proposition: Lemma comparable_lt_max : (z < max x y) = (z < x) || (z < y).
proof: Proof. case: comparableP cmp_xy => // [||<-//]; rewrite ?orbb//; first rewrite orbC; by move=> xy _; apply/idP/idP => [->|/orP[]]// /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)