(* Lemma union_default_filter_legal: forall m, m <> nil -> legal_compact_sum_filter (union_default_filter m) m = true. *)
Definition union_default_val (m : members) := compact_sum_gen (fun it => true) (fun it => default_val (field_type (fst it) m)) m.

(* Specifications: *)
Lemma compact_prod_sigT_compact_prod_gen:
forall {A B} {P: A -> Type} (genT: B -> A) (genV: forall b: B, P (genT b)) (gen: B -> sigT P) (l: list B),
(forall b, gen b = existT P (genT b) (genV b)) ->
JMeq (compact_prod_sigT_value (map gen l)) (compact_prod_gen genV l).
Lemma compact_sum_sigT_compact_sum_gen:
forall {A B} {P: A -> Type} (genT: B -> A) (genV: forall b: B, P (genT b)) (filter: B -> bool) (gen: B -> sigT P) (l: list B),
(forall b, gen b = existT P (genT b) (genV b)) ->
is_default_filter filter l ->
JMeq (compact_sum_sigT_value (map gen l)) (compact_sum_gen filter genV l).
Lemma default_val_eq: forall t,
default_val t =
fold_reptype
match t as t' return REPTYPE t'
with
| Tvoid
| Tfunction _ _ _ => tt
| Tint _ _ _
| Tlong _ _
| Tfloat _ _
| Tpointer _ _ => Vundef
| Tarray t0 n _ => list_repeat (Z.to_nat n) (default_val t0)
| Tstruct id _ => struct_default_val (co_members (get_co id))
| Tunion id _ => union_default_val (co_members (get_co id))
end.