\[ \eqn{ Merge Ends }{
X \not\haspatch \p \land
Y \haspatch \p
- \implies \left[
- \bigforall_{E \in \pendsof{X}{\py}}
- E \le Y
- \right]
+ \implies
+ \begin{cases}
+ M \haspatch \p : & \displaystyle
+ \bigforall_{E \in \pendsof{Y}{\py}} E \le M \\
+ M \nothaspatch \p : & \displaystyle
+ \bigforall_{E \in \pendsof{X}{\py}} E \le Y
+ \end{cases}
}\]
\subsection{No Replay}
Thus $D \not\le C$. By $\merge$, $D \not\isin C$. OK.
Consider $D \neq C, M \haspatch P, D \isin Y$:
-$D \le Y$ so $D \le M$
-
-%anyway D \not\isin X
-% D \isin Y
-% D \le Y
-
-%bad case
-% D \not\le M
-% D \not\isin M
-% results
-% D \isin C wrong
-
-%ok case
-% D \le M
-% D \isin M
-% results
-% D \not\isin C OK
+$D \le Y$ so $D \in \pancsof{Y}{\py}$ so by Merge Ends
+and Transitive Ancestors $D \le M$.
+Thus $D \isin M$. By $\merge$, $D \not\isin C$. OK.
\end{document}