data.fun_like.equiv
⟷
Mathlib.Data.FunLike.Equiv
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
@@ -262,7 +262,7 @@ theorem comp_bijective (f : α → β) (e : F) : Function.Bijective (e ∘ f)
#print EquivLike.subsingleton_dom /-
/-- This is not an instance to avoid slowing down every single `subsingleton` typeclass search.-/
theorem subsingleton_dom [Subsingleton β] : Subsingleton F :=
- ⟨fun f g => FunLike.ext f g fun x => (right_inv f).Injective <| Subsingleton.elim _ _⟩
+ ⟨fun f g => DFunLike.ext f g fun x => (right_inv f).Injective <| Subsingleton.elim _ _⟩
#align equiv_like.subsingleton_dom EquivLike.subsingleton_dom
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
-import Mathbin.Data.FunLike.Embedding
+import Data.FunLike.Embedding
#align_import data.fun_like.equiv from "leanprover-community/mathlib"@"448144f7ae193a8990cb7473c9e9a01990f64ac7"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-
-! This file was ported from Lean 3 source module data.fun_like.equiv
-! leanprover-community/mathlib commit 448144f7ae193a8990cb7473c9e9a01990f64ac7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.FunLike.Embedding
+#align_import data.fun_like.equiv from "leanprover-community/mathlib"@"448144f7ae193a8990cb7473c9e9a01990f64ac7"
+
/-!
# Typeclass for a type `F` with an injective map to `A ≃ B`
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -135,6 +135,7 @@ instead of linearly increasing the work per `my_iso`-related declaration.
-/
+#print EquivLike /-
/-- The class `equiv_like E α β` expresses that terms of type `E` have an
injective coercion to bijections between `α` and `β`.
@@ -149,16 +150,17 @@ class EquivLike (E : Sort _) (α β : outParam (Sort _)) where
-- The `inv` hypothesis makes this easier to prove with `congr'`
coe_injective' : ∀ e g, coe e = coe g → inv e = inv g → e = g
#align equiv_like EquivLike
+-/
namespace EquivLike
variable {E F α β γ : Sort _} [iE : EquivLike E α β] [iF : EquivLike F β γ]
-include iE
-
+#print EquivLike.inv_injective /-
theorem inv_injective : Function.Injective (EquivLike.inv : E → β → α) := fun e g h =>
coe_injective' e g ((right_inv e).eq_rightInverse (h.symm ▸ left_inv g)) h
#align equiv_like.inv_injective EquivLike.inv_injective
+-/
#print EquivLike.toEmbeddingLike /-
instance (priority := 100) toEmbeddingLike : EmbeddingLike E α β
@@ -169,37 +171,52 @@ instance (priority := 100) toEmbeddingLike : EmbeddingLike E α β
#align equiv_like.to_embedding_like EquivLike.toEmbeddingLike
-/
+#print EquivLike.injective /-
protected theorem injective (e : E) : Function.Injective e :=
EmbeddingLike.injective e
#align equiv_like.injective EquivLike.injective
+-/
+#print EquivLike.surjective /-
protected theorem surjective (e : E) : Function.Surjective e :=
(right_inv e).Surjective
#align equiv_like.surjective EquivLike.surjective
+-/
+#print EquivLike.bijective /-
protected theorem bijective (e : E) : Function.Bijective (e : α → β) :=
⟨EquivLike.injective e, EquivLike.surjective e⟩
#align equiv_like.bijective EquivLike.bijective
+-/
+#print EquivLike.apply_eq_iff_eq /-
theorem apply_eq_iff_eq (f : E) {x y : α} : f x = f y ↔ x = y :=
EmbeddingLike.apply_eq_iff_eq f
#align equiv_like.apply_eq_iff_eq EquivLike.apply_eq_iff_eq
+-/
+#print EquivLike.injective_comp /-
@[simp]
theorem injective_comp (e : E) (f : β → γ) : Function.Injective (f ∘ e) ↔ Function.Injective f :=
Function.Injective.of_comp_iff' f (EquivLike.bijective e)
#align equiv_like.injective_comp EquivLike.injective_comp
+-/
+#print EquivLike.surjective_comp /-
@[simp]
theorem surjective_comp (e : E) (f : β → γ) : Function.Surjective (f ∘ e) ↔ Function.Surjective f :=
(EquivLike.surjective e).of_comp_iff f
#align equiv_like.surjective_comp EquivLike.surjective_comp
+-/
+#print EquivLike.bijective_comp /-
@[simp]
theorem bijective_comp (e : E) (f : β → γ) : Function.Bijective (f ∘ e) ↔ Function.Bijective f :=
(EquivLike.bijective e).of_comp_iff f
#align equiv_like.bijective_comp EquivLike.bijective_comp
+-/
+#print EquivLike.inv_apply_apply /-
/-- This lemma is only supposed to be used in the generic context, when working with instances
of classes extending `equiv_like`.
For concrete isomorphism types such as `equiv`, you should use `equiv.symm_apply_apply`
@@ -210,7 +227,9 @@ TODO: define a generic form of `equiv.symm`. -/
theorem inv_apply_apply (e : E) (a : α) : EquivLike.inv e (e a) = a :=
left_inv _ _
#align equiv_like.inv_apply_apply EquivLike.inv_apply_apply
+-/
+#print EquivLike.apply_inv_apply /-
/-- This lemma is only supposed to be used in the generic context, when working with instances
of classes extending `equiv_like`.
For concrete isomorphism types such as `equiv`, you should use `equiv.apply_symm_apply`
@@ -221,24 +240,27 @@ TODO: define a generic form of `equiv.symm`. -/
theorem apply_inv_apply (e : E) (b : β) : e (EquivLike.inv e b) = b :=
right_inv _ _
#align equiv_like.apply_inv_apply EquivLike.apply_inv_apply
+-/
-omit iE
-
-include iF
-
+#print EquivLike.comp_injective /-
theorem comp_injective (f : α → β) (e : F) : Function.Injective (e ∘ f) ↔ Function.Injective f :=
EmbeddingLike.comp_injective f e
#align equiv_like.comp_injective EquivLike.comp_injective
+-/
+#print EquivLike.comp_surjective /-
@[simp]
theorem comp_surjective (f : α → β) (e : F) : Function.Surjective (e ∘ f) ↔ Function.Surjective f :=
Function.Surjective.of_comp_iff' (EquivLike.bijective e) f
#align equiv_like.comp_surjective EquivLike.comp_surjective
+-/
+#print EquivLike.comp_bijective /-
@[simp]
theorem comp_bijective (f : α → β) (e : F) : Function.Bijective (e ∘ f) ↔ Function.Bijective f :=
(EquivLike.bijective e).of_comp_iff' f
#align equiv_like.comp_bijective EquivLike.comp_bijective
+-/
#print EquivLike.subsingleton_dom /-
/-- This is not an instance to avoid slowing down every single `subsingleton` typeclass search.-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -135,12 +135,6 @@ instead of linearly increasing the work per `my_iso`-related declaration.
-/
-/- warning: equiv_like -> EquivLike is a dubious translation:
-lean 3 declaration is
- Sort.{u1} -> (outParam.{succ u2} Sort.{u2}) -> (outParam.{succ u3} Sort.{u3}) -> Sort.{max 1 (imax u1 u2 u3) (imax u1 u3 u2)}
-but is expected to have type
- Sort.{u1} -> (outParam.{succ u2} Sort.{u2}) -> (outParam.{succ u3} Sort.{u3}) -> Sort.{max (max (max 1 u1) u2) u3}
-Case conversion may be inaccurate. Consider using '#align equiv_like EquivLikeₓ'. -/
/-- The class `equiv_like E α β` expresses that terms of type `E` have an
injective coercion to bijections between `α` and `β`.
@@ -162,12 +156,6 @@ variable {E F α β γ : Sort _} [iE : EquivLike E α β] [iF : EquivLike F β
include iE
-/- warning: equiv_like.inv_injective -> EquivLike.inv_injective is a dubious translation:
-lean 3 declaration is
- forall {E : Sort.{u1}} {α : Sort.{u2}} {β : Sort.{u3}} [iE : EquivLike.{u1, u2, u3} E α β], Function.Injective.{u1, imax u3 u2} E (β -> α) (EquivLike.inv.{u1, u2, u3} E α β iE)
-but is expected to have type
- forall {E : Sort.{u3}} {α : Sort.{u1}} {β : Sort.{u2}} [iE : EquivLike.{u3, u1, u2} E α β], Function.Injective.{u3, imax u2 u1} E (β -> α) (EquivLike.inv.{u3, u1, u2} E α β iE)
-Case conversion may be inaccurate. Consider using '#align equiv_like.inv_injective EquivLike.inv_injectiveₓ'. -/
theorem inv_injective : Function.Injective (EquivLike.inv : E → β → α) := fun e g h =>
coe_injective' e g ((right_inv e).eq_rightInverse (h.symm ▸ left_inv g)) h
#align equiv_like.inv_injective EquivLike.inv_injective
@@ -181,85 +169,37 @@ instance (priority := 100) toEmbeddingLike : EmbeddingLike E α β
#align equiv_like.to_embedding_like EquivLike.toEmbeddingLike
-/
-/- warning: equiv_like.injective -> EquivLike.injective is a dubious translation:
-lean 3 declaration is
- forall {E : Sort.{u1}} {α : Sort.{u2}} {β : Sort.{u3}} [iE : EquivLike.{u1, u2, u3} E α β] (e : E), Function.Injective.{u2, u3} α β (coeFn.{u1, imax u2 u3} E (fun (_x : E) => α -> β) (FunLike.hasCoeToFun.{u1, u2, u3} E α (fun (_x : α) => β) (EmbeddingLike.toFunLike.{u1, u2, u3} E α β (EquivLike.toEmbeddingLike.{u1, u2, u3} E α β iE))) e)
-but is expected to have type
- forall {E : Sort.{u1}} {α : Sort.{u3}} {β : Sort.{u2}} [iE : EquivLike.{u1, u3, u2} E α β] (e : E), Function.Injective.{u3, u2} α β (FunLike.coe.{u1, u3, u2} E α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{u1, u3, u2} E α β (EquivLike.toEmbeddingLike.{u1, u3, u2} E α β iE)) e)
-Case conversion may be inaccurate. Consider using '#align equiv_like.injective EquivLike.injectiveₓ'. -/
protected theorem injective (e : E) : Function.Injective e :=
EmbeddingLike.injective e
#align equiv_like.injective EquivLike.injective
-/- warning: equiv_like.surjective -> EquivLike.surjective is a dubious translation:
-lean 3 declaration is
- forall {E : Sort.{u1}} {α : Sort.{u2}} {β : Sort.{u3}} [iE : EquivLike.{u1, u2, u3} E α β] (e : E), Function.Surjective.{u2, u3} α β (coeFn.{u1, imax u2 u3} E (fun (_x : E) => α -> β) (FunLike.hasCoeToFun.{u1, u2, u3} E α (fun (_x : α) => β) (EmbeddingLike.toFunLike.{u1, u2, u3} E α β (EquivLike.toEmbeddingLike.{u1, u2, u3} E α β iE))) e)
-but is expected to have type
- forall {E : Sort.{u1}} {α : Sort.{u3}} {β : Sort.{u2}} [iE : EquivLike.{u1, u3, u2} E α β] (e : E), Function.Surjective.{u3, u2} α β (FunLike.coe.{u1, u3, u2} E α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{u1, u3, u2} E α β (EquivLike.toEmbeddingLike.{u1, u3, u2} E α β iE)) e)
-Case conversion may be inaccurate. Consider using '#align equiv_like.surjective EquivLike.surjectiveₓ'. -/
protected theorem surjective (e : E) : Function.Surjective e :=
(right_inv e).Surjective
#align equiv_like.surjective EquivLike.surjective
-/- warning: equiv_like.bijective -> EquivLike.bijective is a dubious translation:
-lean 3 declaration is
- forall {E : Sort.{u1}} {α : Sort.{u2}} {β : Sort.{u3}} [iE : EquivLike.{u1, u2, u3} E α β] (e : E), Function.Bijective.{u2, u3} α β (coeFn.{u1, imax u2 u3} E (fun (_x : E) => α -> β) (FunLike.hasCoeToFun.{u1, u2, u3} E α (fun (_x : α) => β) (EmbeddingLike.toFunLike.{u1, u2, u3} E α β (EquivLike.toEmbeddingLike.{u1, u2, u3} E α β iE))) e)
-but is expected to have type
- forall {E : Sort.{u1}} {α : Sort.{u3}} {β : Sort.{u2}} [iE : EquivLike.{u1, u3, u2} E α β] (e : E), Function.Bijective.{u3, u2} α β (FunLike.coe.{u1, u3, u2} E α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{u1, u3, u2} E α β (EquivLike.toEmbeddingLike.{u1, u3, u2} E α β iE)) e)
-Case conversion may be inaccurate. Consider using '#align equiv_like.bijective EquivLike.bijectiveₓ'. -/
protected theorem bijective (e : E) : Function.Bijective (e : α → β) :=
⟨EquivLike.injective e, EquivLike.surjective e⟩
#align equiv_like.bijective EquivLike.bijective
-/- warning: equiv_like.apply_eq_iff_eq -> EquivLike.apply_eq_iff_eq is a dubious translation:
-lean 3 declaration is
- forall {E : Sort.{u1}} {α : Sort.{u2}} {β : Sort.{u3}} [iE : EquivLike.{u1, u2, u3} E α β] (f : E) {x : α} {y : α}, Iff (Eq.{u3} β (coeFn.{u1, imax u2 u3} E (fun (_x : E) => α -> β) (FunLike.hasCoeToFun.{u1, u2, u3} E α (fun (_x : α) => β) (EmbeddingLike.toFunLike.{u1, u2, u3} E α β (EquivLike.toEmbeddingLike.{u1, u2, u3} E α β iE))) f x) (coeFn.{u1, imax u2 u3} E (fun (_x : E) => α -> β) (FunLike.hasCoeToFun.{u1, u2, u3} E α (fun (_x : α) => β) (EmbeddingLike.toFunLike.{u1, u2, u3} E α β (EquivLike.toEmbeddingLike.{u1, u2, u3} E α β iE))) f y)) (Eq.{u2} α x y)
-but is expected to have type
- forall {E : Sort.{u2}} {α : Sort.{u1}} {β : Sort.{u3}} [iE : EquivLike.{u2, u1, u3} E α β] (f : E) {x : α} {y : α}, Iff (Eq.{u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) x) (FunLike.coe.{u2, u1, u3} E α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{u2, u1, u3} E α β (EquivLike.toEmbeddingLike.{u2, u1, u3} E α β iE)) f x) (FunLike.coe.{u2, u1, u3} E α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{u2, u1, u3} E α β (EquivLike.toEmbeddingLike.{u2, u1, u3} E α β iE)) f y)) (Eq.{u1} α x y)
-Case conversion may be inaccurate. Consider using '#align equiv_like.apply_eq_iff_eq EquivLike.apply_eq_iff_eqₓ'. -/
theorem apply_eq_iff_eq (f : E) {x y : α} : f x = f y ↔ x = y :=
EmbeddingLike.apply_eq_iff_eq f
#align equiv_like.apply_eq_iff_eq EquivLike.apply_eq_iff_eq
-/- warning: equiv_like.injective_comp -> EquivLike.injective_comp is a dubious translation:
-lean 3 declaration is
- forall {E : Sort.{u1}} {α : Sort.{u2}} {β : Sort.{u3}} {γ : Sort.{u4}} [iE : EquivLike.{u1, u2, u3} E α β] (e : E) (f : β -> γ), Iff (Function.Injective.{u2, u4} α γ (Function.comp.{u2, u3, u4} α β γ f (coeFn.{u1, imax u2 u3} E (fun (_x : E) => α -> β) (FunLike.hasCoeToFun.{u1, u2, u3} E α (fun (_x : α) => β) (EmbeddingLike.toFunLike.{u1, u2, u3} E α β (EquivLike.toEmbeddingLike.{u1, u2, u3} E α β iE))) e))) (Function.Injective.{u3, u4} β γ f)
-but is expected to have type
- forall {E : Sort.{u1}} {α : Sort.{u4}} {β : Sort.{u2}} {γ : Sort.{u3}} [iE : EquivLike.{u1, u4, u2} E α β] (e : E) (f : β -> γ), Iff (Function.Injective.{u4, u3} α γ (Function.comp.{u4, u2, u3} α β γ f (FunLike.coe.{u1, u4, u2} E α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{u1, u4, u2} E α β (EquivLike.toEmbeddingLike.{u1, u4, u2} E α β iE)) e))) (Function.Injective.{u2, u3} β γ f)
-Case conversion may be inaccurate. Consider using '#align equiv_like.injective_comp EquivLike.injective_compₓ'. -/
@[simp]
theorem injective_comp (e : E) (f : β → γ) : Function.Injective (f ∘ e) ↔ Function.Injective f :=
Function.Injective.of_comp_iff' f (EquivLike.bijective e)
#align equiv_like.injective_comp EquivLike.injective_comp
-/- warning: equiv_like.surjective_comp -> EquivLike.surjective_comp is a dubious translation:
-lean 3 declaration is
- forall {E : Sort.{u1}} {α : Sort.{u2}} {β : Sort.{u3}} {γ : Sort.{u4}} [iE : EquivLike.{u1, u2, u3} E α β] (e : E) (f : β -> γ), Iff (Function.Surjective.{u2, u4} α γ (Function.comp.{u2, u3, u4} α β γ f (coeFn.{u1, imax u2 u3} E (fun (_x : E) => α -> β) (FunLike.hasCoeToFun.{u1, u2, u3} E α (fun (_x : α) => β) (EmbeddingLike.toFunLike.{u1, u2, u3} E α β (EquivLike.toEmbeddingLike.{u1, u2, u3} E α β iE))) e))) (Function.Surjective.{u3, u4} β γ f)
-but is expected to have type
- forall {E : Sort.{u1}} {α : Sort.{u4}} {β : Sort.{u2}} {γ : Sort.{u3}} [iE : EquivLike.{u1, u4, u2} E α β] (e : E) (f : β -> γ), Iff (Function.Surjective.{u4, u3} α γ (Function.comp.{u4, u2, u3} α β γ f (FunLike.coe.{u1, u4, u2} E α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{u1, u4, u2} E α β (EquivLike.toEmbeddingLike.{u1, u4, u2} E α β iE)) e))) (Function.Surjective.{u2, u3} β γ f)
-Case conversion may be inaccurate. Consider using '#align equiv_like.surjective_comp EquivLike.surjective_compₓ'. -/
@[simp]
theorem surjective_comp (e : E) (f : β → γ) : Function.Surjective (f ∘ e) ↔ Function.Surjective f :=
(EquivLike.surjective e).of_comp_iff f
#align equiv_like.surjective_comp EquivLike.surjective_comp
-/- warning: equiv_like.bijective_comp -> EquivLike.bijective_comp is a dubious translation:
-lean 3 declaration is
- forall {E : Sort.{u1}} {α : Sort.{u2}} {β : Sort.{u3}} {γ : Sort.{u4}} [iE : EquivLike.{u1, u2, u3} E α β] (e : E) (f : β -> γ), Iff (Function.Bijective.{u2, u4} α γ (Function.comp.{u2, u3, u4} α β γ f (coeFn.{u1, imax u2 u3} E (fun (_x : E) => α -> β) (FunLike.hasCoeToFun.{u1, u2, u3} E α (fun (_x : α) => β) (EmbeddingLike.toFunLike.{u1, u2, u3} E α β (EquivLike.toEmbeddingLike.{u1, u2, u3} E α β iE))) e))) (Function.Bijective.{u3, u4} β γ f)
-but is expected to have type
- forall {E : Sort.{u1}} {α : Sort.{u4}} {β : Sort.{u2}} {γ : Sort.{u3}} [iE : EquivLike.{u1, u4, u2} E α β] (e : E) (f : β -> γ), Iff (Function.Bijective.{u4, u3} α γ (Function.comp.{u4, u2, u3} α β γ f (FunLike.coe.{u1, u4, u2} E α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{u1, u4, u2} E α β (EquivLike.toEmbeddingLike.{u1, u4, u2} E α β iE)) e))) (Function.Bijective.{u2, u3} β γ f)
-Case conversion may be inaccurate. Consider using '#align equiv_like.bijective_comp EquivLike.bijective_compₓ'. -/
@[simp]
theorem bijective_comp (e : E) (f : β → γ) : Function.Bijective (f ∘ e) ↔ Function.Bijective f :=
(EquivLike.bijective e).of_comp_iff f
#align equiv_like.bijective_comp EquivLike.bijective_comp
-/- warning: equiv_like.inv_apply_apply -> EquivLike.inv_apply_apply is a dubious translation:
-lean 3 declaration is
- forall {E : Sort.{u1}} {α : Sort.{u2}} {β : Sort.{u3}} [iE : EquivLike.{u1, u2, u3} E α β] (e : E) (a : α), Eq.{u2} α (EquivLike.inv.{u1, u2, u3} E α β iE e (coeFn.{u1, imax u2 u3} E (fun (_x : E) => α -> β) (FunLike.hasCoeToFun.{u1, u2, u3} E α (fun (_x : α) => β) (EmbeddingLike.toFunLike.{u1, u2, u3} E α β (EquivLike.toEmbeddingLike.{u1, u2, u3} E α β iE))) e a)) a
-but is expected to have type
- forall {E : Sort.{u2}} {α : Sort.{u3}} {β : Sort.{u1}} [iE : EquivLike.{u2, u3, u1} E α β] (e : E) (a : α), Eq.{u3} α (EquivLike.inv.{u2, u3, u1} E α ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) iE e (FunLike.coe.{u2, u3, u1} E α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{u2, u3, u1} E α β (EquivLike.toEmbeddingLike.{u2, u3, u1} E α β iE)) e a)) a
-Case conversion may be inaccurate. Consider using '#align equiv_like.inv_apply_apply EquivLike.inv_apply_applyₓ'. -/
/-- This lemma is only supposed to be used in the generic context, when working with instances
of classes extending `equiv_like`.
For concrete isomorphism types such as `equiv`, you should use `equiv.symm_apply_apply`
@@ -271,12 +211,6 @@ theorem inv_apply_apply (e : E) (a : α) : EquivLike.inv e (e a) = a :=
left_inv _ _
#align equiv_like.inv_apply_apply EquivLike.inv_apply_apply
-/- warning: equiv_like.apply_inv_apply -> EquivLike.apply_inv_apply is a dubious translation:
-lean 3 declaration is
- forall {E : Sort.{u1}} {α : Sort.{u2}} {β : Sort.{u3}} [iE : EquivLike.{u1, u2, u3} E α β] (e : E) (b : β), Eq.{u3} β (coeFn.{u1, imax u2 u3} E (fun (_x : E) => α -> β) (FunLike.hasCoeToFun.{u1, u2, u3} E α (fun (_x : α) => β) (EmbeddingLike.toFunLike.{u1, u2, u3} E α β (EquivLike.toEmbeddingLike.{u1, u2, u3} E α β iE))) e (EquivLike.inv.{u1, u2, u3} E α β iE e b)) b
-but is expected to have type
- forall {E : Sort.{u2}} {α : Sort.{u1}} {β : Sort.{u3}} [iE : EquivLike.{u2, u1, u3} E α β] (e : E) (b : β), Eq.{u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (EquivLike.inv.{u2, u1, u3} E α β iE e b)) (FunLike.coe.{u2, u1, u3} E α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{u2, u1, u3} E α β (EquivLike.toEmbeddingLike.{u2, u1, u3} E α β iE)) e (EquivLike.inv.{u2, u1, u3} E α β iE e b)) b
-Case conversion may be inaccurate. Consider using '#align equiv_like.apply_inv_apply EquivLike.apply_inv_applyₓ'. -/
/-- This lemma is only supposed to be used in the generic context, when working with instances
of classes extending `equiv_like`.
For concrete isomorphism types such as `equiv`, you should use `equiv.apply_symm_apply`
@@ -292,33 +226,15 @@ omit iE
include iF
-/- warning: equiv_like.comp_injective -> EquivLike.comp_injective is a dubious translation:
-lean 3 declaration is
- forall {F : Sort.{u1}} {α : Sort.{u2}} {β : Sort.{u3}} {γ : Sort.{u4}} [iF : EquivLike.{u1, u3, u4} F β γ] (f : α -> β) (e : F), Iff (Function.Injective.{u2, u4} α γ (Function.comp.{u2, u3, u4} α β γ (coeFn.{u1, imax u3 u4} F (fun (_x : F) => β -> γ) (FunLike.hasCoeToFun.{u1, u3, u4} F β (fun (_x : β) => γ) (EmbeddingLike.toFunLike.{u1, u3, u4} F β γ (EquivLike.toEmbeddingLike.{u1, u3, u4} F β γ iF))) e) f)) (Function.Injective.{u2, u3} α β f)
-but is expected to have type
- forall {F : Sort.{u1}} {α : Sort.{u4}} {β : Sort.{u2}} {γ : Sort.{u3}} [iF : EquivLike.{u1, u2, u3} F β γ] (f : α -> β) (e : F), Iff (Function.Injective.{u4, u3} α γ (Function.comp.{u4, u2, u3} α β γ (FunLike.coe.{u1, u2, u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{u1, u2, u3} F β γ (EquivLike.toEmbeddingLike.{u1, u2, u3} F β γ iF)) e) f)) (Function.Injective.{u4, u2} α β f)
-Case conversion may be inaccurate. Consider using '#align equiv_like.comp_injective EquivLike.comp_injectiveₓ'. -/
theorem comp_injective (f : α → β) (e : F) : Function.Injective (e ∘ f) ↔ Function.Injective f :=
EmbeddingLike.comp_injective f e
#align equiv_like.comp_injective EquivLike.comp_injective
-/- warning: equiv_like.comp_surjective -> EquivLike.comp_surjective is a dubious translation:
-lean 3 declaration is
- forall {F : Sort.{u1}} {α : Sort.{u2}} {β : Sort.{u3}} {γ : Sort.{u4}} [iF : EquivLike.{u1, u3, u4} F β γ] (f : α -> β) (e : F), Iff (Function.Surjective.{u2, u4} α γ (Function.comp.{u2, u3, u4} α β γ (coeFn.{u1, imax u3 u4} F (fun (_x : F) => β -> γ) (FunLike.hasCoeToFun.{u1, u3, u4} F β (fun (_x : β) => γ) (EmbeddingLike.toFunLike.{u1, u3, u4} F β γ (EquivLike.toEmbeddingLike.{u1, u3, u4} F β γ iF))) e) f)) (Function.Surjective.{u2, u3} α β f)
-but is expected to have type
- forall {F : Sort.{u1}} {α : Sort.{u4}} {β : Sort.{u2}} {γ : Sort.{u3}} [iF : EquivLike.{u1, u2, u3} F β γ] (f : α -> β) (e : F), Iff (Function.Surjective.{u4, u3} α γ (Function.comp.{u4, u2, u3} α β γ (FunLike.coe.{u1, u2, u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{u1, u2, u3} F β γ (EquivLike.toEmbeddingLike.{u1, u2, u3} F β γ iF)) e) f)) (Function.Surjective.{u4, u2} α β f)
-Case conversion may be inaccurate. Consider using '#align equiv_like.comp_surjective EquivLike.comp_surjectiveₓ'. -/
@[simp]
theorem comp_surjective (f : α → β) (e : F) : Function.Surjective (e ∘ f) ↔ Function.Surjective f :=
Function.Surjective.of_comp_iff' (EquivLike.bijective e) f
#align equiv_like.comp_surjective EquivLike.comp_surjective
-/- warning: equiv_like.comp_bijective -> EquivLike.comp_bijective is a dubious translation:
-lean 3 declaration is
- forall {F : Sort.{u1}} {α : Sort.{u2}} {β : Sort.{u3}} {γ : Sort.{u4}} [iF : EquivLike.{u1, u3, u4} F β γ] (f : α -> β) (e : F), Iff (Function.Bijective.{u2, u4} α γ (Function.comp.{u2, u3, u4} α β γ (coeFn.{u1, imax u3 u4} F (fun (_x : F) => β -> γ) (FunLike.hasCoeToFun.{u1, u3, u4} F β (fun (_x : β) => γ) (EmbeddingLike.toFunLike.{u1, u3, u4} F β γ (EquivLike.toEmbeddingLike.{u1, u3, u4} F β γ iF))) e) f)) (Function.Bijective.{u2, u3} α β f)
-but is expected to have type
- forall {F : Sort.{u1}} {α : Sort.{u4}} {β : Sort.{u2}} {γ : Sort.{u3}} [iF : EquivLike.{u1, u2, u3} F β γ] (f : α -> β) (e : F), Iff (Function.Bijective.{u4, u3} α γ (Function.comp.{u4, u2, u3} α β γ (FunLike.coe.{u1, u2, u3} F β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => γ) _x) (EmbeddingLike.toFunLike.{u1, u2, u3} F β γ (EquivLike.toEmbeddingLike.{u1, u2, u3} F β γ iF)) e) f)) (Function.Bijective.{u4, u2} α β f)
-Case conversion may be inaccurate. Consider using '#align equiv_like.comp_bijective EquivLike.comp_bijectiveₓ'. -/
@[simp]
theorem comp_bijective (f : α → β) (e : F) : Function.Bijective (e ∘ f) ↔ Function.Bijective f :=
(EquivLike.bijective e).of_comp_iff' f
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.
@@ -233,7 +233,7 @@ theorem comp_bijective (f : α → β) (e : F) : Function.Bijective (e ∘ f)
(EquivLike.bijective e).of_comp_iff' f
#align equiv_like.comp_bijective EquivLike.comp_bijective
-/-- This is not an instance to avoid slowing down every single `Subsingleton` typeclass search.-/
+/-- This is not an instance to avoid slowing down every single `Subsingleton` typeclass search. -/
lemma subsingleton_dom [Subsingleton β] : Subsingleton F :=
⟨fun f g ↦ DFunLike.ext f g fun _ ↦ (right_inv f).injective <| Subsingleton.elim _ _⟩
#align equiv_like.subsingleton_dom EquivLike.subsingleton_dom
Fully update the module docstrings (in particular, the examples given therein) after #8386.
This includes switching to where syntax, but also replacing Lean 3 syntax, replacing => by "\mapsto" while at it and indenting code per the style guide. As such, it's also a follow-up to #11301.
Co-authored-by: @Vierkantor
Co-authored-by: Vierkantor <vierkantor@vierkantor.com>
@@ -14,37 +14,33 @@ This typeclass is primarily for use by isomorphisms like `MonoidEquiv` and `Line
## Basic usage of `EquivLike`
-A typical type of morphisms should be declared as:
+A typical type of isomorphisms should be declared as:
```
-structure MyIso (A B : Type*) [MyClass A] [MyClass B]
- extends Equiv A B :=
-(map_op' : ∀ {x y : A}, toFun (MyClass.op x y) = MyClass.op (toFun x) (toFun y))
+structure MyIso (A B : Type*) [MyClass A] [MyClass B] extends Equiv A B :=
+ (map_op' : ∀ (x y : A), toFun (MyClass.op x y) = MyClass.op (toFun x) (toFun y))
namespace MyIso
variable (A B : Type*) [MyClass A] [MyClass B]
--- This instance is optional if you follow the "Isomorphism class" design below:
-instance : EquivLike (MyIso A B) A (λ _, B) :=
- { coe := MyIso.toEquiv.toFun,
- inv := MyIso.toEquiv.invFun,
- left_inv := MyIso.toEquiv.left_inv,
- right_inv := MyIso.toEquiv.right_inv,
- coe_injective' := λ f g h, by cases f; cases g; congr' }
-
-/-- Helper instance for when there's too many metavariables to apply `EquivLike.coe` directly. -/
-instance : CoeFun (MyIso A B) := DFunLike.instCoeFunForAll
+instance instEquivLike : EquivLike (MyIso A B) A B where
+ coe f := f.toFun
+ inv f := f.invFun
+ left_inv f := f.left_inv
+ right_inv f := f.right_inv
+ coe_injective' f g h₁ h₂ := by cases f; cases g; congr; exact EquivLike.coe_injective' _ _ h₁ h₂
@[ext] theorem ext {f g : MyIso A B} (h : ∀ x, f x = g x) : f = g := DFunLike.ext f g h
/-- Copy of a `MyIso` with a new `toFun` equal to the old one. Useful to fix definitional
equalities. -/
-protected def copy (f : MyIso A B) (f' : A → B) (f_inv : B → A) (h : f' = ⇑f) : MyIso A B :=
- { toFun := f',
- invFun := f_inv,
- left_inv := h.symm ▸ f.left_inv,
- right_inv := h.symm ▸ f.right_inv,
- map_op' := h.symm ▸ f.map_op' }
+protected def copy (f : MyIso A B) (f' : A → B) (f_inv : B → A)
+ (h₁ : f' = f) (h₂ : f_inv = f.invFun) : MyIso A B where
+ toFun := f'
+ invFun := f_inv
+ left_inv := h₁.symm ▸ h₂.symm ▸ f.left_inv
+ right_inv := h₁.symm ▸ h₂.symm ▸ f.right_inv
+ map_op' := h₁.symm ▸ f.map_op'
end MyIso
```
@@ -60,61 +56,67 @@ the axioms of your new type of isomorphisms.
Continuing the example above:
```
-
/-- `MyIsoClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyIso`. -/
class MyIsoClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
- extends EquivLike F A (λ _, B), MyHomClass F A B
+ [EquivLike F A B]
+ extends MyHomClass F A B
+
+namespace MyIso
+
+variable {A B : Type*} [MyClass A] [MyClass B]
-end
+-- This goes after `MyIsoClass.instEquivLike`:
+instance : MyIsoClass (MyIso A B) A B where
+ map_op := MyIso.map_op'
--- You can replace `MyIso.EquivLike` with the below instance:
-instance : MyIsoClass (MyIso A B) A B :=
- { coe := MyIso.toFun,
- inv := MyIso.invFun,
- left_inv := MyIso.left_inv,
- right_inv := MyIso.right_inv,
- coe_injective' := λ f g h, by cases f; cases g; congr',
- map_op := MyIso.map_op' }
+-- [Insert `ext` and `copy` here]
--- [Insert `CoeFun`, `ext` and `copy` here]
+end MyIso
```
The second step is to add instances of your new `MyIsoClass` for all types extending `MyIso`.
Typically, you can just declare a new class analogous to `MyIsoClass`:
```
-structure CoolerIso (A B : Type*) [CoolClass A] [CoolClass B]
- extends MyIso A B :=
-(map_cool' : toFun CoolClass.cool = CoolClass.cool)
-
-section
-set_option old_structure_cmd true
+structure CoolerIso (A B : Type*) [CoolClass A] [CoolClass B] extends MyIso A B :=
+ (map_cool' : toFun CoolClass.cool = CoolClass.cool)
class CoolerIsoClass (F : Type*) (A B : outParam <| Type*) [CoolClass A] [CoolClass B]
- extends MyIsoClass F A B :=
-(map_cool : ∀ (f : F), f CoolClass.cool = CoolClass.cool)
+ [EquivLike F A B]
+ extends MyIsoClass F A B :=
+ (map_cool : ∀ (f : F), f CoolClass.cool = CoolClass.cool)
+
+@[simp] lemma map_cool {F A B : Type*} [CoolClass A] [CoolClass B]
+ [EquivLike F A B] [CoolerIsoClass F A B] (f : F) :
+ f CoolClass.cool = CoolClass.cool :=
+ CoolerIsoClass.map_cool _
+
+namespace CoolerIso
+
+variable {A B : Type*} [CoolClass A] [CoolClass B]
-end
+instance : EquivLike (CoolerIso A B) A B where
+ coe f := f.toFun
+ inv f := f.invFun
+ left_inv f := f.left_inv
+ right_inv f := f.right_inv
+ coe_injective' f g h₁ h₂ := by cases f; cases g; congr; exact EquivLike.coe_injective' _ _ h₁ h₂
-@[simp] lemma map_cool {F A B : Type*} [CoolClass A] [CoolClass B] [CoolerIsoClass F A B]
- (f : F) : f CoolClass.cool = CoolClass.cool :=
-CoolerIsoClass.map_cool
+instance : CoolerIsoClass (CoolerIso A B) A B where
+ map_op f := f.map_op'
+ map_cool f := f.map_cool'
-instance : CoolerIsoClass (CoolerIso A B) A B :=
- { coe := CoolerIso.toFun,
- coe_injective' := λ f g h, by cases f; cases g; congr',
- map_op := CoolerIso.map_op',
- map_cool := CoolerIso.map_cool' }
+-- [Insert `ext` and `copy` here]
--- [Insert `CoeFun`, `ext` and `copy` here]
+end CoolerIso
```
Then any declaration taking a specific type of morphisms as parameter can instead take the
class you just defined:
```
-- Compare with: lemma do_something (f : MyIso A B) : sorry := sorry
-lemma do_something {F : Type*} [MyIsoClass F A B] (f : F) : sorry := sorry
+lemma do_something {F : Type*} [EquivLike F A B] [MyIsoClass F A B] (f : F) : sorry := sorry
```
This means anything set up for `MyIso`s will automatically work for `CoolerIsoClass`es,
variables
, universes
' syntax in doc comments (#11404)
It's deprecated in favour of variable
; likely a leftover from the port.
Also replace universes
, which is invalid now.
@@ -22,7 +22,7 @@ structure MyIso (A B : Type*) [MyClass A] [MyClass B]
namespace MyIso
-variables (A B : Type*) [MyClass A] [MyClass B]
+variable (A B : Type*) [MyClass A] [MyClass B]
-- This instance is optional if you follow the "Isomorphism class" design below:
instance : EquivLike (MyIso A B) A (λ _, B) :=
Add one lemma stating that an element is a unit if and only if its image through a ring equivalence is a unit.
@@ -130,7 +130,7 @@ injective coercion to bijections between `α` and `β`.
Note that this does not directly extend `FunLike`, nor take `FunLike` as a parameter,
so we can state `coe_injective'` in a nicer way.
-This typeclass is used in the definition of the homomorphism typeclasses,
+This typeclass is used in the definition of the isomorphism (or equivalence) typeclasses,
such as `ZeroEquivClass`, `MulEquivClass`, `MonoidEquivClass`, ....
-/
class EquivLike (E : Sort*) (α β : outParam (Sort*)) where
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>
@@ -127,6 +127,9 @@ instead of linearly increasing the work per `MyIso`-related declaration.
/-- The class `EquivLike E α β` expresses that terms of type `E` have an
injective coercion to bijections between `α` and `β`.
+Note that this does not directly extend `FunLike`, nor take `FunLike` as a parameter,
+so we can state `coe_injective'` in a nicer way.
+
This typeclass is used in the definition of the homomorphism typeclasses,
such as `ZeroEquivClass`, `MulEquivClass`, `MonoidEquivClass`, ....
-/
@@ -153,10 +156,12 @@ theorem inv_injective : Function.Injective (EquivLike.inv : E → β → α) :=
coe_injective' e g ((right_inv e).eq_rightInverse (h.symm ▸ left_inv g)) h
#align equiv_like.inv_injective EquivLike.inv_injective
-instance (priority := 100) toEmbeddingLike : EmbeddingLike E α β where
+instance (priority := 100) toFunLike : FunLike E α β where
coe := (coe : E → α → β)
coe_injective' e g h :=
coe_injective' e g h ((left_inv e).eq_rightInverse (h.symm ▸ right_inv g))
+
+instance (priority := 100) toEmbeddingLike : EmbeddingLike E α β where
injective' e := (left_inv e).injective
protected theorem injective (e : E) : Function.Injective e :=
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>
@@ -33,9 +33,9 @@ instance : EquivLike (MyIso A B) A (λ _, B) :=
coe_injective' := λ f g h, by cases f; cases g; congr' }
/-- Helper instance for when there's too many metavariables to apply `EquivLike.coe` directly. -/
-instance : CoeFun (MyIso A B) := FunLike.instCoeFunForAll
+instance : CoeFun (MyIso A B) := DFunLike.instCoeFunForAll
-@[ext] theorem ext {f g : MyIso A B} (h : ∀ x, f x = g x) : f = g := FunLike.ext f g h
+@[ext] theorem ext {f g : MyIso A B} (h : ∀ x, f x = g x) : f = g := DFunLike.ext f g h
/-- Copy of a `MyIso` with a new `toFun` equal to the old one. Useful to fix definitional
equalities. -/
@@ -228,7 +228,7 @@ theorem comp_bijective (f : α → β) (e : F) : Function.Bijective (e ∘ f)
/-- This is not an instance to avoid slowing down every single `Subsingleton` typeclass search.-/
lemma subsingleton_dom [Subsingleton β] : Subsingleton F :=
- ⟨fun f g ↦ FunLike.ext f g fun _ ↦ (right_inv f).injective <| Subsingleton.elim _ _⟩
+ ⟨fun f g ↦ DFunLike.ext f g fun _ ↦ (right_inv f).injective <| Subsingleton.elim _ _⟩
#align equiv_like.subsingleton_dom EquivLike.subsingleton_dom
end EquivLike
$
with <|
(#9319)
See Zulip thread for the discussion.
@@ -228,7 +228,7 @@ theorem comp_bijective (f : α → β) (e : F) : Function.Bijective (e ∘ f)
/-- This is not an instance to avoid slowing down every single `Subsingleton` typeclass search.-/
lemma subsingleton_dom [Subsingleton β] : Subsingleton F :=
- ⟨fun f g ↦ FunLike.ext f g fun _ ↦ (right_inv f).injective $ Subsingleton.elim _ _⟩
+ ⟨fun f g ↦ FunLike.ext f g fun _ ↦ (right_inv f).injective <| Subsingleton.elim _ _⟩
#align equiv_like.subsingleton_dom EquivLike.subsingleton_dom
end EquivLike
@@ -228,7 +228,7 @@ theorem comp_bijective (f : α → β) (e : F) : Function.Bijective (e ∘ f)
/-- This is not an instance to avoid slowing down every single `Subsingleton` typeclass search.-/
lemma subsingleton_dom [Subsingleton β] : Subsingleton F :=
- ⟨fun f g ↦ FunLike.ext f g $ fun _ ↦ (right_inv f).injective $ Subsingleton.elim _ _⟩
+ ⟨fun f g ↦ FunLike.ext f g fun _ ↦ (right_inv f).injective $ Subsingleton.elim _ _⟩
#align equiv_like.subsingleton_dom EquivLike.subsingleton_dom
end EquivLike
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -16,13 +16,13 @@ This typeclass is primarily for use by isomorphisms like `MonoidEquiv` and `Line
A typical type of morphisms should be declared as:
```
-structure MyIso (A B : Type _) [MyClass A] [MyClass B]
+structure MyIso (A B : Type*) [MyClass A] [MyClass B]
extends Equiv A B :=
(map_op' : ∀ {x y : A}, toFun (MyClass.op x y) = MyClass.op (toFun x) (toFun y))
namespace MyIso
-variables (A B : Type _) [MyClass A] [MyClass B]
+variables (A B : Type*) [MyClass A] [MyClass B]
-- This instance is optional if you follow the "Isomorphism class" design below:
instance : EquivLike (MyIso A B) A (λ _, B) :=
@@ -63,7 +63,7 @@ Continuing the example above:
/-- `MyIsoClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyIso`. -/
-class MyIsoClass (F : Type _) (A B : outParam <| Type _) [MyClass A] [MyClass B]
+class MyIsoClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
extends EquivLike F A (λ _, B), MyHomClass F A B
end
@@ -84,20 +84,20 @@ The second step is to add instances of your new `MyIsoClass` for all types exten
Typically, you can just declare a new class analogous to `MyIsoClass`:
```
-structure CoolerIso (A B : Type _) [CoolClass A] [CoolClass B]
+structure CoolerIso (A B : Type*) [CoolClass A] [CoolClass B]
extends MyIso A B :=
(map_cool' : toFun CoolClass.cool = CoolClass.cool)
section
set_option old_structure_cmd true
-class CoolerIsoClass (F : Type _) (A B : outParam <| Type _) [CoolClass A] [CoolClass B]
+class CoolerIsoClass (F : Type*) (A B : outParam <| Type*) [CoolClass A] [CoolClass B]
extends MyIsoClass F A B :=
(map_cool : ∀ (f : F), f CoolClass.cool = CoolClass.cool)
end
-@[simp] lemma map_cool {F A B : Type _} [CoolClass A] [CoolClass B] [CoolerIsoClass F A B]
+@[simp] lemma map_cool {F A B : Type*} [CoolClass A] [CoolClass B] [CoolerIsoClass F A B]
(f : F) : f CoolClass.cool = CoolClass.cool :=
CoolerIsoClass.map_cool
@@ -114,7 +114,7 @@ Then any declaration taking a specific type of morphisms as parameter can instea
class you just defined:
```
-- Compare with: lemma do_something (f : MyIso A B) : sorry := sorry
-lemma do_something {F : Type _} [MyIsoClass F A B] (f : F) : sorry := sorry
+lemma do_something {F : Type*} [MyIsoClass F A B] (f : F) : sorry := sorry
```
This means anything set up for `MyIso`s will automatically work for `CoolerIsoClass`es,
@@ -130,7 +130,7 @@ injective coercion to bijections between `α` and `β`.
This typeclass is used in the definition of the homomorphism typeclasses,
such as `ZeroEquivClass`, `MulEquivClass`, `MonoidEquivClass`, ....
-/
-class EquivLike (E : Sort _) (α β : outParam (Sort _)) where
+class EquivLike (E : Sort*) (α β : outParam (Sort*)) where
/-- The coercion to a function in the forward direction. -/
coe : E → α → β
/-- The coercion to a function in the backwards direction. -/
@@ -147,7 +147,7 @@ class EquivLike (E : Sort _) (α β : outParam (Sort _)) where
namespace EquivLike
-variable {E F α β γ : Sort _} [iE : EquivLike E α β] [iF : EquivLike F β γ]
+variable {E F α β γ : Sort*} [iE : EquivLike E α β] [iF : EquivLike F β γ]
theorem inv_injective : Function.Injective (EquivLike.inv : E → β → α) := fun e g h ↦
coe_injective' e g ((right_inv e).eq_rightInverse (h.symm ▸ left_inv g)) h
@@ -139,7 +139,7 @@ class EquivLike (E : Sort _) (α β : outParam (Sort _)) where
left_inv : ∀ e, Function.LeftInverse (inv e) (coe e)
/-- The coercions are right inverses. -/
right_inv : ∀ e, Function.RightInverse (inv e) (coe e)
- /-- If two coercions to functions are jointly injective. -/
+ /-- The two coercions to functions are jointly injective. -/
coe_injective' : ∀ e g, coe e = coe g → inv e = inv g → e = g
-- This is mathematically equivalent to either of the coercions to functions being injective, but
-- the `inv` hypothesis makes this easier to prove with `congr'`
@@ -2,14 +2,11 @@
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-
-! This file was ported from Lean 3 source module data.fun_like.equiv
-! leanprover-community/mathlib commit f340f229b1f461aa1c8ee11e0a172d0a3b301a4a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Data.FunLike.Embedding
+#align_import data.fun_like.equiv from "leanprover-community/mathlib"@"f340f229b1f461aa1c8ee11e0a172d0a3b301a4a"
+
/-!
# Typeclass for a type `F` with an injective map to `A ≃ B`
@@ -29,11 +29,11 @@ variables (A B : Type _) [MyClass A] [MyClass B]
-- This instance is optional if you follow the "Isomorphism class" design below:
instance : EquivLike (MyIso A B) A (λ _, B) :=
-{ coe := MyIso.toEquiv.toFun,
- inv := MyIso.toEquiv.invFun,
- left_inv := MyIso.toEquiv.left_inv,
- right_inv := MyIso.toEquiv.right_inv,
- coe_injective' := λ f g h, by cases f; cases g; congr' }
+ { coe := MyIso.toEquiv.toFun,
+ inv := MyIso.toEquiv.invFun,
+ left_inv := MyIso.toEquiv.left_inv,
+ right_inv := MyIso.toEquiv.right_inv,
+ coe_injective' := λ f g h, by cases f; cases g; congr' }
/-- Helper instance for when there's too many metavariables to apply `EquivLike.coe` directly. -/
instance : CoeFun (MyIso A B) := FunLike.instCoeFunForAll
@@ -43,11 +43,11 @@ instance : CoeFun (MyIso A B) := FunLike.instCoeFunForAll
/-- Copy of a `MyIso` with a new `toFun` equal to the old one. Useful to fix definitional
equalities. -/
protected def copy (f : MyIso A B) (f' : A → B) (f_inv : B → A) (h : f' = ⇑f) : MyIso A B :=
-{ toFun := f',
- invFun := f_inv,
- left_inv := h.symm ▸ f.left_inv,
- right_inv := h.symm ▸ f.right_inv,
- map_op' := h.symm ▸ f.map_op' }
+ { toFun := f',
+ invFun := f_inv,
+ left_inv := h.symm ▸ f.left_inv,
+ right_inv := h.symm ▸ f.right_inv,
+ map_op' := h.symm ▸ f.map_op' }
end MyIso
```
@@ -73,12 +73,12 @@ end
-- You can replace `MyIso.EquivLike` with the below instance:
instance : MyIsoClass (MyIso A B) A B :=
-{ coe := MyIso.toFun,
- inv := MyIso.invFun,
- left_inv := MyIso.left_inv,
- right_inv := MyIso.right_inv,
- coe_injective' := λ f g h, by cases f; cases g; congr',
- map_op := MyIso.map_op' }
+ { coe := MyIso.toFun,
+ inv := MyIso.invFun,
+ left_inv := MyIso.left_inv,
+ right_inv := MyIso.right_inv,
+ coe_injective' := λ f g h, by cases f; cases g; congr',
+ map_op := MyIso.map_op' }
-- [Insert `CoeFun`, `ext` and `copy` here]
```
@@ -105,10 +105,10 @@ end
CoolerIsoClass.map_cool
instance : CoolerIsoClass (CoolerIso A B) A B :=
-{ coe := CoolerIso.toFun,
- coe_injective' := λ f g h, by cases f; cases g; congr',
- map_op := CoolerIso.map_op',
- map_cool := CoolerIso.map_cool' }
+ { coe := CoolerIso.toFun,
+ coe_injective' := λ f g h, by cases f; cases g; congr',
+ map_op := CoolerIso.map_op',
+ map_cool := CoolerIso.map_cool' }
-- [Insert `CoeFun`, `ext` and `copy` here]
```
@@ -231,7 +231,7 @@ theorem comp_bijective (f : α → β) (e : F) : Function.Bijective (e ∘ f)
/-- This is not an instance to avoid slowing down every single `Subsingleton` typeclass search.-/
lemma subsingleton_dom [Subsingleton β] : Subsingleton F :=
-⟨fun f g ↦ FunLike.ext f g $ fun _ ↦ (right_inv f).injective $ Subsingleton.elim _ _⟩
+ ⟨fun f g ↦ FunLike.ext f g $ fun _ ↦ (right_inv f).injective $ Subsingleton.elim _ _⟩
#align equiv_like.subsingleton_dom EquivLike.subsingleton_dom
end EquivLike
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)@@ -146,6 +146,7 @@ class EquivLike (E : Sort _) (α β : outParam (Sort _)) where
coe_injective' : ∀ e g, coe e = coe g → inv e = inv g → e = g
-- This is mathematically equivalent to either of the coercions to functions being injective, but
-- the `inv` hypothesis makes this easier to prove with `congr'`
+#align equiv_like EquivLike
namespace EquivLike
@@ -153,6 +154,7 @@ variable {E F α β γ : Sort _} [iE : EquivLike E α β] [iF : EquivLike F β
theorem inv_injective : Function.Injective (EquivLike.inv : E → β → α) := fun e g h ↦
coe_injective' e g ((right_inv e).eq_rightInverse (h.symm ▸ left_inv g)) h
+#align equiv_like.inv_injective EquivLike.inv_injective
instance (priority := 100) toEmbeddingLike : EmbeddingLike E α β where
coe := (coe : E → α → β)
@@ -162,27 +164,34 @@ instance (priority := 100) toEmbeddingLike : EmbeddingLike E α β where
protected theorem injective (e : E) : Function.Injective e :=
EmbeddingLike.injective e
+#align equiv_like.injective EquivLike.injective
protected theorem surjective (e : E) : Function.Surjective e :=
(right_inv e).surjective
+#align equiv_like.surjective EquivLike.surjective
protected theorem bijective (e : E) : Function.Bijective (e : α → β) :=
⟨EquivLike.injective e, EquivLike.surjective e⟩
+#align equiv_like.bijective EquivLike.bijective
theorem apply_eq_iff_eq (f : E) {x y : α} : f x = f y ↔ x = y :=
EmbeddingLike.apply_eq_iff_eq f
+#align equiv_like.apply_eq_iff_eq EquivLike.apply_eq_iff_eq
@[simp]
theorem injective_comp (e : E) (f : β → γ) : Function.Injective (f ∘ e) ↔ Function.Injective f :=
Function.Injective.of_comp_iff' f (EquivLike.bijective e)
+#align equiv_like.injective_comp EquivLike.injective_comp
@[simp]
theorem surjective_comp (e : E) (f : β → γ) : Function.Surjective (f ∘ e) ↔ Function.Surjective f :=
(EquivLike.surjective e).of_comp_iff f
+#align equiv_like.surjective_comp EquivLike.surjective_comp
@[simp]
theorem bijective_comp (e : E) (f : β → γ) : Function.Bijective (f ∘ e) ↔ Function.Bijective f :=
(EquivLike.bijective e).of_comp_iff f
+#align equiv_like.bijective_comp EquivLike.bijective_comp
/-- This lemma is only supposed to be used in the generic context, when working with instances
of classes extending `EquivLike`.
@@ -193,6 +202,7 @@ TODO: define a generic form of `Equiv.symm`. -/
@[simp]
theorem inv_apply_apply (e : E) (a : α) : EquivLike.inv e (e a) = a :=
left_inv _ _
+#align equiv_like.inv_apply_apply EquivLike.inv_apply_apply
/-- This lemma is only supposed to be used in the generic context, when working with instances
of classes extending `EquivLike`.
@@ -203,20 +213,25 @@ TODO: define a generic form of `Equiv.symm`. -/
@[simp]
theorem apply_inv_apply (e : E) (b : β) : e (EquivLike.inv e b) = b :=
right_inv _ _
+#align equiv_like.apply_inv_apply EquivLike.apply_inv_apply
theorem comp_injective (f : α → β) (e : F) : Function.Injective (e ∘ f) ↔ Function.Injective f :=
EmbeddingLike.comp_injective f e
+#align equiv_like.comp_injective EquivLike.comp_injective
@[simp]
theorem comp_surjective (f : α → β) (e : F) : Function.Surjective (e ∘ f) ↔ Function.Surjective f :=
Function.Surjective.of_comp_iff' (EquivLike.bijective e) f
+#align equiv_like.comp_surjective EquivLike.comp_surjective
@[simp]
theorem comp_bijective (f : α → β) (e : F) : Function.Bijective (e ∘ f) ↔ Function.Bijective f :=
(EquivLike.bijective e).of_comp_iff' f
+#align equiv_like.comp_bijective EquivLike.comp_bijective
/-- This is not an instance to avoid slowing down every single `Subsingleton` typeclass search.-/
lemma subsingleton_dom [Subsingleton β] : Subsingleton F :=
⟨fun f g ↦ FunLike.ext f g $ fun _ ↦ (right_inv f).injective $ Subsingleton.elim _ _⟩
+#align equiv_like.subsingleton_dom EquivLike.subsingleton_dom
end EquivLike
Type*
to Type _
(#1866)
A bunch of docstrings were still mentioning Type*
. This changes them to Type _
.
@@ -19,13 +19,13 @@ This typeclass is primarily for use by isomorphisms like `MonoidEquiv` and `Line
A typical type of morphisms should be declared as:
```
-structure MyIso (A B : Type*) [MyClass A] [MyClass B]
+structure MyIso (A B : Type _) [MyClass A] [MyClass B]
extends Equiv A B :=
(map_op' : ∀ {x y : A}, toFun (MyClass.op x y) = MyClass.op (toFun x) (toFun y))
namespace MyIso
-variables (A B : Type*) [MyClass A] [MyClass B]
+variables (A B : Type _) [MyClass A] [MyClass B]
-- This instance is optional if you follow the "Isomorphism class" design below:
instance : EquivLike (MyIso A B) A (λ _, B) :=
@@ -66,7 +66,7 @@ Continuing the example above:
/-- `MyIsoClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyIso`. -/
-class MyIsoClass (F : Type*) (A B : outParam <| Type _) [MyClass A] [MyClass B]
+class MyIsoClass (F : Type _) (A B : outParam <| Type _) [MyClass A] [MyClass B]
extends EquivLike F A (λ _, B), MyHomClass F A B
end
@@ -87,20 +87,20 @@ The second step is to add instances of your new `MyIsoClass` for all types exten
Typically, you can just declare a new class analogous to `MyIsoClass`:
```
-structure CoolerIso (A B : Type*) [CoolClass A] [CoolClass B]
+structure CoolerIso (A B : Type _) [CoolClass A] [CoolClass B]
extends MyIso A B :=
(map_cool' : toFun CoolClass.cool = CoolClass.cool)
section
set_option old_structure_cmd true
-class CoolerIsoClass (F : Type*) (A B : outParam <| Type _) [CoolClass A] [CoolClass B]
+class CoolerIsoClass (F : Type _) (A B : outParam <| Type _) [CoolClass A] [CoolClass B]
extends MyIsoClass F A B :=
(map_cool : ∀ (f : F), f CoolClass.cool = CoolClass.cool)
end
-@[simp] lemma map_cool {F A B : Type*} [CoolClass A] [CoolClass B] [CoolerIsoClass F A B]
+@[simp] lemma map_cool {F A B : Type _} [CoolClass A] [CoolClass B] [CoolerIsoClass F A B]
(f : F) : f CoolClass.cool = CoolClass.cool :=
CoolerIsoClass.map_cool
@@ -117,7 +117,7 @@ Then any declaration taking a specific type of morphisms as parameter can instea
class you just defined:
```
-- Compare with: lemma do_something (f : MyIso A B) : sorry := sorry
-lemma do_something {F : Type*} [MyIsoClass F A B] (f : F) : sorry := sorry
+lemma do_something {F : Type _} [MyIsoClass F A B] (f : F) : sorry := sorry
```
This means anything set up for `MyIso`s will automatically work for `CoolerIsoClass`es,
Fix a lot of wrong casing mostly in the docstrings but also sometimes in def/theorem names. E.g. fin 2 --> Fin 2
, add_monoid_hom --> AddMonoidHom
Remove \n
from to_additive
docstrings that were inserted by mathport.
Move files and directories with Gcd
and Smul
to GCD
and SMul
@@ -131,7 +131,7 @@ instead of linearly increasing the work per `MyIso`-related declaration.
injective coercion to bijections between `α` and `β`.
This typeclass is used in the definition of the homomorphism typeclasses,
-such as `zero_equiv_class`, `mul_equiv_class`, `monoid_equiv_class`, ....
+such as `ZeroEquivClass`, `MulEquivClass`, `MonoidEquivClass`, ....
-/
class EquivLike (E : Sort _) (α β : outParam (Sort _)) where
/-- The coercion to a function in the forward direction. -/
The script used to do this is included. The yaml file was obtained from https://raw.githubusercontent.com/wiki/leanprover-community/mathlib/mathlib4-port-status.md
@@ -2,6 +2,11 @@
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
+
+! This file was ported from Lean 3 source module data.fun_like.equiv
+! leanprover-community/mathlib commit f340f229b1f461aa1c8ee11e0a172d0a3b301a4a
+! Please do not edit these lines, except to modify the commit id
+! if you have ported upstream changes.
-/
import Mathlib.Data.FunLike.Embedding
All dependencies are ported!