group_theory.subgroup.simple
⟷
Mathlib.GroupTheory.Subgroup.Simple
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -77,7 +77,7 @@ theorem isSimpleGroup_of_surjective {H : Type _} [Group H] [IsSimpleGroup G] [No
by
refine' (iH.comap f).eq_bot_or_eq_top.imp (fun h => _) fun h => _
· rw [← map_bot f, ← h, map_comap_eq_self_of_surjective hf]
- · rw [← comap_top f] at h ; exact comap_injective hf h⟩
+ · rw [← comap_top f] at h; exact comap_injective hf h⟩
#align is_simple_group.is_simple_group_of_surjective IsSimpleGroup.isSimpleGroup_of_surjective
#align is_simple_add_group.is_simple_add_group_of_surjective IsSimpleAddGroup.isSimpleAddGroup_of_surjective
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
-import Mathbin.GroupTheory.Subgroup.Actions
+import GroupTheory.Subgroup.Actions
#align_import group_theory.subgroup.simple from "leanprover-community/mathlib"@"fac369018417f980cec5fcdafc766a69f88d8cfe"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-
-! This file was ported from Lean 3 source module group_theory.subgroup.simple
-! leanprover-community/mathlib commit fac369018417f980cec5fcdafc766a69f88d8cfe
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.GroupTheory.Subgroup.Actions
+#align_import group_theory.subgroup.simple from "leanprover-community/mathlib"@"fac369018417f980cec5fcdafc766a69f88d8cfe"
+
/-!
# Simple groups
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -55,12 +55,14 @@ attribute [to_additive] IsSimpleGroup
variable {G} {A}
+#print Subgroup.Normal.eq_bot_or_eq_top /-
@[to_additive]
theorem Subgroup.Normal.eq_bot_or_eq_top [IsSimpleGroup G] {H : Subgroup G} (Hn : H.Normal) :
H = ⊥ ∨ H = ⊤ :=
IsSimpleGroup.eq_bot_or_eq_top_of_normal H Hn
#align subgroup.normal.eq_bot_or_eq_top Subgroup.Normal.eq_bot_or_eq_top
#align add_subgroup.normal.eq_bot_or_eq_top AddSubgroup.Normal.eq_bot_or_eq_top
+-/
namespace IsSimpleGroup
@@ -70,6 +72,7 @@ instance {C : Type _} [CommGroup C] [IsSimpleGroup C] : IsSimpleOrder (Subgroup
open _Root_.Subgroup
+#print IsSimpleGroup.isSimpleGroup_of_surjective /-
@[to_additive]
theorem isSimpleGroup_of_surjective {H : Type _} [Group H] [IsSimpleGroup G] [Nontrivial H]
(f : G →* H) (hf : Function.Surjective f) : IsSimpleGroup H :=
@@ -80,6 +83,7 @@ theorem isSimpleGroup_of_surjective {H : Type _} [Group H] [IsSimpleGroup G] [No
· rw [← comap_top f] at h ; exact comap_injective hf h⟩
#align is_simple_group.is_simple_group_of_surjective IsSimpleGroup.isSimpleGroup_of_surjective
#align is_simple_add_group.is_simple_add_group_of_surjective IsSimpleAddGroup.isSimpleAddGroup_of_surjective
+-/
end IsSimpleGroup
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -77,7 +77,7 @@ theorem isSimpleGroup_of_surjective {H : Type _} [Group H] [IsSimpleGroup G] [No
by
refine' (iH.comap f).eq_bot_or_eq_top.imp (fun h => _) fun h => _
· rw [← map_bot f, ← h, map_comap_eq_self_of_surjective hf]
- · rw [← comap_top f] at h; exact comap_injective hf h⟩
+ · rw [← comap_top f] at h ; exact comap_injective hf h⟩
#align is_simple_group.is_simple_group_of_surjective IsSimpleGroup.isSimpleGroup_of_surjective
#align is_simple_add_group.is_simple_add_group_of_surjective IsSimpleAddGroup.isSimpleAddGroup_of_surjective
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -55,12 +55,6 @@ attribute [to_additive] IsSimpleGroup
variable {G} {A}
-/- warning: subgroup.normal.eq_bot_or_eq_top -> Subgroup.Normal.eq_bot_or_eq_top is a dubious translation:
-lean 3 declaration is
- forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] [_inst_3 : IsSimpleGroup.{u1} G _inst_1] {H : Subgroup.{u1} G _inst_1}, (Subgroup.Normal.{u1} G _inst_1 H) -> (Or (Eq.{succ u1} (Subgroup.{u1} G _inst_1) H (Bot.bot.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.hasBot.{u1} G _inst_1))) (Eq.{succ u1} (Subgroup.{u1} G _inst_1) H (Top.top.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.hasTop.{u1} G _inst_1))))
-but is expected to have type
- forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] [_inst_3 : IsSimpleGroup.{u1} G _inst_1] {H : Subgroup.{u1} G _inst_1}, (Subgroup.Normal.{u1} G _inst_1 H) -> (Or (Eq.{succ u1} (Subgroup.{u1} G _inst_1) H (Bot.bot.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instBotSubgroup.{u1} G _inst_1))) (Eq.{succ u1} (Subgroup.{u1} G _inst_1) H (Top.top.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.instTopSubgroup.{u1} G _inst_1))))
-Case conversion may be inaccurate. Consider using '#align subgroup.normal.eq_bot_or_eq_top Subgroup.Normal.eq_bot_or_eq_topₓ'. -/
@[to_additive]
theorem Subgroup.Normal.eq_bot_or_eq_top [IsSimpleGroup G] {H : Subgroup G} (Hn : H.Normal) :
H = ⊥ ∨ H = ⊤ :=
@@ -76,12 +70,6 @@ instance {C : Type _} [CommGroup C] [IsSimpleGroup C] : IsSimpleOrder (Subgroup
open _Root_.Subgroup
-/- warning: is_simple_group.is_simple_group_of_surjective -> IsSimpleGroup.isSimpleGroup_of_surjective is a dubious translation:
-lean 3 declaration is
- forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {H : Type.{u2}} [_inst_3 : Group.{u2} H] [_inst_4 : IsSimpleGroup.{u1} G _inst_1] [_inst_5 : Nontrivial.{u2} H] (f : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))), (Function.Surjective.{succ u1, succ u2} G H (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (fun (_x : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) => G -> H) (MonoidHom.hasCoeToFun.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) f)) -> (IsSimpleGroup.{u2} H _inst_3)
-but is expected to have type
- forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {H : Type.{u2}} [_inst_3 : Group.{u2} H] [_inst_4 : IsSimpleGroup.{u1} G _inst_1] [_inst_5 : Nontrivial.{u2} H] (f : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))), (Function.Surjective.{succ u1, succ u2} G H (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f)) -> (IsSimpleGroup.{u2} H _inst_3)
-Case conversion may be inaccurate. Consider using '#align is_simple_group.is_simple_group_of_surjective IsSimpleGroup.isSimpleGroup_of_surjectiveₓ'. -/
@[to_additive]
theorem isSimpleGroup_of_surjective {H : Type _} [Group H] [IsSimpleGroup G] [Nontrivial H]
(f : G →* H) (hf : Function.Surjective f) : IsSimpleGroup H :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -89,8 +89,7 @@ theorem isSimpleGroup_of_surjective {H : Type _} [Group H] [IsSimpleGroup G] [No
by
refine' (iH.comap f).eq_bot_or_eq_top.imp (fun h => _) fun h => _
· rw [← map_bot f, ← h, map_comap_eq_self_of_surjective hf]
- · rw [← comap_top f] at h
- exact comap_injective hf h⟩
+ · rw [← comap_top f] at h; exact comap_injective hf h⟩
#align is_simple_group.is_simple_group_of_surjective IsSimpleGroup.isSimpleGroup_of_surjective
#align is_simple_add_group.is_simple_add_group_of_surjective IsSimpleAddGroup.isSimpleAddGroup_of_surjective
mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4
@@ -80,7 +80,7 @@ open _Root_.Subgroup
lean 3 declaration is
forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {H : Type.{u2}} [_inst_3 : Group.{u2} H] [_inst_4 : IsSimpleGroup.{u1} G _inst_1] [_inst_5 : Nontrivial.{u2} H] (f : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))), (Function.Surjective.{succ u1, succ u2} G H (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (fun (_x : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) => G -> H) (MonoidHom.hasCoeToFun.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) f)) -> (IsSimpleGroup.{u2} H _inst_3)
but is expected to have type
- forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {H : Type.{u2}} [_inst_3 : Group.{u2} H] [_inst_4 : IsSimpleGroup.{u1} G _inst_1] [_inst_5 : Nontrivial.{u2} H] (f : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))), (Function.Surjective.{succ u1, succ u2} G H (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f)) -> (IsSimpleGroup.{u2} H _inst_3)
+ forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {H : Type.{u2}} [_inst_3 : Group.{u2} H] [_inst_4 : IsSimpleGroup.{u1} G _inst_1] [_inst_5 : Nontrivial.{u2} H] (f : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))), (Function.Surjective.{succ u1, succ u2} G H (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f)) -> (IsSimpleGroup.{u2} H _inst_3)
Case conversion may be inaccurate. Consider using '#align is_simple_group.is_simple_group_of_surjective IsSimpleGroup.isSimpleGroup_of_surjectiveₓ'. -/
@[to_additive]
theorem isSimpleGroup_of_surjective {H : Type _} [Group H] [IsSimpleGroup G] [Nontrivial H]
mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212
@@ -80,7 +80,7 @@ open _Root_.Subgroup
lean 3 declaration is
forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {H : Type.{u2}} [_inst_3 : Group.{u2} H] [_inst_4 : IsSimpleGroup.{u1} G _inst_1] [_inst_5 : Nontrivial.{u2} H] (f : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))), (Function.Surjective.{succ u1, succ u2} G H (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (fun (_x : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) => G -> H) (MonoidHom.hasCoeToFun.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) f)) -> (IsSimpleGroup.{u2} H _inst_3)
but is expected to have type
- forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {H : Type.{u2}} [_inst_3 : Group.{u2} H] [_inst_4 : IsSimpleGroup.{u1} G _inst_1] [_inst_5 : Nontrivial.{u2} H] (f : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))), (Function.Surjective.{succ u1, succ u2} G H (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f)) -> (IsSimpleGroup.{u2} H _inst_3)
+ forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {H : Type.{u2}} [_inst_3 : Group.{u2} H] [_inst_4 : IsSimpleGroup.{u1} G _inst_1] [_inst_5 : Nontrivial.{u2} H] (f : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))), (Function.Surjective.{succ u1, succ u2} G H (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f)) -> (IsSimpleGroup.{u2} H _inst_3)
Case conversion may be inaccurate. Consider using '#align is_simple_group.is_simple_group_of_surjective IsSimpleGroup.isSimpleGroup_of_surjectiveₓ'. -/
@[to_additive]
theorem isSimpleGroup_of_surjective {H : Type _} [Group H] [IsSimpleGroup G] [Nontrivial H]
mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5
@@ -80,7 +80,7 @@ open _Root_.Subgroup
lean 3 declaration is
forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {H : Type.{u2}} [_inst_3 : Group.{u2} H] [_inst_4 : IsSimpleGroup.{u1} G _inst_1] [_inst_5 : Nontrivial.{u2} H] (f : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))), (Function.Surjective.{succ u1, succ u2} G H (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (fun (_x : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) => G -> H) (MonoidHom.hasCoeToFun.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) f)) -> (IsSimpleGroup.{u2} H _inst_3)
but is expected to have type
- forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {H : Type.{u2}} [_inst_3 : Group.{u2} H] [_inst_4 : IsSimpleGroup.{u1} G _inst_1] [_inst_5 : Nontrivial.{u2} H] (f : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))), (Function.Surjective.{succ u1, succ u2} G H (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f)) -> (IsSimpleGroup.{u2} H _inst_3)
+ forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {H : Type.{u2}} [_inst_3 : Group.{u2} H] [_inst_4 : IsSimpleGroup.{u1} G _inst_1] [_inst_5 : Nontrivial.{u2} H] (f : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))), (Function.Surjective.{succ u1, succ u2} G H (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f)) -> (IsSimpleGroup.{u2} H _inst_3)
Case conversion may be inaccurate. Consider using '#align is_simple_group.is_simple_group_of_surjective IsSimpleGroup.isSimpleGroup_of_surjectiveₓ'. -/
@[to_additive]
theorem isSimpleGroup_of_surjective {H : Type _} [Group H] [IsSimpleGroup G] [Nontrivial H]
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Empty lines were removed by executing the following Python script twice
import os
import re
# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
for filename in files:
if filename.endswith('.lean'):
file_path = os.path.join(dir_path, filename)
# Open the file and read its contents
with open(file_path, 'r') as file:
content = file.read()
# Use a regular expression to replace sequences of "variable" lines separated by empty lines
# with sequences without empty lines
modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)
# Write the modified content back to the file
with open(file_path, 'w') as file:
file.write(modified_content)
@@ -24,7 +24,6 @@ subgroup, subgroups
variable {G : Type*} [Group G]
-
variable {A : Type*} [AddGroup A]
section
@@ -3,7 +3,7 @@ Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
-import Mathlib.GroupTheory.Subgroup.Actions
+import Mathlib.GroupTheory.Subgroup.Basic
#align_import group_theory.subgroup.simple from "leanprover-community/mathlib"@"f93c11933efbc3c2f0299e47b8ff83e9b539cbf6"
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -23,9 +23,9 @@ subgroup, subgroups
-/
-variable {G : Type _} [Group G]
+variable {G : Type*} [Group G]
-variable {A : Type _} [AddGroup A]
+variable {A : Type*} [AddGroup A]
section
@@ -57,13 +57,13 @@ theorem Subgroup.Normal.eq_bot_or_eq_top [IsSimpleGroup G] {H : Subgroup G} (Hn
namespace IsSimpleGroup
@[to_additive]
-instance {C : Type _} [CommGroup C] [IsSimpleGroup C] : IsSimpleOrder (Subgroup C) :=
+instance {C : Type*} [CommGroup C] [IsSimpleGroup C] : IsSimpleOrder (Subgroup C) :=
⟨fun H => H.normal_of_comm.eq_bot_or_eq_top⟩
open Subgroup
@[to_additive]
-theorem isSimpleGroup_of_surjective {H : Type _} [Group H] [IsSimpleGroup G] [Nontrivial H]
+theorem isSimpleGroup_of_surjective {H : Type*} [Group H] [IsSimpleGroup G] [Nontrivial H]
(f : G →* H) (hf : Function.Surjective f) : IsSimpleGroup H :=
⟨fun H iH => by
refine' (iH.comap f).eq_bot_or_eq_top.imp (fun h => _) fun h => _
@@ -2,14 +2,11 @@
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-
-! This file was ported from Lean 3 source module group_theory.subgroup.simple
-! leanprover-community/mathlib commit f93c11933efbc3c2f0299e47b8ff83e9b539cbf6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.GroupTheory.Subgroup.Actions
+#align_import group_theory.subgroup.simple from "leanprover-community/mathlib"@"f93c11933efbc3c2f0299e47b8ff83e9b539cbf6"
+
/-!
# Simple groups
The unported dependencies are