wip merge complex - a fix

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index 6a5023c3ceaf24813e16dfbe0d309a2a38e22178..b97f7bb606db5b814b129ec5561dc39ef6c62042 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -572,8 +572,23 @@ So indeed $L \haspatch \p \land R \haspatch \p \implies C \haspatch \p$.
 
 \subsubsection{For (wlog) $X \not\haspatch \p, Y \haspatch \p$:}
 
-$C \haspatch \p \equiv C \nothaspatch M$.
+$C \haspatch \p \equiv M \nothaspatch \p$.
 
 \proofstarts
 
+Merge Ends applies.
+
+$D \isin Y \equiv D \le Y$.  $D \not\isin X$.  Recall that we
+are considering $D \in \py$.
+
+Consider $D = C$.  Thus $C \in \py, L \in \py$.  
+But $X \not\haspatch \p$ means xxx wip
+But $X \not\haspatch \p$ means $D \not\in X$, 
+
+so we have $L = Y, R =
+X$.  Thus $R \not\haspatch \p$ and by Tip Self Inpatch $R \not\in
+\py$.  Thus by Tip Merge $R \in \pn$ and $M = \baseof{L}$.
+So by Base Acyclic, $M \nothaspatch \py$.  Thus we are expecting 
+$C \haspatch \py$.  And indeed $D \isin C$ and $D \le C$.  OK.
+
 \end{document}