Let $P = (\mathbb{Z}, {\leq})$ be the D1098: Ordered set of integers such that
| (i) | $X$ is a D11: Set |
| (ii) | $a \in \mathbb{Z}$ is an D995: Integer |
| (iii) | \begin{equation} [a, \infty) : = \{ n \in \mathbb{Z} : n \geq a \} \end{equation} |
| (iv) | \begin{equation} a \in X \subseteq [a, \infty) \end{equation} |
| (v) | \begin{equation} \forall \, n \in \mathbb{Z} \left( n \in X \quad \implies \quad n + 1 \in X \right) \end{equation} |
Then
\begin{equation}
X
= [a, \infty)
\end{equation}