proposition: Lemma lt_trans: transitive (<%O : rel T).
proof: Proof. by move=> y x z le1 /ltW le2; apply/(@lt_le_trans y). Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)