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

## Auxiliary and Approximating Relations

Warsaw University, Bialystok

### Summary.

The aim of this paper is to formalize the second part of Chapter I Section 1 (1.9-1.19) in [10]. Definitions of Scott's auxiliary and approximating relations are introduced in this work. We showed that in a meet-continuous lattice, the way-below relation is the intersection of all approximating auxiliary relations (proposition (40) - compare 1.13 in [10, pp. 43-47]). By (41) a continuous lattice is a complete lattice in which $\ll$ is the smallest approximating auxiliary relation. The notions of the strong interpolation property and the interpolation property are also introduced.

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

#### MML Identifier: WAYBEL_4

The terminology and notation used in this paper have been introduced in the following articles [18] [9] [20] [16] [19] [17] [8] [2] [21] [23] [22] [6] [7] [3] [15] [1] [14] [11] [24] [12] [4] [13] [5]

#### Contents (PDF format)

1. Auxiliary Relations
2. Approximating Relations
3. Exercises

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