wip dependency insertion

diff --git a/article.tex b/article.tex
index c096e07474c761333a7666d5724e8294eb36d295..ab0b51cc47be09d22826c241807dbc3fcfd48a3e 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -812,13 +812,13 @@ dependency.
  L \in \pqn
 }\]
 \[ \eqn{ Currently Excluded }{
- L \nothaspatch \pry
+ L \nothaspatch \pr
 }\]
 \[ \eqn{ Inserted's Ends }{
  E \in \pendsof{L}{\pry} \implies E \le R^+
 }\]
 \[ \eqn{ Others' Ends }{
- \bigforall_{\p \neq \pr, L \haspatch \p}
+ \bigforall_{\p \patchisin \L}
  E \in \pendsof{R^+}{\py} \implies E \le L
 }\]
 \[ \eqn{ Insertion Acyclic }{
@@ -879,20 +879,17 @@ OK.
 
 \subsubsection{For $\p \neq \pr$:}
 
-xxx up to here
-
-By Insertion Acyclic, $D \not\isin R^+$. xxx this is wrong
-By Tip Contents for $R^+$,
-$D \isin R^+ \equiv D \isin R^- \lor (D \in \pry \land ...)$
-but $D \in \py$ so $D \not\in \pry$.  So $D \not\isin R^-$.
-By $\merge$, $D \isin C \equiv D \isin L$.
+By Exclusive Tip Contents for $R^+$ ($D \not\in \pry$ case)
+$D \isin R^+ \equiv D \isin R^-$.
+So by $\merge$, $D \isin C \equiv D \isin L$.
 
 If $L \nothaspatch \p$, $D \not\isin L$ so $C \nothaspatch \p$.  OK.
 
 If $L \haspatch \p$, Others' Ends applies; by Transitive
 Ancestors, $A \in \pancsof{R^+}{\py} \implies A \le L$.
-So $D \le R^+$, which is the same as $D \in \pancsof{R^+}{\py}$,
-$\implies D \le L$.  Thus $D le C \equiv D \le L$.
+So $D \le R^+ \implies D \le L$,
+since $D \le R^+ \equiv D \in \pancsof{R^+}{\py}$.
+Thus $D \le C \equiv D \le L$.
 And by $\haspatch$, $D \le L \equiv D \isin L$ so
 $D \isin C \equiv D \le C$.  Thus $C \haspatch \p$.
 OK.