X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=trav-proofs.tex;h=e69de29bb2d1d6434b8b29ae775ad8c2e48c5391;hp=67e1b113b696e79de2680381c0df917654b7488a;hb=6e7093d49c00150e48ebc264fb1a29de2004aeed;hpb=6e2f1b176fed02ad882ba53b5f930f0bf8e3a9ef diff --git a/trav-proofs.tex b/trav-proofs.tex index 67e1b11..e69de29 100644 --- a/trav-proofs.tex +++ b/trav-proofs.tex @@ -1,27 +0,0 @@ -\section{Traversal phase --- proofs} - -For each operation called for by the traversal algorithms, we prove -that the commit generation preconditions are met. - -\subsection{Tip Base Merge} - -$L = W$, $R = \tipcn$. - -TODO TBD - -Afterwards, $\baseof{W} = \tipcn$. - -\subsection{Tip Source Merge} - -In fact, we do this backwards: $L = S$, $R = W$. Since $S \in \pcy$, -the resulting $C \in \pcy$ and the remaining properties of the Merge -commit construction are symmetrical in $L$ and $R$ so this is fine. - -By the results of Tip Base Merge, $\baseof{W} = \tipcn$. - -By Base Ends Supreme, $\tipcn \ge \baseof{S}$ i.e. -$\baseof{R} \ge \baseof{L}$. - -Either $\baseof{L} = \baseof{M}$, or we must choose a different $M$ in -which case $M = \baseof{S}$ will suffice. -