Two properties of maximal antichains in strict chain product posets

We present two results on maximal antichains in the strict chain product poset $[t_1+1]\times[t_2+1]\times\ldots\times[t_n+1]$. 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 $[t_1+1]\times[t_2+1]\times\ldots\times[t_n+1]$ and antichains in the non-strict chain product poset $[t_1]\times[t_2]\times\ldots\times[t_n]$.