Definition:Principle of General Induction/Minimally Closed Class/Induction Step

Terminology of Principle of General Induction for Minimally Closed Class

Consider a Proof by General Induction for a minimally closed class under $g$ with respect to $b$.

The step which shows that $\map P x = \T \implies \map P {\map g x} = \T$ is called the induction step.

Also known as

The basis for the induction is often informally referred to as the base case.