Ceiling of Half of n+m plus Ceiling of Half of n-m+1

Theorem
Let $n, m \in \Z$ be integers.


 * $\ceiling {\dfrac {n + m} 2} + \ceiling {\dfrac {n - m + 1} 2} = n + 1$

where $\ceiling x$ denotes the ceiling of $x$.

Proof
Either $n + m$ or $n - m + 1$ is even.

Thus either $\dfrac {n + m} 2$ or $\dfrac {n - m + 1} 2$ is an integer.

So: