Integer Divisor Results/Integer Divides its Absolute Value

Theorem
Let $n \in \Z$, i.e. let $n$ be an integer.

Then:

where $\left|{n}\right|$ is the absolute value of $n$.

Proof
Let $n > 0$. Then $\left|{n}\right| = n$ and Integer Divides Itself applies.

Let $n = 0$. Then Integer Divides Itself holds again.

Let $n < 0$. Then $\left|{n}\right| = -n$ and Integer Divides its Negative applies.