Integer Divisor Results/Integer Divides its Absolute Value

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

Then:

where:
 * $\left\lvert{n}\right\rvert$ is the absolute value of $n$
 * $\backslash$ denotes divisibility.

Proof
Let $n > 0$.

Then $\left\lvert{n}\right\rvert = n$ and Integer Divides Itself applies.

Let $n = 0$.

Then Integer Divides Itself holds again.

Let $n < 0$.

Then $\left\lvert{n}\right\rvert = -n$ and Integer Divides its Negative applies.