G-Tower is Closed under Chain Unions

Theorem
Let $M$ be a class.

Let $g: M \to M$ be a progressing mapping on $M$.

Let $M$ be a $g$-tower.

Then $M$ is closed under chain unions.

Proof
By definition:
 * a $g$-tower is a class which is minimally superinductive under $g$
 * a class which is minimally superinductive under $g$ is superinductive under $g$
 * a superinductive class is closed under chain unions.

Hence the result.