apply INC_EQ; unfold INC in |- *.
intros A i.
cut (INC A E').
intros; apply INC_IN_Power; assumption.
cut (INC A E); intros.
apply INC_sound_right with E; auto with zfc.
apply IN_Power_INC; assumption.
intros A i.
cut (INC A E).
intros; apply INC_IN_Power; assumption.
cut (INC A E'); intros.
apply INC_sound_right with E'; auto with zfc.
apply IN_Power_INC; assumption.
Qed.
(* small lemma *)

Theorem not_EQ_Sing_Vide : forall E : Ens, EQ (Sing E) Vide -> F.
intros E e; cut False.