simpl in |- *; auto with algebra.
unfold eq_part in |- *; auto with algebra.
simpl in |- *; unfold not in |- *.
intros A B H' x; try assumption.
elim (H' x).
apply NNPP.
tauto.
Qed.

Lemma compl_compl : forall A : part_set E, Equal (compl (compl A)) A.
simpl in |- *; auto with algebra.