Double Induction Principle

Theorem
Let $M$ be a class.

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

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

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

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

Minimally Closed Class
The Double Induction Principle can be made more general by applying it to a minimally closed class:

Also known as
The Double Induction Principle can also be referred to as the Principle of Double Induction.

Some authors refer to this principle by its initials: D.I.P.

Also see

 * Double Superinduction Principle