merge: State C's inclusion in terms of stmtmergeof

[topbloke-formulae.git] / merge.tex

diff --git a/merge.tex b/merge.tex
index 746ba2d6f6dead05b0e72c95cc1fef058365a505..e62282073f7d109da371696ff8fc37dfc1c58320 100644 (file)
--- a/merge.tex
+++ b/merge.tex
@@ -131,6 +131,14 @@ $\qed$
 
 \subsection{Coherence and Patch Inclusion}
 
+$C$ satisfies
+\gathbegin
+  C \haspatch \p \lor C \nothaspatch \p
+\gathnext
+C \haspatch \p \equiv
+  \stmtmergeof{L \haspatch \p}{M \haspatch \p}{R \haspatch \p}
+\end{gather}
+which (given Coherence of $L$,$M$,$R$) is equivalent to
 $$
 \begin{cases}
   L \nothaspatch \p \land R \nothaspatch \p : & C \nothaspatch \p  \\
@@ -146,7 +154,7 @@ $$
 $D \not\isin L \land D \not\isin R$.  $C \not\in \py$ (otherwise $L
 \in \py$ ie $L \haspatch \p$ by Tip Own Contents for $L$).
 So $D \neq C$.
-Applying \commitmergename gives $D \not\isin C$ i.e. $C \nothaspatch \p$.
+Applying \commitmergename\ gives $D \not\isin C$ i.e. $C \nothaspatch \p$.
 OK.
 
 \subsubsection{For $L \haspatch \p, R \haspatch \p$:}