Volume 5, 1993

University of Bialystok

Copyright (c) 1993 Association of Mizar Users

**Andrzej Trybulec**- Warsaw University, Bialystok
**Yatsuka Nakamura**- Shinshu University, Nagano

- We prove some results on {\bf SCM} needed for the proof of the correctness of Euclid's algorithm. We introduce the following concepts: \begin{itemize} \item[-] starting finite partial state (Start-At$(l)$), then assigns to the instruction counter an instruction location (and consists only of this assignment), \item[-] programmed finite partial state, that consists of the instructions (to be more precise, a finite partial state with the domain consisting of instruction locations). \end{itemize} We define for a total state $s$ what it means that $s$ starts at $l$ (the value of the instruction counter in the state $s$ is $l$) and $s$ halts at $l$ (the halt instruction is assigned to $l$ in the state $s$). Similar notions are defined for finite partial states.

- A small concrete machine
- Users guide
- Preliminaries
- Some Remarks on AMI-Struct
- Instruction Locations and Data Locations
- Halt Instruction

- [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]
Grzegorz Bancerek.
Sequences of ordinal numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [4]
Grzegorz Bancerek.
K\"onig's theorem.
*Journal of Formalized Mathematics*, 2, 1990. - [5]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
*Journal of Formalized Mathematics*, 1, 1989. - [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]
Czeslaw Bylinski.
A classical first order language.
*Journal of Formalized Mathematics*, 2, 1990. - [9]
Czeslaw Bylinski.
The modification of a function by a function and the iteration of the composition of a function.
*Journal of Formalized Mathematics*, 2, 1990. - [10]
Agata Darmochwal.
Finite sets.
*Journal of Formalized Mathematics*, 1, 1989. - [11]
Yatsuka Nakamura and Andrzej Trybulec.
A mathematical model of CPU.
*Journal of Formalized Mathematics*, 4, 1992. - [12]
Yatsuka Nakamura and Andrzej Trybulec.
On a mathematical model of programs.
*Journal of Formalized Mathematics*, 4, 1992. - [13]
Dariusz Surowik.
Cyclic groups and some of their properties --- part I.
*Journal of Formalized Mathematics*, 3, 1991. - [14]
Andrzej Trybulec.
Enumerated sets.
*Journal of Formalized Mathematics*, 1, 1989. - [15]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [16]
Andrzej Trybulec.
Tuples, projections and Cartesian products.
*Journal of Formalized Mathematics*, 1, 1989. - [17]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [18]
Michal J. Trybulec.
Integers.
*Journal of Formalized Mathematics*, 2, 1990. - [19]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [20]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

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