(* The following four lemmas is not now used. but after deep embedded hoare logic (SL_as_Logic) is ported, the frame does not need to be quantified in the semantic definition of semax. Then, these two lemmas can replace the other two afterwards. *)

Lemma rguard_bupd:
forall {Espec: OracleKind} ge Delta F (P: ret_assert) k,
rguard Espec ge Delta (frame_ret_assert P F) k = rguard Espec ge Delta (frame_ret_assert (bupd_ret_assert P) F) k.