--- a/text/evmap.tex	Wed Apr 14 18:12:03 2010 -0700
+++ b/text/evmap.tex	Mon Apr 26 10:43:42 2010 -0700
@@ -508,7 +508,13 @@
 Thus we can apply Lemma \ref{xxxx} \nn{backward acyclic models lemma, from appendix}
 to get the desired map $\alpha$, well-defined up to a contractible set of choices.
 
+By construction, the image of $\alpha$ lies in the union of $G^{i,m}_*$ 
+(with $m$ fixed and $i$ varying).
+Furthermore, if $q\ot c$ 
+appears in the boundary of $p\ot b$ and $\alpha(p\ot b) \in G^{s,m}_*$, then
+$\alpha(q\ot c) \in G^{t,m}_*$ for some $t \le s$.
 
+\nn{...}