From e855f75b357a56be5f66cd8adb8deb08b10c55a9 Mon Sep 17 00:00:00 2001
From: Ian Jackson <ijackson@chiark.greenend.org.uk>
Date: Mon, 12 Mar 2012 15:35:30 +0000
Subject: [PATCH] add purported proof of calculation of ends

---
 article.tex | 11 ++++++++++-
 1 file changed, 10 insertions(+), 1 deletion(-)

diff --git a/article.tex b/article.tex
index b48a31e..b26a120 100644
--- a/article.tex
+++ b/article.tex
@@ -310,7 +310,16 @@ by the LHS.  And $A \le A''$.
        \right\}
       \end{cases}
 }\]
-xxx proof tbd
+\proof{
+Trivial for $C \in \set P$.  For $C \not\in \set P$,
+$\pancsof{C}{\set P} = \bigcup_{A \in \set A} \pancsof{A}{\set P}$.
+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 $F$.
+Otherwise, $E$ meets all the conditions for $\pends$.
+}
 
 \[ \eqn{Ingredients Prevent Replay:}{
   \left[
-- 
2.30.2