third_isomorphism_theorem_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), @ThirdIsoTheoremEvidence.{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 (rel_lift : forall (a : G), forall (b : G), forall (h : @NormalRel.{succ u} G one mul inv N a b), @NormalRel.{succ u} G one mul inv Hpred a b), forall (surjective : forall (q : @NormalQuot.{u} G one mul inv Hpred group_args h_normal), forall (Q : Prop), forall (mk_surj : forall (src : @NormalQuot.{u} G one mul inv N group_args n_normal), forall (h : @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 src) q), Q), Q), forall (kernel_evidence : @ThirdIsoKernelEvidence.{u} G one mul inv N Hpred group_args n_normal h_normal n_le_h), P) => mk (@third_iso_rel_lift.{u} G one mul inv N Hpred n_le_h) (@third_iso_phi_surjective.{u} G one mul inv N Hpred group_args n_normal h_normal n_le_h) (@third_iso_kernel_evidence.{u} G one mul inv N Hpred group_args n_normal h_normal n_le_h)