X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=lemmas.tex;h=937398207615e337585cdf7773d0c33f66f6a9f6;hp=8509c895ec46e213c6db96ade1442d814189f2a2;hb=0c3db5a204f508f8a8a59c74ea8a9bf56d3ab59e;hpb=3a8cce8e2c30335e973bcaa8b98a7d8238bdaacb

diff --git a/lemmas.tex b/lemmas.tex
index 8509c89..9373982 100644
--- a/lemmas.tex
+++ b/lemmas.tex
@@ -125,6 +125,23 @@ an $F''$) which disqualifies $F$ and $E$.
 Otherwise, $E$ meets all the conditions for $\pends$.
 }
 
+\subsection{Single Parent Unique Tips}
+
+Unique Tips is satisfied for single-parent commits.  Formally,
+given a conformant commit $A$,
+$$
+ \Big[
+   C \hasparents \{ A \}
+ \Big] \implies \left[
+   \bigforall_{P \patchisin C} \pendsof{C}{\py} = \{ T \}
+ \right]
+$$
+\proof{
+  Trivial for $C \in \py$.
+  For $C \not\in \py$, $\pancsof{C}{\py} = \pancsof{A}{\py}$,
+  so Unique Tips of $A$ suffices.
+}
+
 \subsection{Ingredients Prevent Replay}
 Given conformant commits $A \in \set A$,
 $$