proposition: Lemma le_variation a b f s x : variation a b f s <= variation a b f (x :: s).
proof: Proof. case: s => [|h t]. by rewrite variation_nil /variation/= big_nat_recl//= big_nil addr0. rewrite /variation/= !big_nat_recl//= addrA lerD2r. by rewrite (le_trans _ (ler_normD _ _))// (addrC (f x - _)) addrA subrK. 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)