third_iso_hn_to_kernel_sound

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 (n_le_h : forall (x : G), forall (hn : N x), Hpred x), forall (q : @NormalQuot.{u} G one mul inv N group_args n_normal), forall (hk : @ThirdIsoKernelPred.{u} G one mul inv N Hpred group_args n_normal q), @Eq.{succ u} (@NormalQuot.{u} G one mul inv Hpred group_args h_normal) (@ThirdIsoPhi.{u} G one mul inv N Hpred group_args n_normal h_normal n_le_h q) (@NormalQuotOne.{u} G one mul inv Hpred group_args h_normal)

fun G => fun one => fun mul => fun inv => fun N => fun Hpred => fun group_args => fun n_normal => fun h_normal => fun n_le_h => fun q => fun hk => hk (@Eq.{succ u} (@NormalQuot.{u} G one mul inv Hpred group_args h_normal) (@ThirdIsoPhi.{u} G one mul inv N Hpred group_args n_normal h_normal n_le_h q) (@NormalQuotOne.{u} G one mul inv Hpred group_args h_normal)) (fun (h : G) => fun (hh : Hpred h) => fun (eq_q : @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 h) q) => @eq_trans.{succ u} (@NormalQuot.{u} G one mul inv Hpred group_args h_normal) (@ThirdIsoPhi.{u} G one mul inv N Hpred group_args n_normal h_normal n_le_h q) (@ThirdIsoPhi.{u} G one mul inv N Hpred group_args n_normal h_normal n_le_h (@NormalQuotMk.{u} G one mul inv N group_args n_normal h)) (@NormalQuotOne.{u} G one mul inv Hpred group_args h_normal) (@eq_symm.{succ u} (@NormalQuot.{u} G one mul inv Hpred group_args h_normal) (@ThirdIsoPhi.{u} G one mul inv N Hpred group_args n_normal h_normal n_le_h (@NormalQuotMk.{u} G one mul inv N group_args n_normal h)) (@ThirdIsoPhi.{u} G one mul inv N Hpred group_args n_normal h_normal n_le_h q) (@eq_congr_arg.{succ u,succ u} (@NormalQuot.{u} G one mul inv N group_args n_normal) (@NormalQuot.{u} G one mul inv Hpred group_args h_normal) (@ThirdIsoPhi.{u} G one mul inv N Hpred group_args n_normal h_normal n_le_h) (@NormalQuotMk.{u} G one mul inv N group_args n_normal h) q eq_q)) (@eq_trans.{succ u} (@NormalQuot.{u} G one mul inv Hpred group_args h_normal) (@ThirdIsoPhi.{u} G one mul inv N Hpred group_args n_normal h_normal n_le_h (@NormalQuotMk.{u} G one mul inv N group_args n_normal h)) (@NormalQuotMk.{u} G one mul inv Hpred group_args h_normal h) (@NormalQuotOne.{u} G one mul inv Hpred group_args h_normal) (@third_iso_phi_mk.{u} G one mul inv N Hpred group_args n_normal h_normal n_le_h h) (@normal_quot_sound.{u} G one mul inv Hpred group_args h_normal h one (@normal_rel_one_of_mem.{succ u} G one mul inv group_args Hpred h_normal h hh))))