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 unfold_lseg_cons (ls: listspec list_structid list_link list_token):
forall P Q1 Q R e dsh psh s,
~ (readable_share dsh) ->
PROPx P (LOCALx (Q1::Q) (SEPx (lseg ls dsh psh s e nullval :: R))) |--
!! (typed_true (tptr list_struct) e) ->
PROPx P (LOCALx (Q1::Q) (SEPx (lseg ls dsh psh s e nullval :: R))) |--
EX hryp: elemtype ls * list val * val * val,
match hryp with (h,r,y,p) =>
!! (s=p::r /\ is_pointer_or_null y) &&
!! (p = e) &&
PROPx P (LOCALx Q
(SEPx (list_token dsh e :: list_cell ls dsh h e ::
field_at psh list_struct (StructField list_link :: nil) (valinject (nested_field_type list_struct (StructField list_link :: nil)) y) e ::
lseg ls dsh psh r y nullval ::
R)))
end.