--- a/text/ncat.tex	Mon Oct 03 16:40:16 2011 -0700
+++ b/text/ncat.tex	Tue Oct 04 22:44:54 2011 -0700
@@ -819,7 +819,7 @@
 After a small perturbation, we may assume that $q$ is simultaneously transverse to all the splittings in $P$, and
 (by Axiom \ref{axiom:splittings}) that $c$ splits along $q$.
 We can now choose, for each splitting $p$ in $P$, a common refinement $p'$ of $p$ and $q$.
-This constitutes the middle part of $\vcone(P)$.
+This constitutes the middle part ($P\times \{0\}$ above) of $\vcone(P)$.
 \end{proof}