simple induction V; intros A f HR.
intros W i E inc.
change (IN E (Union (sup A (fun a : A => Power (Vee (f a)))))) in |- *.
apply IN_Union with (Power (Vee W)).
elim i; intros a h.
exists a.
apply Power_sound; apply Vee_sound; auto with zfc.
auto with zfc.
apply INC_IN_Power.
assumption.
Qed.

(* Specifications: *)
Lemma INC_IN_Vee_Succ :
forall E L : Ens, Ord L -> INC E (Vee L) -> IN E (Vee (Succ L)).