From: Ian Jackson <ijackson@chiark.greenend.org.uk>
Date: Thu, 8 Mar 2012 16:40:16 +0000 (+0000)
Subject: wip merge complex - fix bug, improve merge ends condition
X-Git-Tag: f0.2~128
X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=commitdiff_plain;h=38b8505b333047f5e586c6060a3a6b5e11ea050a

wip merge complex - fix bug, improve merge ends condition
---

diff --git a/article.tex b/article.tex
index b2f943b..080e482 100644
--- a/article.tex
+++ b/article.tex
@@ -491,10 +491,13 @@ We will occasionally use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
 \[ \eqn{ Merge Ends }{
     X \not\haspatch \p \land
     Y \haspatch \p
-  \implies \left[
-  \bigforall_{E \in \pendsof{X}{\py}}
-    E \le Y
-  \right]
+  \implies
+  \begin{cases}
+    M \haspatch \p :    & \displaystyle
+                          \bigforall_{E \in \pendsof{Y}{\py}} E \le M \\
+    M \nothaspatch \p : & \displaystyle
+                          \bigforall_{E \in \pendsof{X}{\py}} E \le Y
+  \end{cases}
 }\]
 
 \subsection{No Replay}
@@ -599,22 +602,8 @@ Transitive Ancestors $D \le Y$ --- a contradiction, so $D \not\le X$.
 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}