  The lambda-Pi-calculus modulo theory is a logical framework in which many
type systems can be expressed as theories. We present such a theory, the theory
U, where proofs of several logical systems can be expressed. Moreover, we
identify a sub-theory of U corresponding to each of these systems, and prove
that, when a proof in U uses only symbols of a sub-theory, then it is a proof
in that sub-theory.
