intros E X o i.
elim (IN_Vee_EXType _ _ i).
intros Y; simple induction 1; intros i1 inc.
exists Y; split.
apply IN_Succ_INC; auto with zfc.
split.
auto with zfc.
apply IN_Ord_Ord with (Succ E); auto with zfc.
auto with zfc.
Qed.

(* Specifications: *)
Lemma IN_Vee_Succ :
forall E X : Ens,
Ord E ->
forall Y : Ens, Ord Y -> INC Y E -> INC X (Vee Y) -> IN X (Vee (Succ E)).