Journal of Formalized Mathematics
Volume 8, 1996
University of Bialystok
Copyright (c) 1996 Association of Mizar Users

Miscellaneous Facts about Functions


Grzegorz Bancerek
Institute of Mathematics, Polish Academy of Sciences
Andrzej Trybulec
Warsaw University, Bialystok

MML Identifier: FUNCT_7

The terminology and notation used in this paper have been introduced in the following articles [21] [10] [25] [23] [2] [17] [22] [20] [1] [16] [26] [7] [27] [6] [5] [15] [11] [14] [9] [19] [8] [12] [13] [3] [24] [18] [4]

Contents (PDF format)

  1. Preliminaries
  2. Some useful schemes
  3. Some auxiliary concepts
  4. On the composition of a finite sequence of functions

Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Grzegorz Bancerek. Curried and uncurried functions. Journal of Formalized Mathematics, 2, 1990.
[4] Grzegorz Bancerek. Reduction relations. Journal of Formalized Mathematics, 7, 1995.
[5] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[9] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[10] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[11] Czeslaw Bylinski. A classical first order language. Journal of Formalized Mathematics, 2, 1990.
[12] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[13] 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.
[14] Czeslaw Bylinski. Cartesian categories. Journal of Formalized Mathematics, 4, 1992.
[15] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[16] Beata Madras. Product of family of universal algebras. Journal of Formalized Mathematics, 5, 1993.
[17] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[18] Dariusz Surowik. Cyclic groups and some of their properties --- part I. Journal of Formalized Mathematics, 3, 1991.
[19] Andrzej Trybulec. Binary operations applied to functions. Journal of Formalized Mathematics, 1, 1989.
[20] Andrzej Trybulec. Domains and their Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[21] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[22] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[23] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[24] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[25] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[26] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[27] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

Received January 12, 1996

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