Definition field_at (t: type) (nf: list ident) (v: reptype (nested_field_type t nf)) (p: val) : Pred := data_at_rec (nested_field_type t nf) v (offset_val (nested_field_offset t nf) p).
Definition data_at (t: type) (v: reptype t) (p: val) : Pred := field_at t nil v p.
Definition field_address (t: type) (nf: list ident) (p: val) : val := offset_val (nested_field_offset t nf) p.

(* Specifications: *)
(* Unfolding Equations *)
Lemma data_at_field_at: forall t v p,
data_at t v p = field_at t nil v p.
Lemma field_at_Tint: forall t nf v1 v2 p,
nested_field_type t nf = Tint ->
JMeq v1 v2 ->
field_at t nf v1 p = mapsto (field_address t nf p) v2.
Lemma field_at_Tstruct: forall t nf id fs v p,
nested_field_type t nf = Tstruct id fs ->
members_no_replicate fs ->
field_at t nf v p =
(fix field_at_struct fs :=
match fs with
| Fnil => emp
| Fcons (i0, t0) fs0 =>
field_at t (i0 :: nf) (proj_reptype _ (i0 :: nil) v) p *
field_at_struct fs0
end) fs.
Lemma field_at_Tstruct': forall t nf id fs v p i,
nested_field_type t nf = Tstruct id fs ->
members_no_replicate fs ->
in_members i fs ->
field_at t nf v p =
field_at t (i :: nf) (proj_reptype _ (i :: nil) v) p *
(fix field_at_struct fs :=
match fs with
| Fnil => emp
| Fcons (i0, t0) fs0 =>
(if (ident_eq i0 i)
then emp
else field_at t (i0 :: nf) (proj_reptype _ (i0 :: nil) v) p) *
field_at_struct fs0
end) fs.