merge base acyclic (and condition)

diff --git a/article.tex b/article.tex
index ecd671ea2bc40e0f05e396bd788c33130b11b21a..d5451ea30c0e6b127615466679d03dd789417931 100644 (file)
--- 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}
 }\]
       \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
 \[ \eqn{ Removal Merge Ends }{
     X \not\haspatch \p \land
     Y \haspatch \p \land


@@ -616,6 +621,16 @@ By $\merge$, $D \not\isin C$.  OK.
 
 $\qed$
 
 
 $\qed$
 

+\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.
 \subsection{Tip Contents}
 
 We will consider some $D$ and prove the Exclusive Tip Contents form.