{ "challenge": { "bytes": 2027, "canonical_olean_sha256": "4db0185320ba018c937874ef03bb5044c585717fdd0ef23f133835dbfa71a500", "dependencies": [ { "provenance": "allowlisted", "repository": "leanprover-community/mathlib4" } ], "direct_imports": [ "Mathlib.Algebra.Polynomial.Basic", "Mathlib.RingTheory.Localization.Basic", "Mathlib.RingTheory.Noetherian.Defs", "Mathlib.RingTheory.UniqueFactorizationDomain.Defs" ], "lines": 59, "module": "Challenge", "path": "Challenge.lean", "sha256": "76dd7103a3fc14ea71e25a6f494930dd56217971e2ed83cb6f89b66680181d25", "transitive_source_count": 5, "trust_level": "high", "untrusted_sources": [] }, "checked_at": "2026-08-27T23:55:51Z", "classification": { "arxiv": [ { "code": "math.AC", "name": "Commutative Algebra" }, { "code": "cs.LO", "name": "Logic in Computer Science" } ], "msc2020": [ { "code": "13A05", "name": "Divisibility and factorizations in commutative rings" }, { "code": "13B30", "name": "Rings of fractions and localization for commutative rings" }, { "code": "03B35", "name": "Mechanization of proofs and logical operations" } ] }, "comparator": { "challenge_module": "Challenge", "definition_names": [], "path": "comparator.json", "permitted_axioms": [ "propext", "Quot.sound", "Classical.choice" ], "sha256": "1f3f57f1e001e00a323bdb0c5376757ce5cca460d9b78c012fb6a72fe72385ce", "solution_module": "Solution", "theorem_names": [ "NagataFactoriality.palomar_nagata_factoriality", "NagataFactoriality.palomar_nagata_factoriality_of_prime_generators", "NagataFactoriality.palomar_polynomial_ufd" ] }, "comparator_commit": "575674928e239f5bc452aab72d1dd7b0f1326494", "comparator_log_tail": "Building Challenge\n\u26a0 [1277/1278] Built Challenge (1.4s)\nwarning: Challenge.lean:27:8: declaration uses `sorry`\nwarning: Challenge.lean:41:8: declaration uses `sorry`\nwarning: Challenge.lean:53:8: declaration uses `sorry`\nBuild completed successfully (1278 jobs).\nExporting #[Nat, String, String.mk, Char, Quot, Quot.mk, Quot.lift, Quot.ind, NagataFactoriality.palomar_nagata_factoriality, NagataFactoriality.palomar_nagata_factoriality_of_prime_generators, NagataFactoriality.palomar_polynomial_ufd, propext, Quot.sound, Classical.choice, Nat.add, Nat.sub, Nat.mul, Nat.pow, Nat.gcd, Nat.div, Nat.mod, Nat.beq, Nat.ble, Nat.land, Nat.lor, Nat.xor, Nat.shiftLeft, Nat.shiftRight, String.ofList, Char.ofNat, List, eagerReduce] from Challenge\nBuilding Solution\n\u2714 [1626/1638] Built NagataFactoriality.Basic.Ring (292ms)\n\u2714 [1627/1638] Built NagataFactoriality.Basic.Divisibility (1.6s)\n\u2714 [1628/1638] Built NagataFactoriality.Localization.MultSet (1.6s)\n\u26a0 [1629/1638] Built NagataFactoriality.Basic.Noetherian (1.5s)\nwarning: NagataFactoriality/Basic/Noetherian.lean:12:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\n\u26a0 [1630/1638] Built NagataFactoriality.Basic.UFD (2.4s)\nwarning: NagataFactoriality/Basic/UFD.lean:11:6: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Basic/UFD.lean:14:6: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Basic/UFD.lean:18:6: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Basic/UFD.lean:49:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Basic/UFD.lean:60:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\n\u2714 [1631/1638] Built NagataFactoriality.Localization.Localization (2.7s)\n\u2714 [1632/1638] Built NagataFactoriality.Localization.IsLocalization (2.8s)\n\u2714 [1633/1638] Built NagataFactoriality.Localization.Properties (1.3s)\n\u26a0 [1634/1638] Built NagataFactoriality.Nagata.Lemmas (2.6s)\nwarning: NagataFactoriality/Nagata/Lemmas.lean:14:0: Definition `_private.NagataFactoriality.Nagata.Lemmas.0.NagataFactoriality.submonoidZeroNotMemFact` of class type is semireducible. Most type class instances should be instance-reducible, so consider marking this\ndefinition with `@[instance_reducible]`. If it is intentionally semireducible, this warning can be disabled with `set_option warn.classDefReducibility false`.\nwarning: NagataFactoriality/Nagata/Lemmas.lean:14:0: Definition `submonoidZeroNotMemFact` is a proposition; use `theorem` instead of `def`\n\nNote: This linter can be disabled with `set_option linter.defProp false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:152:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:171:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:172:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:264:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:338:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:339:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:348:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:366:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:367:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:376:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:399:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:400:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:401:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:419:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:545:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:546:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:556:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:585:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:586:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:595:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:611:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:612:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:621:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:644:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:645:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Lemmas.lean:646:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\n\u26a0 [1635/1638] Built NagataFactoriality.Nagata.Theorem (1.5s)\nwarning: NagataFactoriality/Nagata/Theorem.lean:13:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Theorem.lean:14:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Theorem.lean:24:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Theorem.lean:77:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Theorem.lean:78:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Nagata/Theorem.lean:89:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\n\u26a0 [1636/1638] Built NagataFactoriality.Applications.Laurent (2.2s)\nwarning: NagataFactoriality/Applications/Laurent.lean:44:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Applications/Laurent.lean:93:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Applications/Laurent.lean:99:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\nwarning: NagataFactoriality/Applications/Laurent.lean:105:2: Try this: \n letI\u0335\n\nThe goal is a proposition, so `let` is preferred over `letI`.\nThe difference between `let` and `letI` is that `letI` inlines the value.\nBut this is not relevant for proofs because of proof irrelevance.\n\nNote: This linter can be disabled with `set_option linter.style.haveILetI false`\n\u2714 [1637/1638] Built Solution (1.5s)\nBuild completed successfully (1638 jobs).\nExporting #[Nat, String, String.mk, Char, Quot, Quot.mk, Quot.lift, Quot.ind, NagataFactoriality.palomar_nagata_factoriality, NagataFactoriality.palomar_nagata_factoriality_of_prime_generators, NagataFactoriality.palomar_polynomial_ufd, propext, Quot.sound, Classical.choice, Nat.add, Nat.sub, Nat.mul, Nat.pow, Nat.gcd, Nat.div, Nat.mod, Nat.beq, Nat.ble, Nat.land, Nat.lor, Nat.xor, Nat.shiftLeft, Nat.shiftRight, String.ofList, Char.ofNat, List, eagerReduce] from Solution\nRunning nanoda kernel on solution\nnanoda kernel accepts the solution\nRunning Lean default kernel on solution.\nLean default kernel accepts the solution\nYour solution is okay!", "errors": [], "existing_id": null, "formalization": { "automation_method_count": 2, "path": "formalization.yaml", "project_name": "Prime-generated Nagata factoriality in Lean", "review_status": "self-assessed", "sha256": "fc19fcb04be28037ea066d932a6be76b33106b5b987e14d9d64f163fd8c4e3c9", "source_count": 3 }, "lake_manifest": { "path": "lake-manifest.json", "sha256": "5236edc07514faff14f8517a9e64dfd3669917a01792fc9558207cc912729044" }, "lakefile": { "format": "lean", "path": "lakefile.lean", "sha256": "6be0d6013c001719bd4a9a0e1385da0b126195f82e3d12fe5938b92a84de5fff" }, "landrun_commit": "811cfff51ceaf3d9843708aa6d22e9b84ccac8b4", "lean4export_commit": "15f6055e299ad5b89345e533cc2192f4cc00f659", "lean_toolchain": "leanprover/lean4:v4.33.0", "lean_toolchain_path": "lean-toolchain", "license": { "declared_identifier": "Apache-2.0", "detected_identifier": "Apache-2.0", "path": "LICENSE", "sha256": "cfc7749b96f63bd31c3c42b5c471bf756814053e847c10f3eb003417bc523d30" }, "mathlib_cache": { "available": true, "required": true }, "nanoda_commit": "68d5ca9db226849b41a6fff59d796ff19d0a8840", "phase": "verification", "project_dependencies": [ { "name": "mathlib", "repository": "leanprover-community/mathlib4", "revision": "db584cd6d46c92f209a44c0f1c829460d327499d", "url": "https://github.com/leanprover-community/mathlib4.git" }, { "name": "plausible", 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