Volume 7, 1995

University of Bialystok

Copyright (c) 1995 Association of Mizar Users

**Artur Kornilowicz**- Institute of Mathematics, Warsaw University, Bialystok

- The aim of the article is to prove the fact that if extensions of mappings on generator set are equal then these mappings are equal. The article contains the properties of epimorphisms and monomorphisms between Many Sorted Algebras.

- Preliminaries
- Facts about Many Sorted Functions
- dom's and rng's of Many Sorted Functions
- Other properties of ``onto" and ``1-1"
- Extensions of Mappings on Generator Set

- [1]
Grzegorz Bancerek.
K\"onig's theorem.
*Journal of Formalized Mathematics*, 2, 1990. - [2]
Grzegorz Bancerek.
Cartesian product of functions.
*Journal of Formalized Mathematics*, 3, 1991. - [3]
Grzegorz Bancerek.
Joining of decorated trees.
*Journal of Formalized Mathematics*, 5, 1993. - [4]
Grzegorz Bancerek and Piotr Rudnicki.
On defining functions on trees.
*Journal of Formalized Mathematics*, 5, 1993. - [5]
Ewa Burakowska.
Subalgebras of many sorted algebra. Lattice of subalgebras.
*Journal of Formalized Mathematics*, 6, 1994. - [6]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [7]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [8]
Patricia L. Carlson and Grzegorz Bancerek.
Context-free grammar --- part I.
*Journal of Formalized Mathematics*, 4, 1992. - [9]
Artur Kornilowicz.
On the group of automorphisms of universal algebra and many sorted algebra.
*Journal of Formalized Mathematics*, 6, 1994. - [10]
Malgorzata Korolkiewicz.
Homomorphisms of many sorted algebras.
*Journal of Formalized Mathematics*, 6, 1994. - [11]
Beata Madras.
Product of family of universal algebras.
*Journal of Formalized Mathematics*, 5, 1993. - [12]
Beata Perkowska.
Free many sorted universal algebra.
*Journal of Formalized Mathematics*, 6, 1994. - [13]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [14]
Andrzej Trybulec.
Many-sorted sets.
*Journal of Formalized Mathematics*, 5, 1993. - [15]
Andrzej Trybulec.
Many sorted algebras.
*Journal of Formalized Mathematics*, 6, 1994. - [16]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [17]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [18]
Edmund Woronowicz.
Relations defined on sets.
*Journal of Formalized Mathematics*, 1, 1989.

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