unfold not in |- *; intros.
cut (in_part x A \/ in_part x B).
intros H'; try assumption.
intuition.
auto with *.
Qed.
Hint Resolve union_not_in: algebra.

(* Specifications: *)
Lemma disjoint_not_in_r :
forall (A B : part_set E) (x : E),
disjoint A B -> in_part x A -> ~ in_part x B.