Journal of Formalized Mathematics
Volume 13, 2001
University of Bialystok
Copyright (c) 2001
Association of Mizar Users
Classes of Independent Partitions

Andrzej Trybulec

University of Bialystok
Summary.

The paper includes proofs of few theorems proved earlier by
Shunichi Kobayashi in many different settings.
The terminology and notation used in this paper have been
introduced in the following articles
[10]
[4]
[12]
[8]
[16]
[15]
[13]
[17]
[1]
[14]
[3]
[2]
[11]
[9]
[6]
[5]
[7]

Preliminaries

BooleanValued Functions

Independent Classes of Partitions
Bibliography
 [1]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Partial functions.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Shunichi Kobayashi and Kui Jia.
A theory of Boolean valued functions and partitions.
Journal of Formalized Mathematics,
10, 1998.
 [6]
Shunichi Kobayashi and Kui Jia.
A theory of partitions. Part I.
Journal of Formalized Mathematics,
10, 1998.
 [7]
Shunichi Kobayashi and Yatsuka Nakamura.
A theory of Boolean valued functions and quantifiers with respect to partitions.
Journal of Formalized Mathematics,
10, 1998.
 [8]
Beata Padlewska.
Families of sets.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Konrad Raczkowski and Pawel Sadowski.
Equivalence relations and classes of abstraction.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [11]
Andrzej Trybulec.
Function domains and Fr\aenkel operator.
Journal of Formalized Mathematics,
2, 1990.
 [12]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [13]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [14]
Edmund Woronowicz.
Relations defined on sets.
Journal of Formalized Mathematics,
1, 1989.
 [15]
Edmund Woronowicz.
Interpretation and satisfiability in the first order logic.
Journal of Formalized Mathematics,
2, 1990.
 [16]
Edmund Woronowicz.
Manyargument relations.
Journal of Formalized Mathematics,
2, 1990.
 [17]
Edmund Woronowicz and Anna Zalewska.
Properties of binary relations.
Journal of Formalized Mathematics,
1, 1989.
Received February 14, 2001
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