Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
The Lattice of Real Numbers.
The Lattice of Real Functions

Marek Chmur

Warsaw University, Bialystok

Supported by RPBP.III24.C1.
Summary.

A proof of the fact, that
$\llangle {\Bbb R}, {\rm max}, {\rm min} \rrangle$ is
a lattice (real lattice). Some basic properties (real lattice is
distributive and modular) of it are proved.
The same is done for the set ${\Bbb R}^A$ with operations:
max($f(A)$) and min($f(A)$), where ${\Bbb R}^A$ means the
set of all functions from $A$
(being nonempty set) to $\Bbb R$, $f$ is just such a function.
The terminology and notation used in this paper have been
introduced in the following articles
[7]
[5]
[6]
[9]
[1]
[3]
[8]
[2]
[4]
Contents (PDF format)
Bibliography
 [1]
Czeslaw Bylinski.
Binary operations.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Henryk Oryszczyszyn and Krzysztof Prazmowski.
Real functions spaces.
Journal of Formalized Mathematics,
2, 1990.
 [4]
Andrzej Trybulec.
Function domains and Fr\aenkel operator.
Journal of Formalized Mathematics,
2, 1990.
 [5]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [6]
Andrzej Trybulec and Czeslaw Bylinski.
Some properties of real numbers operations: min, max, square, and square root.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Stanislaw Zukowski.
Introduction to lattice theory.
Journal of Formalized Mathematics,
1, 1989.
Received May 22, 1990
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