src/HOL/Probability/Probability_Mass_Function.thy
changeset 67489 f1ba59ddd9a6
parent 67486 d617e84bb2b1
child 67601 b34be3010273
equal deleted inserted replaced
67488:3d33847dc911 67489:f1ba59ddd9a6
  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 .