Minimally Inductive Class under Slowly Progressing Mapping is Nest/Proof 2

Theorem

Let $M$ be a class.

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

Let $M$ be a minimally inductive class under $g$.

Then $M$ is a nest.

Proof

By definition, a slowly progressing mapping is indeed a progressing mapping.

The result then follows from Minimally Inductive Class under Progressing Mapping induces Nest.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 9$ Supplement -- optional