Open Scope pred.
(* Section 4.1, equation 19 *)
Definition approx_eq (n : nat) (tau1 tau2 : predicate) : Prop :=
approx n tau1 = approx n tau2.

(* Specifications: *)
Lemma approx_eq_downward : forall n m p q,
m <= n ->
approx_eq n p q ->
approx_eq m p q.
Lemma approx_eq_sub n P Q :
((|> (P <=> Q)) n -> approx_eq n P Q).