(* begin hide *)
  Definition atom := nat.Definition t := atom.Definition eq_dec := eq_nat_dec.

(* Specifications: *)
Lemma max_lt_r : forall x y z, x <= z -> x <= max y z.
Lemma nat_list_max : forall (xs : list nat), { n : nat | forall x, List.In x xs -> x <= n }.
Lemma atom_fresh_for_list : forall (xs : list nat), { n : nat | ~ List.In n xs }.