(* 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 IN_EXType : forall E E' : Ens, IN E' E -> EXType (pi1 E) (fun a : pi1 E => EQ E' (pi2 E a)).