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.

#### MML Identifier: MEMBERED

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

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[2] Grzegorz Bancerek. Sequences of ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Andrzej Kondracki. Basic properties of rational numbers. Journal of Formalized Mathematics, 2, 1990.
[4] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[5] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[6] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[7] Michal J. Trybulec. Integers. Journal of Formalized Mathematics, 2, 1990.
[8] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.