proposition: Lemma segment_continuous_ge_surjective a b f : a <= b -> f b <= f a -> {within `[a, b], continuous f} -> set_surj `[a, b] `[f b, f a] f.
proof: Proof. move=> le_ab f_ab /(segment_continuous_surjective le_ab). by rewrite (min_idPr _)// (max_idPl _). 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)