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Extending the HOL theorem prover with a Computer Algebra System to Reason about the Reals
 Higher Order Logic Theorem Proving and its Applications (HUG `93
, 1993
"... In this paper we describe an environment for reasoning about the reals which combines the rigour of a theorem prover with the power of a computer algebra system. 1 Introduction Computer theorem provers are a topic of research interest in their own right. However much of their popularity stems from ..."
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In this paper we describe an environment for reasoning about the reals which combines the rigour of a theorem prover with the power of a computer algebra system. 1 Introduction Computer theorem provers are a topic of research interest in their own right. However much of their popularity stems from their application in computeraided verification, i.e. proving that designs of electronic or computer systems, programs, protocols and cryptosystems satisfy certain properties. Such proofs, as compared with the proofs one finds in mathematics books, usually involve less sophisticated central ideas, but contain far more technical Supported by the Science and Engineering Research Council, UK. y Supported by SERC grant GR/G 33837 and a grant from DSTO Australia. details and therefore tend to be much more difficult for humans to write or check without making mistakes. Hence it is appealing to let computers help. Some fundamental mathematical theories, such as arithmetic, are usually requi...
THE FUSSLER SAMPLING TECHNIQUE FOR POPULATIONS WITH A DISCRETE OR A CONTINUOUS DISTRIBUTION OF THICKNESSES
"... In this paper we show that the Fussler sampling technique in book shelves is always better than systematic sampling by length. So far this result was only known to be true in the idealized situation of two categories of books: "thin " and "thick " books (Bookstein ..."
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In this paper we show that the Fussler sampling technique in book shelves is always better than systematic sampling by length. So far this result was only known to be true in the idealized situation of two categories of books: &quot;thin &quot; and &quot;thick &quot; books (Bookstein, Rousseau).
1 The Vitali covering theorem in constructive mathematics HANNES DIENER
"... Abstract: This paper investigates the Vitali Covering Theorem from various constructive angles. A Vitali Cover of a metric space is a cover such that for every point there exists an arbitrarily small element of the cover containing this point. The Vitali Covering Theorem now states, that for any Vit ..."
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Abstract: This paper investigates the Vitali Covering Theorem from various constructive angles. A Vitali Cover of a metric space is a cover such that for every point there exists an arbitrarily small element of the cover containing this point. The Vitali Covering Theorem now states, that for any Vitali Cover one can find a finite family of pairwise disjoint sets in the Vitali Cover that cover the entire space up to a set of a given nonzero measure. We will show, by means of a recursive counterexample, that there cannot be a fully constructive proof, but that adding a very weak semiconstructive principle suffices to give such a proof. Lastly, we will show that with an appropriate formalization in formal topology the nonconstructive problems can be avoided completely.