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.
Definition lseg_cons_right (ls: listspec list_structid list_link list_token)
dsh psh (l: list val) (x z: val) : mpred :=
!! (~ ptr_eq x z) &&
EX r:list val , EX y:val,
!!(l=r++y::nil /\ is_pointer_or_null y)  &&
list_cell ls dsh (vund ls) y *
field_at psh list_struct (StructField list_link :: nil) (valinject (nested_field_type list_struct (StructField list_link :: nil)) z) y *
lseg ls dsh psh r x y.
Abort.  (* not likely true *)
Definition lseg_cell  (ls: listspec list_structid list_link list_token)
(dsh psh : share)
(v: elemtype ls) (x y: val) :=
!!is_pointer_or_null y && list_token dsh x * list_cell ls dsh v x * field_at psh list_struct (StructField list_link :: nil) (valinject (nested_field_type list_struct (StructField list_link :: nil)) y) x.

Lemma list_append: forall {dsh psh: share}
{ls : listspec list_structid list_link list_token} (hd mid tl:val) ct1 ct2 P,
(forall tl', lseg_cell ls dsh psh (vund ls) tl tl' * P tl |-- FF) ->
(lseg ls dsh psh ct1 hd mid) * lseg ls dsh psh ct2 mid tl * P tl|--
(lseg ls dsh psh (ct1 ++ ct2) hd tl) * P tl.