simple induction E.
intros A f HR.
simpl in |- *.
intros E' E'' I' I'' e.
simple induction 1.
intros o1 o2.
clear H.
split.
auto with zfc.
intros; apply o1.
apply IN_sound_right with E''; auto with zfc.
intros.
apply IN_sound_right with E'; auto with zfc.
apply (o2 a) with (p := p).
apply IN_sound_right with E''; auto with zfc.
auto with zfc.
Qed.

(* Specifications: *)
Lemma ord_sound :
forall E E' : Ens,
EQ E E' ->
forall (E'' : Ens) (p : INC E'' E) (p' : INC E'' E'),
(ord E E'' p -> ord E' E'' p') /\ (ord E' E'' p' -> ord E E'' p).