WIP WHAT ABOUT PROVING ALL THE TRAVERSAL RESULTS
+\subsection{Traversal Lemmas}
+
+Firstly, some lemmas.
+\statement{Tip Correct Contents}{
+ \tipcy \haspatch \pa E
+ \equiv
+ \pa E = \pc \lor \pa E \isdep \pc
+}
+\proof{
+ For $\pc = \pa E$, Tip Own Contents suffices.
+ For $\pc \neq \pa E$, Exclusive Tip Contents
+ gives $D \isin \tipcy \equiv D \isin \baseof{\tipcy}$
+ which by Correct Base $\equiv D \isin \tipcn$.
+}
+
\subsection{Base Dependency Merge, Base Sibling Merge}
We do not prove that the preconditions are met. Instead, we check
\subsection{Recreate Base Beginning}
-WHAT IF $\pendsof{L}{\pqy} \neq \{\}$ ?
+\subsubsection{Create Acyclic}
+
+$L = \tipdy$ so
\subsection{Tip Base Merge}