author Manuel Eberl Wed, 18 May 2016 12:24:33 +0200 changeset 63101 65f1d7829463 parent 63100 aa5cffd8a606 child 63102 71059cf60658
Resolved name clash
```--- a/src/HOL/Groups_List.thy	Tue May 17 19:27:42 2016 +0200
+++ b/src/HOL/Groups_List.thy	Wed May 18 12:24:33 2016 +0200
@@ -259,7 +259,7 @@
"(\<And>x. x \<in> set xs \<Longrightarrow> (x :: 'a :: ordered_comm_monoid_add) \<ge> 0) \<Longrightarrow> listsum xs \<ge> 0"
by (induction xs) simp_all

-lemma listsum_map_filter:
"listsum (map f (filter P xs)) = listsum (map (\<lambda>x. if P x then f x else 0) xs)"
by (induction xs) simp_all
```
```--- a/src/HOL/Probability/Probability_Mass_Function.thy	Tue May 17 19:27:42 2016 +0200
+++ b/src/HOL/Probability/Probability_Mass_Function.thy	Wed May 18 12:24:33 2016 +0200
@@ -1809,7 +1809,7 @@
proof -
have "(\<integral>\<^sup>+ x. ennreal (listsum (map snd (filter (\<lambda>z. fst z = x) xs))) \<partial>count_space UNIV) =
(\<integral>\<^sup>+ x. ennreal (listsum (map (\<lambda>(x',p). indicator {x'} x * p) xs)) \<partial>count_space UNIV)"
-    by (intro nn_integral_cong ennreal_cong, subst listsum_map_filter) (auto intro: listsum_cong)
+    by (intro nn_integral_cong ennreal_cong, subst listsum_map_filter') (auto intro: listsum_cong)
also have "\<dots> = (\<Sum>(x',p)\<leftarrow>xs. (\<integral>\<^sup>+ x. ennreal (indicator {x'} x * p) \<partial>count_space UNIV))"
using assms(1)
proof (induction xs)
@@ -1901,7 +1901,7 @@
by (intro setsum.cong) (auto simp: indicator_def)
also have "\<dots> = (\<Sum>x\<in>set (map fst xs). (\<Sum>xa = 0..<length xs.
if fst (xs ! xa) = x \<and> x \<in> A then snd (xs ! xa) else 0))"
-    by (intro setsum.cong refl, subst listsum_map_filter, subst listsum_setsum_nth) simp
+    by (intro setsum.cong refl, subst listsum_map_filter', subst listsum_setsum_nth) simp
also have "\<dots> = (\<Sum>xa = 0..<length xs. (\<Sum>x\<in>set (map fst xs).
if fst (xs ! xa) = x \<and> x \<in> A then snd (xs ! xa) else 0))"
by (rule setsum.commute)
@@ -1911,7 +1911,7 @@
also have "\<dots> = (\<Sum>xa = 0..<length xs. if fst (xs ! xa) \<in> A then snd (xs ! xa) else 0)"
by (intro setsum.cong refl) (simp_all add: setsum.delta)
also have "\<dots> = listsum (map snd (filter (\<lambda>x. fst x \<in> A) xs))"
-    by (subst listsum_map_filter, subst listsum_setsum_nth) simp_all
+    by (subst listsum_map_filter', subst listsum_setsum_nth) simp_all
finally show ?thesis .
qed
```