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.
Definition lseg_cons (ls: listspec list_structid list_link list_token) dsh psh (l: list (val * elemtype ls)) (x z: val) : mpred :=
!! (~ ptr_eq x z) &&
EX h:(elemtype ls), EX r:list (val * elemtype ls), EX y:val,
!!(l=(x,h)::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.

Lemma lseg_unroll_nonempty1 (ls: listspec list_structid list_link list_token):
forall p P dsh psh h tail v1 v2,
~ ptr_eq v1 v2 ->
is_pointer_or_null p ->
P |-- 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)) p) v1 *
lseg ls dsh psh tail p v2) ->
P |-- lseg ls dsh psh ((v1,h)::tail) v1 v2.