(** ** Remaining constants not defined in Stdlib.Init.Nat *)

(** NB: Aliasing [le] is mandatory, since only a Definition can implement
    an interface Parameter... *)

Definition eq := @Logic.eq nat.Definition le := Peano.le.Definition lt := Peano.lt.

(* Specifications: *)
Lemma pred_succ n : pred (S n) = n.
Lemma pred_0 : pred 0 = 0.
Lemma one_succ : 1 = S 0.
Lemma two_succ : 2 = S 1.
Lemma add_0_l n : 0 + n = n.
Lemma add_succ_l n m : (S n) + m = S (n + m).
Lemma sub_0_r n : n - 0 = n.
Lemma sub_succ_r n m : n - (S m) = pred (n - m).
Lemma mul_0_l n : 0 * n = 0.
Lemma mul_succ_l n m : S n * m = n * m + m.
Lemma lt_succ_r n m : n < S m <-> n <= m.
Lemma eqb_eq n m : eqb n m = true <-> n = m.