Let $P$ be a D1687: Inclusion-ordered collection of sets such that
| (i) | $\max(P)$ is the D4464: Set of maximal elements in $P$ |
Then
\begin{equation}
|\max(P)| \geq 1
\end{equation}
| (i) | $\max(P)$ is the D4464: Set of maximal elements in $P$ |
| ▶ | R4291: Vector space always has an inclusion-maximal linearly independent set |
| (i) | $\max(P)$ is the D4464: Set of maximal elements in $P$ |