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

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## 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**.