simple induction 1.
cut (IN E Vide).
simpl in |- *; simple induction 1; intros xx; elim xx; simple induction 1.
apply IN_sound_right with (Sing E); auto with zfc.
Qed.

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