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

## Binary Operations

Czeslaw Bylinski
Warsaw University, Bialystok
Supported by RPBP.III-24.C1.

### Summary.

In this paper we define binary and unary operations on domains. We also define the following predicates concerning the operations: \$\dots\$ is commutative, \$\dots\$ is associative, \$\dots\$ is the unity of \$\dots\$, and \$\dots\$ is distributive wrt \$\dots\$. A number of schemes useful in justifying the existence of the operations are proved.

#### MML Identifier: BINOP_1

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

Contents (PDF format)

#### Bibliography

[1] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[2] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[3] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[4] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[5] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[6] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.