simple induction E'; simple induction E''; unfold CINC in |- *; simpl in |- *;
intros.
elim (X2 E0); try assumption; intros.
elim X1; intros XA XB; elim (XA x); intros.
exists x0; apply EQC_tran with (e x); auto with zfc.
Qed.

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