(* 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) f k,
_guard Espec ge Delta (fun rho => F rho * P rho) f k = _guard Espec ge Delta (fun rho => F rho * bupd (P rho)) f k.