From: Ian Jackson <ijackson@chiark.greenend.org.uk>
Date: Thu, 8 Mar 2012 18:35:32 +0000 (+0000)
Subject: merge base acyclic (and condition)
X-Git-Tag: f0.2~120
X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=commitdiff_plain;h=30d302a353da9ae7f08a02468d19b741e4657de0;ds=sidebyside

merge base acyclic (and condition)
---

diff --git a/article.tex b/article.tex
index ecd671e..d5451ea 100644
--- a/article.tex
+++ b/article.tex
@@ -488,6 +488,11 @@ We will occasionally use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
       \text{otherwise} : & \false
    \end{cases}
 }\]
+\[ \eqn{ Merge Acyclic }{
+    L \in \pn
+   \implies
+    R \nothaspatch \p
+}\]
 \[ \eqn{ Removal Merge Ends }{
     X \not\haspatch \p \land
     Y \haspatch \p \land
@@ -616,6 +621,16 @@ By $\merge$, $D \not\isin C$.  OK.
 
 $\qed$
 
+\subsection{Base Acyclic}
+
+This applies when $C \in \pn$.
+$C \in \pn$ when $L \in \pn$ so by Merge Acyclic, $R \nothaspatch \p$.
+
+Consider some $D \in \py$.
+
+By Base Acyclic of $L$, $D \not\isin L$.  By the above, $D \not\isin
+R$.  And $D \neq C$.  So $D \not\isin C$.  $\qed$
+
 \subsection{Tip Contents}
 
 We will consider some $D$ and prove the Exclusive Tip Contents form.