diff -r 374caac3d624 -r 125705f5965f src/HOL/Analysis/Equivalence_Lebesgue_Henstock_Integration.thy --- a/src/HOL/Analysis/Equivalence_Lebesgue_Henstock_Integration.thy Sun Sep 15 17:24:31 2019 +0200 +++ b/src/HOL/Analysis/Equivalence_Lebesgue_Henstock_Integration.thy Mon Sep 16 17:03:13 2019 +0100 @@ -4611,7 +4611,7 @@ have "(UNIV::'a set) \ sets lborel" by simp then show ?thesis - using assms borel_measurable_if_D borel_measurable_UNIV_eq integrable_imp_measurable_weak integrable_restrict_UNIV by blast + by (metis (mono_tags, lifting) assms borel_measurable_if_D integrable_imp_measurable_weak integrable_restrict_UNIV lebesgue_on_UNIV_eq sets_lebesgue_on_refl) qed lemma integrable_iff_integrable_on: @@ -4767,7 +4767,7 @@ then have "(\x. if x \ S then f x else 0) integrable_on UNIV" by (simp add: integrable_restrict_UNIV) then have borel: "(\x. if x \ S then f x else 0) \ borel_measurable (lebesgue_on UNIV)" - using integrable_imp_measurable borel_measurable_UNIV_eq by blast + using integrable_imp_measurable lebesgue_on_UNIV_eq by blast then show "{x \ S. f x \ 0} \ sets lebesgue" unfolding borel_measurable_vimage_open by (rule allE [where x = "-{0}"]) auto @@ -4777,7 +4777,7 @@ then have "(\x. if x \ T then f x else 0) integrable_on UNIV" by (simp add: integrable_restrict_UNIV) then have borel: "(\x. if x \ T then f x else 0) \ borel_measurable (lebesgue_on UNIV)" - using integrable_imp_measurable borel_measurable_UNIV_eq by blast + using integrable_imp_measurable lebesgue_on_UNIV_eq by blast then show "{x \ T. f x \ 0} \ sets lebesgue" unfolding borel_measurable_vimage_open by (rule allE [where x = "-{0}"]) auto