https://github.com/smimram/div2

An Agda formalization of "division by 2" in classical ZF without choice.
https://github.com/smimram/div2

agda axiom-of-choice classical-logic division homotopy-type-theory

Last synced: 4 days ago
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An Agda formalization of "division by 2" in classical ZF without choice.

• Host: GitHub
• URL: https://github.com/smimram/div2
• Owner: smimram
• Created: 2022-01-19T08:37:09.000Z (almost 3 years ago)
• Default Branch: main
• Last Pushed: 2023-02-16T13:25:42.000Z (almost 2 years ago)
• Last Synced: 2024-10-31T02:05:32.148Z (about 2 months ago)
• Topics: agda, axiom-of-choice, classical-logic, division, homotopy-type-theory
• Language: Agda
• Homepage: https://smimram.github.io/div2/
• Size: 3.05 MB
• Stars: 2
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
Division by 2 in homotopy type theory

=====================================

This is a formalization in cubical [Agda](https://wiki.portal.chalmers.se/agda/)

of division by two in type theory, as [detailed in this

article](http://www.lix.polytechnique.fr/Labo/Samuel.Mimram/docs/mimram_div2.pdf).

The main result here is that

> `A × 2 ≃ B × 2`

implies

> `A ≃ B`

where `A` and `B` are arbitrary types and `2` is a type with two elements

(e.g. the booleans).

The proof is based on the explanation of given in Doyle and Conway's _[Division

by three](https://arxiv.org/abs/math/0605779)_, and you can [nicely read the

Agda code here](https://smimram.github.io/div2/).