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 Smod2_1: forall k, S k mod 2 = 1 -> k mod 2 = 0.