  Type theories with higher-order subtyping or singleton types are examples of
systems where computation rules for variables are affected by type information
in the context. A complication for these systems is that bounds declared in the
context do not interact well with the logical relation proof of completeness or
termination. This paper proposes a natural modification to the type syntax for
F-Omega-Sub, adding variable's bound to the variable type constructor, thereby
separating the computational behavior of the variable from the context. The
algorithm for subtyping in F-Omega-Sub can then be given on types without
context or kind information. As a consequence, the metatheory follows the
general approach for type systems without computational information in the
context, including a simple logical relation definition without Kripke-style
indexing by context. This new presentation of the system is shown to be
equivalent to the traditional presentation without bounds on the variable type
constructor.
