Section LIST2.
Context {cs: compspecs}.
Context  {list_structid: ident} {list_link: ident}{list_token: share -> val -> mpred}.
Definition vund  (ls: listspec list_structid list_link list_token) : elemtype ls :=
compact_prod_gen
(fun it => default_val (field_type (fst it) list_fields)) (@all_but_link list_link  list_fields).
Definition lseg (ls: listspec list_structid list_link list_token) (dsh psh: share)
(contents: list val) (x z: val) : mpred :=
LsegGeneral.lseg ls dsh psh (map (fun v => (v, vund ls)) contents) x z.
Definition lseg_cons (ls: listspec list_structid list_link list_token) dsh psh
(l: list val) (x z: val) : mpred :=
!! (~ ptr_eq x z) &&
EX h:(elemtype ls), EX r:list val, EX y:val,
!!(l=x::r  /\ is_pointer_or_null y) &&
list_token dsh x * list_cell ls dsh h x *
field_at psh list_struct (StructField list_link :: nil) (valinject (nested_field_type list_struct (StructField list_link :: nil)) y) x *
lseg ls dsh psh r y z.
intros. rewrite lseg_unroll by auto.
apply pred_ext. apply orp_left; auto.
rewrite andp_assoc.
do 2 (apply derives_extract_prop; intro).
congruence.
apply orp_right2. auto.
Qed.

Lemma semax_lseg_nonnull (ls: listspec list_structid list_link list_token):
forall (Espec: OracleKind)
Delta P Q dsh psh s v R c Post,
~ (readable_share dsh) ->
ENTAIL Delta, PROPx P (LOCALx Q
(SEPx (lseg ls dsh psh s v nullval :: R))) |--
!!(typed_true (tptr list_struct) v)  ->
(forall (h: elemtype ls) (r: list val) (y: val),
s=v::r -> is_pointer_or_null y ->
semax Delta
(PROPx P (LOCALx Q
(SEPx (list_token dsh v :: list_cell ls dsh h v ::
field_at psh list_struct (StructField list_link :: nil) (valinject (nested_field_type list_struct (StructField list_link :: nil)) y) v ::
lseg ls dsh psh r y nullval ::
R)))) c Post) ->
semax Delta
(PROPx P (LOCALx Q (SEPx (lseg ls dsh psh s v nullval :: R))))
c Post.