Definition elemtype (ls: listspec list_structid list_link list_token) :=
  compact_prod
  (map (fun it => reptype (field_type (fst it) list_fields)) (all_but_link list_fields)).Definition field_type'  (F: members) (it: ident * type) :=
   reptype (field_type (fst it) F).Definition add_link_back' {F f: members}
  (v: compact_prod (map (field_type' F) (all_but_link f))) :
  compact_prod (map (field_type' F) f).Definition add_link_back
 (F f : members)
  (v : compact_prod
         (map (fun it : ident * type => reptype (field_type (fst it) F))
            (all_but_link f)))
  : compact_prod (map (fun it => reptype (field_type (fst it) F)) f)
  :=
list_rect
  (fun f0 : list (ident * type) =>
   compact_prod (map (field_type' F) (all_but_link f0)) ->
   compact_prod (map (field_type' F) f0))
  (fun _ : compact_prod (map (field_type' F) (all_but_link nil)) => tt)
  (fun (it0 : ident * type) (f0 : list (ident * type))
     (IHf : compact_prod (map (field_type' F) (all_but_link f0)) ->
            compact_prod (map (field_type' F) f0))
     (v0 : compact_prod (map (field_type' F) (all_but_link (it0 :: f0)))) =>
   match
     f0 as l
     return
       (compact_prod (map (field_type' F) (all_but_link (it0 :: l))) ->
        (compact_prod (map (field_type' F) (all_but_link l)) ->
         compact_prod (map (field_type' F) l)) ->
        compact_prod (map (field_type' F) (it0 :: l)))
   with
   | nil =>
       fun
         (_ : compact_prod (map (field_type' F) (all_but_link (it0 :: nil))))
         (_ : compact_prod (map (field_type' F) (all_but_link nil)) ->
              compact_prod (map (field_type' F) nil)) =>
       default_val (field_type (fst it0) F)
   | it1 :: f1 =>
       fun
         (v1 : compact_prod
                 (map (field_type' F) (all_but_link (it0 :: it1 :: f1))))
         (IHf0 : compact_prod
                   (map (field_type' F) (all_but_link (it1 :: f1))) ->
                 compact_prod (map (field_type' F) (it1 :: f1))) =>
       (if ident_eq (fst it0) list_link as s0
         return
           (compact_prod
              (map (field_type' F)
                 (if s0 then it1 :: f1 else it0 :: all_but_link (it1 :: f1))) ->
            reptype (field_type (fst it0) F) *
            compact_prod (map (field_type' F) (it1 :: f1)))
        then
         fun v2 : compact_prod (map (field_type' F) (it1 :: f1)) =>
         (default_val (field_type (fst it0) F), v2)
        else
         fun
           v2 : compact_prod
                  (map (field_type' F) (it0 :: all_but_link (it1 :: f1))) =>
         match
           all_but_link (it1 :: f1) as l
           return
             (all_but_link (it1 :: f1) = l ->
              compact_prod (map (field_type' F) (it0 :: l)) ->
              (compact_prod (map (field_type' F) l) ->
               compact_prod (map (field_type' F) (it1 :: f1))) ->
              reptype (field_type (fst it0) F) *
              compact_prod (map (field_type' F) (it1 :: f1)))
         with
         | nil =>
             fun (Heqm0 : all_but_link (it1 :: f1) = nil)
               (v3 : compact_prod (map (field_type' F) (it0 :: nil)))
               (IHf1 : compact_prod (map (field_type' F) nil) ->
                       compact_prod (map (field_type' F) (it1 :: f1))) =>
             let s0 := ident_eq (fst it1) list_link in
             (if s0
               return
                 ((if s0 then f1 else it1 :: all_but_link f1) = nil ->
                  reptype (field_type (fst it0) F) *
                  compact_prod (map (field_type' F) (it1 :: f1)))
              then
               fun Heqm1 : f1 = nil =>
               eq_rect_r
                 (fun f2 : members =>
                  (compact_prod (map (field_type' F) nil) ->
                   compact_prod (map (field_type' F) (it1 :: f2))) ->
                  reptype (field_type (fst it0) F) *
                  compact_prod (map (field_type' F) (it1 :: f2)))
                 (fun
                    _ : compact_prod (map (field_type' F) nil) ->
                        compact_prod (map (field_type' F) (it1 :: nil)) =>
                  (v3, default_val (field_type (fst it1) F)))
                 Heqm1 IHf1
              else
               fun Heqm1 : it1 :: all_but_link f1 = nil =>
                 False_rect
                   (reptype (field_type (fst it0) F) *
                    compact_prod (map (field_type' F) (it1 :: f1)))
                 (eq_rect (it1 :: all_but_link f1)
                    (fun e : members =>
                     match e with
                     | nil => False
                     | _ :: _ => True
                     end) I nil Heqm1)) Heqm0
         | p :: m0 =>
             fun (_ : all_but_link (it1 :: f1) = p :: m0)
               (v3 : compact_prod (map (field_type' F) (it0 :: p :: m0)))
               (IHf1 : compact_prod (map (field_type' F) (p :: m0)) ->
                       compact_prod (map (field_type' F) (it1 :: f1))) =>
             (fst v3, IHf1 (snd v3))
         end eq_refl v2 IHf0) v1
   end v0 IHf) f v.(*
Definition add_link_back {ls: listspec list_structid list_link} {f F: members}
  (v: compact_prod (map (fun it => reptype (field_type (fst it) F)) (all_but_link f))) :
  compact_prod (map (fun it => reptype (field_type (fst it) F)) f).
  unfold all_but_link in v.
  induction f as [| [i0 t0] f].
  + exact tt.
  + simpl in *; destruct f as [| [i1 t1] f0] eqn:?; [| destruct (ident_eq i0 list_link)].
    - exact (default_val _).
    - exact (default_val _, v).
    - fold (all_but_link ((i1, t1) :: f0)) in IHf, v.
      destruct (all_but_link ((i1, t1) :: f0)) eqn:?.
      * simpl in Heqm.
        if_tac in Heqm; [| congruence].
        subst f0.
        exact (v, default_val _).
      * exact (fst v, IHf (snd v)).
Defined.
*)

Definition list_data {ls: listspec list_structid list_link list_token} (v: elemtype ls): reptype list_struct.

Lemma list_cell_link_join: forall (LS: listspec list_structid list_link list_token) sh v p, list_cell LS sh v p * spacer sh (field_offset cenv_cs list_link list_fields + sizeof (field_type list_link list_fields)) (field_offset_next cenv_cs list_link list_fields (co_sizeof (get_co list_structid))) (offset_val 0 p) * field_at_ sh list_struct (StructField list_link :: nil) p = data_at sh list_struct (list_data v) p.