wip merge content

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index 4c7f22cbc50446b5a2997c39107e60932727085c..0018429e2a80618059f63b2189d3a4103d3b8994 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -461,6 +461,8 @@ Need to consider only $C \in \py$, ie $L \in \py$.
 
 xxx tbd
 
+xxx need to finish anticommit
+
 \section{Merge}
 
 Merge commits $L$ and $R$ using merge base $M$ ($M < L, M < R$):
@@ -523,4 +525,42 @@ That is, $\baseof{C} = R$.
 
 $\qed$
 
+\subsection{Coherence and patch inclusion}
+
+Need to determine $C \haspatch P$ based on $L,M,R \haspatch P$.
+This involves considering $D \in \py$.  
+
+We will use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
+
+\subsubsection{For $L \nothaspatch P, R \nothaspatch P$:}
+$D \not\isin L \land D \not\isin R$.  $C \not\in \py$ (otherwise $L
+\in \py$ ie $L \haspatch P$ by Tip Self Inpatch).  So $D \neq C$.
+Applying $\merge$ gives $D \not\isin C$ i.e. $C \nothaspatch P$.
+
+\subsubsection{For $L \haspatch P, R \haspatch P$:}
+$D \isin L \equiv D \le L$ and $D \isin R \equiv D \le R$.
+(Likewise $D \isin X \equiv D \le X$ and $D \isin Y \equiv D \le Y$.)
+
+Consider $D = C$: $D \isin C$, $D \le C$, OK for $C \haspatch P$.
+
+For $D \neq C$: $D \le C \equiv D \le L \lor D \le R
+ \equiv D \isin L \lor D \isin R$.  
+(Likewise $D \le C \equiv D \le X \lor D \le Y$.)
+
+Consider $D \neq C, D \isin X \land D \isin Y$:
+By $\merge$, $D \isin C$.  Also $D \le X$ 
+so $D \le C$.  OK for $C \haspatch P$.
+
+Consider $D \neq C, D \not\isin X \land D \not\isin Y$:
+By $\merge$, $D \not\isin C$.  
+And $D \not\le X \land D \not\le Y$ so $D \not\le C$.  
+OK for $C \haspatch P$.
+
+Remaining case, wlog, is $D \not\isin X \land D \isin Y$.
+$D \not\le X$ so $D \not\le M$ so $D \not\isin M$.  
+Thus by $\merge$, $D \isin C$.  And $D \le Y$ so $D \le C$.
+OK for $C \haspatch P$.
+
+So indeed $L \haspatch P \land R \haspatch P \implies C \haspatch P$.
+
 \end{document}