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Declaration
subgroup_inter_inv_closed
Mathlib.Algebra.Group.Subgroup
Packages
2
Module
63
Theorems
750
Declarations
1016
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Statement
forall (G : Sort u), forall (one : G), forall (mul : forall (a : G), forall (b : G), G), forall (inv : forall (a : G), G), forall (S : forall (x : G), Prop), forall (T : forall (x : G), Prop), forall (s_args : @SubgroupLawArgs.{u} G one mul inv S), forall (t_args : @SubgroupLawArgs.{u} G one mul inv T), forall (a : G), forall (ha : @SubgroupInterPred.{u} G S T a), @SubgroupInterPred.{u} G S T (inv a)Proof term
fun G => fun one => fun mul => fun inv => fun S => fun T => fun s_args => fun t_args => fun a => fun ha => ha (@SubgroupInterPred.{u} G S T (inv a)) (fun (haS : S a) => fun (haT : T a) => @subgroup_inter_intro.{u} G S T (inv a) (@subgroup_inv_closed.{u} G one mul inv S s_args a haS) (@subgroup_inv_closed.{u} G one mul inv T t_args a haT))