apply Ord_intro.
intros.
apply IN_Comp_P with (Power E).
intros w1 w2 o1 e; apply Ord_sound with w1; auto with zfc.
auto with zfc.
intros E1 E2 o1 o2 i inc.
apply IN_P_Comp; auto with zfc.
intros w1 w2 ow1 e; apply Ord_sound with w1; auto with zfc.
apply INC_IN_Power.
apply INC_tran with E1; auto with zfc.
cut (IN E1 (Power E)).
intros i1.
apply IN_Power_INC; try trivial with zfc.
cut (INC (Comp (Power E) Ord) (Power E)).
intros inc1.
apply inc1; try trivial with zfc.
apply Comp_INC; try trivial with zfc.
Qed.

(* Specifications: *)
Lemma Succ_incr : forall E : Ens, Ord E -> IN E (Succ E).
unfold Succ in |- *; intros.