src/HOL/Probability/Probability_Mass_Function.thy
changeset 70532 fcf3b891ccb1
parent 69597 ff784d5a5bfb
child 70817 dd675800469d
equal deleted inserted replaced
70531:2d2b5a8e8d59 70532:fcf3b891ccb1
   854           using bnd by (auto intro!: mult_mono simp: from_nat_into set_pmf_not_empty)
   854           using bnd by (auto intro!: mult_mono simp: from_nat_into set_pmf_not_empty)
   855       next
   855       next
   856         have "integrable (map_pmf (to_nat_on M) M) (\<lambda>n. B)"
   856         have "integrable (map_pmf (to_nat_on M) M) (\<lambda>n. B)"
   857           by auto
   857           by auto
   858         then show "summable (\<lambda>n. pmf (map_pmf (to_nat_on (set_pmf M)) M) n * B)"
   858         then show "summable (\<lambda>n. pmf (map_pmf (to_nat_on (set_pmf M)) M) n * B)"
   859           by (simp add: measure_pmf_eq_density integrable_density integrable_count_space_nat_iff summable_rabs_cancel)
   859           by (fastforce simp add: measure_pmf_eq_density integrable_density integrable_count_space_nat_iff summable_mult2)
   860       qed
   860       qed
   861     qed simp
   861     qed simp
   862   qed simp
   862   qed simp
   863 qed
   863 qed
   864 
   864