Definition offset_in_range ofs p :=
  match p with
  | Vptr b iofs => 0 <= Ptrofs.unsigned iofs + ofs <= Ptrofs.modulus
  | _ => True
  end.Definition offset_strict_in_range ofs p :=
  match p with
  | Vptr b iofs => 0 <= Ptrofs.unsigned iofs + ofs < Ptrofs.modulus
  | _ => True
  end.Definition data_at_rec: forall t, reptype t -> val -> mpred :=
  type_func (fun t => reptype t -> val -> mpred)
    (fun t v p =>
       if type_is_volatile t
       then memory_block sh (sizeof t) p
       else mapsto sh t p (repinject t v))
    (fun t n a P v => array_pred 0 (Z.max 0 n) (fun i v => at_offset (P v) (sizeof t * i)) (unfold_reptype v))
    (fun id a P v => struct_data_at_rec_aux sh (co_members (get_co id)) (co_members (get_co id)) (co_sizeof (get_co id)) P (unfold_reptype v))
    (fun id a P v => union_data_at_rec_aux sh (co_members (get_co id)) (co_members (get_co id)) (co_sizeof (get_co id)) P (unfold_reptype v)).

Lemma by_value_data_at_rec_default_val2: forall sh t b ofs, type_is_by_value t = true -> 0 <= ofs /\ ofs + sizeof t < Ptrofs.modulus -> align_compatible_rec cenv_cs t ofs -> data_at_rec sh t (default_val t) (Vptr b (Ptrofs.repr ofs)) = memory_block sh (sizeof t) (Vptr b (Ptrofs.repr ofs)).