X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=trav-proofs.tex;h=06a54cfb0521161bd329823d9d685a877c52e30b;hp=a9ed5cd30a428f45ec78706534ce86b77ceeb425;hb=8f439786bda0cd262aee087f20fc6322ed7a144f;hpb=45660137914fb1a7e7efe44ef84305add6468c05

diff --git a/trav-proofs.tex b/trav-proofs.tex
index a9ed5cd..06a54cf 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 \pa E
+    \equiv
+  \pa E = \pc \lor \pa E \isdep \pc
+}
+\proof{
+  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}
 
 We do not prove that the preconditions are met.  Instead, we check
@@ -17,7 +32,28 @@ WIP WHAT ABOUT PROVING ALL THE TRAVERSAL RESULTS
 
 \subsection{Recreate Base Beginning}
 
+To recap we are executing Create Base with
+$L = \tipdy$ and $\pq = \pc$.
+
+\subsubsection{Create Acyclic}
+
+By Tip Correct Contents of $L$,
+$L \haspatch \pa E \equiv \pa E = \pd \lor \pa E \isdep \pd$.
+Now $\pd \isdirdep \pc$,
+so by Coherence, and setting $\pa E = \pc$,
+$L \nothaspatch \pc$. I.e. $L \nothaspatch \pq$. OK.
+
+That's everything for Create Base.  $\qed$
+
+\subsection{Recreate Base Final Declaration}
+
+\subsubsection{Base Only} $\patchof{W} = \patchof{L} = \pn$.  OK.
+
+\subsubsection{Unique Tips}
+
+Want to prove that for any $\p \isin C$, $\tipdy$ is a suitable $T$.
 
+WIP
 
 \subsection{Tip Base Merge}