proposition: Lemma total_variationD a b c f : a <= c -> c <= b -> (TV a b f = TV a c f + TV c b f)%E.
proof: Proof. by move=> ac cb; apply/eqP; rewrite eq_le; apply/andP; split; [exact: total_variationD2|exact: total_variationD1]. 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)