Let $P = (X, {\preceq})$ be a D1103: Partially ordered set such that
| (i) | $\mathsf{Chains}(P)$ is the D4636: Set of chains in $P$ |
| (iii) | $\max(P)$ is the D4464: Set of maximal elements in $P$ |
| (iii) | \begin{equation} \forall \, C \in \mathsf{Chains}(P) : \exists \, M \in X : \forall \, x \in C : x \preceq M \end{equation} |
Then
\begin{equation}
|\max(P)| \geq 1
\end{equation}