(* 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 guard_bupd:
forall {Espec: OracleKind} ge Delta (F P: environ -> pred rmap) k,
guard Espec ge Delta (fun rho => F rho * P rho) k = guard Espec ge Delta (fun rho => F rho * bupd (P rho)) k.