\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
$\qed$
+\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.