\subsection{Conditions}
\[ \eqn{ Create Acyclic }{
- \pendsof{L}{\pqy} = \{ \}
+ L \nothaspatch \pq
+}\]
+\[ \eqn{ Ingredients }{
+ \patchof L = \foreign \lor \patchof L = \py
}\]
\subsection{No Replay}
\subsection{Base Acyclic}
Consider some $D \isin B$. If $D = B$, $D \in \pqn$.
-If $D \neq B$, $D \isin L$, so by No Replay $D \le L$
-and by Create Acyclic
+If $D \neq B$, $D \isin L$, so by Create Acyclic
$D \not\in \pqy$. $\qed$
\subsection{Coherence and Patch Inclusion}
$B \not\in \py$ so $D \neq B$. So $D \isin B \equiv D \isin L$
and $D \le B \equiv D \le L$.
-Thus $L \haspatch \p \implies B \haspatch P$
-and $L \nothaspatch \p \implies B \nothaspatch P$.
+Thus $L \haspatch \p \equiv B \haspatch P$
+and $L \nothaspatch \p \equiv B \nothaspatch P$.
+
+$\qed$
-$\qed$.
+\subsection{Unique Tips:}
+
+Single Parent Unique Tips applies. $\qed$
\subsection{Foreign Inclusion}
Simple Foreign Inclusion applies. $\qed$
-\subsection{Foreign Contents}
+\subsection{Foreign Ancestry}
Not applicable.
+\subsection{Bases' Children}
+
+Not applicable, by Ingredients.
+$\qed$