X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?a=blobdiff_plain;f=article.tex;h=701422d9c0157c5b2ad0158bb16ba1fb6beddadb;hb=0ea398fd0deefa25d31fb4caa8903a930aea5cf8;hp=6a5023c3ceaf24813e16dfbe0d309a2a38e22178;hpb=e600e19a18c0f5b4595c68dd305f093b62fed9e4;p=topbloke-formulae.git

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@@ -572,8 +572,19 @@ 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.  Recall that we are considering $D \in \py$.
+$D \isin Y \equiv D \le Y$.  $D \not\isin X$.
+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
+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.
+
 \end{document}