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

\begin{proposition}\label{phase6_admitted_omission}
    For all $x$ we have $x = x$.
\end{proposition}
\begin{proof}
    Omitted.
\end{proof}

\begin{proposition}\label{phase6_rejected_declaration}
    For all $x$ we have if $x = x$, then $x = x$.
\end{proposition}
\begin{proof}
    Fix $x$.
    Assume $x = \emptyset$.
    Follows by assumption.
\end{proof}

\begin{axiom}\label{phase6_unadmitted_axiom}
    For all $x$ we have $x = x$.
\end{axiom}

\begin{proposition}\label{phase6_unadmitted_omission}
    For all $x$ we have $x = x$.
\end{proposition}
\begin{proof}
    Omitted.
\end{proof}