(* Bounded Universal Quantification *)
Definition AllBnd (T:pred world) (X:pred world -> pred world)
:= ALL tau:pred world, !!(TT |-- tau >=> T) --> X tau.

Lemma T_UnivBoundedI : forall G e T (X:pred world -> pred world),
openValue e ->
(forall tau, TT |-- tau >=> T -> Typ G e (X tau)) ->
Typ G e (AllBnd T X).