(** * Proofs of specifications *)
(** ** Specification of constants *)

(* Specifications: *)
Lemma one_succ : 1 = succ 0.
Lemma two_succ : 2 = succ 1.
(** ** Specification of addition *)
Lemma add_0_l n : 0 + n = n.
Lemma add_succ_l n m : succ n + m = succ (n + m).
(** ** Specification of opposite *)
Lemma opp_0 : -0 = 0.
Lemma opp_succ n : -(succ n) = pred (-n).
Local Arguments pos_sub : simpl nomatch.