lie-algebras-and-their-representations

diff --git a/sections/mathieu.tex b/sections/mathieu.tex
@@ -877,15 +877,14 @@ family are cuspidal representations?
   \end{enumerate}
 \end{proposition}
 
-% TODO: Turn this first footnote into part of the proof
 \begin{proof}
   The fact that \strong{(i)} and \strong{(iii)} are equivalent follows directly
   from Corollary~\ref{thm:cuspidal-mod-equivs}. Likewise, it is clear from the
-  corollary that \strong{(iii)} implies \strong{(ii)}. All it is left is to show
-  \strong{(ii)} implies \strong{(iii)}\footnote{This isn't already clear from
+  corollary that \strong{(iii)} implies \strong{(ii)}. All it is left is to
+  show \strong{(ii)} implies \strong{(iii)}. This isn't already clear from
   Corollary~\ref{thm:cuspidal-mod-equivs} because, at first glance,
   $\mathcal{M}[\lambda]$ may not be simple for some $\lambda$ satisfying
-  \strong{(ii)}. We will show this is never the case.}.
+  \strong{(ii)}. We will show this is never the case.
 
   Suppose \(F_\alpha\) acts injectively on the submodule
   \(\mathcal{M}[\lambda]\), for all \(\alpha \in \Delta\). Since