Fixpoint bodd (n : nat) : bool :=
  match n with
  | O => false
  | S n' => negb (bodd n')
  end.

(* Specifications: *)
Lemma boddIsPR : isPRrel 1 bodd.
Lemma beq_nat_not_refl : forall a b : nat, a <> b -> beq_nat a b = false.
Lemma neqIsPR : isPRrel 2 (fun a b : nat => negb (beq_nat a b)).
Lemma eqIsPR : isPRrel 2 beq_nat.