(** Note that in the proofs of the two lemmas above, the assumption (wf_nat n) is not used. *)
(** ** Fourth axiom of Peano **)

(* Specifications: *)
Lemma eq_S_S :
forall n : nat,
wf_nat n -> forall p : nat, wf_nat p -> eq nat (S n) (S p) -> eq nat n p.