proposition: Lemma variation_le a b f g s : variation a b (f \+ g)%R s <= variation a b f s + variation a b g s.
proof: Proof. rewrite [in leRHS]/variation -big_split/=. apply: ler_sum => k _; apply: le_trans; last exact: ler_normD. by rewrite /= addrACA addrA opprD addrA. Qed.
imports: mathcomp(all_ssreflect ssralg ssrint ssrnum finmap) mathcomp(matrix interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality) ereal reals signed topology prodnormedzmodule normedtype derive sequences real_interval HB(structures)