unfold union in |- *; simpl in |- *.
unfold eq_part in |- *; simpl in |- *.
intros A B C x; split; [ try assumption | idtac ].
intuition.
intuition.
Qed.

Lemma union_com : forall A B : part_set E, Equal (union A B) (union B A).
unfold union in |- *; simpl in |- *.