Fixpoint inj_value_rec (n: nat) (v: val) (q: quantity) {struct n}: list memval :=
  match n with
  | O => nil
  | S m => Fragment v q m :: inj_value_rec m v q
  end.Definition inj_value (q: quantity) (v: val): list memval :=
  inj_value_rec (size_quantity_nat q) v q.Fixpoint check_value (n: nat) (v: val) (q: quantity) (vl: list memval)
                       {struct n} : bool :=
  match n, vl with
  | O, nil => true
  | S m, Fragment v' q' m' :: vl' =>
      Val.eq v v' && quantity_eq q q' && Nat.eqb m m' && check_value m v q vl'
  | _, _ => false
  end.Definition proj_value (q: quantity) (vl: list memval) : val :=
  match vl with
  | Fragment v q' n :: vl' =>
      if check_value (size_quantity_nat q) v q vl then v else Vundef
  | _ => Vundef
  end.Definition encode_val (chunk: memory_chunk) (v: val) : list memval :=
  match v, chunk with
  | Vint n, (Mint8signed | Mint8unsigned) => inj_bytes (encode_int 1%nat (Int.unsigned n))
  | Vint n, (Mint16signed | Mint16unsigned) => inj_bytes (encode_int 2%nat (Int.unsigned n))
  | Vint n, Mint32 => inj_bytes (encode_int 4%nat (Int.unsigned n))
  | Vptr b ofs, Mint32 => if Archi.ptr64 then list_repeat 4%nat Undef else inj_value Q32 v
  | Vlong n, Mint64 => inj_bytes (encode_int 8%nat (Int64.unsigned n))
  | Vptr b ofs, Mint64 => if Archi.ptr64 then inj_value Q64 v else list_repeat 8%nat Undef
  | Vsingle n, Mfloat32 => inj_bytes (encode_int 4%nat (Int.unsigned (Float32.to_bits n)))
  | Vfloat n, Mfloat64 => inj_bytes (encode_int 8%nat (Int64.unsigned (Float.to_bits n)))
  | _, Many32 => inj_value Q32 v
  | _, Many64 => inj_value Q64 v
  | _, _ => list_repeat (size_chunk_nat chunk) Undef
  end.Definition decode_val (chunk: memory_chunk) (vl: list memval) : val :=
  match proj_bytes vl with
  | Some bl =>
      match chunk with
      | Mint8signed => Vint(Int.sign_ext 8 (Int.repr (decode_int bl)))
      | Mint8unsigned => Vint(Int.zero_ext 8 (Int.repr (decode_int bl)))
      | Mint16signed => Vint(Int.sign_ext 16 (Int.repr (decode_int bl)))
      | Mint16unsigned => Vint(Int.zero_ext 16 (Int.repr (decode_int bl)))
      | Mint32 => Vint(Int.repr(decode_int bl))
      | Mint64 => Vlong(Int64.repr(decode_int bl))
      | Mfloat32 => Vsingle(Float32.of_bits (Int.repr (decode_int bl)))
      | Mfloat64 => Vfloat(Float.of_bits (Int64.repr (decode_int bl)))
      | Many32 => Vundef
      | Many64 => Vundef
      end
  | None =>
      match chunk with
      | Mint32 => if Archi.ptr64 then Vundef else Val.load_result chunk (proj_value Q32 vl)
      | Many32 => Val.load_result chunk (proj_value Q32 vl)
      | Mint64 => if Archi.ptr64 then Val.load_result chunk (proj_value Q64 vl) else Vundef
      | Many64 => Val.load_result chunk (proj_value Q64 vl)
      | _ => Vundef
      end
  end.Ltac solve_encode_val_length :=
  match goal with
  | [ |- length (inj_bytes _) = _ ] => rewrite length_inj_bytes; solve_encode_val_length
  | [ |- length (encode_int _ _) = _ ] => apply encode_int_length
  | [ |- length (if ?x then _ else _) = _ ] => destruct x eqn:?; solve_encode_val_length
  | _ => reflexivity
  end.

Lemma proj_inj_value: forall q v, proj_value q (inj_value q v) = v.