Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Partial Functions from a Domain to a Domain

Jaroslaw Kotowicz

Warsaw University, Bialystok

Supported by RPBP.III24.C8.
Summary.

The value of a partial function from a domain
to a domain and a inverse partial function are introduced. The value and inverse function
were defined in the article [1], but
new definitions are introduced.
The basic properties of the value, the inverse partial function,
the identity partial function, the composition of partial functions, the $1{}1$
partial function, the restriction of a partial function, the image,
the inverse image and the graph are proved.
Constant partial functions are introduced, too.
The terminology and notation used in this paper have been
introduced in the following articles
[5]
[7]
[8]
[9]
[1]
[2]
[4]
[3]
[6]
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.
Partial functions.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Andrzej Trybulec.
Binary operations applied to functions.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [6]
Wojciech A. Trybulec.
Pigeon hole principle.
Journal of Formalized Mathematics,
2, 1990.
 [7]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Edmund Woronowicz.
Relations defined on sets.
Journal of Formalized Mathematics,
1, 1989.
Received May 31, 1990
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