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Autarkic Computations in Formal Proofs
 J. Autom. Reasoning
, 1997
"... Formal proofs in mathematics and computer science are being studied because these objects can be verified by a very simple computer program. An important open problem is whether these formal proofs can be generated with an effort not much greater than writing a mathematical paper in, say, L A ..."
Abstract

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Formal proofs in mathematics and computer science are being studied because these objects can be verified by a very simple computer program. An important open problem is whether these formal proofs can be generated with an effort not much greater than writing a mathematical paper in, say, L A T E X. Modern systems for proofdevelopment make the formalization of reasoning relatively easy. Formalizing computations such that the results can be used in formal proofs is not immediate. In this paper it is shown how to obtain formal proofs of statements like Prime(61) in the context of Peano arithmetic or (x + 1)(x + 1) = x 2 + 2x + 1 in the context of rings. It is hoped that the method will help bridge the gap between the efficient systems of computer algebra and the reliable systems of proofdevelopment. 1. The problem Usual mathematics is informal but precise. One speaks about informal rigor. Formal mathematics on the other hand consists of definitions, statements and proo...