Let's take the left child of the node indexed by ⌊𝑛/2⌋+1⌊*n*/2⌋+1.

LEFT(⌊𝑛/2⌋+1)

=2(⌊𝑛/2⌋+1)

>2(𝑛/2−1)+2

=𝑛−2+2

=n.

Since the index of the left child is larger than the number of elements in the heap, the node doesn't have childrens and thus is a leaf. The same goes for all nodes with larger indices.

Note that if we take element indexed by ⌊*n*/2⌋, it will not be a leaf. In case of even number of nodes, it will have a left child with index *n* and in the case of odd number of nodes, it will have a left child with index *n*−1 and a right child with index *n*.

This makes the number of leaves in a heap of size *n* equal to ⌈*n*/2⌉.

I can't understand this statement: LEFT(⌊n/2⌋+1)>2(n/2−1)+2