refactor for coherence cases - simple, fix leftover ~

[topbloke-formulae.git] / merge.tex

diff --git a/merge.tex b/merge.tex
index ca3304d26b0b5442f968f7f92a461f783e6ded13..1ca4af73574a7343d367fed94ebc945d105dc7a3 100644 (file)
--- a/merge.tex
+++ b/merge.tex
@@ -116,7 +116,7 @@ This involves considering $D \in \py$.
 
 \subsubsection{For $L \nothaspatch \p, R \nothaspatch \p$:}
 $D \not\isin L \land D \not\isin R$.  $C \not\in \py$ (otherwise $L
-\in \py$ ie $\neg[ L \nothaspatch \p ]$ by Tip Own Contents for $L$).
+\in \py$ ie $L \haspatch \p$ by Tip Own Contents for $L$).
 So $D \neq C$.
 Applying $\merge$ gives $D \not\isin C$ i.e. $C \nothaspatch \p$.
 
@@ -162,6 +162,8 @@ We will show for each of
 various cases that
 if $M \haspatch \p$, $D \not\isin C$,
 whereas if $M \nothaspatch \p$, $D \isin C \equiv \land D \le C$.
+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 $L \neq X$,