Divisor Relation is Antisymmetric/Corollary/Proof 1

Corollary to Divisor Relation is Antisymmetric

Let $a, b \in \Z$.

If $a \divides b$ and $b \divides a$ then $a = b$ or $a = -b$.

Proof

Let $a \divides b$ and $b \divides a$.

Then from Divisor Relation is Antisymmetric:

$\size a = \size b$

The result follows from Integer Divides its Negative and Integer Divides its Absolute Value.

$\blacksquare$