proposition: Lemma commr_sum (I : Type) (s : seq I) (P : pred I) (F : I -> R) x : (forall i, P i -> comm x (F i)) -> comm x (\sum_(i <- s | P i) F i).
proof: Proof. move=> comm_x_F; rewrite /comm mulr_suml mulr_sumr. by apply: eq_bigr => i /comm_x_F. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop prime binomial)