Successor Mapping on Natural Numbers is Progressing/Proof 2

Theorem

Let $\omega$ denote the set of natural numbers as defined by the von Neumann construction.

Let $s: \omega \to \omega$ denote the successor mapping on $\omega$.

Then $s$ is a progressing mapping.

Proof

By definition, the successor mapping on $\omega$ is indeed an example of a successor mapping.

The result follows from Successor Mapping is Progressing.

$\blacksquare$