[/math], and we are done by the discussion at the beginning of the proof. We have handled the case in which at least one of the slicings of the 00-point set is of the form 00=00+00+00. The only remaining case is when all slicings of the 00-point set are of the form 00+00+00 or 00+00+00 (or a permutation thereof). By the symmetries of the situation, we may assume that the 0*** slice has 00 points, and thus by Lemma 0 takes the form 