Definition field_address t gfs p :=
  if (field_compatible_dec t gfs p)
  then offset_val (nested_field_offset t gfs) p
  else Vundef.Definition field_address0 t gfs p :=
  if (field_compatible0_dec t gfs p)
  then offset_val (nested_field_offset t gfs) p
  else Vundef.

Lemma legal_nested_field_app_inv: forall t gfs0 gfs1, legal_nested_field t gfs0 -> legal_nested_field (nested_field_type t gfs0) gfs1 -> legal_nested_field t (gfs1 ++ gfs0).