Finite Ordinal Times Ordinal/Lemma

Lemma
Let $m$ be a finite ordinal.

Let $m \ne 0$, where $0$ is the zero ordinal.

Then:


 * $m \times \omega = \omega$

where $\omega$ denotes the minimal infinite successor set.

Proof
Also, by Subset is Right Compatible with Ordinal Multiplication:
 * $\omega \le \paren {m \times \omega}$

The lemma follows from the definition of equality.