intros.
cut (INC E' E).
intros inc; elim (ord_sound E E' H E' inc (INC_refl E')).
intros h1 h2.
unfold Ord in |- *.
apply h1.
apply ord_ext with E (INC_refl E); auto with zfc.
auto with zfc.
Qed.

(* Specifications: *)
Lemma IN_Ord_Ord : forall E E' : Ens, Ord E -> IN E' E -> Ord E'.
simple induction E; intros A f HR E'.