correspondence_subgroup_saturates

forall (G : Sort succ u), forall (one : G), forall (mul : forall (a : G), forall (b : G), G), forall (inv : forall (a : G), G), forall (N : forall (x : G), Prop), forall (Hpred : forall (x : G), Prop), forall (group_args : @GroupLawArgs.{succ u} G one mul inv), forall (h_args : @SubgroupLawArgs.{succ u} G one mul inv Hpred), forall (n_le_h : forall (x : G), forall (hn : N x), Hpred x), forall (h : G), forall (x : G), forall (hh : Hpred h), forall (rel : @NormalRel.{succ u} G one mul inv N h x), Hpred x

fun G => fun one => fun mul => fun inv => fun N => fun Hpred => fun group_args => fun h_args => fun n_le_h => fun h => fun x => fun hh => fun rel => @eq_subst.{succ u} G Hpred (mul h (mul (inv h) x)) x (@correspondence_group_mul_inv_left_reassoc.{succ u} G one mul inv group_args h x) (@subgroup_mul_closed.{succ u} G one mul inv Hpred h_args h (mul (inv h) x) hh (n_le_h (mul (inv h) x) rel))