Added citation for the type 1 proof.
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\item There exists a complex Hilbert space $K$ and a *-isomorphism $\pi: A \to B(K)$.
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\end{enumerate}
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\end{theorem}
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\begin{proof}
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\begin{proof}[Proof, {{\cite{TownesType1}}}. ]
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(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.
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(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 $Q \preceq P$.
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