(* Again, extentionality is not stated, but easy *)


(* Projections of a set: *)
(*  1: its base type     *)

Definition pi1 : Ens -> Type.(*  2: the function      *)

Definition pi2 : forall E : Ens, pi1 E -> Ens.(* The Union set   *)

Definition Union : forall E : Ens, Ens.

Theorem EQ_EXType : forall E E' : Ens, EQ E E' -> forall a : pi1 E, EXType (pi1 E') (fun b : pi1 E' => EQ (pi2 E a) (pi2 E' b)).