third_iso_kernel_evidence

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), @ThirdIsoKernelEvidence.{u} G one mul inv N Hpred group_args n_normal h_normal n_le_h

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 (P : Prop) => fun (mk : forall (kernel_sound : 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)), forall (kernel_intro : forall (a : G), forall (ha : Hpred a), @ThirdIsoKernelPred.{u} G one mul inv N Hpred group_args n_normal (@NormalQuotMk.{u} G one mul inv N group_args n_normal a)), P) => mk (@third_iso_hn_to_kernel_sound.{u} G one mul inv N Hpred group_args n_normal h_normal n_le_h) (@third_iso_kernel_intro.{u} G one mul inv N Hpred group_args n_normal)