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Jeffrey Kegler authored and Jeffrey Kegler committed Feb 21, 2014
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Expand Up @@ -732,14 +732,11 @@ if and only if we have both

\begin{lemma}
\label{l:eim-correctness-is-transitive}
Let \Vdr{predecessor} be the dotted rule
\begin{equation}
\textup{ $[\Vsym{lhs} \de \Vsf{before} \mydot \Vsym{transition} \cat \Vsf{after}]$ }
\end{equation}
and \Vdr{successor} be its successor
\begin{equation}
\textup{ $[\Vsym{lhs} \de \Vsf{before} \cat \Vsym{transition} \mydot \Vsf{after}]$ }
\end{equation}
Let \textup{\Vdr{predecessor}} be a dotted rule,
let \textup{\Vdr{successor}} be its successor,
and let \textup{\Vsym{transition}} be the postdot symbol in
\textup{\Vdr{predecessor}} and the predot symbol in
\textup{\Vdr{successor}}.
If the EIM
\begin{equation}
\label{e:eim-reduction-1}
Expand All @@ -765,6 +762,14 @@ then the EIM
\end{lemma}

\begin{proof}
Let \Vdr{predecessor} be the dotted rule
\begin{equation}
\textup{ $[\Vsym{lhs} \de \Vsf{before} \mydot \Vsym{transition} \cat \Vsf{after}].$ }
\end{equation}
\Vdr{successor} is therefore
\begin{equation}
\textup{ $[\Vsym{lhs} \de \Vsf{before} \cat \Vsym{transition} \mydot \Vsf{after}].$ }
\end{equation}
From assumption \eqref{e:eim-reduction-1}, we know that
\begin{equation}
\label{e:eim-reduction-4}
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