apply X1.
exists x; auto with zfc.
cut (depprod A (fun x : A => EQC (e0 y) (e x)));
try (simple induction 1; intros x p; exists x; auto with zfc).
apply X2; exists y; auto with zfc.
Qed.
Hint Resolve CINC_EQC: zfc.

(* Specifications: *)
Theorem CIN_sound_left :
forall E E' E'' : Ens, EQC E E' -> CIN E E'' -> CIN E' E''.
Theorem CIN_sound_left :
forall E E' E'' : Ens, EQC E E' -> CIN E E'' -> CIN E' E''.