--- a/src/HOL/Probability/Regularity.thy Sat Mar 15 16:54:32 2014 +0100
+++ b/src/HOL/Probability/Regularity.thy Sun Mar 16 18:09:04 2014 +0100
@@ -319,8 +319,8 @@
by (rule INF_superset_mono) (auto simp add: compact_imp_closed)
also have "(INF U:{U. U \<subseteq> B \<and> closed U}. M (space M - U)) =
(INF U:{U. space M - B \<subseteq> U \<and> open U}. emeasure M U)"
- by (subst INF_image[of "\<lambda>u. space M - u", symmetric])
- (rule INF_cong, auto simp add: sU intro!: INF_cong)
+ by (subst INF_image [of "\<lambda>u. space M - u", symmetric, unfolded comp_def])
+ (rule INF_cong, auto simp add: sU intro!: INF_cong)
finally have
"(INF U:{U. space M - B \<subseteq> U \<and> open U}. emeasure M U) \<le> emeasure M (space M - B)" .
moreover have
@@ -335,7 +335,7 @@
also have "\<dots> = (SUP U:{U. B \<subseteq> U \<and> open U}. M (space M - U))"
by (rule SUP_cong) (auto simp add: emeasure_compl sb compact_imp_closed)
also have "\<dots> = (SUP K:{K. K \<subseteq> space M - B \<and> closed K}. emeasure M K)"
- by (subst SUP_image[of "\<lambda>u. space M - u", symmetric])
+ by (subst SUP_image [of "\<lambda>u. space M - u", symmetric, simplified comp_def])
(rule SUP_cong, auto simp: sU)
also have "\<dots> = (SUP K:{K. K \<subseteq> space M - B \<and> compact K}. emeasure M K)"
proof (safe intro!: antisym SUP_least)