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.
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]

Some Basic Theorems

Definition of Replace Function and its Properties

Definition of Swap Function and its Properties

Properties of Combination Function of Replace Function and Swap Function
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Received August 28, 2000
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