Journal of Formalized Mathematics
Volume 12, 2000
University of Bialystok
Copyright (c) 2000 Association of Mizar Users

The Canonical Formulae


Andrzej Trybulec
University of Bialystok

MML Identifier: HILBERT3

The terminology and notation used in this paper have been introduced in the following articles [18] [9] [25] [23] [24] [26] [6] [4] [2] [17] [8] [7] [5] [19] [10] [1] [3] [13] [14] [20] [21] [15] [12] [16] [11] [22]

Contents (PDF format)

  1. Preliminaries
  2. The Cartesian Product of Functions and the Frege Function
  3. About Permutations
  4. Set Valuations
  5. Permuting Set Valuations
  6. Canonical Formulae
  7. Pseudo-Canonical Formulae

Bibliography

[1] Grzegorz Bancerek. Curried and uncurried functions. Journal of Formalized Mathematics, 2, 1990.
[2] Grzegorz Bancerek. K\"onig's theorem. Journal of Formalized Mathematics, 2, 1990.
[3] Grzegorz Bancerek. Cartesian product of functions. Journal of Formalized Mathematics, 3, 1991.
[4] Jozef Bialas. Group and field definitions. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Basic functions and operations on functions. 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. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[9] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[10] 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.
[11] Adam Grabowski. Hilbert positive propositional calculus. Journal of Formalized Mathematics, 11, 1999.
[12] Malgorzata Korolkiewicz. Homomorphisms of many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[13] Beata Madras. Product of family of universal algebras. Journal of Formalized Mathematics, 5, 1993.
[14] Beata Madras. Products of many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[15] Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto. Preliminaries to circuits, I. Journal of Formalized Mathematics, 6, 1994.
[16] Piotr Rudnicki and Andrzej Trybulec. Fixpoints in complete lattices. Journal of Formalized Mathematics, 8, 1996.
[17] Piotr Rudnicki and Andrzej Trybulec. Abian's fixed point theorem. Journal of Formalized Mathematics, 9, 1997.
[18] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[19] Andrzej Trybulec. Function domains and Fr\aenkel operator. Journal of Formalized Mathematics, 2, 1990.
[20] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[21] Andrzej Trybulec. Many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[22] Andrzej Trybulec. Defining by structural induction in the positive propositional language. Journal of Formalized Mathematics, 11, 1999.
[23] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[24] Michal J. Trybulec. Integers. Journal of Formalized Mathematics, 2, 1990.
[25] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[26] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received July 4, 2000

[ Download a postscript version, MML identifier index, Mizar home page]