proposition: Lemma npeseries_le0 P N : (forall n : nat, P n -> u_ n <= 0) -> \sum_(N <= i <oo | P i) u_ i <= 0.
proof: Proof. move=> u0; apply: (lime_le (is_cvg_npeseries u0)). by apply: nearW => k; rewrite sume_le0. 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