\begin{definition}\label{phase5_before_runtime_failure}
    $\phasefivebeforeruntimefailure = \emptyset$.
\end{definition}

\begin{proposition}\label{phase5_runtime_failure}
    For all $x$ we have $x = x$.
\end{proposition}
\begin{proof}
    Fix $x$.
    We have $x = x$ by assumption.
    Follows by assumption.
\end{proof}