simple induction E; intros A f HR o E' i.
unfold INC in |- *.
intros E'' i'.
apply plump with E'.
auto with zfc.
apply IN_Ord_Ord with (sup A f); auto with zfc.
apply IN_Ord_Ord with E'; auto with zfc; apply IN_Ord_Ord with (sup A f);
auto with zfc.
auto with zfc.
elim i; intros a e.
apply INC_sound_right with (f a); auto with zfc.
apply HR; auto with zfc.
apply IN_Ord_Ord with (sup A f); auto with zfc; exists a;
auto with zfc.
apply IN_sound_right with E'; auto with zfc.
Qed.

(* Specifications: *)
Lemma inter_ord : forall E : Ens, Ord E -> Ord (Inter E).
simple induction E; intros A f HR o; apply Ord_intro.