(* 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 Union_IN : forall E E' : Ens, IN E' (Union E) -> EXType _ (fun E1 : Ens => IN E1 E /\ IN E' E1).