simple induction E; intros A f HR h1 h2; split.
intros a i.
change (Ord (f a)) in |- *; apply h1; exists a; auto with zfc.
intros a E1 i inc o.
apply h2 with (E1 := f a).
auto with zfc.
auto with zfc.
unfold Ord in |- *.
apply (ord_tech (f a)) with (p1 := inc) (p2 := INC_refl E1);
auto with zfc.
exists a; auto with zfc.
auto with zfc.
Qed.

Lemma Ord_trans :
forall E : Ens, Ord E -> forall E' : Ens, IN E' E -> INC E' E.