\end{gather}
We will occasionally use $X,Y$ s.t. $\{X,Y\} = \{L,R\}$.
-This can also be used for dependency re-insertion, by setting
-$L \in \pn$, $R \in \pry$, $M = \baseof{R}$.
+This can also be used for dependency re-insertion, by setting $L \in
+\pn$, $R \in \pry$, $M = \baseof{R}$, provided that the Conditions are
+satisfied; in particular, provided that $L \ge \baseof{R}$.
\subsection{Conditions}
\[ \eqn{ Ingredients }{
\bigforall_{E \in \pendsof{X}{\py}} E \le Y
\right]
}\]
+\[ \eqn{ Suitable Tip }{
+ \bigexists_T
+ \pendsof{J}{\py} = \{ T \}
+ \land
+ \forall_{E \in \pendsof{K}{\py}} T \ge E
+ , \text{where} \{J,K\} = \{L,R\}
+}\]
\[ \eqn{ Foreign Merges }{
\patchof{L} = \bot \implies \patchof{R} = \bot
}\]
$\qed$
+\subsection{Unique Tips}
+
+For $L \in \py$, trivially $\pendsof{C}{\py} = C$ so $T = C$ is
+suitable.
+
+For $L \not\in \py$, $\pancsof{C}{\py} = \pancsof{L}{\py} \cup
+\pancsof{R}{\py}$. So $T$ from Suitable Tip is a suitable $T$ for
+Unique Tips.
+
+$\qed$
+
\subsection{Foreign Inclusion}
Consider some $D$ s.t. $\patchof{D} = \bot$.