lie-algebras-and-their-representations

diff --git a/sections/coherent-families.tex b/sections/coherent-families.tex
@@ -284,7 +284,7 @@ all \(i\) and \(j\).
 % TODO: Perhaps this could be incorporated into the proof of the following
 % theorem? Perhaps it's best to create another lemma for this
 % TODO: Restate the notation for σ_i beforehand
-\begin{proposition}
+\begin{lemma}
   The connected component of some \(m \in \mathscr{B}\) is given by the
   following.
   \begin{enumerate}
@@ -351,7 +351,7 @@ all \(i\) and \(j\).
       with \(m' \in \mathscr{B}^+\) and \(\sigma_{n-1} \cdots \sigma_1 \cdot m'
       \in \mathscr{B}^-\).
   \end{enumerate}
-\end{proposition}
+\end{lemma}
 
 % TODO: Add pictures of parts of the graph 𝓑 ?