1.1 --- a/src/HOL/Multivariate_Analysis/Convex_Euclidean_Space.thy	Sun Jul 24 22:38:13 2011 +0200
     1.2 +++ b/src/HOL/Multivariate_Analysis/Convex_Euclidean_Space.thy	Mon Jul 25 23:26:55 2011 +0200
     1.3 @@ -2539,7 +2539,7 @@
     1.4    fixes s :: "'a::real_normed_vector set"
     1.5    assumes "open s"
     1.6    shows "open(convex hull s)"
     1.7 -  unfolding open_contains_cball convex_hull_explicit unfolding mem_Collect_eq ball_simps(10)
     1.8 +  unfolding open_contains_cball convex_hull_explicit unfolding mem_Collect_eq ball_simps(8)
     1.9  proof(rule, rule) fix a
    1.10    assume "\<exists>sa u. finite sa \<and> sa \<subseteq> s \<and> (\<forall>x\<in>sa. 0 \<le> u x) \<and> setsum u sa = 1 \<and> (\<Sum>v\<in>sa. u v *\<^sub>R v) = a"
    1.11    then obtain t u where obt:"finite t" "t\<subseteq>s" "\<forall>x\<in>t. 0 \<le> u x" "setsum u t = 1" "(\<Sum>v\<in>t. u v *\<^sub>R v) = a" by auto