subgroup_inter_normal_in_left

forall (G : Sort u), forall (one : G), forall (mul : forall (a : G), forall (b : G), G), forall (inv : forall (a : G), G), forall (Hpred : forall (x : G), Prop), forall (N : forall (x : G), Prop), forall (h_args : @SubgroupLawArgs.{u} G one mul inv Hpred), forall (n_normal : @NormalSubgroupLawArgs.{u} G one mul inv N), forall (h : G), forall (n : G), forall (hh : Hpred h), forall (hn : @SubgroupInterPred.{u} G Hpred N n), @SubgroupInterPred.{u} G Hpred N (mul (mul h n) (inv h))

fun G => fun one => fun mul => fun inv => fun Hpred => fun N => fun h_args => fun n_normal => fun h => fun n => fun hh => fun hn => hn (@SubgroupInterPred.{u} G Hpred N (mul (mul h n) (inv h))) (fun (hnH : Hpred n) => fun (hnN : N n) => @subgroup_inter_intro.{u} G Hpred N (mul (mul h n) (inv h)) (@subgroup_mul_closed.{u} G one mul inv Hpred h_args (mul h n) (inv h) (@subgroup_mul_closed.{u} G one mul inv Hpred h_args h n hh hnH) (@subgroup_inv_closed.{u} G one mul inv Hpred h_args h hh)) (@normal_conj_closed.{u} G one mul inv N n_normal h n hnN))