Journal of Formalized Mathematics
Volume 15, 2003
University of Bialystok
Copyright (c) 2003
Association of Mizar Users
On the Sets Inhabited by Numbers
-
Andrzej Trybulec
-
University of Bialystok
Summary.
-
The information that all members of a set enjoy a property expressed
by an adjective can be processed in a systematic way. The purpose
of the work is to find out how to do that. If it works, `membered'
will become a reserved word and the work with it will be automated.
I have chosen {\it membered} rather than {\it inhabited} because of
the compatibility with the Automath terminology.
The phrase $\tau$ {\it inhabits}
$\theta$ could be translated to $\tau$ {\bfseries\itshape is}
$\theta$ in Mizar.
This work has been partially supported by the CALCULEMUS
grant HPRN-CT-2000-00102.
The terminology and notation used in this paper have been
introduced in the following articles
[5]
[8]
[4]
[6]
[3]
[7]
[1]
[2]
Contents (PDF format)
Acknowledgments
I am grateful to Dr. Czeslaw Bylinski for the discussion,
particularly for his advice to prove more trivial but useful theorems.
Bibliography
- [1]
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- [2]
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1, 1989.
- [3]
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2, 1990.
- [4]
Beata Padlewska.
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Journal of Formalized Mathematics,
1, 1989.
- [5]
Andrzej Trybulec.
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Axiomatics, 1989.
- [6]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
- [7]
Michal J. Trybulec.
Integers.
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2, 1990.
- [8]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
Received August 23, 2003
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