proposition: Lemma integralZl_indic_nnsfun (f : {nnsfun T >-> R}) (k : R) : \int[m]_(x in D) (k * \1_(f @^-1` [set k]) x)%:E = k%:E * \int[m]_(x in D) (\1_(f @^-1` [set k]) x)%:E.
proof: Proof. rewrite (@integralZl_indic (fun k => f @^-1` [set k]))// => k0. by rewrite preimage_nnfun0. 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