simple induction E; intros A f HR.
simple induction 1; intros o1 o2.
intros E1 E2 o11 o22 i inc.
elim (IN_EXType _ _ i).
intros a eq; simpl in a; simpl in eq.
cut (INC E2 (f a)).
intros inc0; apply (o2 a) with (p := inc0).
exists a; auto with zfc.
apply ord_tech with (E1 := E2) (p1 := INC_refl E2) (p2 := inc0).
assumption.
apply INC_sound_right with E1; auto with zfc.
Qed.

(* Specifications: *)
Lemma Ord_intro :
forall E : Ens,
(forall E' : Ens, IN E' E -> Ord E') ->
(forall E1 E2 : Ens, Ord E1 -> Ord E2 -> IN E1 E -> INC E2 E1 -> IN E2 E) ->
Ord E.