simpl in |- *.
intro.
case A; simpl in |- *.
intros a pa.
intuition.
Qed.
Hint Resolve minus_part_not_in: algebra.

Lemma minus_part_com :
forall (A : part_set E) (x y : E),
Equal (minus_part (minus_part A x) y) (minus_part (minus_part A y) x).