Journal of Formalized Mathematics
Volume 8, 1996
University of Bialystok
Copyright (c) 1996 Association of Mizar Users

## Bounds in Posets and Relational Substructures

Grzegorz Bancerek
Institute of Mathematics, Polish Academy of Sciences

### Summary.

Notation and facts necessary to start with the formalization of continuous lattices according to [4] are introduced.

This work was partially supported by Office of Naval Research Grant N00014-95-1-1336.

#### MML Identifier: YELLOW_0

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

#### Contents (PDF format)

1. Reexamination of poset concepts
2. Least upper and greatest lower bounds
3. Relational substructures

#### Bibliography

[1] Grzegorz Bancerek. Complete lattices. Journal of Formalized Mathematics, 4, 1992.
[2] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[3] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[4] G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, and D.S. Scott. \em A Compendium of Continuous Lattices. Springer-Verlag, Berlin, Heidelberg, New York, 1980.
[5] Krzysztof Hryniewiecki. Relations of tolerance. Journal of Formalized Mathematics, 2, 1990.
[6] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[7] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[8] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[9] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.
[10] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Journal of Formalized Mathematics, 1, 1989.
[11] Stanislaw Zukowski. Introduction to lattice theory. Journal of Formalized Mathematics, 1, 1989.