Volume 3, 1991

University of Bialystok

Copyright (c) 1991 Association of Mizar Users

**Jaroslaw Kotowicz**- Warsaw University, Bialystok
**Konrad Raczkowski**- Warsaw University, Bialystok

- A continuation of [16]. We prove equivalent definition of the derivative of the real function at the point and theorems about derivative of composite functions, inverse function and derivative of quotient of two functions. At the beginning of the paper a few facts which rather belong to [8], [9] and [7] are proved.

Contents (PDF format)

- [1]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [2]
Grzegorz Bancerek.
The ordinal numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [3]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [4]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [5]
Czeslaw Bylinski.
Partial functions.
*Journal of Formalized Mathematics*, 1, 1989. - [6]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [7]
Jaroslaw Kotowicz.
Convergent real sequences. Upper and lower bound of sets of real numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [8]
Jaroslaw Kotowicz.
Convergent sequences and the limit of sequences.
*Journal of Formalized Mathematics*, 1, 1989. - [9]
Jaroslaw Kotowicz.
Monotone real sequences. Subsequences.
*Journal of Formalized Mathematics*, 1, 1989. - [10]
Jaroslaw Kotowicz.
Real sequences and basic operations on them.
*Journal of Formalized Mathematics*, 1, 1989. - [11]
Jaroslaw Kotowicz.
The limit of a real function at infinity.
*Journal of Formalized Mathematics*, 2, 1990. - [12]
Jaroslaw Kotowicz.
Partial functions from a domain to a domain.
*Journal of Formalized Mathematics*, 2, 1990. - [13]
Jaroslaw Kotowicz.
Partial functions from a domain to the set of real numbers.
*Journal of Formalized Mathematics*, 2, 1990. - [14]
Jaroslaw Kotowicz.
Properties of real functions.
*Journal of Formalized Mathematics*, 2, 1990. - [15]
Jan Popiolek.
Some properties of functions modul and signum.
*Journal of Formalized Mathematics*, 1, 1989. - [16]
Konrad Raczkowski and Pawel Sadowski.
Real function differentiability.
*Journal of Formalized Mathematics*, 2, 1990. - [17]
Konrad Raczkowski and Pawel Sadowski.
Topological properties of subsets in real numbers.
*Journal of Formalized Mathematics*, 2, 1990. - [18]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [19]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [20]
Andrzej Trybulec and Czeslaw Bylinski.
Some properties of real numbers operations: min, max, square, and square root.
*Journal of Formalized Mathematics*, 1, 1989. - [21]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [22]
Edmund Woronowicz.
Relations defined on sets.
*Journal of Formalized Mathematics*, 1, 1989.

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