lie-algebras-and-their-representations

diff --git a/sections/complete-reducibility.tex b/sections/complete-reducibility.tex
@@ -940,11 +940,11 @@ This sequence always splits, which implies we can deduce information about
 part'' \(\mfrac{\mathfrak{g}}{\mathfrak{rad}(\mathfrak{g})}\) -- see
 Proposition~\ref{thm:quotients-by-rads}. In practice this translates to\dots
 
-\begin{theorem}\label{thm:semi-simple-part-decomposition}
+\begin{proposition}
   Every simple \(\mathfrak{g}\)-module is the tensor product of
   a simple \(\mfrac{\mathfrak{g}}{\mathfrak{rad}(\mathfrak{g})}\)-module 
   and a \(1\)-dimensional \(\mathfrak{rad}(\mathfrak{g})\)-module.
-\end{theorem}
+\end{proposition}
 
 Having finally reduced our initial classification problem to that of
 classifying the finite-dimensional simple \(\mathfrak{g}\)-modules, we can now