simpl in |- *; auto with algebra.
unfold eq_part in |- *; auto with algebra.
intros A B H' x; try assumption.
elim (H' x).
simpl in |- *; unfold not in |- *.
intuition.
Qed.
Hint Resolve compl_comp: algebra.

Lemma compl_comp_rev :
forall A B : part_set E, Equal (compl A) (compl B) -> Equal A B.