Ltac simpl_compb := first [ rewrite if_trueb by (apply NPeano.Nat.ltb_lt; rewrite Nat2Z.inj_lt; omega)
                          | rewrite if_falseb by (apply NPeano.Nat.ltb_nlt; rewrite Nat2Z.inj_lt; omega)].

Lemma body_lookup: semax_body Vprog Gprog f_lookup lookup_spec.