traversal: proof of Tip Correct Contents

[topbloke-formulae.git] / trav-proofs.tex

diff --git a/trav-proofs.tex b/trav-proofs.tex
index b451a6175d0c1d9b4e06cba476f9f76f263972e4..876525dd7253d56f8963a23d41f6d71f02a1a52e 100644 (file)
--- 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}
 
 $L = W$, $R = \tipcn$.