# How is it possible for nodes at height \$h\$ in Tree \$T\$ to be at height \$h-1\$ at T’

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 $$T$$.