equal
deleted
inserted
replaced
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 |