(* From introduction; this is the judgment psi |- v : tau *)
Definition forces (psi : mtype) (v : value) (tau : pred world) :=
  tau (psi, v).(* Section 4.1, equation 17 *)
Program Definition ty_nat : pred world :=
  fun w => match w with (k, v) =>
    exists n, v = v_Nat n
  end.

(* Specifications: *)
Lemma ty_nat_extends : boxy extendM ty_nat.