traversal: proof of Tip Correct Contents

diff --git a/trav-alg.tex b/trav-alg.tex
index 8a9a68ad1e63e19d05bf44ccb19912935373f84d..210b20b9ed32971aac20f940397a91bf0671f05e 100644 (file)
--- 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 3c2a1754cd8991bcc8cd1c4877812297cc9cdbd4..876525dd7253d56f8963a23d41f6d71f02a1a52e 100644 (file)
--- 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}