Ltac solve_Ptrofs_eqm_unsigned :=
  solve
   [ autorewrite with norm;
    rewrite ?Ptrofs_repr_Int_unsigned_special by reflexivity;
    rewrite ?Ptrofs_repr_Int64_unsigned_special by reflexivity;
    match goal with
    | |- Ptrofs_eqm_unsigned ?V _ =>
      match V with
      | Ptrofs.repr _ => idtac
      | Ptrofs.sub _ _ => unfold Ptrofs.sub at 1
      | Ptrofs.add _ _ => unfold Ptrofs.add at 1
      | Ptrofs.mul _ _ => unfold Ptrofs.mul at 1
      | Ptrofs.and _ _ => unfold Ptrofs.and at 1
      | Ptrofs.or _ _ => unfold Ptrofs.or at 1
(*      | Int.shl _ _ => unfold Int.shl at 1
      | Int.shr _ _ => unfold Int.shr at 1*)
      | _ => rewrite <- (Ptrofs.repr_unsigned V) at 1
      end
    end;
    apply Ptrofs_eqm_unsigned_repr
  ].Inductive msubst_efield_denote {cs: compspecs} (Delta: tycontext) (T1: PTree.t val) (T2: PTree.t (type * val)) (GV: option globals): list efield -> list gfield -> Prop :=
| msubst_efield_denote_nil: msubst_efield_denote Delta T1 T2 GV nil nil
| msubst_efield_denote_cons_array: forall ei i i' efs gfs,
    is_int_type (typeof ei) = true ->
    msubst_eval_expr Delta T1 T2 GV  ei = Some (Vint i) ->
    int_signed_or_unsigned (typeof ei) i = i' ->
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eArraySubsc ei :: efs) (ArraySubsc i' :: gfs)
| msubst_efield_denote_cons_array_ptrofs: forall ei i i' efs gfs,
    is_ptrofs_type (typeof ei) = true ->
    msubst_eval_expr Delta T1 T2 GV  ei = Some (Vptrofs i) ->
    Ptrofs_eqm_unsigned i i' ->
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eArraySubsc ei :: efs) (ArraySubsc i' :: gfs)
| msubst_efield_denote_cons_struct: forall i efs gfs,
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eStructField i :: efs) (StructField i :: gfs)
| msubst_efield_denote_cons_union: forall i efs gfs,
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eUnionField i :: efs) (UnionField i :: gfs).Inductive msubst_efield_denote {cs: compspecs} (Delta: tycontext) (T1: PTree.t val) (T2: PTree.t (type * val)) (GV: option globals): list efield -> list gfield -> Prop :=
| msubst_efield_denote_nil: msubst_efield_denote Delta T1 T2 GV nil nil
| msubst_efield_denote_cons_array: forall ei i i' efs gfs,
    is_int_type (typeof ei) = true ->
    msubst_eval_expr Delta T1 T2 GV  ei = Some (Vint i) ->
    int_signed_or_unsigned (typeof ei) i = i' ->
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eArraySubsc ei :: efs) (ArraySubsc i' :: gfs)
| msubst_efield_denote_cons_array_ptrofs: forall ei i i' efs gfs,
    is_ptrofs_type (typeof ei) = true ->
    msubst_eval_expr Delta T1 T2 GV  ei = Some (Vptrofs i) ->
    Ptrofs_eqm_unsigned i i' ->
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eArraySubsc ei :: efs) (ArraySubsc i' :: gfs)
| msubst_efield_denote_cons_struct: forall i efs gfs,
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eStructField i :: efs) (StructField i :: gfs)
| msubst_efield_denote_cons_union: forall i efs gfs,
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eUnionField i :: efs) (UnionField i :: gfs).Inductive msubst_efield_denote {cs: compspecs} (Delta: tycontext) (T1: PTree.t val) (T2: PTree.t (type * val)) (GV: option globals): list efield -> list gfield -> Prop :=
| msubst_efield_denote_nil: msubst_efield_denote Delta T1 T2 GV nil nil
| msubst_efield_denote_cons_array: forall ei i i' efs gfs,
    is_int_type (typeof ei) = true ->
    msubst_eval_expr Delta T1 T2 GV  ei = Some (Vint i) ->
    int_signed_or_unsigned (typeof ei) i = i' ->
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eArraySubsc ei :: efs) (ArraySubsc i' :: gfs)
| msubst_efield_denote_cons_array_ptrofs: forall ei i i' efs gfs,
    is_ptrofs_type (typeof ei) = true ->
    msubst_eval_expr Delta T1 T2 GV  ei = Some (Vptrofs i) ->
    Ptrofs_eqm_unsigned i i' ->
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eArraySubsc ei :: efs) (ArraySubsc i' :: gfs)
| msubst_efield_denote_cons_struct: forall i efs gfs,
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eStructField i :: efs) (StructField i :: gfs)
| msubst_efield_denote_cons_union: forall i efs gfs,
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eUnionField i :: efs) (UnionField i :: gfs).Inductive msubst_efield_denote {cs: compspecs} (Delta: tycontext) (T1: PTree.t val) (T2: PTree.t (type * val)) (GV: option globals): list efield -> list gfield -> Prop :=
| msubst_efield_denote_nil: msubst_efield_denote Delta T1 T2 GV nil nil
| msubst_efield_denote_cons_array: forall ei i i' efs gfs,
    is_int_type (typeof ei) = true ->
    msubst_eval_expr Delta T1 T2 GV  ei = Some (Vint i) ->
    int_signed_or_unsigned (typeof ei) i = i' ->
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eArraySubsc ei :: efs) (ArraySubsc i' :: gfs)
| msubst_efield_denote_cons_array_ptrofs: forall ei i i' efs gfs,
    is_ptrofs_type (typeof ei) = true ->
    msubst_eval_expr Delta T1 T2 GV  ei = Some (Vptrofs i) ->
    Ptrofs_eqm_unsigned i i' ->
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eArraySubsc ei :: efs) (ArraySubsc i' :: gfs)
| msubst_efield_denote_cons_struct: forall i efs gfs,
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eStructField i :: efs) (StructField i :: gfs)
| msubst_efield_denote_cons_union: forall i efs gfs,
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eUnionField i :: efs) (UnionField i :: gfs).Inductive msubst_efield_denote {cs: compspecs} (Delta: tycontext) (T1: PTree.t val) (T2: PTree.t (type * val)) (GV: option globals): list efield -> list gfield -> Prop :=
| msubst_efield_denote_nil: msubst_efield_denote Delta T1 T2 GV nil nil
| msubst_efield_denote_cons_array: forall ei i i' efs gfs,
    is_int_type (typeof ei) = true ->
    msubst_eval_expr Delta T1 T2 GV  ei = Some (Vint i) ->
    int_signed_or_unsigned (typeof ei) i = i' ->
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eArraySubsc ei :: efs) (ArraySubsc i' :: gfs)
| msubst_efield_denote_cons_array_ptrofs: forall ei i i' efs gfs,
    is_ptrofs_type (typeof ei) = true ->
    msubst_eval_expr Delta T1 T2 GV  ei = Some (Vptrofs i) ->
    Ptrofs_eqm_unsigned i i' ->
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eArraySubsc ei :: efs) (ArraySubsc i' :: gfs)
| msubst_efield_denote_cons_struct: forall i efs gfs,
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eStructField i :: efs) (StructField i :: gfs)
| msubst_efield_denote_cons_union: forall i efs gfs,
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eUnionField i :: efs) (UnionField i :: gfs).Inductive msubst_efield_denote {cs: compspecs} (Delta: tycontext) (T1: PTree.t val) (T2: PTree.t (type * val)) (GV: option globals): list efield -> list gfield -> Prop :=
| msubst_efield_denote_nil: msubst_efield_denote Delta T1 T2 GV nil nil
| msubst_efield_denote_cons_array: forall ei i i' efs gfs,
    is_int_type (typeof ei) = true ->
    msubst_eval_expr Delta T1 T2 GV  ei = Some (Vint i) ->
    int_signed_or_unsigned (typeof ei) i = i' ->
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eArraySubsc ei :: efs) (ArraySubsc i' :: gfs)
| msubst_efield_denote_cons_array_ptrofs: forall ei i i' efs gfs,
    is_ptrofs_type (typeof ei) = true ->
    msubst_eval_expr Delta T1 T2 GV  ei = Some (Vptrofs i) ->
    Ptrofs_eqm_unsigned i i' ->
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eArraySubsc ei :: efs) (ArraySubsc i' :: gfs)
| msubst_efield_denote_cons_struct: forall i efs gfs,
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eStructField i :: efs) (StructField i :: gfs)
| msubst_efield_denote_cons_union: forall i efs gfs,
    msubst_efield_denote Delta T1 T2 GV efs gfs ->
    msubst_efield_denote Delta T1 T2 GV (eUnionField i :: efs) (UnionField i :: gfs).Ltac insist_rep_omega :=
 (auto; rep_omega) ||
 match goal with |- ?A =>
  fail 1000 "load or store subscript failure: rep_omega cannot prove "A
 end.Ltac solve_msubst_efield_denote :=
  solve 
  [ repeat first
   [ eapply msubst_efield_denote_cons_array_ptrofs;
     [ reflexivity
     | etransitivity; 
       [solve_msubst_eval_expr 
       | apply f_equal_Some;
          match goal with
          | |- Vint ?a = Vptrofs ?b =>
             is_evar b;
             unify b (Ptrofs.of_int a);
             unfold Vptrofs; change Archi.ptr64 with false; cbv iota;
             rewrite (Ptrofs.to_int_of_int (eq_refl _));
             reflexivity
           | |- Vlong ?a = Vptrofs ?b =>
             is_evar b;
             unify b (Ptrofs.of_int64 a);
             unfold Vptrofs; change Archi.ptr64 with true; cbv iota;
             rewrite (Ptrofs.to_int64_of_int64 (eq_refl _));
             reflexivity
            | |- Vptrofs _ = Vptrofs _ => reflexivity
           end
        ]
      | solve_Ptrofs_eqm_unsigned
      | ]
    | eapply msubst_efield_denote_cons_array;
      [ reflexivity
      | solve_msubst_eval_expr
      | rewrite ?ptrofs_to_int_repr; autorewrite with norm;
(* Maybe this lazymatch...end is not needed because the
   autorewrite with norm takes care of it? *)
        lazymatch goal with
        | |- int_signed_or_unsigned _ (Int.repr ?i) = ?j =>
            let x := fresh "x" in set (x:=i); 
            let y := fresh "y" in set (y:=j);
            unfold int_signed_or_unsigned; simpl;
            subst x;
            rewrite ?(Int.signed_repr i) by insist_rep_omega;
            rewrite ?(Int.unsigned_repr i) by insist_rep_omega;
            subst y
        | |- int_signed_or_unsigned ?t _ = _ =>
              try change (int_signed_or_unsigned t) with Int.signed;
              try change (int_signed_or_unsigned t) with Int.unsigned
        | |- _ => idtac
         end;
         reflexivity
(*      | solve_Ptrofs_eqm_unsigned *)
      | ]
    | apply msubst_efield_denote_cons_struct
    | apply msubst_efield_denote_cons_union
    | apply msubst_efield_denote_nil
    ]
  ].Inductive field_address_gen {cs: compspecs}: type * list gfield * val -> type * list gfield * val -> Prop :=
| field_address_gen_nil: forall t1 t2 gfs p tgp,
    nested_field_type t2 gfs = t1 ->
    field_address_gen (t2, gfs, p) tgp ->
    field_address_gen (t1, nil, (field_address t2 gfs p)) tgp
| field_address_gen_app: forall t1 t2 gfs1 gfs2 p tgp,
    nested_field_type t2 gfs2 = t1 ->
    field_address_gen (t2, gfs1 ++ gfs2, p) tgp ->
    field_address_gen (t1, gfs1, (field_address t2 gfs2 p)) tgp
| field_address_gen_assu: forall t gfs p1 p2 tgp,
    p1 = p2 ->
    field_address_gen (t, gfs, p2) tgp ->
    field_address_gen (t, gfs, p1) tgp    
| field_address_gen_refl: forall tgp, field_address_gen tgp tgp.Inductive field_address_gen {cs: compspecs}: type * list gfield * val -> type * list gfield * val -> Prop :=
| field_address_gen_nil: forall t1 t2 gfs p tgp,
    nested_field_type t2 gfs = t1 ->
    field_address_gen (t2, gfs, p) tgp ->
    field_address_gen (t1, nil, (field_address t2 gfs p)) tgp
| field_address_gen_app: forall t1 t2 gfs1 gfs2 p tgp,
    nested_field_type t2 gfs2 = t1 ->
    field_address_gen (t2, gfs1 ++ gfs2, p) tgp ->
    field_address_gen (t1, gfs1, (field_address t2 gfs2 p)) tgp
| field_address_gen_assu: forall t gfs p1 p2 tgp,
    p1 = p2 ->
    field_address_gen (t, gfs, p2) tgp ->
    field_address_gen (t, gfs, p1) tgp    
| field_address_gen_refl: forall tgp, field_address_gen tgp tgp.Inductive field_address_gen {cs: compspecs}: type * list gfield * val -> type * list gfield * val -> Prop :=
| field_address_gen_nil: forall t1 t2 gfs p tgp,
    nested_field_type t2 gfs = t1 ->
    field_address_gen (t2, gfs, p) tgp ->
    field_address_gen (t1, nil, (field_address t2 gfs p)) tgp
| field_address_gen_app: forall t1 t2 gfs1 gfs2 p tgp,
    nested_field_type t2 gfs2 = t1 ->
    field_address_gen (t2, gfs1 ++ gfs2, p) tgp ->
    field_address_gen (t1, gfs1, (field_address t2 gfs2 p)) tgp
| field_address_gen_assu: forall t gfs p1 p2 tgp,
    p1 = p2 ->
    field_address_gen (t, gfs, p2) tgp ->
    field_address_gen (t, gfs, p1) tgp    
| field_address_gen_refl: forall tgp, field_address_gen tgp tgp.Inductive field_address_gen {cs: compspecs}: type * list gfield * val -> type * list gfield * val -> Prop :=
| field_address_gen_nil: forall t1 t2 gfs p tgp,
    nested_field_type t2 gfs = t1 ->
    field_address_gen (t2, gfs, p) tgp ->
    field_address_gen (t1, nil, (field_address t2 gfs p)) tgp
| field_address_gen_app: forall t1 t2 gfs1 gfs2 p tgp,
    nested_field_type t2 gfs2 = t1 ->
    field_address_gen (t2, gfs1 ++ gfs2, p) tgp ->
    field_address_gen (t1, gfs1, (field_address t2 gfs2 p)) tgp
| field_address_gen_assu: forall t gfs p1 p2 tgp,
    p1 = p2 ->
    field_address_gen (t, gfs, p2) tgp ->
    field_address_gen (t, gfs, p1) tgp    
| field_address_gen_refl: forall tgp, field_address_gen tgp tgp.Inductive field_address_gen {cs: compspecs}: type * list gfield * val -> type * list gfield * val -> Prop :=
| field_address_gen_nil: forall t1 t2 gfs p tgp,
    nested_field_type t2 gfs = t1 ->
    field_address_gen (t2, gfs, p) tgp ->
    field_address_gen (t1, nil, (field_address t2 gfs p)) tgp
| field_address_gen_app: forall t1 t2 gfs1 gfs2 p tgp,
    nested_field_type t2 gfs2 = t1 ->
    field_address_gen (t2, gfs1 ++ gfs2, p) tgp ->
    field_address_gen (t1, gfs1, (field_address t2 gfs2 p)) tgp
| field_address_gen_assu: forall t gfs p1 p2 tgp,
    p1 = p2 ->
    field_address_gen (t, gfs, p2) tgp ->
    field_address_gen (t, gfs, p1) tgp    
| field_address_gen_refl: forall tgp, field_address_gen tgp tgp.

(* Specifications: *)
Lemma field_address_gen_fact: forall {cs: compspecs} t1 gfs1 p1 t2 gfs2 p2, field_address_gen (t1, gfs1, p1) (t2, gfs2, p2) -> field_address t1 gfs1 p1 = field_address t2 gfs2 p2 /\ nested_field_type t1 gfs1 = nested_field_type t2 gfs2 /\ (field_compatible t2 gfs2 p2 -> field_compatible t1 gfs1 p1).