+\section{Dependency Insertion}
+
+Given $L$ construct $C$ which additionally
+contains $\pr$ as represented by $R^+$ and $R^-$.
+This may even be used for reintroducing a previous-removed branch
+dependency.
+\gathbegin
+ C \hasparents \{ L, R^+ \}
+\gathnext
+ \patchof{C} = \patchof{L}
+\gathnext
+ \mergeof{C}{L}{R^-}{R^+}
+\end{gather}
+
+\subsection{Conditions}
+
+\[ \eqn{ Ingredients }{
+ R^- = \baseof{R^+}
+}\]
+\[ \eqn{ Into Base }{
+ L \in \pqn
+}\]
+\[ \eqn{ Currently Excluded }{
+ L \nothaspatch \pry
+}\]
+\[ \eqn{ Insertion Acyclic }{
+ R^+ \nothaspatch \pqy
+}\]
+
+\subsection{No Replay}
+
+By $\merge$,
+$D \isin C \implies D \isin L \lor D \isin R^+ \lor D = C$.
+So Ingredients Prevent Replay applies. $\qed$
+
+\subsection{Unique Base}
+
+Not applicable.
+
+\subsection{Tip Contents}
+
+Not applicable.
+
+\subsection{Base Acyclic}
+
+Consider some $D \isin C$. We will show that $D \not\in \pqy$.
+By $\merge$, $D \isin L \lor D \isin R^+ \lor D = C$.
+
+For $D \isin L$, Base Acyclic for L suffices. For $D \isin R^+$,
+Insertion Acyclic suffices. For $D = C$, trivial. $\qed$.
+
+xxx up to here
+