Definition nested_pred (atom_pred: type -> bool): type -> bool :=
  type_func
    (fun _ => bool)
    (fun t => atom_pred t)
    (fun t n a b => (atom_pred (Tarray t n a) && b)%bool)
    (fun id a bl => (atom_pred (Tstruct id a) && fold_right andb true (decay bl))%bool)
    (fun id a bl => (atom_pred (Tunion id a) && fold_right andb true (decay bl))%bool).Definition nested_fields_pred (atom_pred: type -> bool) (m: members) : bool :=
  fold_right (fun it b => (nested_pred atom_pred (field_type (fst it) m) && b)%bool) true m.

Lemma nested_pred_eq: forall atom_pred t, nested_pred atom_pred t = match t with | Tarray t0 _ _ => (atom_pred t && nested_pred atom_pred t0)%bool | Tstruct id _ | Tunion id _ => (atom_pred t && nested_fields_pred atom_pred (co_members (get_co id)))%bool | _ => atom_pred t end.