(* 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 guard_allp_fun_id: forall {Espec: OracleKind} ge Delta' Delta (F P: environ -> pred rmap) k,
tycontext_sub Delta Delta' ->
guard Espec ge Delta' (fun rho => F rho * P rho) k = guard Espec ge Delta' (fun rho => F rho * (allp_fun_id Delta rho && P rho)) k.