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.

Lemma unfold_lseg_cons (ls: listspec list_structid list_link list_token):
forall P Q1 Q R e sh s,
PROPx P (LOCALx (Q1::Q) (SEPx (lseg ls sh s e nullval :: R))) |--
!!(typed_true (tptr list_struct) e) ->
PROPx P (LOCALx (Q1::Q) (SEPx (lseg ls sh s e nullval :: R))) |--
EX hryp: elemtype ls * list (elemtype ls) * val,
match hryp with (h,r,y) =>
!! (s=h::r /\ is_pointer_or_null y) &&
PROPx P (LOCALx Q
(SEPx (list_token sh e :: list_cell ls sh h e ::
field_at sh list_struct (StructField list_link :: nil) (valinject (nested_field_type list_struct (StructField list_link :: nil)) y) e ::
lseg ls sh r y nullval ::
R)))
end.