Section omega_compat.
Ltac omega ::= lia.
induction n as [|n IHn]; simpl; intuition.
rewrite <- IHn; clear IHn.
case_eq (Npow2 n); intuition.
Qed.
End omega_compat.

Lemma Z_of_N_Npow2: forall n, Z.of_N (Npow2 n) = (2 ^ Z.of_nat n)%Z.