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.III-24.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 non-empty set) to $\Bbb R$, $f$ is just such a function.

MML Identifier: REAL_LAT

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

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