intros.
absurd (dans (natural n) empty); auto.
intros a b H n H0.
replace (sup (add a b)) with (max (Z a) (sup b)).
2: auto.
cut (n < Z a \/ n < sup b).
intro.
elim H1; auto.
intros; apply lt_le_trans with (Z a); auto with arith.
intros; apply lt_le_trans with (sup b); auto with arith.
cut (a = natural n :>Elt \/ dans (natural n) b).
2: apply dans_add; auto.
intro.
elim H1.
intro; left.
rewrite H2; apply lt_n_Z.
intro; right.
apply H; assumption.
Qed.
(*								*)
(*  On en deduit que (natural (sup x)) n'est pas dans x 	*)
(*								*)

Lemma sup_out : forall x : Ensf, ~ dans (natural (sup x)) x.
intro.