Order of Group Element not less than Order of Power

Theorem
Let $\left({G, \circ}\right)$ be a group whose identity is $e$.

Let $g \in G$ be an element of $g$.

Let $\left\lvert{g}\right\rvert$ denote the order of $g$ in $G$.

Then:
 * $\forall m \in \Z: \left\lvert{g^m}\right\rvert \le \left\lvert{g}\right\rvert$

where $g^m$ denotes the $m$th power of $g$ in $G$.