X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=trav-proofs.tex;h=876525dd7253d56f8963a23d41f6d71f02a1a52e;hp=b451a6175d0c1d9b4e06cba476f9f76f263972e4;hb=d5836b17ce78e4f79f38325cdb1ce20f29c881ca;hpb=e53011eb40f80fa71b1c37be544d6b8a2fdf58ab

diff --git a/trav-proofs.tex b/trav-proofs.tex
index b451a61..876525d 100644
--- a/trav-proofs.tex
+++ b/trav-proofs.tex
@@ -5,6 +5,21 @@ that the commit generation preconditions are met.
 
 WIP WHAT ABOUT PROVING ALL THE TRAVERSAL RESULTS
 
+\subsection{Traversal Lemmas}
+
+Firstly, some lemmas.
+\statement{Tip Correct Contents}{
+  \tipcy \haspatch \pd
+    \equiv
+  \pd = \pc \lor \pd \isdep \pc
+}
+\proof{
+  For $\pc = \pd$, Tip Own Contents suffices.
+  For $\pc \neq \pd$, 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
@@ -15,6 +30,12 @@ TODO COMPLETE MERGE-BASE STUFF
 
 WIP WHAT ABOUT PROVING ALL THE TRAVERSAL RESULTS
 
+\subsection{Recreate Base Beginning}
+
+\subsubsection{Create Acyclic}
+
+$L = \tipdy$ so
+
 \subsection{Tip Base Merge}
 
 $L = W$, $R = \tipcn$.