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 lseg_cons_eq (ls: listspec list_structid list_link list_token):
forall dsh psh h r x z ,
~ (readable_share dsh) ->
lseg ls dsh psh (h::r) x z =
!!(x = h /\ ~ ptr_eq x z) &&
(EX  y : val,
!!(is_pointer_or_null y) &&
list_token dsh x * list_cell ls dsh (vund ls) 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).