Added citation for the type 1 proof.

refs.bib

@@ -283,3 +283,13 @@
  volume = {2},
  year = {1951}
 }
+
+
+@MISC {TownesType1,
+    TITLE = {Classification of Type 1 factors},
+    AUTHOR = {Leslie Townes (https://math.stackexchange.com/users/18076/leslie-townes)},
+    HOWPUBLISHED = {Mathematics Stack Exchange},
+    NOTE = {URL:https://math.stackexchange.com/q/150258 (version: 2012-05-27)},
+    EPRINT = {https://math.stackexchange.com/q/150258},
+    URL = {https://math.stackexchange.com/q/150258}
+}

src/op/vn/type-decomp.tex

@@ -234,7 +234,7 @@
         \item There exists a complex Hilbert space $K$ and a *-isomorphism $\pi: A \to B(K)$. 
     \end{enumerate}
 \end{theorem}
-\begin{proof}
+\begin{proof}[Proof, {{\cite{TownesType1}}}. ]
     (1) $\Rightarrow$ (2): Since $A$ is of type $\vnI$, $A$ admits a non-zero abelian projection $Q \in \text{Proj}(A)$. By \autoref{lemma:abelian-minimal-factor}, $Q$ is minimal. 
 
     (2) $\Rightarrow$ (3): Let $P \in \text{Proj}(A)$ and $Q \in \text{Proj}(A)$ be a minimal projection. By the \hyperref[comparability theorem]{corollary:vna-factor-comparability}, either $P \preceq Q$ or $Q \preceq P$.