(** Sub and mul *)

(* Specifications: *)
Theorem mul_pred_r : forall n m, n * (P m) == n * m - n.
Theorem mul_sub_distr_r : forall n m p, (n - m) * p == n * p - m * p.
Theorem mul_sub_distr_l : forall n m p, p * (n - m) == p * n - p * m.
Definition le_alt n m := exists p, p + n == m.