subgroup_inter_mul_closed

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 (b : G), forall (ha : @SubgroupInterPred.{u} G S T a), forall (hb : @SubgroupInterPred.{u} G S T b), @SubgroupInterPred.{u} G S T (mul a b)

fun G => fun one => fun mul => fun inv => fun S => fun T => fun s_args => fun t_args => fun a => fun b => fun ha => fun hb => ha (@SubgroupInterPred.{u} G S T (mul a b)) (fun (haS : S a) => fun (haT : T a) => hb (@SubgroupInterPred.{u} G S T (mul a b)) (fun (hbS : S b) => fun (hbT : T b) => @subgroup_inter_intro.{u} G S T (mul a b) (@subgroup_mul_closed.{u} G one mul inv S s_args a b haS hbS) (@subgroup_mul_closed.{u} G one mul inv T t_args a b haT hbT)))