Definition prim (f:nat -> value) : expr -> expr :=
  Prim (val_to_exp oo f).

Lemma T_ExtE : forall G e f (X:pred world -> pred world) sigma (Hext : forall tau, boxy extendM tau -> boxy extendM (X tau)), Typ G e (ty_ex X) -> (forall tau, Typ (X tau::G) f sigma) -> Typ G (App (Lam f) e) sigma.