\gathnext
\patchof{C} = \patchof{L}
\gathnext
- \mergeof{C}{L}{R^+}{R^-}
+ \commitmergeof{C}{L}{R^+}{R^-}
\end{gather}
\subsection{Conditions}
\subsection{No Replay}
-By $\merge$,
+By \commitmergename,
$D \isin C \implies D \isin L \lor D \isin R^- \lor D = C$.
So, by Ordering of Ingredients,
Ingredients Prevent Replay applies. $\qed$
By Base Acyclic for $R^-$, $D \not\isin R^-$.
-Apply $\merge$: $D \not\isin C$. OK.
+Apply \commitmergename: $D \not\isin C$. OK.
\subsubsection{For $D \neq C, D \le L, D \notin \pry$:}
By Tip Contents for $R^+$, $D \isin R^+ \equiv D \isin R^-$.
-Apply $\merge$: $D \isin C \equiv D \isin L$. OK.
+Apply \commitmergename: $D \isin C \equiv D \isin L$. OK.
$\qed$
\subsection{Foreign Inclusion}
-Consider some $D$ s.t. $\isforeign{D}$. $D \neq C$.
+Consider some $D \in \foreign$. $D \neq C$.
So by Desired Contents $D \isin C \equiv D \isin L$.
By Foreign Inclusion of $D$ in $L$, $D \isin L \equiv D \le L$.