Datasets:

HyperCactus0
/

LeanTransitionCorpus

+{
+  "format": "leangpt-parquet-v2",
+  "batch": "deepseek/000426",
+  "batch_fingerprint": "6e0da72c55669177f4f6097dcc8ab55974084fcee8777cc5449ef6fe0d9187a6",
+  "evidence": {
+    "batch_fingerprint": "6e0da72c55669177f4f6097dcc8ab55974084fcee8777cc5449ef6fe0d9187a6",
+    "contamination_matches": [],
+    "failures": [],
+    "input_proofs": 50,
+    "input_units": 50,
+    "proofs": 50,
+    "published_proofs": 50,
+    "published_transitions": 118,
+    "replay_failures": [],
+    "trace_mode": "individual",
+    "transitions": 118,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/deepseek-000426-0000-1f7394c0f9ae27ba.parquet",
+      "sha256": "1f7394c0f9ae27ba116352cce27eb03c1a4831b67e77de744c460a3b750ad6e4",
+      "bytes": 340629,
+      "rows": 107,
+      "revision": "1426f15e0d5b8b6fa3dd64f88edd216a2f847c64"
+    },
+    {
+      "path": "data/dev/deepseek-000426-0000-a6fd15b9651c0815.parquet",
+      "sha256": "a6fd15b9651c081522038549e8eea3b7cf2471ac2e2de54e5da539206da1bc52",
+      "bytes": 36283,
+      "rows": 3,
+      "revision": "1426f15e0d5b8b6fa3dd64f88edd216a2f847c64"
+    },
+    {
+      "path": "data/internal_test/deepseek-000426-0000-b3d79370c3f7c4dc.parquet",
+      "sha256": "b3d79370c3f7c4dc834066f57d9f720908e3bc5ff32ddaafcf48373bb9f5e9d1",
+      "bytes": 255011,
+      "rows": 8,
+      "revision": "1426f15e0d5b8b6fa3dd64f88edd216a2f847c64"
+    }
+  ],
+  "proof_ids": [
+    "deepseek:thm_21346",
+    "deepseek:thm_21347",
+    "deepseek:thm_21348",
+    "deepseek:thm_21349",
+    "deepseek:thm_21350",
+    "deepseek:thm_21351",
+    "deepseek:thm_21352",
+    "deepseek:thm_21353",
+    "deepseek:thm_21354",
+    "deepseek:thm_21355",
+    "deepseek:thm_21356",
+    "deepseek:thm_21357",
+    "deepseek:thm_21358",
+    "deepseek:thm_21359",
+    "deepseek:thm_21360",
+    "deepseek:thm_21361",
+    "deepseek:thm_21362",
+    "deepseek:thm_21363",
+    "deepseek:thm_21364",
+    "deepseek:thm_21365",
+    "deepseek:thm_21366",
+    "deepseek:thm_21367",
+    "deepseek:thm_21368",
+    "deepseek:thm_21369",
+    "deepseek:thm_21370",
+    "deepseek:thm_21371",
+    "deepseek:thm_21372",
+    "deepseek:thm_21373",
+    "deepseek:thm_21374",
+    "deepseek:thm_21375",
+    "deepseek:thm_21376",
+    "deepseek:thm_21377",
+    "deepseek:thm_21378",
+    "deepseek:thm_21379",
+    "deepseek:thm_21380",
+    "deepseek:thm_21381",
+    "deepseek:thm_21382",
+    "deepseek:thm_21383",
+    "deepseek:thm_21384",
+    "deepseek:thm_21385",
+    "deepseek:thm_21386",
+    "deepseek:thm_21387",
+    "deepseek:thm_21388",
+    "deepseek:thm_21389",
+    "deepseek:thm_21390",
+    "deepseek:thm_21391",
+    "deepseek:thm_21392",
+    "deepseek:thm_21393",
+    "deepseek:thm_21394",
+    "deepseek:thm_21395"
+  ],
+  "proof_keys": [
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021300.lean\",\"ec9ac92fd0e4177e67c9ebe0a030c8af36999734fed1875766f3c0f0c6ffb902\",0,\"thm_21346\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021301.lean\",\"8385d8d66b25c565d98cf9bb71331621d7cfcc74720e3532a316aedf2253fca4\",0,\"thm_21347\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021302.lean\",\"1eec308435d1cae4d5009b3099de303820d867aa1fc39e7593466c836264b768\",0,\"thm_21348\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021303.lean\",\"d17201236789cbd724d85e49aeda91335b1f4255f5aa44e84080f021fc446c23\",0,\"thm_21349\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021304.lean\",\"bda27f0cd012f6fcc720e62b932ddafc9b91a4fd413366a17c5124e9c3690629\",0,\"thm_21350\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021305.lean\",\"b3254027ef6a845b7d1a422254d24a5309ee88a4e92d7183068e9d83bed7b2b6\",0,\"thm_21351\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021306.lean\",\"ffbd4c651f2a4b3a53d23239b9ff35f69f25098bb0ba927a4f85a19c4033281c\",0,\"thm_21352\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021307.lean\",\"a2a3ea540258b0c2e78261c400f128fd58dbb233c5fd250f4a8409a53024826d\",0,\"thm_21353\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021308.lean\",\"57b64c937395632e63bfc61c4c54a875c3ae8a551609e558355ec7dcad25469d\",0,\"thm_21354\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021309.lean\",\"dc5b1e7abab0d5c09d330a4cf98b6132ef06d0c7e25f06ae3495beb03bd5586d\",0,\"thm_21355\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021310.lean\",\"0ef65ca7a029a2748f26451d3056300a6b1d2da42db33a90a8aa09d56146477e\",0,\"thm_21356\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021311.lean\",\"765e8cd9d8b901b26632b6cc13786db3dcb50fb7af3107a6fe597468b9b55fe9\",0,\"thm_21357\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021312.lean\",\"eb450e50c4a17d8e6540a6ded8244d01ee925a6543895f205e17ee830f31c92e\",0,\"thm_21358\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021313.lean\",\"0b69fd94b0b053374df24714ef31072793af1d7f5944b9a2eb452cc0cc54a831\",0,\"thm_21359\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021314.lean\",\"d559126e6a3beaafe472271db11b27f611a738263ceb37c0da738282dbe44df9\",0,\"thm_21360\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021315.lean\",\"4947c6968b248be278619086d15271df30b70441a03969add0f3f30e58f508b8\",0,\"thm_21361\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021316.lean\",\"0b6698c8678320803aa6ef816f7983aab56dfe4405230c452e6a542437b6411d\",0,\"thm_21362\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021317.lean\",\"082cde19803a934b3f6be410bd13b006ea16b1cbb9848cf856fc46ca4fc81393\",0,\"thm_21363\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021318.lean\",\"d57721c54a223c216432c5f648e21749a48e48f7f79805eb2182bb2a5245aa92\",0,\"thm_21364\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021319.lean\",\"2697f2523f9ebd82c417272a8ab7016f7aa222b250e2f843dcf50b13a4a4a155\",0,\"thm_21365\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021320.lean\",\"406ac2c8d6e974cda3cf660a665b9dc433288c02276a01654a570fdb65c43f05\",0,\"thm_21366\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021321.lean\",\"46ce42233e84a15b83a058cceabfba9d2834676718e23833f0eb814ce84dbde4\",0,\"thm_21367\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021322.lean\",\"43ebd64f02c03bd9b4fa0e8dbb0ec55e6eab72e0990f1e840103571def288e2f\",0,\"thm_21368\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021323.lean\",\"7fe8e678a4279b03f9e72c3f0c96d832648a227fee09d82d821ab4c1fcf350c7\",0,\"thm_21369\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021324.lean\",\"8ab3067a03a8b487cfd3dbfef69b89555d8e69f07cfc649b24e0537c6a286175\",0,\"thm_21370\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021325.lean\",\"2b96d002c4ea89b9fc891fdb655b31ba7bc6f84d3adfed20c26efd98da70be3c\",0,\"thm_21371\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021326.lean\",\"aff9349ed5c80760299752ae68a71e7493caa43174092d3c143ea82778b2c8e4\",0,\"thm_21372\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021327.lean\",\"2b9391d7c5525362b52a7e1783f3a2ac7bd408fea78f1a80c7cd0785b750282a\",0,\"thm_21373\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021328.lean\",\"2fa1c74a54d952562141f67f8e5cfe1dfe28f079ec595a505ffc9da151781e27\",0,\"thm_21374\"]",
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021331.lean\",\"a2874677abc73d41e1ddf227df57bfe1a6afb1ef25da2de3cfb5322f0ddeecd9\",0,\"thm_21377\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021332.lean\",\"88e8901e8a5d3124f4408767c7ef568ec412a3818187b7fe7ecda5ac1f78311b\",0,\"thm_21378\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021333.lean\",\"1a3338b80ec840184f395495555c907e4a5addcb3a95f5b44653c037a6e8a1b0\",0,\"thm_21379\"]",
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021335.lean\",\"42d5d2562e6978fb96e58aaf61a45eef26baa564d8566261ad0429ebc7fdb732\",0,\"thm_21381\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021336.lean\",\"30be62ddace4ad4a75c667e112b7f9f5221edf9036f0b1060fc2a365bcb8f8e9\",0,\"thm_21382\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021337.lean\",\"858505724b77bc62c2e7662830da32fa9d243e538a6e8303ec8cae757d639c53\",0,\"thm_21383\"]",
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021339.lean\",\"820d784220e9487605788efd724dbfcc9c1bac5cbb0907ba2363cd2a7b974c0e\",0,\"thm_21385\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021340.lean\",\"01ac2dc8bca3df494ff7acb93e001c36b03ede967a2040f504123df1a576a86b\",0,\"thm_21386\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021341.lean\",\"621fd43e6db2a1f8cca4e3202af43e6c294e33dc9edc007d14cb4ae5ff88f10a\",0,\"thm_21387\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021342.lean\",\"9ea605e48a39cf12467e338fa46dcfb09effcaffbae6b99e8c43bba477272f4d\",0,\"thm_21388\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021343.lean\",\"ca660c7ddb7636d475cd4bc5ccd5dd55228008c15565ea0bb3750587e9076439\",0,\"thm_21389\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021344.lean\",\"946a69a4dd06ad79dfc6c8b40f2f38ba26579233649a243915ba2105fcf1e2c2\",0,\"thm_21390\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021345.lean\",\"83440a306fb1668ee7b174afd13df49923f65d9f98cedb66ef4b8f525f58a77b\",0,\"thm_21391\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021346.lean\",\"9695318d04bd279ab9682250b1634580a7365977a1c3e20b786b82f07be11cc5\",0,\"thm_21392\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021347.lean\",\"a66e610941ed710370bdf326d4a6157bd6e9300dda4d388cbba2ad6fea848c6e\",0,\"thm_21393\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021348.lean\",\"bf2d758ca701302eb7d073a38957a6e5cde63716a799b7b8d0f49b6228be23de\",0,\"thm_21394\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021349.lean\",\"238838f67d9dba85d795f2a1f0adac57d86ef0dda189ee0c82b9251931e681a2\",0,\"thm_21395\"]"
+  ]
+}

manifests/batches/deepseek/000428.json ADDED Viewed

	@@ -0,0 +1,166 @@

+{
+  "format": "leangpt-parquet-v2",
+  "batch": "deepseek/000428",
+  "batch_fingerprint": "44722aa8e3cb8efbe9f62ee7a0a2553cdcec7de1e78c7ba52ebe7c10052bee7c",
+  "evidence": {
+    "batch_fingerprint": "44722aa8e3cb8efbe9f62ee7a0a2553cdcec7de1e78c7ba52ebe7c10052bee7c",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "final replayable tactic does not close all goals",
+        "id": "thm_21479",
+        "index": 21433,
+        "reason": "import_failure",
+        "selection": {
+          "file_path": "Full/Proof_021433.lean",
+          "id": "thm_21479",
+          "index": 21433,
+          "metadata": {
+            "declaration_kind": "theorem",
+            "source_dataset": "deepseek",
+            "theorem_name": "thm_21479",
+            "theorem_ordinal": 0
+          },
+          "source_sha256": "2c1d59f1f8d952352db002711b00299ff630d1743744b5ae996c152a424addf9"
+        },
+        "source_file": "Full/Proof_021433.lean"
+      }
+    ],
+    "input_proofs": 50,
+    "input_units": 50,
+    "proofs": 49,
+    "published_proofs": 49,
+    "published_transitions": 112,
+    "replay_failures": [],
+    "trace_mode": "individual",
+    "transitions": 112,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/deepseek-000428-0000-0edf4685eb9ad371.parquet",
+      "sha256": "0edf4685eb9ad3713b39ad256a4d078ef08b822f2961126524a6542869254693",
+      "bytes": 293919,
+      "rows": 93,
+      "revision": "1426f15e0d5b8b6fa3dd64f88edd216a2f847c64"
+    },
+    {
+      "path": "data/dev/deepseek-000428-0000-827c22c320be4d57.parquet",
+      "sha256": "827c22c320be4d5747b25151e12fcfdb1b27512b1c4745b401f0ba2ba006746a",
+      "bytes": 37685,
+      "rows": 5,
+      "revision": "1426f15e0d5b8b6fa3dd64f88edd216a2f847c64"
+    },
+    {
+      "path": "data/internal_test/deepseek-000428-0000-f2434f0360243fdc.parquet",
+      "sha256": "f2434f0360243fdcbfc5c1681ebe63ad92ef511c9e6e416335468a3d4120001c",
+      "bytes": 51680,
+      "rows": 14,
+      "revision": "1426f15e0d5b8b6fa3dd64f88edd216a2f847c64"
+    }
+  ],
+  "proof_ids": [
+    "deepseek:thm_21446",
+    "deepseek:thm_21447",
+    "deepseek:thm_21448",
+    "deepseek:thm_21449",
+    "deepseek:thm_21450",
+    "deepseek:thm_21451",
+    "deepseek:thm_21452",
+    "deepseek:thm_21453",
+    "deepseek:thm_21454",
+    "deepseek:thm_21455",
+    "deepseek:thm_21456",
+    "deepseek:thm_21457",
+    "deepseek:thm_21458",
+    "deepseek:thm_21459",
+    "deepseek:thm_21460",
+    "deepseek:thm_21461",
+    "deepseek:thm_21462",
+    "deepseek:thm_21463",
+    "deepseek:thm_21464",
+    "deepseek:thm_21465",
+    "deepseek:thm_21466",
+    "deepseek:thm_21467",
+    "deepseek:thm_21468",
+    "deepseek:thm_21469",
+    "deepseek:thm_21470",
+    "deepseek:thm_21471",
+    "deepseek:thm_21472",
+    "deepseek:thm_21473",
+    "deepseek:thm_21474",
+    "deepseek:thm_21475",
+    "deepseek:thm_21476",
+    "deepseek:thm_21477",
+    "deepseek:thm_21478",
+    "deepseek:thm_21480",
+    "deepseek:thm_21481",
+    "deepseek:thm_21482",
+    "deepseek:thm_21483",
+    "deepseek:thm_21484",
+    "deepseek:thm_21485",
+    "deepseek:thm_21486",
+    "deepseek:thm_21487",
+    "deepseek:thm_21488",
+    "deepseek:thm_21489",
+    "deepseek:thm_21490",
+    "deepseek:thm_21491",
+    "deepseek:thm_21492",
+    "deepseek:thm_21493",
+    "deepseek:thm_21494",
+    "deepseek:thm_21495"
+  ],
+  "proof_keys": [
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021400.lean\",\"34d0a6fcc288875cfd09943af1f926b03902d4bee2e5316717fb03318abcf24d\",0,\"thm_21446\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021401.lean\",\"2a2ae1a11e98edc4cabb953a1971d4590de1795ccb864f83e43a82360679955b\",0,\"thm_21447\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021402.lean\",\"a3a3fa6aea668a9c290f7242e7681466383f4fc938143bce0bf022abc95fd7c4\",0,\"thm_21448\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021403.lean\",\"7392eab2a414563bff93c5bda252fad2d830ab8e1a48c2391d0a7505df1685c0\",0,\"thm_21449\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021404.lean\",\"b75331d98560a51c26716204d6872ccf27eafcb0f66609073ed25bb20adb6552\",0,\"thm_21450\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021405.lean\",\"605f63324f7afa2e94c996e63567d9e4fe1c2c713002d2c8cc8d19d6c8b937fe\",0,\"thm_21451\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021406.lean\",\"5afa3cbc06f5de1cd551c297009934e21e3e408e764f7f83c04e51a44a60b837\",0,\"thm_21452\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021407.lean\",\"45f01ae35acae0971dc6c544e16c2bab1c50355c5c45198240a23b8324c2f3b2\",0,\"thm_21453\"]",
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021438.lean\",\"94cbab20bca4b16ac7cc987cc73d390140194247b788bfad35cdd86f3f8ee0fb\",0,\"thm_21484\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021439.lean\",\"3ad7454383cb76f423914cd563eee05e4675928cdb31a65215e1194c21e10c62\",0,\"thm_21485\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021440.lean\",\"5457e157e1f11f3cc981af359043c6924c63759c392b50cdaa54a6cd05dd6228\",0,\"thm_21486\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021441.lean\",\"aa2ed662ff1e25de92bbaa33858ccc9af8f01c97a252e8c18635050560837203\",0,\"thm_21487\"]",
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021448.lean\",\"cb4074d2121ca7971920cbfff079d88eb7b34739bd7ff7011eccd2eb15e876b4\",0,\"thm_21494\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021449.lean\",\"eb9986d51b582027b8095d5b0b2af534f006762fdfc5e5fa8a2ed1348364f1bc\",0,\"thm_21495\"]"
+  ]
+}

manifests/batches/deepseek/000429.json ADDED Viewed

	@@ -0,0 +1,166 @@

+{
+  "format": "leangpt-parquet-v2",
+  "batch": "deepseek/000429",
+  "batch_fingerprint": "b96976ef9e8f045a7ea0351c4b48034b6f79cc8233b73f2a754f4906c0c5fd48",
+  "evidence": {
+    "batch_fingerprint": "b96976ef9e8f045a7ea0351c4b48034b6f79cc8233b73f2a754f4906c0c5fd48",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "final replayable tactic does not close all goals",
+        "id": "thm_21504",
+        "index": 21458,
+        "reason": "import_failure",
+        "selection": {
+          "file_path": "Full/Proof_021458.lean",
+          "id": "thm_21504",
+          "index": 21458,
+          "metadata": {
+            "declaration_kind": "theorem",
+            "source_dataset": "deepseek",
+            "theorem_name": "thm_21504",
+            "theorem_ordinal": 0
+          },
+          "source_sha256": "e0b20beeefaf1329577278845cd155d5f620badff6a13280d798d1a62e376846"
+        },
+        "source_file": "Full/Proof_021458.lean"
+      }
+    ],
+    "input_proofs": 50,
+    "input_units": 50,
+    "proofs": 49,
+    "published_proofs": 49,
+    "published_transitions": 103,
+    "replay_failures": [],
+    "trace_mode": "individual",
+    "transitions": 103,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/deepseek-000429-0000-5212203f749feb5d.parquet",
+      "sha256": "5212203f749feb5d3efc4dddb01aa67d6d557210dabb84f295f5ddbcba5f4e30",
+      "bytes": 286734,
+      "rows": 85,
+      "revision": "1426f15e0d5b8b6fa3dd64f88edd216a2f847c64"
+    },
+    {
+      "path": "data/dev/deepseek-000429-0000-4b8460b94f90af16.parquet",
+      "sha256": "4b8460b94f90af169ba6ec24de77436e9acdedd30a847939b7c122de4eadbdc0",
+      "bytes": 33250,
+      "rows": 3,
+      "revision": "1426f15e0d5b8b6fa3dd64f88edd216a2f847c64"
+    },
+    {
+      "path": "data/internal_test/deepseek-000429-0000-fb92b99d8e959171.parquet",
+      "sha256": "fb92b99d8e9591714fd2e7184942794b6ee495150e917627fcbbbd8a456f9212",
+      "bytes": 60062,
+      "rows": 15,
+      "revision": "1426f15e0d5b8b6fa3dd64f88edd216a2f847c64"
+    }
+  ],
+  "proof_ids": [
+    "deepseek:thm_21496",
+    "deepseek:thm_21497",
+    "deepseek:thm_21498",
+    "deepseek:thm_21499",
+    "deepseek:thm_21500",
+    "deepseek:thm_21501",
+    "deepseek:thm_21502",
+    "deepseek:thm_21503",
+    "deepseek:thm_21505",
+    "deepseek:thm_21506",
+    "deepseek:thm_21507",
+    "deepseek:thm_21508",
+    "deepseek:thm_21509",
+    "deepseek:thm_21510",
+    "deepseek:thm_21511",
+    "deepseek:thm_21512",
+    "deepseek:thm_21513",
+    "deepseek:thm_21514",
+    "deepseek:thm_21515",
+    "deepseek:thm_21516",
+    "deepseek:thm_21517",
+    "deepseek:thm_21518",
+    "deepseek:thm_21519",
+    "deepseek:thm_21520",
+    "deepseek:thm_21521",
+    "deepseek:thm_21522",
+    "deepseek:thm_21523",
+    "deepseek:thm_21524",
+    "deepseek:thm_21525",
+    "deepseek:thm_21526",
+    "deepseek:thm_21527",
+    "deepseek:thm_21528",
+    "deepseek:thm_21529",
+    "deepseek:thm_21530",
+    "deepseek:thm_21531",
+    "deepseek:thm_21532",
+    "deepseek:thm_21533",
+    "deepseek:thm_21534",
+    "deepseek:thm_21535",
+    "deepseek:thm_21536",
+    "deepseek:thm_21537",
+    "deepseek:thm_21538",
+    "deepseek:thm_21539",
+    "deepseek:thm_21540",
+    "deepseek:thm_21541",
+    "deepseek:thm_21542",
+    "deepseek:thm_21543",
+    "deepseek:thm_21544",
+    "deepseek:thm_21545"
+  ],
+  "proof_keys": [
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021460.lean\",\"df421aee5790f3f09e7a03ab4b091ef84120f2eabb2c694c91b450d43a964589\",0,\"thm_21506\"]",
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021463.lean\",\"f703052a051b9d9b7066c8417408f4d1660e8148a047700a2cf6ed1b39a6e3f3\",0,\"thm_21509\"]",
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+  ]
+}

manifests/batches/deepseek/000430.json ADDED Viewed

	@@ -0,0 +1,148 @@

+{
+  "format": "leangpt-parquet-v2",
+  "batch": "deepseek/000430",
+  "batch_fingerprint": "60c864cba5e22655735cac6488fc7929455fed3841aa7d3e6c56a91e5958f57b",
+  "evidence": {
+    "batch_fingerprint": "60c864cba5e22655735cac6488fc7929455fed3841aa7d3e6c56a91e5958f57b",
+    "contamination_matches": [],
+    "failures": [],
+    "input_proofs": 50,
+    "input_units": 50,
+    "proofs": 50,
+    "published_proofs": 50,
+    "published_transitions": 131,
+    "replay_failures": [],
+    "trace_mode": "individual",
+    "transitions": 131,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/deepseek-000430-0000-b4e81f6b0c80ddfe.parquet",
+      "sha256": "b4e81f6b0c80ddfe7ce5ecdf2e64de8fcf8a130dc3a0e3e042e8ff6e6a01a01d",
+      "bytes": 315006,
+      "rows": 111,
+      "revision": "1426f15e0d5b8b6fa3dd64f88edd216a2f847c64"
+    },
+    {
+      "path": "data/dev/deepseek-000430-0000-7c6446af6e08d449.parquet",
+      "sha256": "7c6446af6e08d44970120aec7581d376ca69b211ac23bbc04569e656baa5c928",
+      "bytes": 57035,
+      "rows": 13,
+      "revision": "1426f15e0d5b8b6fa3dd64f88edd216a2f847c64"
+    },
+    {
+      "path": "data/internal_test/deepseek-000430-0000-ab13e07a300db3cf.parquet",
+      "sha256": "ab13e07a300db3cff157dd0d3f9a4221379fc4b15d3e335660d426d8ca897b30",
+      "bytes": 35577,
+      "rows": 7,
+      "revision": "1426f15e0d5b8b6fa3dd64f88edd216a2f847c64"
+    }
+  ],
+  "proof_ids": [
+    "deepseek:thm_21546",
+    "deepseek:thm_21547",
+    "deepseek:thm_21548",
+    "deepseek:thm_21549",
+    "deepseek:thm_21550",
+    "deepseek:thm_21551",
+    "deepseek:thm_21552",
+    "deepseek:thm_21553",
+    "deepseek:thm_21554",
+    "deepseek:thm_21555",
+    "deepseek:thm_21556",
+    "deepseek:thm_21557",
+    "deepseek:thm_21558",
+    "deepseek:thm_21559",
+    "deepseek:thm_21560",
+    "deepseek:thm_21561",
+    "deepseek:thm_21562",
+    "deepseek:thm_21563",
+    "deepseek:thm_21564",
+    "deepseek:thm_21565",
+    "deepseek:thm_21566",
+    "deepseek:thm_21567",
+    "deepseek:thm_21568",
+    "deepseek:thm_21569",
+    "deepseek:thm_21570",
+    "deepseek:thm_21571",
+    "deepseek:thm_21572",
+    "deepseek:thm_21573",
+    "deepseek:thm_21574",
+    "deepseek:thm_21575",
+    "deepseek:thm_21576",
+    "deepseek:thm_21577",
+    "deepseek:thm_21578",
+    "deepseek:thm_21579",
+    "deepseek:thm_21580",
+    "deepseek:thm_21581",
+    "deepseek:thm_21582",
+    "deepseek:thm_21583",
+    "deepseek:thm_21584",
+    "deepseek:thm_21585",
+    "deepseek:thm_21586",
+    "deepseek:thm_21587",
+    "deepseek:thm_21588",
+    "deepseek:thm_21589",
+    "deepseek:thm_21590",
+    "deepseek:thm_21591",
+    "deepseek:thm_21592",
+    "deepseek:thm_21593",
+    "deepseek:thm_21594",
+    "deepseek:thm_21595"
+  ],
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+  ]
+}

manifests/batches/deepseek/000433.json ADDED Viewed

	@@ -0,0 +1,148 @@

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+    "input_units": 50,
+    "proofs": 50,
+    "published_proofs": 50,
+    "published_transitions": 113,
+    "replay_failures": [],
+    "trace_mode": "individual",
+    "transitions": 113,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
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+  "shards": [
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+      "rows": 10,
+      "revision": "1426f15e0d5b8b6fa3dd64f88edd216a2f847c64"
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+    "deepseek:thm_21697",
+    "deepseek:thm_21698",
+    "deepseek:thm_21699",
+    "deepseek:thm_21700",
+    "deepseek:thm_21701",
+    "deepseek:thm_21702",
+    "deepseek:thm_21703",
+    "deepseek:thm_21704",
+    "deepseek:thm_21705",
+    "deepseek:thm_21706",
+    "deepseek:thm_21707",
+    "deepseek:thm_21708",
+    "deepseek:thm_21709",
+    "deepseek:thm_21710",
+    "deepseek:thm_21711",
+    "deepseek:thm_21712",
+    "deepseek:thm_21713",
+    "deepseek:thm_21714",
+    "deepseek:thm_21715",
+    "deepseek:thm_21716",
+    "deepseek:thm_21717",
+    "deepseek:thm_21718",
+    "deepseek:thm_21719",
+    "deepseek:thm_21720",
+    "deepseek:thm_21721",
+    "deepseek:thm_21722",
+    "deepseek:thm_21723",
+    "deepseek:thm_21724",
+    "deepseek:thm_21725",
+    "deepseek:thm_21726",
+    "deepseek:thm_21727",
+    "deepseek:thm_21728",
+    "deepseek:thm_21729",
+    "deepseek:thm_21730",
+    "deepseek:thm_21731",
+    "deepseek:thm_21732",
+    "deepseek:thm_21733",
+    "deepseek:thm_21734",
+    "deepseek:thm_21735",
+    "deepseek:thm_21736",
+    "deepseek:thm_21737",
+    "deepseek:thm_21738",
+    "deepseek:thm_21739",
+    "deepseek:thm_21740",
+    "deepseek:thm_21741",
+    "deepseek:thm_21742",
+    "deepseek:thm_21743",
+    "deepseek:thm_21744",
+    "deepseek:thm_21745"
+  ],
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_021699.lean\",\"8fc413eda5acabf0a11c012d44aa25fb09906000741db5ce00cfcd5a7d50be1d\",0,\"thm_21745\"]"
+  ]
+}

manifests/batches/mathlib/000358.json ADDED Viewed

	@@ -0,0 +1,190 @@

+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000358",
+  "batch_fingerprint": "a826bc1b0fa4b0023a94fb31baeb8498dd58b2495ac493fc7c5790516645d34d",
+  "evidence": {
+    "batch_fingerprint": "a826bc1b0fa4b0023a94fb31baeb8498dd58b2495ac493fc7c5790516645d34d",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "AlgebraicGeometry.UniversallyClosed.openCover_iff",
+        "id": "AlgebraicGeometry.UniversallyClosed.openCover_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            100,
+            54
+          ],
+          "file_path": "Mathlib/AlgebraicGeometry/Morphisms/UniversallyClosed.lean",
+          "full_name": "AlgebraicGeometry.UniversallyClosed.openCover_iff",
+          "start": [
+            97,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/AlgebraicGeometry/Morphisms/UniversallyClosed.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "AlgebraicGeometry.universallyClosed_respectsIso",
+        "id": "AlgebraicGeometry.universallyClosed_respectsIso",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            50,
+            83
+          ],
+          "file_path": "Mathlib/AlgebraicGeometry/Morphisms/UniversallyClosed.lean",
+          "full_name": "AlgebraicGeometry.universallyClosed_respectsIso",
+          "start": [
+            49,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/AlgebraicGeometry/Morphisms/UniversallyClosed.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "AlgebraicGeometry.universallyClosed_stableUnderBaseChange",
+        "id": "AlgebraicGeometry.universallyClosed_stableUnderBaseChange",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            54,
+            93
+          ],
+          "file_path": "Mathlib/AlgebraicGeometry/Morphisms/UniversallyClosed.lean",
+          "full_name": "AlgebraicGeometry.universallyClosed_stableUnderBaseChange",
+          "start": [
+            53,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/AlgebraicGeometry/Morphisms/UniversallyClosed.lean"
+      }
+    ],
+    "input_proofs": 8,
+    "input_units": 2,
+    "proofs": 5,
+    "published_proofs": 4,
+    "published_transitions": 11,
+    "replay_failures": [],
+    "transitions": 17,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/AlgebraicGeometry/Morphisms/UniversallyClosed.lean",
+        "proof_id": "mathlib:AlgebraicGeometry.universallyClosed_isLocalAtTarget",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              94,
+              64
+            ],
+            "file_path": "Mathlib/AlgebraicGeometry/Morphisms/UniversallyClosed.lean",
+            "full_name": "AlgebraicGeometry.universallyClosed_isLocalAtTarget",
+            "start": [
+              88,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>universallyClosed_eq<\\/a>]\"",
+                  "[{\"full_name\":\"AlgebraicGeometry.universallyClosed_eq\",\"def_path\":\"Mathlib\\/AlgebraicGeometry\\/Morphisms\\/UniversallyClosed.lean\",\"def_pos\":[45,9],\"def_end_pos\":[45,29]}]"
+                ],
+                "state_after": "X Y : Scheme\nf : X \u27f6 Y\n\u22a2 PropertyIsLocalAtTarget (topologically @IsClosedMap).universally",
+                "state_before": "X Y : Scheme\nf : X \u27f6 Y\n\u22a2 PropertyIsLocalAtTarget @UniversallyClosed",
+                "tactic": "rw [universallyClosed_eq]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"apply <a>universally_isLocalAtTarget_of_morphismRestrict<\\/a>\"",
+                  "[{\"full_name\":\"AlgebraicGeometry.universally_isLocalAtTarget_of_morphismRestrict\",\"def_path\":\"Mathlib\\/AlgebraicGeometry\\/Morphisms\\/Constructors.lean\",\"def_pos\":[169,9],\"def_end_pos\":[169,56]}]"
+                ],
+                "state_after": "case hP\u2081\nX Y : Scheme\nf : X \u27f6 Y\n\u22a2 (topologically @IsClosedMap).RespectsIso\n\ncase hP\u2082\nX Y : Scheme\nf : X \u27f6 Y\n\u22a2 \u2200 {X Y : Scheme} (f : X \u27f6 Y) {\u03b9 : Type u_1} (U : \u03b9 \u2192 Opens \u2191\u2191Y.toPresheafedSpace),\n    iSup U = \u22a4 \u2192 (\u2200 (i : \u03b9), topologically (@IsClosedMap) (f \u2223_ U i)) \u2192 topologically (@IsClosedMap) f",
+                "state_before": "X Y : Scheme\nf : X \u27f6 Y\n\u22a2 PropertyIsLocalAtTarget (topologically @IsClosedMap).universally",
+                "tactic": "apply universally_isLocalAtTarget_of_morphismRestrict"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact <a>topologically_isClosedMap_respectsIso<\\/a>\"",
+                  "[{\"full_name\":\"AlgebraicGeometry.topologically_isClosedMap_respectsIso\",\"def_path\":\"Mathlib\\/AlgebraicGeometry\\/Morphisms\\/UniversallyClosed.lean\",\"def_pos\":[72,9],\"def_end_pos\":[72,46]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case hP\u2081\nX Y : Scheme\nf : X \u27f6 Y\n\u22a2 (topologically @IsClosedMap).RespectsIso",
+                "tactic": "exact topologically_isClosedMap_respectsIso"
+              },
+              {
+                "annotated_tactic": [
+                  "\"intro X Y f \\u03b9 U hU H\"",
+                  "[]"
+                ],
+                "state_after": "case hP\u2082\nX\u271d Y\u271d : Scheme\nf\u271d : X\u271d \u27f6 Y\u271d\nX Y : Scheme\nf : X \u27f6 Y\n\u03b9 : Type u_1\nU : \u03b9 \u2192 Opens \u2191\u2191Y.toPresheafedSpace\nhU : iSup U = \u22a4\nH : \u2200 (i : \u03b9), topologically (@IsClosedMap) (f \u2223_ U i)\n\u22a2 topologically (@IsClosedMap) f",
+                "state_before": "case hP\u2082\nX Y : Scheme\nf : X \u27f6 Y\n\u22a2 \u2200 {X Y : Scheme} (f : X \u27f6 Y) {\u03b9 : Type u_1} (U : \u03b9 \u2192 Opens \u2191\u2191Y.toPresheafedSpace),\n    iSup U = \u22a4 \u2192 (\u2200 (i : \u03b9), topologically (@IsClosedMap) (f \u2223_ U i)) \u2192 topologically (@IsClosedMap) f",
+                "tactic": "intro X Y f \u03b9 U hU H"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp_rw [<a>topologically<\\/a>, <a>morphismRestrict_val_base<\\/a>] at H\"",
+                  "[{\"full_name\":\"AlgebraicGeometry.MorphismProperty.topologically\",\"def_path\":\"Mathlib\\/AlgebraicGeometry\\/Morphisms\\/Constructors.lean\",\"def_pos\":[184,5],\"def_end_pos\":[184,35]},{\"full_name\":\"AlgebraicGeometry.morphismRestrict_val_base\",\"def_path\":\"Mathlib\\/AlgebraicGeometry\\/Restrict.lean\",\"def_pos\":[314,9],\"def_end_pos\":[314,34]}]"
+                ],
+                "state_after": "case hP\u2082\nX\u271d Y\u271d : Scheme\nf\u271d : X\u271d \u27f6 Y\u271d\nX Y : Scheme\nf : X \u27f6 Y\n\u03b9 : Type u_1\nU : \u03b9 \u2192 Opens \u2191\u2191Y.toPresheafedSpace\nhU : iSup U = \u22a4\nH : \u2200 (i : \u03b9), IsClosedMap ((U i).carrier.restrictPreimage \u21d1f.val.base)\n\u22a2 topologically (@IsClosedMap) f",
+                "state_before": "case hP\u2082\nX\u271d Y\u271d : Scheme\nf\u271d : X\u271d \u27f6 Y\u271d\nX Y : Scheme\nf : X \u27f6 Y\n\u03b9 : Type u_1\nU : \u03b9 \u2192 Opens \u2191\u2191Y.toPresheafedSpace\nhU : iSup U = \u22a4\nH : \u2200 (i : \u03b9), topologically (@IsClosedMap) (f \u2223_ U i)\n\u22a2 topologically (@IsClosedMap) f",
+                "tactic": "simp_rw [topologically, morphismRestrict_val_base] at H"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact (<a>isClosedMap_iff_isClosedMap_of_iSup_eq_top<\\/a> hU).<a>mpr<\\/a> H\"",
+                  "[{\"full_name\":\"isClosedMap_iff_isClosedMap_of_iSup_eq_top\",\"def_path\":\"Mathlib\\/Topology\\/LocalAtTarget.lean\",\"def_pos\":[116,9],\"def_end_pos\":[116,51]},{\"full_name\":\"Iff.mpr\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[120,3],\"def_end_pos\":[120,6]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case hP\u2082\nX\u271d Y\u271d : Scheme\nf\u271d : X\u271d \u27f6 Y\u271d\nX Y : Scheme\nf : X \u27f6 Y\n\u03b9 : Type u_1\nU : \u03b9 \u2192 Opens \u2191\u2191Y.toPresheafedSpace\nhU : iSup U = \u22a4\nH : \u2200 (i : \u03b9), IsClosedMap ((U i).carrier.restrictPreimage \u21d1f.val.base)\n\u22a2 topologically (@IsClosedMap) f",
+                "tactic": "exact (isClosedMap_iff_isClosedMap_of_iSup_eq_top hU).mpr H"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "AlgebraicGeometry.universallyClosed_isLocalAtTarget"
+      }
+    ],
+    "validation_rejected_proofs": 1,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000358-0000-03fecfcf40d6b2c5.parquet",
+      "sha256": "03fecfcf40d6b2c587b0235b9e17dad127b4d552f0c30005fa72e1fd76d725ee",
+      "bytes": 51331,
+      "rows": 11,
+      "revision": "1426f15e0d5b8b6fa3dd64f88edd216a2f847c64"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:AlgebraicGeometry.IsSeparated.isSeparated_eq_diagonal_isClosedImmersion",
+    "mathlib:AlgebraicGeometry.IsSeparated.respectsIso",
+    "mathlib:AlgebraicGeometry.topologically_isClosedMap_respectsIso",
+    "mathlib:AlgebraicGeometry.universallyClosed_eq"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/AlgebraicGeometry/Morphisms/Separated.lean\",null,null,\"AlgebraicGeometry.IsSeparated.isSeparated_eq_diagonal_isClosedImmersion\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/AlgebraicGeometry/Morphisms/Separated.lean\",null,null,\"AlgebraicGeometry.IsSeparated.respectsIso\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/AlgebraicGeometry/Morphisms/UniversallyClosed.lean\",null,null,\"AlgebraicGeometry.topologically_isClosedMap_respectsIso\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/AlgebraicGeometry/Morphisms/UniversallyClosed.lean\",null,null,\"AlgebraicGeometry.universallyClosed_eq\"]"
+  ]
+}

manifests/batches/mathlib/000359.json ADDED Viewed

The diff for this file is too large to render. See raw diff

manifests/batches/mathlib/000360.json ADDED Viewed

	@@ -0,0 +1,524 @@

+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000360",
+  "batch_fingerprint": "04454758d5a68dd2fb40ae114a6b70b5f7b41b3d05c122323e07f08a88d108ec",
+  "evidence": {
+    "batch_fingerprint": "04454758d5a68dd2fb40ae114a6b70b5f7b41b3d05c122323e07f08a88d108ec",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "AlgebraicGeometry.Polynomial.comap_C_mem_imageOfDf",
+        "id": "AlgebraicGeometry.Polynomial.comap_C_mem_imageOfDf",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            49,
+            64
+          ],
+          "file_path": "Mathlib/AlgebraicGeometry/PrimeSpectrum/IsOpenComapC.lean",
+          "full_name": "AlgebraicGeometry.Polynomial.comap_C_mem_imageOfDf",
+          "start": [
+            46,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/AlgebraicGeometry/PrimeSpectrum/IsOpenComapC.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'refine \u27e8fun hx => \u27e8\u27e8map C x.asIdeal, isPrime_map_C_of_isPrime x.isPrime\u27e9, \u27e8?_, ?_\u27e9\u27e9, ?_\u27e9'",
+        "full_name": "AlgebraicGeometry.Polynomial.imageOfDf_eq_comap_C_compl_zeroLocus",
+        "id": "AlgebraicGeometry.Polynomial.imageOfDf_eq_comap_C_compl_zeroLocus",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            66,
+            43
+          ],
+          "file_path": "Mathlib/AlgebraicGeometry/PrimeSpectrum/IsOpenComapC.lean",
+          "full_name": "AlgebraicGeometry.Polynomial.imageOfDf_eq_comap_C_compl_zeroLocus",
+          "start": [
+            54,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"ext x\"",
+                "[]"
+              ],
+              "state_after": "case h\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nx : PrimeSpectrum R\n\u22a2 x \u2208 imageOfDf f \u2194 x \u2208 \u21d1(PrimeSpectrum.comap C) '' (zeroLocus {f})\u1d9c",
+              "state_before": "R : Type u_1\ninst\u271d : CommRing R\nf : R[X]\n\u22a2 imageOfDf f = \u21d1(PrimeSpectrum.comap C) '' (zeroLocus {f})\u1d9c",
+              "tactic": "ext x"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine \\u27e8fun hx => \\u27e8\\u27e8<a>map<\\/a> <a>C<\\/a> x.asIdeal, <a>isPrime_map_C_of_isPrime<\\/a> x.isPrime\\u27e9, \\u27e8?_, ?_\\u27e9\\u27e9, ?_\\u27e9\"",
+                "[{\"full_name\":\"Ideal.map\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Maps.lean\",\"def_pos\":[36,5],\"def_end_pos\":[36,8]},{\"full_name\":\"Polynomial.C\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Basic.lean\",\"def_pos\":[501,5],\"def_end_pos\":[501,6]},{\"full_name\":\"Ideal.isPrime_map_C_of_isPrime\",\"def_path\":\"Mathlib\\/RingTheory\\/Polynomial\\/Basic.lean\",\"def_pos\":[808,9],\"def_end_pos\":[808,33]}]"
+              ],
+              "state_after": "case h.refine_1\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nx : PrimeSpectrum R\nhx : x \u2208 imageOfDf f\n\u22a2 { asIdeal := Ideal.map C x.asIdeal, isPrime := \u22ef } \u2208 (zeroLocus {f})\u1d9c\n\ncase h.refine_2\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nx : PrimeSpectrum R\nhx : x \u2208 imageOfDf f\n\u22a2 (PrimeSpectrum.comap C) { asIdeal := Ideal.map C x.asIdeal, isPrime := \u22ef } = x\n\ncase h.refine_3\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nx : PrimeSpectrum R\n\u22a2 x \u2208 \u21d1(PrimeSpectrum.comap C) '' (zeroLocus {f})\u1d9c \u2192 x \u2208 imageOfDf f",
+              "state_before": "case h\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nx : PrimeSpectrum R\n\u22a2 x \u2208 imageOfDf f \u2194 x \u2208 \u21d1(PrimeSpectrum.comap C) '' (zeroLocus {f})\u1d9c",
+              "tactic": "refine \u27e8fun hx => \u27e8\u27e8map C x.asIdeal, isPrime_map_C_of_isPrime x.isPrime\u27e9, \u27e8?_, ?_\u27e9\u27e9, ?_\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>mem_compl_iff<\\/a>, <a>mem_zeroLocus<\\/a>, <a>singleton_subset_iff<\\/a>]\"",
+                "[{\"full_name\":\"Set.mem_compl_iff\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Defs.lean\",\"def_pos\":[87,17],\"def_end_pos\":[87,30]},{\"full_name\":\"PrimeSpectrum.mem_zeroLocus\",\"def_path\":\"Mathlib\\/AlgebraicGeometry\\/PrimeSpectrum\\/Basic.lean\",\"def_pos\":[144,9],\"def_end_pos\":[144,22]},{\"full_name\":\"Set.singleton_subset_iff\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[1287,9],\"def_end_pos\":[1287,29]}]"
+              ],
+              "state_after": "case h.refine_1\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nx : PrimeSpectrum R\nhx : x \u2208 imageOfDf f\n\u22a2 f \u2209 \u2191{ asIdeal := Ideal.map C x.asIdeal, isPrime := \u22ef }.asIdeal",
+              "state_before": "case h.refine_1\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nx : PrimeSpectrum R\nhx : x \u2208 imageOfDf f\n\u22a2 { asIdeal := Ideal.map C x.asIdeal, isPrime := \u22ef } \u2208 (zeroLocus {f})\u1d9c",
+              "tactic": "rw [mem_compl_iff, mem_zeroLocus, singleton_subset_iff]"
+            },
+            {
+              "annotated_tactic": [
+                "\"cases' hx with i hi\"",
+                "[]"
+              ],
+              "state_after": "case h.refine_1.intro\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nx : PrimeSpectrum R\ni : \u2115\nhi : f.coeff i \u2209 x.asIdeal\n\u22a2 f \u2209 \u2191{ asIdeal := Ideal.map C x.asIdeal, isPrime := \u22ef }.asIdeal",
+              "state_before": "case h.refine_1\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nx : PrimeSpectrum R\nhx : x \u2208 imageOfDf f\n\u22a2 f \u2209 \u2191{ asIdeal := Ideal.map C x.asIdeal, isPrime := \u22ef }.asIdeal",
+              "tactic": "cases' hx with i hi"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact fun a => hi (mem_map_C_iff.mp a i)\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.refine_1.intro\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nx : PrimeSpectrum R\ni : \u2115\nhi : f.coeff i \u2209 x.asIdeal\n\u22a2 f \u2209 \u2191{ asIdeal := Ideal.map C x.asIdeal, isPrime := \u22ef }.asIdeal",
+              "tactic": "exact fun a => hi (mem_map_C_iff.mp a i)"
+            },
+            {
+              "annotated_tactic": [
+                "\"ext x\"",
+                "[]"
+              ],
+              "state_after": "case h.refine_2.asIdeal.h\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nx\u271d : PrimeSpectrum R\nhx : x\u271d \u2208 imageOfDf f\nx : R\n\u22a2 x \u2208 ((PrimeSpectrum.comap C) { asIdeal := Ideal.map C x\u271d.asIdeal, isPrime := \u22ef }).asIdeal \u2194 x \u2208 x\u271d.asIdeal",
+              "state_before": "case h.refine_2\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nx : PrimeSpectrum R\nhx : x \u2208 imageOfDf f\n\u22a2 (PrimeSpectrum.comap C) { asIdeal := Ideal.map C x.asIdeal, isPrime := \u22ef } = x",
+              "tactic": "ext x"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine \\u27e8fun h => ?_, fun h => <a>subset_span<\\/a> (<a>mem_image_of_mem<\\/a> <a>C<\\/a>.1 h)\\u27e9\"",
+                "[{\"full_name\":\"Ideal.subset_span\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Basic.lean\",\"def_pos\":[146,9],\"def_end_pos\":[146,20]},{\"full_name\":\"Set.mem_image_of_mem\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Defs.lean\",\"def_pos\":[132,9],\"def_end_pos\":[132,25]},{\"full_name\":\"Polynomial.C\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Basic.lean\",\"def_pos\":[501,5],\"def_end_pos\":[501,6]}]"
+              ],
+              "state_after": "case h.refine_2.asIdeal.h\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nx\u271d : PrimeSpectrum R\nhx : x\u271d \u2208 imageOfDf f\nx : R\nh : x \u2208 ((PrimeSpectrum.comap C) { asIdeal := Ideal.map C x\u271d.asIdeal, isPrime := \u22ef }).asIdeal\n\u22a2 x \u2208 x\u271d.asIdeal",
+              "state_before": "case h.refine_2.asIdeal.h\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nx\u271d : PrimeSpectrum R\nhx : x\u271d \u2208 imageOfDf f\nx : R\n\u22a2 x \u2208 ((PrimeSpectrum.comap C) { asIdeal := Ideal.map C x\u271d.asIdeal, isPrime := \u22ef }).asIdeal \u2194 x \u2208 x\u271d.asIdeal",
+              "tactic": "refine \u27e8fun h => ?_, fun h => subset_span (mem_image_of_mem C.1 h)\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 @<a>coeff_C_zero<\\/a> R x _]\"",
+                "[{\"full_name\":\"Polynomial.coeff_C_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Basic.lean\",\"def_pos\":[740,9],\"def_end_pos\":[740,21]}]"
+              ],
+              "state_after": "case h.refine_2.asIdeal.h\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nx\u271d : PrimeSpectrum R\nhx : x\u271d \u2208 imageOfDf f\nx : R\nh : x \u2208 ((PrimeSpectrum.comap C) { asIdeal := Ideal.map C x\u271d.asIdeal, isPrime := \u22ef }).asIdeal\n\u22a2 (C x).coeff 0 \u2208 x\u271d.asIdeal",
+              "state_before": "case h.refine_2.asIdeal.h\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nx\u271d : PrimeSpectrum R\nhx : x\u271d \u2208 imageOfDf f\nx : R\nh : x \u2208 ((PrimeSpectrum.comap C) { asIdeal := Ideal.map C x\u271d.asIdeal, isPrime := \u22ef }).asIdeal\n\u22a2 x \u2208 x\u271d.asIdeal",
+              "tactic": "rw [\u2190 @coeff_C_zero R x _]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact mem_map_C_iff.mp h 0\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.refine_2.asIdeal.h\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nx\u271d : PrimeSpectrum R\nhx : x\u271d \u2208 imageOfDf f\nx : R\nh : x \u2208 ((PrimeSpectrum.comap C) { asIdeal := Ideal.map C x\u271d.asIdeal, isPrime := \u22ef }).asIdeal\n\u22a2 (C x).coeff 0 \u2208 x\u271d.asIdeal",
+              "tactic": "exact mem_map_C_iff.mp h 0"
+            },
+            {
+              "annotated_tactic": [
+                "\"rintro \\u27e8xli, complement, rfl\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "case h.refine_3.intro.intro\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nxli : PrimeSpectrum R[X]\ncomplement : xli \u2208 (zeroLocus {f})\u1d9c\n\u22a2 (PrimeSpectrum.comap C) xli \u2208 imageOfDf f",
+              "state_before": "case h.refine_3\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nx : PrimeSpectrum R\n\u22a2 x \u2208 \u21d1(PrimeSpectrum.comap C) '' (zeroLocus {f})\u1d9c \u2192 x \u2208 imageOfDf f",
+              "tactic": "rintro \u27e8xli, complement, rfl\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>comap_C_mem_imageOfDf<\\/a> complement\"",
+                "[{\"full_name\":\"AlgebraicGeometry.Polynomial.comap_C_mem_imageOfDf\",\"def_path\":\"Mathlib\\/AlgebraicGeometry\\/PrimeSpectrum\\/IsOpenComapC.lean\",\"def_pos\":[46,9],\"def_end_pos\":[46,30]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.refine_3.intro.intro\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nxli : PrimeSpectrum R[X]\ncomplement : xli \u2208 (zeroLocus {f})\u1d9c\n\u22a2 (PrimeSpectrum.comap C) xli \u2208 imageOfDf f",
+              "tactic": "exact comap_C_mem_imageOfDf complement"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/AlgebraicGeometry/PrimeSpectrum/IsOpenComapC.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'intro hdenom'",
+        "full_name": "MaximalSpectrum.iInf_localization_eq_bot",
+        "id": "MaximalSpectrum.iInf_localization_eq_bot",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            117,
+            83
+          ],
+          "file_path": "Mathlib/AlgebraicGeometry/PrimeSpectrum/Maximal.lean",
+          "full_name": "MaximalSpectrum.iInf_localization_eq_bot",
+          "start": [
+            92,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"ext x\"",
+                "[]"
+              ],
+              "state_after": "case h\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 x \u2208 \u2a05 v, Localization.subalgebra.ofField K v.asIdeal.primeCompl \u22ef \u2194 x \u2208 \u22a5",
+              "state_before": "R : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\n\u22a2 \u2a05 v, Localization.subalgebra.ofField K v.asIdeal.primeCompl \u22ef = \u22a5",
+              "tactic": "ext x"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Algebra.mem_bot<\\/a>, <a>Algebra.mem_iInf<\\/a>]\"",
+                "[{\"full_name\":\"Algebra.mem_bot\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Subalgebra\\/Basic.lean\",\"def_pos\":[884,9],\"def_end_pos\":[884,16]},{\"full_name\":\"Algebra.mem_iInf\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Subalgebra\\/Basic.lean\",\"def_pos\":[871,9],\"def_end_pos\":[871,17]}]"
+              ],
+              "state_after": "case h\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 (\u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef) \u2194\n    x \u2208 range \u21d1(algebraMap R K)",
+              "state_before": "case h\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 x \u2208 \u2a05 v, Localization.subalgebra.ofField K v.asIdeal.primeCompl \u22ef \u2194 x \u2208 \u22a5",
+              "tactic": "rw [Algebra.mem_bot, Algebra.mem_iInf]"
+            },
+            {
+              "annotated_tactic": [
+                "\"constructor\"",
+                "[]"
+              ],
+              "state_after": "case h.mp\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 (\u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef) \u2192\n    x \u2208 range \u21d1(algebraMap R K)\n\ncase h.mpr\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 x \u2208 range \u21d1(algebraMap R K) \u2192 \u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef",
+              "state_before": "case h\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 (\u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef) \u2194\n    x \u2208 range \u21d1(algebraMap R K)",
+              "tactic": "constructor"
+            },
+            {
+              "annotated_tactic": [
+                "\"contrapose\"",
+                "[]"
+              ],
+              "state_after": "case h.mp\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 x \u2209 range \u21d1(algebraMap R K) \u2192 \u00ac\u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef",
+              "state_before": "case h.mp\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 (\u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef) \u2192\n    x \u2208 range \u21d1(algebraMap R K)",
+              "tactic": "contrapose"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro hrange hlocal\"",
+                "[]"
+              ],
+              "state_after": "case h.mp\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\nhrange : x \u2209 range \u21d1(algebraMap R K)\nhlocal : \u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\n\u22a2 False",
+              "state_before": "case h.mp\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 x \u2209 range \u21d1(algebraMap R K) \u2192 \u00ac\u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef",
+              "tactic": "intro hrange hlocal"
+            },
+            {
+              "annotated_tactic": [
+                "\"let denom : <a>Ideal<\\/a> R := (<a>Submodule.span<\\/a> R {1} : <a>Submodule<\\/a> R K).<a>colon<\\/a> (<a>Submodule.span<\\/a> R {x})\"",
+                "[{\"full_name\":\"Ideal\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Basic.lean\",\"def_pos\":[41,8],\"def_end_pos\":[41,13]},{\"full_name\":\"Submodule.span\",\"def_path\":\"Mathlib\\/LinearAlgebra\\/Span.lean\",\"def_pos\":[51,5],\"def_end_pos\":[51,9]},{\"full_name\":\"Submodule\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Submodule\\/Basic.lean\",\"def_pos\":[37,11],\"def_end_pos\":[37,20]},{\"full_name\":\"Submodule.colon\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Colon.lean\",\"def_pos\":[25,5],\"def_end_pos\":[25,10]},{\"full_name\":\"Submodule.span\",\"def_path\":\"Mathlib\\/LinearAlgebra\\/Span.lean\",\"def_pos\":[51,5],\"def_end_pos\":[51,9]}]"
+              ],
+              "state_after": "case h.mp\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\nhrange : x \u2209 range \u21d1(algebraMap R K)\nhlocal : \u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {x})\n\u22a2 False",
+              "state_before": "case h.mp\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\nhrange : x \u2209 range \u21d1(algebraMap R K)\nhlocal : \u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\n\u22a2 False",
+              "tactic": "let denom : Ideal R := (Submodule.span R {1} : Submodule R K).colon (Submodule.span R {x})"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hdenom : (1 : R) \\u2209 denom := by\\n      intro hdenom\\n      rcases Submodule.mem_span_singleton.mp\\n        (Submodule.mem_colon.mp hdenom x <| <a>Submodule.mem_span_singleton_self<\\/a> x) with \\u27e8y, hy\\u27e9\\n      exact hrange \\u27e8y, by rw [\\u2190 <a>mul_one<\\/a> <| <a>algebraMap<\\/a> R K y, \\u2190 <a>Algebra.smul_def<\\/a>, hy, <a>one_smul<\\/a>]\\u27e9\"",
+                "[{\"full_name\":\"Submodule.mem_span_singleton_self\",\"def_path\":\"Mathlib\\/LinearAlgebra\\/Span.lean\",\"def_pos\":[474,9],\"def_end_pos\":[474,32]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"algebraMap\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Defs.lean\",\"def_pos\":[110,5],\"def_end_pos\":[110,15]},{\"full_name\":\"Algebra.smul_def\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Defs.lean\",\"def_pos\":[326,9],\"def_end_pos\":[326,17]},{\"full_name\":\"one_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[453,7],\"def_end_pos\":[453,15]}]"
+              ],
+              "state_after": "case h.mp\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\nhrange : x \u2209 range \u21d1(algebraMap R K)\nhlocal : \u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {x})\nhdenom : 1 \u2209 denom\n\u22a2 False",
+              "state_before": "case h.mp\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\nhrange : x \u2209 range \u21d1(algebraMap R K)\nhlocal : \u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {x})\n\u22a2 False",
+              "tactic": "have hdenom : (1 : R) \u2209 denom := by\n  intro hdenom\n  rcases Submodule.mem_span_singleton.mp\n    (Submodule.mem_colon.mp hdenom x <| Submodule.mem_span_singleton_self x) with \u27e8y, hy\u27e9\n  exact hrange \u27e8y, by rw [\u2190 mul_one <| algebraMap R K y, \u2190 Algebra.smul_def, hy, one_smul]\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rcases denom.exists_le_maximal fun h => (h \\u25b8 hdenom) <a>Submodule.mem_top<\\/a> with \\u27e8max, hmax, hle\\u27e9\"",
+                "[{\"full_name\":\"Submodule.mem_top\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Submodule\\/Lattice.lean\",\"def_pos\":[160,9],\"def_end_pos\":[160,16]}]"
+              ],
+              "state_after": "case h.mp.intro.intro\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\nhrange : x \u2209 range \u21d1(algebraMap R K)\nhlocal : \u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {x})\nhdenom : 1 \u2209 denom\nmax : Ideal R\nhmax : max.IsMaximal\nhle : denom \u2264 max\n\u22a2 False",
+              "state_before": "case h.mp\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\nhrange : x \u2209 range \u21d1(algebraMap R K)\nhlocal : \u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {x})\nhdenom : 1 \u2209 denom\n\u22a2 False",
+              "tactic": "rcases denom.exists_le_maximal fun h => (h \u25b8 hdenom) Submodule.mem_top with \u27e8max, hmax, hle\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rcases hlocal \\u27e8max, hmax\\u27e9 with \\u27e8n, d, hd, rfl\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "case h.mp.intro.intro.intro.intro.intro\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nmax : Ideal R\nhmax : max.IsMaximal\nn d : R\nhd : d \u2208 { asIdeal := max, IsMaximal := hmax }.asIdeal.primeCompl\nhrange : (algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9 \u2209 range \u21d1(algebraMap R K)\nhlocal :\n  \u2200 (i : MaximalSpectrum R),\n    (algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9 \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {(algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9})\nhdenom : 1 \u2209 denom\nhle : denom \u2264 max\n\u22a2 False",
+              "state_before": "case h.mp.intro.intro\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\nhrange : x \u2209 range \u21d1(algebraMap R K)\nhlocal : \u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {x})\nhdenom : 1 \u2209 denom\nmax : Ideal R\nhmax : max.IsMaximal\nhle : denom \u2264 max\n\u22a2 False",
+              "tactic": "rcases hlocal \u27e8max, hmax\u27e9 with \u27e8n, d, hd, rfl\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply hd (hle <| Submodule.mem_colon.mpr fun _ hy => _)\"",
+                "[]"
+              ],
+              "state_after": "R : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nmax : Ideal R\nhmax : max.IsMaximal\nn d : R\nhd : d \u2208 { asIdeal := max, IsMaximal := hmax }.asIdeal.primeCompl\nhrange : (algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9 \u2209 range \u21d1(algebraMap R K)\nhlocal :\n  \u2200 (i : MaximalSpectrum R),\n    (algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9 \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {(algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9})\nhdenom : 1 \u2209 denom\nhle : denom \u2264 max\n\u22a2 \u2200 x \u2208 Submodule.span R {(algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9}, d \u2022 x \u2208 Submodule.span R {1}",
+              "state_before": "case h.mp.intro.intro.intro.intro.intro\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nmax : Ideal R\nhmax : max.IsMaximal\nn d : R\nhd : d \u2208 { asIdeal := max, IsMaximal := hmax }.asIdeal.primeCompl\nhrange : (algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9 \u2209 range \u21d1(algebraMap R K)\nhlocal :\n  \u2200 (i : MaximalSpectrum R),\n    (algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9 \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {(algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9})\nhdenom : 1 \u2209 denom\nhle : denom \u2264 max\n\u22a2 False",
+              "tactic": "apply hd (hle <| Submodule.mem_colon.mpr fun _ hy => _)"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro _ hy\"",
+                "[]"
+              ],
+              "state_after": "R : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nmax : Ideal R\nhmax : max.IsMaximal\nn d : R\nhd : d \u2208 { asIdeal := max, IsMaximal := hmax }.asIdeal.primeCompl\nhrange : (algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9 \u2209 range \u21d1(algebraMap R K)\nhlocal :\n  \u2200 (i : MaximalSpectrum R),\n    (algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9 \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {(algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9})\nhdenom : 1 \u2209 denom\nhle : denom \u2264 max\nx\u271d : K\nhy : x\u271d \u2208 Submodule.span R {(algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9}\n\u22a2 d \u2022 x\u271d \u2208 Submodule.span R {1}",
+              "state_before": "R : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nmax : Ideal R\nhmax : max.IsMaximal\nn d : R\nhd : d \u2208 { asIdeal := max, IsMaximal := hmax }.asIdeal.primeCompl\nhrange : (algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9 \u2209 range \u21d1(algebraMap R K)\nhlocal :\n  \u2200 (i : MaximalSpectrum R),\n    (algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9 \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {(algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9})\nhdenom : 1 \u2209 denom\nhle : denom \u2264 max\n\u22a2 \u2200 x \u2208 Submodule.span R {(algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9}, d \u2022 x \u2208 Submodule.span R {1}",
+              "tactic": "intro _ hy"
+            },
+            {
+              "annotated_tactic": [
+                "\"rcases Submodule.mem_span_singleton.mp hy with \\u27e8y, rfl\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "case intro\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nmax : Ideal R\nhmax : max.IsMaximal\nn d : R\nhd : d \u2208 { asIdeal := max, IsMaximal := hmax }.asIdeal.primeCompl\nhrange : (algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9 \u2209 range \u21d1(algebraMap R K)\nhlocal :\n  \u2200 (i : MaximalSpectrum R),\n    (algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9 \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {(algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9})\nhdenom : 1 \u2209 denom\nhle : denom \u2264 max\ny : R\nhy : y \u2022 ((algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9) \u2208 Submodule.span R {(algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9}\n\u22a2 d \u2022 y \u2022 ((algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9) \u2208 Submodule.span R {1}",
+              "state_before": "R : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nmax : Ideal R\nhmax : max.IsMaximal\nn d : R\nhd : d \u2208 { asIdeal := max, IsMaximal := hmax }.asIdeal.primeCompl\nhrange : (algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9 \u2209 range \u21d1(algebraMap R K)\nhlocal :\n  \u2200 (i : MaximalSpectrum R),\n    (algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9 \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {(algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9})\nhdenom : 1 \u2209 denom\nhle : denom \u2264 max\nx\u271d : K\nhy : x\u271d \u2208 Submodule.span R {(algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9}\n\u22a2 d \u2022 x\u271d \u2208 Submodule.span R {1}",
+              "tactic": "rcases Submodule.mem_span_singleton.mp hy with \u27e8y, rfl\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact Submodule.mem_span_singleton.mpr \\u27e8y * n, by\\n      rw [<a>Algebra.smul_def<\\/a>, <a>mul_one<\\/a>, <a>map_mul<\\/a>, <a>smul_comm<\\/a>, <a>Algebra.smul_def<\\/a>, <a>Algebra.smul_def<\\/a>,\\n        <a>mul_comm<\\/a> <| <a>algebraMap<\\/a> R K d,\\n        <a>inv_mul_cancel_right\\u2080<\\/a> <|\\n          (<a>map_ne_zero_iff<\\/a> _ <| <a>NoZeroSMulDivisors.algebraMap_injective<\\/a> R K).<a>mpr<\\/a> fun h =>\\n            (h \\u25b8 hd) max.zero_mem]\\u27e9\"",
+                "[{\"full_name\":\"Algebra.smul_def\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Defs.lean\",\"def_pos\":[326,9],\"def_end_pos\":[326,17]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"map_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[309,9],\"def_end_pos\":[309,16]},{\"full_name\":\"SMulCommClass.smul_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[183,3],\"def_end_pos\":[183,12]},{\"full_name\":\"Algebra.smul_def\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Defs.lean\",\"def_pos\":[326,9],\"def_end_pos\":[326,17]},{\"full_name\":\"Algebra.smul_def\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Defs.lean\",\"def_pos\":[326,9],\"def_end_pos\":[326,17]},{\"full_name\":\"mul_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[332,9],\"def_end_pos\":[332,17]},{\"full_name\":\"algebraMap\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Defs.lean\",\"def_pos\":[110,5],\"def_end_pos\":[110,15]},{\"full_name\":\"inv_mul_cancel_right\\u2080\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Basic.lean\",\"def_pos\":[294,9],\"def_end_pos\":[294,30]},{\"full_name\":\"map_ne_zero_iff\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[226,3],\"def_end_pos\":[226,14]},{\"full_name\":\"NoZeroSMulDivisors.algebraMap_injective\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Basic.lean\",\"def_pos\":[353,9],\"def_end_pos\":[353,29]},{\"full_name\":\"Iff.mpr\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[120,3],\"def_end_pos\":[120,6]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case intro\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nmax : Ideal R\nhmax : max.IsMaximal\nn d : R\nhd : d \u2208 { asIdeal := max, IsMaximal := hmax }.asIdeal.primeCompl\nhrange : (algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9 \u2209 range \u21d1(algebraMap R K)\nhlocal :\n  \u2200 (i : MaximalSpectrum R),\n    (algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9 \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {(algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9})\nhdenom : 1 \u2209 denom\nhle : denom \u2264 max\ny : R\nhy : y \u2022 ((algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9) \u2208 Submodule.span R {(algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9}\n\u22a2 d \u2022 y \u2022 ((algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9) \u2208 Submodule.span R {1}",
+              "tactic": "exact Submodule.mem_span_singleton.mpr \u27e8y * n, by\n  rw [Algebra.smul_def, mul_one, map_mul, smul_comm, Algebra.smul_def, Algebra.smul_def,\n    mul_comm <| algebraMap R K d,\n    inv_mul_cancel_right\u2080 <|\n      (map_ne_zero_iff _ <| NoZeroSMulDivisors.algebraMap_injective R K).mpr fun h =>\n        (h \u25b8 hd) max.zero_mem]\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro hdenom\"",
+                "[]"
+              ],
+              "state_after": "R : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\nhrange : x \u2209 range \u21d1(algebraMap R K)\nhlocal : \u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {x})\nhdenom : 1 \u2208 denom\n\u22a2 False",
+              "state_before": "R : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\nhrange : x \u2209 range \u21d1(algebraMap R K)\nhlocal : \u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {x})\n\u22a2 1 \u2209 denom",
+              "tactic": "intro hdenom"
+            },
+            {
+              "annotated_tactic": [
+                "\"rcases Submodule.mem_span_singleton.mp\\n        (Submodule.mem_colon.mp hdenom x <| <a>Submodule.mem_span_singleton_self<\\/a> x) with \\u27e8y, hy\\u27e9\"",
+                "[{\"full_name\":\"Submodule.mem_span_singleton_self\",\"def_path\":\"Mathlib\\/LinearAlgebra\\/Span.lean\",\"def_pos\":[474,9],\"def_end_pos\":[474,32]}]"
+              ],
+              "state_after": "case intro\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\nhrange : x \u2209 range \u21d1(algebraMap R K)\nhlocal : \u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {x})\nhdenom : 1 \u2208 denom\ny : R\nhy : y \u2022 1 = 1 \u2022 x\n\u22a2 False",
+              "state_before": "R : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\nhrange : x \u2209 range \u21d1(algebraMap R K)\nhlocal : \u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {x})\nhdenom : 1 \u2208 denom\n\u22a2 False",
+              "tactic": "rcases Submodule.mem_span_singleton.mp\n  (Submodule.mem_colon.mp hdenom x <| Submodule.mem_span_singleton_self x) with \u27e8y, hy\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact hrange \\u27e8y, by rw [\\u2190 <a>mul_one<\\/a> <| <a>algebraMap<\\/a> R K y, \\u2190 <a>Algebra.smul_def<\\/a>, hy, <a>one_smul<\\/a>]\\u27e9\"",
+                "[{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"algebraMap\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Defs.lean\",\"def_pos\":[110,5],\"def_end_pos\":[110,15]},{\"full_name\":\"Algebra.smul_def\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Defs.lean\",\"def_pos\":[326,9],\"def_end_pos\":[326,17]},{\"full_name\":\"one_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[453,7],\"def_end_pos\":[453,15]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case intro\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\nhrange : x \u2209 range \u21d1(algebraMap R K)\nhlocal : \u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {x})\nhdenom : 1 \u2208 denom\ny : R\nhy : y \u2022 1 = 1 \u2022 x\n\u22a2 False",
+              "tactic": "exact hrange \u27e8y, by rw [\u2190 mul_one <| algebraMap R K y, \u2190 Algebra.smul_def, hy, one_smul]\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>mul_one<\\/a> <| <a>algebraMap<\\/a> R K y, \\u2190 <a>Algebra.smul_def<\\/a>, hy, <a>one_smul<\\/a>]\"",
+                "[{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"algebraMap\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Defs.lean\",\"def_pos\":[110,5],\"def_end_pos\":[110,15]},{\"full_name\":\"Algebra.smul_def\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Defs.lean\",\"def_pos\":[326,9],\"def_end_pos\":[326,17]},{\"full_name\":\"one_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[453,7],\"def_end_pos\":[453,15]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\nhrange : x \u2209 range \u21d1(algebraMap R K)\nhlocal : \u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {x})\nhdenom : 1 \u2208 denom\ny : R\nhy : y \u2022 1 = 1 \u2022 x\n\u22a2 (algebraMap R K) y = x",
+              "tactic": "rw [\u2190 mul_one <| algebraMap R K y, \u2190 Algebra.smul_def, hy, one_smul]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Algebra.smul_def<\\/a>, <a>mul_one<\\/a>, <a>map_mul<\\/a>, <a>smul_comm<\\/a>, <a>Algebra.smul_def<\\/a>, <a>Algebra.smul_def<\\/a>,\\n        <a>mul_comm<\\/a> <| <a>algebraMap<\\/a> R K d,\\n        <a>inv_mul_cancel_right\\u2080<\\/a> <|\\n          (<a>map_ne_zero_iff<\\/a> _ <| <a>NoZeroSMulDivisors.algebraMap_injective<\\/a> R K).<a>mpr<\\/a> fun h =>\\n            (h \\u25b8 hd) max.zero_mem]\"",
+                "[{\"full_name\":\"Algebra.smul_def\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Defs.lean\",\"def_pos\":[326,9],\"def_end_pos\":[326,17]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"map_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[309,9],\"def_end_pos\":[309,16]},{\"full_name\":\"SMulCommClass.smul_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[183,3],\"def_end_pos\":[183,12]},{\"full_name\":\"Algebra.smul_def\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Defs.lean\",\"def_pos\":[326,9],\"def_end_pos\":[326,17]},{\"full_name\":\"Algebra.smul_def\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Defs.lean\",\"def_pos\":[326,9],\"def_end_pos\":[326,17]},{\"full_name\":\"mul_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[332,9],\"def_end_pos\":[332,17]},{\"full_name\":\"algebraMap\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Defs.lean\",\"def_pos\":[110,5],\"def_end_pos\":[110,15]},{\"full_name\":\"inv_mul_cancel_right\\u2080\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Basic.lean\",\"def_pos\":[294,9],\"def_end_pos\":[294,30]},{\"full_name\":\"map_ne_zero_iff\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[226,3],\"def_end_pos\":[226,14]},{\"full_name\":\"NoZeroSMulDivisors.algebraMap_injective\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Basic.lean\",\"def_pos\":[353,9],\"def_end_pos\":[353,29]},{\"full_name\":\"Iff.mpr\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[120,3],\"def_end_pos\":[120,6]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nmax : Ideal R\nhmax : max.IsMaximal\nn d : R\nhd : d \u2208 { asIdeal := max, IsMaximal := hmax }.asIdeal.primeCompl\nhrange : (algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9 \u2209 range \u21d1(algebraMap R K)\nhlocal :\n  \u2200 (i : MaximalSpectrum R),\n    (algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9 \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef\ndenom : Ideal R := (Submodule.span R {1}).colon (Submodule.span R {(algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9})\nhdenom : 1 \u2209 denom\nhle : denom \u2264 max\ny : R\nhy : y \u2022 ((algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9) \u2208 Submodule.span R {(algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9}\n\u22a2 (y * n) \u2022 1 = d \u2022 y \u2022 ((algebraMap R K) n * ((algebraMap R K) d)\u207b\u00b9)",
+              "tactic": "rw [Algebra.smul_def, mul_one, map_mul, smul_comm, Algebra.smul_def, Algebra.smul_def,\n  mul_comm <| algebraMap R K d,\n  inv_mul_cancel_right\u2080 <|\n    (map_ne_zero_iff _ <| NoZeroSMulDivisors.algebraMap_injective R K).mpr fun h =>\n      (h \u25b8 hd) max.zero_mem]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rintro \\u27e8y, rfl\\u27e9 \\u27e8v, hv\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "case h.mpr.intro.mk\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\ny : R\nv : Ideal R\nhv : v.IsMaximal\n\u22a2 (algebraMap R K) y \u2208 Localization.subalgebra.ofField K { asIdeal := v, IsMaximal := hv }.asIdeal.primeCompl \u22ef",
+              "state_before": "case h.mpr\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 x \u2208 range \u21d1(algebraMap R K) \u2192 \u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef",
+              "tactic": "rintro \u27e8y, rfl\u27e9 \u27e8v, hv\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact \\u27e8y, 1, v.ne_top_iff_one.mp hv.ne_top, by rw [<a>map_one<\\/a>, <a>inv_one<\\/a>, <a>mul_one<\\/a>]\\u27e9\"",
+                "[{\"full_name\":\"map_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[204,9],\"def_end_pos\":[204,16]},{\"full_name\":\"inv_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1118,9],\"def_end_pos\":[1118,16]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.mpr.intro.mk\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\ny : R\nv : Ideal R\nhv : v.IsMaximal\n\u22a2 (algebraMap R K) y \u2208 Localization.subalgebra.ofField K { asIdeal := v, IsMaximal := hv }.asIdeal.primeCompl \u22ef",
+              "tactic": "exact \u27e8y, 1, v.ne_top_iff_one.mp hv.ne_top, by rw [map_one, inv_one, mul_one]\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>map_one<\\/a>, <a>inv_one<\\/a>, <a>mul_one<\\/a>]\"",
+                "[{\"full_name\":\"map_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[204,9],\"def_end_pos\":[204,16]},{\"full_name\":\"inv_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1118,9],\"def_end_pos\":[1118,16]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\ny : R\nv : Ideal R\nhv : v.IsMaximal\n\u22a2 (algebraMap R K) y = (algebraMap R K) y * ((algebraMap R K) 1)\u207b\u00b9",
+              "tactic": "rw [map_one, inv_one, mul_one]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/AlgebraicGeometry/PrimeSpectrum/Maximal.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MaximalSpectrum.toPrimeSpectrum_continuous",
+        "id": "MaximalSpectrum.toPrimeSpectrum_continuous",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            84,
+            25
+          ],
+          "file_path": "Mathlib/AlgebraicGeometry/PrimeSpectrum/Maximal.lean",
+          "full_name": "MaximalSpectrum.toPrimeSpectrum_continuous",
+          "start": [
+            83,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/AlgebraicGeometry/PrimeSpectrum/Maximal.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rw [map_one, inv_one, mul_one]'",
+        "full_name": "PrimeSpectrum.iInf_localization_eq_bot",
+        "id": "PrimeSpectrum.iInf_localization_eq_bot",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            138,
+            83
+          ],
+          "file_path": "Mathlib/AlgebraicGeometry/PrimeSpectrum/Maximal.lean",
+          "full_name": "PrimeSpectrum.iInf_localization_eq_bot",
+          "start": [
+            129,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"ext x\"",
+                "[]"
+              ],
+              "state_after": "case h\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 x \u2208 \u2a05 v, Localization.subalgebra.ofField K v.asIdeal.primeCompl \u22ef \u2194 x \u2208 \u22a5",
+              "state_before": "R : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\n\u22a2 \u2a05 v, Localization.subalgebra.ofField K v.asIdeal.primeCompl \u22ef = \u22a5",
+              "tactic": "ext x"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Algebra.mem_iInf<\\/a>]\"",
+                "[{\"full_name\":\"Algebra.mem_iInf\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Subalgebra\\/Basic.lean\",\"def_pos\":[871,9],\"def_end_pos\":[871,17]}]"
+              ],
+              "state_after": "case h\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 (\u2200 (i : PrimeSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef) \u2194 x \u2208 \u22a5",
+              "state_before": "case h\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 x \u2208 \u2a05 v, Localization.subalgebra.ofField K v.asIdeal.primeCompl \u22ef \u2194 x \u2208 \u22a5",
+              "tactic": "rw [Algebra.mem_iInf]"
+            },
+            {
+              "annotated_tactic": [
+                "\"constructor\"",
+                "[]"
+              ],
+              "state_after": "case h.mp\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 (\u2200 (i : PrimeSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef) \u2192 x \u2208 \u22a5\n\ncase h.mpr\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 x \u2208 \u22a5 \u2192 \u2200 (i : PrimeSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef",
+              "state_before": "case h\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 (\u2200 (i : PrimeSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef) \u2194 x \u2208 \u22a5",
+              "tactic": "constructor"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>MaximalSpectrum.iInf_localization_eq_bot<\\/a>, <a>Algebra.mem_iInf<\\/a>]\"",
+                "[{\"full_name\":\"MaximalSpectrum.iInf_localization_eq_bot\",\"def_path\":\"Mathlib\\/AlgebraicGeometry\\/PrimeSpectrum\\/Maximal.lean\",\"def_pos\":[92,9],\"def_end_pos\":[92,33]},{\"full_name\":\"Algebra.mem_iInf\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Subalgebra\\/Basic.lean\",\"def_pos\":[871,9],\"def_end_pos\":[871,17]}]"
+              ],
+              "state_after": "case h.mp\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 (\u2200 (i : PrimeSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef) \u2192\n    \u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef",
+              "state_before": "case h.mp\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 (\u2200 (i : PrimeSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef) \u2192 x \u2208 \u22a5",
+              "tactic": "rw [\u2190 MaximalSpectrum.iInf_localization_eq_bot, Algebra.mem_iInf]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact fun hx \\u27e8v, hv\\u27e9 => hx \\u27e8v, hv.isPrime\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.mp\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 (\u2200 (i : PrimeSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef) \u2192\n    \u2200 (i : MaximalSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef",
+              "tactic": "exact fun hx \u27e8v, hv\u27e9 => hx \u27e8v, hv.isPrime\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Algebra.mem_bot<\\/a>]\"",
+                "[{\"full_name\":\"Algebra.mem_bot\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Subalgebra\\/Basic.lean\",\"def_pos\":[884,9],\"def_end_pos\":[884,16]}]"
+              ],
+              "state_after": "case h.mpr\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 x \u2208 Set.range \u21d1(algebraMap R K) \u2192\n    \u2200 (i : PrimeSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef",
+              "state_before": "case h.mpr\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 x \u2208 \u22a5 \u2192 \u2200 (i : PrimeSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef",
+              "tactic": "rw [Algebra.mem_bot]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rintro \\u27e8y, rfl\\u27e9 \\u27e8v, hv\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "case h.mpr.intro.mk\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\ny : R\nv : Ideal R\nhv : v.IsPrime\n\u22a2 (algebraMap R K) y \u2208 Localization.subalgebra.ofField K { asIdeal := v, isPrime := hv }.asIdeal.primeCompl \u22ef",
+              "state_before": "case h.mpr\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\nx : K\n\u22a2 x \u2208 Set.range \u21d1(algebraMap R K) \u2192\n    \u2200 (i : PrimeSpectrum R), x \u2208 Localization.subalgebra.ofField K i.asIdeal.primeCompl \u22ef",
+              "tactic": "rintro \u27e8y, rfl\u27e9 \u27e8v, hv\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact \\u27e8y, 1, v.ne_top_iff_one.mp hv.ne_top, by rw [<a>map_one<\\/a>, <a>inv_one<\\/a>, <a>mul_one<\\/a>]\\u27e9\"",
+                "[{\"full_name\":\"map_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[204,9],\"def_end_pos\":[204,16]},{\"full_name\":\"inv_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1118,9],\"def_end_pos\":[1118,16]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.mpr.intro.mk\nR : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\ny : R\nv : Ideal R\nhv : v.IsPrime\n\u22a2 (algebraMap R K) y \u2208 Localization.subalgebra.ofField K { asIdeal := v, isPrime := hv }.asIdeal.primeCompl \u22ef",
+              "tactic": "exact \u27e8y, 1, v.ne_top_iff_one.mp hv.ne_top, by rw [map_one, inv_one, mul_one]\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>map_one<\\/a>, <a>inv_one<\\/a>, <a>mul_one<\\/a>]\"",
+                "[{\"full_name\":\"map_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[204,9],\"def_end_pos\":[204,16]},{\"full_name\":\"inv_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1118,9],\"def_end_pos\":[1118,16]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u\ninst\u271d\u2074 : CommRing R\ninst\u271d\u00b3 : IsDomain R\nK : Type v\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Algebra R K\ninst\u271d : IsFractionRing R K\ny : R\nv : Ideal R\nhv : v.IsPrime\n\u22a2 (algebraMap R K) y = (algebraMap R K) y * ((algebraMap R K) 1)\u207b\u00b9",
+              "tactic": "rw [map_one, inv_one, mul_one]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/AlgebraicGeometry/PrimeSpectrum/Maximal.lean"
+      }
+    ],
+    "input_proofs": 9,
+    "input_units": 2,
+    "proofs": 4,
+    "published_proofs": 4,
+    "published_transitions": 10,
+    "replay_failures": [],
+    "transitions": 10,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000360-0000-effb24ffb2d9fb20.parquet",
+      "sha256": "effb24ffb2d9fb20a41e570a18c5782a459ca548d6e557e7dc3b29e638deeb1c",
+      "bytes": 64690,
+      "rows": 10,
+      "revision": "1426f15e0d5b8b6fa3dd64f88edd216a2f847c64"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:AlgebraicGeometry.Polynomial.isOpenMap_comap_C",
+    "mathlib:AlgebraicGeometry.Polynomial.isOpen_imageOfDf",
+    "mathlib:MaximalSpectrum.toPrimeSpectrum_injective",
+    "mathlib:MaximalSpectrum.toPrimeSpectrum_range"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/AlgebraicGeometry/PrimeSpectrum/IsOpenComapC.lean\",null,null,\"AlgebraicGeometry.Polynomial.isOpenMap_comap_C\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/AlgebraicGeometry/PrimeSpectrum/IsOpenComapC.lean\",null,null,\"AlgebraicGeometry.Polynomial.isOpen_imageOfDf\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/AlgebraicGeometry/PrimeSpectrum/Maximal.lean\",null,null,\"MaximalSpectrum.toPrimeSpectrum_injective\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/AlgebraicGeometry/PrimeSpectrum/Maximal.lean\",null,null,\"MaximalSpectrum.toPrimeSpectrum_range\"]"
+  ]
+}

manifests/batches/mathlib/000362.json ADDED Viewed

The diff for this file is too large to render. See raw diff

manifests/batches/numina/001116.json ADDED Viewed

	@@ -0,0 +1,51 @@

+{
+  "format": "leangpt-parquet-v2",
+  "batch": "numina/001116",
+  "batch_fingerprint": "0a0e27b5dd4066c5799656173c86a4d49881b24ff2dc30ebd18345fee7e7af03",
+  "evidence": {
+    "batch_fingerprint": "0a0e27b5dd4066c5799656173c86a4d49881b24ff2dc30ebd18345fee7e7af03",
+    "contamination_matches": [],
+    "failures": [],
+    "input_proofs": 5,
+    "input_units": 5,
+    "proofs": 5,
+    "published_proofs": 5,
+    "published_transitions": 23,
+    "replay_failures": [],
+    "trace_mode": "bundle",
+    "transitions": 23,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/numina-001116-0000-b18c6c56a64b64ea.parquet",
+      "sha256": "b18c6c56a64b64ea29af62d242d4ade244179e47abc9b75cf4914c32e8764a86",
+      "bytes": 417198,
+      "rows": 18,
+      "revision": "1426f15e0d5b8b6fa3dd64f88edd216a2f847c64"
+    },
+    {
+      "path": "data/dev/numina-001116-0000-3fe6e9cb874021c7.parquet",
+      "sha256": "3fe6e9cb874021c780580749505f65dc380789dc4def123b03763034cd115282",
+      "bytes": 195680,
+      "rows": 5,
+      "revision": "1426f15e0d5b8b6fa3dd64f88edd216a2f847c64"
+    }
+  ],
+  "proof_ids": [
+    "numina:2d5b5c8e-f408-5127-81dd-a7286d2559c1",
+    "numina:5df84962-d536-58b0-9d6c-6aab4f6f7142",
+    "numina:9d27788d-fd99-5a8d-b126-293d217a55b9",
+    "numina:bbfc9edd-9a73-5b59-a0a6-bcc76244d529",
+    "numina:fed20448-a86c-5b92-a1b5-bc9bb1e236d4"
+  ],
+  "proof_keys": [
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005580.lean\",\"30e569a2bd494e046a3575dad9f56073dc91215e36646538212b3a40fa677d89\",0,\"number_theory_611248\"]",
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005581.lean\",\"2d9dc81d4c4f04d692972bb8b5f75902084d94f90e51925830c99480a762363c\",0,\"inequalities_104785\"]",
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005582.lean\",\"a4b37c41f12a20b3a498eac5bc018e3848320cc02c0829fcbf86a4b915bb6d00\",0,\"Inequalities_613610\"]",
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005583.lean\",\"74adacce9d72feaf4e3487cc76b8b3b49d5a4c170e7a7b154249f53d7ab59985\",0,\"algebra_97758\"]",
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005584.lean\",\"46e6bac318074e762fe0ba022114eadd526f8a64b6833b60236434c0884a87ab\",0,\"algebra_228096\"]"
+  ]
+}

manifests/batches/numina/001117.json ADDED Viewed

	@@ -0,0 +1,51 @@

+{
+  "format": "leangpt-parquet-v2",
+  "batch": "numina/001117",
+  "batch_fingerprint": "c880b790803284b573fc8d0fe5aa871c9e3c57b16a748a575e4d5a8886e30f87",
+  "evidence": {
+    "batch_fingerprint": "c880b790803284b573fc8d0fe5aa871c9e3c57b16a748a575e4d5a8886e30f87",
+    "contamination_matches": [],
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manifests/batches/numina/001118.json ADDED Viewed

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manifests/batches/numina/001119.json ADDED Viewed

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manifests/batches/numina/001121.json ADDED Viewed

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