(* 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_Union : forall E E' E'' : Ens, IN E' E -> IN E'' E' -> IN E'' (Union E).