equal
deleted
inserted
replaced
2057 using Cons(1) by (intro Cons) simp_all |
2057 using Cons(1) by (intro Cons) simp_all |
2058 finally show ?case by (simp add: case_prod_unfold) |
2058 finally show ?case by (simp add: case_prod_unfold) |
2059 qed simp |
2059 qed simp |
2060 also have "\<dots> = (\<Sum>(x',p)\<leftarrow>xs. ennreal p * (\<integral>\<^sup>+ x. indicator {x'} x \<partial>count_space UNIV))" |
2060 also have "\<dots> = (\<Sum>(x',p)\<leftarrow>xs. ennreal p * (\<integral>\<^sup>+ x. indicator {x'} x \<partial>count_space UNIV))" |
2061 using assms(1) |
2061 using assms(1) |
2062 by (intro sum_list_cong, simp only: case_prod_unfold, subst nn_integral_cmult [symmetric]) |
2062 by (simp cong: map_cong only: case_prod_unfold, subst nn_integral_cmult [symmetric]) |
2063 (auto intro!: assms(1) simp: max_def times_ereal.simps [symmetric] mult_ac ereal_indicator |
2063 (auto intro!: assms(1) simp: max_def times_ereal.simps [symmetric] mult_ac ereal_indicator |
2064 simp del: times_ereal.simps)+ |
2064 simp del: times_ereal.simps)+ |
2065 also from assms have "\<dots> = sum_list (map snd xs)" by (simp add: case_prod_unfold sum_list_ennreal) |
2065 also from assms have "\<dots> = sum_list (map snd xs)" by (simp add: case_prod_unfold sum_list_ennreal) |
2066 also have "\<dots> = 1" using assms(2) by simp |
2066 also have "\<dots> = 1" using assms(2) by simp |
2067 finally show ?thesis . |
2067 finally show ?thesis . |