simple induction 1; intros o1 o2.
change (forall a : A, IN (f a) (sup A f) -> Ord (f a)) in o1.
intros i.
elim i; intros a eq.
apply Ord_sound with (f a); auto with zfc.
apply o1.
auto with zfc.
exists a; auto with zfc.
Qed.

(* Specifications: *)
Lemma ord_tech :
forall (E1 E2 E : Ens) (p1 : INC E E1) (p2 : INC E E2),
ord E1 E p1 -> ord E2 E p2.