Journal of Formalized Mathematics
Volume 9, 1997
University of Bialystok
Copyright (c) 1997 Association of Mizar Users

## Subsequences of Standard Special Circular Sequences in $\cal E^2_\rm T$

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

### Summary.

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.

#### MML Identifier: JORDAN4

The terminology and notation used in this paper have been introduced in the following articles [15] [8] [1] [13] [18] [2] [3] [17] [4] [6] [7] [10] [12] [14] [5] [16] [9] [11]

#### Contents (PDF format)

1. Preliminaries
2. Some facts about cutting of finite sequences
3. Dividing of special circular sequences into parts

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