X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=trav-proofs.tex;h=67e1b113b696e79de2680381c0df917654b7488a;hp=14f6cd8942edbc6af512430fa6be7042948d2218;hb=29344b6ad90d4bc445e67d9b0025509ea555512e;hpb=8ee16bd8a84437fc51257805eb234c4dee054889

diff --git a/trav-proofs.tex b/trav-proofs.tex
index 14f6cd8..67e1b11 100644
--- a/trav-proofs.tex
+++ b/trav-proofs.tex
@@ -5,3 +5,23 @@ 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.
+