{"id":32721743,"url":"https://github.com/mdbrnowski/lean-doodles","last_synced_at":"2026-06-29T12:31:29.431Z","repository":{"id":303441900,"uuid":"1011433593","full_name":"mdbrnowski/lean-doodles","owner":"mdbrnowski","description":"Doodles in Lean.","archived":false,"fork":false,"pushed_at":"2026-05-28T15:39:08.000Z","size":34,"stargazers_count":1,"open_issues_count":0,"forks_count":0,"subscribers_count":0,"default_branch":"main","last_synced_at":"2026-06-05T00:13:31.237Z","etag":null,"topics":["formal-verification","interactive-theorem-proving","lean4"],"latest_commit_sha":null,"homepage":"","language":"Lean","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"apache-2.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/mdbrnowski.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","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,"zenodo":null,"notice":null,"maintainers":null,"copyright":null,"agents":null,"dco":null,"cla":null}},"created_at":"2025-06-30T20:10:02.000Z","updated_at":"2026-05-28T15:39:13.000Z","dependencies_parsed_at":"2025-07-07T17:33:20.613Z","dependency_job_id":"7470fdc4-0211-4c83-94bb-1adb0575045a","html_url":"https://github.com/mdbrnowski/lean-doodles","commit_stats":null,"previous_names":["mdbrnowski/lean-doodles"],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/mdbrnowski/lean-doodles","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mdbrnowski%2Flean-doodles","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mdbrnowski%2Flean-doodles/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mdbrnowski%2Flean-doodles/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mdbrnowski%2Flean-doodles/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/mdbrnowski","download_url":"https://codeload.github.com/mdbrnowski/lean-doodles/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mdbrnowski%2Flean-doodles/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":34927675,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-05-26T15:22:16.424Z","status":"online","status_checked_at":"2026-06-29T02:00:05.398Z","response_time":58,"last_error":null,"robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":true,"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":["formal-verification","interactive-theorem-proving","lean4"],"created_at":"2025-11-02T21:01:08.953Z","updated_at":"2026-06-29T12:31:29.422Z","avatar_url":"https://github.com/mdbrnowski.png","language":"Lean","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Lean Doodles\n\nCasual notes in [Lean](https://lean-lang.org): proofs of various theorems not tied to any specific project.\n\n## Finite Integral Domain\n\n[`FiniteIntegralDomain.lean`](/LeanDoodles/FiniteIntegralDomain.lean)\n\nEvery finite integral domain is a field.\n\n## May's Theorem\n\n[`MaysTheorem.lean`](/LeanDoodles/MaysTheorem.lean)\n\nMay's theorem states that majority rule is the only reasonable (near decisive, anonymous, neutral, and monotone) voting system for two candidates.\n\nYou can learn more about it on [my blog](https://dobranow.ski/posts/mays-theorem) or [Wikipedia](https://en.wikipedia.org/wiki/May%27s_theorem).\n\n## Number Pairs\n\n[`NumberPairs.lean`](/LeanDoodles/NumberPairs.lean)\n\nA *Number Pair* for a given $d \\in \\mathbb{N}$ is a pair of numbers $(a, b)$ such that $b - a = d$ and the sum of the digits of $a$ is equal to the sum of the digits of $b$.\n\nThis module contains a constructive proof that a Number Pair exists if and only if $d$ is divisible by $9$.\n\nInspired by the Wincent DragonByte 2025, [problem N](https://www.wincentdragonbyte.com/static/qual2025/N_statement.html) from the qualification round.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmdbrnowski%2Flean-doodles","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fmdbrnowski%2Flean-doodles","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmdbrnowski%2Flean-doodles/lists"}