Journal of Formalized Mathematics
Volume 8, 1996
University of Bialystok
Copyright (c) 1996 Association of Mizar Users

## Reconstructions of Special Sequences

Yatsuka Nakamura
Shinshu University, Nagano
Roman Matuszewski
Warsaw University, Bialystok

### Summary.

We discuss here some methods for reconstructing special sequences which generate special polygonal arcs in ${\cal E}^{2}_{\rm T}$. For such reconstructions we introduce a mid" function which cuts out the middle part of a sequence; the $\downharpoonleft$" function, which cuts down the left part of a sequence at some point; the $\downharpoonright$" function for cutting down the right part at some point; and the $\downharpoonleft \downharpoonright$" function for cutting down both sides at two given points.\par We also introduce some methods glueing two special sequences. By such cutting and glueing methods, the speciality of sequences (generatability of special polygonal arcs) is shown to be preserved.

The work has been done while the second author was visiting Nagano in autumn 1996.

#### MML Identifier: JORDAN3

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

#### Contents (PDF format)

1. Preliminaries
2. Middle Function for Finite Sequences
3. A Concept of Index for Finite Sequences in ${\cal E}^{2}_{\rm T}$
4. Left and Right Cutting Functions for Finite Sequences in ${\cal E}^{2}_{\rm T}$
5. Cutting Both Sides of a Finite Sequence and a Discussion of Speciality of Sequences in ${\cal E}^{2}_{\rm T}$

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