(* The following two 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 semax_bupd_elim {CS: compspecs} {Espec: OracleKind}:
forall Delta P c R,
semax Espec Delta P c R -> semax Espec Delta (fun rho => bupd (P rho)) c R.