Section Finite_nat_set.
Variable set_size : nat.
Definition fnat_subset : Type := counted_list bool set_size.
Definition fnat_member(fs : fnat_subset)(n : nat) : Prop :=
is_true (counted_def_nth fs n false).

Lemma fnat_subset_member_eq : forall(fs1 fs2 : fnat_subset),
fs1 = fs2 <->
forall(n : nat), fnat_member fs1 n <-> fnat_member fs2 n.