From d5836b17ce78e4f79f38325cdb1ce20f29c881ca Mon Sep 17 00:00:00 2001
From: Ian Jackson <ijackson@chiark.greenend.org.uk>
Date: Sun, 8 Jul 2012 00:05:10 +0100
Subject: [PATCH] traversal: proof of Tip Correct Contents

---
 trav-alg.tex    | 2 +-
 trav-proofs.tex | 8 +++++---
 2 files changed, 6 insertions(+), 4 deletions(-)

diff --git a/trav-alg.tex b/trav-alg.tex
index 8a9a68a..210b20b 100644
--- a/trav-alg.tex
+++ b/trav-alg.tex
@@ -32,7 +32,7 @@ such that:
 \statement{Base Correct Contents}{
   \tipcn \haspatch \pd
    \equiv
-  \pc \hasdep \pd
+  \pd \isdep \pc
 }
 \statement{Tip Exceeds Inputs}{
   \tipcy \ge \pendsof{\allsrcs}{\pcy}
diff --git a/trav-proofs.tex b/trav-proofs.tex
index 3c2a175..876525d 100644
--- a/trav-proofs.tex
+++ b/trav-proofs.tex
@@ -8,14 +8,16 @@ WIP WHAT ABOUT PROVING ALL THE TRAVERSAL RESULTS
 \subsection{Traversal Lemmas}
 
 Firstly, some lemmas.
-
 \statement{Tip Correct Contents}{
   \tipcy \haspatch \pd
     \equiv
-  \pc = \pd \lor \pc \hasdep \pd
+  \pd = \pc \lor \pd \isdep \pc
 }
 \proof{
-   WIP
+  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}
-- 
2.30.2