proposition: Lemma lee_npeseries (R : realType) (u v : (\bar R)^nat) (P : pred nat) : (forall i, P i -> u i <= 0) -> (forall n, P n -> v n <= u n) -> \sum_(i <oo | P i) v i <= \sum_(i <oo | P i) u i.
proof: Proof. move=> u0 Puv; apply: lee_lim. - apply: is_cvg_ereal_npos_natsum_cond => n _ /[dup] Pn /Puv/le_trans; apply. exact/u0. - by apply: is_cvg_ereal_npos_natsum_cond => n _ Pn; exact/u0. - by near=> n; exact: lee_sum. Unshelve. all: by end_near. 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