Let $P = (\mathbb{N}, {\leq})$ be the D1095: Ordered set of natural numbers such that
| (i) | $f : \mathbb{N} \to \{ 0, 1 \}$ is a D218: Boolean function on $\mathbb{N}$ |
| (ii) | \begin{equation} X : = \{ n \in \mathbb{N} : f(n) = 1 \} \end{equation} |
| (iii) | \begin{equation} 0 \in X \subseteq \mathbb{N} \end{equation} |
| (iv) | \begin{equation} \forall \, n \in \mathbb{N} \left( n \in X \quad \implies \quad n + 1 \in X \right) \end{equation} |
Then
\begin{equation}
X
= \mathbb{N}
\end{equation}