Section fparts2_def.
Variable E : Setoid.
Definition disjoint (A B : part_set E) := Equal (inter A B) (empty E).
unfold disjoint in |- *.
intros A A' B B' H' H'0 H'1; try assumption.
apply Trans with (inter A B).
auto with *.
auto with *.
Qed.
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.