Semigroup Operations on Finite Subsets

Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990 Association of Mizar Users

Semigroup Operations on Finite Subsets

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

Summary.

A continuation of [10]. The propositions and theorems proved in [10] are extended to finite sequences. Several additional theorems related to semigroup operations of functions not included in [10] are proved. The special notation for operations on finite sequences is introduced.

MML Identifier: SETWOP_2

The terminology and notation used in this paper have been introduced in the following articles [11] [15] [12] [1] [16] [17] [4] [2] [13] [6] [5] [3] [9] [10] [8] [7] [14]

Contents (PDF format)

Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.

[2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.

[3] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.

[4] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[5] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.

[6] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.

[7] Czeslaw Bylinski. Binary operations applied to finite sequences. Journal of Formalized Mathematics, 2, 1990.

[8] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.

[9] Andrzej Trybulec. Binary operations applied to functions. Journal of Formalized Mathematics, 1, 1989.

[10] Andrzej Trybulec. Semilattice operations on finite subsets. Journal of Formalized Mathematics, 1, 1989.

[11] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[12] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.

[13] Andrzej Trybulec and Agata Darmochwal. Boolean domains. Journal of Formalized Mathematics, 1, 1989.

[14] Wojciech A. Trybulec. Binary operations on finite sequences. Journal of Formalized Mathematics, 2, 1990.

[15] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

[16] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[17] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

Received May 4, 1990

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