From 8922ddb1523c8785fadbc19d130eeea0c71b2b71 Mon Sep 17 00:00:00 2001
From: Ian Jackson <ijackson@chiark.greenend.org.uk>
Date: Wed, 21 Mar 2012 21:42:22 +0000
Subject: [PATCH] refactor for coherence cases - anticommit

---
 anticommit.tex | 19 ++++++++++++++-----
 1 file changed, 14 insertions(+), 5 deletions(-)

diff --git a/anticommit.tex b/anticommit.tex
index e4f5d48..90f2ea4 100644
--- a/anticommit.tex
+++ b/anticommit.tex
@@ -96,23 +96,32 @@ $\implies D \not\in \ply$.  $\qed$.
 
 \subsection{Coherence and Patch Inclusion}
 
-Need to consider some $D \in \py$.  By Into Base, $D \neq C$.
+$$
+\begin{cases}
+  \p = \pr                            : & C \nothaspatch \p  \\
+  \p \neq \pr \land L \nothaspatch \p : & C \nothaspatch \p  \\
+  \p \neq \pr \land L \haspatch    \p : & C \haspatch    \p
+\end{cases}
+$$
+\proofstarts
+~ Need to consider some $D \in \py$.  By Into Base, $D \neq C$.
 
 \subsubsection{For $\p = \pr$:}
 By Desired Contents, above, $D \not\isin C$.
-So $C \nothaspatch \pr$.
+OK.
 
 \subsubsection{For $\p \neq \pr$:}
 By Desired Contents, $D \isin C \equiv D \isin L$
 (since $D \in \py$ so $D \not\in \pry$).
 
 If $L \nothaspatch \p$, $D \not\isin L$ so $D \not\isin C$.
-So $L \nothaspatch \p \implies C \nothaspatch \p$.
+OK.
 
 Whereas, if $L \haspatch \p$, $D \isin L \equiv D \le L$,
 so $C \zhaspatch \p$;
-and $\exists_{F \in \py} F \le L$ so this $F \le C$.
-Thus $\p \neq R \land L \haspatch \p \implies C \haspatch \p$.
+and $\exists_{F \in \py} F \le L$ and this $F \le C$.
+Thus $C \haspatch \p$.
+OK.
 
 $\qed$
 
-- 
2.30.2