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=876525dd7253d56f8963a23d41f6d71f02a1a52e;hb=8f439786bda0cd262aee087f20fc6322ed7a144f;hpb=d5836b17ce78e4f79f38325cdb1ce20f29c881ca

diff --git a/trav-proofs.tex b/trav-proofs.tex
index 876525d..06a54cf 100644
--- a/trav-proofs.tex
+++ b/trav-proofs.tex
@@ -9,13 +9,13 @@ WIP WHAT ABOUT PROVING ALL THE TRAVERSAL RESULTS
 
 Firstly, some lemmas.
 \statement{Tip Correct Contents}{
-  \tipcy \haspatch \pd
+  \tipcy \haspatch \pa E
     \equiv
-  \pd = \pc \lor \pd \isdep \pc
+  \pa E = \pc \lor \pa E \isdep \pc
 }
 \proof{
-  For $\pc = \pd$, Tip Own Contents suffices.
-  For $\pc \neq \pd$, Exclusive Tip Contents
+  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 $\equiv D \isin \tipcn$.
 }
@@ -32,9 +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}
 
-$L = \tipdy$ so
+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}