--- a/src/HOL/Multivariate_Analysis/Brouwer_Fixpoint.thy Wed Sep 07 14:58:40 2011 +0200
+++ b/src/HOL/Multivariate_Analysis/Brouwer_Fixpoint.thy Wed Sep 07 09:02:58 2011 -0700
@@ -93,7 +93,7 @@
have even_minus_odd:"\<And>x y. even x \<Longrightarrow> odd (y::int) \<Longrightarrow> odd (x - y)" using assms by auto
have odd_minus_even:"\<And>x y. odd x \<Longrightarrow> even (y::int) \<Longrightarrow> odd (x - y)" using assms by auto
show ?thesis unfolding even_nat_def unfolding card_eq_setsum and lem4[THEN sym] and *[unfolded card_eq_setsum]
- unfolding card_eq_setsum[THEN sym] apply (rule odd_minus_even) unfolding zadd_int[THEN sym] apply(rule odd_plus_even)
+ unfolding card_eq_setsum[THEN sym] apply (rule odd_minus_even) unfolding of_nat_add apply(rule odd_plus_even)
apply(rule assms(7)[unfolded even_nat_def]) unfolding int_mult by auto qed
subsection {* The odd/even result for faces of complete vertices, generalized. *}