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 div_mul_undo: forall a b,
b <> 0 ->
a mod b = 0 ->
a / b * b = a.