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- Freek Wiedijk
- TYPES
- 2003

We define the notion of formal proof sketch for the mathematical language Mizar. We show by examples that formal proof sketches are very close to informal mathematical proofs. We discuss some ways in which formal proof sketches might be used to improve mathematical proof assistants.

- Herman Geuvers, Freek Wiedijk, Jan Zwanenburg
- TYPES
- 2000

In the FTA project in Nijmegen we have formalized a constructive proof of the Fundamental Theorem of Algebra. In the formalization, we have first defined the (constructive) algebraic hierarchy of groups, rings, fields, etcetera. For the reals we have then defined the notion of real number structure, which is basically a Cauchy complete Archimedean orderedâ€¦ (More)

- Freek Wiedijk
- TYPES
- 2009

We present a version of the HOL Light system that supports undoing definitions in such a way that this does not compromise the soundness of the logic. In our system the code that keeps track of the constants that have been defined thus far has been moved out of the kernel. This means that the kernel now is purely functional. The changes to the system areâ€¦ (More)

- LuÃs Cruz-Filipe, Herman Geuvers, Freek Wiedijk
- MKM
- 2004

We present C-CoRN, the Constructive Coq Repository at Nijmegen. It consists of a library of constructive algebra and analysis, formalized in the theorem prover Coq. In this paper we explain the structure, the contents and the use of the library. Moreover we discuss the motivation and the (possible) applications of such a library.

- Herman Geuvers, Randy Pollack, Freek Wiedijk, Jan Zwanenburg
- J. Symb. Comput.
- 2002

We describe a framework of algebraic structures in the proof assistant Coq. We have developed this framework as part of the FTA project in Nijmegen, in which a constructive proof of the Fundamental Theorem of Algebra has been formalized in Coq. The algebraic hierarchy that is described here is both abstract and structured. Structures like groups and ringsâ€¦ (More)

We describe a framework for algebraic expressions for the proof assistant Coq. This framework has been developed as part of the FTA project in Nijmegen, in which a complete proof of the fundamental theorem of algebra has been formalized in Coq. The algebraic framework that is described here is both abstract and structured. We apply a combination of recordâ€¦ (More)

- Freek Wiedijk
- 2008

Let A, Bâ€² be non empty sets, let B be a non empty subset of B â€², let f be a function from A into B, and let x be an element of A. Then f(x) is an element of B. Next we state two propositions: (1) For every finite set A such that cardA â‰¥ 2 and for every element a of A there exists an element b of A such that b 6= a. (2) Let A be a finite set. Suppose cardA â‰¥â€¦ (More)

- Markus Wenzel, Freek Wiedijk
- Journal of Automated Reasoning
- 2002

The mathematical proof checker Mizar by Andrzej Trybulec uses a proof input language that is much more readable than the input languages of most other proof assistants. This system also differs in many other respects from most current systems. John Harrison has shown that one can have a Mizar mode on top of a tactical prover, allowing one to combine aâ€¦ (More)

- Freek Wiedijk
- 1999

This note presents an introduction to the Mizar system, followed by a brief comparison between Mizar and Coq. Appended are a Mizar grammar and an annotated example of a complete Mizar article. 1 What It Is Mizar is a system for representing mathematical proof in a computer such that a program can check the correctness. It has been developed by Andrzejâ€¦ (More)

This article describes the system ProofWeb that is currently being developed in Nijmegen and Amsterdam for teaching logic to undergraduate computer science students. This system is based on the higher order proof assistant Coq, and is made available to the students through an interactive web interface. Part of this system will be a large database of logicâ€¦ (More)