Definition lseg_cons_right (ls: listspec list_structid list_link list_token)
dsh psh (l: list val) (x z: val) : mpred :=
!! (~ ptr_eq x z) &&
EX r:list val , EX y:val,
!!(l=r++y::nil /\ is_pointer_or_null y)  &&
list_cell ls dsh (vund ls) y *
field_at psh list_struct (StructField list_link :: nil) (valinject (nested_field_type list_struct (StructField list_link :: nil)) z) y *
lseg ls dsh psh r x y.

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