traversal: Base/Tip Correct Contents chane notation

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

diff --git a/trav-proofs.tex b/trav-proofs.tex
index 3c2a1754cd8991bcc8cd1c4877812297cc9cdbd4..f1993d31191fa6ec9798dc9a00bca0903540cc98 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
+  \tipcy \haspatch \pa E
     \equiv
-  \pc = \pd \lor \pc \hasdep \pd
+  \pa E = \pc \lor \pa E \isdep \pc
 }
 \proof{
-   WIP
+  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}