proposition: Lemma sub_series m n : series n - series m = if (m <= n)%N then \sum_(m <= k < n) u_ k else - \sum_(n <= k < m) u_ k.
proof: Proof. by have [mn|/ltnW mn] := leqP m n; rewrite -sub_series_geq// opprB. 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