intros A; case A; intros a pa; simpl in |- *.
unfold eq_part, empty in |- *; simpl in |- *.
intuition.
intros.
elim (H x); auto with *.
Qed.

Lemma disjoint_inclus :
forall A B C : part_set E, included A B -> disjoint B C -> disjoint A C.