\import{test/phase5/exact-escape-producer.tex}

\begin{proposition}\label{phase5_from_source_axiom}
    For all $x$ we have $x = x$.
\end{proposition}
\begin{proof}
    Fix $x$.
    Follows by \cref{phase5_escape_source_axiom}.
\end{proof}

\begin{proposition}\label{phase5_from_omitted_theorem}
    For all $x$ we have $x = x$.
\end{proposition}
\begin{proof}
    Fix $x$.
    Follows by \cref{phase5_escape_omitted_theorem}.
\end{proof}

\begin{proposition}\label{phase5_source_axiom_through_local}
    For all $x$ we have $x = x$.
\end{proposition}
\begin{proof}
    Fix $x$.
    We have $x = x$ by \cref{phase5_escape_source_axiom}.
    Follows by assumption.
\end{proof}

\begin{proposition}\label{phase5_omitted_with_checked_continuation}
    For all $x$ we have $x = x$.
\end{proposition}
\begin{proof}
    Fix $x$.
    Show $x = x$.
    \begin{subproof}
        Omitted.
    \end{subproof}
    Follows by \cref{phase5_escape_source_axiom}.
\end{proof}