Department of Computer Science,; Cornell University, Ithaca
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This paper provides an account of how mathematical knowledge is represented, reasoned about, and used computationally in a mechanized constructive theorem proving environment. We accomplish this by presenting a particular theory developed in the Nuprl proof development system: finite set theory culminating in Ramsey's theorem. We believe that this development is interesting as a case study in the relationship between constructive mathematics and computer science. Moreover, the aspects we emphasize --- the high-level development of definitions and lemmas, the use of tactics to automate reasoning, and the use of type theory as a programming logic --- are not restricted in relevance to this particular theory, and indicate the promise of our approach for other branches of constructive mathematics. 1 Introduction This paper describes our ongoing research in theory development in the Nuprl proof development system. Nuprl supports the interactive creation of definitions, formulas, proofs, an...
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Logic at Botik 89, number 363 in Lecture Notes in Computer Science