merge ends condition - change condition to one that is equivalent but looks stronger...

diff --git a/article.tex b/article.tex
index dd4538988cdb51cc42c6dee6ab12edaf486126db..1feeb4834899e942a4d300f7d48df120e58426ec 100644 (file)
--- 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 $D \neq C, M \haspatch P, D \not\isin Y$: