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.

(* Specifications: *)
Lemma lseg_cons_right_neq (ls: listspec list_structid list_link list_token): forall sh l x h y w z,
sepalg.nonidentity sh ->
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 l x y * field_at sh list_struct (StructField list_link :: nil) (valinject (nested_field_type list_struct (StructField list_link :: nil)) w) z
|--   lseg ls sh (l++h::nil) x z * field_at sh list_struct (StructField list_link :: nil) (valinject (nested_field_type list_struct (StructField list_link :: nil)) w) z.
Lemma lseg_cons_right_null (ls: listspec list_structid list_link list_token): forall sh l x h 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)) nullval) y *
lseg ls sh l x y
|--   lseg ls sh (l++h::nil) x nullval.
Lemma lseg_cons_right_list (ls: listspec list_structid list_link list_token): forall sh l l' x h y z,
sepalg.nonidentity sh ->
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 l x y * lseg ls sh l' z nullval
|--   lseg ls sh (l++h::nil) x z * lseg ls sh l' z nullval.
Lemma lseg_unroll_right (ls: listspec list_structid list_link list_token): forall sh l x z ,
lseg ls sh l x z = (!! (ptr_eq x z) && !! (l=nil) && emp) || lseg_cons_right ls sh l x z.