intros A B.
case A; case B; simpl in |- *.
intros a pa b pb.
unfold eq_part in |- *; simpl in |- *.
intuition.
Qed.
Hint Resolve in_diff: algebra.

(* Specifications: *)
Lemma union_diff :
forall A B : part_set E, Equal (union A (diff B A)) (union A B).