X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=anticommit.tex;h=eab42047d6d7cb0163a5b134b3b8ce9bd75f336a;hp=3d2057ef298e25e30d09b23b4ac0c822c411772f;hb=8d37b843888b4da3d31f1a038fbc15729037e858;hpb=d184b00db1787fe98bdf3df1c4f72b259d9940d3

diff --git a/anticommit.tex b/anticommit.tex
index 3d2057e..eab4204 100644
--- a/anticommit.tex
+++ b/anticommit.tex
@@ -61,7 +61,7 @@ $D \not\isin R^-$.  Thus $D \not\isin C$.  OK.
 
 By Currently Included, $D \isin L$.
 
-By Tip Own Contents for $R^+$, $D \isin R^+ \equiv D \le R^+$, but by
+By Tip Own Contents for $R^+$, $D \isin R^+ \equiv D \le R^+$, but
 by Unique Tip, $D \le R^+ \equiv D \le L$.
 So $D \isin R^+$.
 
@@ -96,25 +96,39 @@ $\implies D \not\in \ply$.  $\qed$.
 
 \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 $L \haspatch \p \implies C \zhaspatch \p$.
-fixme up to here pdf page 13
+Whereas, if $L \haspatch \p$, $D \isin L \equiv D \le L$,
+so $C \zhaspatch \p$;
+and $\exists_{F \in \py} F \le L$ and this $F \le C$.
+Thus $C \haspatch \p$.
+OK.
 
 $\qed$
 
+\subsection{Unique Tips:}
+
+Single Parent Unique Tips applies.  $\qed$
+
 \subsection{Foreign Inclusion}
 
 Consider some $D$ s.t. $\patchof{D} = \bot$.  $D \neq C$.