Proving that an $n$-element heap has at most $\lceil \frac{n}{2^{h+1}-1} \rceil$ nodes
Probably, you mean this:
A heap of size $n$ has at most $\lceil \frac{n}{2^{h+1}} \rceil$ nodes with height $h$.

Proof can be found for example here:
http://www.cs.sfu.ca/CourseCentral/307/petra/2009/SLN_2.pdf