Section LIST.
Context {cs: compspecs}.
Context  {list_structid: ident} {list_link: ident} {list_token: share -> val -> mpred}.
Definition lseg (ls: listspec list_structid list_link list_token) (sh: share)
(contents: list (elemtype ls)) (x y: val) : mpred :=
EX al:list (val*elemtype ls),
!! (contents = map snd al) &&
LsegGeneral.lseg ls sh sh al x y.
Definition lseg_cons (ls: listspec list_structid list_link list_token) sh (l: list (elemtype ls)) (x z: val) : mpred :=
!! (~ ptr_eq x z) &&
EX h:(elemtype ls), EX r:list (elemtype ls), EX y:val,
!!(l=h::r  /\ is_pointer_or_null y) &&
list_token sh x * list_cell ls sh h x *
field_at sh list_struct (StructField list_link :: nil) (valinject (nested_field_type list_struct (StructField list_link :: nil)) y) x *
lseg ls sh r y z.
intros. rewrite lseg_unroll.
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)
sh (l: list (elemtype ls)) (x z: val) : mpred :=
!! (~ ptr_eq x z) &&
EX h:(elemtype ls), EX r:list (elemtype ls), EX y:val,
!!(l=r++(h::nil) /\ is_pointer_or_null y)  &&
list_token sh y * list_cell ls sh h y *
field_at sh list_struct (StructField list_link :: nil) (valinject (nested_field_type list_struct (StructField list_link :: nil)) z) y *
lseg ls sh r x y.
Abort.  (* not likely true *)
Definition lseg_cell (ls: listspec list_structid list_link list_token)
(sh : share)
(v: elemtype ls) (x y: val) :=
!!is_pointer_or_null y && list_token sh x * list_cell ls sh v x * field_at sh list_struct (StructField list_link :: nil) (valinject (nested_field_type list_struct (StructField list_link :: nil)) y) x.

Lemma lseg_cons_eq2: forall
(ls : listspec list_structid list_link list_token) (sh : share) (h : elemtype ls)
(r : list (elemtype ls))
(x z : val), lseg ls sh (h :: r) x z =
!!(~ ptr_eq x z) && (EX  y : val, lseg_cell ls sh h x y * lseg ls sh r y z).