proposition: Lemma inc_surj_image_segment a b f : a <= b -> {in `[a, b] &, {mono f : x y / x <= y}} -> set_surj `[a, b] `[f a, f b] f -> f @` `[a, b] = `[f a, f b]%classic.
proof: Proof. move=> leab fle f_surj; have fafb : f a <= f b by rewrite fle ?bound_itvE. by rewrite mono_surj_image_segment ?inc_segment_image//; left. 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