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 sub_mod_0: forall (a b m: nat),
a mod m = 0 ->
b mod m = 0 ->
(a - b) mod m = 0.