(** ** Fifth axiom of Peano **)

(* Specifications: *)
Lemma nat_ind :
forall P : nat -> Prop,
P O ->
(forall p : nat, wf_nat p -> P p -> P (S p)) ->
forall n : nat, wf_nat n -> P n.
Lemma nat_ind' :
forall n : nat,
wf_nat n ->
forall P : nat -> Prop,
P O -> (forall p : nat, wf_nat p -> P p -> P (S p)) -> P n.