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

Lemma sub_AllBnd : forall T1 T2 (X1 X2:pred world -> pred world),
TT |-- T2 >=> T1 ->
(forall x, TT |-- x >=> T2 -> TT |-- X1 x >=> X2 x) ->
TT |-- AllBnd T1 X1 >=> AllBnd T2 X2.