# A HOL decision procedure for elementary real algebra

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## Abstract

The elementary theory of real algebra, including multiplication, is decidable. More precisely, there is an algorithm to eliminate quantifiers which does not introduce new free variables or new constants other than rational numbers. Therefore if a closed term of elementary real algebra involves no constants other than the rational numbers, its truth or falsity can be determined automatically. Quite a number of interesting algebraic and geometric problems can be expressed in this decidable subset. In this paper we describe a HOL implementation of a quantifier-elimination procedure and give some preliminary results.

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## References

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1994