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