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 mul_div_exact: forall (a b: nat),
b <> 0 ->
a mod b = 0 ->
b * (a / b) = a.