wip merge complex - a bug

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index fac5c82efd6483ac6cc865cbd2db836f2d29d81e..b2f943b04c0b051059c70ab61d44a8cb8535d276 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -583,9 +583,38 @@ We will show for each of
 various cases that $D \isin C \equiv M \nothaspatch \p \land D \le C$
 (which suffices by definition of $\haspatch$ and $\nothaspatch$).
 
-Consider $D = C$.  Thus $C \in \py, L \in \py$, and by Tip
+Consider $D = C$:  Thus $C \in \py, L \in \py$, and by Tip
 Self Inpatch $L \haspatch \p$, so $L=Y, R=X$.  By Tip Merge,
 $M=\baseof{L}$.  So by Base Acyclic $D \not\isin M$, i.e.
 $M \nothaspatch \p$.  And indeed $D \isin C$ and $D \le C$.  OK.
 
+Consider $D \neq C, M \nothaspatch P, D \isin Y$:
+$D \le Y$ so $D \le C$.  
+$D \not\isin M$ so by $\merge$, $D \isin C$.  OK.
+
+Consider $D \neq C, M \nothaspatch P, D \not\isin Y$:
+$D \not\le Y$.  If $D \le X$ then
+$D \in \pancsof{X}{\py}$, so by Merge Ends and 
+Transitive Ancestors $D \le Y$ --- a contradiction, so $D \not\le X$.
+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 $D \le M$
+
+%anyway     D \not\isin X
+%           D \isin Y
+%           D \le Y
+
+%bad case
+%           D \not\le M
+%           D \not\isin M
+% results
+%           D \isin C    wrong
+
+%ok case
+%           D \le M
+%           D \isin M
+% results
+%           D \not\isin C  OK
+
 \end{document}