proposition: Lemma mono_surj_image_segmentP a b f : a <= b -> monotonous `[a, b] f -> set_surj `[a, b] (f @`[a, b]) f -> forall y, reflect (exists2 x, x \in `[a, b] & f x = y) (y \in f @`[a, b]).
proof: Proof. move=> /mono_surj_image_segment/[apply]/[apply]/predeqP + y => /(_ y) fab. by apply/(equivP idP); symmetry. 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