From: Ian Jackson <ijackson@chiark.greenend.org.uk>
Date: Fri, 16 Mar 2012 22:25:11 +0000 (+0000)
Subject: merge fixes/clarifications - sort out complex case D = C
X-Git-Tag: f0.2~12
X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=commitdiff_plain;h=88703e57b78158a4ee558d4744e736e90fb008f0

merge fixes/clarifications - sort out complex case D = C
---

diff --git a/merge.tex b/merge.tex
index f6a3e93..a34c9bc 100644
--- a/merge.tex
+++ b/merge.tex
@@ -158,10 +158,12 @@ 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 for $L$, $L \haspatch \p$, 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 $D = C$:  Thus $C \in \py, L \in \py$.  By Tip Contents
+for $L$, $L \isin L$ so $\neg [ L \nothaspatch \p ]$.
+Therefore we must have $L=Y$, $R=X$.
+By Tip Merge $M = \baseof{L}$ so $M \in \pn$ so
+by Base Acyclic $M \nothaspatch \p$.  By $\merge$, $D \isin C$,
+and $D \le C$, consistent with $C \haspatch \p$.  OK.
 
 Consider $D \neq C, M \nothaspatch \p, D \isin Y$:
 $D \le Y$ so $D \le C$.