Definition ty_bool := ALL a:pred world, ty_lam a (ty_lam a a).
Definition e_true := Lam (Lam (Var 1)).
Definition e_false := Lam (Lam (Var 0)).
Definition e_if b t f :=
(App (App (App b (Lam t)) (Lam f)) (Nat 0)).

Lemma e_true_typ :
Typ nil e_true ty_bool.