proposition: Lemma sumnB I r (P : pred I) (E1 E2 : I -> nat) : (forall i, P i -> E1 i <= E2 i) -> \sum_(i <- r | P i) (E2 i - E1 i) = \sum_(i <- r | P i) E2 i - \sum_(i <- r | P i) E1 i.
proof: Proof. by move=> /(_ _ _)/subnK-/(eq_bigr _)<-; rewrite big_split addnK. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div fintype tuple finfun)