unfold minus_part in |- *.
intros.
simpl in |- *.
unfold eq_part, diff, single in |- *; simpl in |- *.
intro.
intuition.
Qed.
Hint Immediate minus_part_com: algebra.

Lemma minus_not_in :
forall (A : part_set E) (x : E), ~ in_part x A -> Equal (minus_part A x) A.