{"id":18056960,"url":"https://github.com/smimram/div2","last_synced_at":"2026-03-19T03:04:40.348Z","repository":{"id":65312974,"uuid":"449610753","full_name":"smimram/div2","owner":"smimram","description":"An Agda formalization of \"division by 2\" in classical ZF without choice.","archived":false,"fork":false,"pushed_at":"2023-02-16T13:25:42.000Z","size":3202,"stargazers_count":3,"open_issues_count":0,"forks_count":0,"subscribers_count":2,"default_branch":"main","last_synced_at":"2025-06-08T14:43:00.751Z","etag":null,"topics":["agda","axiom-of-choice","classical-logic","division","homotopy-type-theory"],"latest_commit_sha":null,"homepage":"https://smimram.github.io/div2/","language":"Agda","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/smimram.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2022-01-19T08:37:09.000Z","updated_at":"2025-06-06T05:56:09.000Z","dependencies_parsed_at":"2025-02-10T21:10:19.933Z","dependency_job_id":null,"html_url":"https://github.com/smimram/div2","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/smimram/div2","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/smimram%2Fdiv2","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/smimram%2Fdiv2/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/smimram%2Fdiv2/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/smimram%2Fdiv2/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/smimram","download_url":"https://codeload.github.com/smimram/div2/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/smimram%2Fdiv2/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":28900336,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-01-30T03:36:35.398Z","status":"ssl_error","status_checked_at":"2026-01-30T03:36:34.949Z","response_time":66,"last_error":"SSL_read: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["agda","axiom-of-choice","classical-logic","division","homotopy-type-theory"],"created_at":"2024-10-31T02:05:33.508Z","updated_at":"2026-01-30T03:52:07.500Z","avatar_url":"https://github.com/smimram.png","language":"Agda","funding_links":[],"categories":[],"sub_categories":[],"readme":"Division by 2 in homotopy type theory\n=====================================\n\nThis is a formalization in cubical [Agda](https://wiki.portal.chalmers.se/agda/)\nof division by two in type theory, as [detailed in this\narticle](http://www.lix.polytechnique.fr/Labo/Samuel.Mimram/docs/mimram_div2.pdf).\n\nThe main result here is that\n\n\u003e `A × 2 ≃ B × 2`\n\nimplies\n\n\u003e `A ≃ B`\n\nwhere `A` and `B` are arbitrary types and `2` is a type with two elements\n(e.g. the booleans).\n\nThe proof is based on the explanation of given in Doyle and Conway's _[Division\nby three](https://arxiv.org/abs/math/0605779)_, and you can [nicely read the\nAgda code here](https://smimram.github.io/div2/).\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fsmimram%2Fdiv2","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fsmimram%2Fdiv2","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fsmimram%2Fdiv2/lists"}