Least Fixed Point of Enumeration Operator

Theorem
Let $\psi : \powerset \N \to \powerset \N$ be an enumeration operator.

Let $A_i$ be defined recursively as:
 * $A_0 = \empty$
 * $A_{n + 1} = \map \psi {A_n}$

Let $A = \ds \bigcup_{i \mathop \in \N} A_i$.

Then:
 * $A$ is a fixed point of $\psi$
 * Every fixed point of $\psi$ is a superset of $A$