Journal of Formalized Mathematics
Volume 1, 1989
University of Bialystok
Copyright (c) 1989
Association of Mizar Users
Partial Functions

Czeslaw Bylinski

Warsaw University, Bialystok

Supported by RPBP.III24.C1.
Summary.

In the article we define partial functions.
We also define the following notions related to partial functions
and functions themselves:
the empty function, the restriction of a function to a partial function from a set
into a set, the set of all partial functions from a set into a set,
the total functions, the relation of tolerance of two functions and
the set of all total functions which are tolerated by a partial function.
Some simple propositions related to the introduced notions are proved.
In the beginning of this article we prove some auxiliary theorems
and schemes related to the articles: [1] and [2].
The terminology and notation used in this paper have been
introduced in the following articles
[4]
[3]
[5]
[6]
[7]
[1]

Main Part

Appendix
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]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [5]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Edmund Woronowicz.
Relations defined on sets.
Journal of Formalized Mathematics,
1, 1989.
Received September 18, 1989
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