simpl in |- *.
unfold eq_part, minus_part, diff, single in |- *; simpl in |- *.
intro.
case A; simpl in |- *.
intros a pa.
intuition.
Qed.
Hint Resolve minus_trans_not_in: algebra.
(* Some lemmas. *)

Lemma union_unit_l : forall A : part_set E, Equal (union (empty E) A) A.
simpl in |- *.