proposition: Lemma P_of_nat_correct: nat_of_P P_of_nat = n.
proof: Proof. unfold P_of_nat. destruct n. exfalso. intuition. apply nat_of_P_o_P_of_succ_nat_eq_succ. Qed.
imports: Coq.Setoids.Setoid Coq.PArith.BinPos Coq.PArith.Pnat ZArith_base