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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}