simple induction E''; simpl in |- *; intros.
elim X1; intros y p; exists y.
apply EQC_tran with E; auto with zfc.
Qed.

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