Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998 Association of Mizar Users

## A Theory of Boolean Valued Functions and Partitions

Shunichi Kobayashi
Shinshu University, Nagano
Kui Jia
Shinshu University, Nagano

### Summary.

In this paper, we define Boolean valued functions. Some of their algebraic properties are proved. We also introduce and examine the infimum and supremum of Boolean valued functions and their properties. In the last section, relations between Boolean valued functions and partitions are discussed.

#### MML Identifier: BVFUNC_1

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

#### Contents (PDF format)

1. Boolean Operations
2. Boolean Valued Functions
3. Infimum and Supremum
4. Boolean Valued Functions and Partitions

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