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.

翻译：lambda\ Pi-calculus modulo理论是一个逻辑框架,许多类型系统都可以在其中以理论的形式表达。 我们提出了这样一个理论,即U理论,其中可以表达若干逻辑系统的证据。 此外,我们确定了一个与上述每个系统相对应的U子理论,并证明当在 U 中的证据只使用子理论的符号时,它就是该子理论中的一个证据。