(* 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'_pre_bupd:
forall {CS: compspecs} {Espec: OracleKind} P' Delta R P c,
(forall rho, typecheck_environ Delta rho ->   P rho |-- bupd (P' rho))
->   semax' Espec Delta P' c R |-- semax' Espec Delta P c R.