proposition: Lemma psumr_neq0P (I : finType) (P : pred I) (F : I -> R) : (forall i, P i -> 0 <= F i) -> \sum_(i | P i) F i <> 0 -> (exists i, P i && (0 < F i)).
proof: Proof. by move=> ? /eqP; rewrite psumr_neq0// => /hasP[x _ ?]; exists x. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)