proposition: Lemma real_nmono : {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_ltP xR yR. by rewrite lt_geF ?mf. by rewrite ltW_nhomo. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)