Power Function Preserves Ordering in Ordered Semigroup/Proof 1

Proof
By definition of ordered semigroup:
 * $\preceq$ is compatible with $\circ$.

By definition of ordering:
 * $\preceq$ is transitive.

Thus by Transitive Relation Compatible with Semigroup Operation Relates Powers of Related Elements:
 * $x^n \preceq y^n$