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          

#### 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

#### Bibliography

 Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
 Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
 Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Journal of Formalized Mathematics, 8, 1996.
 Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
 Agata Darmochwal and Yatsuka Nakamura. The topological space \$\calE^2_\rmT\$. Arcs, line segments and special polygonal arcs. Journal of Formalized Mathematics, 3, 1991.
 Jaroslaw Kotowicz. Functions and finite sequences of real numbers. Journal of Formalized Mathematics, 5, 1993.
 Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Journal of Formalized Mathematics, 5, 1993.
 Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
 Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
 Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.