proposition: Lemma add_inclus : forall (x : Elt) (a b : Ensf), dans x b -> inclus a b -> inclus (add x a) b.
proof: Proof. unfold inclus in |- *. intros. cut (x = x0 \/ dans x0 a). 2: apply dans_add; auto. intro H2; elim H2; clear H2. intro H2; rewrite <- H2; auto. auto. Qed.
imports: Ensf_types Ensf_dans Ensf_union Ensf_produit