proposition: Lemma additive_nnsfunl (g f : {nnsfun T >-> R}) x : \sum_(i \in range g) m (g @^-1` [set i] `&` (f @^-1` [set x])) = m (\big[setU/set0]_(i \in range g) (g @^-1` [set i]) `&` f @^-1` [set x]).
proof: Proof. by under eq_fsbigr do rewrite setIC; rewrite setIC additive_nnsfunr. 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