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

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