\begin{proposition}\label{phase5_top_level_omitted}
    For all $x$ we have $x = x$.
\end{proposition}
\begin{proof}
    Omitted.
\end{proof}

\begin{proposition}\label{phase5_nested_omitted}
    For all $x$ we have $x = x$.
\end{proposition}
\begin{proof}
    Fix $x$.
    Show $x = x$.
    \begin{subproof}
        Omitted.
    \end{subproof}
    Follows by assumption.
\end{proof}