proposition: Lemma N_to_Z_to_nat: forall (a: N), Z.to_nat (Z.of_N a) = N.to_nat a.
proof: Proof. intros. rewrite <- (N2Z.id a) at 2. rewrite Z_N_nat. reflexivity. Qed.
imports: Coq.Classes.Morphisms Coq.Classes.Morphisms_Prop Coq.Arith.Arith Coq.NArith.NArith Coq.ZArith.ZArith Coq.micromega.Lia