Divisor Relation on Positive Integers is Partial Ordering

Theorem
Divides is a partial ordering of $\Z_{>0}$.

Proof
Checking in turn each of the critera for an ordering:

Divides is Transitive

 * $\forall x, y, z \in \Z: x \backslash y \land y \backslash z \implies x \backslash z$