chiark / gitweb /
 author Ian Jackson Wed, 14 Mar 2012 23:12:18 +0000 (23:12 +0000) committer Ian Jackson Wed, 14 Mar 2012 23:12:18 +0000 (23:12 +0000)
 article.tex patch | blob | history

index c096e07..ab0b51c 100644 (file)
@@ -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.