proposition: Fact lt_def x y : lt x y = (y != x) && le x y.
proof: Proof. by rewrite /lt lt_def (inj_eq (pcan_inj f_can)). Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)