proposition: Lemma ltxU x y z : (x < join y z) = (x < y) || (x < z).
proof: Proof. by rewrite !ltNge leUx negb_and. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)