Divisor Relation is Antisymmetric

Theorem
Divides is a antisymmetric relation on $\Z_{>0}$, the set of positive integers.

That is:
 * $\forall a, b \in \Z_{>0}: a \mathrel \backslash b \land b \mathrel \backslash a \implies a = b$

Proof
Let $a, b \in \Z_{> 0}$ such that $a \mathrel \backslash b$ and $b \mathrel \backslash a$.

Then:

If we restrict ourselves to the domain of positive integers, we can see:


 * $\forall a, b \in \Z_{>0}: a \mathrel \backslash b \land b \mathrel \backslash a \implies a = b$