\subsection{No Replay for Merge Results}
-If we are constructing $C$ such that $\merge{C}{L}{M}{R}$, No Replay
-is preserved. {\it Proof:}
+If we are constructing $C$, given
+\gathbegin
+ \merge{C}{L}{M}{R}
+\gathnext
+ L \le C
+\gathnext
+ R \le C
+\end{gather}
+No Replay is preserved. {\it Proof:}
\subsubsection{For $D=C$:} $D \isin C, D \le C$. OK.
\subsubsection{For $D \neq C \land D \not\isin L \land D \not\isin R$:}
$D \not\isin C$. OK.
-\subsubsection{For $D \neq C \land D \not\isin L \land D \not\isin R$:}
-$D \not\isin C$. OK.
-
\subsubsection{For $D \neq C \land (D \isin L \equiv D \not\isin R)
\land D \not\isin M$:}
$D \isin C$. Also $D \isin L \lor D \isin R$ so $D \le L \lor D \le
\subsubsection{For $D \neq C \land (D \isin L \equiv D \not\isin R)
\land D \isin M$:}
-$D \not\isin C$. Also $D \isin L \lor D \isin R$ so $D \le L \lor D \le
-R$ so $D \le C$. OK.
+$D \not\isin C$. OK.
$\qed$