Definition LR_of_type (t: type) :=
  match t with
  | Tarray _ _ _ => RRRR
  | _ => LLLL
  end.

Lemma weakened_legal_nested_efield_spec: forall t_root e gfs efs tts rho, legal_nested_efield_rec t_root gfs tts = true -> type_almost_match e t_root (LR_of_type t_root) = true -> efield_denote efs gfs rho -> typeconv' (nested_field_type t_root gfs) = typeconv' (typeof (nested_efield e efs tts)).