X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=simple.tex;h=297103adf419b066cb5269773de20409c14c0135;hp=82b90762d9c04eaad53142b866e2a3c84587126a;hb=c497f56e8a7f09c4c328bd7560631d8773b7e676;hpb=2daa9f7411a0be9dfd8f1e762e46fc42d4e1c95a

diff --git a/simple.tex b/simple.tex
index 82b9076..297103a 100644
--- a/simple.tex
+++ b/simple.tex
@@ -47,9 +47,22 @@ $L$, $D \isin C \implies D \not\in \py$.
 
 $\qed$
 
-\subsection{Coherence and patch inclusion}
+\subsection{Coherence and Patch Inclusion}
 
-Need to consider $D \in \py$
+$$
+\begin{cases}
+  L \haspatch    \p : & C \haspatch    \p \\
+  L \nothaspatch \p : & C \nothaspatch \p
+\end{cases}
+$$
+\proofstarts
+
+Firstly, if $L \haspatch \p$, $\exists_{F \in \py} F \le L$
+and this $F$ is also $\le C$
+so $C \zhaspatch \p \implies C \haspatch \p$.
+We will prove $\zhaspatch$
+
+We need to consider $D \in \py$.
 
 \subsubsection{For $L \haspatch \p, D = C$:}
 
@@ -57,36 +70,36 @@ Ancestors of $C$:
 $ D \le C $.
 
 Contents of $C$:
-$ D \isin C \equiv \ldots \lor \true \text{ so } D \haspatch C $.
+$ D \isin C \equiv \ldots \lor \true$.  So $ D \zhaspatch C $.
+OK.
 
 \subsubsection{For $L \haspatch \p, D \neq C$:}
 Ancestors: $ D \le C \equiv D \le L $.
 
 Contents: $ D \isin C \equiv D \isin L \lor f $
 so $ D \isin C \equiv D \isin L $, i.e. $ C \zhaspatch P $.
-By $\haspatch$ for $L$, $\exists_{F \in \py} F \le L$
-and this $F$ is also $\le C$.  So $\haspatch$.
-
-So:
-\[ L \haspatch \p \implies C \haspatch \p \]
+OK.
 
 \subsubsection{For $L \nothaspatch \p$:}
 
 Firstly, $C \not\in \py$ since if it were, $L \in \py$.
 Thus $D \neq C$.
 
-Now by contents of $L$, $D \notin L$, so $D \notin C$.
+Now by $\nothaspatch$, $D \not\isin L$ so $D \not\isin C$.
+OK.
 
-So:
-\[ L \nothaspatch \p \implies C \nothaspatch \p \]
 $\qed$
 
+\subsection{Unique Tips:}
+
+Single Parent Unique Tips applies.  $\qed$
+
 \subsection{Foreign Inclusion:}
 
 Simple Foreign Inclusion applies.  $\qed$
 
 \subsection{Foreign Contents:}
 
-Only relevant if $\patchof{C} = \bot$, and in that case Totally
+Only relevant if $\isforeign{C}$, and in that case Totally
 Foreign Contents applies. $\qed$