Volume 14, 2002

University of Bialystok

Copyright (c) 2002 Association of Mizar Users

**Grzegorz Bancerek**- Bialystok Technical University
**Shin'nosuke Yamaguchi**- Shinshu University, Nagano
**Yasunari Shidama**- Shinshu University, Nagano

- In this article we continue the investigations from [10] and [2] of verification of a circuit design. We concentrate on the combination of multi cell circuits from given cells (circuit modules). Namely, we formalize a design of the form \\ \input CIRCCMB2.PIC and prove its stability. The formalization proposed consists in a series of schemes which allow to define multi cells circuits and prove their properties. Our goal is to achive mathematical formalization which will allow to verify designs of real circuits.

- One Gate Circuits
- Defining Multi Cell Circuit Structures
- Input of Multi Cell Circuit
- Defining Multi Cell Circuits
- Stability of Multi Cell Circuit

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Grzegorz Bancerek.
The fundamental properties of natural numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [2]
Grzegorz Bancerek and Yatsuka Nakamura.
Full adder circuit. Part I.
*Journal of Formalized Mathematics*, 7, 1995. - [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]
Czeslaw Bylinski.
Finite sequences and tuples of elements of a non-empty sets.
*Journal of Formalized Mathematics*, 2, 1990. - [7]
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. - [8]
Agata Darmochwal.
Finite sets.
*Journal of Formalized Mathematics*, 1, 1989. - [9]
Jaroslaw Kotowicz.
The limit of a real function at infinity.
*Journal of Formalized Mathematics*, 2, 1990. - [10]
Yatsuka Nakamura and Grzegorz Bancerek.
Combining of circuits.
*Journal of Formalized Mathematics*, 7, 1995. - [11]
Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto.
Introduction to circuits, I.
*Journal of Formalized Mathematics*, 6, 1994. - [12]
Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto.
Preliminaries to circuits, II.
*Journal of Formalized Mathematics*, 6, 1994. - [13]
Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto.
Introduction to circuits, II.
*Journal of Formalized Mathematics*, 7, 1995. - [14]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [15]
Andrzej Trybulec.
Many-sorted sets.
*Journal of Formalized Mathematics*, 5, 1993. - [16]
Andrzej Trybulec.
Many sorted algebras.
*Journal of Formalized Mathematics*, 6, 1994. - [17]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [18]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

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