intros A B.
case A; case B; simpl in |- *.
intros a pa b pb.
unfold eq_part in |- *; simpl in |- *.
intuition.
Qed.

Lemma in_diff :
forall (A B : part_set E) (x : E),
in_part x A -> ~ in_part x B -> in_part x (diff A B).