src/HOL/Analysis/Equivalence_Lebesgue_Henstock_Integration.thy
changeset 70802 160eaf566bcb
parent 70726 91587befabfd
child 70817 dd675800469d
equal deleted inserted replaced
70801:5352449209b1 70802:160eaf566bcb
  1277 proof -
  1277 proof -
  1278   have "negligible ((+) (-a) ` S)"
  1278   have "negligible ((+) (-a) ` S)"
  1279   proof (subst negligible_on_intervals, intro allI)
  1279   proof (subst negligible_on_intervals, intro allI)
  1280     fix u v
  1280     fix u v
  1281     show "negligible ((+) (- a) ` S \<inter> cbox u v)"
  1281     show "negligible ((+) (- a) ` S \<inter> cbox u v)"
  1282       using \<open>closed S\<close> eq1 by (auto simp add: negligible_iff_null_sets field_simps
  1282       using \<open>closed S\<close> eq1 by (auto simp add: negligible_iff_null_sets algebra_simps
  1283         intro!: closed_translation_subtract starlike_negligible_compact cong: image_cong_simp)
  1283         intro!: closed_translation_subtract starlike_negligible_compact cong: image_cong_simp)
       
  1284         (metis add_diff_eq diff_add_cancel scale_right_diff_distrib)
  1284   qed
  1285   qed
  1285   then show ?thesis
  1286   then show ?thesis
  1286     by (rule negligible_translation_rev)
  1287     by (rule negligible_translation_rev)
  1287 qed
  1288 qed
  1288 
  1289