comments from mdw - add note re universal quantification

[topbloke-formulae.git] / merge.tex

diff --git a/merge.tex b/merge.tex
index 94b38fe9648d88f2022ba9ee57aae96d35806a2e..48e72702c780d17648ffe6ef5d5e5a6b1253fcce 100644 (file)
--- a/merge.tex
+++ b/merge.tex
@@ -165,14 +165,15 @@ $D \isin Y \equiv D \le Y$.  $D \not\isin X$.
 We will show for each of
 various cases that
 if $M \haspatch \p$, $D \not\isin C$,
-whereas if $M \nothaspatch \p$, $D \isin C \equiv \land D \le C$.
+whereas if $M \nothaspatch \p$, $D \isin C \equiv D \le C$.
 And by $Y \haspatch \p$, $\exists_{F \in \py} F \le Y$ and this
 $F \le C$ so this suffices.
 
 Consider $D = C$:  Thus $C \in \py, L \in \py$.
-By Tip Own Contents, $\neg[ L \nothaspatch \p ]$ so $L \neq X$,
+By Tip Own Contents, $L \haspatch \p$ so $L \neq X$,
 therefore we must have $L=Y$, $R=X$.
-By Tip Merge $M = \baseof{L}$ so $M \in \pn$ so
+Conversely $R \not\in \py$
+so by Tip Merge $M = \baseof{L}$.  Thus $M \in \pn$ so
 by Base Acyclic $M \nothaspatch \p$.  By $\merge$, $D \isin C$,
 and $D \le C$.  OK.