Let me refer you to:
http://www.math.iitb.ac.in/atm/caag1/balwant.pdf
Part (2) line $4$ can someone please explain why $x_{ni}=x_{n(m)i}$ for all $i \leq m$ and $n \geq n(m)$. I know it should follow by the fact that $n(m+1) \geq n(m)$ for every $m$ but I'm confused with this part.