We give a simple and direct proof that super-consistency implies the cut elimination property in deduction modulo. This proof can be seen as a simplification of the proof that super-consistency implies proof normalization. It also takes ideas from the semantic proofs of cut elimination that proceed by proving the completeness of the cut-free calculus. As an application, we compare our work with the cut elimination theorems in higher-order logic that involve V-complexes.

翻译：摘要：我们给出了一个简单和直接的证明，即在演绎模型中，超一致性蕴含删减规则。这个证明可以看作是超一致性蕴含证明标准化的简化。它还采用了cut-free演算的完备性证明的有关思想。作为应用，我们将我们的工作与涉及V-复合物的高阶逻辑删减定理进行比较。