src/HOL/Probability/Independent_Family.thy
changeset 44282 f0de18b62d63
parent 43920 cedb5cb948fd
child 45777 c36637603821
equal deleted inserted replaced
44275:d995733b635d 44282:f0de18b62d63
   561         using dis by (rule disjoint_family_on_bisimulation) auto
   561         using dis by (rule disjoint_family_on_bisimulation) auto
   562     qed
   562     qed
   563     with F have "(\<lambda>i. prob X * prob (F i)) sums prob (X \<inter> (\<Union>i. F i))"
   563     with F have "(\<lambda>i. prob X * prob (F i)) sums prob (X \<inter> (\<Union>i. F i))"
   564       by simp
   564       by simp
   565     moreover have "(\<lambda>i. prob X * prob (F i)) sums (prob X * prob (\<Union>i. F i))"
   565     moreover have "(\<lambda>i. prob X * prob (F i)) sums (prob X * prob (\<Union>i. F i))"
   566       by (intro mult_right.sums finite_measure_UNION F dis)
   566       by (intro sums_mult finite_measure_UNION F dis)
   567     ultimately have "prob (X \<inter> (\<Union>i. F i)) = prob X * prob (\<Union>i. F i)"
   567     ultimately have "prob (X \<inter> (\<Union>i. F i)) = prob X * prob (\<Union>i. F i)"
   568       by (auto dest!: sums_unique)
   568       by (auto dest!: sums_unique)
   569     with F show "(\<Union>i. F i) \<in> sets ?D"
   569     with F show "(\<Union>i. F i) \<in> sets ?D"
   570       by auto
   570       by auto
   571   qed
   571   qed