Volume 9, 1997

University of Bialystok

Copyright (c) 1997 Association of Mizar Users

**Yatsuka Nakamura**- Shinshu University, Nagano
**Roman Matuszewski**- Warsaw University, Bialystok
- This paper was written while the author visited Shinshu University in fall 1996.
**Adam Grabowski**- Warsaw University, Bialystok
- This paper was written while the author visited Shinshu University in winter 1997.

- It is known that a standard special circular sequence in ${\cal E}^2_{\rm T}$ properly defines a special polygon. We are interested in a part of such a sequence. It is shown that if the first point and the last point of the subsequence are different, it becomes a special polygonal sequence. The concept of ``a part of" is introduced, and the subsequence having this property can be characterized by using ``mid" function. For such subsequences, the concepts of ``Upper" and ``Lower" parts are introduced.

- Preliminaries
- Some facts about cutting of finite sequences
- Dividing of special circular sequences into parts

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The fundamental properties of natural numbers.
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