Definition ltezN_nat := (lezN_nat, ltzN_nat).Definition ltez_natE := (ltez_nat, lteNz_nat, ltezN_nat, le0z_nat, lez0_nat).

(* Specifications: *)
Lemma gtz0_ge1 x : (0 < x) = (1 <= x).
Lemma lez_add1r x y : (1 + x <= y) = (x < y).
Lemma lez_addr1 x y : (x + 1 <= y) = (x < y).
Lemma ltz_add1r x y : (x < 1 + y) = (x <= y).
Lemma ltz_addr1 x y : (x < y + 1) = (x <= y).