proposition: Lemma psumr_eq0 (I : eqType) (r : seq I) (P : pred I) (F : I -> R) : (forall i, P i -> 0 <= F i) -> (\sum_(i <- r | P i) (F i) == 0) = (all (fun i => (P i) ==> (F i == 0)) r).
proof: Proof. elim: r=> [|a r ihr hr] /=; rewrite (big_nil, big_cons); first by rewrite eqxx. by case: ifP=> pa /=; rewrite ?paddr_eq0 ?ihr ?hr // sumr_ge0. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)