Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Binary Operations on Finite Sequences

Wojciech A. Trybulec

Warsaw University

Supported by RPBP.III24.C1.
Summary.

We generalize the semigroup operation on finite sequences
introduced in [8] for binary operations that have a unity
or for nonempty finite sequences.
The terminology and notation used in this paper have been
introduced in the following articles
[11]
[15]
[12]
[3]
[6]
[2]
[14]
[16]
[17]
[4]
[13]
[10]
[5]
[1]
[9]
[7]
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.
Finite sequences and tuples of elements of a nonempty sets.
Journal of Formalized Mathematics,
2, 1990.
 [7]
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.
 [8]
Czeslaw Bylinski.
Semigroup operations on finite subsets.
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.
Pigeon hole principle.
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 August 10, 1990
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