unfold inter in |- *.
intros.
elim H0; clear H0.
intros H0 H1; elim H1; clear H1; intros H1 H2.
elim H; clear H.
intros H3 H4; elim H4; clear H4; intros H4 H5.
split; auto.
split.
apply empty_inclus.
intros.
cut (dans x b \/ dans x c); auto.
intro H7; elim H7; auto.
Qed.

Lemma inter_union :
forall A B C : Ensf,
inter A C empty -> inter B C empty -> inter (union A B) C empty.