proposition: Lemma real_mono : {homo f : x y / x < y} -> {in real &, {mono f : x y / x <= y}}.
proof: Proof. move=> mf x y xR yR /=; have [lt_xy | le_yx] := real_leP xR yR. by rewrite ltW_homo. by rewrite lt_geF ?mf. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)