Journal of Formalized Mathematics
Volume 7, 1995
University of Bialystok
Copyright (c) 1995 Association of Mizar Users

Definitions and Basic Properties of Boolean and Union of Many Sorted Sets


Artur Kornilowicz
Institute of Mathematics, Warsaw University, Bialystok

Summary.

In the first part of this article I have proved theorems about boolean of many sorted sets which are corresponded to theorems about boolean of sets, whereas the second part of this article contains propositions about union of many sorted sets. Boolean as well as union of many sorted sets are defined as boolean and union on every sorts.

MML Identifier: MBOOLEAN

The terminology and notation used in this paper have been introduced in the following articles [9] [3] [11] [1] [2] [5] [4] [10] [7] [6] [8]

Contents (PDF format)

  1. Boolean of Many Sorted Sets
  2. Union of Many Sorted Sets

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] Czeslaw Bylinski. The modification of a function by a function and the iteration of the composition of a function. Journal of Formalized Mathematics, 2, 1990.
[5] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[6] Artur Kornilowicz. On the group of automorphisms of universal algebra and many sorted algebra. Journal of Formalized Mathematics, 6, 1994.
[7] Beata Madras. Products of many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[8] Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto. Preliminaries to circuits, I. Journal of Formalized Mathematics, 6, 1994.
[9] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[10] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[11] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received April 27, 1995


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