Indexed Summation over Interval of Length Two

Theorem
Let $a\in\Z$ be an integer.

Let $f : \{a, a+1\} \to \R$ be a real-valued function.

Then the indexed summation:


 * $\displaystyle \sum_{i \mathop = a}^{a+1} f(i) = f(a) + f(a+1)$.