(*
Definition initial_core' (ge: Genv.t fundef type) (G: funspecs) (n: nat) (loc: address) : resource :=
   if Z.eq_dec (snd loc) 0
   then match Genv.invert_symbol ge (fst loc) with
           | Some id =>
                  match find_id id G with
                  | Some (mk_funspec fsig cc A P Q _ _) =>
                           PURE (FUN fsig cc) (SomeP (SpecTT A) (fun ts => fmap _ (approx n) (approx n) (packPQ P Q ts)))
                  | None => NO Share.bot bot_unreadable
                  end
           | None => NO Share.bot bot_unreadable
          end
   else NO Share.bot bot_unreadable.*)
Notation initial_core' := (initial_core' function).(* This version starts with an empty ghost. 
Program Definition initial_core (ge: Genv.t fundef type) (G: funspecs) (n: nat): rmap :=
  proj1_sig (make_rmap (initial_core' ge G n) nil n _ eq_refl).
Next Obligation.
intros.
extensionality loc; unfold compose, initial_core'.
if_tac; [ | simpl; auto].
destruct (Genv.invert_symbol ge (fst loc)); [ | simpl; auto].
destruct (find_id i G); [ | simpl; auto].
destruct f.
unfold resource_fmap.
f_equal.
simpl.
f_equal.
change R.approx with approx.
extensionality i0 ts b rho.
rewrite fmap_app.
pattern (approx n) at 7 8 9.
rewrite <- approx_oo_approx.
auto.
Qed.*)
Notation initial_core := (@initial_core function).(*
Program Definition initial_core_ext {Z} (ora : Z) (ge: Genv.t fundef type) (G: funspecs) (n: nat): rmap :=
  proj1_sig (make_rmap (initial_core' ge G n) (Some (ext_ghost ora, NoneP) :: nil) n _ eq_refl).
Next Obligation.
intros.
extensionality loc; unfold compose, initial_core'.
if_tac; [ | simpl; auto].
destruct (Genv.invert_symbol ge (fst loc)); [ | simpl; auto].
destruct (find_id i G); [ | simpl; auto].
destruct f.
unfold resource_fmap.
f_equal.
simpl.
f_equal.
change R.approx with approx.
extensionality i0 ts b rho.
rewrite fmap_app.
pattern (approx n) at 7 8 9.
rewrite <- approx_oo_approx.
auto.
Qed.
*)
Notation initial_core_ext := (@initial_core_ext  function).(*Definition prog_funct (p: program) := prog_funct' (prog_defs p).*)
Notation prog_funct := (@prog_funct function).Inductive match_fdecs: list  (ident * fundef) -> funspecs -> Prop :=
| match_fdecs_nil: match_fdecs nil nil
| match_fdecs_cons: forall i fd fspec fs G,
                  type_of_fundef fd = type_of_funspec fspec ->
                  match_fdecs fs G ->
                  match_fdecs ((i,fd)::fs) ((i,fspec)::G)
(* EXPERIMENT
| match_fdecs_skip: forall ifd fs G,
                 match_fdecs fs G ->
                 match_fdecs (ifd::fs) G*)
.Inductive match_fdecs: list  (ident * fundef) -> funspecs -> Prop :=
| match_fdecs_nil: match_fdecs nil nil
| match_fdecs_cons: forall i fd fspec fs G,
                  type_of_fundef fd = type_of_funspec fspec ->
                  match_fdecs fs G ->
                  match_fdecs ((i,fd)::fs) ((i,fspec)::G)
(* EXPERIMENT
| match_fdecs_skip: forall ifd fs G,
                 match_fdecs fs G ->
                 match_fdecs (ifd::fs) G*)
.Inductive match_fdecs: list  (ident * fundef) -> funspecs -> Prop :=
| match_fdecs_nil: match_fdecs nil nil
| match_fdecs_cons: forall i fd fspec fs G,
                  type_of_fundef fd = type_of_funspec fspec ->
                  match_fdecs fs G ->
                  match_fdecs ((i,fd)::fs) ((i,fspec)::G)
(* EXPERIMENT
| match_fdecs_skip: forall ifd fs G,
                 match_fdecs fs G ->
                 match_fdecs (ifd::fs) G*)
.

Lemma match_fdecs_exists_Gfun: forall prog G i f, find_id i G = Some f -> match_fdecs (prog_funct prog) G -> exists fd, In (i, Gfun fd) (prog_defs prog) /\ type_of_fundef fd = type_of_funspec f.