proposition: Theorem shift_nat_correct n x : Zpos (shift_nat n x) = Zpower_nat 2 n * Zpos x.
proof: Proof. induction n as [|n IHn]. - trivial. - now rewrite Zpower_nat_succ_r, <- Z.mul_assoc, <- IHn. Qed.
imports: Wf_nat ZArith_base Zcomplements Zpow_def