I was searching for answers to the Question:

Show that there are at most $ \lceil n / 2^{h + 1} \rceil$ nodes of height $ h$ in any $ n$ -element heap.

Recently I asked a related question and found out the solution was flawed so I looked for another one.

So I took over to another answer and found this

It took over to prove by induction and it is quite understood on the first read except for the statement:

Note that the nodes at height $ h$ in $ T$ would be at height $ h − 1$ in tree $ T’$ .

Preface:

Let $ N_h$ be the number of nodes at height $ h$ in the n-node tree $ T$ . Consider the tree $ T’$ formed by removing the leaves of $ T$ .

Please help me clarify my doubts. Thank you.