proposition: Lemma dec_surj_image_segment a b f : a <= b -> {in `[a, b] &, {mono f : x y /~ x <= y}} -> set_surj `[a, b] `[f b, f a] f -> f @` `[a, b] = `[f b, f a]%classic.
proof: Proof. move=> leab fge f_surj; have fafb : f b <= f a by rewrite fge ?bound_itvE. by rewrite mono_surj_image_segment ?dec_segment_image//; right. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrint ssrnum finmap matrix) mathcomp(rat interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality set_interval Rstruct) ereal reals signed topology prodnormedzmodule