Datasets:

HyperCactus0
/

LeanTransitionCorpus

+{
+  "format": "leangpt-parquet-v2",
+  "batch": "deepseek/000306",
+  "batch_fingerprint": "25c9480dca54a5716fc1c117cd5c36b822591f1f986daff6f9228be8f312e075",
+  "evidence": {
+    "batch_fingerprint": "25c9480dca54a5716fc1c117cd5c36b822591f1f986daff6f9228be8f312e075",
+    "contamination_matches": [],
+    "failures": [],
+    "input_proofs": 50,
+    "input_units": 50,
+    "proofs": 50,
+    "published_proofs": 50,
+    "published_transitions": 122,
+    "replay_failures": [],
+    "trace_mode": "individual",
+    "transitions": 122,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/deepseek-000306-0000-5c81d134a1c4d45e.parquet",
+      "sha256": "5c81d134a1c4d45e5eac589fccfa1803db3d324cb39a579cad52bea48579a768",
+      "bytes": 347017,
+      "rows": 105,
+      "revision": "3590753b680b8e28dc2714818766a6fd7f4a158f"
+    },
+    {
+      "path": "data/dev/deepseek-000306-0000-cd286d51ec52dffb.parquet",
+      "sha256": "cd286d51ec52dffbc2f3a23288298aac56fd31c798583f4d881e62872a5e595b",
+      "bytes": 45094,
+      "rows": 9,
+      "revision": "3590753b680b8e28dc2714818766a6fd7f4a158f"
+    },
+    {
+      "path": "data/internal_test/deepseek-000306-0000-6d69e9ec17fc780c.parquet",
+      "sha256": "6d69e9ec17fc780c18bcbf13d2ed842c792d6f93792497258e2426fce7fc5af5",
+      "bytes": 43543,
+      "rows": 8,
+      "revision": "3590753b680b8e28dc2714818766a6fd7f4a158f"
+    }
+  ],
+  "proof_ids": [
+    "deepseek:thm_15342",
+    "deepseek:thm_15343",
+    "deepseek:thm_15344",
+    "deepseek:thm_15345",
+    "deepseek:thm_15346",
+    "deepseek:thm_15347",
+    "deepseek:thm_15348",
+    "deepseek:thm_15349",
+    "deepseek:thm_15350",
+    "deepseek:thm_15351",
+    "deepseek:thm_15352",
+    "deepseek:thm_15353",
+    "deepseek:thm_15354",
+    "deepseek:thm_15355",
+    "deepseek:thm_15356",
+    "deepseek:thm_15357",
+    "deepseek:thm_15358",
+    "deepseek:thm_15359",
+    "deepseek:thm_15360",
+    "deepseek:thm_15361",
+    "deepseek:thm_15362",
+    "deepseek:thm_15363",
+    "deepseek:thm_15364",
+    "deepseek:thm_15365",
+    "deepseek:thm_15366",
+    "deepseek:thm_15367",
+    "deepseek:thm_15368",
+    "deepseek:thm_15369",
+    "deepseek:thm_15370",
+    "deepseek:thm_15371",
+    "deepseek:thm_15372",
+    "deepseek:thm_15373",
+    "deepseek:thm_15374",
+    "deepseek:thm_15375",
+    "deepseek:thm_15376",
+    "deepseek:thm_15377",
+    "deepseek:thm_15378",
+    "deepseek:thm_15379",
+    "deepseek:thm_15380",
+    "deepseek:thm_15381",
+    "deepseek:thm_15382",
+    "deepseek:thm_15383",
+    "deepseek:thm_15384",
+    "deepseek:thm_15385",
+    "deepseek:thm_15386",
+    "deepseek:thm_15387",
+    "deepseek:thm_15388",
+    "deepseek:thm_15389",
+    "deepseek:thm_15390",
+    "deepseek:thm_15391"
+  ],
+  "proof_keys": [
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015300.lean\",\"5589dc0594f985e1891024d56a74a67f709c859168938fbadfffd5d52426c511\",0,\"thm_15342\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015301.lean\",\"1ec9ec96047711460f0cfe9427c267a5a5fa74a233f0a6ca873f44db9fdb5e7c\",0,\"thm_15343\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015302.lean\",\"8d65a24ec634eec6add8613d90440cc37cc617fd225ac4973e8ed420ffb661d2\",0,\"thm_15344\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015303.lean\",\"d22a722eafc9d8b67e12b9ffe139e5f31baf7acf73decc64dc66e36279f9a111\",0,\"thm_15345\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015304.lean\",\"c318d0616b87dcca7e55b6bb9975909d33739498a6ec661b5418a6f4166ff8bc\",0,\"thm_15346\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015305.lean\",\"d040d01015cebe8dccf6334d960603a1a491bf8068a1025ed1ceed9c98c4e1ba\",0,\"thm_15347\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015306.lean\",\"087f8ae36bab625027971f92276a4bb07f3fe366dfe679762d79f7e4db8b2687\",0,\"thm_15348\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015307.lean\",\"8327fbdb56ae3ef513bc890fcaa3affc4663d91783185c6803a7c3ce6526d243\",0,\"thm_15349\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015308.lean\",\"9a034d45a443056fb6c377dd994bcde924865d838dae4ea3c104ce631929c429\",0,\"thm_15350\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015309.lean\",\"da86ddcb730faa1f5d7e67b6b374e9a5348f96e46efe22664617df437c7e53aa\",0,\"thm_15351\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015310.lean\",\"3bec80ad600b549ea14bbf930c743cc2309ff1fb0d771da99060519b2964967e\",0,\"thm_15352\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015311.lean\",\"dd0f4fd122b956972e46433d667142e95b0f26a2b72571a4087a14e4cc50baef\",0,\"thm_15353\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015312.lean\",\"84a3788cb3338a6a996e3eea6c4020455aed3b926ed2208ba8bef270150990c7\",0,\"thm_15354\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015313.lean\",\"8ff8cdb2888492f44886a0e14881dfb651b22fe8bc6505b8c753945f3968756c\",0,\"thm_15355\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015314.lean\",\"3d37cac74c8d96bed2916f171fc280cb5853b08699f5494d3ac6d106adb149a6\",0,\"thm_15356\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015315.lean\",\"1b581cdc868c6b9b145d71b454ab72b3e5029c7ce18be9f21f322bff34a8bfa3\",0,\"thm_15357\"]",
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015321.lean\",\"e9ad3147cf116b07baba8397700daca4bbc2884ae61c09bcf1ee58cf1a399949\",0,\"thm_15363\"]",
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015324.lean\",\"72ed5505862ae1b745e911c64674a089f5fd8e121d51bbf97cc5a45671a0c073\",0,\"thm_15366\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015325.lean\",\"90f06169e0479f96ffca29d520c542c5760efd24bf209502ebb6b838a279fb52\",0,\"thm_15367\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015326.lean\",\"2008e6d03c3f9303f61b3301ee8e32f44b9d106b4abd0ee74b60634d1628dace\",0,\"thm_15368\"]",
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015329.lean\",\"77cd0335bc388e1cbbea00f1b30b78725d7ca99a2d7dd4df2c9ede3ab6b89d2b\",0,\"thm_15371\"]",
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015341.lean\",\"64a03658c3e2ba15857a490d58e01f4070f38a4cca0f4e632a211723ac5df608\",0,\"thm_15383\"]",
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015343.lean\",\"1e7ef8c71bc03bc517096916a229b2cc707d4620cabdb27e568fabb792beafc6\",0,\"thm_15385\"]",
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015346.lean\",\"0a89ca197dc3958af03508aada5707e13db148a807d9174d1090bd6373e500b4\",0,\"thm_15388\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015347.lean\",\"ad00052b63bdba46600140faac4db8c1f783ec4a2c68b637826ac4e8bd7c9a35\",0,\"thm_15389\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015348.lean\",\"323d004b64071f41c2d9ed7ab49879421c909d0ebb2a2d449bc14378fda2ecc8\",0,\"thm_15390\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015349.lean\",\"da6c7c1bc5f6e2c723bb11655364ffb4f96fe0036bc1a544752ba40bfcfef284\",0,\"thm_15391\"]"
+  ]
+}

manifests/batches/deepseek/000308.json ADDED Viewed

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

+{
+  "format": "leangpt-parquet-v2",
+  "batch": "deepseek/000308",
+  "batch_fingerprint": "f45774ba8cb36d2d247d75d1f6770d5d72b4eb2202915bb220e3d51c1ec28324",
+  "evidence": {
+    "batch_fingerprint": "f45774ba8cb36d2d247d75d1f6770d5d72b4eb2202915bb220e3d51c1ec28324",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "final replayable tactic does not close all goals",
+        "id": "thm_15455",
+        "index": 15413,
+        "reason": "import_failure",
+        "selection": {
+          "file_path": "Full/Proof_015413.lean",
+          "id": "thm_15455",
+          "index": 15413,
+          "metadata": {
+            "declaration_kind": "theorem",
+            "source_dataset": "deepseek",
+            "theorem_name": "thm_15455",
+            "theorem_ordinal": 0
+          },
+          "source_sha256": "3a810fcf1428d469436d5317069842bafb55a832d59b504c97afc5a927520bd4"
+        },
+        "source_file": "Full/Proof_015413.lean"
+      }
+    ],
+    "input_proofs": 50,
+    "input_units": 50,
+    "proofs": 49,
+    "published_proofs": 49,
+    "published_transitions": 114,
+    "replay_failures": [],
+    "trace_mode": "individual",
+    "transitions": 114,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/deepseek-000308-0000-34ffda329720007c.parquet",
+      "sha256": "34ffda329720007c75143889e1dbb3e40b10140ffc1b7f39bd271a31d0c6c870",
+      "bytes": 323618,
+      "rows": 97,
+      "revision": "3590753b680b8e28dc2714818766a6fd7f4a158f"
+    },
+    {
+      "path": "data/dev/deepseek-000308-0000-8c3a78e21f8a2703.parquet",
+      "sha256": "8c3a78e21f8a2703e13b773642d425b0e85f04419b3cc8a3bcb7176d6a16673d",
+      "bytes": 26657,
+      "rows": 1,
+      "revision": "3590753b680b8e28dc2714818766a6fd7f4a158f"
+    },
+    {
+      "path": "data/internal_test/deepseek-000308-0000-d9a1e25fd41f6c66.parquet",
+      "sha256": "d9a1e25fd41f6c661464ff6b1954462373a90906ce022aea79c4eefc79e934c7",
+      "bytes": 72034,
+      "rows": 16,
+      "revision": "3590753b680b8e28dc2714818766a6fd7f4a158f"
+    }
+  ],
+  "proof_ids": [
+    "deepseek:thm_15442",
+    "deepseek:thm_15443",
+    "deepseek:thm_15444",
+    "deepseek:thm_15445",
+    "deepseek:thm_15446",
+    "deepseek:thm_15447",
+    "deepseek:thm_15448",
+    "deepseek:thm_15449",
+    "deepseek:thm_15450",
+    "deepseek:thm_15451",
+    "deepseek:thm_15452",
+    "deepseek:thm_15453",
+    "deepseek:thm_15454",
+    "deepseek:thm_15456",
+    "deepseek:thm_15457",
+    "deepseek:thm_15458",
+    "deepseek:thm_15459",
+    "deepseek:thm_15460",
+    "deepseek:thm_15461",
+    "deepseek:thm_15462",
+    "deepseek:thm_15463",
+    "deepseek:thm_15464",
+    "deepseek:thm_15465",
+    "deepseek:thm_15466",
+    "deepseek:thm_15467",
+    "deepseek:thm_15468",
+    "deepseek:thm_15469",
+    "deepseek:thm_15470",
+    "deepseek:thm_15471",
+    "deepseek:thm_15472",
+    "deepseek:thm_15473",
+    "deepseek:thm_15474",
+    "deepseek:thm_15475",
+    "deepseek:thm_15476",
+    "deepseek:thm_15477",
+    "deepseek:thm_15478",
+    "deepseek:thm_15479",
+    "deepseek:thm_15480",
+    "deepseek:thm_15481",
+    "deepseek:thm_15482",
+    "deepseek:thm_15483",
+    "deepseek:thm_15484",
+    "deepseek:thm_15486",
+    "deepseek:thm_15487",
+    "deepseek:thm_15488",
+    "deepseek:thm_15489",
+    "deepseek:thm_15490",
+    "deepseek:thm_15491",
+    "deepseek:thm_15492"
+  ],
+  "proof_keys": [
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015400.lean\",\"8e535a081429c14b48cac0867772723b457349f5f38c10d6067ab31889487cc8\",0,\"thm_15442\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015401.lean\",\"b1c7c8c22e530234cef4e3e0a43d5fbc433d43ac5c228f99d79b97f3846f4e6a\",0,\"thm_15443\"]",
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015403.lean\",\"c8db4a6bae284219425025e3b51336ac981aa4a16b87650cc8c6cf0028bc2a6d\",0,\"thm_15445\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015404.lean\",\"5a20fc8e9bac656ab562327034ecdeff7b5ed5eea034e82a3f168ce5d7b37515\",0,\"thm_15446\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015405.lean\",\"b05cdf6c4f7b8afd6453c94711fca9c52b88893910977fc7d148d4592f724529\",0,\"thm_15447\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015406.lean\",\"79ab7b574f9f0a378694f0687250799400b31c1350494cbcf43448498548c6ce\",0,\"thm_15448\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015407.lean\",\"7d3253730393495fa8a851b6fb23f6dba3161960f58821386b30de1135c52b96\",0,\"thm_15449\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015408.lean\",\"3e8cbac640b75a321be3f6a36e5da778be13bee48b0c1ca18f08f5d00e60476f\",0,\"thm_15450\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015409.lean\",\"4edf4955a48294f79b9cf40505b00846695ef4883f6506d584c339df43c0fb85\",0,\"thm_15451\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015410.lean\",\"3c86be13afe45d6ffcd03286bb2df2facc9a0fd99fbf95eed4a3f02b00123113\",0,\"thm_15452\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015411.lean\",\"2e58e836070046c2d0138a3acc38eadb8179c2ef0132a24aa28624101def38d9\",0,\"thm_15453\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015412.lean\",\"b60074c36aa0fe2cff54987a0b16049cfda980b109d4701b2f5051d63deb7310\",0,\"thm_15454\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015414.lean\",\"05c2b60a6a0d8db03d12652ca49ae1dbfadb833512eb67ef5b4f6551e4af9be1\",0,\"thm_15456\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015415.lean\",\"a79503b6198636826e06885e948e0909805d14a58e0169528c2445ed6b4efa7b\",0,\"thm_15457\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015416.lean\",\"d673489f151f0ae2c7f8fd8a71d716d9e283fdb458eec13ffb7e7aee34c809f7\",0,\"thm_15458\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015417.lean\",\"57bdc4d50f4376611f91c5dc3d87b7becf0fdf29d43ef6e994d53617d8184b45\",0,\"thm_15459\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015418.lean\",\"23f163bea9ab5a03e6cdcc56865862575dfd4e457c23a45e8878d33c60bbeb73\",0,\"thm_15460\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015419.lean\",\"e6e92d5246c5c0b481fa4fddf73dfe4e2e0c4a9c54b12ed5cff589a0f2f965bd\",0,\"thm_15461\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015420.lean\",\"b4b9a6b91e8b03f71588f5c83d9edc3db2b195f670eee5922bd56332fae11197\",0,\"thm_15462\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015421.lean\",\"7c822747d9e31dc29e63b284193a80df58a387d2236094845e9e6c25424972bf\",0,\"thm_15463\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015422.lean\",\"26f5d452bcd30e09d4a1c1fae34d50c4004ad2e0d3148eaec1968158bb8bb5f7\",0,\"thm_15464\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015423.lean\",\"1f337fe07ec9502ea9dc6ef6f0d95f7f0d11ff1ecf4e54cdb3f28be333c2c95f\",0,\"thm_15465\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015424.lean\",\"b3409ddb0ac1e74c0ae075155130927bf4dc8232d1d209825bfff8e6ef85551f\",0,\"thm_15466\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015425.lean\",\"ad4756f161ca3b391c5b91b0f718a0a83abd6a423c497a452848637fa62b7381\",0,\"thm_15467\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015426.lean\",\"5f564f9339874b9cd82617ff091a358e8b3b4f6d86b2871e29ed953f36cc381d\",0,\"thm_15468\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015427.lean\",\"bb8a89650333655855cff118d14f3c5b68a727aec8ba0dfdb92400b251b34033\",0,\"thm_15469\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015428.lean\",\"079045174da60f99f965fae070f7ad2f34ee6a21baf4d95accb4f851ab63ddf8\",0,\"thm_15470\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015429.lean\",\"155bfed2999004efff4027b5c1cd9160a24f2a6d688a9bcbbcdfa5a9a59fc1e0\",0,\"thm_15471\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015430.lean\",\"ca52bbba302ae67a81ade63335f47d434f9267643cd214f5ab01beffc65f1d0e\",0,\"thm_15472\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015431.lean\",\"e0e827f7eb414da9a186bdda23acf92198976e21c195854cf29edcc9c1f106b1\",0,\"thm_15473\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015432.lean\",\"dc14cfe0e436ee110f8570b9337e4024589e51079f7ac1ed0748ddca97c08666\",0,\"thm_15474\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015433.lean\",\"78b6b368be7e3ad2431d081817a356cae16c854e7fe138aa98abace14e629235\",0,\"thm_15475\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015434.lean\",\"41da76fe7f874264945404ded05555007721e78a6f4d096a01ea51bfcce31958\",0,\"thm_15476\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015435.lean\",\"96be70242519d43482ba96b077b95eb011e5a00e03318ec183874f17e52b5616\",0,\"thm_15477\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015436.lean\",\"4687edd6d694f8a5f2eae49c5635a55bc0333a53019d802c7266a992f934cde6\",0,\"thm_15478\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015437.lean\",\"c1d5e01ce63d900466e12f8cd6540e78c0e0b9a5c3e2ba2f9899c415e2da7289\",0,\"thm_15479\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015438.lean\",\"d4213bfac9d018f2dee248727741a0fa9ce6bae5a3e740d707e42a8893cd08fe\",0,\"thm_15480\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015439.lean\",\"19208ae11290c81c550fbca9572eb1a71fd1e2abdc111910334dcc6f36295f14\",0,\"thm_15481\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015440.lean\",\"6f2aa2bb955053cb9ba25c255a4860f280e28548976903ea74c1ff4884b019e3\",0,\"thm_15482\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015441.lean\",\"b47efac3acc7145ef90776bc8b7e0e42b6d7ac8448bd6077a6d37a84c6ecbc05\",0,\"thm_15483\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015442.lean\",\"46a5ce744bc91149950c92b1995d94624a41443aa44fa3d6c5abaa86bcc94392\",0,\"thm_15484\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015443.lean\",\"66786f460a0398fdc97e71be0e8ca16a74df900ace097c5740820099eccc9992\",0,\"thm_15486\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015444.lean\",\"ad79c40040c010da02e9d632d95b73b0bfcc2b088bbbdbc26b98788ca76f62bf\",0,\"thm_15487\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015445.lean\",\"f99f25cabc64bb5f4d13ab3582d6a0d6a2f27e9dc9f81bd567c165949892dce5\",0,\"thm_15488\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015446.lean\",\"2fe8b177031f1bd2559bdd5385a94477ca2dd1a4322582c8c1fd534e4cdb8cc8\",0,\"thm_15489\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015447.lean\",\"e2c7331cec9eed54a3703a55bad1111c00cd23ac1e38f9b4aa8c24ae34f1e368\",0,\"thm_15490\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015448.lean\",\"214df1aa936d73d93ad058a7b8e939940ea791bf402c5762c65f2b014d4e69ce\",0,\"thm_15491\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_015449.lean\",\"7c0bcfdf2ceb433e1dce9d5c6f4935dff2e10be38eef108c722367aea78401a2\",0,\"thm_15492\"]"
+  ]
+}

manifests/batches/mathlib/000236.json ADDED Viewed

	@@ -0,0 +1,538 @@

+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000236",
+  "batch_fingerprint": "b01c1566f417eba7862bccec4f283ec8d445913f9ef645b7f4564723f15ac54b",
+  "evidence": {
+    "batch_fingerprint": "b01c1566f417eba7862bccec4f283ec8d445913f9ef645b7f4564723f15ac54b",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MvPolynomial.pderiv_C",
+        "id": "MvPolynomial.pderiv_C",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            81,
+            19
+          ],
+          "file_path": "Mathlib/Algebra/MvPolynomial/PDeriv.lean",
+          "full_name": "MvPolynomial.pderiv_C",
+          "start": [
+            80,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Algebra/MvPolynomial/PDeriv.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'simp [h]'",
+        "full_name": "MvPolynomial.pderiv_X_of_ne",
+        "id": "MvPolynomial.pderiv_X_of_ne",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            102,
+            21
+          ],
+          "file_path": "Mathlib/Algebra/MvPolynomial/PDeriv.lean",
+          "full_name": "MvPolynomial.pderiv_X_of_ne",
+          "start": [
+            101,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"classical simp [h]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d : CommSemiring R\ni j : \u03c3\nh : j \u2260 i\n\u22a2 (pderiv i) (X j) = 0",
+              "tactic": "classical simp [h]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [h]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d : CommSemiring R\ni j : \u03c3\nh : j \u2260 i\n\u22a2 (pderiv i) (X j) = 0",
+              "tactic": "simp [h]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Algebra/MvPolynomial/PDeriv.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'simp'",
+        "full_name": "MvPolynomial.pderiv_X_self",
+        "id": "MvPolynomial.pderiv_X_self",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            96,
+            91
+          ],
+          "file_path": "Mathlib/Algebra/MvPolynomial/PDeriv.lean",
+          "full_name": "MvPolynomial.pderiv_X_self",
+          "start": [
+            96,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"classical simp\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d : CommSemiring R\ni : \u03c3\n\u22a2 (pderiv i) (X i) = 1",
+              "tactic": "classical simp"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d : CommSemiring R\ni : \u03c3\n\u22a2 (pderiv i) (X i) = 1",
+              "tactic": "simp"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Algebra/MvPolynomial/PDeriv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MvPolynomial.pderiv_eq_zero_of_not_mem_vars",
+        "id": "MvPolynomial.pderiv_eq_zero_of_not_mem_vars",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            108,
+            96
+          ],
+          "file_path": "Mathlib/Algebra/MvPolynomial/PDeriv.lean",
+          "full_name": "MvPolynomial.pderiv_eq_zero_of_not_mem_vars",
+          "start": [
+            106,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Algebra/MvPolynomial/PDeriv.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'simp'",
+        "full_name": "MvPolynomial.pderiv_map",
+        "id": "MvPolynomial.pderiv_map",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            135,
+            17
+          ],
+          "file_path": "Mathlib/Algebra/MvPolynomial/PDeriv.lean",
+          "full_name": "MvPolynomial.pderiv_map",
+          "start": [
+            130,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"apply <a>induction_on<\\/a> f (fun r \\u21a6 by simp) (fun p q hp hq \\u21a6 by simp [hp, hq]) fun p j eq \\u21a6 ?_\"",
+                "[{\"full_name\":\"MvPolynomial.induction_on\",\"def_path\":\"Mathlib\\/Algebra\\/MvPolynomial\\/Basic.lean\",\"def_pos\":[455,9],\"def_end_pos\":[455,21]}]"
+              ],
+              "state_after": "R : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d\u00b9 : CommSemiring R\nS : Type u_1\ninst\u271d : CommSemiring S\n\u03c6 : R \u2192+* S\nf : MvPolynomial \u03c3 R\ni : \u03c3\np : MvPolynomial \u03c3 R\nj : \u03c3\neq : (pderiv i) ((map \u03c6) p) = (map \u03c6) ((pderiv i) p)\n\u22a2 (pderiv i) ((map \u03c6) (p * X j)) = (map \u03c6) ((pderiv i) (p * X j))",
+              "state_before": "R : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d\u00b9 : CommSemiring R\nS : Type u_1\ninst\u271d : CommSemiring S\n\u03c6 : R \u2192+* S\nf : MvPolynomial \u03c3 R\ni : \u03c3\n\u22a2 (pderiv i) ((map \u03c6) f) = (map \u03c6) ((pderiv i) f)",
+              "tactic": "apply induction_on f (fun r \u21a6 by simp) (fun p q hp hq \u21a6 by simp [hp, hq]) fun p j eq \u21a6 ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain rfl | h := <a>eq_or_ne<\\/a> j i\"",
+                "[{\"full_name\":\"eq_or_ne\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[212,9],\"def_end_pos\":[212,17]}]"
+              ],
+              "state_after": "case inl\nR : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d\u00b9 : CommSemiring R\nS : Type u_1\ninst\u271d : CommSemiring S\n\u03c6 : R \u2192+* S\nf p : MvPolynomial \u03c3 R\nj : \u03c3\neq : (pderiv j) ((map \u03c6) p) = (map \u03c6) ((pderiv j) p)\n\u22a2 (pderiv j) ((map \u03c6) (p * X j)) = (map \u03c6) ((pderiv j) (p * X j))\n\ncase inr\nR : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d\u00b9 : CommSemiring R\nS : Type u_1\ninst\u271d : CommSemiring S\n\u03c6 : R \u2192+* S\nf : MvPolynomial \u03c3 R\ni : \u03c3\np : MvPolynomial \u03c3 R\nj : \u03c3\neq : (pderiv i) ((map \u03c6) p) = (map \u03c6) ((pderiv i) p)\nh : j \u2260 i\n\u22a2 (pderiv i) ((map \u03c6) (p * X j)) = (map \u03c6) ((pderiv i) (p * X j))",
+              "state_before": "R : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d\u00b9 : CommSemiring R\nS : Type u_1\ninst\u271d : CommSemiring S\n\u03c6 : R \u2192+* S\nf : MvPolynomial \u03c3 R\ni : \u03c3\np : MvPolynomial \u03c3 R\nj : \u03c3\neq : (pderiv i) ((map \u03c6) p) = (map \u03c6) ((pderiv i) p)\n\u22a2 (pderiv i) ((map \u03c6) (p * X j)) = (map \u03c6) ((pderiv i) (p * X j))",
+              "tactic": "obtain rfl | h := eq_or_ne j i"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d\u00b9 : CommSemiring R\nS : Type u_1\ninst\u271d : CommSemiring S\n\u03c6 : R \u2192+* S\nf : MvPolynomial \u03c3 R\ni : \u03c3\nr : R\n\u22a2 (pderiv i) ((map \u03c6) (C r)) = (map \u03c6) ((pderiv i) (C r))",
+              "tactic": "simp"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [hp, hq]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d\u00b9 : CommSemiring R\nS : Type u_1\ninst\u271d : CommSemiring S\n\u03c6 : R \u2192+* S\nf : MvPolynomial \u03c3 R\ni : \u03c3\np q : MvPolynomial \u03c3 R\nhp : (pderiv i) ((map \u03c6) p) = (map \u03c6) ((pderiv i) p)\nhq : (pderiv i) ((map \u03c6) q) = (map \u03c6) ((pderiv i) q)\n\u22a2 (pderiv i) ((map \u03c6) (p + q)) = (map \u03c6) ((pderiv i) (p + q))",
+              "tactic": "simp [hp, hq]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [eq]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inl\nR : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d\u00b9 : CommSemiring R\nS : Type u_1\ninst\u271d : CommSemiring S\n\u03c6 : R \u2192+* S\nf p : MvPolynomial \u03c3 R\nj : \u03c3\neq : (pderiv j) ((map \u03c6) p) = (map \u03c6) ((pderiv j) p)\n\u22a2 (pderiv j) ((map \u03c6) (p * X j)) = (map \u03c6) ((pderiv j) (p * X j))",
+              "tactic": "simp [eq]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [eq, h]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inr\nR : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d\u00b9 : CommSemiring R\nS : Type u_1\ninst\u271d : CommSemiring S\n\u03c6 : R \u2192+* S\nf : MvPolynomial \u03c3 R\ni : \u03c3\np : MvPolynomial \u03c3 R\nj : \u03c3\neq : (pderiv i) ((map \u03c6) p) = (map \u03c6) ((pderiv i) p)\nh : j \u2260 i\n\u22a2 (pderiv i) ((map \u03c6) (p * X j)) = (map \u03c6) ((pderiv i) (p * X j))",
+              "tactic": "simp [eq, h]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Algebra/MvPolynomial/PDeriv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MvPolynomial.pderiv_one",
+        "id": "MvPolynomial.pderiv_one",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            85,
+            77
+          ],
+          "file_path": "Mathlib/Algebra/MvPolynomial/PDeriv.lean",
+          "full_name": "MvPolynomial.pderiv_one",
+          "start": [
+            85,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Algebra/MvPolynomial/PDeriv.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'simp'",
+        "full_name": "MvPolynomial.eval_polynomial_eval_finSuccEquiv",
+        "id": "MvPolynomial.eval_polynomial_eval_finSuccEquiv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            40,
+            41
+          ],
+          "file_path": "Mathlib/Algebra/MvPolynomial/Polynomial.lean",
+          "full_name": "MvPolynomial.eval_polynomial_eval_finSuccEquiv",
+          "start": [
+            30,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>finSuccEquiv_apply<\\/a>, <a>coe_eval\\u2082Hom<\\/a>, <a>polynomial_eval_eval\\u2082<\\/a>, <a>eval_eval\\u2082<\\/a>]\"",
+                "[{\"full_name\":\"MvPolynomial.finSuccEquiv_apply\",\"def_path\":\"Mathlib\\/Algebra\\/MvPolynomial\\/Equiv.lean\",\"def_pos\":[351,9],\"def_end_pos\":[351,27]},{\"full_name\":\"MvPolynomial.coe_eval\\u2082Hom\",\"def_path\":\"Mathlib\\/Algebra\\/MvPolynomial\\/Basic.lean\",\"def_pos\":[1111,9],\"def_end_pos\":[1111,21]},{\"full_name\":\"MvPolynomial.polynomial_eval_eval\\u2082\",\"def_path\":\"Mathlib\\/Algebra\\/MvPolynomial\\/Polynomial.lean\",\"def_pos\":[19,9],\"def_end_pos\":[19,30]},{\"full_name\":\"MvPolynomial.eval_eval\\u2082\",\"def_path\":\"Mathlib\\/Algebra\\/MvPolynomial\\/Basic.lean\",\"def_pos\":[1270,9],\"def_end_pos\":[1270,19]}]"
+              ],
+              "state_after": "R : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\nn : \u2115\nx : Fin n \u2192 R\ninst\u271d : CommSemiring R\nf : MvPolynomial (Fin (n + 1)) R\nq : MvPolynomial (Fin n) R\n\u22a2 eval\u2082 ((eval x).comp ((Polynomial.evalRingHom q).comp (Polynomial.C.comp C)))\n      (fun s => (eval x) (Polynomial.eval q (Fin.cases Polynomial.X (fun k => Polynomial.C (X k)) s))) f =\n    (eval fun i => Fin.cases ((eval x) q) x i) f",
+              "state_before": "R : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\nn : \u2115\nx : Fin n \u2192 R\ninst\u271d : CommSemiring R\nf : MvPolynomial (Fin (n + 1)) R\nq : MvPolynomial (Fin n) R\n\u22a2 (eval x) (Polynomial.eval q ((finSuccEquiv R n) f)) = (eval fun i => Fin.cases ((eval x) q) x i) f",
+              "tactic": "simp only [finSuccEquiv_apply, coe_eval\u2082Hom, polynomial_eval_eval\u2082, eval_eval\u2082]"
+            },
+            {
+              "annotated_tactic": [
+                "\"conv in <a>RingHom.comp<\\/a> _ _ =>\\n    refine @<a>RingHom.ext<\\/a> _ _ _ _ _ (<a>RingHom.id<\\/a> _) fun r => ?_\\n    simp\"",
+                "[{\"full_name\":\"RingHom.comp\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Hom\\/Defs.lean\",\"def_pos\":[655,5],\"def_end_pos\":[655,9]},{\"full_name\":\"RingHom.ext\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Hom\\/Defs.lean\",\"def_pos\":[524,9],\"def_end_pos\":[524,12]},{\"full_name\":\"RingHom.id\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Hom\\/Defs.lean\",\"def_pos\":[626,5],\"def_end_pos\":[626,7]}]"
+              ],
+              "state_after": "R : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\nn : \u2115\nx : Fin n \u2192 R\ninst\u271d : CommSemiring R\nf : MvPolynomial (Fin (n + 1)) R\nq : MvPolynomial (Fin n) R\n\u22a2 eval\u2082 (RingHom.id R) (fun s => (eval x) (Polynomial.eval q (Fin.cases Polynomial.X (fun k => Polynomial.C (X k)) s)))\n      f =\n    (eval fun i => Fin.cases ((eval x) q) x i) f",
+              "state_before": "R : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\nn : \u2115\nx : Fin n \u2192 R\ninst\u271d : CommSemiring R\nf : MvPolynomial (Fin (n + 1)) R\nq : MvPolynomial (Fin n) R\n\u22a2 eval\u2082 ((eval x).comp ((Polynomial.evalRingHom q).comp (Polynomial.C.comp C)))\n      (fun s => (eval x) (Polynomial.eval q (Fin.cases Polynomial.X (fun k => Polynomial.C (X k)) s))) f =\n    (eval fun i => Fin.cases ((eval x) q) x i) f",
+              "tactic": "conv in RingHom.comp _ _ =>\n  refine @RingHom.ext _ _ _ _ _ (RingHom.id _) fun r => ?_\n  simp"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>eval\\u2082_id<\\/a>]\"",
+                "[{\"full_name\":\"MvPolynomial.eval\\u2082_id\",\"def_path\":\"Mathlib\\/Algebra\\/MvPolynomial\\/Basic.lean\",\"def_pos\":[1266,9],\"def_end_pos\":[1266,17]}]"
+              ],
+              "state_after": "R : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\nn : \u2115\nx : Fin n \u2192 R\ninst\u271d : CommSemiring R\nf : MvPolynomial (Fin (n + 1)) R\nq : MvPolynomial (Fin n) R\n\u22a2 (eval fun s => (eval x) (Polynomial.eval q (Fin.cases Polynomial.X (fun k => Polynomial.C (X k)) s))) f =\n    (eval fun i => Fin.cases ((eval x) q) x i) f",
+              "state_before": "R : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\nn : \u2115\nx : Fin n \u2192 R\ninst\u271d : CommSemiring R\nf : MvPolynomial (Fin (n + 1)) R\nq : MvPolynomial (Fin n) R\n\u22a2 eval\u2082 (RingHom.id R) (fun s => (eval x) (Polynomial.eval q (Fin.cases Polynomial.X (fun k => Polynomial.C (X k)) s)))\n      f =\n    (eval fun i => Fin.cases ((eval x) q) x i) f",
+              "tactic": "simp only [eval\u2082_id]"
+            },
+            {
+              "annotated_tactic": [
+                "\"congr\"",
+                "[]"
+              ],
+              "state_after": "case e_a.e_f\nR : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\nn : \u2115\nx : Fin n \u2192 R\ninst\u271d : CommSemiring R\nf : MvPolynomial (Fin (n + 1)) R\nq : MvPolynomial (Fin n) R\n\u22a2 (fun s => (eval x) (Polynomial.eval q (Fin.cases Polynomial.X (fun k => Polynomial.C (X k)) s))) = fun i =>\n    Fin.cases ((eval x) q) x i",
+              "state_before": "R : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\nn : \u2115\nx : Fin n \u2192 R\ninst\u271d : CommSemiring R\nf : MvPolynomial (Fin (n + 1)) R\nq : MvPolynomial (Fin n) R\n\u22a2 (eval fun s => (eval x) (Polynomial.eval q (Fin.cases Polynomial.X (fun k => Polynomial.C (X k)) s))) f =\n    (eval fun i => Fin.cases ((eval x) q) x i) f",
+              "tactic": "congr"
+            },
+            {
+              "annotated_tactic": [
+                "\"funext i\"",
+                "[]"
+              ],
+              "state_after": "case e_a.e_f.h\nR : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\nn : \u2115\nx : Fin n \u2192 R\ninst\u271d : CommSemiring R\nf : MvPolynomial (Fin (n + 1)) R\nq : MvPolynomial (Fin n) R\ni : Fin (n + 1)\n\u22a2 (eval x) (Polynomial.eval q (Fin.cases Polynomial.X (fun k => Polynomial.C (X k)) i)) = Fin.cases ((eval x) q) x i",
+              "state_before": "case e_a.e_f\nR : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\nn : \u2115\nx : Fin n \u2192 R\ninst\u271d : CommSemiring R\nf : MvPolynomial (Fin (n + 1)) R\nq : MvPolynomial (Fin n) R\n\u22a2 (fun s => (eval x) (Polynomial.eval q (Fin.cases Polynomial.X (fun k => Polynomial.C (X k)) s))) = fun i =>\n    Fin.cases ((eval x) q) x i",
+              "tactic": "funext i"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine <a>Fin.cases<\\/a> (by simp) (by simp) i\"",
+                "[{\"full_name\":\"Fin.cases\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[654,21],\"def_end_pos\":[654,26]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case e_a.e_f.h\nR : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\nn : \u2115\nx : Fin n \u2192 R\ninst\u271d : CommSemiring R\nf : MvPolynomial (Fin (n + 1)) R\nq : MvPolynomial (Fin n) R\ni : Fin (n + 1)\n\u22a2 (eval x) (Polynomial.eval q (Fin.cases Polynomial.X (fun k => Polynomial.C (X k)) i)) = Fin.cases ((eval x) q) x i",
+              "tactic": "refine Fin.cases (by simp) (by simp) i"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\nn : \u2115\nx : Fin n \u2192 R\ninst\u271d : CommSemiring R\nf : MvPolynomial (Fin (n + 1)) R\nq : MvPolynomial (Fin n) R\ni : Fin (n + 1)\n\u22a2 (eval x) (Polynomial.eval q (Fin.cases Polynomial.X (fun k => Polynomial.C (X k)) 0)) = Fin.cases ((eval x) q) x 0",
+              "tactic": "simp"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\nn : \u2115\nx : Fin n \u2192 R\ninst\u271d : CommSemiring R\nf : MvPolynomial (Fin (n + 1)) R\nq : MvPolynomial (Fin n) R\ni : Fin (n + 1)\n\u22a2 \u2200 (i : Fin n),\n    (eval x) (Polynomial.eval q (Fin.cases Polynomial.X (fun k => Polynomial.C (X k)) i.succ)) =\n      Fin.cases ((eval x) q) x i.succ",
+              "tactic": "simp"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Algebra/MvPolynomial/Polynomial.lean"
+      }
+    ],
+    "input_proofs": 15,
+    "input_units": 2,
+    "proofs": 8,
+    "published_proofs": 6,
+    "published_transitions": 7,
+    "replay_failures": [],
+    "transitions": 19,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Algebra/MvPolynomial/PDeriv.lean",
+        "proof_id": "mathlib:MvPolynomial.pderiv_monomial",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              77,
+              11
+            ],
+            "file_path": "Mathlib/Algebra/MvPolynomial/PDeriv.lean",
+            "full_name": "MvPolynomial.pderiv_monomial",
+            "start": [
+              69,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"simp only [<a>pderiv_def<\\/a>, <a>mkDerivation_monomial<\\/a>, <a>Finsupp.smul_sum<\\/a>, <a>smul_eq_mul<\\/a>, \\u2190 <a>smul_mul_assoc<\\/a>,\\n      \\u2190 (<a>monomial<\\/a> _).<a>map_smul<\\/a>]\"",
+                  "[{\"full_name\":\"MvPolynomial.pderiv_def\",\"def_path\":\"Mathlib\\/Algebra\\/MvPolynomial\\/PDeriv.lean\",\"def_pos\":[64,9],\"def_end_pos\":[64,19]},{\"full_name\":\"MvPolynomial.mkDerivation_monomial\",\"def_path\":\"Mathlib\\/Algebra\\/MvPolynomial\\/Derivation.lean\",\"def_pos\":[143,9],\"def_end_pos\":[143,30]},{\"full_name\":\"Finsupp.smul_sum\",\"def_path\":\"Mathlib\\/LinearAlgebra\\/Finsupp.lean\",\"def_pos\":[57,9],\"def_end_pos\":[57,17]},{\"full_name\":\"smul_eq_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[89,7],\"def_end_pos\":[89,18]},{\"full_name\":\"smul_mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[408,7],\"def_end_pos\":[408,21]},{\"full_name\":\"MvPolynomial.monomial\",\"def_path\":\"Mathlib\\/Algebra\\/MvPolynomial\\/Basic.lean\",\"def_pos\":[162,5],\"def_end_pos\":[162,13]},{\"full_name\":\"LinearMap.map_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/LinearMap\\/Defs.lean\",\"def_pos\":[376,19],\"def_end_pos\":[376,27]}]"
+                ],
+                "state_after": "R : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d : CommSemiring R\ni : \u03c3\n\u22a2 (s.sum fun a_1 b => (monomial (s - single a_1 1)) (a * \u2191b) * Pi.single i 1 a_1) =\n    (monomial (s - single i 1)) (a * \u2191(s i))",
+                "state_before": "R : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d : CommSemiring R\ni : \u03c3\n\u22a2 (pderiv i) ((monomial s) a) = (monomial (s - single i 1)) (a * \u2191(s i))",
+                "tactic": "simp only [pderiv_def, mkDerivation_monomial, Finsupp.smul_sum, smul_eq_mul, \u2190 smul_mul_assoc,\n  \u2190 (monomial _).map_smul]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"refine (<a>Finset.sum_eq_single<\\/a> i (fun j _ hne => ?_) fun hi => ?_).<a>trans<\\/a> ?_\"",
+                  "[{\"full_name\":\"Finset.sum_eq_single\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Finset.lean\",\"def_pos\":[998,3],\"def_end_pos\":[998,14]},{\"full_name\":\"Eq.trans\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[335,9],\"def_end_pos\":[335,17]}]"
+                ],
+                "state_after": "case refine_1\nR : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d : CommSemiring R\ni j : \u03c3\nx\u271d : j \u2208 s.support\nhne : j \u2260 i\n\u22a2 (fun a_1 b => (monomial (s - single a_1 1)) (a * \u2191b) * Pi.single i 1 a_1) j (s j) = 0\n\ncase refine_2\nR : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d : CommSemiring R\ni : \u03c3\nhi : i \u2209 s.support\n\u22a2 (fun a_1 b => (monomial (s - single a_1 1)) (a * \u2191b) * Pi.single i 1 a_1) i (s i) = 0\n\ncase refine_3\nR : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d : CommSemiring R\ni : \u03c3\n\u22a2 (fun a_1 b => (monomial (s - single a_1 1)) (a * \u2191b) * Pi.single i 1 a_1) i (s i) =\n    (monomial (s - single i 1)) (a * \u2191(s i))",
+                "state_before": "R : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d : CommSemiring R\ni : \u03c3\n\u22a2 (s.sum fun a_1 b => (monomial (s - single a_1 1)) (a * \u2191b) * Pi.single i 1 a_1) =\n    (monomial (s - single i 1)) (a * \u2191(s i))",
+                "tactic": "refine (Finset.sum_eq_single i (fun j _ hne => ?_) fun hi => ?_).trans ?_"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp [<a>Pi.single_eq_of_ne<\\/a> hne]\"",
+                  "[{\"full_name\":\"Pi.single_eq_of_ne\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[360,3],\"def_end_pos\":[360,14]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case refine_1\nR : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d : CommSemiring R\ni j : \u03c3\nx\u271d : j \u2208 s.support\nhne : j \u2260 i\n\u22a2 (fun a_1 b => (monomial (s - single a_1 1)) (a * \u2191b) * Pi.single i 1 a_1) j (s j) = 0",
+                "tactic": "simp [Pi.single_eq_of_ne hne]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>Finsupp.not_mem_support_iff<\\/a>] at hi\"",
+                  "[{\"full_name\":\"Finsupp.not_mem_support_iff\",\"def_path\":\"Mathlib\\/Data\\/Finsupp\\/Defs.lean\",\"def_pos\":[180,9],\"def_end_pos\":[180,28]}]"
+                ],
+                "state_after": "case refine_2\nR : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d : CommSemiring R\ni : \u03c3\nhi : s i = 0\n\u22a2 (fun a_1 b => (monomial (s - single a_1 1)) (a * \u2191b) * Pi.single i 1 a_1) i (s i) = 0",
+                "state_before": "case refine_2\nR : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d : CommSemiring R\ni : \u03c3\nhi : i \u2209 s.support\n\u22a2 (fun a_1 b => (monomial (s - single a_1 1)) (a * \u2191b) * Pi.single i 1 a_1) i (s i) = 0",
+                "tactic": "rw [Finsupp.not_mem_support_iff] at hi"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp [hi]\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case refine_2\nR : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d : CommSemiring R\ni : \u03c3\nhi : s i = 0\n\u22a2 (fun a_1 b => (monomial (s - single a_1 1)) (a * \u2191b) * Pi.single i 1 a_1) i (s i) = 0",
+                "tactic": "simp [hi]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case refine_3\nR : Type u\n\u03c3 : Type v\na a' a\u2081 a\u2082 : R\ns : \u03c3 \u2192\u2080 \u2115\ninst\u271d : CommSemiring R\ni : \u03c3\n\u22a2 (fun a_1 b => (monomial (s - single a_1 1)) (a * \u2191b) * Pi.single i 1 a_1) i (s i) =\n    (monomial (s - single i 1)) (a * \u2191(s i))",
+                "tactic": "simp"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "MvPolynomial.pderiv_monomial"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Algebra/MvPolynomial/Polynomial.lean",
+        "proof_id": "mathlib:MvPolynomial.polynomial_eval_eval\u2082",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              28,
+              14
+            ],
+            "file_path": "Mathlib/Algebra/MvPolynomial/Polynomial.lean",
+            "full_name": "MvPolynomial.polynomial_eval_eval\u2082",
+            "start": [
+              19,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"apply <a>induction_on<\\/a> p\"",
+                  "[{\"full_name\":\"MvPolynomial.induction_on\",\"def_path\":\"Mathlib\\/Algebra\\/MvPolynomial\\/Basic.lean\",\"def_pos\":[455,9],\"def_end_pos\":[455,21]}]"
+                ],
+                "state_after": "case h_C\nR : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\ninst\u271d\u00b9 : CommSemiring R\ninst\u271d : CommSemiring S\nx : S\nf : R \u2192+* Polynomial S\ng : \u03c3 \u2192 Polynomial S\np : MvPolynomial \u03c3 R\n\u22a2 \u2200 (a : R),\n    Polynomial.eval x (eval\u2082 f g (C a)) =\n      eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) (C a)\n\ncase h_add\nR : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\ninst\u271d\u00b9 : CommSemiring R\ninst\u271d : CommSemiring S\nx : S\nf : R \u2192+* Polynomial S\ng : \u03c3 \u2192 Polynomial S\np : MvPolynomial \u03c3 R\n\u22a2 \u2200 (p q : MvPolynomial \u03c3 R),\n    Polynomial.eval x (eval\u2082 f g p) = eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) p \u2192\n      Polynomial.eval x (eval\u2082 f g q) = eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) q \u2192\n        Polynomial.eval x (eval\u2082 f g (p + q)) =\n          eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) (p + q)\n\ncase h_X\nR : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\ninst\u271d\u00b9 : CommSemiring R\ninst\u271d : CommSemiring S\nx : S\nf : R \u2192+* Polynomial S\ng : \u03c3 \u2192 Polynomial S\np : MvPolynomial \u03c3 R\n\u22a2 \u2200 (p : MvPolynomial \u03c3 R) (n : \u03c3),\n    Polynomial.eval x (eval\u2082 f g p) = eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) p \u2192\n      Polynomial.eval x (eval\u2082 f g (p * X n)) =\n        eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) (p * X n)",
+                "state_before": "R : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\ninst\u271d\u00b9 : CommSemiring R\ninst\u271d : CommSemiring S\nx : S\nf : R \u2192+* Polynomial S\ng : \u03c3 \u2192 Polynomial S\np : MvPolynomial \u03c3 R\n\u22a2 Polynomial.eval x (eval\u2082 f g p) = eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) p",
+                "tactic": "apply induction_on p"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case h_C\nR : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\ninst\u271d\u00b9 : CommSemiring R\ninst\u271d : CommSemiring S\nx : S\nf : R \u2192+* Polynomial S\ng : \u03c3 \u2192 Polynomial S\np : MvPolynomial \u03c3 R\n\u22a2 \u2200 (a : R),\n    Polynomial.eval x (eval\u2082 f g (C a)) =\n      eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) (C a)",
+                "tactic": "simp"
+              },
+              {
+                "annotated_tactic": [
+                  "\"intro p q hp hq\"",
+                  "[]"
+                ],
+                "state_after": "case h_add\nR : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\ninst\u271d\u00b9 : CommSemiring R\ninst\u271d : CommSemiring S\nx : S\nf : R \u2192+* Polynomial S\ng : \u03c3 \u2192 Polynomial S\np\u271d p q : MvPolynomial \u03c3 R\nhp : Polynomial.eval x (eval\u2082 f g p) = eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) p\nhq : Polynomial.eval x (eval\u2082 f g q) = eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) q\n\u22a2 Polynomial.eval x (eval\u2082 f g (p + q)) =\n    eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) (p + q)",
+                "state_before": "case h_add\nR : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\ninst\u271d\u00b9 : CommSemiring R\ninst\u271d : CommSemiring S\nx : S\nf : R \u2192+* Polynomial S\ng : \u03c3 \u2192 Polynomial S\np : MvPolynomial \u03c3 R\n\u22a2 \u2200 (p q : MvPolynomial \u03c3 R),\n    Polynomial.eval x (eval\u2082 f g p) = eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) p \u2192\n      Polynomial.eval x (eval\u2082 f g q) = eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) q \u2192\n        Polynomial.eval x (eval\u2082 f g (p + q)) =\n          eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) (p + q)",
+                "tactic": "intro p q hp hq"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp [hp, hq]\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case h_add\nR : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\ninst\u271d\u00b9 : CommSemiring R\ninst\u271d : CommSemiring S\nx : S\nf : R \u2192+* Polynomial S\ng : \u03c3 \u2192 Polynomial S\np\u271d p q : MvPolynomial \u03c3 R\nhp : Polynomial.eval x (eval\u2082 f g p) = eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) p\nhq : Polynomial.eval x (eval\u2082 f g q) = eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) q\n\u22a2 Polynomial.eval x (eval\u2082 f g (p + q)) =\n    eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) (p + q)",
+                "tactic": "simp [hp, hq]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"intro p n hp\"",
+                  "[]"
+                ],
+                "state_after": "case h_X\nR : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\ninst\u271d\u00b9 : CommSemiring R\ninst\u271d : CommSemiring S\nx : S\nf : R \u2192+* Polynomial S\ng : \u03c3 \u2192 Polynomial S\np\u271d p : MvPolynomial \u03c3 R\nn : \u03c3\nhp : Polynomial.eval x (eval\u2082 f g p) = eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) p\n\u22a2 Polynomial.eval x (eval\u2082 f g (p * X n)) =\n    eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) (p * X n)",
+                "state_before": "case h_X\nR : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\ninst\u271d\u00b9 : CommSemiring R\ninst\u271d : CommSemiring S\nx : S\nf : R \u2192+* Polynomial S\ng : \u03c3 \u2192 Polynomial S\np : MvPolynomial \u03c3 R\n\u22a2 \u2200 (p : MvPolynomial \u03c3 R) (n : \u03c3),\n    Polynomial.eval x (eval\u2082 f g p) = eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) p \u2192\n      Polynomial.eval x (eval\u2082 f g (p * X n)) =\n        eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) (p * X n)",
+                "tactic": "intro p n hp"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp [hp]\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case h_X\nR : Type u_1\nS : Type u_2\n\u03c3 : Type u_3\ninst\u271d\u00b9 : CommSemiring R\ninst\u271d : CommSemiring S\nx : S\nf : R \u2192+* Polynomial S\ng : \u03c3 \u2192 Polynomial S\np\u271d p : MvPolynomial \u03c3 R\nn : \u03c3\nhp : Polynomial.eval x (eval\u2082 f g p) = eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) p\n\u22a2 Polynomial.eval x (eval\u2082 f g (p * X n)) =\n    eval\u2082 ((Polynomial.evalRingHom x).comp f) (fun s => Polynomial.eval x (g s)) (p * X n)",
+                "tactic": "simp [hp]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "MvPolynomial.polynomial_eval_eval\u2082"
+      }
+    ],
+    "validation_rejected_proofs": 2,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000236-0000-ef6e2a053f8cf8a4.parquet",
+      "sha256": "ef6e2a053f8cf8a44c333c40d81dcbed2ef245f4a67b3c2eff3793d43187aab0",
+      "bytes": 42313,
+      "rows": 4,
+      "revision": "3590753b680b8e28dc2714818766a6fd7f4a158f"
+    },
+    {
+      "path": "data/internal_test/mathlib-000236-0000-00d536a6e0b75794.parquet",
+      "sha256": "00d536a6e0b75794ca3247c611e99817e8f1dfaedee5586fe6b202a45121be73",
+      "bytes": 43192,
+      "rows": 3,
+      "revision": "3590753b680b8e28dc2714818766a6fd7f4a158f"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:MvPolynomial.pderiv_C_mul",
+    "mathlib:MvPolynomial.pderiv_X",
+    "mathlib:MvPolynomial.pderiv_def",
+    "mathlib:MvPolynomial.pderiv_monomial_single",
+    "mathlib:MvPolynomial.pderiv_mul",
+    "mathlib:MvPolynomial.pderiv_pow"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/MvPolynomial/PDeriv.lean\",null,null,\"MvPolynomial.pderiv_C_mul\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/MvPolynomial/PDeriv.lean\",null,null,\"MvPolynomial.pderiv_X\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/MvPolynomial/PDeriv.lean\",null,null,\"MvPolynomial.pderiv_def\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/MvPolynomial/PDeriv.lean\",null,null,\"MvPolynomial.pderiv_monomial_single\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/MvPolynomial/PDeriv.lean\",null,null,\"MvPolynomial.pderiv_mul\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/MvPolynomial/PDeriv.lean\",null,null,\"MvPolynomial.pderiv_pow\"]"
+  ]
+}

manifests/batches/mathlib/000237.json ADDED Viewed