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\begin{inductive}\label{phase5_nested_outside_membership}
Define $\phasefiveoutside{A}\subseteq\cumul{A}$ inductively as follows.
\begin{enumerate}
\item If $\phasefiveoutside{A}=\phasefiveoutside{A}$, then
$A\in\phasefiveoutside{A}$.
\end{enumerate}
\end{inductive}
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