Given any real number $\displaystyle x$ and positive integer $\displaystyle n$, prove that $\displaystyle \left \lfloor\frac{\left \lfloor x\right \rfloor}{n}\right \rfloor = \left \lfloor\frac{x}{n}\right \rfloor$

Deduce that for any real number $\displaystyle y$ and positive integers $\displaystyle n$ and $\displaystyle m$, one has

$\displaystyle \left \lfloor\frac{\left \lfloor \frac{y}{m}\right \rfloor}{n}\right \rfloor = \left \lfloor\frac{\left \lfloor \frac{y}{n}\right \rfloor}{m}\right \rfloor$

I think the second part is very straightforward i.e. $\displaystyle \left \lfloor\frac{\left \lfloor \frac{y}{m}\right \rfloor}{n}\right \rfloor = \left \lfloor\frac{\frac{y}{m}}{n}\right \rfloor = \left \lfloor\frac{\frac{y}{n}}{m}\right \rfloor = \left \lfloor\frac{\left \lfloor \frac{y}{n}\right \rfloor}{m}\right \rfloor$

I just can't prove the initial part.

Any help appreciated!