{\hbox{\scriptsize$\forall$}}}%
}
+\newcommand{\Largeexists}{\mathop{\hbox{\Large$\exists$}}}
+\newcommand{\Largenexists}{\mathop{\hbox{\Large$\nexists$}}}
\newcommand{\qed}{\square}
\newcommand{\proof}[1]{{\it Proof.} #1 $\qed$}
\item[ $ \pendsof{C}{\set P} $ ]
$ \{ E \; | \; E \in \pancsof{C}{\set P}
\land \mathop{\not\exists}_{A \in \pancsof{C}{\set P}}
- A \neq E \land E \le A \} $
+ E \neq A \land E \le A \} $
i.e. all $\le$-maximal commits in $\pancsof{C}{\set P}$.
\item[ $ \baseof{C} $ ]
\subsection{Conditions}
-\[ \eqn{ Merges Exhaustive }{
- L \in \py => \Bigl[ R \in \py \lor R \in \pn \Bigr]
-}\]
\[ \eqn{ Tip Merge }{
- L \in \py \land R \in \py \implies \Bigl[ \text{TBD} \Bigr]
-}\]
-\[ \eqn{ Base Merge }{
- L \in \py \land R \in \pn \implies \Bigl[ R \ge \baseof{L} \land M =
- \baseof{L} \Bigr]
+ L \in \py \implies
+ \begin{cases}
+ R \in \py : & \baseof{R} \ge \baseof{L}
+ \land [\baseof{L} = M \lor \baseof{L} = \baseof{M}] \\
+ R \in \pn : & R \ge \baseof{L}
+ \land M = \baseof{L} \\
+ \text{otherwise} : & \false
+ \end{cases}
}\]
+\subsection{No Replay}
+
+\subsubsection{For $D=C$:} $D \isin C, D \le C$. OK.
+
+\subsubsection{For $D \isin L \land D \isin R$:}
+$D \isin C$. And $D \isin L \implies D \le L \implies D \le C$. 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 $D \le L \lor D \le
+R$ so $D \le C$. OK.
+
+\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.
+
+$\qed$
+
\end{document}