proposition: Lemma comparable_le_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[]]// /le_trans->//; apply/ltW. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)