Divisor Relation on Positive Integers is Well-Founded Ordering

Theorem
The divisor relation on $\Z_{>0}$ is a well-founded ordering.

Proof
Let $\struct {\Z_{>0}, \divides}$ denote the relational structure formed from the strictly positive integers $\Z_{>0}$ under the divisor relation $\divides$.

From Divisor Relation on Positive Integers is Partial Ordering, $\struct {\Z_{>0}, \divides}$ is a partially ordered set.

It remains to be shown that $\divides$ is well-founded.