proposition: Lemma integral_ge0N (D : set T) (f : T -> \bar R) : (forall x, D x -> 0 <= f x) -> \int[mu]_(x in D) - f x = - \int[mu]_(x in D) f x.
proof: Proof. move=> f0; rewrite integralN // (eq_integral _ _ (ge0_funenegE _))// integral0. by rewrite oppe0 fin_num_adde_defl. 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