strategy: wip reachable etc.

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

diff --git a/trav-proofs.tex b/trav-proofs.tex
index 876525dd7253d56f8963a23d41f6d71f02a1a52e..06a54cfb0521161bd329823d9d685a877c52e30b 100644 (file)
--- 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}{
 
 Firstly, some lemmas.
 \statement{Tip Correct Contents}{

-  \tipcy \haspatch \pd
+  \tipcy \haspatch \pa E

     \equiv
     \equiv

-  \pd = \pc \lor \pd \isdep \pc
+  \pa E = \pc \lor \pa E \isdep \pc

 }
 \proof{
 }
 \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 $\equiv D \isin \tipcn$.
 }
   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}
 
 
 \subsection{Recreate Base Beginning}
 

+To recap we are executing Create Base with
+$L = \tipdy$ and $\pq = \pc$.
+

 \subsubsection{Create Acyclic}
 
 \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}
 
 
 \subsection{Tip Base Merge}