https://github.com/coq-community/dedekind-reals

A formalization of the Dedekind real numbers in Coq [maintainer=@andrejbauer]
https://github.com/coq-community/dedekind-reals

coq dedekind-reals real-analysis

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A formalization of the Dedekind real numbers in Coq [maintainer=@andrejbauer]

• Host: GitHub
• URL: https://github.com/coq-community/dedekind-reals
• Owner: coq-community
• License: mit
• Created: 2013-10-14T11:54:08.000Z (over 11 years ago)
• Default Branch: master
• Last Pushed: 2024-07-14T19:55:01.000Z (6 months ago)
• Last Synced: 2024-12-05T21:33:43.213Z (about 2 months ago)
• Topics: coq, dedekind-reals, real-analysis
• Language: Coq
• Homepage:
• Size: 182 KB
• Stars: 43
• Watchers: 9
• Forks: 6
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        

# Dedekind Reals

[![Docker CI][docker-action-shield]][docker-action-link]

[![Contributing][contributing-shield]][contributing-link]

[![Code of Conduct][conduct-shield]][conduct-link]

[![Zulip][zulip-shield]][zulip-link]

[docker-action-shield]: https://github.com/coq-community/dedekind-reals/actions/workflows/docker-action.yml/badge.svg?branch=master

[docker-action-link]: https://github.com/coq-community/dedekind-reals/actions/workflows/docker-action.yml

[contributing-shield]: https://img.shields.io/badge/contributions-welcome-%23f7931e.svg

[contributing-link]: https://github.com/coq-community/manifesto/blob/master/CONTRIBUTING.md

[conduct-shield]: https://img.shields.io/badge/%E2%9D%A4-code%20of%20conduct-%23f15a24.svg

[conduct-link]: https://github.com/coq-community/manifesto/blob/master/CODE_OF_CONDUCT.md

[zulip-shield]: https://img.shields.io/badge/chat-on%20zulip-%23c1272d.svg

[zulip-link]: https://coq.zulipchat.com/#narrow/stream/237663-coq-community-devs.20.26.20users

A formalization of Dedekind reals numbers that started as a

student project at the University of Ljubljana under the supervision

of Andrej Bauer, and was brought to the present state by Vincent Semeria.

At this point the formalization of the field of reals is finished.

There are still several unfinished theorems concering the lattice-theoretic

structure of the reals (search for `todo` in the Coq files). We would be

delighted by contributions that would bring the formalization

closer to completion.

## Meta

- Author(s):

  - Andrej Bauer

  - Vincent Semeria

- Coq-community maintainer(s):

  - Andrej Bauer ([**@andrejbauer**](https://github.com/andrejbauer))

- License: [MIT License](LICENSE)

- Compatible Coq versions: 8.16 and later

- Additional dependencies: none

- Coq namespace: `DedekindReals`

- Related publication(s): none

## Building instructions

To build and install, do:

```shell

git clone https://github.com/coq-community/dedekind-reals.git

cd dedekind-reals

make   # or make -j  

make install

```

## Structure of the modules

- `MiscLemmas`: various lemmas about rational numbers

- `Cut`: definition of Dedekind cuts and several other basic notions

- `Additive`: Additive structure of the reals

- `Multiplication` : Multiplicative structure of the relas

- `Order` : The order on the reals

- `Archimedean`: the proof that the reals satisfy the archimedean property

- `Completeness`: the reals are Dedekind-complete