Two properties of maximal antichains in strict chain product posets

We present two results on maximal antichains in the strict chain product poset [t1 + 1] x [t2 + 1] _ _ _ _ _ [tn + 1]. First, we prove that these maximal antichains are also maximum. Second, we prove that there is a bijection between maximal antichains in the strict chain product poset [t1 + 1] x [t2 + 1] _ _ _ _ _ [tn + 1] and antichains in the nonstrict chain product poset [t1] x [t2] _ _ _ _ _ [tn].