(** From this, we prove that the predecessor cancels a previous application of the successor function (by induction) *)

(* Specifications: *)
Lemma pred_S : forall n : nat, wf_nat n -> eq nat (pred (S n)) n.
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(** * Deriving Peano's axioms  *)
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(** ** First axiom of Peano **)
Lemma wf_nat_O : wf_nat O.
Proof fun P HO HS => HO.