## Erdos-Szekeres variation

Show that in every sequence of length m*n that had no sub sequence monotonically increasing in length of n+1 and had no sub sequence monotonically decreasing in length of m+1, have m sub sequences monotonically increasing in length of n and n sub sequences monotonically decreasing in length of m so that every monotonic decreasing sub sequence and every monotonic decreasing sub sequence had one element in common.

Can somebody prove me that?