Let $R$ be a D273: Division ring.

Let $V$ be a D29: Vector space over $R$ such that

Let $V$ be a D29: Vector space over $R$ such that

(i) | $\mathcal{L} : = \mathcal{L}_R(V)$ is the D2043: Set of linearly independent sets in $V$ over $R$ |

(ii) | \begin{equation} \max(\mathcal{L}) : = \{ M \in \mathcal{L} \mid \forall \, L \in \mathcal{L} : L \subseteq M \} \end{equation} |

Then
\begin{equation}
|\max(\mathcal{L})|
\geq 1
\end{equation}