Journal of Formalized Mathematics
Volume 1, 1989
University of Bialystok
Copyright (c) 1989 Association of Mizar Users

## Partially Ordered Sets

Wojciech A. Trybulec
Warsaw University
Supported by RPBP.III-24.C1.

### Summary.

In the beginning of this article we define the choice function of a non-empty set family that does not contain $\emptyset$ as introduced in [6, pages 88-89]. We define order of a set as a relation being reflexive, antisymmetric and transitive in the set, partially ordered set as structure non-empty set and order of the set, chains, lower and upper cone of a subset, initial segments of element and subset of partially ordered set. Some theorems that belong rather to [5] or [12] are proved.

#### MML Identifier: ORDERS_1

The terminology and notation used in this paper have been introduced in the following articles [8] [5] [9] [10] [12] [2] [11] [4] [3] [1] [7]

Contents (PDF format)

#### Bibliography

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