(* 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'_post:
forall {CS: compspecs} {Espec: OracleKind} (R': ret_assert) Delta (R: ret_assert) P c,
(forall ek vl rho,  !!(typecheck_environ Delta rho) &&
proj_ret_assert R' ek vl rho
|-- proj_ret_assert R ek vl rho) ->
semax' Espec Delta P c R' |-- semax' Espec Delta P c R.