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83
An Overview of the MIZAR Project
- UNIVERSITY OF TECHNOLOGY, BASTAD
, 1992
"... The Mizar project is a long-term effort aimed at developing software to support a working mathematician in preparing papers. A. Trybulec, the leader of the project, has designed a language for writing formal mathematics. The logical structure of the language is based on a natural deduction system ..."
Abstract
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Cited by 94 (1 self)
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The Mizar project is a long-term effort aimed at developing software to support a working mathematician in preparing papers. A. Trybulec, the leader of the project, has designed a language for writing formal mathematics. The logical structure of the language is based on a natural deduction system developed by Ja'skowski. The texts written in the language are called Mizar articles and are organized into a data base. The Tarski-Grothendieck set theory forms the basis of doing mathematics in Mizar. The implemented processor of the language checks the articles for logical consistency and correctness of references to other articles.
Brouwer fixed point theorem for disks on the plane.
- Formalized Mathematics,
, 2005
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Baire’s category theorem and some spaces generated from real normed space
- Formalized Mathematics
, 2006
"... Summary. As application of complete metric space, we proved a Baire’s category theorem. Then we defined some spaces generated from real normed space and discussed each of them. In the second section, we showed the equivalence of convergence and the continuity of a function. In other sections, we sho ..."
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Cited by 5 (4 self)
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Summary. As application of complete metric space, we proved a Baire’s category theorem. Then we defined some spaces generated from real normed space and discussed each of them. In the second section, we showed the equivalence of convergence and the continuity of a function. In other sections, we showed some topological properties of two spaces, which are topological space and linear topological space generated from real normed space.
Go-Board Theorem
, 1999
"... this paper. For simplicity, we adopt the following convention: p, p 1 , p 2 , q 1 , q 2 denote points of E ..."
Abstract
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Cited by 4 (1 self)
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this paper. For simplicity, we adopt the following convention: p, p 1 , p 2 , q 1 , q 2 denote points of E
A Theory of Matrices of Real Elements
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, 2006
"... Here, the concept of matrix of real elements is introduced. This is defined as a special case of the general concept of matrix of a field. For such a real matrix, the notions of addition, subtraction, scalar product are defined. For any real finite sequences, two transformations to matrices are in ..."
Abstract
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Cited by 4 (3 self)
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Here, the concept of matrix of real elements is introduced. This is defined as a special case of the general concept of matrix of a field. For such a real matrix, the notions of addition, subtraction, scalar product are defined. For any real finite sequences, two transformations to matrices are introduced. One of the matrices is of width 1, and the other is of length 1. By such transformations, two products of a matrix and a finite sequence are defined. Also the linearity of such product is shown.
