst_2 _inst_3)))) (Bot.bot.{max u1 u2} (α -> β) (Pi.hasBot.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Bot.{u2} α] [_inst_2 : Preorder.{u1} β] [_inst_3 : OrderBot.{u1} β (Preorder.toLE.{u1} β _inst_2)], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3))) (Bot.bot.{max u2 u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) (OrderBot.toBot.{max u2 u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) (Preorder.toLE.{max u2 u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) (BotHom.instPreorderBotHom.{u2, u1} α β _inst_1 _inst_2 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3))) (BotHom.instOrderBotBotHomToBotToLEToLEInstPreorderBotHom.{u2, u1} α β _inst_1 _inst_2 _inst_3)))) (Bot.bot.{max u2 u1} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (Pi.instBotForAll.{u2, u1} α (fun (ᾰ : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (fun (i : α) => OrderBot.toBot.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) i) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) i) _inst_2) _inst_3)))
Case conversion may be inaccurate. Consider using '#align bot_hom.coe_bot BotHom.coe_botₓ'. -/
@@ -759,7 +767,7 @@ theorem coe_bot : ⇑(⊥ : BotHom α β) = ⊥ :=
/- warning: bot_hom.bot_apply -> BotHom.bot_apply is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2)] (a : α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (Bot.bot.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (OrderBot.toHasBot.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (Preorder.toLE.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (BotHom.preorder.{u1, u2} α β _inst_1 _inst_2 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))) (BotHom.orderBot.{u1, u2} α β _inst_1 _inst_2 _inst_3))) a) (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2)] (a : α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (Bot.bot.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (OrderBot.toHasBot.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (Preorder.toHasLe.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)) (BotHom.preorder.{u1, u2} α β _inst_1 _inst_2 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3))) (BotHom.orderBot.{u1, u2} α β _inst_1 _inst_2 _inst_3))) a) (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3))
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2)] (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))) (Bot.bot.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (OrderBot.toBot.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (Preorder.toLE.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (BotHom.instPreorderBotHom.{u1, u2} α β _inst_1 _inst_2 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))) (BotHom.instOrderBotBotHomToBotToLEToLEInstPreorderBotHom.{u1, u2} α β _inst_1 _inst_2 _inst_3))) a) (Bot.bot.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (OrderBot.toBot.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) _inst_2) _inst_3))
Case conversion may be inaccurate. Consider using '#align bot_hom.bot_apply BotHom.bot_applyₓ'. -/
@@ -782,7 +790,7 @@ instance : SemilatticeInf (BotHom α β) :=
/- warning: bot_hom.coe_inf -> BotHom.coe_inf is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : SemilatticeInf.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2)))] (f : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)), Eq.{succ (max u1 u2)} (α -> β) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (Inf.inf.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (BotHom.hasInf.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g)) (Inf.inf.{max u1 u2} (α -> β) (Pi.hasInf.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => SemilatticeInf.toHasInf.{u2} β _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) f) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) g))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Bot.{u2} α] [_inst_2 : SemilatticeInf.{u1} β] [_inst_3 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2)))] (f : BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) (g : BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3))) (Inf.inf.{max u2 u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) (BotHom.instInfBotHomToBotToLEToPreorderToPartialOrder.{u2, u1} α β _inst_1 _inst_2 _inst_3) f g)) (Inf.inf.{max u2 u1} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (Pi.instInfForAll.{u2, u1} α (fun (ᾰ : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (fun (i : α) => SemilatticeInf.toInf.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) i) _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3))) g))
Case conversion may be inaccurate. Consider using '#align bot_hom.coe_inf BotHom.coe_infₓ'. -/
@@ -793,7 +801,7 @@ theorem coe_inf : ⇑(f ⊓ g) = f ⊓ g :=
/- warning: bot_hom.inf_apply -> BotHom.inf_apply is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : SemilatticeInf.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2)))] (f : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (Inf.inf.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (BotHom.hasInf.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Inf.inf.{u2} β (SemilatticeInf.toHasInf.{u2} β _inst_2) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) f a) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) g a))
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : SemilatticeInf.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2)))] (f : BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) (Inf.inf.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (BotHom.instInfBotHomToBotToLEToPreorderToPartialOrder.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Inf.inf.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (SemilatticeInf.toInf.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) f a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) g a))
Case conversion may be inaccurate. Consider using '#align bot_hom.inf_apply BotHom.inf_applyₓ'. -/
@@ -816,7 +824,7 @@ instance : SemilatticeSup (BotHom α β) :=
/- warning: bot_hom.coe_sup -> BotHom.coe_sup is a dubious translation:
lean 3 declaration is
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but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Bot.{u2} α] [_inst_2 : SemilatticeSup.{u1} β] [_inst_3 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2)))] (f : BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) (g : BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3))) (Sup.sup.{max u2 u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) (BotHom.instSupBotHomToBotToLEToPreorderToPartialOrder.{u2, u1} α β _inst_1 _inst_2 _inst_3) f g)) (Sup.sup.{max u2 u1} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (Pi.instSupForAll.{u2, u1} α (fun (ᾰ : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (fun (i : α) => SemilatticeSup.toSup.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) i) _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3))) g))
Case conversion may be inaccurate. Consider using '#align bot_hom.coe_sup BotHom.coe_supₓ'. -/
@@ -827,7 +835,7 @@ theorem coe_sup : ⇑(f ⊔ g) = f ⊔ g :=
/- warning: bot_hom.sup_apply -> BotHom.sup_apply is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)))] (f : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (Sup.sup.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (BotHom.hasSup.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Sup.sup.{u2} β (SemilatticeSup.toHasSup.{u2} β _inst_2) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) f a) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) g a))
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forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)))] (f : BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) (Sup.sup.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (BotHom.instSupBotHomToBotToLEToPreorderToPartialOrder.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Sup.sup.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (SemilatticeSup.toSup.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) f a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) g a))
Case conversion may be inaccurate. Consider using '#align bot_hom.sup_apply BotHom.sup_applyₓ'. -/
@@ -856,7 +864,7 @@ variable [Preorder α] [Preorder β] [Preorder γ] [Preorder δ] [BoundedOrder
/- warning: bounded_order_hom.to_top_hom -> BoundedOrderHom.toTopHom is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_5 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toHasLe.{u2} β _inst_2)], (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) -> (TopHom.{u1, u2} α β (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (BoundedOrder.toOrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_5)) (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (BoundedOrder.toOrderTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_6)))
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β _inst_2)], (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) -> (TopHom.{u1, u2} α β (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β _inst_2) (BoundedOrder.toOrderTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_6)))
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.to_top_hom BoundedOrderHom.toTopHomₓ'. -/
@@ -867,7 +875,7 @@ def toTopHom (f : BoundedOrderHom α β) : TopHom α β :=
/- warning: bounded_order_hom.to_bot_hom -> BoundedOrderHom.toBotHom is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_5 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toHasLe.{u2} β _inst_2)], (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) -> (BotHom.{u1, u2} α β (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_5)) (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (BoundedOrder.toOrderBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_6)))
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β _inst_2)], (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) -> (BotHom.{u1, u2} α β (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) (BoundedOrder.toOrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_6)))
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.to_bot_hom BoundedOrderHom.toBotHomₓ'. -/
@@ -892,7 +900,7 @@ instance : CoeFun (BoundedOrderHom α β) fun _ => α → β :=
/- warning: bounded_order_hom.to_fun_eq_coe clashes with [anonymous] -> [anonymous]
warning: bounded_order_hom.to_fun_eq_coe -> [anonymous] is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_5 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toHasLe.{u2} β _inst_2)] {f : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6}, Eq.{max (succ u1) (succ u2)} (α -> β) (OrderHom.toFun.{u1, u2} α β _inst_1 _inst_2 (BoundedOrderHom.toOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6 f)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (fun (_x : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) => α -> β) (BoundedOrderHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) f)
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}}, (Nat -> α -> β) -> Nat -> (List.{u1} α) -> (List.{u2} β)
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.to_fun_eq_coe [anonymous]ₓ'. -/
@@ -903,7 +911,7 @@ theorem [anonymous] {f : BoundedOrderHom α β} : f.toFun = (f : α → β) :=
/- warning: bounded_order_hom.ext -> BoundedOrderHom.ext is a dubious translation:
lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align bounded_order_hom.ext BoundedOrderHom.extₓ'. -/
@@ -914,7 +922,7 @@ theorem ext {f g : BoundedOrderHom α β} (h : ∀ a, f a = g a) : f = g :=
/- warning: bounded_order_hom.copy -> BoundedOrderHom.copy is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_5 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toHasLe.{u2} β _inst_2)] (f : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (f' : α -> β), (Eq.{max (succ u1) (succ u2)} (α -> β) f' (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (fun (_x : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) => α -> β) (BoundedOrderHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) f)) -> (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6)
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β _inst_2)] (f : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (f' : α -> β), (Eq.{max (succ u1) (succ u2)} (α -> β) f' (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) (BoundedOrder.toOrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6))) f)) -> (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6)
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.copy BoundedOrderHom.copyₓ'. -/
@@ -926,7 +934,7 @@ protected def copy (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : B
/- warning: bounded_order_hom.coe_copy -> BoundedOrderHom.coe_copy is a dubious translation:
lean 3 declaration is
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but is expected to have type
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Case conversion may be inaccurate. Consider using '#align bounded_order_hom.coe_copy BoundedOrderHom.coe_copyₓ'. -/
@@ -937,7 +945,7 @@ theorem coe_copy (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : ⇑
/- warning: bounded_order_hom.copy_eq -> BoundedOrderHom.copy_eq is a dubious translation:
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+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_5 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toHasLe.{u2} β _inst_2)] (f : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (f' : α -> β) (h : Eq.{max (succ u1) (succ u2)} (α -> β) f' (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (fun (_x : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) => α -> β) (BoundedOrderHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) f)), Eq.{max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (BoundedOrderHom.copy.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6 f f' h) f
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] [_inst_5 : BoundedOrder.{u2} α (Preorder.toLE.{u2} α _inst_1)] [_inst_6 : BoundedOrder.{u1} β (Preorder.toLE.{u1} β _inst_2)] (f : BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) (f' : α -> β) (h : Eq.{max (succ u2) (succ u1)} (α -> β) f' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u2} α (Preorder.toLE.{u2} α _inst_1) (BoundedOrder.toOrderBot.{u2} α (Preorder.toLE.{u2} α _inst_1) _inst_5)) (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) (BoundedOrder.toOrderBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6))) f)), Eq.{max (succ u2) (succ u1)} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) (BoundedOrderHom.copy.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6 f f' h) f
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.copy_eq BoundedOrderHom.copy_eqₓ'. -/
@@ -947,19 +955,23 @@ theorem copy_eq (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : f.co
variable (α)
-#print BoundedOrderHom.id /-
+/- warning: bounded_order_hom.id -> BoundedOrderHom.id is a dubious translation:
+lean 3 declaration is
+ forall (α : Type.{u1}) [_inst_1 : Preorder.{u1} α] [_inst_5 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1)], BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5
+but is expected to have type
+ forall (α : Type.{u1}) [_inst_1 : Preorder.{u1} α] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)], BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5
+Case conversion may be inaccurate. Consider using '#align bounded_order_hom.id BoundedOrderHom.idₓ'. -/
/-- `id` as a `bounded_order_hom`. -/
protected def id : BoundedOrderHom α α :=
{ OrderHom.id, TopHom.id α, BotHom.id α with }
#align bounded_order_hom.id BoundedOrderHom.id
--/
instance : Inhabited (BoundedOrderHom α α) :=
⟨BoundedOrderHom.id α⟩
/- warning: bounded_order_hom.coe_id -> BoundedOrderHom.coe_id is a dubious translation:
lean 3 declaration is
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+ forall (α : Type.{u1}) [_inst_1 : Preorder.{u1} α] [_inst_5 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1)], Eq.{succ u1} (α -> α) (coeFn.{succ u1, succ u1} (BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) (fun (_x : BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) => α -> α) (BoundedOrderHom.hasCoeToFun.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) (BoundedOrderHom.id.{u1} α _inst_1 _inst_5)) (id.{succ u1} α)
but is expected to have type
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Case conversion may be inaccurate. Consider using '#align bounded_order_hom.coe_id BoundedOrderHom.coe_idₓ'. -/
@@ -972,7 +984,7 @@ variable {α}
/- warning: bounded_order_hom.id_apply -> BoundedOrderHom.id_apply is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_5 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] (a : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) (fun (_x : BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) => α -> α) (BoundedOrderHom.hasCoeToFun.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) (BoundedOrderHom.id.{u1} α _inst_1 _inst_5) a) a
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Case conversion may be inaccurate. Consider using '#align bounded_order_hom.id_apply BoundedOrderHom.id_applyₓ'. -/
@@ -981,16 +993,20 @@ theorem id_apply (a : α) : BoundedOrderHom.id α a = a :=
rfl
#align bounded_order_hom.id_apply BoundedOrderHom.id_apply
-#print BoundedOrderHom.comp /-
+/- warning: bounded_order_hom.comp -> BoundedOrderHom.comp is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align bounded_order_hom.comp BoundedOrderHom.compₓ'. -/
/-- Composition of `bounded_order_hom`s as a `bounded_order_hom`. -/
def comp (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) : BoundedOrderHom α γ :=
{ f.toOrderHom.comp g.toOrderHom, f.toTopHom.comp g.toTopHom, f.toBotHom.comp g.toBotHom with }
#align bounded_order_hom.comp BoundedOrderHom.comp
--/
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+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toHasLe.{u2} β _inst_2)] [_inst_7 : BoundedOrder.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)] (f : BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) (g : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6), Eq.{max (succ u1) (succ u3)} ((fun (_x : BoundedOrderHom.{u1, u3} α γ _inst_1 _inst_3 _inst_5 _inst_7) => α -> γ) (BoundedOrderHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 f g)) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (BoundedOrderHom.{u1, u3} α γ _inst_1 _inst_3 _inst_5 _inst_7) (fun (_x : BoundedOrderHom.{u1, u3} α γ _inst_1 _inst_3 _inst_5 _inst_7) => α -> γ) (BoundedOrderHom.hasCoeToFun.{u1, u3} α γ _inst_1 _inst_3 _inst_5 _inst_7) (BoundedOrderHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 f g)) (Function.comp.{succ u1, succ u2, succ u3} α β γ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) (fun (_x : BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) => β -> γ) (BoundedOrderHom.hasCoeToFun.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) f) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (fun (_x : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) => α -> β) (BoundedOrderHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) g))
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u3} β (Preorder.toLE.{u3} β _inst_2)] [_inst_7 : BoundedOrder.{u2} γ (Preorder.toLE.{u2} γ _inst_3)] (f : BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) (g : BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6), Eq.{max (succ u1) (succ u2)} (forall (a : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => γ) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => γ) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α γ (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (BoundedOrderHomClass.toBotHomClass.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α γ (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} γ _inst_3) _inst_5 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7))) (BoundedOrderHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 f g)) (Function.comp.{succ u1, succ u3, succ u2} α β γ (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β (fun (_x : β) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : β) => γ) _x) (BotHomClass.toFunLike.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (OrderBot.toBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (BoundedOrderHomClass.toBotHomClass.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3) _inst_6 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7))) f) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6))) g))
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.coe_comp BoundedOrderHom.coe_compₓ'. -/
@@ -1001,7 +1017,7 @@ theorem coe_comp (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) : (f.co
/- warning: bounded_order_hom.comp_apply -> BoundedOrderHom.comp_apply is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toHasLe.{u2} β _inst_2)] [_inst_7 : BoundedOrder.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)] (f : BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) (g : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (a : α), Eq.{succ u3} γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (BoundedOrderHom.{u1, u3} α γ _inst_1 _inst_3 _inst_5 _inst_7) (fun (_x : BoundedOrderHom.{u1, u3} α γ _inst_1 _inst_3 _inst_5 _inst_7) => α -> γ) (BoundedOrderHom.hasCoeToFun.{u1, u3} α γ _inst_1 _inst_3 _inst_5 _inst_7) (BoundedOrderHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 f g) a) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) (fun (_x : BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) => β -> γ) (BoundedOrderHom.hasCoeToFun.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) f (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (fun (_x : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) => α -> β) (BoundedOrderHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) g a))
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u3} β (Preorder.toLE.{u3} β _inst_2)] [_inst_7 : BoundedOrder.{u2} γ (Preorder.toLE.{u2} γ _inst_3)] (f : BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) (g : BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => γ) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => γ) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α γ (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (BoundedOrderHomClass.toBotHomClass.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α γ (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} γ _inst_3) _inst_5 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7))) (BoundedOrderHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 f g) a) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β (fun (_x : β) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : β) => γ) _x) (BotHomClass.toFunLike.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (OrderBot.toBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (BoundedOrderHomClass.toBotHomClass.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3) _inst_6 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7))) f (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6))) g a))
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.comp_apply BoundedOrderHom.comp_applyₓ'. -/
@@ -1013,7 +1029,7 @@ theorem comp_apply (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) (a :
/- warning: bounded_order_hom.coe_comp_order_hom -> BoundedOrderHom.coe_comp_orderHom is a dubious translation:
lean 3 declaration is
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but is expected to have type
forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u3} β (Preorder.toLE.{u3} β _inst_2)] [_inst_7 : BoundedOrder.{u2} γ (Preorder.toLE.{u2} γ _inst_3)] (f : BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) (g : BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6), Eq.{max (succ u1) (succ u2)} (OrderHom.{u1, u2} α γ _inst_1 _inst_3) (OrderHomClass.toOrderHom.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α γ _inst_1 _inst_3 (BoundedOrderHomClass.toRelHomClass.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α γ (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} γ _inst_3) _inst_5 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7)) (BoundedOrderHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 f g)) (OrderHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 (OrderHomClass.toOrderHom.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ _inst_2 _inst_3 (BoundedOrderHomClass.toRelHomClass.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3) _inst_6 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7)) f) (OrderHomClass.toOrderHom.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β _inst_1 _inst_2 (BoundedOrderHomClass.toRelHomClass.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6)) g))
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.coe_comp_order_hom BoundedOrderHom.coe_comp_orderHomₓ'. -/
@@ -1025,7 +1041,7 @@ theorem coe_comp_orderHom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β
/- warning: bounded_order_hom.coe_comp_top_hom -> BoundedOrderHom.coe_comp_topHom is a dubious translation:
lean 3 declaration is
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(BoundedOrderHomClass.toTopHomClass.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.boundedOrderHomClass.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6))))) g))
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toHasLe.{u2} β _inst_2)] [_inst_7 : BoundedOrder.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)] (f : BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) (g : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6), Eq.{max (succ u1) (succ u3)} (TopHom.{u1, u3} α γ (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (BoundedOrder.toOrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_5)) (OrderTop.toHasTop.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3) (BoundedOrder.toOrderTop.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3) _inst_7))) ((fun (a : Sort.{max (succ u1) (succ u3)}) (b : Sort.{max (succ u1) (succ u3)}) [self : HasLiftT.{max (succ u1) (succ u3), max (succ u1) (succ u3)} a b] => self.0) (BoundedOrderHom.{u1, u3} α γ _inst_1 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(OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (BoundedOrder.toOrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_5)) (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (BoundedOrder.toOrderTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_6)) (OrderTop.toHasTop.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3) (BoundedOrder.toOrderTop.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3) _inst_7)) ((fun (a : Sort.{max (succ u2) (succ u3)}) (b : Sort.{max (succ u2) (succ u3)}) [self : HasLiftT.{max (succ u2) (succ u3), max (succ u2) (succ u3)} a b] => self.0) (BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) (TopHom.{u2, u3} β γ (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (BoundedOrder.toOrderTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_6)) (OrderTop.toHasTop.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3) (BoundedOrder.toOrderTop.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3) _inst_7))) (HasLiftT.mk.{max (succ u2) (succ u3), max (succ u2) (succ u3)} 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(BoundedOrder.toOrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_5)) (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (BoundedOrder.toOrderTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_6)) (BoundedOrderHomClass.toTopHomClass.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.boundedOrderHomClass.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6))))) g))
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u3} β (Preorder.toLE.{u3} β _inst_2)] [_inst_7 : BoundedOrder.{u2} γ (Preorder.toLE.{u2} γ _inst_3)] (f : BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) (g : BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6), Eq.{max (succ u1) (succ u2)} (TopHom.{u1, u2} α γ (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderTop.toTop.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderTop.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7))) (TopHomClass.toTopHom.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α γ (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderTop.toTop.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderTop.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (BoundedOrderHomClass.toTopHomClass.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α γ (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} γ _inst_3) _inst_5 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7)) (BoundedOrderHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 f g)) (TopHom.comp.{u1, u3, u2} α β γ (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderTop.toTop.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderTop.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (OrderTop.toTop.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderTop.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (TopHomClass.toTopHom.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (OrderTop.toTop.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderTop.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (OrderTop.toTop.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderTop.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (BoundedOrderHomClass.toTopHomClass.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3) _inst_6 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7)) f) (TopHomClass.toTopHom.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderTop.toTop.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderTop.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (BoundedOrderHomClass.toTopHomClass.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6)) g))
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.coe_comp_top_hom BoundedOrderHom.coe_comp_topHomₓ'. -/
@@ -1037,7 +1053,7 @@ theorem coe_comp_topHom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β)
/- warning: bounded_order_hom.coe_comp_bot_hom -> BoundedOrderHom.coe_comp_botHom is a dubious translation:
lean 3 declaration is
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but is expected to have type
forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u3} β (Preorder.toLE.{u3} β _inst_2)] [_inst_7 : BoundedOrder.{u2} γ (Preorder.toLE.{u2} γ _inst_3)] (f : BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) (g : BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6), Eq.{max (succ u1) (succ u2)} (BotHom.{u1, u2} α γ (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7))) (BotHomClass.toBotHom.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α γ (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (BoundedOrderHomClass.toBotHomClass.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α γ (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} γ _inst_3) _inst_5 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7)) (BoundedOrderHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 f g)) (BotHom.comp.{u1, u3, u2} α β γ (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (OrderBot.toBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (BotHomClass.toBotHom.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (OrderBot.toBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (BoundedOrderHomClass.toBotHomClass.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3) _inst_6 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7)) f) (BotHomClass.toBotHom.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6)) g))
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.coe_comp_bot_hom BoundedOrderHom.coe_comp_botHomₓ'. -/
@@ -1049,7 +1065,7 @@ theorem coe_comp_botHom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β)
/- warning: bounded_order_hom.comp_assoc -> BoundedOrderHom.comp_assoc is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} {δ : Type.{u4}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_4 : Preorder.{u4} δ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toHasLe.{u2} β _inst_2)] [_inst_7 : BoundedOrder.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)] [_inst_8 : BoundedOrder.{u4} δ (Preorder.toHasLe.{u4} δ _inst_4)] (f : BoundedOrderHom.{u3, u4} γ δ _inst_3 _inst_4 _inst_7 _inst_8) (g : BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) (h : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6), Eq.{max (succ u1) (succ u4)} (BoundedOrderHom.{u1, u4} α δ _inst_1 _inst_4 _inst_5 _inst_8) (BoundedOrderHom.comp.{u1, u2, u4} α β δ _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_8 (BoundedOrderHom.comp.{u2, u3, u4} β γ δ _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 _inst_8 f g) h) (BoundedOrderHom.comp.{u1, u3, u4} α γ δ _inst_1 _inst_3 _inst_4 _inst_5 _inst_7 _inst_8 f (BoundedOrderHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 g h))
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forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u4}} {δ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : Preorder.{u4} γ] [_inst_4 : Preorder.{u3} δ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_7 : BoundedOrder.{u4} γ (Preorder.toLE.{u4} γ _inst_3)] [_inst_8 : BoundedOrder.{u3} δ (Preorder.toLE.{u3} δ _inst_4)] (f : BoundedOrderHom.{u4, u3} γ δ _inst_3 _inst_4 _inst_7 _inst_8) (g : BoundedOrderHom.{u2, u4} β γ _inst_2 _inst_3 _inst_6 _inst_7) (h : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6), Eq.{max (succ u1) (succ u3)} (BoundedOrderHom.{u1, u3} α δ _inst_1 _inst_4 _inst_5 _inst_8) (BoundedOrderHom.comp.{u1, u2, u3} α β δ _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_8 (BoundedOrderHom.comp.{u2, u4, u3} β γ δ _inst_2 _inst_3 _inst_4 _inst_6 _inst_7 _inst_8 f g) h) (BoundedOrderHom.comp.{u1, u4, u3} α γ δ _inst_1 _inst_3 _inst_4 _inst_5 _inst_7 _inst_8 f (BoundedOrderHom.comp.{u1, u2, u4} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 g h))
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.comp_assoc BoundedOrderHom.comp_assocₓ'. -/
@@ -1061,7 +1077,7 @@ theorem comp_assoc (f : BoundedOrderHom γ δ) (g : BoundedOrderHom β γ) (h :
/- warning: bounded_order_hom.comp_id -> BoundedOrderHom.comp_id is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_5 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toHasLe.{u2} β _inst_2)] (f : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6), Eq.{max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (BoundedOrderHom.comp.{u1, u1, u2} α α β _inst_1 _inst_1 _inst_2 _inst_5 _inst_5 _inst_6 f (BoundedOrderHom.id.{u1} α _inst_1 _inst_5)) f
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] [_inst_5 : BoundedOrder.{u2} α (Preorder.toLE.{u2} α _inst_1)] [_inst_6 : BoundedOrder.{u1} β (Preorder.toLE.{u1} β _inst_2)] (f : BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6), Eq.{max (succ u2) (succ u1)} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) (BoundedOrderHom.comp.{u2, u2, u1} α α β _inst_1 _inst_1 _inst_2 _inst_5 _inst_5 _inst_6 f (BoundedOrderHom.id.{u2} α _inst_1 _inst_5)) f
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.comp_id BoundedOrderHom.comp_idₓ'. -/
@@ -1072,7 +1088,7 @@ theorem comp_id (f : BoundedOrderHom α β) : f.comp (BoundedOrderHom.id α) = f
/- warning: bounded_order_hom.id_comp -> BoundedOrderHom.id_comp is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β _inst_2)] (f : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6), Eq.{max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (BoundedOrderHom.comp.{u1, u2, u2} α β β _inst_1 _inst_2 _inst_2 _inst_5 _inst_6 _inst_6 (BoundedOrderHom.id.{u2} β _inst_2 _inst_6) f) f
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_5 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toHasLe.{u2} β _inst_2)] (f : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6), Eq.{max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (BoundedOrderHom.comp.{u1, u2, u2} α β β _inst_1 _inst_2 _inst_2 _inst_5 _inst_6 _inst_6 (BoundedOrderHom.id.{u2} β _inst_2 _inst_6) f) f
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] [_inst_5 : BoundedOrder.{u2} α (Preorder.toLE.{u2} α _inst_1)] [_inst_6 : BoundedOrder.{u1} β (Preorder.toLE.{u1} β _inst_2)] (f : BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6), Eq.{max (succ u2) (succ u1)} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) (BoundedOrderHom.comp.{u2, u1, u1} α β β _inst_1 _inst_2 _inst_2 _inst_5 _inst_6 _inst_6 (BoundedOrderHom.id.{u1} β _inst_2 _inst_6) f) f
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.id_comp BoundedOrderHom.id_compₓ'. -/
@@ -1083,7 +1099,7 @@ theorem id_comp (f : BoundedOrderHom α β) : (BoundedOrderHom.id β).comp f = f
/- warning: bounded_order_hom.cancel_right -> BoundedOrderHom.cancel_right is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_7 : BoundedOrder.{u3} γ (Preorder.toLE.{u3} γ _inst_3)] {g₁ : BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7} {g₂ : BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7} {f : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6}, (Function.Surjective.{succ u1, succ u2} α β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (fun (_x : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) => α -> β) (BoundedOrderHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) f)) -> (Iff (Eq.{max (succ u1) (succ u3)} (BoundedOrderHom.{u1, u3} α γ _inst_1 _inst_3 _inst_5 _inst_7) (BoundedOrderHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 g₁ f) (BoundedOrderHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 g₂ f)) (Eq.{max (succ u2) (succ u3)} (BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) g₁ g₂))
+ forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toHasLe.{u2} β _inst_2)] [_inst_7 : BoundedOrder.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)] {g₁ : BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7} {g₂ : BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7} {f : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6}, (Function.Surjective.{succ u1, succ u2} α β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (fun (_x : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) => α -> β) (BoundedOrderHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) f)) -> (Iff (Eq.{max (succ u1) (succ u3)} (BoundedOrderHom.{u1, u3} α γ _inst_1 _inst_3 _inst_5 _inst_7) (BoundedOrderHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 g₁ f) (BoundedOrderHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 g₂ f)) (Eq.{max (succ u2) (succ u3)} (BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) g₁ g₂))
but is expected to have type
forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u3} β (Preorder.toLE.{u3} β _inst_2)] [_inst_7 : BoundedOrder.{u2} γ (Preorder.toLE.{u2} γ _inst_3)] {g₁ : BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7} {g₂ : BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7} {f : BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6}, (Function.Surjective.{succ u1, succ u3} α β (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6))) f)) -> (Iff (Eq.{max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) (BoundedOrderHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 g₁ f) (BoundedOrderHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 g₂ f)) (Eq.{max (succ u3) (succ u2)} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) g₁ g₂))
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.cancel_right BoundedOrderHom.cancel_rightₓ'. -/
@@ -1094,7 +1110,7 @@ theorem cancel_right {g₁ g₂ : BoundedOrderHom β γ} {f : BoundedOrderHom α
/- warning: bounded_order_hom.cancel_left -> BoundedOrderHom.cancel_left is a dubious translation:
lean 3 declaration is
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@@ -1249,7 +1265,12 @@ namespace BoundedOrderHom
variable [Preorder α] [BoundedOrder α] [Preorder β] [BoundedOrder β] [Preorder γ] [BoundedOrder γ]
-#print BoundedOrderHom.dual /-
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/-- Reinterpret a bounded order homomorphism as a bounded order homomorphism between the dual
orders. -/
@[simps]
@@ -1260,18 +1281,21 @@ protected def dual : BoundedOrderHom α β ≃ BoundedOrderHom αᵒᵈ βᵒᵈ
left_inv f := ext fun a => rfl
right_inv f := ext fun a => rfl
#align bounded_order_hom.dual BoundedOrderHom.dual
--/
-#print BoundedOrderHom.dual_id /-
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@[simp]
theorem dual_id : (BoundedOrderHom.id α).dual = BoundedOrderHom.id _ :=
rfl
#align bounded_order_hom.dual_id BoundedOrderHom.dual_id
--/
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@@ -1281,16 +1305,20 @@ theorem dual_comp (g : BoundedOrderHom β γ) (f : BoundedOrderHom α β) :
rfl
#align bounded_order_hom.dual_comp BoundedOrderHom.dual_comp
-#print BoundedOrderHom.symm_dual_id /-
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@[simp]
theorem symm_dual_id : BoundedOrderHom.dual.symm (BoundedOrderHom.id _) = BoundedOrderHom.id α :=
rfl
#align bounded_order_hom.symm_dual_id BoundedOrderHom.symm_dual_id
--/
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(Preorder.toLE.{u3} β _inst_3) _inst_4)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : BoundedOrderHom.{u1, u3} (OrderDual.{u1} α) (OrderDual.{u3} β) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.preorder.{u3} β _inst_3) (OrderDual.boundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2) (OrderDual.boundedOrder.{u3} β (Preorder.toLE.{u3} β _inst_3) _inst_4)) => BoundedOrderHom.{u1, u3} α β _inst_1 _inst_3 _inst_2 _inst_4) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (BoundedOrderHom.{u1, u3} (OrderDual.{u1} α) (OrderDual.{u3} β) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.preorder.{u3} β _inst_3) (OrderDual.boundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2) (OrderDual.boundedOrder.{u3} β (Preorder.toLE.{u3} β _inst_3) _inst_4)) (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_3 _inst_2 _inst_4)) (Equiv.symm.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_3 _inst_2 _inst_4) (BoundedOrderHom.{u1, u3} (OrderDual.{u1} α) (OrderDual.{u3} β) (OrderDual.preorder.{u1} α _inst_1) (OrderDual.preorder.{u3} β _inst_3) (OrderDual.boundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_2) (OrderDual.boundedOrder.{u3} β (Preorder.toLE.{u3} β _inst_3) _inst_4)) (BoundedOrderHom.dual.{u1, u3} α β _inst_1 _inst_2 _inst_3 _inst_4)) f))
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.symm_dual_comp BoundedOrderHom.symm_dual_compₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/347636a7a80595d55bedf6e6fbd996a3c39da69a
@@ -110,7 +110,7 @@ attribute [simp] map_top map_bot
lean 3 declaration is
forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : LE.{u3} β] [_inst_3 : BoundedOrder.{u2} α _inst_1] [_inst_4 : BoundedOrder.{u3} β _inst_2] [_inst_5 : BoundedOrderHomClass.{u1, u2, u3} F α β _inst_1 _inst_2 _inst_3 _inst_4], TopHomClass.{u1, u2, u3} F α β (OrderTop.toHasTop.{u2} α _inst_1 (BoundedOrder.toOrderTop.{u2} α _inst_1 _inst_3)) (OrderTop.toHasTop.{u3} β _inst_2 (BoundedOrder.toOrderTop.{u3} β _inst_2 _inst_4))
but is expected to have type
- forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} {_inst_1 : LE.{u2} α} {_inst_2 : LE.{u3} β} {_inst_3 : BoundedOrder.{u2} α _inst_1} {_inst_4 : BoundedOrder.{u3} β _inst_2} [_inst_5 : BoundedOrderHomClass.{u1, u2, u3} F α β _inst_1 _inst_2 _inst_3 _inst_4], TopHomClass.{u1, u2, u3} F α β (OrderTop.toTop.{u2} α _inst_1 (BoundedOrder.toOrderTop.{u2} α _inst_1 _inst_3)) (OrderTop.toTop.{u3} β _inst_2 (BoundedOrder.toOrderTop.{u3} β _inst_2 _inst_4))
+ forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : LE.{u3} β] [_inst_3 : BoundedOrder.{u2} α _inst_1] [_inst_4 : BoundedOrder.{u3} β _inst_2] [_inst_5 : BoundedOrderHomClass.{u1, u2, u3} F α β _inst_1 _inst_2 _inst_3 _inst_4], TopHomClass.{u1, u2, u3} F α β (OrderTop.toTop.{u2} α _inst_1 (BoundedOrder.toOrderTop.{u2} α _inst_1 _inst_3)) (OrderTop.toTop.{u3} β _inst_2 (BoundedOrder.toOrderTop.{u3} β _inst_2 _inst_4))
Case conversion may be inaccurate. Consider using '#align bounded_order_hom_class.to_top_hom_class BoundedOrderHomClass.toTopHomClassₓ'. -/
-- See note [lower instance priority]
instance (priority := 100) BoundedOrderHomClass.toTopHomClass [LE α] [LE β] [BoundedOrder α]
@@ -122,7 +122,7 @@ instance (priority := 100) BoundedOrderHomClass.toTopHomClass [LE α] [LE β] [B
lean 3 declaration is
forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : LE.{u3} β] [_inst_3 : BoundedOrder.{u2} α _inst_1] [_inst_4 : BoundedOrder.{u3} β _inst_2] [_inst_5 : BoundedOrderHomClass.{u1, u2, u3} F α β _inst_1 _inst_2 _inst_3 _inst_4], BotHomClass.{u1, u2, u3} F α β (OrderBot.toHasBot.{u2} α _inst_1 (BoundedOrder.toOrderBot.{u2} α _inst_1 _inst_3)) (OrderBot.toHasBot.{u3} β _inst_2 (BoundedOrder.toOrderBot.{u3} β _inst_2 _inst_4))
but is expected to have type
- forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} {_inst_1 : LE.{u2} α} {_inst_2 : LE.{u3} β} {_inst_3 : BoundedOrder.{u2} α _inst_1} {_inst_4 : BoundedOrder.{u3} β _inst_2} [_inst_5 : BoundedOrderHomClass.{u1, u2, u3} F α β _inst_1 _inst_2 _inst_3 _inst_4], BotHomClass.{u1, u2, u3} F α β (OrderBot.toBot.{u2} α _inst_1 (BoundedOrder.toOrderBot.{u2} α _inst_1 _inst_3)) (OrderBot.toBot.{u3} β _inst_2 (BoundedOrder.toOrderBot.{u3} β _inst_2 _inst_4))
+ forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : LE.{u3} β] [_inst_3 : BoundedOrder.{u2} α _inst_1] [_inst_4 : BoundedOrder.{u3} β _inst_2] [_inst_5 : BoundedOrderHomClass.{u1, u2, u3} F α β _inst_1 _inst_2 _inst_3 _inst_4], BotHomClass.{u1, u2, u3} F α β (OrderBot.toBot.{u2} α _inst_1 (BoundedOrder.toOrderBot.{u2} α _inst_1 _inst_3)) (OrderBot.toBot.{u3} β _inst_2 (BoundedOrder.toOrderBot.{u3} β _inst_2 _inst_4))
Case conversion may be inaccurate. Consider using '#align bounded_order_hom_class.to_bot_hom_class BoundedOrderHomClass.toBotHomClassₓ'. -/
-- See note [lower instance priority]
instance (priority := 100) BoundedOrderHomClass.toBotHomClass [LE α] [LE β] [BoundedOrder α]
@@ -134,7 +134,7 @@ instance (priority := 100) BoundedOrderHomClass.toBotHomClass [LE α] [LE β] [B
lean 3 declaration is
forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : OrderTop.{u2} α _inst_1] [_inst_3 : PartialOrder.{u3} β] [_inst_4 : OrderTop.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))], TopHomClass.{u1, u2, u3} F α β (OrderTop.toHasTop.{u2} α _inst_1 _inst_2) (OrderTop.toHasTop.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4)
but is expected to have type
- forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} {_inst_1 : LE.{u2} α} {_inst_2 : OrderTop.{u2} α _inst_1} {_inst_3 : PartialOrder.{u3} β} {_inst_4 : OrderTop.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))} [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))], TopHomClass.{u1, u2, u3} F α β (OrderTop.toTop.{u2} α _inst_1 _inst_2) (OrderTop.toTop.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4)
+ forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : OrderTop.{u2} α _inst_1] [_inst_3 : PartialOrder.{u3} β] [_inst_4 : OrderTop.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))], TopHomClass.{u1, u2, u3} F α β (OrderTop.toTop.{u2} α _inst_1 _inst_2) (OrderTop.toTop.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4)
Case conversion may be inaccurate. Consider using '#align order_iso_class.to_top_hom_class OrderIsoClass.toTopHomClassₓ'. -/
-- See note [lower instance priority]
instance (priority := 100) OrderIsoClass.toTopHomClass [LE α] [OrderTop α] [PartialOrder β]
@@ -147,7 +147,7 @@ instance (priority := 100) OrderIsoClass.toTopHomClass [LE α] [OrderTop α] [Pa
lean 3 declaration is
forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : OrderBot.{u2} α _inst_1] [_inst_3 : PartialOrder.{u3} β] [_inst_4 : OrderBot.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))], BotHomClass.{u1, u2, u3} F α β (OrderBot.toHasBot.{u2} α _inst_1 _inst_2) (OrderBot.toHasBot.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4)
but is expected to have type
- forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} {_inst_1 : LE.{u2} α} {_inst_2 : OrderBot.{u2} α _inst_1} {_inst_3 : PartialOrder.{u3} β} {_inst_4 : OrderBot.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))} [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))], BotHomClass.{u1, u2, u3} F α β (OrderBot.toBot.{u2} α _inst_1 _inst_2) (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4)
+ forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : OrderBot.{u2} α _inst_1] [_inst_3 : PartialOrder.{u3} β] [_inst_4 : OrderBot.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))], BotHomClass.{u1, u2, u3} F α β (OrderBot.toBot.{u2} α _inst_1 _inst_2) (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4)
Case conversion may be inaccurate. Consider using '#align order_iso_class.to_bot_hom_class OrderIsoClass.toBotHomClassₓ'. -/
-- See note [lower instance priority]
instance (priority := 100) OrderIsoClass.toBotHomClass [LE α] [OrderBot α] [PartialOrder β]
@@ -170,7 +170,7 @@ instance (priority := 100) OrderIsoClass.toBoundedOrderHomClass [LE α] [Bounded
lean 3 declaration is
forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : OrderTop.{u2} α _inst_1] [_inst_3 : PartialOrder.{u3} β] [_inst_4 : OrderTop.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] (f : F) {a : α}, Iff (Eq.{succ u3} β (coeFn.{succ u1, max (succ u2) (succ u3)} F (fun (_x : F) => α -> β) (FunLike.hasCoeToFun.{succ u1, succ u2, succ u3} F α (fun (_x : α) => β) (TopHomClass.toFunLike.{u1, u2, u3} F α β (OrderTop.toHasTop.{u2} α _inst_1 _inst_2) (OrderTop.toHasTop.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4) (OrderIsoClass.toTopHomClass.{u1, u2, u3} F α β _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) f a) (Top.top.{u3} β (OrderTop.toHasTop.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4))) (Eq.{succ u2} α a (Top.top.{u2} α (OrderTop.toHasTop.{u2} α _inst_1 _inst_2)))
but is expected to have type
- forall {F : Type.{u1}} {α : Type.{u3}} {β : Type.{u2}} [_inst_1 : LE.{u3} α] [_inst_2 : OrderTop.{u3} α _inst_1] [_inst_3 : PartialOrder.{u2} β] [_inst_4 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u3, u2} F α β _inst_1 (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_3))] (f : F) {a : α}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => β) a) (FunLike.coe.{succ u1, succ u3, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => β) _x) (RelHomClass.toFunLike.{u1, u3, u2} F α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1896 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1898 : α) => LE.le.{u3} α _inst_1 x._@.Mathlib.Order.Hom.Basic._hyg.1896 x._@.Mathlib.Order.Hom.Basic._hyg.1898) (fun (_x : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1920 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_3)) _x x._@.Mathlib.Order.Hom.Basic._hyg.1920) (OrderIsoClass.toOrderHomClass.{u1, u3, u2} F α β _inst_1 (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_3)) _inst_5)) f a) (Top.top.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => β) a) (OrderTop.toTop.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => β) a) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => β) a) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => β) a) _inst_3)) _inst_4))) (Eq.{succ u3} α a (Top.top.{u3} α (OrderTop.toTop.{u3} α _inst_1 _inst_2)))
+ forall {F : Type.{u1}} {α : Type.{u3}} {β : Type.{u2}} [_inst_1 : LE.{u3} α] [_inst_2 : OrderTop.{u3} α _inst_1] [_inst_3 : PartialOrder.{u2} β] [_inst_4 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u3, u2} F α β _inst_1 (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_3))] (f : F) {a : α}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (FunLike.coe.{succ u1, succ u3, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{u1, u3, u2} F α β (OrderTop.toTop.{u3} α _inst_1 _inst_2) (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_3)) _inst_4) (OrderIsoClass.toTopHomClass.{u1, u3, u2} F α β _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) f a) (Top.top.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (OrderTop.toTop.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) _inst_3)) _inst_4))) (Eq.{succ u3} α a (Top.top.{u3} α (OrderTop.toTop.{u3} α _inst_1 _inst_2)))
Case conversion may be inaccurate. Consider using '#align map_eq_top_iff map_eq_top_iffₓ'. -/
@[simp]
theorem map_eq_top_iff [LE α] [OrderTop α] [PartialOrder β] [OrderTop β] [OrderIsoClass F α β]
@@ -181,7 +181,7 @@ theorem map_eq_top_iff [LE α] [OrderTop α] [PartialOrder β] [OrderTop β] [Or
lean 3 declaration is
forall {F : Type.{u1}} {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : LE.{u2} α] [_inst_2 : OrderBot.{u2} α _inst_1] [_inst_3 : PartialOrder.{u3} β] [_inst_4 : OrderBot.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u2, u3} F α β _inst_1 (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3))] (f : F) {a : α}, Iff (Eq.{succ u3} β (coeFn.{succ u1, max (succ u2) (succ u3)} F (fun (_x : F) => α -> β) (FunLike.hasCoeToFun.{succ u1, succ u2, succ u3} F α (fun (_x : α) => β) (BotHomClass.toFunLike.{u1, u2, u3} F α β (OrderBot.toHasBot.{u2} α _inst_1 _inst_2) (OrderBot.toHasBot.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4) (OrderIsoClass.toBotHomClass.{u1, u2, u3} F α β _inst_1 _inst_2 _inst_3 _inst_4 _inst_5))) f a) (Bot.bot.{u3} β (OrderBot.toHasBot.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β _inst_3)) _inst_4))) (Eq.{succ u2} α a (Bot.bot.{u2} α (OrderBot.toHasBot.{u2} α _inst_1 _inst_2)))
but is expected to have type
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+ forall {F : Type.{u1}} {α : Type.{u3}} {β : Type.{u2}} [_inst_1 : LE.{u3} α] [_inst_2 : OrderBot.{u3} α _inst_1] [_inst_3 : PartialOrder.{u2} β] [_inst_4 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_3))] [_inst_5 : OrderIsoClass.{u1, u3, u2} F α β _inst_1 (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_3))] (f : F) {a : α}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (FunLike.coe.{succ u1, succ u3, succ u2} F α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{u1, u3, u2} F α β (OrderBot.toBot.{u3} α _inst_1 _inst_2) (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_3)) _inst_4) (OrderIsoClass.toBotHomClass.{u1, u3, u2} F α β _inst_1 _inst_2 _inst_3 _inst_4 _inst_5)) f a) (Bot.bot.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (OrderBot.toBot.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (PartialOrder.toPreorder.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) _inst_3)) _inst_4))) (Eq.{succ u3} α a (Bot.bot.{u3} α (OrderBot.toBot.{u3} α _inst_1 _inst_2)))
Case conversion may be inaccurate. Consider using '#align map_eq_bot_iff map_eq_bot_iffₓ'. -/
@[simp]
theorem map_eq_bot_iff [LE α] [OrderBot α] [PartialOrder β] [OrderBot β] [OrderIsoClass F α β]
mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212
@@ -565,7 +565,7 @@ initialize_simps_projections BotHom (toFun → apply)
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Bot.{u2} β] {f : BotHom.{u1, u2} α β _inst_1 _inst_2} {g : BotHom.{u1, u2} α β _inst_1 _inst_2}, (forall (a : α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BotHom.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f a) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BotHom.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) g a)) -> (Eq.{max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 _inst_2) f g)
but is expected to have type
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+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Bot.{u2} α] [_inst_2 : Bot.{u1} β] {f : BotHom.{u2, u1} α β _inst_1 _inst_2} {g : BotHom.{u2, u1} α β _inst_1 _inst_2}, (forall (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 _inst_2)) f a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 _inst_2)) g a)) -> (Eq.{max (succ u2) (succ u1)} (BotHom.{u2, u1} α β _inst_1 _inst_2) f g)
Case conversion may be inaccurate. Consider using '#align bot_hom.ext BotHom.extₓ'. -/
@[ext]
theorem ext {f g : BotHom α β} (h : ∀ a, f a = g a) : f = g :=
@@ -576,7 +576,7 @@ theorem ext {f g : BotHom α β} (h : ∀ a, f a = g a) : f = g :=
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Bot.{u2} β] (f : BotHom.{u1, u2} α β _inst_1 _inst_2) (f' : α -> β), (Eq.{max (succ u1) (succ u2)} (α -> β) f' (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BotHom.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f)) -> (BotHom.{u1, u2} α β _inst_1 _inst_2)
but is expected to have type
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+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Bot.{u2} β] (f : BotHom.{u1, u2} α β _inst_1 _inst_2) (f' : α -> β), (Eq.{max (succ u1) (succ u2)} (α -> β) f' (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 _inst_2)) f)) -> (BotHom.{u1, u2} α β _inst_1 _inst_2)
Case conversion may be inaccurate. Consider using '#align bot_hom.copy BotHom.copyₓ'. -/
/-- Copy of a `bot_hom` with a new `to_fun` equal to the old one. Useful to fix definitional
equalities. -/
@@ -590,7 +590,7 @@ protected def copy (f : BotHom α β) (f' : α → β) (h : f' = f) : BotHom α
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Bot.{u2} β] (f : BotHom.{u1, u2} α β _inst_1 _inst_2) (f' : α -> β) (h : Eq.{max (succ u1) (succ u2)} (α -> β) f' (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BotHom.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f)), Eq.{max (succ u1) (succ u2)} (α -> β) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BotHom.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) (BotHom.copy.{u1, u2} α β _inst_1 _inst_2 f f' h)) f'
but is expected to have type
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+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Bot.{u2} α] [_inst_2 : Bot.{u1} β] (f : BotHom.{u2, u1} α β _inst_1 _inst_2) (f' : α -> β) (h : Eq.{max (succ u2) (succ u1)} (α -> β) f' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 _inst_2)) f)), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 _inst_2)) (BotHom.copy.{u2, u1} α β _inst_1 _inst_2 f f' h)) f'
Case conversion may be inaccurate. Consider using '#align bot_hom.coe_copy BotHom.coe_copyₓ'. -/
@[simp]
theorem coe_copy (f : BotHom α β) (f' : α → β) (h : f' = f) : ⇑(f.copy f' h) = f' :=
@@ -601,7 +601,7 @@ theorem coe_copy (f : BotHom α β) (f' : α → β) (h : f' = f) : ⇑(f.copy f
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Bot.{u2} β] (f : BotHom.{u1, u2} α β _inst_1 _inst_2) (f' : α -> β) (h : Eq.{max (succ u1) (succ u2)} (α -> β) f' (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BotHom.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f)), Eq.{max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 _inst_2) (BotHom.copy.{u1, u2} α β _inst_1 _inst_2 f f' h) f
but is expected to have type
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+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Bot.{u2} α] [_inst_2 : Bot.{u1} β] (f : BotHom.{u2, u1} α β _inst_1 _inst_2) (f' : α -> β) (h : Eq.{max (succ u2) (succ u1)} (α -> β) f' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 _inst_2)) f)), Eq.{max (succ u2) (succ u1)} (BotHom.{u2, u1} α β _inst_1 _inst_2) (BotHom.copy.{u2, u1} α β _inst_1 _inst_2 f f' h) f
Case conversion may be inaccurate. Consider using '#align bot_hom.copy_eq BotHom.copy_eqₓ'. -/
theorem copy_eq (f : BotHom α β) (f' : α → β) (h : f' = f) : f.copy f' h = f :=
FunLike.ext' h
@@ -623,7 +623,7 @@ protected def id : BotHom α α :=
lean 3 declaration is
forall (α : Type.{u1}) [_inst_1 : Bot.{u1} α], Eq.{succ u1} (α -> α) (coeFn.{succ u1, succ u1} (BotHom.{u1, u1} α α _inst_1 _inst_1) (fun (_x : BotHom.{u1, u1} α α _inst_1 _inst_1) => α -> α) (BotHom.hasCoeToFun.{u1, u1} α α _inst_1 _inst_1) (BotHom.id.{u1} α _inst_1)) (id.{succ u1} α)
but is expected to have type
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+ forall (α : Type.{u1}) [_inst_1 : Bot.{u1} α], Eq.{succ u1} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => α) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (BotHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => α) _x) (BotHomClass.toFunLike.{u1, u1, u1} (BotHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (BotHom.instBotHomClassBotHom.{u1, u1} α α _inst_1 _inst_1)) (BotHom.id.{u1} α _inst_1)) (id.{succ u1} α)
Case conversion may be inaccurate. Consider using '#align bot_hom.coe_id BotHom.coe_idₓ'. -/
@[simp]
theorem coe_id : ⇑(BotHom.id α) = id :=
@@ -636,7 +636,7 @@ variable {α}
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : Bot.{u1} α] (a : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (BotHom.{u1, u1} α α _inst_1 _inst_1) (fun (_x : BotHom.{u1, u1} α α _inst_1 _inst_1) => α -> α) (BotHom.hasCoeToFun.{u1, u1} α α _inst_1 _inst_1) (BotHom.id.{u1} α _inst_1) a) a
but is expected to have type
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+ forall {α : Type.{u1}} [_inst_1 : Bot.{u1} α] (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (BotHom.{u1, u1} α α _inst_1 _inst_1) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => α) _x) (BotHomClass.toFunLike.{u1, u1, u1} (BotHom.{u1, u1} α α _inst_1 _inst_1) α α _inst_1 _inst_1 (BotHom.instBotHomClassBotHom.{u1, u1} α α _inst_1 _inst_1)) (BotHom.id.{u1} α _inst_1) a) a
Case conversion may be inaccurate. Consider using '#align bot_hom.id_apply BotHom.id_applyₓ'. -/
@[simp]
theorem id_apply (a : α) : BotHom.id α a = a :=
@@ -656,7 +656,7 @@ def comp (f : BotHom β γ) (g : BotHom α β) : BotHom α γ
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Bot.{u1} α] [_inst_2 : Bot.{u2} β] [_inst_3 : Bot.{u3} γ] (f : BotHom.{u2, u3} β γ _inst_2 _inst_3) (g : BotHom.{u1, u2} α β _inst_1 _inst_2), Eq.{max (succ u1) (succ u3)} ((fun (_x : BotHom.{u1, u3} α γ _inst_1 _inst_3) => α -> γ) (BotHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 f g)) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (BotHom.{u1, u3} α γ _inst_1 _inst_3) (fun (_x : BotHom.{u1, u3} α γ _inst_1 _inst_3) => α -> γ) (BotHom.hasCoeToFun.{u1, u3} α γ _inst_1 _inst_3) (BotHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 f g)) (Function.comp.{succ u1, succ u2, succ u3} α β γ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (BotHom.{u2, u3} β γ _inst_2 _inst_3) (fun (_x : BotHom.{u2, u3} β γ _inst_2 _inst_3) => β -> γ) (BotHom.hasCoeToFun.{u2, u3} β γ _inst_2 _inst_3) f) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BotHom.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) g))
but is expected to have type
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+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Bot.{u3} β] [_inst_3 : Bot.{u2} γ] (f : BotHom.{u3, u2} β γ _inst_2 _inst_3) (g : BotHom.{u1, u3} α β _inst_1 _inst_2), Eq.{max (succ u1) (succ u2)} (forall (a : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => γ) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α γ _inst_1 _inst_3) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => γ) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α γ _inst_1 _inst_3) α γ _inst_1 _inst_3 (BotHom.instBotHomClassBotHom.{u1, u2} α γ _inst_1 _inst_3)) (BotHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 f g)) (Function.comp.{succ u1, succ u3, succ u2} α β γ (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (BotHom.{u3, u2} β γ _inst_2 _inst_3) β (fun (_x : β) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : β) => γ) _x) (BotHomClass.toFunLike.{max u3 u2, u3, u2} (BotHom.{u3, u2} β γ _inst_2 _inst_3) β γ _inst_2 _inst_3 (BotHom.instBotHomClassBotHom.{u3, u2} β γ _inst_2 _inst_3)) f) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (BotHom.{u1, u3} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u3, u1, u3} (BotHom.{u1, u3} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BotHom.instBotHomClassBotHom.{u1, u3} α β _inst_1 _inst_2)) g))
Case conversion may be inaccurate. Consider using '#align bot_hom.coe_comp BotHom.coe_compₓ'. -/
@[simp]
theorem coe_comp (f : BotHom β γ) (g : BotHom α β) : (f.comp g : α → γ) = f ∘ g :=
@@ -667,7 +667,7 @@ theorem coe_comp (f : BotHom β γ) (g : BotHom α β) : (f.comp g : α → γ)
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Bot.{u1} α] [_inst_2 : Bot.{u2} β] [_inst_3 : Bot.{u3} γ] (f : BotHom.{u2, u3} β γ _inst_2 _inst_3) (g : BotHom.{u1, u2} α β _inst_1 _inst_2) (a : α), Eq.{succ u3} γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (BotHom.{u1, u3} α γ _inst_1 _inst_3) (fun (_x : BotHom.{u1, u3} α γ _inst_1 _inst_3) => α -> γ) (BotHom.hasCoeToFun.{u1, u3} α γ _inst_1 _inst_3) (BotHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 f g) a) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (BotHom.{u2, u3} β γ _inst_2 _inst_3) (fun (_x : BotHom.{u2, u3} β γ _inst_2 _inst_3) => β -> γ) (BotHom.hasCoeToFun.{u2, u3} β γ _inst_2 _inst_3) f (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BotHom.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) g a))
but is expected to have type
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Case conversion may be inaccurate. Consider using '#align bot_hom.comp_apply BotHom.comp_applyₓ'. -/
@[simp]
theorem comp_apply (f : BotHom β γ) (g : BotHom α β) (a : α) : (f.comp g) a = f (g a) :=
@@ -712,7 +712,7 @@ theorem id_comp (f : BotHom α β) : (BotHom.id β).comp f = f :=
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Bot.{u1} α] [_inst_2 : Bot.{u2} β] [_inst_3 : Bot.{u3} γ] {g₁ : BotHom.{u2, u3} β γ _inst_2 _inst_3} {g₂ : BotHom.{u2, u3} β γ _inst_2 _inst_3} {f : BotHom.{u1, u2} α β _inst_1 _inst_2}, (Function.Surjective.{succ u1, succ u2} α β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 _inst_2) (fun (_x : BotHom.{u1, u2} α β _inst_1 _inst_2) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) f)) -> (Iff (Eq.{max (succ u1) (succ u3)} (BotHom.{u1, u3} α γ _inst_1 _inst_3) (BotHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 g₁ f) (BotHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 g₂ f)) (Eq.{max (succ u2) (succ u3)} (BotHom.{u2, u3} β γ _inst_2 _inst_3) g₁ g₂))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Bot.{u3} β] [_inst_3 : Bot.{u2} γ] {g₁ : BotHom.{u3, u2} β γ _inst_2 _inst_3} {g₂ : BotHom.{u3, u2} β γ _inst_2 _inst_3} {f : BotHom.{u1, u3} α β _inst_1 _inst_2}, (Function.Surjective.{succ u1, succ u3} α β (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (BotHom.{u1, u3} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u3, u1, u3} (BotHom.{u1, u3} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BotHom.instBotHomClassBotHom.{u1, u3} α β _inst_1 _inst_2)) f)) -> (Iff (Eq.{max (succ u1) (succ u2)} (BotHom.{u1, u2} α γ _inst_1 _inst_3) (BotHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 g₁ f) (BotHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 g₂ f)) (Eq.{max (succ u3) (succ u2)} (BotHom.{u3, u2} β γ _inst_2 _inst_3) g₁ g₂))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Bot.{u3} β] [_inst_3 : Bot.{u2} γ] {g₁ : BotHom.{u3, u2} β γ _inst_2 _inst_3} {g₂ : BotHom.{u3, u2} β γ _inst_2 _inst_3} {f : BotHom.{u1, u3} α β _inst_1 _inst_2}, (Function.Surjective.{succ u1, succ u3} α β (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (BotHom.{u1, u3} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u3, u1, u3} (BotHom.{u1, u3} α β _inst_1 _inst_2) α β _inst_1 _inst_2 (BotHom.instBotHomClassBotHom.{u1, u3} α β _inst_1 _inst_2)) f)) -> (Iff (Eq.{max (succ u1) (succ u2)} (BotHom.{u1, u2} α γ _inst_1 _inst_3) (BotHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 g₁ f) (BotHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 g₂ f)) (Eq.{max (succ u3) (succ u2)} (BotHom.{u3, u2} β γ _inst_2 _inst_3) g₁ g₂))
Case conversion may be inaccurate. Consider using '#align bot_hom.cancel_right BotHom.cancel_rightₓ'. -/
theorem cancel_right {g₁ g₂ : BotHom β γ} {f : BotHom α β} (hf : Surjective f) :
g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
@@ -723,7 +723,7 @@ theorem cancel_right {g₁ g₂ : BotHom β γ} {f : BotHom α β} (hf : Surject
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Bot.{u1} α] [_inst_2 : Bot.{u2} β] [_inst_3 : Bot.{u3} γ] {g : BotHom.{u2, u3} β γ _inst_2 _inst_3} {f₁ : BotHom.{u1, u2} α β _inst_1 _inst_2} {f₂ : BotHom.{u1, u2} α β _inst_1 _inst_2}, (Function.Injective.{succ u2, succ u3} β γ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (BotHom.{u2, u3} β γ _inst_2 _inst_3) (fun (_x : BotHom.{u2, u3} β γ _inst_2 _inst_3) => β -> γ) (BotHom.hasCoeToFun.{u2, u3} β γ _inst_2 _inst_3) g)) -> (Iff (Eq.{max (succ u1) (succ u3)} (BotHom.{u1, u3} α γ _inst_1 _inst_3) (BotHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 g f₁) (BotHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 g f₂)) (Eq.{max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 _inst_2) f₁ f₂))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Bot.{u3} β] [_inst_3 : Bot.{u2} γ] {g : BotHom.{u3, u2} β γ _inst_2 _inst_3} {f₁ : BotHom.{u1, u3} α β _inst_1 _inst_2} {f₂ : BotHom.{u1, u3} α β _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u2} β γ (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (BotHom.{u3, u2} β γ _inst_2 _inst_3) β (fun (_x : β) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : β) => γ) _x) (BotHomClass.toFunLike.{max u3 u2, u3, u2} (BotHom.{u3, u2} β γ _inst_2 _inst_3) β γ _inst_2 _inst_3 (BotHom.instBotHomClassBotHom.{u3, u2} β γ _inst_2 _inst_3)) g)) -> (Iff (Eq.{max (succ u1) (succ u2)} (BotHom.{u1, u2} α γ _inst_1 _inst_3) (BotHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 g f₁) (BotHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 g f₂)) (Eq.{max (succ u1) (succ u3)} (BotHom.{u1, u3} α β _inst_1 _inst_2) f₁ f₂))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Bot.{u3} β] [_inst_3 : Bot.{u2} γ] {g : BotHom.{u3, u2} β γ _inst_2 _inst_3} {f₁ : BotHom.{u1, u3} α β _inst_1 _inst_2} {f₂ : BotHom.{u1, u3} α β _inst_1 _inst_2}, (Function.Injective.{succ u3, succ u2} β γ (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (BotHom.{u3, u2} β γ _inst_2 _inst_3) β (fun (_x : β) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : β) => γ) _x) (BotHomClass.toFunLike.{max u3 u2, u3, u2} (BotHom.{u3, u2} β γ _inst_2 _inst_3) β γ _inst_2 _inst_3 (BotHom.instBotHomClassBotHom.{u3, u2} β γ _inst_2 _inst_3)) g)) -> (Iff (Eq.{max (succ u1) (succ u2)} (BotHom.{u1, u2} α γ _inst_1 _inst_3) (BotHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 g f₁) (BotHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 g f₂)) (Eq.{max (succ u1) (succ u3)} (BotHom.{u1, u3} α β _inst_1 _inst_2) f₁ f₂))
Case conversion may be inaccurate. Consider using '#align bot_hom.cancel_left BotHom.cancel_leftₓ'. -/
theorem cancel_left {g : BotHom β γ} {f₁ f₂ : BotHom α β} (hg : Injective g) :
g.comp f₁ = g.comp f₂ ↔ f₁ = f₂ :=
@@ -750,7 +750,7 @@ instance : OrderBot (BotHom α β) :=
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2)], Eq.{succ (max u1 u2)} (α -> β) (coeFn.{max (succ u1) (succ u2), succ (max u1 u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (Bot.bot.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (OrderBot.toHasBot.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (Preorder.toLE.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (BotHom.preorder.{u1, u2} α β _inst_1 _inst_2 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))) (BotHom.orderBot.{u1, u2} α β _inst_1 _inst_2 _inst_3)))) (Bot.bot.{max u1 u2} (α -> β) (Pi.hasBot.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Bot.{u2} α] [_inst_2 : Preorder.{u1} β] [_inst_3 : OrderBot.{u1} β (Preorder.toLE.{u1} β _inst_2)], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3))) (Bot.bot.{max u2 u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) (OrderBot.toBot.{max u2 u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) (Preorder.toLE.{max u2 u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) (BotHom.instPreorderBotHom.{u2, u1} α β _inst_1 _inst_2 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3))) (BotHom.instOrderBotBotHomToBotToLEToLEInstPreorderBotHom.{u2, u1} α β _inst_1 _inst_2 _inst_3)))) (Bot.bot.{max u2 u1} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) ᾰ) (Pi.instBotForAll.{u2, u1} α (fun (ᾰ : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) ᾰ) (fun (i : α) => OrderBot.toBot.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) i) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) i) _inst_2) _inst_3)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Bot.{u2} α] [_inst_2 : Preorder.{u1} β] [_inst_3 : OrderBot.{u1} β (Preorder.toLE.{u1} β _inst_2)], Eq.{max (succ u2) (succ u1)} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3))) (Bot.bot.{max u2 u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) (OrderBot.toBot.{max u2 u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) (Preorder.toLE.{max u2 u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3)) (BotHom.instPreorderBotHom.{u2, u1} α β _inst_1 _inst_2 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_3))) (BotHom.instOrderBotBotHomToBotToLEToLEInstPreorderBotHom.{u2, u1} α β _inst_1 _inst_2 _inst_3)))) (Bot.bot.{max u2 u1} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (Pi.instBotForAll.{u2, u1} α (fun (ᾰ : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (fun (i : α) => OrderBot.toBot.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) i) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) i) _inst_2) _inst_3)))
Case conversion may be inaccurate. Consider using '#align bot_hom.coe_bot BotHom.coe_botₓ'. -/
@[simp]
theorem coe_bot : ⇑(⊥ : BotHom α β) = ⊥ :=
@@ -761,7 +761,7 @@ theorem coe_bot : ⇑(⊥ : BotHom α β) = ⊥ :=
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2)] (a : α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (Bot.bot.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (OrderBot.toHasBot.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (Preorder.toLE.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (BotHom.preorder.{u1, u2} α β _inst_1 _inst_2 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))) (BotHom.orderBot.{u1, u2} α β _inst_1 _inst_2 _inst_3))) a) (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2)] (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))) (Bot.bot.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (OrderBot.toBot.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (Preorder.toLE.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (BotHom.instPreorderBotHom.{u1, u2} α β _inst_1 _inst_2 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))) (BotHom.instOrderBotBotHomToBotToLEToLEInstPreorderBotHom.{u1, u2} α β _inst_1 _inst_2 _inst_3))) a) (Bot.bot.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) (OrderBot.toBot.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) _inst_2) _inst_3))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2)] (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))) (Bot.bot.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (OrderBot.toBot.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (Preorder.toLE.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)) (BotHom.instPreorderBotHom.{u1, u2} α β _inst_1 _inst_2 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))) (BotHom.instOrderBotBotHomToBotToLEToLEInstPreorderBotHom.{u1, u2} α β _inst_1 _inst_2 _inst_3))) a) (Bot.bot.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (OrderBot.toBot.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (Preorder.toLE.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) _inst_2) _inst_3))
Case conversion may be inaccurate. Consider using '#align bot_hom.bot_apply BotHom.bot_applyₓ'. -/
@[simp]
theorem bot_apply (a : α) : (⊥ : BotHom α β) a = ⊥ :=
@@ -784,7 +784,7 @@ instance : SemilatticeInf (BotHom α β) :=
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : SemilatticeInf.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2)))] (f : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)), Eq.{succ (max u1 u2)} (α -> β) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (Inf.inf.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (BotHom.hasInf.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g)) (Inf.inf.{max u1 u2} (α -> β) (Pi.hasInf.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => SemilatticeInf.toHasInf.{u2} β _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) f) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) g))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Bot.{u2} α] [_inst_2 : SemilatticeInf.{u1} β] [_inst_3 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2)))] (f : BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) (g : BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3))) (Inf.inf.{max u2 u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) (BotHom.instInfBotHomToBotToLEToPreorderToPartialOrder.{u2, u1} α β _inst_1 _inst_2 _inst_3) f g)) (Inf.inf.{max u2 u1} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) ᾰ) (Pi.instInfForAll.{u2, u1} α (fun (ᾰ : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) ᾰ) (fun (i : α) => SemilatticeInf.toInf.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) i) _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3))) g))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Bot.{u2} α] [_inst_2 : SemilatticeInf.{u1} β] [_inst_3 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2)))] (f : BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) (g : BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3))) (Inf.inf.{max u2 u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) (BotHom.instInfBotHomToBotToLEToPreorderToPartialOrder.{u2, u1} α β _inst_1 _inst_2 _inst_3) f g)) (Inf.inf.{max u2 u1} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (Pi.instInfForAll.{u2, u1} α (fun (ᾰ : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (fun (i : α) => SemilatticeInf.toInf.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) i) _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3))) g))
Case conversion may be inaccurate. Consider using '#align bot_hom.coe_inf BotHom.coe_infₓ'. -/
@[simp]
theorem coe_inf : ⇑(f ⊓ g) = f ⊓ g :=
@@ -795,7 +795,7 @@ theorem coe_inf : ⇑(f ⊓ g) = f ⊓ g :=
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : SemilatticeInf.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2)))] (f : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (Inf.inf.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (BotHom.hasInf.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Inf.inf.{u2} β (SemilatticeInf.toHasInf.{u2} β _inst_2) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) f a) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) g a))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : SemilatticeInf.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2)))] (f : BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) (Inf.inf.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (BotHom.instInfBotHomToBotToLEToPreorderToPartialOrder.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Inf.inf.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) (SemilatticeInf.toInf.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) f a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) g a))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : SemilatticeInf.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2)))] (f : BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) (Inf.inf.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (BotHom.instInfBotHomToBotToLEToPreorderToPartialOrder.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Inf.inf.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (SemilatticeInf.toInf.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) f a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) g a))
Case conversion may be inaccurate. Consider using '#align bot_hom.inf_apply BotHom.inf_applyₓ'. -/
@[simp]
theorem inf_apply (a : α) : (f ⊓ g) a = f a ⊓ g a :=
@@ -818,7 +818,7 @@ instance : SemilatticeSup (BotHom α β) :=
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)))] (f : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)), Eq.{succ (max u1 u2)} (α -> β) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (Sup.sup.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (BotHom.hasSup.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g)) (Sup.sup.{max u1 u2} (α -> β) (Pi.hasSup.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => SemilatticeSup.toHasSup.{u2} β _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) f) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) g))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Bot.{u2} α] [_inst_2 : SemilatticeSup.{u1} β] [_inst_3 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2)))] (f : BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) (g : BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3))) (Sup.sup.{max u2 u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) (BotHom.instSupBotHomToBotToLEToPreorderToPartialOrder.{u2, u1} α β _inst_1 _inst_2 _inst_3) f g)) (Sup.sup.{max u2 u1} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) ᾰ) (Pi.instSupForAll.{u2, u1} α (fun (ᾰ : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) ᾰ) (fun (i : α) => SemilatticeSup.toSup.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) i) _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3))) g))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Bot.{u2} α] [_inst_2 : SemilatticeSup.{u1} β] [_inst_3 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2)))] (f : BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) (g : BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3))) (Sup.sup.{max u2 u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) (BotHom.instSupBotHomToBotToLEToPreorderToPartialOrder.{u2, u1} α β _inst_1 _inst_2 _inst_3) f g)) (Sup.sup.{max u2 u1} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (Pi.instSupForAll.{u2, u1} α (fun (ᾰ : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (fun (i : α) => SemilatticeSup.toSup.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) i) _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3))) g))
Case conversion may be inaccurate. Consider using '#align bot_hom.coe_sup BotHom.coe_supₓ'. -/
@[simp]
theorem coe_sup : ⇑(f ⊔ g) = f ⊔ g :=
@@ -829,7 +829,7 @@ theorem coe_sup : ⇑(f ⊔ g) = f ⊔ g :=
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)))] (f : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (Sup.sup.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (BotHom.hasSup.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Sup.sup.{u2} β (SemilatticeSup.toHasSup.{u2} β _inst_2) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) f a) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) g a))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)))] (f : BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) (Sup.sup.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (BotHom.instSupBotHomToBotToLEToPreorderToPartialOrder.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Sup.sup.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) (SemilatticeSup.toSup.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) f a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) g a))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)))] (f : BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) (Sup.sup.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (BotHom.instSupBotHomToBotToLEToPreorderToPartialOrder.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Sup.sup.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (SemilatticeSup.toSup.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) f a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) g a))
Case conversion may be inaccurate. Consider using '#align bot_hom.sup_apply BotHom.sup_applyₓ'. -/
@[simp]
theorem sup_apply (a : α) : (f ⊔ g) a = f a ⊔ g a :=
@@ -905,7 +905,7 @@ theorem [anonymous] {f : BoundedOrderHom α β} : f.toFun = (f : α → β) :=
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β _inst_2)] {f : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6} {g : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6}, (forall (a : α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (fun (_x : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) => α -> β) (BoundedOrderHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) f a) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (fun (_x : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) => α -> β) (BoundedOrderHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) g a)) -> (Eq.{max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) f g)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] [_inst_5 : BoundedOrder.{u2} α (Preorder.toLE.{u2} α _inst_1)] [_inst_6 : BoundedOrder.{u1} β (Preorder.toLE.{u1} β _inst_2)] {f : BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6} {g : BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6}, (forall (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u2} α (Preorder.toLE.{u2} α _inst_1) (BoundedOrder.toOrderBot.{u2} α (Preorder.toLE.{u2} α _inst_1) _inst_5)) (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) (BoundedOrder.toOrderBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6))) f a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u2} α (Preorder.toLE.{u2} α _inst_1) (BoundedOrder.toOrderBot.{u2} α (Preorder.toLE.{u2} α _inst_1) _inst_5)) (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) (BoundedOrder.toOrderBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6))) g a)) -> (Eq.{max (succ u2) (succ u1)} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) f g)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] [_inst_5 : BoundedOrder.{u2} α (Preorder.toLE.{u2} α _inst_1)] [_inst_6 : BoundedOrder.{u1} β (Preorder.toLE.{u1} β _inst_2)] {f : BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6} {g : BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6}, (forall (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u2} α (Preorder.toLE.{u2} α _inst_1) (BoundedOrder.toOrderBot.{u2} α (Preorder.toLE.{u2} α _inst_1) _inst_5)) (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) (BoundedOrder.toOrderBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6))) f a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u2} α (Preorder.toLE.{u2} α _inst_1) (BoundedOrder.toOrderBot.{u2} α (Preorder.toLE.{u2} α _inst_1) _inst_5)) (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) (BoundedOrder.toOrderBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6))) g a)) -> (Eq.{max (succ u2) (succ u1)} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) f g)
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.ext BoundedOrderHom.extₓ'. -/
@[ext]
theorem ext {f g : BoundedOrderHom α β} (h : ∀ a, f a = g a) : f = g :=
@@ -916,7 +916,7 @@ theorem ext {f g : BoundedOrderHom α β} (h : ∀ a, f a = g a) : f = g :=
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β _inst_2)] (f : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (f' : α -> β), (Eq.{max (succ u1) (succ u2)} (α -> β) f' (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (fun (_x : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) => α -> β) (BoundedOrderHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) f)) -> (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6)
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β _inst_2)] (f : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (f' : α -> β), (Eq.{max (succ u1) (succ u2)} (α -> β) f' (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) (BoundedOrder.toOrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6))) f)) -> (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β _inst_2)] (f : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (f' : α -> β), (Eq.{max (succ u1) (succ u2)} (α -> β) f' (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) (BoundedOrder.toOrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6))) f)) -> (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6)
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.copy BoundedOrderHom.copyₓ'. -/
/-- Copy of a `bounded_order_hom` with a new `to_fun` equal to the old one. Useful to fix
definitional equalities. -/
@@ -928,7 +928,7 @@ protected def copy (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : B
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β _inst_2)] (f : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (f' : α -> β) (h : Eq.{max (succ u1) (succ u2)} (α -> β) f' (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (fun (_x : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) => α -> β) (BoundedOrderHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) f)), Eq.{max (succ u1) (succ u2)} (α -> β) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (fun (_x : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) => α -> β) (BoundedOrderHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (BoundedOrderHom.copy.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6 f f' h)) f'
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] [_inst_5 : BoundedOrder.{u2} α (Preorder.toLE.{u2} α _inst_1)] [_inst_6 : BoundedOrder.{u1} β (Preorder.toLE.{u1} β _inst_2)] (f : BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) (f' : α -> β) (h : Eq.{max (succ u2) (succ u1)} (α -> β) f' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u2} α (Preorder.toLE.{u2} α _inst_1) (BoundedOrder.toOrderBot.{u2} α (Preorder.toLE.{u2} α _inst_1) _inst_5)) (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) (BoundedOrder.toOrderBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6))) f)), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u2} α (Preorder.toLE.{u2} α _inst_1) (BoundedOrder.toOrderBot.{u2} α (Preorder.toLE.{u2} α _inst_1) _inst_5)) (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) (BoundedOrder.toOrderBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6))) (BoundedOrderHom.copy.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6 f f' h)) f'
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] [_inst_5 : BoundedOrder.{u2} α (Preorder.toLE.{u2} α _inst_1)] [_inst_6 : BoundedOrder.{u1} β (Preorder.toLE.{u1} β _inst_2)] (f : BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) (f' : α -> β) (h : Eq.{max (succ u2) (succ u1)} (α -> β) f' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u2} α (Preorder.toLE.{u2} α _inst_1) (BoundedOrder.toOrderBot.{u2} α (Preorder.toLE.{u2} α _inst_1) _inst_5)) (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) (BoundedOrder.toOrderBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6))) f)), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u2} α (Preorder.toLE.{u2} α _inst_1) (BoundedOrder.toOrderBot.{u2} α (Preorder.toLE.{u2} α _inst_1) _inst_5)) (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) (BoundedOrder.toOrderBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6))) (BoundedOrderHom.copy.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6 f f' h)) f'
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.coe_copy BoundedOrderHom.coe_copyₓ'. -/
@[simp]
theorem coe_copy (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : ⇑(f.copy f' h) = f' :=
@@ -939,7 +939,7 @@ theorem coe_copy (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : ⇑
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β _inst_2)] (f : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (f' : α -> β) (h : Eq.{max (succ u1) (succ u2)} (α -> β) f' (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (fun (_x : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) => α -> β) (BoundedOrderHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) f)), Eq.{max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (BoundedOrderHom.copy.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6 f f' h) f
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] [_inst_5 : BoundedOrder.{u2} α (Preorder.toLE.{u2} α _inst_1)] [_inst_6 : BoundedOrder.{u1} β (Preorder.toLE.{u1} β _inst_2)] (f : BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) (f' : α -> β) (h : Eq.{max (succ u2) (succ u1)} (α -> β) f' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u2} α (Preorder.toLE.{u2} α _inst_1) (BoundedOrder.toOrderBot.{u2} α (Preorder.toLE.{u2} α _inst_1) _inst_5)) (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) (BoundedOrder.toOrderBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6))) f)), Eq.{max (succ u2) (succ u1)} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) (BoundedOrderHom.copy.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6 f f' h) f
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] [_inst_5 : BoundedOrder.{u2} α (Preorder.toLE.{u2} α _inst_1)] [_inst_6 : BoundedOrder.{u1} β (Preorder.toLE.{u1} β _inst_2)] (f : BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) (f' : α -> β) (h : Eq.{max (succ u2) (succ u1)} (α -> β) f' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u2} α (Preorder.toLE.{u2} α _inst_1) (BoundedOrder.toOrderBot.{u2} α (Preorder.toLE.{u2} α _inst_1) _inst_5)) (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β _inst_2) (BoundedOrder.toOrderBot.{u1} β (Preorder.toLE.{u1} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u2 u1, u2, u1} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6))) f)), Eq.{max (succ u2) (succ u1)} (BoundedOrderHom.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6) (BoundedOrderHom.copy.{u2, u1} α β _inst_1 _inst_2 _inst_5 _inst_6 f f' h) f
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.copy_eq BoundedOrderHom.copy_eqₓ'. -/
theorem copy_eq (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : f.copy f' h = f :=
FunLike.ext' h
@@ -961,7 +961,7 @@ instance : Inhabited (BoundedOrderHom α α) :=
lean 3 declaration is
forall (α : Type.{u1}) [_inst_1 : Preorder.{u1} α] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)], Eq.{succ u1} (α -> α) (coeFn.{succ u1, succ u1} (BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) (fun (_x : BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) => α -> α) (BoundedOrderHom.hasCoeToFun.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) (BoundedOrderHom.id.{u1} α _inst_1 _inst_5)) (id.{succ u1} α)
but is expected to have type
- forall (α : Type.{u1}) [_inst_1 : Preorder.{u1} α] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)], Eq.{succ u1} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => α) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => α) _x) (BotHomClass.toFunLike.{u1, u1, u1} (BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) α α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (BoundedOrderHomClass.toBotHomClass.{u1, u1, u1} (BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1) _inst_5 _inst_5 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5))) (BoundedOrderHom.id.{u1} α _inst_1 _inst_5)) (id.{succ u1} α)
+ forall (α : Type.{u1}) [_inst_1 : Preorder.{u1} α] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)], Eq.{succ u1} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => α) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => α) _x) (BotHomClass.toFunLike.{u1, u1, u1} (BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) α α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (BoundedOrderHomClass.toBotHomClass.{u1, u1, u1} (BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1) _inst_5 _inst_5 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5))) (BoundedOrderHom.id.{u1} α _inst_1 _inst_5)) (id.{succ u1} α)
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.coe_id BoundedOrderHom.coe_idₓ'. -/
@[simp]
theorem coe_id : ⇑(BoundedOrderHom.id α) = id :=
@@ -974,7 +974,7 @@ variable {α}
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] (a : α), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) (fun (_x : BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) => α -> α) (BoundedOrderHom.hasCoeToFun.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) (BoundedOrderHom.id.{u1} α _inst_1 _inst_5) a) a
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => α) _x) (BotHomClass.toFunLike.{u1, u1, u1} (BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) α α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (BoundedOrderHomClass.toBotHomClass.{u1, u1, u1} (BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1) _inst_5 _inst_5 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5))) (BoundedOrderHom.id.{u1} α _inst_1 _inst_5) a) a
+ forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => α) a) (FunLike.coe.{succ u1, succ u1, succ u1} (BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => α) _x) (BotHomClass.toFunLike.{u1, u1, u1} (BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) α α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (BoundedOrderHomClass.toBotHomClass.{u1, u1, u1} (BoundedOrderHom.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5) α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1) _inst_5 _inst_5 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u1} α α _inst_1 _inst_1 _inst_5 _inst_5))) (BoundedOrderHom.id.{u1} α _inst_1 _inst_5) a) a
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.id_apply BoundedOrderHom.id_applyₓ'. -/
@[simp]
theorem id_apply (a : α) : BoundedOrderHom.id α a = a :=
@@ -992,7 +992,7 @@ def comp (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) : BoundedOrderH
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_7 : BoundedOrder.{u3} γ (Preorder.toLE.{u3} γ _inst_3)] (f : BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) (g : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6), Eq.{max (succ u1) (succ u3)} ((fun (_x : BoundedOrderHom.{u1, u3} α γ _inst_1 _inst_3 _inst_5 _inst_7) => α -> γ) (BoundedOrderHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 f g)) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (BoundedOrderHom.{u1, u3} α γ _inst_1 _inst_3 _inst_5 _inst_7) (fun (_x : BoundedOrderHom.{u1, u3} α γ _inst_1 _inst_3 _inst_5 _inst_7) => α -> γ) (BoundedOrderHom.hasCoeToFun.{u1, u3} α γ _inst_1 _inst_3 _inst_5 _inst_7) (BoundedOrderHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 f g)) (Function.comp.{succ u1, succ u2, succ u3} α β γ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) (fun (_x : BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) => β -> γ) (BoundedOrderHom.hasCoeToFun.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) f) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (fun (_x : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) => α -> β) (BoundedOrderHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) g))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u3} β (Preorder.toLE.{u3} β _inst_2)] [_inst_7 : BoundedOrder.{u2} γ (Preorder.toLE.{u2} γ _inst_3)] (f : BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) (g : BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6), Eq.{max (succ u1) (succ u2)} (forall (a : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => γ) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => γ) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α γ (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (BoundedOrderHomClass.toBotHomClass.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α γ (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} γ _inst_3) _inst_5 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7))) (BoundedOrderHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 f g)) (Function.comp.{succ u1, succ u3, succ u2} α β γ (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β (fun (_x : β) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : β) => γ) _x) (BotHomClass.toFunLike.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (OrderBot.toBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (BoundedOrderHomClass.toBotHomClass.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3) _inst_6 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7))) f) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6))) g))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u3} β (Preorder.toLE.{u3} β _inst_2)] [_inst_7 : BoundedOrder.{u2} γ (Preorder.toLE.{u2} γ _inst_3)] (f : BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) (g : BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6), Eq.{max (succ u1) (succ u2)} (forall (a : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => γ) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => γ) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α γ (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (BoundedOrderHomClass.toBotHomClass.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α γ (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} γ _inst_3) _inst_5 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7))) (BoundedOrderHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 f g)) (Function.comp.{succ u1, succ u3, succ u2} α β γ (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β (fun (_x : β) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : β) => γ) _x) (BotHomClass.toFunLike.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (OrderBot.toBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (BoundedOrderHomClass.toBotHomClass.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3) _inst_6 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7))) f) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6))) g))
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.coe_comp BoundedOrderHom.coe_compₓ'. -/
@[simp]
theorem coe_comp (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) : (f.comp g : α → γ) = f ∘ g :=
@@ -1003,7 +1003,7 @@ theorem coe_comp (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) : (f.co
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_7 : BoundedOrder.{u3} γ (Preorder.toLE.{u3} γ _inst_3)] (f : BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) (g : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (a : α), Eq.{succ u3} γ (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (BoundedOrderHom.{u1, u3} α γ _inst_1 _inst_3 _inst_5 _inst_7) (fun (_x : BoundedOrderHom.{u1, u3} α γ _inst_1 _inst_3 _inst_5 _inst_7) => α -> γ) (BoundedOrderHom.hasCoeToFun.{u1, u3} α γ _inst_1 _inst_3 _inst_5 _inst_7) (BoundedOrderHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 f g) a) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) (fun (_x : BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) => β -> γ) (BoundedOrderHom.hasCoeToFun.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) f (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (fun (_x : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) => α -> β) (BoundedOrderHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) g a))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u3} β (Preorder.toLE.{u3} β _inst_2)] [_inst_7 : BoundedOrder.{u2} γ (Preorder.toLE.{u2} γ _inst_3)] (f : BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) (g : BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => γ) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => γ) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α γ (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (BoundedOrderHomClass.toBotHomClass.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α γ (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} γ _inst_3) _inst_5 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7))) (BoundedOrderHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 f g) a) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β (fun (_x : β) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : β) => γ) _x) (BotHomClass.toFunLike.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (OrderBot.toBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (BoundedOrderHomClass.toBotHomClass.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3) _inst_6 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7))) f (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6))) g a))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u3} β (Preorder.toLE.{u3} β _inst_2)] [_inst_7 : BoundedOrder.{u2} γ (Preorder.toLE.{u2} γ _inst_3)] (f : BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) (g : BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => γ) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => γ) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α γ (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (BoundedOrderHomClass.toBotHomClass.{max u1 u2, u1, u2} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) α γ (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} γ _inst_3) _inst_5 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7))) (BoundedOrderHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 f g) a) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β (fun (_x : β) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : β) => γ) _x) (BotHomClass.toFunLike.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (OrderBot.toBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (BoundedOrderHomClass.toBotHomClass.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3) _inst_6 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7))) f (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6))) g a))
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.comp_apply BoundedOrderHom.comp_applyₓ'. -/
@[simp]
theorem comp_apply (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) (a : α) :
@@ -1085,7 +1085,7 @@ theorem id_comp (f : BoundedOrderHom α β) : (BoundedOrderHom.id β).comp f = f
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_7 : BoundedOrder.{u3} γ (Preorder.toLE.{u3} γ _inst_3)] {g₁ : BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7} {g₂ : BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7} {f : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6}, (Function.Surjective.{succ u1, succ u2} α β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) (fun (_x : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) => α -> β) (BoundedOrderHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) f)) -> (Iff (Eq.{max (succ u1) (succ u3)} (BoundedOrderHom.{u1, u3} α γ _inst_1 _inst_3 _inst_5 _inst_7) (BoundedOrderHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 g₁ f) (BoundedOrderHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 g₂ f)) (Eq.{max (succ u2) (succ u3)} (BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) g₁ g₂))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u3} β (Preorder.toLE.{u3} β _inst_2)] [_inst_7 : BoundedOrder.{u2} γ (Preorder.toLE.{u2} γ _inst_3)] {g₁ : BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7} {g₂ : BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7} {f : BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6}, (Function.Surjective.{succ u1, succ u3} α β (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6))) f)) -> (Iff (Eq.{max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) (BoundedOrderHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 g₁ f) (BoundedOrderHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 g₂ f)) (Eq.{max (succ u3) (succ u2)} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) g₁ g₂))
+ forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u3} β (Preorder.toLE.{u3} β _inst_2)] [_inst_7 : BoundedOrder.{u2} γ (Preorder.toLE.{u2} γ _inst_3)] {g₁ : BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7} {g₂ : BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7} {f : BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6}, (Function.Surjective.{succ u1, succ u3} α β (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.278 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_5)) (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (BoundedOrderHomClass.toBotHomClass.{max u1 u3, u1, u3} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) _inst_5 _inst_6 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6))) f)) -> (Iff (Eq.{max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) (BoundedOrderHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 g₁ f) (BoundedOrderHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 g₂ f)) (Eq.{max (succ u3) (succ u2)} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) g₁ g₂))
Case conversion may be inaccurate. Consider using '#align bounded_order_hom.cancel_right BoundedOrderHom.cancel_rightₓ'. -/
theorem cancel_right {g₁ g₂ : BoundedOrderHom β γ} {f : BoundedOrderHom α β} (hf : Surjective f) :
g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
@@ -1096,7 +1096,7 @@ theorem cancel_right {g₁ g₂ : BoundedOrderHom β γ} {f : BoundedOrderHom α
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : Preorder.{u3} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_7 : BoundedOrder.{u3} γ (Preorder.toLE.{u3} γ _inst_3)] {g : BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7} {f₁ : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6} {f₂ : BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6}, (Function.Injective.{succ u2, succ u3} β γ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) (fun (_x : BoundedOrderHom.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) => β -> γ) (BoundedOrderHom.hasCoeToFun.{u2, u3} β γ _inst_2 _inst_3 _inst_6 _inst_7) g)) -> (Iff (Eq.{max (succ u1) (succ u3)} (BoundedOrderHom.{u1, u3} α γ _inst_1 _inst_3 _inst_5 _inst_7) (BoundedOrderHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 g f₁) (BoundedOrderHom.comp.{u1, u2, u3} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 g f₂)) (Eq.{max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α β _inst_1 _inst_2 _inst_5 _inst_6) f₁ f₂))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u3} β] [_inst_3 : Preorder.{u2} γ] [_inst_5 : BoundedOrder.{u1} α (Preorder.toLE.{u1} α _inst_1)] [_inst_6 : BoundedOrder.{u3} β (Preorder.toLE.{u3} β _inst_2)] [_inst_7 : BoundedOrder.{u2} γ (Preorder.toLE.{u2} γ _inst_3)] {g : BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7} {f₁ : BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6} {f₂ : BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6}, (Function.Injective.{succ u3, succ u2} β γ (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β (fun (_x : β) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : β) => γ) _x) (BotHomClass.toFunLike.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (OrderBot.toBot.{u3} β (Preorder.toLE.{u3} β _inst_2) (BoundedOrder.toOrderBot.{u3} β (Preorder.toLE.{u3} β _inst_2) _inst_6)) (OrderBot.toBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) (BoundedOrder.toOrderBot.{u2} γ (Preorder.toLE.{u2} γ _inst_3) _inst_7)) (BoundedOrderHomClass.toBotHomClass.{max u3 u2, u3, u2} (BoundedOrderHom.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7) β γ (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3) _inst_6 _inst_7 (BoundedOrderHom.instBoundedOrderHomClassBoundedOrderHomToLEToLE.{u3, u2} β γ _inst_2 _inst_3 _inst_6 _inst_7))) g)) -> (Iff (Eq.{max (succ u1) (succ u2)} (BoundedOrderHom.{u1, u2} α γ _inst_1 _inst_3 _inst_5 _inst_7) (BoundedOrderHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 g f₁) (BoundedOrderHom.comp.{u1, u3, u2} α β γ _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 _inst_7 g f₂)) (Eq.{max (succ u1) (succ u3)} (BoundedOrderHom.{u1, u3} α β _inst_1 _inst_2 _inst_5 _inst_6) f₁ f₂))
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Case conversion may be inaccurate. Consider using '#align bounded_order_hom.cancel_left BoundedOrderHom.cancel_leftₓ'. -/
theorem cancel_left {g : BoundedOrderHom β γ} {f₁ f₂ : BoundedOrderHom α β} (hg : Injective g) :
g.comp f₁ = g.comp f₂ ↔ f₁ = f₂ :=
@@ -1135,7 +1135,7 @@ protected def dual : TopHom α β ≃ BotHom αᵒᵈ βᵒᵈ
lean 3 declaration is
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but is expected to have type
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Case conversion may be inaccurate. Consider using '#align top_hom.dual_id TopHom.dual_idₓ'. -/
@[simp]
theorem dual_id : (TopHom.id α).dual = BotHom.id _ :=
@@ -1146,7 +1146,7 @@ theorem dual_id : (TopHom.id α).dual = BotHom.id _ :=
lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align top_hom.dual_comp TopHom.dual_compₓ'. -/
@[simp]
theorem dual_comp (g : TopHom β γ) (f : TopHom α β) : (g.comp f).dual = g.dual.comp f.dual :=
@@ -1157,7 +1157,7 @@ theorem dual_comp (g : TopHom β γ) (f : TopHom α β) : (g.comp f).dual = g.du
lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align top_hom.symm_dual_id TopHom.symm_dual_idₓ'. -/
@[simp]
theorem symm_dual_id : TopHom.dual.symm (BotHom.id _) = TopHom.id α :=
@@ -1168,7 +1168,7 @@ theorem symm_dual_id : TopHom.dual.symm (BotHom.id _) = TopHom.id α :=
lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align top_hom.symm_dual_comp TopHom.symm_dual_compₓ'. -/
@[simp]
theorem symm_dual_comp (g : BotHom βᵒᵈ γᵒᵈ) (f : BotHom αᵒᵈ βᵒᵈ) :
@@ -1202,7 +1202,7 @@ protected def dual : BotHom α β ≃ TopHom αᵒᵈ βᵒᵈ
lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align bot_hom.dual_id BotHom.dual_idₓ'. -/
@[simp]
theorem dual_id : (BotHom.id α).dual = TopHom.id _ :=
@@ -1213,7 +1213,7 @@ theorem dual_id : (BotHom.id α).dual = TopHom.id _ :=
lean 3 declaration is
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@[simp]
theorem dual_comp (g : BotHom β γ) (f : BotHom α β) : (g.comp f).dual = g.dual.comp f.dual :=
@@ -1224,7 +1224,7 @@ theorem dual_comp (g : BotHom β γ) (f : BotHom α β) : (g.comp f).dual = g.du
lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align bot_hom.symm_dual_id BotHom.symm_dual_idₓ'. -/
@[simp]
theorem symm_dual_id : BotHom.dual.symm (TopHom.id _) = BotHom.id α :=
@@ -1235,7 +1235,7 @@ theorem symm_dual_id : BotHom.dual.symm (TopHom.id _) = BotHom.id α :=
lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align bot_hom.symm_dual_comp BotHom.symm_dual_compₓ'. -/
@[simp]
theorem symm_dual_comp (g : TopHom βᵒᵈ γᵒᵈ) (f : TopHom αᵒᵈ βᵒᵈ) :
@@ -1273,7 +1273,7 @@ theorem dual_id : (BoundedOrderHom.id α).dual = BoundedOrderHom.id _ :=
lean 3 declaration is
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@[simp]
theorem dual_comp (g : BoundedOrderHom β γ) (f : BoundedOrderHom α β) :
@@ -1292,7 +1292,7 @@ theorem symm_dual_id : BoundedOrderHom.dual.symm (BoundedOrderHom.id _) = Bounde
lean 3 declaration is
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Case conversion may be inaccurate. Consider using '#align bounded_order_hom.symm_dual_comp BoundedOrderHom.symm_dual_compₓ'. -/
@[simp]
theorem symm_dual_comp (g : BoundedOrderHom βᵒᵈ γᵒᵈ) (f : BoundedOrderHom αᵒᵈ βᵒᵈ) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -452,7 +452,7 @@ section SemilatticeInf
variable [SemilatticeInf β] [OrderTop β] (f g : TopHom α β)
-instance : HasInf (TopHom α β) :=
+instance : Inf (TopHom α β) :=
⟨fun f g => ⟨f ⊓ g, by rw [Pi.inf_apply, map_top, map_top, inf_top_eq]⟩⟩
instance : SemilatticeInf (TopHom α β) :=
@@ -460,9 +460,9 @@ instance : SemilatticeInf (TopHom α β) :=
/- warning: top_hom.coe_inf -> TopHom.coe_inf is a dubious translation:
lean 3 declaration is
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but is expected to have type
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+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Top.{u2} α] [_inst_2 : SemilatticeInf.{u1} β] [_inst_3 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2)))] (f : TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) (g : TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u2 u1, u2, u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3))) (Inf.inf.{max u2 u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) (TopHom.instInfTopHomToTopToLEToPreorderToPartialOrder.{u2, u1} α β _inst_1 _inst_2 _inst_3) f g)) (Inf.inf.{max u2 u1} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) ᾰ) (Pi.instInfForAll.{u2, u1} α (fun (ᾰ : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) ᾰ) (fun (i : α) => SemilatticeInf.toInf.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) i) _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u2 u1, u2, u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u2 u1, u2, u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3))) g))
Case conversion may be inaccurate. Consider using '#align top_hom.coe_inf TopHom.coe_infₓ'. -/
@[simp]
theorem coe_inf : ⇑(f ⊓ g) = f ⊓ g :=
@@ -471,9 +471,9 @@ theorem coe_inf : ⇑(f ⊓ g) = f ⊓ g :=
/- warning: top_hom.inf_apply -> TopHom.inf_apply is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Top.{u1} α] [_inst_2 : SemilatticeInf.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2)))] (f : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (Inf.inf.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (TopHom.hasInf.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Inf.inf.{u2} β (SemilatticeInf.toHasInf.{u2} β _inst_2) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) f a) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) g a))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Top.{u1} α] [_inst_2 : SemilatticeInf.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2)))] (f : TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u1 u2, u1, u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) (HasInf.inf.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (TopHom.instHasInfTopHomToTopToLEToPreorderToPartialOrder.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (HasInf.inf.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (SemilatticeInf.toHasInf.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u1 u2, u1, u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) f a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u1 u2, u1, u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) g a))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Top.{u1} α] [_inst_2 : SemilatticeInf.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2)))] (f : TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u1 u2, u1, u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) (Inf.inf.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (TopHom.instInfTopHomToTopToLEToPreorderToPartialOrder.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Inf.inf.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (SemilatticeInf.toInf.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u1 u2, u1, u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) f a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u1 u2, u1, u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) g a))
Case conversion may be inaccurate. Consider using '#align top_hom.inf_apply TopHom.inf_applyₓ'. -/
@[simp]
theorem inf_apply (a : α) : (f ⊓ g) a = f a ⊓ g a :=
@@ -486,7 +486,7 @@ section SemilatticeSup
variable [SemilatticeSup β] [OrderTop β] (f g : TopHom α β)
-instance : HasSup (TopHom α β) :=
+instance : Sup (TopHom α β) :=
⟨fun f g => ⟨f ⊔ g, by rw [Pi.sup_apply, map_top, map_top, sup_top_eq]⟩⟩
instance : SemilatticeSup (TopHom α β) :=
@@ -494,9 +494,9 @@ instance : SemilatticeSup (TopHom α β) :=
/- warning: top_hom.coe_sup -> TopHom.coe_sup is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Top.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)))] (f : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)), Eq.{succ (max u1 u2)} (α -> β) (coeFn.{succ (max u1 u2), succ (max u1 u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (Sup.sup.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (TopHom.hasSup.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g)) (Sup.sup.{max u1 u2} (α -> β) (Pi.hasSup.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => SemilatticeSup.toHasSup.{u2} β _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) f) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : TopHom.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (TopHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) g))
but is expected to have type
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+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Top.{u2} α] [_inst_2 : SemilatticeSup.{u1} β] [_inst_3 : OrderTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2)))] (f : TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) (g : TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u2 u1, u2, u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3))) (Sup.sup.{max u2 u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) (TopHom.instSupTopHomToTopToLEToPreorderToPartialOrder.{u2, u1} α β _inst_1 _inst_2 _inst_3) f g)) (Sup.sup.{max u2 u1} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) ᾰ) (Pi.instSupForAll.{u2, u1} α (fun (ᾰ : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) ᾰ) (fun (i : α) => SemilatticeSup.toSup.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) i) _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u2 u1, u2, u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u2 u1, u2, u1} (TopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u2, u1} α β _inst_1 (OrderTop.toTop.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3))) g))
Case conversion may be inaccurate. Consider using '#align top_hom.coe_sup TopHom.coe_supₓ'. -/
@[simp]
theorem coe_sup : ⇑(f ⊔ g) = f ⊔ g :=
@@ -505,9 +505,9 @@ theorem coe_sup : ⇑(f ⊔ g) = f ⊔ g :=
/- warning: top_hom.sup_apply -> TopHom.sup_apply is a dubious translation:
lean 3 declaration is
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but is expected to have type
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+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Top.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)))] (f : TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u1 u2, u1, u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) (Sup.sup.{max u1 u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (TopHom.instSupTopHomToTopToLEToPreorderToPartialOrder.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Sup.sup.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) (SemilatticeSup.toSup.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) a) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u1 u2, u1, u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) f a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.231 : α) => β) _x) (TopHomClass.toFunLike.{max u1 u2, u1, u2} (TopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (TopHom.instTopHomClassTopHom.{u1, u2} α β _inst_1 (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) g a))
Case conversion may be inaccurate. Consider using '#align top_hom.sup_apply TopHom.sup_applyₓ'. -/
@[simp]
theorem sup_apply (a : α) : (f ⊔ g) a = f a ⊔ g a :=
@@ -774,7 +774,7 @@ section SemilatticeInf
variable [SemilatticeInf β] [OrderBot β] (f g : BotHom α β)
-instance : HasInf (BotHom α β) :=
+instance : Inf (BotHom α β) :=
⟨fun f g => ⟨f ⊓ g, by rw [Pi.inf_apply, map_bot, map_bot, inf_bot_eq]⟩⟩
instance : SemilatticeInf (BotHom α β) :=
@@ -782,9 +782,9 @@ instance : SemilatticeInf (BotHom α β) :=
/- warning: bot_hom.coe_inf -> BotHom.coe_inf is a dubious translation:
lean 3 declaration is
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but is expected to have type
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+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Bot.{u2} α] [_inst_2 : SemilatticeInf.{u1} β] [_inst_3 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2)))] (f : BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) (g : BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3))) (Inf.inf.{max u2 u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) (BotHom.instInfBotHomToBotToLEToPreorderToPartialOrder.{u2, u1} α β _inst_1 _inst_2 _inst_3) f g)) (Inf.inf.{max u2 u1} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) ᾰ) (Pi.instInfForAll.{u2, u1} α (fun (ᾰ : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) ᾰ) (fun (i : α) => SemilatticeInf.toInf.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) i) _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_2))) _inst_3))) g))
Case conversion may be inaccurate. Consider using '#align bot_hom.coe_inf BotHom.coe_infₓ'. -/
@[simp]
theorem coe_inf : ⇑(f ⊓ g) = f ⊓ g :=
@@ -793,9 +793,9 @@ theorem coe_inf : ⇑(f ⊓ g) = f ⊓ g :=
/- warning: bot_hom.inf_apply -> BotHom.inf_apply is a dubious translation:
lean 3 declaration is
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but is expected to have type
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+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : SemilatticeInf.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2)))] (f : BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) (Inf.inf.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) (BotHom.instInfBotHomToBotToLEToPreorderToPartialOrder.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Inf.inf.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) (SemilatticeInf.toInf.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) f a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_2))) _inst_3))) g a))
Case conversion may be inaccurate. Consider using '#align bot_hom.inf_apply BotHom.inf_applyₓ'. -/
@[simp]
theorem inf_apply (a : α) : (f ⊓ g) a = f a ⊓ g a :=
@@ -808,7 +808,7 @@ section SemilatticeSup
variable [SemilatticeSup β] [OrderBot β] (f g : BotHom α β)
-instance : HasSup (BotHom α β) :=
+instance : Sup (BotHom α β) :=
⟨fun f g => ⟨f ⊔ g, by rw [Pi.sup_apply, map_bot, map_bot, sup_bot_eq]⟩⟩
instance : SemilatticeSup (BotHom α β) :=
@@ -816,9 +816,9 @@ instance : SemilatticeSup (BotHom α β) :=
/- warning: bot_hom.coe_sup -> BotHom.coe_sup is a dubious translation:
lean 3 declaration is
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but is expected to have type
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+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Bot.{u2} α] [_inst_2 : SemilatticeSup.{u1} β] [_inst_3 : OrderBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2)))] (f : BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) (g : BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3))) (Sup.sup.{max u2 u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) (BotHom.instSupBotHomToBotToLEToPreorderToPartialOrder.{u2, u1} α β _inst_1 _inst_2 _inst_3) f g)) (Sup.sup.{max u2 u1} (forall (ᾰ : α), (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) ᾰ) (Pi.instSupForAll.{u2, u1} α (fun (ᾰ : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) ᾰ) (fun (i : α) => SemilatticeSup.toSup.{u1} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) i) _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3))) f) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u2 u1, u2, u1} (BotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u2, u1} α β _inst_1 (OrderBot.toBot.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) _inst_3))) g))
Case conversion may be inaccurate. Consider using '#align bot_hom.coe_sup BotHom.coe_supₓ'. -/
@[simp]
theorem coe_sup : ⇑(f ⊔ g) = f ⊔ g :=
@@ -827,9 +827,9 @@ theorem coe_sup : ⇑(f ⊔ g) = f ⊔ g :=
/- warning: bot_hom.sup_apply -> BotHom.sup_apply is a dubious translation:
lean 3 declaration is
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+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)))] (f : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (Sup.sup.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (BotHom.hasSup.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Sup.sup.{u2} β (SemilatticeSup.toHasSup.{u2} β _inst_2) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) f a) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (fun (_x : BotHom.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) => α -> β) (BotHom.hasCoeToFun.{u1, u2} α β _inst_1 (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) g a))
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)))] (f : BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) (HasSup.sup.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (BotHom.instHasSupBotHomToBotToLEToPreorderToPartialOrder.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (HasSup.sup.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) (SemilatticeSup.toHasSup.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) f a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) g a))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Bot.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)))] (f : BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (g : BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) (Sup.sup.{max u1 u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) (BotHom.instSupBotHomToBotToLEToPreorderToPartialOrder.{u1, u2} α β _inst_1 _inst_2 _inst_3) f g) a) (Sup.sup.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) (SemilatticeSup.toSup.{u2} ((fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) a) _inst_2) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) f a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.Hom.Bounded._hyg.277 : α) => β) _x) (BotHomClass.toFunLike.{max u1 u2, u1, u2} (BotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3)) α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3) (BotHom.instBotHomClassBotHom.{u1, u2} α β _inst_1 (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) _inst_3))) g a))
Case conversion may be inaccurate. Consider using '#align bot_hom.sup_apply BotHom.sup_applyₓ'. -/
@[simp]
theorem sup_apply (a : α) : (f ⊔ g) a = f a ⊔ g a :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
I removed some redundant instance arguments throughout Mathlib. To do this, I used VS Code's regex search. See https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/repeating.20instances.20from.20variable.20command I closed the previous PR for this and reopened it.
@@ -181,8 +181,6 @@ def BotHomClass.toBotHom [Bot α] [Bot β] [BotHomClass F α β] (f : F) : BotHo
instance [Bot α] [Bot β] [BotHomClass F α β] : CoeTC F (BotHom α β) :=
⟨BotHomClass.toBotHom⟩
-variable [FunLike F α β]
-
/-- Turn an element of a type `F` satisfying `BoundedOrderHomClass F α β` into an actual
`BoundedOrderHom`. This is declared as the default coercion from `F` to `BoundedOrderHom α β`. -/
@[coe]
Two comments with Lean 3 code looked like they should have been labelled "porting note". Do so; one of them can be fixed now.
@@ -129,9 +129,7 @@ instance (priority := 100) OrderIsoClass.toTopHomClass [LE α] [OrderTop α]
-- See note [lower instance priority]
instance (priority := 100) OrderIsoClass.toBotHomClass [LE α] [OrderBot α]
[PartialOrder β] [OrderBot β] [OrderIsoClass F α β] : BotHomClass F α β :=
- { --⟨λ f, le_bot_iff.1 <| (le_map_inv_iff f).1 bot_le⟩
- show OrderHomClass F α β from inferInstance with
- map_bot := fun f => le_bot_iff.1 <| (le_map_inv_iff f).1 bot_le }
+ { map_bot := fun f => le_bot_iff.1 <| (le_map_inv_iff f).1 bot_le }
#align order_iso_class.to_bot_hom_class OrderIsoClass.toBotHomClass
-- See note [lower instance priority]
@@ -584,7 +584,7 @@ end BotHom
/-! ### Bounded order homomorphisms -/
--- Porting note: todo: remove this configuration and use the default configuration.
+-- Porting note (#11215): TODO: remove this configuration and use the default configuration.
-- We keep this to be consistent with Lean 3.
initialize_simps_projections BoundedOrderHom (+toOrderHom, -toFun)
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>
@@ -64,8 +64,7 @@ section
/-- `TopHomClass F α β` states that `F` is a type of `⊤`-preserving morphisms.
You should extend this class when you extend `TopHom`. -/
-class TopHomClass (F : Type*) (α β : outParam <| Type*) [Top α] [Top β] extends
- DFunLike F α fun _ => β where
+class TopHomClass (F α β : Type*) [Top α] [Top β] [FunLike F α β] : Prop where
/-- A `TopHomClass` morphism preserves the top element. -/
map_top (f : F) : f ⊤ = ⊤
#align top_hom_class TopHomClass
@@ -73,8 +72,7 @@ class TopHomClass (F : Type*) (α β : outParam <| Type*) [Top α] [Top β] exte
/-- `BotHomClass F α β` states that `F` is a type of `⊥`-preserving morphisms.
You should extend this class when you extend `BotHom`. -/
-class BotHomClass (F : Type*) (α β : outParam <| Type*) [Bot α] [Bot β] extends
- DFunLike F α fun _ => β where
+class BotHomClass (F α β : Type*) [Bot α] [Bot β] [FunLike F α β] : Prop where
/-- A `BotHomClass` morphism preserves the bottom element. -/
map_bot (f : F) : f ⊥ = ⊥
#align bot_hom_class BotHomClass
@@ -82,8 +80,9 @@ class BotHomClass (F : Type*) (α β : outParam <| Type*) [Bot α] [Bot β] exte
/-- `BoundedOrderHomClass F α β` states that `F` is a type of bounded order morphisms.
You should extend this class when you extend `BoundedOrderHom`. -/
-class BoundedOrderHomClass (F : Type*) (α β : outParam <| Type*) [LE α] [LE β] [BoundedOrder α]
- [BoundedOrder β] extends RelHomClass F ((· ≤ ·) : α → α → Prop) ((· ≤ ·) : β → β → Prop) where
+class BoundedOrderHomClass (F α β : Type*) [LE α] [LE β]
+ [BoundedOrder α] [BoundedOrder β] [FunLike F α β]
+ extends RelHomClass F ((· ≤ ·) : α → α → Prop) ((· ≤ ·) : β → β → Prop) : Prop where
/-- Morphisms preserve the top element. The preferred spelling is `_root_.map_top`. -/
map_top (f : F) : f ⊤ = ⊤
/-- Morphisms preserve the bottom element. The preferred spelling is `_root_.map_bot`. -/
@@ -98,6 +97,10 @@ export BotHomClass (map_bot)
attribute [simp] map_top map_bot
+section Hom
+
+variable [FunLike F α β]
+
-- See note [lower instance priority]
instance (priority := 100) BoundedOrderHomClass.toTopHomClass [LE α] [LE β]
[BoundedOrder α] [BoundedOrder β] [BoundedOrderHomClass F α β] : TopHomClass F α β :=
@@ -110,6 +113,12 @@ instance (priority := 100) BoundedOrderHomClass.toBotHomClass [LE α] [LE β]
{ ‹BoundedOrderHomClass F α β› with }
#align bounded_order_hom_class.to_bot_hom_class BoundedOrderHomClass.toBotHomClass
+end Hom
+
+section Equiv
+
+variable [EquivLike F α β]
+
-- See note [lower instance priority]
instance (priority := 100) OrderIsoClass.toTopHomClass [LE α] [OrderTop α]
[PartialOrder β] [OrderTop β] [OrderIsoClass F α β] : TopHomClass F α β :=
@@ -152,6 +161,10 @@ theorem map_eq_bot_iff [LE α] [OrderBot α] [PartialOrder β] [OrderBot β] [Or
rw [← map_bot f, (EquivLike.injective f).eq_iff]
#align map_eq_bot_iff map_eq_bot_iff
+end Equiv
+
+variable [FunLike F α β]
+
/-- Turn an element of a type `F` satisfying `TopHomClass F α β` into an actual
`TopHom`. This is declared as the default coercion from `F` to `TopHom α β`. -/
@[coe]
@@ -170,6 +183,8 @@ def BotHomClass.toBotHom [Bot α] [Bot β] [BotHomClass F α β] (f : F) : BotHo
instance [Bot α] [Bot β] [BotHomClass F α β] : CoeTC F (BotHom α β) :=
⟨BotHomClass.toBotHom⟩
+variable [FunLike F α β]
+
/-- Turn an element of a type `F` satisfying `BoundedOrderHomClass F α β` into an actual
`BoundedOrderHom`. This is declared as the default coercion from `F` to `BoundedOrderHom α β`. -/
@[coe]
@@ -192,10 +207,11 @@ section Top
variable [Top β] [Top γ] [Top δ]
-instance : TopHomClass (TopHom α β) α
- β where
+instance : FunLike (TopHom α β) α β where
coe := TopHom.toFun
coe_injective' f g h := by cases f; cases g; congr
+
+instance : TopHomClass (TopHom α β) α β where
map_top := TopHom.map_top'
#noalign top_hom.to_fun_eq_coe
@@ -384,10 +400,11 @@ section Bot
variable [Bot β] [Bot γ] [Bot δ]
-instance : BotHomClass (BotHom α β) α
- β where
+instance : FunLike (BotHom α β) α β where
coe := BotHom.toFun
coe_injective' f g h := by cases f; cases g; congr
+
+instance : BotHomClass (BotHom α β) α β where
map_bot := BotHom.map_bot'
#noalign bot_hom.to_fun_eq_coe
@@ -586,10 +603,11 @@ def toBotHom (f : BoundedOrderHom α β) : BotHom α β :=
{ f with }
#align bounded_order_hom.to_bot_hom BoundedOrderHom.toBotHom
-instance : BoundedOrderHomClass (BoundedOrderHom α β) α
- β where
+instance : FunLike (BoundedOrderHom α β) α β where
coe f := f.toFun
coe_injective' f g h := by obtain ⟨⟨_, _⟩, _⟩ := f; obtain ⟨⟨_, _⟩, _⟩ := g; congr
+
+instance : BoundedOrderHomClass (BoundedOrderHom α β) α β where
map_rel f := @(f.monotone')
map_top f := f.map_top'
map_bot f := f.map_bot'
FunLike
to DFunLike
(#9785)
This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.
This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:
sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
@@ -13,7 +13,7 @@ import Mathlib.Order.BoundedOrder
This file defines (bounded) order homomorphisms.
-We use the `FunLike` design, so each type of morphisms has a companion typeclass which is meant to
+We use the `DFunLike` design, so each type of morphisms has a companion typeclass which is meant to
be satisfied by itself and all stricter types.
## Types of morphisms
@@ -36,7 +36,7 @@ variable {F α β γ δ : Type*}
/-- The type of `⊤`-preserving functions from `α` to `β`. -/
structure TopHom (α β : Type*) [Top α] [Top β] where
- /-- The underlying function. The preferred spelling is `FunLike.coe`. -/
+ /-- The underlying function. The preferred spelling is `DFunLike.coe`. -/
toFun : α → β
/-- The function preserves the top element. The preferred spelling is `map_top`. -/
map_top' : toFun ⊤ = ⊤
@@ -44,7 +44,7 @@ structure TopHom (α β : Type*) [Top α] [Top β] where
/-- The type of `⊥`-preserving functions from `α` to `β`. -/
structure BotHom (α β : Type*) [Bot α] [Bot β] where
- /-- The underlying function. The preferred spelling is `FunLike.coe`. -/
+ /-- The underlying function. The preferred spelling is `DFunLike.coe`. -/
toFun : α → β
/-- The function preserves the bottom element. The preferred spelling is `map_bot`. -/
map_bot' : toFun ⊥ = ⊥
@@ -65,7 +65,7 @@ section
You should extend this class when you extend `TopHom`. -/
class TopHomClass (F : Type*) (α β : outParam <| Type*) [Top α] [Top β] extends
- FunLike F α fun _ => β where
+ DFunLike F α fun _ => β where
/-- A `TopHomClass` morphism preserves the top element. -/
map_top (f : F) : f ⊤ = ⊤
#align top_hom_class TopHomClass
@@ -74,7 +74,7 @@ class TopHomClass (F : Type*) (α β : outParam <| Type*) [Top α] [Top β] exte
You should extend this class when you extend `BotHom`. -/
class BotHomClass (F : Type*) (α β : outParam <| Type*) [Bot α] [Bot β] extends
- FunLike F α fun _ => β where
+ DFunLike F α fun _ => β where
/-- A `BotHomClass` morphism preserves the bottom element. -/
map_bot (f : F) : f ⊥ = ⊥
#align bot_hom_class BotHomClass
@@ -205,7 +205,7 @@ initialize_simps_projections TopHom (toFun → apply)
@[ext]
theorem ext {f g : TopHom α β} (h : ∀ a, f a = g a) : f = g :=
- FunLike.ext f g h
+ DFunLike.ext f g h
#align top_hom.ext TopHom.ext
/-- Copy of a `TopHom` with a new `toFun` equal to the old one. Useful to fix definitional
@@ -222,7 +222,7 @@ theorem coe_copy (f : TopHom α β) (f' : α → β) (h : f' = f) : ⇑(f.copy f
#align top_hom.coe_copy TopHom.coe_copy
theorem copy_eq (f : TopHom α β) (f' : α → β) (h : f' = f) : f.copy f' h = f :=
- FunLike.ext' h
+ DFunLike.ext' h
#align top_hom.copy_eq TopHom.copy_eq
instance : Inhabited (TopHom α β) :=
@@ -283,7 +283,7 @@ theorem id_comp (f : TopHom α β) : (TopHom.id β).comp f = f :=
@[simp]
theorem cancel_right {g₁ g₂ : TopHom β γ} {f : TopHom α β} (hf : Surjective f) :
g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
- ⟨fun h => TopHom.ext <| hf.forall.2 <| FunLike.ext_iff.1 h, congr_arg (fun g => comp g f)⟩
+ ⟨fun h => TopHom.ext <| hf.forall.2 <| DFunLike.ext_iff.1 h, congr_arg (fun g => comp g f)⟩
#align top_hom.cancel_right TopHom.cancel_right
@[simp]
@@ -296,10 +296,10 @@ theorem cancel_left {g : TopHom β γ} {f₁ f₂ : TopHom α β} (hg : Injectiv
end Top
instance [Preorder β] [Top β] : Preorder (TopHom α β) :=
- Preorder.lift (FunLike.coe : TopHom α β → α → β)
+ Preorder.lift (DFunLike.coe : TopHom α β → α → β)
instance [PartialOrder β] [Top β] : PartialOrder (TopHom α β) :=
- PartialOrder.lift _ FunLike.coe_injective
+ PartialOrder.lift _ DFunLike.coe_injective
section OrderTop
@@ -329,7 +329,7 @@ instance : Inf (TopHom α β) :=
⟨fun f g => ⟨f ⊓ g, by rw [Pi.inf_apply, map_top, map_top, inf_top_eq]⟩⟩
instance : SemilatticeInf (TopHom α β) :=
- (FunLike.coe_injective.semilatticeInf _) fun _ _ => rfl
+ (DFunLike.coe_injective.semilatticeInf _) fun _ _ => rfl
@[simp]
theorem coe_inf : ⇑(f ⊓ g) = ⇑f ⊓ ⇑g :=
@@ -351,7 +351,7 @@ instance : Sup (TopHom α β) :=
⟨fun f g => ⟨f ⊔ g, by rw [Pi.sup_apply, map_top, map_top, sup_top_eq]⟩⟩
instance : SemilatticeSup (TopHom α β) :=
- (FunLike.coe_injective.semilatticeSup _) fun _ _ => rfl
+ (DFunLike.coe_injective.semilatticeSup _) fun _ _ => rfl
@[simp]
theorem coe_sup : ⇑(f ⊔ g) = ⇑f ⊔ ⇑g :=
@@ -366,10 +366,10 @@ theorem sup_apply (a : α) : (f ⊔ g) a = f a ⊔ g a :=
end SemilatticeSup
instance [Lattice β] [OrderTop β] : Lattice (TopHom α β) :=
- FunLike.coe_injective.lattice _ (fun _ _ => rfl) fun _ _ => rfl
+ DFunLike.coe_injective.lattice _ (fun _ _ => rfl) fun _ _ => rfl
instance [DistribLattice β] [OrderTop β] : DistribLattice (TopHom α β) :=
- FunLike.coe_injective.distribLattice _ (fun _ _ => rfl) fun _ _ => rfl
+ DFunLike.coe_injective.distribLattice _ (fun _ _ => rfl) fun _ _ => rfl
end TopHom
@@ -397,7 +397,7 @@ initialize_simps_projections BotHom (toFun → apply)
@[ext]
theorem ext {f g : BotHom α β} (h : ∀ a, f a = g a) : f = g :=
- FunLike.ext f g h
+ DFunLike.ext f g h
#align bot_hom.ext BotHom.ext
/-- Copy of a `BotHom` with a new `toFun` equal to the old one. Useful to fix definitional
@@ -414,7 +414,7 @@ theorem coe_copy (f : BotHom α β) (f' : α → β) (h : f' = f) : ⇑(f.copy f
#align bot_hom.coe_copy BotHom.coe_copy
theorem copy_eq (f : BotHom α β) (f' : α → β) (h : f' = f) : f.copy f' h = f :=
- FunLike.ext' h
+ DFunLike.ext' h
#align bot_hom.copy_eq BotHom.copy_eq
instance : Inhabited (BotHom α β) :=
@@ -475,7 +475,7 @@ theorem id_comp (f : BotHom α β) : (BotHom.id β).comp f = f :=
@[simp]
theorem cancel_right {g₁ g₂ : BotHom β γ} {f : BotHom α β} (hf : Surjective f) :
g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
- ⟨fun h => BotHom.ext <| hf.forall.2 <| FunLike.ext_iff.1 h, congr_arg (comp · f)⟩
+ ⟨fun h => BotHom.ext <| hf.forall.2 <| DFunLike.ext_iff.1 h, congr_arg (comp · f)⟩
#align bot_hom.cancel_right BotHom.cancel_right
@[simp]
@@ -488,10 +488,10 @@ theorem cancel_left {g : BotHom β γ} {f₁ f₂ : BotHom α β} (hg : Injectiv
end Bot
instance [Preorder β] [Bot β] : Preorder (BotHom α β) :=
- Preorder.lift (FunLike.coe : BotHom α β → α → β)
+ Preorder.lift (DFunLike.coe : BotHom α β → α → β)
instance [PartialOrder β] [Bot β] : PartialOrder (BotHom α β) :=
- PartialOrder.lift _ FunLike.coe_injective
+ PartialOrder.lift _ DFunLike.coe_injective
section OrderBot
@@ -521,7 +521,7 @@ instance : Inf (BotHom α β) :=
⟨fun f g => ⟨f ⊓ g, by rw [Pi.inf_apply, map_bot, map_bot, inf_bot_eq]⟩⟩
instance : SemilatticeInf (BotHom α β) :=
- (FunLike.coe_injective.semilatticeInf _) fun _ _ => rfl
+ (DFunLike.coe_injective.semilatticeInf _) fun _ _ => rfl
@[simp]
theorem coe_inf : ⇑(f ⊓ g) = ⇑f ⊓ ⇑g :=
@@ -543,7 +543,7 @@ instance : Sup (BotHom α β) :=
⟨fun f g => ⟨f ⊔ g, by rw [Pi.sup_apply, map_bot, map_bot, sup_bot_eq]⟩⟩
instance : SemilatticeSup (BotHom α β) :=
- (FunLike.coe_injective.semilatticeSup _) fun _ _ => rfl
+ (DFunLike.coe_injective.semilatticeSup _) fun _ _ => rfl
@[simp]
theorem coe_sup : ⇑(f ⊔ g) = ⇑f ⊔ ⇑g :=
@@ -558,10 +558,10 @@ theorem sup_apply (a : α) : (f ⊔ g) a = f a ⊔ g a :=
end SemilatticeSup
instance [Lattice β] [OrderBot β] : Lattice (BotHom α β) :=
- FunLike.coe_injective.lattice _ (fun _ _ => rfl) fun _ _ => rfl
+ DFunLike.coe_injective.lattice _ (fun _ _ => rfl) fun _ _ => rfl
instance [DistribLattice β] [OrderBot β] : DistribLattice (BotHom α β) :=
- FunLike.coe_injective.distribLattice _ (fun _ _ => rfl) fun _ _ => rfl
+ DFunLike.coe_injective.distribLattice _ (fun _ _ => rfl) fun _ _ => rfl
end BotHom
@@ -598,7 +598,7 @@ instance : BoundedOrderHomClass (BoundedOrderHom α β) α
@[ext]
theorem ext {f g : BoundedOrderHom α β} (h : ∀ a, f a = g a) : f = g :=
- FunLike.ext f g h
+ DFunLike.ext f g h
#align bounded_order_hom.ext BoundedOrderHom.ext
/-- Copy of a `BoundedOrderHom` with a new `toFun` equal to the old one. Useful to fix
@@ -613,7 +613,7 @@ theorem coe_copy (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : ⇑
#align bounded_order_hom.coe_copy BoundedOrderHom.coe_copy
theorem copy_eq (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : f.copy f' h = f :=
- FunLike.ext' h
+ DFunLike.ext' h
#align bounded_order_hom.copy_eq BoundedOrderHom.copy_eq
variable (α)
@@ -691,7 +691,7 @@ theorem id_comp (f : BoundedOrderHom α β) : (BoundedOrderHom.id β).comp f = f
@[simp]
theorem cancel_right {g₁ g₂ : BoundedOrderHom β γ} {f : BoundedOrderHom α β} (hf : Surjective f) :
g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
- ⟨fun h => BoundedOrderHom.ext <| hf.forall.2 <| FunLike.ext_iff.1 h,
+ ⟨fun h => BoundedOrderHom.ext <| hf.forall.2 <| DFunLike.ext_iff.1 h,
congr_arg (fun g => comp g f)⟩
#align bounded_order_hom.cancel_right BoundedOrderHom.cancel_right
$
with <|
(#9319)
See Zulip thread for the discussion.
@@ -120,7 +120,7 @@ instance (priority := 100) OrderIsoClass.toTopHomClass [LE α] [OrderTop α]
-- See note [lower instance priority]
instance (priority := 100) OrderIsoClass.toBotHomClass [LE α] [OrderBot α]
[PartialOrder β] [OrderBot β] [OrderIsoClass F α β] : BotHomClass F α β :=
- { --⟨λ f, le_bot_iff.1 $ (le_map_inv_iff f).1 bot_le⟩
+ { --⟨λ f, le_bot_iff.1 <| (le_map_inv_iff f).1 bot_le⟩
show OrderHomClass F α β from inferInstance with
map_bot := fun f => le_bot_iff.1 <| (le_map_inv_iff f).1 bot_le }
#align order_iso_class.to_bot_hom_class OrderIsoClass.toBotHomClass
@@ -280,11 +280,13 @@ theorem id_comp (f : TopHom α β) : (TopHom.id β).comp f = f :=
TopHom.ext fun _ => rfl
#align top_hom.id_comp TopHom.id_comp
+@[simp]
theorem cancel_right {g₁ g₂ : TopHom β γ} {f : TopHom α β} (hf : Surjective f) :
g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
⟨fun h => TopHom.ext <| hf.forall.2 <| FunLike.ext_iff.1 h, congr_arg (fun g => comp g f)⟩
#align top_hom.cancel_right TopHom.cancel_right
+@[simp]
theorem cancel_left {g : TopHom β γ} {f₁ f₂ : TopHom α β} (hg : Injective g) :
g.comp f₁ = g.comp f₂ ↔ f₁ = f₂ :=
⟨fun h => TopHom.ext fun a => hg <| by rw [← TopHom.comp_apply, h, TopHom.comp_apply],
@@ -470,11 +472,13 @@ theorem id_comp (f : BotHom α β) : (BotHom.id β).comp f = f :=
BotHom.ext fun _ => rfl
#align bot_hom.id_comp BotHom.id_comp
+@[simp]
theorem cancel_right {g₁ g₂ : BotHom β γ} {f : BotHom α β} (hf : Surjective f) :
g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
⟨fun h => BotHom.ext <| hf.forall.2 <| FunLike.ext_iff.1 h, congr_arg (comp · f)⟩
#align bot_hom.cancel_right BotHom.cancel_right
+@[simp]
theorem cancel_left {g : BotHom β γ} {f₁ f₂ : BotHom α β} (hg : Injective g) :
g.comp f₁ = g.comp f₂ ↔ f₁ = f₂ :=
⟨fun h => BotHom.ext fun a => hg <| by rw [← BotHom.comp_apply, h, BotHom.comp_apply],
@@ -684,12 +688,14 @@ theorem id_comp (f : BoundedOrderHom α β) : (BoundedOrderHom.id β).comp f = f
BoundedOrderHom.ext fun _ => rfl
#align bounded_order_hom.id_comp BoundedOrderHom.id_comp
+@[simp]
theorem cancel_right {g₁ g₂ : BoundedOrderHom β γ} {f : BoundedOrderHom α β} (hf : Surjective f) :
g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
⟨fun h => BoundedOrderHom.ext <| hf.forall.2 <| FunLike.ext_iff.1 h,
congr_arg (fun g => comp g f)⟩
#align bounded_order_hom.cancel_right BoundedOrderHom.cancel_right
+@[simp]
theorem cancel_left {g : BoundedOrderHom β γ} {f₁ f₂ : BoundedOrderHom α β} (hg : Injective g) :
g.comp f₁ = g.comp f₂ ↔ f₁ = f₂ :=
⟨fun h =>
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -32,10 +32,10 @@ be satisfied by itself and all stricter types.
open Function OrderDual
-variable {F α β γ δ : Type _}
+variable {F α β γ δ : Type*}
/-- The type of `⊤`-preserving functions from `α` to `β`. -/
-structure TopHom (α β : Type _) [Top α] [Top β] where
+structure TopHom (α β : Type*) [Top α] [Top β] where
/-- The underlying function. The preferred spelling is `FunLike.coe`. -/
toFun : α → β
/-- The function preserves the top element. The preferred spelling is `map_top`. -/
@@ -43,7 +43,7 @@ structure TopHom (α β : Type _) [Top α] [Top β] where
#align top_hom TopHom
/-- The type of `⊥`-preserving functions from `α` to `β`. -/
-structure BotHom (α β : Type _) [Bot α] [Bot β] where
+structure BotHom (α β : Type*) [Bot α] [Bot β] where
/-- The underlying function. The preferred spelling is `FunLike.coe`. -/
toFun : α → β
/-- The function preserves the bottom element. The preferred spelling is `map_bot`. -/
@@ -51,7 +51,7 @@ structure BotHom (α β : Type _) [Bot α] [Bot β] where
#align bot_hom BotHom
/-- The type of bounded order homomorphisms from `α` to `β`. -/
-structure BoundedOrderHom (α β : Type _) [Preorder α] [Preorder β] [BoundedOrder α]
+structure BoundedOrderHom (α β : Type*) [Preorder α] [Preorder β] [BoundedOrder α]
[BoundedOrder β] extends OrderHom α β where
/-- The function preserves the top element. The preferred spelling is `map_top`. -/
map_top' : toFun ⊤ = ⊤
@@ -64,7 +64,7 @@ section
/-- `TopHomClass F α β` states that `F` is a type of `⊤`-preserving morphisms.
You should extend this class when you extend `TopHom`. -/
-class TopHomClass (F : Type _) (α β : outParam <| Type _) [Top α] [Top β] extends
+class TopHomClass (F : Type*) (α β : outParam <| Type*) [Top α] [Top β] extends
FunLike F α fun _ => β where
/-- A `TopHomClass` morphism preserves the top element. -/
map_top (f : F) : f ⊤ = ⊤
@@ -73,7 +73,7 @@ class TopHomClass (F : Type _) (α β : outParam <| Type _) [Top α] [Top β] ex
/-- `BotHomClass F α β` states that `F` is a type of `⊥`-preserving morphisms.
You should extend this class when you extend `BotHom`. -/
-class BotHomClass (F : Type _) (α β : outParam <| Type _) [Bot α] [Bot β] extends
+class BotHomClass (F : Type*) (α β : outParam <| Type*) [Bot α] [Bot β] extends
FunLike F α fun _ => β where
/-- A `BotHomClass` morphism preserves the bottom element. -/
map_bot (f : F) : f ⊥ = ⊥
@@ -82,7 +82,7 @@ class BotHomClass (F : Type _) (α β : outParam <| Type _) [Bot α] [Bot β] ex
/-- `BoundedOrderHomClass F α β` states that `F` is a type of bounded order morphisms.
You should extend this class when you extend `BoundedOrderHom`. -/
-class BoundedOrderHomClass (F : Type _) (α β : outParam <| Type _) [LE α] [LE β] [BoundedOrder α]
+class BoundedOrderHomClass (F : Type*) (α β : outParam <| Type*) [LE α] [LE β] [BoundedOrder α]
[BoundedOrder β] extends RelHomClass F ((· ≤ ·) : α → α → Prop) ((· ≤ ·) : β → β → Prop) where
/-- Morphisms preserve the top element. The preferred spelling is `_root_.map_top`. -/
map_top (f : F) : f ⊤ = ⊤
@@ -2,15 +2,12 @@
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-
-! This file was ported from Lean 3 source module order.hom.bounded
-! leanprover-community/mathlib commit f1a2caaf51ef593799107fe9a8d5e411599f3996
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Order.Hom.Basic
import Mathlib.Order.BoundedOrder
+#align_import order.hom.bounded from "leanprover-community/mathlib"@"f1a2caaf51ef593799107fe9a8d5e411599f3996"
+
/-!
# Bounded order homomorphisms
@@ -101,43 +101,36 @@ export BotHomClass (map_bot)
attribute [simp] map_top map_bot
--- Porting note: the `BoundedOrder` parameters can't be inferred through unification in all cases
--- so they should really be instance parameters once this is technically possible.
--- We have to supply these instances through `letI` in some cases as a work-around.
-- See note [lower instance priority]
-instance (priority := 100) BoundedOrderHomClass.toTopHomClass {_ : LE α} {_ : LE β}
- {_ : BoundedOrder α} {_ : BoundedOrder β} [BoundedOrderHomClass F α β] : TopHomClass F α β :=
+instance (priority := 100) BoundedOrderHomClass.toTopHomClass [LE α] [LE β]
+ [BoundedOrder α] [BoundedOrder β] [BoundedOrderHomClass F α β] : TopHomClass F α β :=
{ ‹BoundedOrderHomClass F α β› with }
#align bounded_order_hom_class.to_top_hom_class BoundedOrderHomClass.toTopHomClass
-- See note [lower instance priority]
-instance (priority := 100) BoundedOrderHomClass.toBotHomClass {_ : LE α} {_ : LE β}
- {_ : BoundedOrder α} {_ : BoundedOrder β} [BoundedOrderHomClass F α β] : BotHomClass F α β :=
+instance (priority := 100) BoundedOrderHomClass.toBotHomClass [LE α] [LE β]
+ [BoundedOrder α] [BoundedOrder β] [BoundedOrderHomClass F α β] : BotHomClass F α β :=
{ ‹BoundedOrderHomClass F α β› with }
#align bounded_order_hom_class.to_bot_hom_class BoundedOrderHomClass.toBotHomClass
-@[nolint dangerousInstance] -- The `OrderTop`s should be instance parameters but depend on outParams
-- See note [lower instance priority]
-instance (priority := 100) OrderIsoClass.toTopHomClass {_ : LE α} {_ : OrderTop α}
- {_ : PartialOrder β} {_ : OrderTop β} [OrderIsoClass F α β] : TopHomClass F α β :=
+instance (priority := 100) OrderIsoClass.toTopHomClass [LE α] [OrderTop α]
+ [PartialOrder β] [OrderTop β] [OrderIsoClass F α β] : TopHomClass F α β :=
{ show OrderHomClass F α β from inferInstance with
map_top := fun f => top_le_iff.1 <| (map_inv_le_iff f).1 le_top }
#align order_iso_class.to_top_hom_class OrderIsoClass.toTopHomClass
-@[nolint dangerousInstance] -- The `OrderBot`s should be instance parameters but depend on outParams
-- See note [lower instance priority]
-instance (priority := 100) OrderIsoClass.toBotHomClass {_ : LE α} {_ : OrderBot α}
- {_ : PartialOrder β} {_ : OrderBot β} [OrderIsoClass F α β] : BotHomClass F α β :=
+instance (priority := 100) OrderIsoClass.toBotHomClass [LE α] [OrderBot α]
+ [PartialOrder β] [OrderBot β] [OrderIsoClass F α β] : BotHomClass F α β :=
{ --⟨λ f, le_bot_iff.1 $ (le_map_inv_iff f).1 bot_le⟩
show OrderHomClass F α β from inferInstance with
map_bot := fun f => le_bot_iff.1 <| (le_map_inv_iff f).1 bot_le }
#align order_iso_class.to_bot_hom_class OrderIsoClass.toBotHomClass
-@[nolint dangerousInstance] -- The `BoundedOrder`s should be instance parameters but depend on
- -- outParams
-- See note [lower instance priority]
-instance (priority := 100) OrderIsoClass.toBoundedOrderHomClass {_ : LE α} {_ : BoundedOrder α}
- {_ : PartialOrder β} {_ : BoundedOrder β} [OrderIsoClass F α β] : BoundedOrderHomClass F α β :=
+instance (priority := 100) OrderIsoClass.toBoundedOrderHomClass [LE α] [BoundedOrder α]
+ [PartialOrder β] [BoundedOrder β] [OrderIsoClass F α β] : BoundedOrderHomClass F α β :=
{ show OrderHomClass F α β from inferInstance, OrderIsoClass.toTopHomClass,
OrderIsoClass.toBotHomClass with }
#align order_iso_class.to_bounded_order_hom_class OrderIsoClass.toBoundedOrderHomClass
initialize_simps_projections
now by default generates all projections of all parent structures, and doesn't generate the projections to those parent structures.TwoPointed
)Internal changes:
ParsedProjectionData
to avoid the bug reported here (and to another bug where it seemed that the wrong data was inserted in ParsedProjectionData
, but it was hard to minimize because of all the crashes). If we manage to fix the bug in that Zulip thread, I'll see if I can track down the other bug in commit 97454284Co-authored-by: Johan Commelin <johan@commelin.net>
@@ -573,6 +573,9 @@ end BotHom
/-! ### Bounded order homomorphisms -/
+-- Porting note: todo: remove this configuration and use the default configuration.
+-- We keep this to be consistent with Lean 3.
+initialize_simps_projections BoundedOrderHom (+toOrderHom, -toFun)
namespace BoundedOrderHom
@@ -333,7 +333,7 @@ section SemilatticeInf
variable [SemilatticeInf β] [OrderTop β] (f g : TopHom α β)
-instance : HasInf (TopHom α β) :=
+instance : Inf (TopHom α β) :=
⟨fun f g => ⟨f ⊓ g, by rw [Pi.inf_apply, map_top, map_top, inf_top_eq]⟩⟩
instance : SemilatticeInf (TopHom α β) :=
@@ -355,7 +355,7 @@ section SemilatticeSup
variable [SemilatticeSup β] [OrderTop β] (f g : TopHom α β)
-instance : HasSup (TopHom α β) :=
+instance : Sup (TopHom α β) :=
⟨fun f g => ⟨f ⊔ g, by rw [Pi.sup_apply, map_top, map_top, sup_top_eq]⟩⟩
instance : SemilatticeSup (TopHom α β) :=
@@ -523,7 +523,7 @@ section SemilatticeInf
variable [SemilatticeInf β] [OrderBot β] (f g : BotHom α β)
-instance : HasInf (BotHom α β) :=
+instance : Inf (BotHom α β) :=
⟨fun f g => ⟨f ⊓ g, by rw [Pi.inf_apply, map_bot, map_bot, inf_bot_eq]⟩⟩
instance : SemilatticeInf (BotHom α β) :=
@@ -545,7 +545,7 @@ section SemilatticeSup
variable [SemilatticeSup β] [OrderBot β] (f g : BotHom α β)
-instance : HasSup (BotHom α β) :=
+instance : Sup (BotHom α β) :=
⟨fun f g => ⟨f ⊔ g, by rw [Pi.sup_apply, map_bot, map_bot, sup_bot_eq]⟩⟩
instance : SemilatticeSup (BotHom α β) :=
This PR is the result of a slight variant on the following "algorithm"
_
and make all uppercase letters into lowercase_
and make all uppercase letters into lowercase(original_lean3_name, OriginalLean4Name)
#align
statement just before the next empty line#align
statement to have been inserted too early)@@ -723,6 +723,8 @@ protected def dual :
left_inv _ := TopHom.ext fun _ => rfl
right_inv _ := BotHom.ext fun _ => rfl
#align top_hom.dual TopHom.dual
+#align top_hom.dual_apply_apply TopHom.dual_apply_apply
+#align top_hom.dual_symm_apply_apply TopHom.dual_symm_apply_apply
@[simp]
theorem dual_id : TopHom.dual (TopHom.id α) = BotHom.id _ :=
@@ -761,6 +763,8 @@ protected def dual :
left_inv _ := BotHom.ext fun _ => rfl
right_inv _ := TopHom.ext fun _ => rfl
#align bot_hom.dual BotHom.dual
+#align bot_hom.dual_apply_apply BotHom.dual_apply_apply
+#align bot_hom.dual_symm_apply_apply BotHom.dual_symm_apply_apply
@[simp]
theorem dual_id : BotHom.dual (BotHom.id α) = TopHom.id _ :=
@@ -802,6 +806,8 @@ protected def dual :
left_inv _ := ext fun _ => rfl
right_inv _ := ext fun _ => rfl
#align bounded_order_hom.dual BoundedOrderHom.dual
+#align bounded_order_hom.dual_apply_to_order_hom BoundedOrderHom.dual_apply_toOrderHom
+#align bounded_order_hom.dual_symm_apply_to_order_hom BoundedOrderHom.dual_symm_apply_toOrderHom
@[simp]
theorem dual_id : BoundedOrderHom.dual (BoundedOrderHom.id α) = BoundedOrderHom.id _ :=
@@ -16,20 +16,20 @@ import Mathlib.Order.BoundedOrder
This file defines (bounded) order homomorphisms.
-We use the `fun_like` design, so each type of morphisms has a companion typeclass which is meant to
+We use the `FunLike` design, so each type of morphisms has a companion typeclass which is meant to
be satisfied by itself and all stricter types.
## Types of morphisms
-* `top_hom`: Maps which preserve `⊤`.
-* `bot_hom`: Maps which preserve `⊥`.
-* `bounded_order_hom`: Bounded order homomorphisms. Monotone maps which preserve `⊤` and `⊥`.
+* `TopHom`: Maps which preserve `⊤`.
+* `BotHom`: Maps which preserve `⊥`.
+* `BoundedOrderHom`: Bounded order homomorphisms. Monotone maps which preserve `⊤` and `⊥`.
## Typeclasses
-* `top_hom_class`
-* `bot_hom_class`
-* `bounded_order_hom_class`
+* `TopHomClass`
+* `BotHomClass`
+* `BoundedOrderHomClass`
-/
@@ -64,27 +64,27 @@ structure BoundedOrderHom (α β : Type _) [Preorder α] [Preorder β] [BoundedO
section
-/-- `top_hom_class F α β` states that `F` is a type of `⊤`-preserving morphisms.
+/-- `TopHomClass F α β` states that `F` is a type of `⊤`-preserving morphisms.
-You should extend this class when you extend `top_hom`. -/
+You should extend this class when you extend `TopHom`. -/
class TopHomClass (F : Type _) (α β : outParam <| Type _) [Top α] [Top β] extends
FunLike F α fun _ => β where
/-- A `TopHomClass` morphism preserves the top element. -/
map_top (f : F) : f ⊤ = ⊤
#align top_hom_class TopHomClass
-/-- `bot_hom_class F α β` states that `F` is a type of `⊥`-preserving morphisms.
+/-- `BotHomClass F α β` states that `F` is a type of `⊥`-preserving morphisms.
-You should extend this class when you extend `bot_hom`. -/
+You should extend this class when you extend `BotHom`. -/
class BotHomClass (F : Type _) (α β : outParam <| Type _) [Bot α] [Bot β] extends
FunLike F α fun _ => β where
/-- A `BotHomClass` morphism preserves the bottom element. -/
map_bot (f : F) : f ⊥ = ⊥
#align bot_hom_class BotHomClass
-/-- `bounded_order_hom_class F α β` states that `F` is a type of bounded order morphisms.
+/-- `BoundedOrderHomClass F α β` states that `F` is a type of bounded order morphisms.
-You should extend this class when you extend `bounded_order_hom`. -/
+You should extend this class when you extend `BoundedOrderHom`. -/
class BoundedOrderHomClass (F : Type _) (α β : outParam <| Type _) [LE α] [LE β] [BoundedOrder α]
[BoundedOrder β] extends RelHomClass F ((· ≤ ·) : α → α → Prop) ((· ≤ ·) : β → β → Prop) where
/-- Morphisms preserve the top element. The preferred spelling is `_root_.map_top`. -/
@@ -218,7 +218,7 @@ theorem ext {f g : TopHom α β} (h : ∀ a, f a = g a) : f = g :=
FunLike.ext f g h
#align top_hom.ext TopHom.ext
-/-- Copy of a `top_hom` with a new `to_fun` equal to the old one. Useful to fix definitional
+/-- Copy of a `TopHom` with a new `toFun` equal to the old one. Useful to fix definitional
equalities. -/
protected def copy (f : TopHom α β) (f' : α → β) (h : f' = f) :
TopHom α β where
@@ -240,7 +240,7 @@ instance : Inhabited (TopHom α β) :=
variable (α)
-/-- `id` as a `top_hom`. -/
+/-- `id` as a `TopHom`. -/
protected def id : TopHom α α :=
⟨id, rfl⟩
#align top_hom.id TopHom.id
@@ -257,7 +257,7 @@ theorem id_apply (a : α) : TopHom.id α a = a :=
rfl
#align top_hom.id_apply TopHom.id_apply
-/-- Composition of `top_hom`s as a `top_hom`. -/
+/-- Composition of `TopHom`s as a `TopHom`. -/
def comp (f : TopHom β γ) (g : TopHom α β) :
TopHom α γ where
toFun := f ∘ g
@@ -408,7 +408,7 @@ theorem ext {f g : BotHom α β} (h : ∀ a, f a = g a) : f = g :=
FunLike.ext f g h
#align bot_hom.ext BotHom.ext
-/-- Copy of a `bot_hom` with a new `to_fun` equal to the old one. Useful to fix definitional
+/-- Copy of a `BotHom` with a new `toFun` equal to the old one. Useful to fix definitional
equalities. -/
protected def copy (f : BotHom α β) (f' : α → β) (h : f' = f) :
BotHom α β where
@@ -430,7 +430,7 @@ instance : Inhabited (BotHom α β) :=
variable (α)
-/-- `id` as a `bot_hom`. -/
+/-- `id` as a `BotHom`. -/
protected def id : BotHom α α :=
⟨id, rfl⟩
#align bot_hom.id BotHom.id
@@ -447,7 +447,7 @@ theorem id_apply (a : α) : BotHom.id α a = a :=
rfl
#align bot_hom.id_apply BotHom.id_apply
-/-- Composition of `bot_hom`s as a `bot_hom`. -/
+/-- Composition of `BotHom`s as a `BotHom`. -/
def comp (f : BotHom β γ) (g : BotHom α β) :
BotHom α γ where
toFun := f ∘ g
@@ -579,12 +579,12 @@ namespace BoundedOrderHom
variable [Preorder α] [Preorder β] [Preorder γ] [Preorder δ] [BoundedOrder α] [BoundedOrder β]
[BoundedOrder γ] [BoundedOrder δ]
-/-- Reinterpret a `bounded_order_hom` as a `top_hom`. -/
+/-- Reinterpret a `BoundedOrderHom` as a `TopHom`. -/
def toTopHom (f : BoundedOrderHom α β) : TopHom α β :=
{ f with }
#align bounded_order_hom.to_top_hom BoundedOrderHom.toTopHom
-/-- Reinterpret a `bounded_order_hom` as a `bot_hom`. -/
+/-- Reinterpret a `BoundedOrderHom` as a `BotHom`. -/
def toBotHom (f : BoundedOrderHom α β) : BotHom α β :=
{ f with }
#align bounded_order_hom.to_bot_hom BoundedOrderHom.toBotHom
@@ -604,7 +604,7 @@ theorem ext {f g : BoundedOrderHom α β} (h : ∀ a, f a = g a) : f = g :=
FunLike.ext f g h
#align bounded_order_hom.ext BoundedOrderHom.ext
-/-- Copy of a `bounded_order_hom` with a new `to_fun` equal to the old one. Useful to fix
+/-- Copy of a `BoundedOrderHom` with a new `toFun` equal to the old one. Useful to fix
definitional equalities. -/
protected def copy (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : BoundedOrderHom α β :=
{ f.toOrderHom.copy f' h, f.toTopHom.copy f' h, f.toBotHom.copy f' h with }
@@ -621,7 +621,7 @@ theorem copy_eq (f : BoundedOrderHom α β) (f' : α → β) (h : f' = f) : f.co
variable (α)
-/-- `id` as a `bounded_order_hom`. -/
+/-- `id` as a `BoundedOrderHom`. -/
protected def id : BoundedOrderHom α α :=
{ OrderHom.id, TopHom.id α, BotHom.id α with }
#align bounded_order_hom.id BoundedOrderHom.id
@@ -641,7 +641,7 @@ theorem id_apply (a : α) : BoundedOrderHom.id α a = a :=
rfl
#align bounded_order_hom.id_apply BoundedOrderHom.id_apply
-/-- Composition of `bounded_order_hom`s as a `bounded_order_hom`. -/
+/-- Composition of `BoundedOrderHom`s as a `BoundedOrderHom`. -/
def comp (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) : BoundedOrderHom α γ :=
{ f.toOrderHom.comp g.toOrderHom, f.toTopHom.comp g.toTopHom, f.toBotHom.comp g.toBotHom with }
#align bounded_order_hom.comp BoundedOrderHom.comp
@@ -658,22 +658,22 @@ theorem comp_apply (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) (a :
#align bounded_order_hom.comp_apply BoundedOrderHom.comp_apply
@[simp]
-theorem coe_comp_order_hom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) :
+theorem coe_comp_orderHom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) :
(f.comp g : OrderHom α γ) = (f : OrderHom β γ).comp g :=
rfl
-#align bounded_order_hom.coe_comp_order_hom BoundedOrderHom.coe_comp_order_hom
+#align bounded_order_hom.coe_comp_order_hom BoundedOrderHom.coe_comp_orderHom
@[simp]
-theorem coe_comp_top_hom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) :
+theorem coe_comp_topHom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) :
(f.comp g : TopHom α γ) = (f : TopHom β γ).comp g :=
rfl
-#align bounded_order_hom.coe_comp_top_hom BoundedOrderHom.coe_comp_top_hom
+#align bounded_order_hom.coe_comp_top_hom BoundedOrderHom.coe_comp_topHom
@[simp]
-theorem coe_comp_bot_hom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) :
+theorem coe_comp_botHom (f : BoundedOrderHom β γ) (g : BoundedOrderHom α β) :
(f.comp g : BotHom α γ) = (f : BotHom β γ).comp g :=
rfl
-#align bounded_order_hom.coe_comp_bot_hom BoundedOrderHom.coe_comp_bot_hom
+#align bounded_order_hom.coe_comp_bot_hom BoundedOrderHom.coe_comp_botHom
@[simp]
theorem comp_assoc (f : BoundedOrderHom γ δ) (g : BoundedOrderHom β γ) (h : BoundedOrderHom α β) :
mathlib3 SHA : f1a2caaf
Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Vierkantor <vierkantor@vierkantor.com>
All dependencies are ported!