proposition: Lemma comparable_gt_max : (max x y < z) = (x < z) && (y < z).
proof: Proof. case: comparableP cmp_xy => // [||<-//]; rewrite ?andbb//; first rewrite andbC; by case: (comparableP z) => // ylt /lt_trans->. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)