Minimally Superinductive Class is Well-Ordered under Subset Relation

Theorem

Let $M$ be a class.

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

Let $M$ be minimally superinductive under $g$.

Then $M$ is well-ordered under the subset relation.

Proof

We have a priori that $M$ is a $g$-tower.

The result follows from $g$-Tower is Well-Ordered under Subset Relation.

$\blacksquare$