From 8d5ef87515410d728d2d6443bdc779ff97befecc Mon Sep 17 00:00:00 2001
From: Ian Jackson <ijackson@chiark.greenend.org.uk>
Date: Thu, 8 Mar 2012 16:56:57 +0000
Subject: [PATCH] merge ends condition - change condition to one that is
 equivalent but looks stronger and is easier to compute

---
 article.tex | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/article.tex b/article.tex
index dd45389..1feeb48 100644
--- a/article.tex
+++ b/article.tex
@@ -493,8 +493,8 @@ We will occasionally use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
     Y \haspatch \p
   \implies
   \begin{cases}
-    M \haspatch \p :    & \displaystyle
-                          \bigforall_{E \in \pendsof{Y}{\py}} E \le M \\
+    M \haspatch \p :    & \pendsof{Y}{\py} = \pendsof{M}{\py}
+   \\
     M \nothaspatch \p : & \displaystyle
                           \bigforall_{E \in \pendsof{X}{\py}} E \le Y
   \end{cases}
@@ -603,7 +603,7 @@ 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 $D \in \pancsof{Y}{\py}$ so by Merge Ends
-and Transitive Ancestors $D \le M$.
+and Transitive Ancestors $D \in \pancsof{M}{\py}$ so $D \le M$.
 Thus $D \isin M$.  By $\merge$, $D \not\isin C$.  OK.
 
 Consider $D \neq C, M \haspatch P, D \not\isin Y$:
-- 
2.30.2