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

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


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

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

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

Thus:
 * $\dfrac {n + m} 2 \bmod 1 + \dfrac {n - m + 1} 2 \bmod 1 = \dfrac 1 2 < 1$

and so: