avoid using '...' with LIMSEQ (cf. 1cc4ab4b7ff7)
--- a/src/HOL/Probability/Measure.thy Tue May 04 19:53:57 2010 -0700
+++ b/src/HOL/Probability/Measure.thy Tue May 04 21:03:50 2010 -0700
@@ -463,7 +463,7 @@
have "(measure M \<circ> nat_case {} A) ----> measure M (\<Union>i. nat_case {} A i)"
by (rule measure_countable_increasing)
(auto simp add: range_subsetD [OF A] subsetD [OF ASuc] split: nat.splits)
- also have "... = measure M (\<Union>i. A i)"
+ also have "measure M (\<Union>i. nat_case {} A i) = measure M (\<Union>i. A i)"
by (simp add: ueq)
finally have "(measure M \<circ> nat_case {} A) ----> measure M (\<Union>i. A i)" .
thus ?thesis using meq
@@ -652,7 +652,7 @@
show "\<And>n. f -` A n \<inter> space m1 \<subseteq> f -` A (Suc n) \<inter> space m1"
using ASuc by auto
qed
- also have "... = measure m1 (f -` (\<Union>i. A i) \<inter> space m1)"
+ also have "measure m1 (\<Union>i. f -` A i \<inter> space m1) = measure m1 (f -` (\<Union>i. A i) \<inter> space m1)"
by (simp add: vimage_UN)
finally have "(measure m2 \<circ> A) ----> measure m1 (f -` (\<Union>i. A i) \<inter> space m1)" .
moreover