Journal of Formalized Mathematics
Volume 8, 1996
University of Bialystok
Copyright (c) 1996
Association of Mizar Users
Cartesian Products of Relations and Relational Structures

Artur Kornilowicz

Institute of Mathematics, Warsaw University, Bialystok
Summary.

In this paper the definitions of cartesian products of relations and
relational structures are introduced. Facts about these notions are proved.
This work is the continuation of formalization of [8].
This work was partially supported by
Office of Naval Research Grant N000149511336.
The terminology and notation used in this paper have been
introduced in the following articles
[9]
[7]
[12]
[13]
[15]
[14]
[5]
[10]
[6]
[1]
[11]
[2]
[3]
[4]

Preliminaries

Properties of Cartesian Products of Relational Structures
Bibliography
 [1]
Grzegorz Bancerek.
Curried and uncurried functions.
Journal of Formalized Mathematics,
2, 1990.
 [2]
Grzegorz Bancerek.
Complete lattices.
Journal of Formalized Mathematics,
4, 1992.
 [3]
Grzegorz Bancerek.
Bounds in posets and relational substructures.
Journal of Formalized Mathematics,
8, 1996.
 [4]
Grzegorz Bancerek.
Directed sets, nets, ideals, filters, and maps.
Journal of Formalized Mathematics,
8, 1996.
 [5]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [8]
G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, and D.S. Scott.
\em A Compendium of Continuous Lattices.
SpringerVerlag, Berlin, Heidelberg, New York, 1980.
 [9]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [10]
Andrzej Trybulec.
Tuples, projections and Cartesian products.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Wojciech A. Trybulec.
Partially ordered sets.
Journal of Formalized Mathematics,
1, 1989.
 [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 and Anna Zalewska.
Properties of binary relations.
Journal of Formalized Mathematics,
1, 1989.
Received September 25, 1996
[
Download a postscript version,
MML identifier index,
Mizar home page]