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

[topbloke-formulae.git] / merge.tex

diff --git a/merge.tex b/merge.tex
index f6a3e9304b5cc404dd8121d08b39cc95d642b3c8..a34c9bcbac8753ae917462b975e7124aea784712 100644 (file)
--- 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 $D \le C$.