Double Induction Principle/Proof 2

Proof
By definition, a minimally inductive class under $g$ is a minimally closed class under $g$ with respect to $\O$.

Recall the Double Induction Principle for Minimally Closed Class:

Let $\RR$ be a relation on $M$ which satisfies:

Then $\map \RR {x, y}$ holds for all $x, y \in M$.

In this context:
 * $b = \O$

and the result follows.