proposition: Lemma psumr_eq0P (I : finType) (P : pred I) (F : I -> R) : (forall i, P i -> 0 <= F i) -> \sum_(i | P i) F i = 0 -> (forall i, P i -> F i = 0).
proof: Proof. move=> F_ge0 /eqP; rewrite psumr_eq0 // -big_all big_andE => /forallP hF i Pi. by move: (hF i); rewrite implyTb Pi /= => /eqP. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)