logic.equiv.fintype
⟷
Mathlib.Logic.Equiv.Fintype
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
@@ -3,9 +3,9 @@ Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
-import Mathbin.Data.Fintype.Basic
-import Mathbin.GroupTheory.Perm.Sign
-import Mathbin.Logic.Equiv.Defs
+import Data.Fintype.Basic
+import GroupTheory.Perm.Sign
+import Logic.Equiv.Defs
#align_import logic.equiv.fintype from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,16 +2,13 @@
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-
-! This file was ported from Lean 3 source module logic.equiv.fintype
-! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.Fintype.Basic
import Mathbin.GroupTheory.Perm.Sign
import Mathbin.Logic.Equiv.Defs
+#align_import logic.equiv.fintype from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"
+
/-! # Equivalence between fintypes
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -55,14 +55,18 @@ theorem Function.Embedding.toEquivRange_apply (a : α) :
#align function.embedding.to_equiv_range_apply Function.Embedding.toEquivRange_apply
-/
+#print Function.Embedding.toEquivRange_symm_apply_self /-
@[simp]
theorem Function.Embedding.toEquivRange_symm_apply_self (a : α) :
f.toEquivRange.symm ⟨f a, Set.mem_range_self a⟩ = a := by simp [Equiv.symm_apply_eq]
#align function.embedding.to_equiv_range_symm_apply_self Function.Embedding.toEquivRange_symm_apply_self
+-/
+#print Function.Embedding.toEquivRange_eq_ofInjective /-
theorem Function.Embedding.toEquivRange_eq_ofInjective :
f.toEquivRange = Equiv.ofInjective f f.Injective := by ext; simp
#align function.embedding.to_equiv_range_eq_of_injective Function.Embedding.toEquivRange_eq_ofInjective
+-/
#print Equiv.Perm.viaFintypeEmbedding /-
/-- Extend the domain of `e : equiv.perm α`, mapping it through `f : α ↪ β`.
@@ -101,11 +105,13 @@ theorem Equiv.Perm.viaFintypeEmbedding_apply_not_mem_range {b : β} (h : b ∉ S
#align equiv.perm.via_fintype_embedding_apply_not_mem_range Equiv.Perm.viaFintypeEmbedding_apply_not_mem_range
-/
+#print Equiv.Perm.viaFintypeEmbedding_sign /-
@[simp]
theorem Equiv.Perm.viaFintypeEmbedding_sign [DecidableEq α] [Fintype β] :
Equiv.Perm.sign (e.viaFintypeEmbedding f) = Equiv.Perm.sign e := by
simp [Equiv.Perm.viaFintypeEmbedding]
#align equiv.perm.via_fintype_embedding_sign Equiv.Perm.viaFintypeEmbedding_sign
+-/
namespace Equiv
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -146,7 +146,7 @@ theorem extendSubtype_apply_of_mem (e : { x // p x } ≃ { x // q x }) (x) (hx :
#print Equiv.extendSubtype_mem /-
theorem extendSubtype_mem (e : { x // p x } ≃ { x // q x }) (x) (hx : p x) :
q (e.extendSubtype x) := by
- convert(e ⟨x, hx⟩).2
+ convert (e ⟨x, hx⟩).2
rw [e.extend_subtype_apply_of_mem _ hx, Subtype.val_eq_coe]
#align equiv.extend_subtype_mem Equiv.extendSubtype_mem
-/
@@ -164,7 +164,7 @@ theorem extendSubtype_apply_of_not_mem (e : { x // p x } ≃ { x // q x }) (x) (
#print Equiv.extendSubtype_not_mem /-
theorem extendSubtype_not_mem (e : { x // p x } ≃ { x // q x }) (x) (hx : ¬p x) :
¬q (e.extendSubtype x) := by
- convert(e.to_compl ⟨x, hx⟩).2
+ convert (e.to_compl ⟨x, hx⟩).2
rw [e.extend_subtype_apply_of_not_mem _ hx, Subtype.val_eq_coe]
#align equiv.extend_subtype_not_mem Equiv.extendSubtype_not_mem
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -55,23 +55,11 @@ theorem Function.Embedding.toEquivRange_apply (a : α) :
#align function.embedding.to_equiv_range_apply Function.Embedding.toEquivRange_apply
-/
-/- warning: function.embedding.to_equiv_range_symm_apply_self -> Function.Embedding.toEquivRange_symm_apply_self is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u2} β] (f : Function.Embedding.{succ u1, succ u2} α β) (a : α), Eq.{succ u1} α (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f))) α) (fun (_x : Equiv.{succ u2, succ u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f))) α) => (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f))) -> α) (Equiv.hasCoeToFun.{succ u2, succ u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f))) α) (Equiv.symm.{succ u1, succ u2} α (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f))) (Function.Embedding.toEquivRange.{u1, u2} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) f)) (Subtype.mk.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Set.range.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f))) (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f a) (Set.mem_range_self.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f) a))) a
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@[simp]
theorem Function.Embedding.toEquivRange_symm_apply_self (a : α) :
f.toEquivRange.symm ⟨f a, Set.mem_range_self a⟩ = a := by simp [Equiv.symm_apply_eq]
#align function.embedding.to_equiv_range_symm_apply_self Function.Embedding.toEquivRange_symm_apply_self
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theorem Function.Embedding.toEquivRange_eq_ofInjective :
f.toEquivRange = Equiv.ofInjective f f.Injective := by ext; simp
#align function.embedding.to_equiv_range_eq_of_injective Function.Embedding.toEquivRange_eq_ofInjective
@@ -113,12 +101,6 @@ theorem Equiv.Perm.viaFintypeEmbedding_apply_not_mem_range {b : β} (h : b ∉ S
#align equiv.perm.via_fintype_embedding_apply_not_mem_range Equiv.Perm.viaFintypeEmbedding_apply_not_mem_range
-/
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@[simp]
theorem Equiv.Perm.viaFintypeEmbedding_sign [DecidableEq α] [Fintype β] :
Equiv.Perm.sign (e.viaFintypeEmbedding f) = Equiv.Perm.sign e := by
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -73,10 +73,7 @@ but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Fintype.{u2} α] [_inst_2 : DecidableEq.{succ u1} β] (f : Function.Embedding.{succ u2, succ u1} α β), Eq.{max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} α (Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f)))) (Function.Embedding.toEquivRange.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) f) (Equiv.ofInjective.{succ u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f) (Function.Embedding.injective.{succ u1, succ u2} α β f))
Case conversion may be inaccurate. Consider using '#align function.embedding.to_equiv_range_eq_of_injective Function.Embedding.toEquivRange_eq_ofInjectiveₓ'. -/
theorem Function.Embedding.toEquivRange_eq_ofInjective :
- f.toEquivRange = Equiv.ofInjective f f.Injective :=
- by
- ext
- simp
+ f.toEquivRange = Equiv.ofInjective f f.Injective := by ext; simp
#align function.embedding.to_equiv_range_eq_of_injective Function.Embedding.toEquivRange_eq_ofInjective
#print Equiv.Perm.viaFintypeEmbedding /-
mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4
@@ -59,7 +59,7 @@ theorem Function.Embedding.toEquivRange_apply (a : α) :
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u2} β] (f : Function.Embedding.{succ u1, succ u2} α β) (a : α), Eq.{succ u1} α (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f))) α) (fun (_x : Equiv.{succ u2, succ u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f))) α) => (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f))) -> α) (Equiv.hasCoeToFun.{succ u2, succ u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f))) α) (Equiv.symm.{succ u1, succ u2} α (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f))) (Function.Embedding.toEquivRange.{u1, u2} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) f)) (Subtype.mk.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Set.range.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f))) (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f a) (Set.mem_range_self.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f) a))) a
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Fintype.{u2} α] [_inst_2 : DecidableEq.{succ u1} β] (f : Function.Embedding.{succ u2, succ u1} α β) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) => α) (Subtype.mk.{succ u1} β (fun (x : β) => Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f a) (Set.mem_range_self.{succ u2, u1} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f) a))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Equiv.{succ u1, succ u2} (Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) α) (Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) (fun (_x : Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u2} (Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) α) (Equiv.symm.{succ u2, succ u1} α (Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) (Function.Embedding.toEquivRange.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) f)) (Subtype.mk.{succ u1} β (fun (x : β) => Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f a) (Set.mem_range_self.{succ u2, u1} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f) a))) a
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Fintype.{u2} α] [_inst_2 : DecidableEq.{succ u1} β] (f : Function.Embedding.{succ u2, succ u1} α β) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) => α) (Subtype.mk.{succ u1} β (fun (x : β) => Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ 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(fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u2} (Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) α) (Equiv.symm.{succ u2, succ u1} α (Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) (Function.Embedding.toEquivRange.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) f)) (Subtype.mk.{succ u1} β (fun (x : β) => Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f a) (Set.mem_range_self.{succ u2, u1} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f) a))) a
Case conversion may be inaccurate. Consider using '#align function.embedding.to_equiv_range_symm_apply_self Function.Embedding.toEquivRange_symm_apply_selfₓ'. -/
@[simp]
theorem Function.Embedding.toEquivRange_symm_apply_self (a : α) :
@@ -120,7 +120,7 @@ theorem Equiv.Perm.viaFintypeEmbedding_apply_not_mem_range {b : β} (h : b ∉ S
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u2} β] (e : Equiv.Perm.{succ u1} α) (f : Function.Embedding.{succ u1, succ u2} α β) [_inst_3 : DecidableEq.{succ u1} α] [_inst_4 : Fintype.{u2} β], Eq.{1} (Units.{0} Int Int.monoid) (coeFn.{succ u2, succ u2} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} β) (Units.{0} Int Int.monoid) (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)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} β) (Units.{0} Int Int.monoid) (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)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u2} β) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u2, 0} (Equiv.Perm.{succ u2} β) (Units.{0} Int Int.monoid) (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)))) (Units.mulOneClass.{0} Int Int.monoid)) (Equiv.Perm.sign.{u2} β (fun (a : β) (b : β) => _inst_2 a b) _inst_4) (Equiv.Perm.viaFintypeEmbedding.{u1, u2} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) e f)) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.monoid) (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)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.monoid) (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)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u1} α) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.monoid) (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)))) (Units.mulOneClass.{0} Int Int.monoid)) (Equiv.Perm.sign.{u1} α (fun (a : α) (b : α) => _inst_3 a b) _inst_1) e)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Fintype.{u2} α] [_inst_2 : DecidableEq.{succ u1} β] (e : Equiv.Perm.{succ u2} α) (f : Function.Embedding.{succ u2, succ u1} α β) [_inst_3 : DecidableEq.{succ u2} α] [_inst_4 : Fintype.{u1} β], Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} β) => Units.{0} Int Int.instMonoidInt) (Equiv.Perm.viaFintypeEmbedding.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) e f)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (fun (_x : Equiv.Perm.{succ u1} β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} β) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} β (fun (a : β) (b : β) => _inst_2 a b) _inst_4) (Equiv.Perm.viaFintypeEmbedding.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) e f)) (FunLike.coe.{succ u2, succ u2, 1} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (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) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u2, u2, 0} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u2, u2, 0} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u2} α (fun (a : α) (b : α) => _inst_3 a b) _inst_1) e)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Fintype.{u2} α] [_inst_2 : DecidableEq.{succ u1} β] (e : Equiv.Perm.{succ u2} α) (f : Function.Embedding.{succ u2, succ u1} α β) [_inst_3 : DecidableEq.{succ u2} α] [_inst_4 : Fintype.{u1} β], Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} β) => Units.{0} Int Int.instMonoidInt) (Equiv.Perm.viaFintypeEmbedding.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) e f)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (fun (_x : Equiv.Perm.{succ u1} β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} β) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} β (fun (a : β) (b : β) => _inst_2 a b) _inst_4) (Equiv.Perm.viaFintypeEmbedding.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) e f)) (FunLike.coe.{succ u2, succ u2, 1} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (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) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u2, u2, 0} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u2, u2, 0} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u2} α (fun (a : α) (b : α) => _inst_3 a b) _inst_1) e)
Case conversion may be inaccurate. Consider using '#align equiv.perm.via_fintype_embedding_sign Equiv.Perm.viaFintypeEmbedding_signₓ'. -/
@[simp]
theorem Equiv.Perm.viaFintypeEmbedding_sign [DecidableEq α] [Fintype β] :
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d
@@ -167,7 +167,7 @@ theorem extendSubtype_apply_of_mem (e : { x // p x } ≃ { x // q x }) (x) (hx :
#print Equiv.extendSubtype_mem /-
theorem extendSubtype_mem (e : { x // p x } ≃ { x // q x }) (x) (hx : p x) :
q (e.extendSubtype x) := by
- convert (e ⟨x, hx⟩).2
+ convert(e ⟨x, hx⟩).2
rw [e.extend_subtype_apply_of_mem _ hx, Subtype.val_eq_coe]
#align equiv.extend_subtype_mem Equiv.extendSubtype_mem
-/
@@ -185,7 +185,7 @@ theorem extendSubtype_apply_of_not_mem (e : { x // p x } ≃ { x // q x }) (x) (
#print Equiv.extendSubtype_not_mem /-
theorem extendSubtype_not_mem (e : { x // p x } ≃ { x // q x }) (x) (hx : ¬p x) :
¬q (e.extendSubtype x) := by
- convert (e.to_compl ⟨x, hx⟩).2
+ convert(e.to_compl ⟨x, hx⟩).2
rw [e.extend_subtype_apply_of_not_mem _ hx, Subtype.val_eq_coe]
#align equiv.extend_subtype_not_mem Equiv.extendSubtype_not_mem
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212
@@ -59,7 +59,7 @@ theorem Function.Embedding.toEquivRange_apply (a : α) :
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u2} β] (f : Function.Embedding.{succ u1, succ u2} α β) (a : α), Eq.{succ u1} α (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f))) α) (fun (_x : Equiv.{succ u2, succ u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f))) α) => (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f))) -> α) (Equiv.hasCoeToFun.{succ u2, succ u1} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f))) α) (Equiv.symm.{succ u1, succ u2} α (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f))) (Function.Embedding.toEquivRange.{u1, u2} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) f)) (Subtype.mk.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Set.range.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f))) (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f a) (Set.mem_range_self.{u2, succ u1} β α (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} α β) (fun (_x : Function.Embedding.{succ u1, succ u2} α β) => α -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} α β) f) a))) a
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Fintype.{u2} α] [_inst_2 : DecidableEq.{succ u1} β] (f : Function.Embedding.{succ u2, succ u1} α β) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) => α) (Subtype.mk.{succ u1} β (fun (x : β) => Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f a) (Set.mem_range_self.{succ u2, u1} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f) a))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Equiv.{succ u1, succ u2} (Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) α) (Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) (fun (_x : Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u2} (Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) α) (Equiv.symm.{succ u2, succ u1} α (Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) (Function.Embedding.toEquivRange.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) f)) (Subtype.mk.{succ u1} β (fun (x : β) => Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f a) (Set.mem_range_self.{succ u2, u1} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f) a))) a
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Fintype.{u2} α] [_inst_2 : DecidableEq.{succ u1} β] (f : Function.Embedding.{succ u2, succ u1} α β) (a : α), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) => α) (Subtype.mk.{succ u1} β (fun (x : β) => Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f a) (Set.mem_range_self.{succ u2, u1} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f) a))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Equiv.{succ u1, succ u2} (Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) α) (Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) (fun (_x : Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (a : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u2} (Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) α) (Equiv.symm.{succ u2, succ u1} α (Set.Elem.{u1} β (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) (Function.Embedding.toEquivRange.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) f)) (Subtype.mk.{succ u1} β (fun (x : β) => Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Set.range.{u1, succ u2} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f a) (Set.mem_range_self.{succ u2, u1} β α (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) f) a))) a
Case conversion may be inaccurate. Consider using '#align function.embedding.to_equiv_range_symm_apply_self Function.Embedding.toEquivRange_symm_apply_selfₓ'. -/
@[simp]
theorem Function.Embedding.toEquivRange_symm_apply_self (a : α) :
@@ -120,7 +120,7 @@ theorem Equiv.Perm.viaFintypeEmbedding_apply_not_mem_range {b : β} (h : b ∉ S
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u2} β] (e : Equiv.Perm.{succ u1} α) (f : Function.Embedding.{succ u1, succ u2} α β) [_inst_3 : DecidableEq.{succ u1} α] [_inst_4 : Fintype.{u2} β], Eq.{1} (Units.{0} Int Int.monoid) (coeFn.{succ u2, succ u2} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} β) (Units.{0} Int Int.monoid) (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)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} β) (Units.{0} Int Int.monoid) (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)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u2} β) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u2, 0} (Equiv.Perm.{succ u2} β) (Units.{0} Int Int.monoid) (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)))) (Units.mulOneClass.{0} Int Int.monoid)) (Equiv.Perm.sign.{u2} β (fun (a : β) (b : β) => _inst_2 a b) _inst_4) (Equiv.Perm.viaFintypeEmbedding.{u1, u2} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) e f)) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.monoid) (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)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.monoid) (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)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u1} α) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.monoid) (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)))) (Units.mulOneClass.{0} Int Int.monoid)) (Equiv.Perm.sign.{u1} α (fun (a : α) (b : α) => _inst_3 a b) _inst_1) e)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Fintype.{u2} α] [_inst_2 : DecidableEq.{succ u1} β] (e : Equiv.Perm.{succ u2} α) (f : Function.Embedding.{succ u2, succ u1} α β) [_inst_3 : DecidableEq.{succ u2} α] [_inst_4 : Fintype.{u1} β], Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Equiv.Perm.{succ u1} β) => Units.{0} Int Int.instMonoidInt) (Equiv.Perm.viaFintypeEmbedding.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) e f)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (fun (_x : Equiv.Perm.{succ u1} β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Equiv.Perm.{succ u1} β) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} β (fun (a : β) (b : β) => _inst_2 a b) _inst_4) (Equiv.Perm.viaFintypeEmbedding.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) e f)) (FunLike.coe.{succ u2, succ u2, 1} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (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) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u2, u2, 0} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u2, u2, 0} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u2} α (fun (a : α) (b : α) => _inst_3 a b) _inst_1) e)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Fintype.{u2} α] [_inst_2 : DecidableEq.{succ u1} β] (e : Equiv.Perm.{succ u2} α) (f : Function.Embedding.{succ u2, succ u1} α β) [_inst_3 : DecidableEq.{succ u2} α] [_inst_4 : Fintype.{u1} β], Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} β) => Units.{0} Int Int.instMonoidInt) (Equiv.Perm.viaFintypeEmbedding.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) e f)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (fun (_x : Equiv.Perm.{succ u1} β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} β) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} β (fun (a : β) (b : β) => _inst_2 a b) _inst_4) (Equiv.Perm.viaFintypeEmbedding.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) e f)) (FunLike.coe.{succ u2, succ u2, 1} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (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) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u2, u2, 0} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u2, u2, 0} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u2} α (fun (a : α) (b : α) => _inst_3 a b) _inst_1) e)
Case conversion may be inaccurate. Consider using '#align equiv.perm.via_fintype_embedding_sign Equiv.Perm.viaFintypeEmbedding_signₓ'. -/
@[simp]
theorem Equiv.Perm.viaFintypeEmbedding_sign [DecidableEq α] [Fintype β] :
mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5
@@ -120,7 +120,7 @@ theorem Equiv.Perm.viaFintypeEmbedding_apply_not_mem_range {b : β} (h : b ∉ S
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Fintype.{u1} α] [_inst_2 : DecidableEq.{succ u2} β] (e : Equiv.Perm.{succ u1} α) (f : Function.Embedding.{succ u1, succ u2} α β) [_inst_3 : DecidableEq.{succ u1} α] [_inst_4 : Fintype.{u2} β], Eq.{1} (Units.{0} Int Int.monoid) (coeFn.{succ u2, succ u2} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} β) (Units.{0} Int Int.monoid) (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)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} β) (Units.{0} Int Int.monoid) (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)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u2} β) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u2, 0} (Equiv.Perm.{succ u2} β) (Units.{0} Int Int.monoid) (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)))) (Units.mulOneClass.{0} Int Int.monoid)) (Equiv.Perm.sign.{u2} β (fun (a : β) (b : β) => _inst_2 a b) _inst_4) (Equiv.Perm.viaFintypeEmbedding.{u1, u2} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) e f)) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.monoid) (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)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.monoid) (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)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u1} α) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u1, 0} (Equiv.Perm.{succ u1} α) (Units.{0} Int Int.monoid) (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)))) (Units.mulOneClass.{0} Int Int.monoid)) (Equiv.Perm.sign.{u1} α (fun (a : α) (b : α) => _inst_3 a b) _inst_1) e)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Fintype.{u2} α] [_inst_2 : DecidableEq.{succ u1} β] (e : Equiv.Perm.{succ u2} α) (f : Function.Embedding.{succ u2, succ u1} α β) [_inst_3 : DecidableEq.{succ u2} α] [_inst_4 : Fintype.{u1} β], Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Equiv.Perm.{succ u1} β) => Units.{0} Int Int.instMonoidInt) (Equiv.Perm.viaFintypeEmbedding.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) e f)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (fun (_x : Equiv.Perm.{succ u1} β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Equiv.Perm.{succ u1} β) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} β (fun (a : β) (b : β) => _inst_2 a b) _inst_4) (Equiv.Perm.viaFintypeEmbedding.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) e f)) (FunLike.coe.{succ u2, succ u2, 1} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (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) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u2, u2, 0} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u2, u2, 0} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u2} α (fun (a : α) (b : α) => _inst_3 a b) _inst_1) e)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Fintype.{u2} α] [_inst_2 : DecidableEq.{succ u1} β] (e : Equiv.Perm.{succ u2} α) (f : Function.Embedding.{succ u2, succ u1} α β) [_inst_3 : DecidableEq.{succ u2} α] [_inst_4 : Fintype.{u1} β], Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Equiv.Perm.{succ u1} β) => Units.{0} Int Int.instMonoidInt) (Equiv.Perm.viaFintypeEmbedding.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) e f)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (fun (_x : Equiv.Perm.{succ u1} β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Equiv.Perm.{succ u1} β) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} β (fun (a : β) (b : β) => _inst_2 a b) _inst_4) (Equiv.Perm.viaFintypeEmbedding.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) e f)) (FunLike.coe.{succ u2, succ u2, 1} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (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) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u2, u2, 0} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u2, u2, 0} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u2} α (fun (a : α) (b : α) => _inst_3 a b) _inst_1) e)
Case conversion may be inaccurate. Consider using '#align equiv.perm.via_fintype_embedding_sign Equiv.Perm.viaFintypeEmbedding_signₓ'. -/
@[simp]
theorem Equiv.Perm.viaFintypeEmbedding_sign [DecidableEq α] [Fintype β] :
mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
! This file was ported from Lean 3 source module logic.equiv.fintype
-! leanprover-community/mathlib commit 9407b03373c8cd201df99d6bc5514fc2db44054f
+! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.Logic.Equiv.Defs
/-! # Equivalence between fintypes
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
This file contains some basic results on equivalences where one or both
sides of the equivalence are `fintype`s.
mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee
@@ -33,6 +33,7 @@ sides of the equivalence are `fintype`s.
variable {α β : Type _} [Fintype α] [DecidableEq β] (e : Equiv.Perm α) (f : α ↪ β)
+#print Function.Embedding.toEquivRange /-
/-- Computably turn an embedding `f : α ↪ β` into an equiv `α ≃ set.range f`,
if `α` is a `fintype`. Has poor computational performance, due to exhaustive searching in
constructed inverse. When a better inverse is known, use `equiv.of_left_inverse'` or
@@ -41,18 +42,33 @@ constructed inverse. When a better inverse is known, use `equiv.of_left_inverse'
def Function.Embedding.toEquivRange : α ≃ Set.range f :=
⟨fun a => ⟨f a, Set.mem_range_self a⟩, f.invOfMemRange, fun _ => by simp, fun _ => by simp⟩
#align function.embedding.to_equiv_range Function.Embedding.toEquivRange
+-/
+#print Function.Embedding.toEquivRange_apply /-
@[simp]
theorem Function.Embedding.toEquivRange_apply (a : α) :
f.toEquivRange a = ⟨f a, Set.mem_range_self a⟩ :=
rfl
#align function.embedding.to_equiv_range_apply Function.Embedding.toEquivRange_apply
+-/
+/- warning: function.embedding.to_equiv_range_symm_apply_self -> Function.Embedding.toEquivRange_symm_apply_self is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align function.embedding.to_equiv_range_symm_apply_self Function.Embedding.toEquivRange_symm_apply_selfₓ'. -/
@[simp]
theorem Function.Embedding.toEquivRange_symm_apply_self (a : α) :
f.toEquivRange.symm ⟨f a, Set.mem_range_self a⟩ = a := by simp [Equiv.symm_apply_eq]
#align function.embedding.to_equiv_range_symm_apply_self Function.Embedding.toEquivRange_symm_apply_self
+/- warning: function.embedding.to_equiv_range_eq_of_injective -> Function.Embedding.toEquivRange_eq_ofInjective is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align function.embedding.to_equiv_range_eq_of_injective Function.Embedding.toEquivRange_eq_ofInjectiveₓ'. -/
theorem Function.Embedding.toEquivRange_eq_ofInjective :
f.toEquivRange = Equiv.ofInjective f f.Injective :=
by
@@ -60,6 +76,7 @@ theorem Function.Embedding.toEquivRange_eq_ofInjective :
simp
#align function.embedding.to_equiv_range_eq_of_injective Function.Embedding.toEquivRange_eq_ofInjective
+#print Equiv.Perm.viaFintypeEmbedding /-
/-- Extend the domain of `e : equiv.perm α`, mapping it through `f : α ↪ β`.
Everything outside of `set.range f` is kept fixed. Has poor computational performance,
due to exhaustive searching in constructed inverse due to using `function.embedding.to_equiv_range`.
@@ -70,7 +87,9 @@ When `[fintype α]` is not available, a noncomputable version is available as
def Equiv.Perm.viaFintypeEmbedding : Equiv.Perm β :=
e.extendDomain f.toEquivRange
#align equiv.perm.via_fintype_embedding Equiv.Perm.viaFintypeEmbedding
+-/
+#print Equiv.Perm.viaFintypeEmbedding_apply_image /-
@[simp]
theorem Equiv.Perm.viaFintypeEmbedding_apply_image (a : α) :
e.viaFintypeEmbedding f (f a) = f (e a) :=
@@ -78,17 +97,28 @@ theorem Equiv.Perm.viaFintypeEmbedding_apply_image (a : α) :
rw [Equiv.Perm.viaFintypeEmbedding]
convert Equiv.Perm.extendDomain_apply_image e _ _
#align equiv.perm.via_fintype_embedding_apply_image Equiv.Perm.viaFintypeEmbedding_apply_image
+-/
+#print Equiv.Perm.viaFintypeEmbedding_apply_mem_range /-
theorem Equiv.Perm.viaFintypeEmbedding_apply_mem_range {b : β} (h : b ∈ Set.range f) :
e.viaFintypeEmbedding f b = f (e (f.invOfMemRange ⟨b, h⟩)) := by
simpa [Equiv.Perm.viaFintypeEmbedding, Equiv.Perm.extendDomain_apply_subtype, h]
#align equiv.perm.via_fintype_embedding_apply_mem_range Equiv.Perm.viaFintypeEmbedding_apply_mem_range
+-/
+#print Equiv.Perm.viaFintypeEmbedding_apply_not_mem_range /-
theorem Equiv.Perm.viaFintypeEmbedding_apply_not_mem_range {b : β} (h : b ∉ Set.range f) :
e.viaFintypeEmbedding f b = b := by
rwa [Equiv.Perm.viaFintypeEmbedding, Equiv.Perm.extendDomain_apply_not_subtype]
#align equiv.perm.via_fintype_embedding_apply_not_mem_range Equiv.Perm.viaFintypeEmbedding_apply_not_mem_range
+-/
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+but is expected to have type
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Fintype.{u2} α] [_inst_2 : DecidableEq.{succ u1} β] (e : Equiv.Perm.{succ u2} α) (f : Function.Embedding.{succ u2, succ u1} α β) [_inst_3 : DecidableEq.{succ u2} α] [_inst_4 : Fintype.{u1} β], Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Equiv.Perm.{succ u1} β) => Units.{0} Int Int.instMonoidInt) (Equiv.Perm.viaFintypeEmbedding.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) e f)) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (fun (_x : Equiv.Perm.{succ u1} β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Equiv.Perm.{succ u1} β) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} β) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} β (fun (a : β) (b : β) => _inst_2 a b) _inst_4) (Equiv.Perm.viaFintypeEmbedding.{u2, u1} α β _inst_1 (fun (a : β) (b : β) => _inst_2 a b) e f)) (FunLike.coe.{succ u2, succ u2, 1} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (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) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u2, u2, 0} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u2, u2, 0} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u2, 0} (Equiv.Perm.{succ u2} α) (Units.{0} Int Int.instMonoidInt) (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)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u2} α (fun (a : α) (b : α) => _inst_3 a b) _inst_1) e)
+Case conversion may be inaccurate. Consider using '#align equiv.perm.via_fintype_embedding_sign Equiv.Perm.viaFintypeEmbedding_signₓ'. -/
@[simp]
theorem Equiv.Perm.viaFintypeEmbedding_sign [DecidableEq α] [Fintype β] :
Equiv.Perm.sign (e.viaFintypeEmbedding f) = Equiv.Perm.sign e := by
@@ -99,6 +129,7 @@ namespace Equiv
variable {p q : α → Prop} [DecidablePred p] [DecidablePred q]
+#print Equiv.toCompl /-
/-- If `e` is an equivalence between two subtypes of a fintype `α`, `e.to_compl`
is an equivalence between the complement of those subtypes.
@@ -108,7 +139,9 @@ noncomputable def toCompl (e : { x // p x } ≃ { x // q x }) : { x // ¬p x }
Classical.choice
(Fintype.card_eq.mp (Fintype.card_compl_eq_card_compl _ _ (Fintype.card_congr e)))
#align equiv.to_compl Equiv.toCompl
+-/
+#print Equiv.extendSubtype /-
/-- If `e` is an equivalence between two subtypes of a fintype `α`, `e.extend_subtype`
is a permutation of `α` acting like `e` on the subtypes and doing something arbitrary outside.
@@ -116,7 +149,9 @@ Note that when `p = q`, `equiv.perm.subtype_congr e (equiv.refl _)` can be used
noncomputable abbrev extendSubtype (e : { x // p x } ≃ { x // q x }) : Perm α :=
subtypeCongr e e.toCompl
#align equiv.extend_subtype Equiv.extendSubtype
+-/
+#print Equiv.extendSubtype_apply_of_mem /-
theorem extendSubtype_apply_of_mem (e : { x // p x } ≃ { x // q x }) (x) (hx : p x) :
e.extendSubtype x = e ⟨x, hx⟩ :=
by
@@ -124,13 +159,17 @@ theorem extendSubtype_apply_of_mem (e : { x // p x } ≃ { x // q x }) (x) (hx :
simp only [subtype_congr, Equiv.trans_apply, Equiv.sumCongr_apply]
rw [sum_compl_apply_symm_of_pos _ _ hx, Sum.map_inl, sum_compl_apply_inl]
#align equiv.extend_subtype_apply_of_mem Equiv.extendSubtype_apply_of_mem
+-/
+#print Equiv.extendSubtype_mem /-
theorem extendSubtype_mem (e : { x // p x } ≃ { x // q x }) (x) (hx : p x) :
q (e.extendSubtype x) := by
convert (e ⟨x, hx⟩).2
rw [e.extend_subtype_apply_of_mem _ hx, Subtype.val_eq_coe]
#align equiv.extend_subtype_mem Equiv.extendSubtype_mem
+-/
+#print Equiv.extendSubtype_apply_of_not_mem /-
theorem extendSubtype_apply_of_not_mem (e : { x // p x } ≃ { x // q x }) (x) (hx : ¬p x) :
e.extendSubtype x = e.toCompl ⟨x, hx⟩ :=
by
@@ -138,12 +177,15 @@ theorem extendSubtype_apply_of_not_mem (e : { x // p x } ≃ { x // q x }) (x) (
simp only [subtype_congr, Equiv.trans_apply, Equiv.sumCongr_apply]
rw [sum_compl_apply_symm_of_neg _ _ hx, Sum.map_inr, sum_compl_apply_inr]
#align equiv.extend_subtype_apply_of_not_mem Equiv.extendSubtype_apply_of_not_mem
+-/
+#print Equiv.extendSubtype_not_mem /-
theorem extendSubtype_not_mem (e : { x // p x } ≃ { x // q x }) (x) (hx : ¬p x) :
¬q (e.extendSubtype x) := by
convert (e.to_compl ⟨x, hx⟩).2
rw [e.extend_subtype_apply_of_not_mem _ hx, Subtype.val_eq_coe]
#align equiv.extend_subtype_not_mem Equiv.extendSubtype_not_mem
+-/
end Equiv
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -27,6 +27,7 @@ sides of the equivalence are `Fintype`s.
computational performance, since it operates by exhaustive search over the input `Fintype`s.
-/
+section Fintype
variable {α β : Type*} [Fintype α] [DecidableEq β] (e : Equiv.Perm α) (f : α ↪ β)
@@ -92,15 +93,19 @@ theorem Equiv.Perm.viaFintypeEmbedding_sign [DecidableEq α] [Fintype β] :
simp [Equiv.Perm.viaFintypeEmbedding]
#align equiv.perm.via_fintype_embedding_sign Equiv.Perm.viaFintypeEmbedding_sign
+end Fintype
+
namespace Equiv
-/-- If `e` is an equivalence between two subtypes of a fintype `α`, `e.toCompl`
+variable {α β : Type*} [Finite α]
+
+/-- If `e` is an equivalence between two subtypes of a finite type `α`, `e.toCompl`
is an equivalence between the complement of those subtypes.
See also `Equiv.compl`, for a computable version when a term of type
`{e' : α ≃ α // ∀ x : {x // p x}, e' x = e x}` is known. -/
-noncomputable def toCompl {α : Type*} [Finite α] {p q : α → Prop}
- (e : { x // p x } ≃ { x // q x }) : { x // ¬p x } ≃ { x // ¬q x } := by
+noncomputable def toCompl {p q : α → Prop} (e : { x // p x } ≃ { x // q x }) :
+ { x // ¬p x } ≃ { x // ¬q x } := by
apply Classical.choice
cases nonempty_fintype α
classical
Fintype
-> Finite
in Equiv.toCompl
(#10305)
Also drop DecidablePred
assumptions.
@@ -94,18 +94,21 @@ theorem Equiv.Perm.viaFintypeEmbedding_sign [DecidableEq α] [Fintype β] :
namespace Equiv
-variable {p q : α → Prop} [DecidablePred p] [DecidablePred q]
-
/-- If `e` is an equivalence between two subtypes of a fintype `α`, `e.toCompl`
is an equivalence between the complement of those subtypes.
See also `Equiv.compl`, for a computable version when a term of type
`{e' : α ≃ α // ∀ x : {x // p x}, e' x = e x}` is known. -/
-noncomputable def toCompl (e : { x // p x } ≃ { x // q x }) : { x // ¬p x } ≃ { x // ¬q x } :=
- Classical.choice
- (Fintype.card_eq.mp (Fintype.card_compl_eq_card_compl _ _ (Fintype.card_congr e)))
+noncomputable def toCompl {α : Type*} [Finite α] {p q : α → Prop}
+ (e : { x // p x } ≃ { x // q x }) : { x // ¬p x } ≃ { x // ¬q x } := by
+ apply Classical.choice
+ cases nonempty_fintype α
+ classical
+ exact Fintype.card_eq.mp <| Fintype.card_compl_eq_card_compl _ _ <| Fintype.card_congr e
#align equiv.to_compl Equiv.toCompl
+variable {p q : α → Prop} [DecidablePred p] [DecidablePred q]
+
/-- If `e` is an equivalence between two subtypes of a fintype `α`, `e.extendSubtype`
is a permutation of `α` acting like `e` on the subtypes and doing something arbitrary outside.
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -28,7 +28,7 @@ sides of the equivalence are `Fintype`s.
-/
-variable {α β : Type _} [Fintype α] [DecidableEq β] (e : Equiv.Perm α) (f : α ↪ β)
+variable {α β : Type*} [Fintype α] [DecidableEq β] (e : Equiv.Perm α) (f : α ↪ β)
/-- Computably turn an embedding `f : α ↪ β` into an equiv `α ≃ Set.range f`,
if `α` is a `Fintype`. Has poor computational performance, due to exhaustive searching in
@@ -2,16 +2,13 @@
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-
-! This file was ported from Lean 3 source module logic.equiv.fintype
-! leanprover-community/mathlib commit 9407b03373c8cd201df99d6bc5514fc2db44054f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Data.Fintype.Basic
import Mathlib.GroupTheory.Perm.Sign
import Mathlib.Logic.Equiv.Defs
+#align_import logic.equiv.fintype from "leanprover-community/mathlib"@"9407b03373c8cd201df99d6bc5514fc2db44054f"
+
/-! # Equivalence between fintypes
This file contains some basic results on equivalences where one or both
The unported dependencies are