Proof using.
unfold doGenericServer.
intros.
repeat break_match; repeat find_inversion; simpl;
eapply applyEntries_spec_ind; eauto.
Qed.
Functional Scheme div2_ind := Induction for div2 Sort Prop.

Theorem div2_correct' :
forall n,
n <= div2 n + S (div2 n).