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 $R$ |

Then
\begin{equation}
\mathcal{L} \neq \emptyset
\end{equation}