\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}