simple induction 1.
elim H; intros x; elim x.
Qed.

(* Specifications: *)
Theorem tout_vide_est_Vide :
forall E : Ens, (forall E' : Ens, IN E' E -> F) -> EQ E Vide.
Theorem tout_vide_est_Vide :
forall E : Ens, (forall E' : Ens, IN E' E -> F) -> EQ E Vide.