Sequence of Recursively Defined Terms forms Minimally Inductive Set

Theorem
Let $g$ be a mapping.

Let $\sequence {a_n}$ be a sequence such that:
 * $a_0 = \O$

and:
 * $\forall n \in \N: a_{n + 1} = \map g {a_n}$

Then the set:
 * $\set {a_0, a_1, \ldots, a_n, a_{n + 1}, \ldots}$

is minimally inductive under $g$.