intros E X i.
cut (IN X (Power E)).
auto with zfc.
auto with zfc.
apply (Comp_INC (Power E) Ord); try trivial with zfc.
Qed.
Hint Resolve Ord_Succ: zfc.

Lemma IN_Vee_Succ_EXType :
forall E X : Ens,
Ord E ->
IN X (Vee (Succ E)) ->
EXType _ (fun Y : Ens => INC Y E /\ Ord Y /\ INC X (Vee Y)).