Abstract
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, LATEX. Modern systems for proof development make the formalization of reasoning relatively easy. However, formalizing computations in such a manner that the results can be used in formal proofs is not immediate. In this paper we show how to obtain formal proofs of statements such as i>Prime$(\underline{61})$ in the context of Peano arithmetic or (i>x+1)(i>x+1)ei>x2+2i>x+1 in the context of rings. We hope that the method will help bridge the gap between the efficient systems of computer algebra and the reliable systems of proof development.
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