proposition: Lemma ge0_integralZr k : (forall x, D x -> 0 <= f x) -> 0 <= k -> \int[mu]_(x in D) (f x * k) = \int[mu]_(x in D) (f x) * k.
proof: Proof. move=> f0 k0; under eq_integral do rewrite muleC. by rewrite ge0_integralZl// muleC. 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