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Revisiting Cut-Elimination: One Difficult Proof Is Really a Proof

  • Christian Urban
  • Bozhi Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5117)

Abstract

Powerful proof techniques, such as logical relation arguments, have been developed for establishing the strong normalisation property of term- rewriting systems. The first author used such a logical relation argument to establish strong normalising for a cut-elimination procedure in classical logic. He presented a rather complicated, but informal, proof establishing this property. The difficulties in this proof arise from a quite subtle substitution operation, which implements proof transformation that permute cuts over other inference rules. We have formalised this proof in the theorem prover Isabelle/HOL using the Nominal Datatype Package, closely following the informal proof given by the first author in his PhD-thesis. In the process, we identified and resolved a gap in one central lemma and a number of smaller problems in others. We also needed to make one informal definition rigorous. We thus show that the original proof is indeed a proof and that present automated proving technology is adequate for formalising such difficult proofs.

Keywords

Inference Rule Classical Logic Strong Normalisation Variable Convention Main Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Christian Urban
    • 1
  • Bozhi Zhu
    • 2
  1. 1.Technical University of Munich 
  2. 2.North China Electric Power University 

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