group_theory.perm.via_embedding
⟷
Mathlib.GroupTheory.Perm.ViaEmbedding
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-/
-import Mathbin.GroupTheory.Perm.Basic
-import Mathbin.Logic.Equiv.Set
+import GroupTheory.Perm.Basic
+import Logic.Equiv.Set
#align_import group_theory.perm.via_embedding from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-
-! This file was ported from Lean 3 source module group_theory.perm.via_embedding
-! leanprover-community/mathlib commit c3291da49cfa65f0d43b094750541c0731edc932
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.GroupTheory.Perm.Basic
import Mathbin.Logic.Equiv.Set
+#align_import group_theory.perm.via_embedding from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
+
/-!
# `equiv.perm.via_embedding`, a noncomputable analogue of `equiv.perm.via_fintype_embedding`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -55,13 +55,17 @@ noncomputable def viaEmbeddingHom : Perm α →* Perm β :=
#align equiv.perm.via_embedding_hom Equiv.Perm.viaEmbeddingHom
-/
+#print Equiv.Perm.viaEmbeddingHom_apply /-
theorem viaEmbeddingHom_apply : viaEmbeddingHom ι e = viaEmbedding e ι :=
rfl
#align equiv.perm.via_embedding_hom_apply Equiv.Perm.viaEmbeddingHom_apply
+-/
+#print Equiv.Perm.viaEmbeddingHom_injective /-
theorem viaEmbeddingHom_injective : Function.Injective (viaEmbeddingHom ι) :=
extendDomainHom_injective (ofInjective ι.1 ι.2)
#align equiv.perm.via_embedding_hom_injective Equiv.Perm.viaEmbeddingHom_injective
+-/
end Perm
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -27,7 +27,7 @@ namespace Perm
variable (e : Perm α) (ι : α ↪ β)
-open Classical
+open scoped Classical
#print Equiv.Perm.viaEmbedding /-
/-- Noncomputable version of `equiv.perm.via_fintype_embedding` that does not assume `fintype` -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -55,22 +55,10 @@ noncomputable def viaEmbeddingHom : Perm α →* Perm β :=
#align equiv.perm.via_embedding_hom Equiv.Perm.viaEmbeddingHom
-/
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theorem viaEmbeddingHom_apply : viaEmbeddingHom ι e = viaEmbedding e ι :=
rfl
#align equiv.perm.via_embedding_hom_apply Equiv.Perm.viaEmbeddingHom_apply
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theorem viaEmbeddingHom_injective : Function.Injective (viaEmbeddingHom ι) :=
extendDomainHom_injective (ofInjective ι.1 ι.2)
#align equiv.perm.via_embedding_hom_injective Equiv.Perm.viaEmbeddingHom_injective
mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4
@@ -59,7 +59,7 @@ noncomputable def viaEmbeddingHom : Perm α →* Perm β :=
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but is expected to have type
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+ forall {α : Type.{u1}} {β : Type.{u2}} (e : Equiv.Perm.{succ u1} α) (ι : Function.Embedding.{succ u1, succ u2} α β), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} α) => Equiv.Perm.{succ u2} β) e) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.Perm.{succ u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} α) => Equiv.Perm.{succ u2} β) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (MulOneClass.toMul.{u2} (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β)))) (MonoidHom.monoidHomClass.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))))) (Equiv.Perm.viaEmbeddingHom.{u1, u2} α β ι) e) (Equiv.Perm.viaEmbedding.{u1, u2} α β e ι)
Case conversion may be inaccurate. Consider using '#align equiv.perm.via_embedding_hom_apply Equiv.Perm.viaEmbeddingHom_applyₓ'. -/
theorem viaEmbeddingHom_apply : viaEmbeddingHom ι e = viaEmbedding e ι :=
rfl
@@ -69,7 +69,7 @@ theorem viaEmbeddingHom_apply : viaEmbeddingHom ι e = viaEmbedding e ι :=
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} (ι : Function.Embedding.{succ u1, succ u2} α β), Function.Injective.{succ u1, succ u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (fun (_x : MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) => (Equiv.Perm.{succ u1} α) -> (Equiv.Perm.{succ u2} β)) (MonoidHom.hasCoeToFun.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.viaEmbeddingHom.{u1, u2} α β ι))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} (ι : Function.Embedding.{succ u2, succ u1} α β), Function.Injective.{succ u2, succ u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (Equiv.Perm.{succ u2} α) (fun (_x : Equiv.Perm.{succ u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u2} α) => Equiv.Perm.{succ u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (MulOneClass.toMul.{u2} (Equiv.Perm.{succ u2} α) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α))))) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β)))) (MonoidHom.monoidHomClass.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))))) (Equiv.Perm.viaEmbeddingHom.{u2, u1} α β ι))
+ forall {α : Type.{u2}} {β : Type.{u1}} (ι : Function.Embedding.{succ u2, succ u1} α β), Function.Injective.{succ u2, succ u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (Equiv.Perm.{succ u2} α) (fun (_x : Equiv.Perm.{succ u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u2} α) => Equiv.Perm.{succ u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (MulOneClass.toMul.{u2} (Equiv.Perm.{succ u2} α) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α))))) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β)))) (MonoidHom.monoidHomClass.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))))) (Equiv.Perm.viaEmbeddingHom.{u2, u1} α β ι))
Case conversion may be inaccurate. Consider using '#align equiv.perm.via_embedding_hom_injective Equiv.Perm.viaEmbeddingHom_injectiveₓ'. -/
theorem viaEmbeddingHom_injective : Function.Injective (viaEmbeddingHom ι) :=
extendDomainHom_injective (ofInjective ι.1 ι.2)
mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212
@@ -59,7 +59,7 @@ noncomputable def viaEmbeddingHom : Perm α →* Perm β :=
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} (e : Equiv.Perm.{succ u1} α) (ι : Function.Embedding.{succ u1, succ u2} α β), Eq.{succ u2} (Equiv.Perm.{succ u2} β) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (fun (_x : MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) => (Equiv.Perm.{succ u1} α) -> (Equiv.Perm.{succ u2} β)) (MonoidHom.hasCoeToFun.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.viaEmbeddingHom.{u1, u2} α β ι) e) (Equiv.Perm.viaEmbedding.{u1, u2} α β e ι)
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} (e : Equiv.Perm.{succ u1} α) (ι : Function.Embedding.{succ u1, succ u2} α β), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Equiv.Perm.{succ u1} α) => Equiv.Perm.{succ u2} β) e) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.Perm.{succ u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Equiv.Perm.{succ u1} α) => Equiv.Perm.{succ u2} β) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (MulOneClass.toMul.{u2} (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β)))) (MonoidHom.monoidHomClass.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))))) (Equiv.Perm.viaEmbeddingHom.{u1, u2} α β ι) e) (Equiv.Perm.viaEmbedding.{u1, u2} α β e ι)
+ forall {α : Type.{u1}} {β : Type.{u2}} (e : Equiv.Perm.{succ u1} α) (ι : Function.Embedding.{succ u1, succ u2} α β), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} α) => Equiv.Perm.{succ u2} β) e) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.Perm.{succ u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} α) => Equiv.Perm.{succ u2} β) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (MulOneClass.toMul.{u2} (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β)))) (MonoidHom.monoidHomClass.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))))) (Equiv.Perm.viaEmbeddingHom.{u1, u2} α β ι) e) (Equiv.Perm.viaEmbedding.{u1, u2} α β e ι)
Case conversion may be inaccurate. Consider using '#align equiv.perm.via_embedding_hom_apply Equiv.Perm.viaEmbeddingHom_applyₓ'. -/
theorem viaEmbeddingHom_apply : viaEmbeddingHom ι e = viaEmbedding e ι :=
rfl
@@ -69,7 +69,7 @@ theorem viaEmbeddingHom_apply : viaEmbeddingHom ι e = viaEmbedding e ι :=
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} (ι : Function.Embedding.{succ u1, succ u2} α β), Function.Injective.{succ u1, succ u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (fun (_x : MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) => (Equiv.Perm.{succ u1} α) -> (Equiv.Perm.{succ u2} β)) (MonoidHom.hasCoeToFun.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.viaEmbeddingHom.{u1, u2} α β ι))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} (ι : Function.Embedding.{succ u2, succ u1} α β), Function.Injective.{succ u2, succ u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (Equiv.Perm.{succ u2} α) (fun (_x : Equiv.Perm.{succ u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Equiv.Perm.{succ u2} α) => Equiv.Perm.{succ u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (MulOneClass.toMul.{u2} (Equiv.Perm.{succ u2} α) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α))))) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β)))) (MonoidHom.monoidHomClass.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))))) (Equiv.Perm.viaEmbeddingHom.{u2, u1} α β ι))
+ forall {α : Type.{u2}} {β : Type.{u1}} (ι : Function.Embedding.{succ u2, succ u1} α β), Function.Injective.{succ u2, succ u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (Equiv.Perm.{succ u2} α) (fun (_x : Equiv.Perm.{succ u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u2} α) => Equiv.Perm.{succ u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (MulOneClass.toMul.{u2} (Equiv.Perm.{succ u2} α) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α))))) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β)))) (MonoidHom.monoidHomClass.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))))) (Equiv.Perm.viaEmbeddingHom.{u2, u1} α β ι))
Case conversion may be inaccurate. Consider using '#align equiv.perm.via_embedding_hom_injective Equiv.Perm.viaEmbeddingHom_injectiveₓ'. -/
theorem viaEmbeddingHom_injective : Function.Injective (viaEmbeddingHom ι) :=
extendDomainHom_injective (ofInjective ι.1 ι.2)
mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5
@@ -59,7 +59,7 @@ noncomputable def viaEmbeddingHom : Perm α →* Perm β :=
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} (e : Equiv.Perm.{succ u1} α) (ι : Function.Embedding.{succ u1, succ u2} α β), Eq.{succ u2} (Equiv.Perm.{succ u2} β) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (fun (_x : MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) => (Equiv.Perm.{succ u1} α) -> (Equiv.Perm.{succ u2} β)) (MonoidHom.hasCoeToFun.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.viaEmbeddingHom.{u1, u2} α β ι) e) (Equiv.Perm.viaEmbedding.{u1, u2} α β e ι)
but is expected to have type
- forall {α : Type.{u1}} {β : Type.{u2}} (e : Equiv.Perm.{succ u1} α) (ι : Function.Embedding.{succ u1, succ u2} α β), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Equiv.Perm.{succ u1} α) => Equiv.Perm.{succ u2} β) e) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.Perm.{succ u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Equiv.Perm.{succ u1} α) => Equiv.Perm.{succ u2} β) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (MulOneClass.toMul.{u2} (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β)))) (MonoidHom.monoidHomClass.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))))) (Equiv.Perm.viaEmbeddingHom.{u1, u2} α β ι) e) (Equiv.Perm.viaEmbedding.{u1, u2} α β e ι)
+ forall {α : Type.{u1}} {β : Type.{u2}} (e : Equiv.Perm.{succ u1} α) (ι : Function.Embedding.{succ u1, succ u2} α β), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Equiv.Perm.{succ u1} α) => Equiv.Perm.{succ u2} β) e) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.{succ u1} α) (fun (_x : Equiv.Perm.{succ u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Equiv.Perm.{succ u1} α) => Equiv.Perm.{succ u2} β) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} α) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α))))) (MulOneClass.toMul.{u2} (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β)))) (MonoidHom.monoidHomClass.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))))) (Equiv.Perm.viaEmbeddingHom.{u1, u2} α β ι) e) (Equiv.Perm.viaEmbedding.{u1, u2} α β e ι)
Case conversion may be inaccurate. Consider using '#align equiv.perm.via_embedding_hom_apply Equiv.Perm.viaEmbeddingHom_applyₓ'. -/
theorem viaEmbeddingHom_apply : viaEmbeddingHom ι e = viaEmbedding e ι :=
rfl
@@ -69,7 +69,7 @@ theorem viaEmbeddingHom_apply : viaEmbeddingHom ι e = viaEmbedding e ι :=
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} (ι : Function.Embedding.{succ u1, succ u2} α β), Function.Injective.{succ u1, succ u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (fun (_x : MonoidHom.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) => (Equiv.Perm.{succ u1} α) -> (Equiv.Perm.{succ u2} β)) (MonoidHom.hasCoeToFun.{u1, u2} (Equiv.Perm.{succ u1} α) (Equiv.Perm.{succ u2} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} α) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} α) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} α) (Equiv.Perm.permGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} β) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} β) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} β) (Equiv.Perm.permGroup.{u2} β))))) (Equiv.Perm.viaEmbeddingHom.{u1, u2} α β ι))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} (ι : Function.Embedding.{succ u2, succ u1} α β), Function.Injective.{succ u2, succ u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (Equiv.Perm.{succ u2} α) (fun (_x : Equiv.Perm.{succ u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Equiv.Perm.{succ u2} α) => Equiv.Perm.{succ u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (MulOneClass.toMul.{u2} (Equiv.Perm.{succ u2} α) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α))))) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β)))) (MonoidHom.monoidHomClass.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))))) (Equiv.Perm.viaEmbeddingHom.{u2, u1} α β ι))
+ forall {α : Type.{u2}} {β : Type.{u1}} (ι : Function.Embedding.{succ u2, succ u1} α β), Function.Injective.{succ u2, succ u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (Equiv.Perm.{succ u2} α) (fun (_x : Equiv.Perm.{succ u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Equiv.Perm.{succ u2} α) => Equiv.Perm.{succ u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (MulOneClass.toMul.{u2} (Equiv.Perm.{succ u2} α) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α))))) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))) (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β)))) (MonoidHom.monoidHomClass.{u2, u1} (Equiv.Perm.{succ u2} α) (Equiv.Perm.{succ u1} β) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} α) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} α) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} α) (Equiv.Perm.permGroup.{u2} α)))) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} β) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} β) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} β) (Equiv.Perm.permGroup.{u1} β))))))) (Equiv.Perm.viaEmbeddingHom.{u2, u1} α β ι))
Case conversion may be inaccurate. Consider using '#align equiv.perm.via_embedding_hom_injective Equiv.Perm.viaEmbeddingHom_injectiveₓ'. -/
theorem viaEmbeddingHom_injective : Function.Injective (viaEmbeddingHom ι) :=
extendDomainHom_injective (ofInjective ι.1 ι.2)
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
open Classical
(#11199)
We remove all but one open Classical
s, instead preferring to use open scoped Classical
. The only real side-effect this led to is moving a couple declarations to use Exists.choose
instead of Classical.choose
.
The first few commits are explicitly labelled regex replaces for ease of review.
@@ -21,7 +21,7 @@ namespace Perm
variable (e : Perm α) (ι : α ↪ β)
-open Classical
+open scoped Classical
/-- Noncomputable version of `Equiv.Perm.viaFintypeEmbedding` that does not assume `Fintype` -/
noncomputable def viaEmbedding : Perm β :=
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -13,7 +13,7 @@ import Mathlib.Logic.Equiv.Set
-/
-variable {α β : Type _}
+variable {α β : Type*}
namespace Equiv
@@ -2,15 +2,12 @@
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Mario Carneiro
-
-! This file was ported from Lean 3 source module group_theory.perm.via_embedding
-! leanprover-community/mathlib commit 9116dd6709f303dcf781632e15fdef382b0fc579
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.GroupTheory.Perm.Basic
import Mathlib.Logic.Equiv.Set
+#align_import group_theory.perm.via_embedding from "leanprover-community/mathlib"@"9116dd6709f303dcf781632e15fdef382b0fc579"
+
/-!
# `Equiv.Perm.viaEmbedding`, a noncomputable analogue of `Equiv.Perm.viaFintypeEmbedding`.
-/
The unported dependencies are