\subsection{Conditions}
\[ \eqn{ Base Only }{
- \patchof{L} \neq \py
+ L \in \pn
}\]
\[ \eqn{ Unique Tips }{
}\]
\[ \eqn{ Foreign Unaffected }{
- \bigforall_{ D \text{ s.t. } \patchof{D} = \bot }
- \left[ \bigexists_{A \in \set A} D \le A \right]
- \implies
- D \le L
+ \pendsof{C}{\foreign} = \pendsof{L}{\foreign}
}\]
- TODO THAT IS IMPOSSIBLE TO CALCULATE
\subsection{Lemma: Foreign Identical}
-$\patchof{D} = \bot \implies \big[ D \le C \equiv D \le L \big]$.
+$\isforeign{D} \implies \big[ D \le C \equiv D \le L \big]$.
\proof{
-If $D \le L$, trivially $D \le C$; so conversely
-$D \not\le C \implies D \not\le L$.
-Whereas if $D \le C$, either $D \le L$ or
-$\exists{A \in \set A} D \le A$ (since $D \neq C$),
-in which case by Foreign Unaffected $D \le L$.
+Trivial by Foreign Unaffected and the definition of $\pends$
}
\subsection{No Replay}
\subsection{Foreign Contents}
Not applicable.
+
+\subsection{Bases' Children}
+
+We need to consider this for $D=L$ and also for $D=R$ ($R \in \set
+R$).
+
+For $D=L$, if $L \in \pn$ then $C \in \pn$, OK; whereas if
+$L \not \in \pn$ Bases' Children is inapplicable.
+
+For $D=R$,
+xxx up to here?
+
+If $L \in \py, R \in \py$: not applicable for either $D=L$ or $D=R$.
+
+If $L \in \py, R \in \pn$: not applicable for $L$, OK for $R$.
+
+Other possibilities for $L \in \py$ are excluded by Tip Merge.
+
+If $L \in \pn, R \in \pn$: satisfied for both $L$ and $R$.
+
+If $L \in \pn, R \in \foreign$: satisfied for $L$, not applicable for
+$R$.
+
+If $L \in \pn, R \in \pqy$: satisfied for $L$, not applicable for
+$R$.
+
+Other possibilities for $L \in \pn$ are excluded by Base Merge.
+
+If $L \in \foreign$: not applicable for $L$; nor for $R$, by Foreign Merges.
+
+