proposition: Lemma integral0_eq D f : (forall x, D x -> f x = 0) -> \int_(x in D) f x = 0.
proof: Proof. move=> f0; under eq_integral; first by move=> x /[1!inE] /f0 ->; over. by rewrite integral0. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrnum ssrint interval finmap) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality fsbigop ) signed reals ereal topology normedtype sequences real_interval esum measure lebesgue_measure numfun