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

## Midpoint algebras

Michal Muzalewski
Warsaw University, Bialystok
Supported by RPBP.III-24.C6.

### Summary.

In this article basic properties of midpoint algebras are proved. We define a congruence relation $\equiv$ on bound vectors and free vectors as the equivalence classes of $\equiv$.

#### MML Identifier: MIDSP_1

The terminology and notation used in this paper have been introduced in the following articles [5] [4] [8] [1] [7] [6] [2] [3]

Contents (PDF format)

#### Bibliography

[1] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.
[2] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[3] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[5] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[6] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[7] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.
[8] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.