simple induction L; intros A f HR.
intros o inc.
unfold Succ in |- *.
apply IN_Vee with (sup A f).
apply IN_P_Comp.
intros; apply Ord_sound with w1; auto with zfc.
auto with zfc.
apply INC_IN_Power; auto with zfc.
assumption.
assumption.
Qed.
Definition PI1 (A : Type) (P : A -> Type) (c : depprod A P) :=
match c with
| dep_i a p => a
end.
Definition PI2 (A : Type) (P : A -> Type) (c : depprod A P) :=
match c return (P (PI1 A P c)) with
| dep_i a p => p
end.

(* Specifications: *)
Lemma IN_Vee_EXType :
forall E X : Ens,
IN X (Vee E) -> EXType Ens (fun Y : Ens => IN Y E /\ INC X (Vee Y)).