(** ** Third axiom of Peano **)

(* Specifications: *)
Lemma eq_S_O : forall n : nat, wf_nat n -> eq nat (S n) O -> bot.
Proof fun n _ H => H (fun p => p Prop bot (fun _ => top)) top_intro.
Lemma eq_O_S : forall n : nat, wf_nat n -> eq nat O (S n) -> bot.
Proof fun n _ H => H (fun p => p Prop top (fun _ => bot)) top_intro.