provide \bigexists

[topbloke-formulae.git] / lemmas.tex

diff --git a/lemmas.tex b/lemmas.tex
index 41ea1c815af7fa6e04a2237255e5b355860888ac..40cc5f488a6403581a1561936be982097dc5327f 100644 (file)
--- a/lemmas.tex
+++ b/lemmas.tex
@@ -121,10 +121,27 @@ So $\pendsof{C}{\set P} \subset \bigcup_{E \in \set E} \pendsof{E}{\set P}$.
 Consider some $E \in \pendsof{A}{\set P}$.  If $\exists_{B,F}$ as
 specified, then either $F$ is going to be in our result and
 disqualifies $E$, or there is some other $F'$ (or, eventually,
-an $F''$) which disqualifies $F$.
+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 $A$,
+$$
+ \Big[
+   C \hasparents \{ A \}
+ \Big] \implies \left[
+   \bigforall_{P \patchisin C} \pendsof{C}{\p} = \{ T \}
+ \right]
+$$
+\proof{
+  Trivial for $C \in \p$.
+  For $C \not\in \p$, $\pancsof{C}{\p} = \pancsof{A}{\p}$,
+  so Unique Tips of $A$ suffices.
+}
+
 \subsection{Ingredients Prevent Replay}
 Given conformant commits $A \in \set A$,
 $$