proposition: Lemma nneseries_ge0 P N : (forall n, P n -> 0 <= u_ n) -> 0 <= \sum_(N <= i <oo | P i) u_ i.
proof: Proof. move=> u0; apply: (lime_ge (is_cvg_nneseries u0)). by apply: nearW => k; rewrite sume_ge0. Qed.
imports: mathcomp(all_ssreflect ssralg ssrint ssrnum matrix) mathcomp(interval rat) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(set_interval) reals ereal signed topology normedtype landau