simple induction E; simple induction E'; simpl in |- *.
intros.
elim X1; intros.
elim (a0 a); intros.
exists x; auto with zfc.
Defined.

(* Specifications: *)
Theorem CIN_EXType :
forall E E' : Ens,
CIN E' E -> depprod (pi1 E) (fun a : pi1 E => EQC E' (pi2 E a)).
Theorem CIN_EXType :
forall E E' : Ens,
CIN E' E -> depprod (pi1 E) (fun a : pi1 E => EQC E' (pi2 E a)).