group_theory.presented_group ⟷ Mathlib.GroupTheory.PresentedGroup

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -3,7 +3,7 @@ Copyright (c) 2019 Michael Howes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Howes
 -/
-import GroupTheory.FreeGroup
+import GroupTheory.FreeGroup.Basic
 import GroupTheory.QuotientGroup
 
 #align_import group_theory.presented_group from "leanprover-community/mathlib"@"0ebfdb71919ac6ca5d7fbc61a082fa2519556818"

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,8 +3,8 @@ Copyright (c) 2019 Michael Howes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Howes
 -/
-import Mathbin.GroupTheory.FreeGroup
-import Mathbin.GroupTheory.QuotientGroup
+import GroupTheory.FreeGroup
+import GroupTheory.QuotientGroup
 
 #align_import group_theory.presented_group from "leanprover-community/mathlib"@"0ebfdb71919ac6ca5d7fbc61a082fa2519556818"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Michael Howes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Howes
-
-! This file was ported from Lean 3 source module group_theory.presented_group
-! leanprover-community/mathlib commit 0ebfdb71919ac6ca5d7fbc61a082fa2519556818
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.GroupTheory.FreeGroup
 import Mathbin.GroupTheory.QuotientGroup
 
+#align_import group_theory.presented_group from "leanprover-community/mathlib"@"0ebfdb71919ac6ca5d7fbc61a082fa2519556818"
+
 /-!
 # Defining a group given by generators and relations
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -66,34 +66,43 @@ from `presented_group rels` to `G`.
 -/
 variable {G : Type _} [Group G] {f : α → G} {rels : Set (FreeGroup α)}
 
--- mathport name: exprF
 local notation "F" => FreeGroup.lift f
 
 variable (h : ∀ r ∈ rels, F r = 1)
 
+#print PresentedGroup.closure_rels_subset_ker /-
 theorem closure_rels_subset_ker : Subgroup.normalClosure rels ≤ MonoidHom.ker F :=
   Subgroup.normalClosure_le_normal fun x w => (MonoidHom.mem_ker _).2 (h x w)
 #align presented_group.closure_rels_subset_ker PresentedGroup.closure_rels_subset_ker
+-/
 
+#print PresentedGroup.to_group_eq_one_of_mem_closure /-
 theorem to_group_eq_one_of_mem_closure : ∀ x ∈ Subgroup.normalClosure rels, F x = 1 := fun x w =>
   (MonoidHom.mem_ker _).1 <| closure_rels_subset_ker h w
 #align presented_group.to_group_eq_one_of_mem_closure PresentedGroup.to_group_eq_one_of_mem_closure
+-/
 
+#print PresentedGroup.toGroup /-
 /-- The extension of a map `f : α → G` that satisfies the given relations to a group homomorphism
 from `presented_group rels → G`. -/
 def toGroup : PresentedGroup rels →* G :=
   QuotientGroup.lift (Subgroup.normalClosure rels) F (to_group_eq_one_of_mem_closure h)
 #align presented_group.to_group PresentedGroup.toGroup
+-/
 
+#print PresentedGroup.toGroup.of /-
 @[simp]
 theorem toGroup.of {x : α} : toGroup h (of x) = f x :=
   FreeGroup.lift.of
 #align presented_group.to_group.of PresentedGroup.toGroup.of
+-/
 
+#print PresentedGroup.toGroup.unique /-
 theorem toGroup.unique (g : PresentedGroup rels →* G) (hg : ∀ x : α, g (of x) = f x) :
     ∀ {x}, g x = toGroup h x := fun x =>
   QuotientGroup.induction_on x fun _ => FreeGroup.lift.unique (g.comp (QuotientGroup.mk' _)) hg
 #align presented_group.to_group.unique PresentedGroup.toGroup.unique
+-/
 
 end ToGroup
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -71,43 +71,25 @@ local notation "F" => FreeGroup.lift f
 
 variable (h : ∀ r ∈ rels, F r = 1)
 
-/- warning: presented_group.closure_rels_subset_ker -> PresentedGroup.closure_rels_subset_ker is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align presented_group.closure_rels_subset_ker PresentedGroup.closure_rels_subset_kerₓ'. -/
 theorem closure_rels_subset_ker : Subgroup.normalClosure rels ≤ MonoidHom.ker F :=
   Subgroup.normalClosure_le_normal fun x w => (MonoidHom.mem_ker _).2 (h x w)
 #align presented_group.closure_rels_subset_ker PresentedGroup.closure_rels_subset_ker
 
-/- warning: presented_group.to_group_eq_one_of_mem_closure -> PresentedGroup.to_group_eq_one_of_mem_closure is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align presented_group.to_group_eq_one_of_mem_closure PresentedGroup.to_group_eq_one_of_mem_closureₓ'. -/
 theorem to_group_eq_one_of_mem_closure : ∀ x ∈ Subgroup.normalClosure rels, F x = 1 := fun x w =>
   (MonoidHom.mem_ker _).1 <| closure_rels_subset_ker h w
 #align presented_group.to_group_eq_one_of_mem_closure PresentedGroup.to_group_eq_one_of_mem_closure
 
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 /-- The extension of a map `f : α → G` that satisfies the given relations to a group homomorphism
 from `presented_group rels → G`. -/
 def toGroup : PresentedGroup rels →* G :=
   QuotientGroup.lift (Subgroup.normalClosure rels) F (to_group_eq_one_of_mem_closure h)
 #align presented_group.to_group PresentedGroup.toGroup
 
-/- warning: presented_group.to_group.of -> PresentedGroup.toGroup.of is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align presented_group.to_group.of PresentedGroup.toGroup.ofₓ'. -/
 @[simp]
 theorem toGroup.of {x : α} : toGroup h (of x) = f x :=
   FreeGroup.lift.of
 #align presented_group.to_group.of PresentedGroup.toGroup.of
 
-/- warning: presented_group.to_group.unique -> PresentedGroup.toGroup.unique is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align presented_group.to_group.unique PresentedGroup.toGroup.uniqueₓ'. -/
 theorem toGroup.unique (g : PresentedGroup rels →* G) (hg : ∀ x : α, g (of x) = f x) :
     ∀ {x}, g x = toGroup h x := fun x =>
   QuotientGroup.induction_on x fun _ => FreeGroup.lift.unique (g.comp (QuotientGroup.mk' _)) hg

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -72,20 +72,14 @@ local notation "F" => FreeGroup.lift f
 variable (h : ∀ r ∈ rels, F r = 1)
 
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 Case conversion may be inaccurate. Consider using '#align presented_group.closure_rels_subset_ker PresentedGroup.closure_rels_subset_kerₓ'. -/
 theorem closure_rels_subset_ker : Subgroup.normalClosure rels ≤ MonoidHom.ker F :=
   Subgroup.normalClosure_le_normal fun x w => (MonoidHom.mem_ker _).2 (h x w)
 #align presented_group.closure_rels_subset_ker PresentedGroup.closure_rels_subset_ker
 
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 Case conversion may be inaccurate. Consider using '#align presented_group.to_group_eq_one_of_mem_closure PresentedGroup.to_group_eq_one_of_mem_closureₓ'. -/
 theorem to_group_eq_one_of_mem_closure : ∀ x ∈ Subgroup.normalClosure rels, F x = 1 := fun x w =>
   (MonoidHom.mem_ker _).1 <| closure_rels_subset_ker h w
@@ -104,10 +98,7 @@ def toGroup : PresentedGroup rels →* G :=
 #align presented_group.to_group PresentedGroup.toGroup
 
 /- warning: presented_group.to_group.of -> PresentedGroup.toGroup.of is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align presented_group.to_group.of PresentedGroup.toGroup.ofₓ'. -/
 @[simp]
 theorem toGroup.of {x : α} : toGroup h (of x) = f x :=
@@ -115,10 +106,7 @@ theorem toGroup.of {x : α} : toGroup h (of x) = f x :=
 #align presented_group.to_group.of PresentedGroup.toGroup.of
 
 /- warning: presented_group.to_group.unique -> PresentedGroup.toGroup.unique is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align presented_group.to_group.unique PresentedGroup.toGroup.uniqueₓ'. -/
 theorem toGroup.unique (g : PresentedGroup rels →* G) (hg : ∀ x : α, g (of x) = f x) :
     ∀ {x}, g x = toGroup h x := fun x =>

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -75,7 +75,7 @@ variable (h : ∀ r ∈ rels, F r = 1)
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align presented_group.closure_rels_subset_ker PresentedGroup.closure_rels_subset_kerₓ'. -/
 theorem closure_rels_subset_ker : Subgroup.normalClosure rels ≤ MonoidHom.ker F :=
   Subgroup.normalClosure_le_normal fun x w => (MonoidHom.mem_ker _).2 (h x w)
@@ -85,7 +85,7 @@ theorem closure_rels_subset_ker : Subgroup.normalClosure rels ≤ MonoidHom.ker
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align presented_group.to_group_eq_one_of_mem_closure PresentedGroup.to_group_eq_one_of_mem_closureₓ'. -/
 theorem to_group_eq_one_of_mem_closure : ∀ x ∈ Subgroup.normalClosure rels, F x = 1 := fun x w =>
   (MonoidHom.mem_ker _).1 <| closure_rels_subset_ker h w
@@ -95,7 +95,7 @@ theorem to_group_eq_one_of_mem_closure : ∀ x ∈ Subgroup.normalClosure rels,
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align presented_group.to_group PresentedGroup.toGroupₓ'. -/
 /-- The extension of a map `f : α → G` that satisfies the given relations to a group homomorphism
 from `presented_group rels → G`. -/
@@ -107,7 +107,7 @@ def toGroup : PresentedGroup rels →* G :=
 lean 3 declaration is
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 but is expected to have type
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(PresentedGroup.{u1} α rels) G (MulOneClass.toMul.{u1} (PresentedGroup.{u1} α rels) (Monoid.toMulOneClass.{u1} (PresentedGroup.{u1} α rels) (DivInvMonoid.toMonoid.{u1} (PresentedGroup.{u1} α rels) (Group.toDivInvMonoid.{u1} (PresentedGroup.{u1} α rels) (PresentedGroup.instGroupPresentedGroup.{u1} α rels))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (PresentedGroup.{u1} α rels) G (Monoid.toMulOneClass.{u1} (PresentedGroup.{u1} α rels) (DivInvMonoid.toMonoid.{u1} (PresentedGroup.{u1} α rels) (Group.toDivInvMonoid.{u1} (PresentedGroup.{u1} α rels) (PresentedGroup.instGroupPresentedGroup.{u1} α rels)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (PresentedGroup.{u1} α rels) G (Monoid.toMulOneClass.{u1} (PresentedGroup.{u1} α rels) (DivInvMonoid.toMonoid.{u1} (PresentedGroup.{u1} α 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 Case conversion may be inaccurate. Consider using '#align presented_group.to_group.of PresentedGroup.toGroup.ofₓ'. -/
 @[simp]
 theorem toGroup.of {x : α} : toGroup h (of x) = f x :=
@@ -118,7 +118,7 @@ theorem toGroup.of {x : α} : toGroup h (of x) = f x :=
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align presented_group.to_group.unique PresentedGroup.toGroup.uniqueₓ'. -/
 theorem toGroup.unique (g : PresentedGroup rels →* G) (hg : ∀ x : α, g (of x) = f x) :
     ∀ {x}, g x = toGroup h x := fun x =>

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -73,7 +73,7 @@ variable (h : ∀ r ∈ rels, F r = 1)
 
 /- warning: presented_group.closure_rels_subset_ker -> PresentedGroup.closure_rels_subset_ker is a dubious translation:
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align presented_group.closure_rels_subset_ker PresentedGroup.closure_rels_subset_kerₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -75,7 +75,7 @@ variable (h : ∀ r ∈ rels, F r = 1)
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align presented_group.closure_rels_subset_ker PresentedGroup.closure_rels_subset_kerₓ'. -/
 theorem closure_rels_subset_ker : Subgroup.normalClosure rels ≤ MonoidHom.ker F :=
   Subgroup.normalClosure_le_normal fun x w => (MonoidHom.mem_ker _).2 (h x w)
@@ -85,7 +85,7 @@ theorem closure_rels_subset_ker : Subgroup.normalClosure rels ≤ MonoidHom.ker
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align presented_group.to_group_eq_one_of_mem_closure PresentedGroup.to_group_eq_one_of_mem_closureₓ'. -/
 theorem to_group_eq_one_of_mem_closure : ∀ x ∈ Subgroup.normalClosure rels, F x = 1 := fun x w =>
   (MonoidHom.mem_ker _).1 <| closure_rels_subset_ker h w
@@ -95,7 +95,7 @@ theorem to_group_eq_one_of_mem_closure : ∀ x ∈ Subgroup.normalClosure rels,
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align presented_group.to_group PresentedGroup.toGroupₓ'. -/
 /-- The extension of a map `f : α → G` that satisfies the given relations to a group homomorphism
 from `presented_group rels → G`. -/
@@ -107,7 +107,7 @@ def toGroup : PresentedGroup rels →* G :=
 lean 3 declaration is
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 but is expected to have type
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(PresentedGroup.{u1} α rels) G (MulOneClass.toMul.{u1} (PresentedGroup.{u1} α rels) (Monoid.toMulOneClass.{u1} (PresentedGroup.{u1} α rels) (DivInvMonoid.toMonoid.{u1} (PresentedGroup.{u1} α rels) (Group.toDivInvMonoid.{u1} (PresentedGroup.{u1} α rels) (PresentedGroup.instGroupPresentedGroup.{u1} α rels))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (PresentedGroup.{u1} α rels) G (Monoid.toMulOneClass.{u1} (PresentedGroup.{u1} α rels) (DivInvMonoid.toMonoid.{u1} (PresentedGroup.{u1} α rels) (Group.toDivInvMonoid.{u1} (PresentedGroup.{u1} α rels) (PresentedGroup.instGroupPresentedGroup.{u1} α rels)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (PresentedGroup.{u1} α rels) G (Monoid.toMulOneClass.{u1} (PresentedGroup.{u1} α rels) (DivInvMonoid.toMonoid.{u1} (PresentedGroup.{u1} α rels) (Group.toDivInvMonoid.{u1} (PresentedGroup.{u1} α rels) (PresentedGroup.instGroupPresentedGroup.{u1} α rels)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (PresentedGroup.{u1} α rels) G (Monoid.toMulOneClass.{u1} (PresentedGroup.{u1} α rels) (DivInvMonoid.toMonoid.{u1} (PresentedGroup.{u1} α rels) (Group.toDivInvMonoid.{u1} (PresentedGroup.{u1} α rels) (PresentedGroup.instGroupPresentedGroup.{u1} α rels)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (PresentedGroup.toGroup.{u1, u2} α G _inst_1 f rels h) (PresentedGroup.of.{u1} α rels x)) (f x)
+  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] {f : α -> G} {rels : Set.{u1} (FreeGroup.{u1} α)} (h : forall (r : FreeGroup.{u1} α), (Membership.mem.{u1, u1} (FreeGroup.{u1} α) (Set.{u1} (FreeGroup.{u1} α)) (Set.instMembershipSet.{u1} (FreeGroup.{u1} α)) r rels) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeGroup.{u1} α) => G) r) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α -> G) => MonoidHom.{u1, u2} (FreeGroup.{u1} α) G (Monoid.toMulOneClass.{u1} (FreeGroup.{u1} α) (DivInvMonoid.toMonoid.{u1} (FreeGroup.{u1} α) (Group.toDivInvMonoid.{u1} (FreeGroup.{u1} α) (FreeGroup.instGroupFreeGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) f) (FreeGroup.{u1} α) (fun (_x : FreeGroup.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeGroup.{u1} α) => G) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} ((fun 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(PresentedGroup.{u1} α rels) G (MulOneClass.toMul.{u1} (PresentedGroup.{u1} α rels) (Monoid.toMulOneClass.{u1} (PresentedGroup.{u1} α rels) (DivInvMonoid.toMonoid.{u1} (PresentedGroup.{u1} α rels) (Group.toDivInvMonoid.{u1} (PresentedGroup.{u1} α rels) (PresentedGroup.instGroupPresentedGroup.{u1} α rels))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (PresentedGroup.{u1} α rels) G (Monoid.toMulOneClass.{u1} (PresentedGroup.{u1} α rels) (DivInvMonoid.toMonoid.{u1} (PresentedGroup.{u1} α rels) (Group.toDivInvMonoid.{u1} (PresentedGroup.{u1} α rels) (PresentedGroup.instGroupPresentedGroup.{u1} α rels)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (PresentedGroup.{u1} α rels) G (Monoid.toMulOneClass.{u1} (PresentedGroup.{u1} α rels) (DivInvMonoid.toMonoid.{u1} (PresentedGroup.{u1} α 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 Case conversion may be inaccurate. Consider using '#align presented_group.to_group.of PresentedGroup.toGroup.ofₓ'. -/
 @[simp]
 theorem toGroup.of {x : α} : toGroup h (of x) = f x :=
@@ -118,7 +118,7 @@ theorem toGroup.of {x : α} : toGroup h (of x) = f x :=
 lean 3 declaration is
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 but is expected to have type
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(Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u2, u1} (PresentedGroup.{u2} α rels) G (Monoid.toMulOneClass.{u2} (PresentedGroup.{u2} α rels) (DivInvMonoid.toMonoid.{u2} (PresentedGroup.{u2} α rels) (Group.toDivInvMonoid.{u2} (PresentedGroup.{u2} α rels) (PresentedGroup.instGroupPresentedGroup.{u2} α rels)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (PresentedGroup.toGroup.{u2, u1} α G _inst_1 f rels h) x))
 Case conversion may be inaccurate. Consider using '#align presented_group.to_group.unique PresentedGroup.toGroup.uniqueₓ'. -/
 theorem toGroup.unique (g : PresentedGroup rels →* G) (hg : ∀ x : α, g (of x) = f x) :
     ∀ {x}, g x = toGroup h x := fun x =>

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

@@ -75,7 +75,7 @@ variable (h : ∀ r ∈ rels, F r = 1)
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align presented_group.closure_rels_subset_ker PresentedGroup.closure_rels_subset_kerₓ'. -/
 theorem closure_rels_subset_ker : Subgroup.normalClosure rels ≤ MonoidHom.ker F :=
   Subgroup.normalClosure_le_normal fun x w => (MonoidHom.mem_ker _).2 (h x w)
@@ -85,7 +85,7 @@ theorem closure_rels_subset_ker : Subgroup.normalClosure rels ≤ MonoidHom.ker
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align presented_group.to_group_eq_one_of_mem_closure PresentedGroup.to_group_eq_one_of_mem_closureₓ'. -/
 theorem to_group_eq_one_of_mem_closure : ∀ x ∈ Subgroup.normalClosure rels, F x = 1 := fun x w =>
   (MonoidHom.mem_ker _).1 <| closure_rels_subset_ker h w
@@ -95,7 +95,7 @@ theorem to_group_eq_one_of_mem_closure : ∀ x ∈ Subgroup.normalClosure rels,
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align presented_group.to_group PresentedGroup.toGroupₓ'. -/
 /-- The extension of a map `f : α → G` that satisfies the given relations to a group homomorphism
 from `presented_group rels → G`. -/
@@ -107,7 +107,7 @@ def toGroup : PresentedGroup rels →* G :=
 lean 3 declaration is
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 but is expected to have type
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(PresentedGroup.{u1} α rels) G (MulOneClass.toMul.{u1} (PresentedGroup.{u1} α rels) (Monoid.toMulOneClass.{u1} (PresentedGroup.{u1} α rels) (DivInvMonoid.toMonoid.{u1} (PresentedGroup.{u1} α rels) (Group.toDivInvMonoid.{u1} (PresentedGroup.{u1} α rels) (PresentedGroup.instGroupPresentedGroup.{u1} α rels))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (PresentedGroup.{u1} α rels) G (Monoid.toMulOneClass.{u1} (PresentedGroup.{u1} α rels) (DivInvMonoid.toMonoid.{u1} (PresentedGroup.{u1} α rels) (Group.toDivInvMonoid.{u1} (PresentedGroup.{u1} α rels) (PresentedGroup.instGroupPresentedGroup.{u1} α rels)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (PresentedGroup.{u1} α rels) G (Monoid.toMulOneClass.{u1} (PresentedGroup.{u1} α rels) (DivInvMonoid.toMonoid.{u1} (PresentedGroup.{u1} α 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+  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] {f : α -> G} {rels : Set.{u1} (FreeGroup.{u1} α)} (h : forall (r : FreeGroup.{u1} α), (Membership.mem.{u1, u1} (FreeGroup.{u1} α) (Set.{u1} (FreeGroup.{u1} α)) (Set.instMembershipSet.{u1} (FreeGroup.{u1} α)) r rels) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : FreeGroup.{u1} α) => G) r) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α -> G) => MonoidHom.{u1, u2} (FreeGroup.{u1} α) G (Monoid.toMulOneClass.{u1} (FreeGroup.{u1} α) (DivInvMonoid.toMonoid.{u1} (FreeGroup.{u1} α) (Group.toDivInvMonoid.{u1} (FreeGroup.{u1} α) (FreeGroup.instGroupFreeGroup.{u1} α)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) f) (FreeGroup.{u1} α) (fun (_x : FreeGroup.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : FreeGroup.{u1} α) => G) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} ((fun 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(PresentedGroup.{u1} α rels) G (MulOneClass.toMul.{u1} (PresentedGroup.{u1} α rels) (Monoid.toMulOneClass.{u1} (PresentedGroup.{u1} α rels) (DivInvMonoid.toMonoid.{u1} (PresentedGroup.{u1} α rels) (Group.toDivInvMonoid.{u1} (PresentedGroup.{u1} α rels) (PresentedGroup.instGroupPresentedGroup.{u1} α rels))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (PresentedGroup.{u1} α rels) G (Monoid.toMulOneClass.{u1} (PresentedGroup.{u1} α rels) (DivInvMonoid.toMonoid.{u1} (PresentedGroup.{u1} α rels) (Group.toDivInvMonoid.{u1} (PresentedGroup.{u1} α rels) (PresentedGroup.instGroupPresentedGroup.{u1} α rels)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (PresentedGroup.{u1} α rels) G (Monoid.toMulOneClass.{u1} (PresentedGroup.{u1} α rels) (DivInvMonoid.toMonoid.{u1} (PresentedGroup.{u1} α 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 Case conversion may be inaccurate. Consider using '#align presented_group.to_group.of PresentedGroup.toGroup.ofₓ'. -/
 @[simp]
 theorem toGroup.of {x : α} : toGroup h (of x) = f x :=
@@ -118,7 +118,7 @@ theorem toGroup.of {x : α} : toGroup h (of x) = f x :=
 lean 3 declaration is
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 but is expected to have type
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G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (PresentedGroup.{u2} α rels) G (Monoid.toMulOneClass.{u2} (PresentedGroup.{u2} α rels) (DivInvMonoid.toMonoid.{u2} (PresentedGroup.{u2} α rels) (Group.toDivInvMonoid.{u2} (PresentedGroup.{u2} α rels) (PresentedGroup.instGroupPresentedGroup.{u2} α rels)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u2, u1} (PresentedGroup.{u2} α rels) G (Monoid.toMulOneClass.{u2} (PresentedGroup.{u2} α rels) (DivInvMonoid.toMonoid.{u2} (PresentedGroup.{u2} α rels) (Group.toDivInvMonoid.{u2} (PresentedGroup.{u2} α rels) (PresentedGroup.instGroupPresentedGroup.{u2} α rels)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) g x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (PresentedGroup.{u2} α rels) G (Monoid.toMulOneClass.{u2} (PresentedGroup.{u2} α rels) (DivInvMonoid.toMonoid.{u2} (PresentedGroup.{u2} α rels) (Group.toDivInvMonoid.{u2} (PresentedGroup.{u2} α rels) (PresentedGroup.instGroupPresentedGroup.{u2} α rels)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (PresentedGroup.{u2} α rels) (fun (_x : PresentedGroup.{u2} α rels) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : PresentedGroup.{u2} α rels) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (PresentedGroup.{u2} α rels) G (Monoid.toMulOneClass.{u2} (PresentedGroup.{u2} α rels) (DivInvMonoid.toMonoid.{u2} (PresentedGroup.{u2} α rels) (Group.toDivInvMonoid.{u2} (PresentedGroup.{u2} α rels) (PresentedGroup.instGroupPresentedGroup.{u2} α rels)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (PresentedGroup.{u2} α rels) G (MulOneClass.toMul.{u2} (PresentedGroup.{u2} α rels) (Monoid.toMulOneClass.{u2} (PresentedGroup.{u2} α rels) (DivInvMonoid.toMonoid.{u2} (PresentedGroup.{u2} α rels) (Group.toDivInvMonoid.{u2} (PresentedGroup.{u2} α rels) (PresentedGroup.instGroupPresentedGroup.{u2} α rels))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (PresentedGroup.{u2} α rels) G (Monoid.toMulOneClass.{u2} (PresentedGroup.{u2} α rels) (DivInvMonoid.toMonoid.{u2} (PresentedGroup.{u2} α rels) (Group.toDivInvMonoid.{u2} (PresentedGroup.{u2} α rels) (PresentedGroup.instGroupPresentedGroup.{u2} α rels)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (PresentedGroup.{u2} α rels) G (Monoid.toMulOneClass.{u2} (PresentedGroup.{u2} α rels) (DivInvMonoid.toMonoid.{u2} (PresentedGroup.{u2} α rels) (Group.toDivInvMonoid.{u2} (PresentedGroup.{u2} α rels) (PresentedGroup.instGroupPresentedGroup.{u2} α rels)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u2, u1} (PresentedGroup.{u2} α rels) G (Monoid.toMulOneClass.{u2} (PresentedGroup.{u2} α rels) (DivInvMonoid.toMonoid.{u2} (PresentedGroup.{u2} α rels) (Group.toDivInvMonoid.{u2} (PresentedGroup.{u2} α rels) (PresentedGroup.instGroupPresentedGroup.{u2} α rels)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (PresentedGroup.toGroup.{u2, u1} α G _inst_1 f rels h) x))
 Case conversion may be inaccurate. Consider using '#align presented_group.to_group.unique PresentedGroup.toGroup.uniqueₓ'. -/
 theorem toGroup.unique (g : PresentedGroup rels →* G) (hg : ∀ x : α, g (of x) = f x) :
     ∀ {x}, g x = toGroup h x := fun x =>

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

Quoting [@digama0](https://github.com/digama0):

These were actually never meant to go in the file, they are basically debugging information and only useful on significantly broken mathport files. You can safely remove all of them.

@@ -66,7 +66,6 @@ from `PresentedGroup rels` to `G`.
 -/
 variable {G : Type*} [Group G] {f : α → G} {rels : Set (FreeGroup α)}
 
--- mathport name: exprF
 local notation "F" => FreeGroup.lift f
 
 -- Porting note: `F` has been expanded, because `F r = 1` produces a sorry.

• Add FreeGroup.closure_range_of: the subgroup closure of the range of FreeGroup.of : α → FreeGroup α is ⊤. (That is, the generators of a free group generate the free group.)
• Add PresentedGroup.closure_range_of: the subgroup closure of the range of PresentedGroup.of : α → PresentedGroup rels is ⊤. (That is, the generators of a presented group generate the presented group.)

@@ -47,6 +47,16 @@ def of {rels : Set (FreeGroup α)} (x : α) : PresentedGroup rels :=
   QuotientGroup.mk (FreeGroup.of x)
 #align presented_group.of PresentedGroup.of
 
+/-- The generators of a presented group generate the presented group. That is, the subgroup closure
+of the set of generators equals `⊤`. -/
+@[simp]
+theorem closure_range_of (rels : Set (FreeGroup α)) :
+    Subgroup.closure (Set.range (PresentedGroup.of : α → PresentedGroup rels)) = ⊤ := by
+  have : (PresentedGroup.of : α → PresentedGroup rels) = QuotientGroup.mk' _ ∘ FreeGroup.of := rfl
+  rw [this, Set.range_comp, ← MonoidHom.map_closure (QuotientGroup.mk' _),
+    FreeGroup.closure_range_of, ← MonoidHom.range_eq_map]
+  exact MonoidHom.range_top_of_surjective _ (QuotientGroup.mk'_surjective _)
+
 section ToGroup
 
 /-

Co-authored-by: Newell Jensen <newell@users.noreply.github.com>

@@ -1,7 +1,7 @@
 /-
 Copyright (c) 2019 Michael Howes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Michael Howes
+Authors: Michael Howes, Newell Jensen
 -/
 import Mathlib.GroupTheory.FreeGroup.Basic
 import Mathlib.GroupTheory.QuotientGroup
@@ -94,6 +94,24 @@ theorem ext {φ ψ : PresentedGroup rels →* G} (hx : ∀ (x : α), φ (.of x)
   ext
   apply hx
 
+variable {β : Type*}
+
+/-- Presented groups of isomorphic types are isomorphic. -/
+def equivPresentedGroup (rels : Set (FreeGroup α)) (e : α ≃ β) :
+    PresentedGroup rels ≃* PresentedGroup (FreeGroup.freeGroupCongr e '' rels) :=
+  QuotientGroup.congr (Subgroup.normalClosure rels)
+    (Subgroup.normalClosure ((FreeGroup.freeGroupCongr e) '' rels)) (FreeGroup.freeGroupCongr e)
+    (Subgroup.map_normalClosure rels (FreeGroup.freeGroupCongr e).toMonoidHom
+      (FreeGroup.freeGroupCongr e).surjective)
+
+theorem equivPresentedGroup_apply_of (x : α) (rels : Set (FreeGroup α)) (e : α ≃ β) :
+    equivPresentedGroup rels e (PresentedGroup.of x) =
+      PresentedGroup.of (rels := FreeGroup.freeGroupCongr e '' rels) (e x) := rfl
+
+theorem equivPresentedGroup_symm_apply_of (x : β) (rels : Set (FreeGroup α)) (e : α ≃ β) :
+    (equivPresentedGroup rels e).symm (PresentedGroup.of x) =
+      PresentedGroup.of (rels := rels) (e.symm x) := rfl
+
 end ToGroup
 
 instance (rels : Set (FreeGroup α)) : Inhabited (PresentedGroup rels) :=

Add ext theorem to PresentedGroup.

Co-authored-by: Newell Jensen <newell@users.noreply.github.com>

@@ -88,6 +88,12 @@ theorem toGroup.unique (g : PresentedGroup rels →* G)
   exact fun _ ↦ FreeGroup.lift.unique (g.comp (QuotientGroup.mk' _)) hg
 #align presented_group.to_group.unique PresentedGroup.toGroup.unique
 
+@[ext]
+theorem ext {φ ψ : PresentedGroup rels →* G} (hx : ∀ (x : α), φ (.of x) = ψ (.of x)) : φ = ψ := by
+  unfold PresentedGroup
+  ext
+  apply hx
+
 end ToGroup
 
 instance (rels : Set (FreeGroup α)) : Inhabited (PresentedGroup rels) :=

@@ -3,7 +3,7 @@ Copyright (c) 2019 Michael Howes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Howes
 -/
-import Mathlib.GroupTheory.FreeGroup
+import Mathlib.GroupTheory.FreeGroup.Basic
 import Mathlib.GroupTheory.QuotientGroup
 
 #align_import group_theory.presented_group from "leanprover-community/mathlib"@"d90e4e186f1d18e375dcd4e5b5f6364b01cb3e46"

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -28,7 +28,7 @@ generators, relations, group presentations
 -/
 
 
-variable {α : Type _}
+variable {α : Type*}
 
 /-- Given a set of relations, `rels`, over a type `α`, `PresentedGroup` constructs the group with
 generators `x : α` and relations `rels` as a quotient of `FreeGroup α`. -/
@@ -54,7 +54,7 @@ Presented groups satisfy a universal property. If `G` is a group and `f : α →
 the images of `f` satisfy all the given relations, then `f` extends uniquely to a group homomorphism
 from `PresentedGroup rels` to `G`.
 -/
-variable {G : Type _} [Group G] {f : α → G} {rels : Set (FreeGroup α)}
+variable {G : Type*} [Group G] {f : α → G} {rels : Set (FreeGroup α)}
 
 -- mathport name: exprF
 local notation "F" => FreeGroup.lift f

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Michael Howes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Howes
-
-! This file was ported from Lean 3 source module group_theory.presented_group
-! leanprover-community/mathlib commit d90e4e186f1d18e375dcd4e5b5f6364b01cb3e46
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.GroupTheory.FreeGroup
 import Mathlib.GroupTheory.QuotientGroup
 
+#align_import group_theory.presented_group from "leanprover-community/mathlib"@"d90e4e186f1d18e375dcd4e5b5f6364b01cb3e46"
+
 /-!
 # Defining a group given by generators and relations