{"id":29101839,"url":"https://github.com/tyilo/nat2","last_synced_at":"2026-02-03T16:35:36.467Z","repository":{"id":273952331,"uuid":"921424788","full_name":"tyilo/nat2","owner":"tyilo","description":null,"archived":false,"fork":false,"pushed_at":"2025-01-23T23:32:12.000Z","size":0,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"master","last_synced_at":"2025-01-24T00:24:13.454Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":null,"language":"Lean","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/tyilo.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":"2025-01-23T23:25:32.000Z","updated_at":"2025-01-23T23:32:16.000Z","dependencies_parsed_at":"2025-01-24T00:34:18.715Z","dependency_job_id":null,"html_url":"https://github.com/tyilo/nat2","commit_stats":null,"previous_names":["tyilo/nat2"],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/tyilo/nat2","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/tyilo%2Fnat2","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/tyilo%2Fnat2/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/tyilo%2Fnat2/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/tyilo%2Fnat2/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/tyilo","download_url":"https://codeload.github.com/tyilo/nat2/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/tyilo%2Fnat2/sbom","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":262497276,"owners_count":23320299,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","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":[],"created_at":"2025-06-28T21:08:32.727Z","updated_at":"2026-02-03T16:35:36.403Z","avatar_url":"https://github.com/tyilo.png","language":"Lean","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Nat2\n\nDo the natural numbers start from 0 or 1?\n\nWell, why not make everyone angry and make them start from 2 instead?\n\nThis repository contains several basic [Lean 4](https://lean-lang.org/) theorems for the type `Nat2` defined as:\n\n```lean\ninductive Nat2 where\n  | two : Nat2\n  | succ : Nat2 → Nat2\n```\n\nAddition and multiplication are defined as follows:\n\n```lean\ndef add : Nat2 → Nat2 → Nat2\n  | a, two =\u003e succ (succ a)\n  | a, succ b =\u003e succ (add a b)\n\ndef mul: Nat2 → Nat2 → Nat2\n  | a, two =\u003e add a a\n  | a, succ b =\u003e add (mul a b) a\n```\n\nThe base cases for these are more \"interesting\" than the usual making proofs harder.\n\nThe theorems are inspired by the [Natural Number Game](https://adam.math.hhu.de/#/g/leanprover-community/nng4). **Beware:** The authors of this game has not seen the light and thus uses natural numbers starting from 0.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Ftyilo%2Fnat2","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Ftyilo%2Fnat2","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Ftyilo%2Fnat2/lists"}