\begin{proposition}\label{prop1}
    $a = a$.
\end{proposition}

\begin{proposition}\label{prop2}
    $b = b$.
\end{proposition}

\begin{proposition}\label{prop3}
    $c = c$.
\end{proposition}
\begin{proof}
    Follows by \ref{prop1}. % Should filter out second_proposition
\end{proof}

\begin{proposition}\label{prop4}
    $e = e$.
\end{proposition}
\begin{proof}
    For all $d$ we have $d = d$ by \ref{prop1}.
\end{proof}

\begin{proposition}\label{prop5}
    $f = f$.
\end{proposition}