ThirdIsoPhi

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), @NormalQuot.{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 => @Quotient.lift.{u,u} G (@NormalQuot.{u} G one mul inv Hpred group_args h_normal) (@NormalSetoid.{u} G one mul inv N group_args n_normal) (fun (a : G) => @NormalQuotMk.{u} G one mul inv Hpred group_args h_normal a) (fun (a : G) => fun (b : G) => fun (h : @Setoid.r.{u} G (@NormalSetoid.{u} G one mul inv N group_args n_normal) a b) => @normal_quot_sound.{u} G one mul inv Hpred group_args h_normal a b (n_le_h (mul (inv a) b) h))