Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991 Association of Mizar Users

## Cartesian Product of Functions

Grzegorz Bancerek
Warsaw University, Bialystok

### Summary.

A supplement of [3] and [2], i.e. some useful and explanatory properties of the product and also the curried and uncurried functions are shown. Besides, the functions yielding functions are considered: two different products and other operation of such functions are introduced. Finally, two facts are presented: quasi-distributivity of the power of the set to other one w.r.t. the union ($X^{\biguplus_{x}f(x)} \approx \prod_{x}X^{f(x)}$) and quasi-distributivity of the product w.r.t. the raising to the power ($\prod_{x}{f(x)^X} \approx (\prod_{x}f(x))^X$).

#### MML Identifier: FUNCT_6

The terminology and notation used in this paper have been introduced in the following articles [16] [15] [9] [17] [18] [6] [4] [13] [7] [8] [5] [1] [14] [10] [11] [2] [12] [3]

#### Contents (PDF format)

1. Properties of Cartesian product
2. Curried and uncurried functions of some functions
3. Functions yielding functions
4. Cartesian product of functions with the same domain
5. Cartesian product of functions
6. Function yielding powers

#### Bibliography

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[3] Grzegorz Bancerek. K\"onig's theorem. Journal of Formalized Mathematics, 2, 1990.
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[13] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
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