End LIST1.
Module LsegGeneral.
Section LIST2.
Context {cs: compspecs}.
Context  {list_structid: ident} {list_link: ident} {list_token: share -> val -> mpred}.
Fixpoint lseg (ls: listspec list_structid list_link list_token) (dsh psh: share)
(contents: list (val * elemtype ls)) (x z: val) : mpred :=
match contents with
| (p,h)::hs => !! (p=x /\ ~ptr_eq x z) &&
EX y:val,  !! 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 hs y z
| nil => !! (ptr_eq x z) && emp
end.

(* Specifications: *)
Lemma lseg_unfold (ls: listspec list_structid list_link list_token): forall dsh psh contents v1 v2,
lseg ls dsh psh contents v1 v2 =
match contents with
| (p,h)::t => !! (p=v1 /\ ~ ptr_eq v1 v2) && EX tail: val,
!! is_pointer_or_null tail &&
list_token dsh v1 * list_cell ls dsh h v1
* field_at psh list_struct (StructField list_link :: nil)
(valinject (nested_field_type list_struct (StructField list_link :: nil)) tail) v1
* lseg ls dsh psh t tail v2
| nil => !! (ptr_eq v1 v2) && emp
end.
Lemma lseg_eq (ls: listspec list_structid list_link list_token):
forall dsh psh l v ,
is_pointer_or_null v ->
lseg ls dsh psh l v v = !!(l=nil) && emp.