Show that in every sequence of lengthm*nthat had no sub sequencemonotonically increasingin length ofn+1and had no sub sequencemonotonically decreasingin length ofm+1, havemsub sequencesmonotonically increasingin length ofnandnsub sequencesmonotonically decreasingin length ofmso that every monotonic decreasing sub sequence and every monotonic decreasing sub sequence had one element in common.

Can somebody prove me that?