Ltac simpl_compb := first [ rewrite if_trueb by (apply Z.ltb_lt; omega)
                          | rewrite if_falseb by (apply Z.ltb_ge; omega)].

(* Specifications: *)
Lemma body_insert: semax_body Vprog Gprog f_insert insert_spec.
Lemma body_lookup: semax_body Vprog Gprog f_lookup lookup_spec.
Lemma body_turn_left: semax_body Vprog Gprog f_turn_left turn_left_spec.
Lemma body_pushdown_left: semax_body Vprog Gprog f_pushdown_left pushdown_left_spec.
Lemma body_insert: semax_body Vprog Gprog f_insert insert_spec.
Lemma body_lookup: semax_body Vprog Gprog f_lookup lookup_spec.
Lemma body_turn_left: semax_body Vprog Gprog f_turn_left turn_left_spec.
Lemma body_pushdown_left: semax_body Vprog Gprog f_pushdown_left pushdown_left_spec.
Lemma body_delete: semax_body Vprog Gprog f_delete delete_spec.
Lemma body_treebox_new: semax_body Vprog Gprog f_treebox_new treebox_new_spec.
Lemma body_tree_free: semax_body Vprog Gprog f_tree_free tree_free_spec.
Lemma body_treebox_free: semax_body Vprog Gprog f_treebox_free treebox_free_spec.