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

## Function Domains and Fr\aenkel Operator

Andrzej Trybulec
Warsaw University, Bialystok
Supported by RPBP.III-24.C1.

### Summary.

We deal with a non-empty set of functions and a non-empty set of functions from a set \$A\$ to a non-empty set \$B\$. In the case when \$B\$ is a non-empty set, \$B^A\$ is redefined. It yields a non-empty set of functions from \$A\$ to \$B\$. An element of such a set is redefined as a function from \$A\$ to \$B\$. Some theorems concerning these concepts are proved, as well as a number of schemes dealing with infinity and the Axiom of Choice. The article contains a number of schemes allowing for simple logical transformations related to terms constructed with the Fr{\ae}nkel Operator.

#### MML Identifier: FRAENKEL

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

Contents (PDF format)

#### 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] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[5] Andrzej Trybulec. Semilattice operations on finite subsets. Journal of Formalized Mathematics, 1, 1989.
[6] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[7] Andrzej Trybulec and Agata Darmochwal. Boolean domains. Journal of Formalized Mathematics, 1, 1989.
[8] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[9] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.