Journal of Formalized Mathematics
Volume 12, 2000
University of Bialystok
Copyright (c) 2000 Association of Mizar Users

## On Replace Function and Swap Function for Finite Sequences

Hiroshi Yamazaki
Shinshu University, Nagano
Yoshinori Fujisawa
Shinshu University, Nagano
Yatsuka Nakamura
Shinshu University, Nagano

### Summary.

In this article, we show the property of the Replace Function and the Swap Function of finite sequences. In the first section, we prepared some useful theorems for finite sequences. In the second section, we defined the Replace function and proved some theorems about the function. This function replaces an element of a sequence by another value. In the third section, we defined the Swap function and proved some theorems about the function. This function swaps two elements of a sequence. In the last section, we show the property of composed functions of the Replace Function and the Swap Function.

#### MML Identifier: FINSEQ_7

The terminology and notation used in this paper have been introduced in the following articles [8] [10] [1] [7] [4] [2] [9] [6] [5] [3]

#### Contents (PDF format)

1. Some Basic Theorems
2. Definition of Replace Function and its Properties
3. Definition of Swap Function and its Properties
4. Properties of Combination Function of Replace Function and Swap Function

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