third_iso_hn_inv_closed

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 (n_normal : @NormalSubgroupLawArgs.{succ u} G one mul inv N), forall (h_normal : @NormalSubgroupLawArgs.{succ u} G one mul inv Hpred), forall (q : @ThirdIsoGN.{u} G one mul inv N group_args n_normal), forall (hq : @ThirdIsoHNPred.{u} G one mul inv N Hpred group_args n_normal q), @ThirdIsoHNPred.{u} G one mul inv N Hpred group_args n_normal (@ThirdIsoGNInv.{u} G one mul inv N group_args n_normal q)

fun G => fun one => fun mul => fun inv => fun N => fun Hpred => fun group_args => fun n_normal => fun h_normal => fun q => fun hq => hq (@ThirdIsoHNPred.{u} G one mul inv N Hpred group_args n_normal (@ThirdIsoGNInv.{u} G one mul inv N group_args n_normal q)) (fun (a : G) => fun (ha : Hpred a) => fun (eqa : @Eq.{succ u} (@NormalQuot.{u} G one mul inv N group_args n_normal) (@NormalQuotMk.{u} G one mul inv N group_args n_normal a) q) => @third_iso_hn_intro.{u} G one mul inv N Hpred group_args n_normal (@ThirdIsoGNInv.{u} G one mul inv N group_args n_normal q) (inv a) (@subgroup_inv_closed.{succ u} G one mul inv Hpred (@normal_subgroup_laws.{succ u} G one mul inv Hpred h_normal) a ha) (@eq_trans.{succ u} (@NormalQuot.{u} G one mul inv N group_args n_normal) (@NormalQuotMk.{u} G one mul inv N group_args n_normal (inv a)) (@ThirdIsoGNInv.{u} G one mul inv N group_args n_normal (@NormalQuotMk.{u} G one mul inv N group_args n_normal a)) (@ThirdIsoGNInv.{u} G one mul inv N group_args n_normal q) (@eq_symm.{succ u} (@NormalQuot.{u} G one mul inv N group_args n_normal) (@ThirdIsoGNInv.{u} G one mul inv N group_args n_normal (@NormalQuotMk.{u} G one mul inv N group_args n_normal a)) (@NormalQuotMk.{u} G one mul inv N group_args n_normal (inv a)) (@normal_quot_inv_mk.{u} G one mul inv N group_args n_normal a)) (@eq_congr_arg.{succ u,succ u} (@NormalQuot.{u} G one mul inv N group_args n_normal) (@NormalQuot.{u} G one mul inv N group_args n_normal) (@ThirdIsoGNInv.{u} G one mul inv N group_args n_normal) (@NormalQuotMk.{u} G one mul inv N group_args n_normal a) q eqa)))