wip merge tip contents

[topbloke-formulae.git] / article.tex

diff --git a/article.tex b/article.tex
index 643ef44e04fca2f36914abd3918a8944ce08c48b..72230e331f1aa22869514bcb957aea9525256982 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -638,24 +638,26 @@ And $\patchof{C} = \patchof{L}$
 so $L \in \py$ so $L \haspatch \p$.  We will use the coherence and
 patch inclusion of $C$ as just proved.
 
-Firstly we prove $C \haspatch \p$: If $R \in \py$, then $R \haspatch
+Firstly we show $C \haspatch \p$: If $R \in \py$, then $R \haspatch
 \p$ and by coherence/inclusion $C \haspatch \p$ .  If $R \not\in \py$
 then by Tip Merge $M = \baseof{L}$ so by Base Acyclic and definition
 of $\nothaspatch$, $M \nothaspatch \p$.  So by coherence/inclusion $C
 \haspatch \p$ (whether $R \haspatch \p$ or $\nothaspatch$).
 
-xxx up to here
-
 We will consider some $D$ and prove the Exclusive Tip Contents form.
 
+\subsubsection{For $D \in \py$:}
+$C \haspatch \p$ so by definition of $\haspatch$, $D \isin C \equiv D
+\le C$.  OK.
 
-So by definition of
-$\haspatch$, $D \isin C \equiv D \le C$.  OK.
+\subsubsection{For $D \not\in \py, R \not\in \py$:}
 
-\subsubsection{For $L \in \py, D \in \py, $:}
-$R \haspatch \p$ so 
+$D \neq C$.  By Tip Contents of $L$,
+$D \isin L \equiv D \isin \baseof{L}$, and by Tip Merge condition,
+$D \isin L \equiv D \isin M$.  xxx up to here
 
-\subsubsection{For $L \in \py, D \not\in \py, R \in \py$:}
+
+\subsubsection{For $D \not\in \py, R \in \py$:}
 
 
 %D \in \py$:}