internal notation: rename \merge and \mergeof to \commitmerge and \commitmergeof...

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

diff --git a/trav-proofs.tex b/trav-proofs.tex
index 14f6cd8942edbc6af512430fa6be7042948d2218..67e1b113b696e79de2680381c0df917654b7488a 100644 (file)
--- 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.
+