Integer Divisor Results/Integer Divides its Absolute Value

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

Then:

where:
 * $\size n$ is the absolute value of $n$
 * $\divides$ denotes divisibility.

Proof
Let $n > 0$.

Then $\size n = n$ and Integer Divides Itself applies.

Let $n = 0$.

Then Integer Divides Itself holds again.

Let $n < 0$.

Then $\size n = -n$ and Integer Divides its Negative applies.