Record 13 verified HPC batch manifests

manifests/batches/deepseek/000495.json

@@ -0,0 +1,148 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "deepseek/000495",
+  "batch_fingerprint": "5df66437b9ce6d242f0c102446d1872f6f382078072af6735d6401334b16c1b8",
+  "evidence": {
+    "batch_fingerprint": "5df66437b9ce6d242f0c102446d1872f6f382078072af6735d6401334b16c1b8",
+    "contamination_matches": [],
+    "failures": [],
+    "input_proofs": 50,
+    "input_units": 50,
+    "proofs": 50,
+    "published_proofs": 50,
+    "published_transitions": 129,
+    "replay_failures": [],
+    "trace_mode": "individual",
+    "transitions": 129,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/deepseek-000495-0000-5f563f7f71aaf040.parquet",
+      "sha256": "5f563f7f71aaf0401ecf45ba0bd88f39ed8f1bd2b4590d9a606ed8434e8abc29",
+      "bytes": 393554,
+      "rows": 113,
+      "revision": "eef9f30926b0307521cf3967e66e7df66c40bfc5"
+    },
+    {
+      "path": "data/dev/deepseek-000495-0000-f9605ee9a4bf9702.parquet",
+      "sha256": "f9605ee9a4bf9702ac1023c49ffb83da14340dc9e1487df8f0c6621eda6a4a0a",
+      "bytes": 36225,
+      "rows": 5,
+      "revision": "eef9f30926b0307521cf3967e66e7df66c40bfc5"
+    },
+    {
+      "path": "data/internal_test/deepseek-000495-0000-46daa6f6072bdd99.parquet",
+      "sha256": "46daa6f6072bdd996d21b31efa582c939fd7653f15ee7ef86e5216e8ac64dc00",
+      "bytes": 53992,
+      "rows": 11,
+      "revision": "eef9f30926b0307521cf3967e66e7df66c40bfc5"
+    }
+  ],
+  "proof_ids": [
+    "deepseek:thm_24797",
+    "deepseek:thm_24798",
+    "deepseek:thm_24799",
+    "deepseek:thm_24800",
+    "deepseek:thm_24801",
+    "deepseek:thm_24802",
+    "deepseek:thm_24803",
+    "deepseek:thm_24804",
+    "deepseek:thm_24805",
+    "deepseek:thm_24806",
+    "deepseek:thm_24807",
+    "deepseek:thm_24808",
+    "deepseek:thm_24809",
+    "deepseek:thm_24810",
+    "deepseek:thm_24811",
+    "deepseek:thm_24812",
+    "deepseek:thm_24813",
+    "deepseek:thm_24814",
+    "deepseek:thm_24815",
+    "deepseek:thm_24816",
+    "deepseek:thm_24817",
+    "deepseek:thm_24818",
+    "deepseek:thm_24819",
+    "deepseek:thm_24820",
+    "deepseek:thm_24821",
+    "deepseek:thm_24822",
+    "deepseek:thm_24823",
+    "deepseek:thm_24824",
+    "deepseek:thm_24825",
+    "deepseek:thm_24826",
+    "deepseek:thm_24827",
+    "deepseek:thm_24828",
+    "deepseek:thm_24829",
+    "deepseek:thm_24830",
+    "deepseek:thm_24831",
+    "deepseek:thm_24832",
+    "deepseek:thm_24833",
+    "deepseek:thm_24834",
+    "deepseek:thm_24835",
+    "deepseek:thm_24836",
+    "deepseek:thm_24837",
+    "deepseek:thm_24838",
+    "deepseek:thm_24839",
+    "deepseek:thm_24840",
+    "deepseek:thm_24841",
+    "deepseek:thm_24842",
+    "deepseek:thm_24843",
+    "deepseek:thm_24844",
+    "deepseek:thm_24845",
+    "deepseek:thm_24846"
+  ],
+  "proof_keys": [
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024773.lean\",\"d352cd7d42f312876eac15f9ef4753bc60de8cbcbd1e55a9523cfbf9c28bab3f\",0,\"thm_24820\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024774.lean\",\"561005a4ec5993c5fc27dc0f0c8466d68bdd9300dd11e85d04c0f13d8f778cef\",0,\"thm_24821\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024775.lean\",\"1b97d4dd7df45d9075b3d378ac41b983943d474dde4b1f90dbc118631c797f5c\",0,\"thm_24822\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024776.lean\",\"a62d72faf3cf8476a7221232b3791bd0fda9136dd208117e0b0e43497ff7118d\",0,\"thm_24823\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024777.lean\",\"f4f40afd15e5c4c8c65f86281e44b31cdbefc45aed387df6ed4c4be73cd4c554\",0,\"thm_24824\"]",
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024779.lean\",\"6c65899aacc5e5a8ec2d3ae596f630c350ae96d4ce6c3f2c380808275bf0cbbb\",0,\"thm_24826\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024780.lean\",\"78dc970d2dcf4b6746d5c94f34e90450dc8589e4b0bdd8dc04fb0747254dc79a\",0,\"thm_24827\"]",
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024787.lean\",\"2ec67352f2a337d0f5a71227d761aaea9d8fa6c605fad211bf2c4420d5264c3e\",0,\"thm_24834\"]",
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+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024789.lean\",\"d3935301ada26a7f8654d33a0a304a32b9b1b72c47f2a02abac1472259d4d09c\",0,\"thm_24836\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024790.lean\",\"ed66381ad3b5e39d7d117d66a416d75408a1ad61450cc59fac813653f13af663\",0,\"thm_24837\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024791.lean\",\"936013d234c5d431d25f6fcf6e40bfd8657aa93523de0f639a35b374432f0b00\",0,\"thm_24838\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024792.lean\",\"e8c7287bf2ca7edd07e3497775dad092ab4c134ce367381541e9f2abdbeae9b8\",0,\"thm_24839\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024793.lean\",\"46a426636995a70124ffc1dc8fdca83a497072243d84a7e354f593c923ae35cf\",0,\"thm_24840\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024794.lean\",\"c4b94268f41faf2f8ab562d60704f7e988d01b7b378ee1df69eb093aaf656e43\",0,\"thm_24841\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024795.lean\",\"76846aa0c3b4ec5e7625fcf6dc5e332809e761a3484eaae0e5f1bbb941e59ea5\",0,\"thm_24842\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024796.lean\",\"891688229ea74fe2184e2f19f45677f521e63972f8d35a144663d7327f10ccce\",0,\"thm_24843\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024797.lean\",\"f71c8e60d1facead2f0740709d68191567cbc3c1bc288bfa31adbe352925e90b\",0,\"thm_24844\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024798.lean\",\"ab89744d9b7a31ec7ecc7f2cd014fda145626b0e50d9160ae6d3f78376a8924e\",0,\"thm_24845\"]",
+    "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024799.lean\",\"f4336b25748b8f33ce3d8c6421fbe1b5fd20249c3d73130ebb9346d6ec4056d4\",0,\"thm_24846\"]"
+  ]
+}

manifests/batches/mathlib/000420.json

@@ -0,0 +1,619 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000420",
+  "batch_fingerprint": "c0e3a52fd178d42ac44a29f7060f1c440fde814643b82beede659c2177553e2e",
+  "evidence": {
+    "batch_fingerprint": "c0e3a52fd178d42ac44a29f7060f1c440fde814643b82beede659c2177553e2e",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Differentiable.restrictScalars",
+        "id": "Differentiable.restrictScalars",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            88,
+            26
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean",
+          "full_name": "Differentiable.restrictScalars",
+          "start": [
+            87,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DifferentiableAt.fderiv_restrictScalars",
+        "id": "DifferentiableAt.fderiv_restrictScalars",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            107,
+            43
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean",
+          "full_name": "DifferentiableAt.fderiv_restrictScalars",
+          "start": [
+            105,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DifferentiableAt.restrictScalars",
+        "id": "DifferentiableAt.restrictScalars",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            72,
+            53
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean",
+          "full_name": "DifferentiableAt.restrictScalars",
+          "start": [
+            71,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DifferentiableOn.restrictScalars",
+        "id": "DifferentiableOn.restrictScalars",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            83,
+            41
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean",
+          "full_name": "DifferentiableOn.restrictScalars",
+          "start": [
+            82,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DifferentiableWithinAt.restrictScalars",
+        "id": "DifferentiableWithinAt.restrictScalars",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            78,
+            65
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean",
+          "full_name": "DifferentiableWithinAt.restrictScalars",
+          "start": [
+            76,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasFDerivAt.restrictScalars",
+        "id": "HasFDerivAt.restrictScalars",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            61,
+            20
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean",
+          "full_name": "HasFDerivAt.restrictScalars",
+          "start": [
+            59,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasFDerivAtFilter.restrictScalars",
+        "id": "HasFDerivAtFilter.restrictScalars",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            55,
+            20
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean",
+          "full_name": "HasFDerivAtFilter.restrictScalars",
+          "start": [
+            53,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasFDerivWithinAt.restrictScalars",
+        "id": "HasFDerivWithinAt.restrictScalars",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            67,
+            20
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean",
+          "full_name": "HasFDerivWithinAt.restrictScalars",
+          "start": [
+            65,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.restrictScalars",
+        "id": "HasStrictFDerivAt.restrictScalars",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            50,
+            4
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean",
+          "full_name": "HasStrictFDerivAt.restrictScalars",
+          "start": [
+            48,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Differentiable.star",
+        "id": "Differentiable.star",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            94,
+            22
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/Star.lean",
+          "full_name": "Differentiable.star",
+          "start": [
+            93,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/Star.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DifferentiableAt.star",
+        "id": "DifferentiableAt.star",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            72,
+            38
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/Star.lean",
+          "full_name": "DifferentiableAt.star",
+          "start": [
+            70,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/Star.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DifferentiableOn.star",
+        "id": "DifferentiableOn.star",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            83,
+            76
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/Star.lean",
+          "full_name": "DifferentiableOn.star",
+          "start": [
+            82,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/Star.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DifferentiableWithinAt.star",
+        "id": "DifferentiableWithinAt.star",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            60,
+            50
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/Star.lean",
+          "full_name": "DifferentiableWithinAt.star",
+          "start": [
+            58,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/Star.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasFDerivAt.star",
+        "id": "HasFDerivAt.star",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            54,
+            9
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/Star.lean",
+          "full_name": "HasFDerivAt.star",
+          "start": [
+            52,
+            8
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/Star.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasFDerivAtFilter.star",
+        "id": "HasFDerivAtFilter.star",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            42,
+            93
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/Star.lean",
+          "full_name": "HasFDerivAtFilter.star",
+          "start": [
+            40,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/Star.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasFDerivWithinAt.star",
+        "id": "HasFDerivWithinAt.star",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            48,
+            9
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/Star.lean",
+          "full_name": "HasFDerivWithinAt.star",
+          "start": [
+            46,
+            8
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/Star.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.star",
+        "id": "HasStrictFDerivAt.star",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            37,
+            74
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/Star.lean",
+          "full_name": "HasStrictFDerivAt.star",
+          "start": [
+            35,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/Star.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "differentiableAt_star_iff",
+        "id": "differentiableAt_star_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            78,
+            51
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/Star.lean",
+          "full_name": "differentiableAt_star_iff",
+          "start": [
+            76,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/Star.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "differentiableOn_star_iff",
+        "id": "differentiableOn_star_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            89,
+            51
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/Star.lean",
+          "full_name": "differentiableOn_star_iff",
+          "start": [
+            87,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/Star.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "differentiableWithinAt_star_iff",
+        "id": "differentiableWithinAt_star_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            66,
+            57
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/Star.lean",
+          "full_name": "differentiableWithinAt_star_iff",
+          "start": [
+            64,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/Star.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "differentiable_star_iff",
+        "id": "differentiable_star_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            99,
+            49
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/Star.lean",
+          "full_name": "differentiable_star_iff",
+          "start": [
+            98,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/Star.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "fderivWithin_star",
+        "id": "fderivWithin_star",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            105,
+            47
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/Star.lean",
+          "full_name": "fderivWithin_star",
+          "start": [
+            102,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/Star.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "fderiv_star",
+        "id": "fderiv_star",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            111,
+            37
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/FDeriv/Star.lean",
+          "full_name": "fderiv_star",
+          "start": [
+            109,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/FDeriv/Star.lean"
+      }
+    ],
+    "input_proofs": 27,
+    "input_units": 2,
+    "proofs": 4,
+    "published_proofs": 3,
+    "published_transitions": 6,
+    "replay_failures": [],
+    "transitions": 11,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean",
+        "proof_id": "mathlib:differentiableWithinAt_iff_restrictScalars",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              117,
+              62
+            ],
+            "file_path": "Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean",
+            "full_name": "differentiableWithinAt_iff_restrictScalars",
+            "start": [
+              110,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"constructor\"",
+                  "[]"
+                ],
+                "state_after": "case mp\n\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\n\ud835\udd5c' : Type u_2\ninst\u271d\u2079 : NontriviallyNormedField \ud835\udd5c'\ninst\u271d\u2078 : NormedAlgebra \ud835\udd5c \ud835\udd5c'\nE : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup E\ninst\u271d\u2076 : NormedSpace \ud835\udd5c E\ninst\u271d\u2075 : NormedSpace \ud835\udd5c' E\ninst\u271d\u2074 : IsScalarTower \ud835\udd5c \ud835\udd5c' E\nF : Type u_4\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c' F\ninst\u271d : IsScalarTower \ud835\udd5c \ud835\udd5c' F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c'] F\ns : Set E\nx : E\nhf : DifferentiableWithinAt \ud835\udd5c f s x\nhs : UniqueDiffWithinAt \ud835\udd5c s x\n\u22a2 DifferentiableWithinAt \ud835\udd5c' f s x \u2192 \u2203 g', restrictScalars \ud835\udd5c g' = fderivWithin \ud835\udd5c f s x\n\ncase mpr\n\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\n\ud835\udd5c' : Type u_2\ninst\u271d\u2079 : NontriviallyNormedField \ud835\udd5c'\ninst\u271d\u2078 : NormedAlgebra \ud835\udd5c \ud835\udd5c'\nE : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup E\ninst\u271d\u2076 : NormedSpace \ud835\udd5c E\ninst\u271d\u2075 : NormedSpace \ud835\udd5c' E\ninst\u271d\u2074 : IsScalarTower \ud835\udd5c \ud835\udd5c' E\nF : Type u_4\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c' F\ninst\u271d : IsScalarTower \ud835\udd5c \ud835\udd5c' F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c'] F\ns : Set E\nx : E\nhf : DifferentiableWithinAt \ud835\udd5c f s x\nhs : UniqueDiffWithinAt \ud835\udd5c s x\n\u22a2 (\u2203 g', restrictScalars \ud835\udd5c g' = fderivWithin \ud835\udd5c f s x) \u2192 DifferentiableWithinAt \ud835\udd5c' f s x",
+                "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\n\ud835\udd5c' : Type u_2\ninst\u271d\u2079 : NontriviallyNormedField \ud835\udd5c'\ninst\u271d\u2078 : NormedAlgebra \ud835\udd5c \ud835\udd5c'\nE : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup E\ninst\u271d\u2076 : NormedSpace \ud835\udd5c E\ninst\u271d\u2075 : NormedSpace \ud835\udd5c' E\ninst\u271d\u2074 : IsScalarTower \ud835\udd5c \ud835\udd5c' E\nF : Type u_4\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c' F\ninst\u271d : IsScalarTower \ud835\udd5c \ud835\udd5c' F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c'] F\ns : Set E\nx : E\nhf : DifferentiableWithinAt \ud835\udd5c f s x\nhs : UniqueDiffWithinAt \ud835\udd5c s x\n\u22a2 DifferentiableWithinAt \ud835\udd5c' f s x \u2194 \u2203 g', restrictScalars \ud835\udd5c g' = fderivWithin \ud835\udd5c f s x",
+                "tactic": "constructor"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rintro \\u27e8g', hg'\\u27e9\"",
+                  "[]"
+                ],
+                "state_after": "case mp.intro\n\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\n\ud835\udd5c' : Type u_2\ninst\u271d\u2079 : NontriviallyNormedField \ud835\udd5c'\ninst\u271d\u2078 : NormedAlgebra \ud835\udd5c \ud835\udd5c'\nE : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup E\ninst\u271d\u2076 : NormedSpace \ud835\udd5c E\ninst\u271d\u2075 : NormedSpace \ud835\udd5c' E\ninst\u271d\u2074 : IsScalarTower \ud835\udd5c \ud835\udd5c' E\nF : Type u_4\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c' F\ninst\u271d : IsScalarTower \ud835\udd5c \ud835\udd5c' F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c'] F\ns : Set E\nx : E\nhf : DifferentiableWithinAt \ud835\udd5c f s x\nhs : UniqueDiffWithinAt \ud835\udd5c s x\ng' : E \u2192L[\ud835\udd5c'] F\nhg' : HasFDerivWithinAt f g' s x\n\u22a2 \u2203 g', restrictScalars \ud835\udd5c g' = fderivWithin \ud835\udd5c f s x",
+                "state_before": "case mp\n\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\n\ud835\udd5c' : Type u_2\ninst\u271d\u2079 : NontriviallyNormedField \ud835\udd5c'\ninst\u271d\u2078 : NormedAlgebra \ud835\udd5c \ud835\udd5c'\nE : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup E\ninst\u271d\u2076 : NormedSpace \ud835\udd5c E\ninst\u271d\u2075 : NormedSpace \ud835\udd5c' E\ninst\u271d\u2074 : IsScalarTower \ud835\udd5c \ud835\udd5c' E\nF : Type u_4\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c' F\ninst\u271d : IsScalarTower \ud835\udd5c \ud835\udd5c' F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c'] F\ns : Set E\nx : E\nhf : DifferentiableWithinAt \ud835\udd5c f s x\nhs : UniqueDiffWithinAt \ud835\udd5c s x\n\u22a2 DifferentiableWithinAt \ud835\udd5c' f s x \u2192 \u2203 g', restrictScalars \ud835\udd5c g' = fderivWithin \ud835\udd5c f s x",
+                "tactic": "rintro \u27e8g', hg'\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact \\u27e8g', hs.eq (hg'.restrictScalars \\ud835\\udd5c) hf.hasFDerivWithinAt\\u27e9\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case mp.intro\n\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\n\ud835\udd5c' : Type u_2\ninst\u271d\u2079 : NontriviallyNormedField \ud835\udd5c'\ninst\u271d\u2078 : NormedAlgebra \ud835\udd5c \ud835\udd5c'\nE : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup E\ninst\u271d\u2076 : NormedSpace \ud835\udd5c E\ninst\u271d\u2075 : NormedSpace \ud835\udd5c' E\ninst\u271d\u2074 : IsScalarTower \ud835\udd5c \ud835\udd5c' E\nF : Type u_4\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c' F\ninst\u271d : IsScalarTower \ud835\udd5c \ud835\udd5c' F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c'] F\ns : Set E\nx : E\nhf : DifferentiableWithinAt \ud835\udd5c f s x\nhs : UniqueDiffWithinAt \ud835\udd5c s x\ng' : E \u2192L[\ud835\udd5c'] F\nhg' : HasFDerivWithinAt f g' s x\n\u22a2 \u2203 g', restrictScalars \ud835\udd5c g' = fderivWithin \ud835\udd5c f s x",
+                "tactic": "exact \u27e8g', hs.eq (hg'.restrictScalars \ud835\udd5c) hf.hasFDerivWithinAt\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rintro \\u27e8f', hf'\\u27e9\"",
+                  "[]"
+                ],
+                "state_after": "case mpr.intro\n\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\n\ud835\udd5c' : Type u_2\ninst\u271d\u2079 : NontriviallyNormedField \ud835\udd5c'\ninst\u271d\u2078 : NormedAlgebra \ud835\udd5c \ud835\udd5c'\nE : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup E\ninst\u271d\u2076 : NormedSpace \ud835\udd5c E\ninst\u271d\u2075 : NormedSpace \ud835\udd5c' E\ninst\u271d\u2074 : IsScalarTower \ud835\udd5c \ud835\udd5c' E\nF : Type u_4\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c' F\ninst\u271d : IsScalarTower \ud835\udd5c \ud835\udd5c' F\nf : E \u2192 F\nf'\u271d : E \u2192L[\ud835\udd5c'] F\ns : Set E\nx : E\nhf : DifferentiableWithinAt \ud835\udd5c f s x\nhs : UniqueDiffWithinAt \ud835\udd5c s x\nf' : E \u2192L[\ud835\udd5c'] F\nhf' : restrictScalars \ud835\udd5c f' = fderivWithin \ud835\udd5c f s x\n\u22a2 DifferentiableWithinAt \ud835\udd5c' f s x",
+                "state_before": "case mpr\n\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\n\ud835\udd5c' : Type u_2\ninst\u271d\u2079 : NontriviallyNormedField \ud835\udd5c'\ninst\u271d\u2078 : NormedAlgebra \ud835\udd5c \ud835\udd5c'\nE : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup E\ninst\u271d\u2076 : NormedSpace \ud835\udd5c E\ninst\u271d\u2075 : NormedSpace \ud835\udd5c' E\ninst\u271d\u2074 : IsScalarTower \ud835\udd5c \ud835\udd5c' E\nF : Type u_4\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c' F\ninst\u271d : IsScalarTower \ud835\udd5c \ud835\udd5c' F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c'] F\ns : Set E\nx : E\nhf : DifferentiableWithinAt \ud835\udd5c f s x\nhs : UniqueDiffWithinAt \ud835\udd5c s x\n\u22a2 (\u2203 g', restrictScalars \ud835\udd5c g' = fderivWithin \ud835\udd5c f s x) \u2192 DifferentiableWithinAt \ud835\udd5c' f s x",
+                "tactic": "rintro \u27e8f', hf'\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact \\u27e8f', hf.hasFDerivWithinAt.of_restrictScalars \\ud835\\udd5c hf'\\u27e9\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case mpr.intro\n\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\n\ud835\udd5c' : Type u_2\ninst\u271d\u2079 : NontriviallyNormedField \ud835\udd5c'\ninst\u271d\u2078 : NormedAlgebra \ud835\udd5c \ud835\udd5c'\nE : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup E\ninst\u271d\u2076 : NormedSpace \ud835\udd5c E\ninst\u271d\u2075 : NormedSpace \ud835\udd5c' E\ninst\u271d\u2074 : IsScalarTower \ud835\udd5c \ud835\udd5c' E\nF : Type u_4\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c' F\ninst\u271d : IsScalarTower \ud835\udd5c \ud835\udd5c' F\nf : E \u2192 F\nf'\u271d : E \u2192L[\ud835\udd5c'] F\ns : Set E\nx : E\nhf : DifferentiableWithinAt \ud835\udd5c f s x\nhs : UniqueDiffWithinAt \ud835\udd5c s x\nf' : E \u2192L[\ud835\udd5c'] F\nhf' : restrictScalars \ud835\udd5c f' = fderivWithin \ud835\udd5c f s x\n\u22a2 DifferentiableWithinAt \ud835\udd5c' f s x",
+                "tactic": "exact \u27e8f', hf.hasFDerivWithinAt.of_restrictScalars \ud835\udd5c hf'\u27e9"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "differentiableWithinAt_iff_restrictScalars"
+      }
+    ],
+    "validation_rejected_proofs": 1,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000420-0000-7117a8548f6cfaf9.parquet",
+      "sha256": "7117a8548f6cfaf926be32c9f7635737b44c7525dbdce6c7f63a21bc103734bf",
+      "bytes": 93563,
+      "rows": 6,
+      "revision": "eef9f30926b0307521cf3967e66e7df66c40bfc5"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:HasFDerivWithinAt.of_restrictScalars",
+    "mathlib:differentiableAt_iff_restrictScalars",
+    "mathlib:hasFDerivAt_of_restrictScalars"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean\",null,null,\"HasFDerivWithinAt.of_restrictScalars\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean\",null,null,\"differentiableAt_iff_restrictScalars\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean\",null,null,\"hasFDerivAt_of_restrictScalars\"]"
+  ]
+}

manifests/batches/mathlib/000422.json

@@ -0,0 +1,1612 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000422",
+  "batch_fingerprint": "b430f58fb42a4ed097e266601f3f3de3502d51311c935f7cf5912ce7b93196fc",
+  "evidence": {
+    "batch_fingerprint": "b430f58fb42a4ed097e266601f3f3de3502d51311c935f7cf5912ce7b93196fc",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DifferentiableOn.hasGradientAt",
+        "id": "DifferentiableOn.hasGradientAt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            144,
+            35
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "DifferentiableOn.hasGradientAt",
+          "start": [
+            142,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Filter.EventuallyEq.gradient",
+        "id": "Filter.EventuallyEq.gradient",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            294,
+            52
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "Filter.EventuallyEq.gradient",
+          "start": [
+            293,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'ext'",
+        "full_name": "HasDerivAtFilter.hasGradientAtFilter",
+        "id": "HasDerivAtFilter.hasGradientAtFilter",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            166,
+            36
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasDerivAtFilter.hasGradientAtFilter",
+          "start": [
+            162,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"have : <a>ContinuousLinearMap.smulRight<\\/a> (1 : \\ud835\\udd5c \\u2192L[\\ud835\\udd5c] \\ud835\\udd5c) g' = (<a>toDual<\\/a> \\ud835\\udd5c \\ud835\\udd5c) (<a>starRingEnd<\\/a> \\ud835\\udd5c g') := by\\n    ext; simp\"",
+                "[{\"full_name\":\"ContinuousLinearMap.smulRight\",\"def_path\":\"Mathlib\\/Topology\\/Algebra\\/Module\\/Basic.lean\",\"def_pos\":[1217,5],\"def_end_pos\":[1217,14]},{\"full_name\":\"InnerProductSpace.toDual\",\"def_path\":\"Mathlib\\/Analysis\\/InnerProductSpace\\/Dual.lean\",\"def_pos\":[107,5],\"def_end_pos\":[107,11]},{\"full_name\":\"starRingEnd\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[371,5],\"def_end_pos\":[371,16]}]"
+              ],
+              "state_after": "\ud835\udd5c : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : RCLike \ud835\udd5c\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : F \u2192 \ud835\udd5c\nf' x : F\ns : Set F\nL : Filter F\ng : \ud835\udd5c \u2192 \ud835\udd5c\ng' u : \ud835\udd5c\nL' : Filter \ud835\udd5c\nh : HasDerivAtFilter g g' u L'\nthis : ContinuousLinearMap.smulRight 1 g' = (toDual \ud835\udd5c \ud835\udd5c) ((starRingEnd \ud835\udd5c) g')\n\u22a2 HasGradientAtFilter g ((starRingEnd \ud835\udd5c) g') u L'",
+              "state_before": "\ud835\udd5c : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : RCLike \ud835\udd5c\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : F \u2192 \ud835\udd5c\nf' x : F\ns : Set F\nL : Filter F\ng : \ud835\udd5c \u2192 \ud835\udd5c\ng' u : \ud835\udd5c\nL' : Filter \ud835\udd5c\nh : HasDerivAtFilter g g' u L'\n\u22a2 HasGradientAtFilter g ((starRingEnd \ud835\udd5c) g') u L'",
+              "tactic": "have : ContinuousLinearMap.smulRight (1 : \ud835\udd5c \u2192L[\ud835\udd5c] \ud835\udd5c) g' = (toDual \ud835\udd5c \ud835\udd5c) (starRingEnd \ud835\udd5c g') := by\n  ext; simp"
+            },
+            {
+              "annotated_tactic": [
+                "\"rwa [<a>HasGradientAtFilter<\\/a>, \\u2190 this]\"",
+                "[{\"full_name\":\"HasGradientAtFilter\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Gradient\\/Basic.lean\",\"def_pos\":[50,5],\"def_end_pos\":[50,24]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\ud835\udd5c : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : RCLike \ud835\udd5c\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : F \u2192 \ud835\udd5c\nf' x : F\ns : Set F\nL : Filter F\ng : \ud835\udd5c \u2192 \ud835\udd5c\ng' u : \ud835\udd5c\nL' : Filter \ud835\udd5c\nh : HasDerivAtFilter g g' u L'\nthis : ContinuousLinearMap.smulRight 1 g' = (toDual \ud835\udd5c \ud835\udd5c) ((starRingEnd \ud835\udd5c) g')\n\u22a2 HasGradientAtFilter g ((starRingEnd \ud835\udd5c) g') u L'",
+              "tactic": "rwa [HasGradientAtFilter, \u2190 this]"
+            },
+            {
+              "annotated_tactic": [
+                "\"ext\"",
+                "[]"
+              ],
+              "state_after": "case h\n\ud835\udd5c : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : RCLike \ud835\udd5c\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : F \u2192 \ud835\udd5c\nf' x : F\ns : Set F\nL : Filter F\ng : \ud835\udd5c \u2192 \ud835\udd5c\ng' u : \ud835\udd5c\nL' : Filter \ud835\udd5c\nh : HasDerivAtFilter g g' u L'\n\u22a2 (ContinuousLinearMap.smulRight 1 g') 1 = ((toDual \ud835\udd5c \ud835\udd5c) ((starRingEnd \ud835\udd5c) g')) 1",
+              "state_before": "\ud835\udd5c : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : RCLike \ud835\udd5c\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : F \u2192 \ud835\udd5c\nf' x : F\ns : Set F\nL : Filter F\ng : \ud835\udd5c \u2192 \ud835\udd5c\ng' u : \ud835\udd5c\nL' : Filter \ud835\udd5c\nh : HasDerivAtFilter g g' u L'\n\u22a2 ContinuousLinearMap.smulRight 1 g' = (toDual \ud835\udd5c \ud835\udd5c) ((starRingEnd \ud835\udd5c) g')",
+              "tactic": "ext"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h\n\ud835\udd5c : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : RCLike \ud835\udd5c\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : F \u2192 \ud835\udd5c\nf' x : F\ns : Set F\nL : Filter F\ng : \ud835\udd5c \u2192 \ud835\udd5c\ng' u : \ud835\udd5c\nL' : Filter \ud835\udd5c\nh : HasDerivAtFilter g g' u L'\n\u22a2 (ContinuousLinearMap.smulRight 1 g') 1 = ((toDual \ud835\udd5c \ud835\udd5c) ((starRingEnd \ud835\udd5c) g')) 1",
+              "tactic": "simp"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasDerivAtFilter.hasGradientAtFilter'",
+        "id": "HasDerivAtFilter.hasGradientAtFilter'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            193,
+            59
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasDerivAtFilter.hasGradientAtFilter'",
+          "start": [
+            192,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasGradientAt.congr_of_eventuallyEq",
+        "id": "HasGradientAt.congr_of_eventuallyEq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            287,
+            74
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasGradientAt.congr_of_eventuallyEq",
+          "start": [
+            285,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasGradientAt.continuousAt",
+        "id": "HasGradientAt.continuousAt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            335,
+            44
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasGradientAt.continuousAt",
+          "start": [
+            334,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasGradientAt.continuousOn",
+        "id": "HasGradientAt.continuousOn",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            339,
+            55
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasGradientAt.continuousOn",
+          "start": [
+            337,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasGradientAt.differentiableAt",
+        "id": "HasGradientAt.differentiableAt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            125,
+            33
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasGradientAt.differentiableAt",
+          "start": [
+            123,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasGradientAt.gradient",
+        "id": "HasGradientAt.gradient",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            147,
+            44
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasGradientAt.gradient",
+          "start": [
+            146,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasGradientAt.hasDerivAt'",
+        "id": "HasGradientAt.hasDerivAt'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            196,
+            38
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasGradientAt.hasDerivAt'",
+          "start": [
+            195,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasGradientAt.unique",
+        "id": "HasGradientAt.unique",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            116,
+            64
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasGradientAt.unique",
+          "start": [
+            113,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'ext'",
+        "full_name": "HasGradientAtFilter.hasDerivAtFilter",
+        "id": "HasGradientAtFilter.hasDerivAtFilter",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            160,
+            31
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasGradientAtFilter.hasDerivAtFilter",
+          "start": [
+            156,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"have : <a>ContinuousLinearMap.smulRight<\\/a> (1 : \\ud835\\udd5c \\u2192L[\\ud835\\udd5c] \\ud835\\udd5c) (<a>starRingEnd<\\/a> \\ud835\\udd5c g') = (<a>toDual<\\/a> \\ud835\\udd5c \\ud835\\udd5c) g' := by\\n    ext; simp\"",
+                "[{\"full_name\":\"ContinuousLinearMap.smulRight\",\"def_path\":\"Mathlib\\/Topology\\/Algebra\\/Module\\/Basic.lean\",\"def_pos\":[1217,5],\"def_end_pos\":[1217,14]},{\"full_name\":\"starRingEnd\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[371,5],\"def_end_pos\":[371,16]},{\"full_name\":\"InnerProductSpace.toDual\",\"def_path\":\"Mathlib\\/Analysis\\/InnerProductSpace\\/Dual.lean\",\"def_pos\":[107,5],\"def_end_pos\":[107,11]}]"
+              ],
+              "state_after": "\ud835\udd5c : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : RCLike \ud835\udd5c\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : F \u2192 \ud835\udd5c\nf' x : F\ns : Set F\nL : Filter F\ng : \ud835\udd5c \u2192 \ud835\udd5c\ng' u : \ud835\udd5c\nL' : Filter \ud835\udd5c\nh : HasGradientAtFilter g g' u L'\nthis : ContinuousLinearMap.smulRight 1 ((starRingEnd \ud835\udd5c) g') = (toDual \ud835\udd5c \ud835\udd5c) g'\n\u22a2 HasDerivAtFilter g ((starRingEnd \ud835\udd5c) g') u L'",
+              "state_before": "\ud835\udd5c : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : RCLike \ud835\udd5c\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : F \u2192 \ud835\udd5c\nf' x : F\ns : Set F\nL : Filter F\ng : \ud835\udd5c \u2192 \ud835\udd5c\ng' u : \ud835\udd5c\nL' : Filter \ud835\udd5c\nh : HasGradientAtFilter g g' u L'\n\u22a2 HasDerivAtFilter g ((starRingEnd \ud835\udd5c) g') u L'",
+              "tactic": "have : ContinuousLinearMap.smulRight (1 : \ud835\udd5c \u2192L[\ud835\udd5c] \ud835\udd5c) (starRingEnd \ud835\udd5c g') = (toDual \ud835\udd5c \ud835\udd5c) g' := by\n  ext; simp"
+            },
+            {
+              "annotated_tactic": [
+                "\"rwa [<a>HasDerivAtFilter<\\/a>, this]\"",
+                "[{\"full_name\":\"HasDerivAtFilter\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Deriv\\/Basic.lean\",\"def_pos\":[109,5],\"def_end_pos\":[109,21]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\ud835\udd5c : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : RCLike \ud835\udd5c\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : F \u2192 \ud835\udd5c\nf' x : F\ns : Set F\nL : Filter F\ng : \ud835\udd5c \u2192 \ud835\udd5c\ng' u : \ud835\udd5c\nL' : Filter \ud835\udd5c\nh : HasGradientAtFilter g g' u L'\nthis : ContinuousLinearMap.smulRight 1 ((starRingEnd \ud835\udd5c) g') = (toDual \ud835\udd5c \ud835\udd5c) g'\n\u22a2 HasDerivAtFilter g ((starRingEnd \ud835\udd5c) g') u L'",
+              "tactic": "rwa [HasDerivAtFilter, this]"
+            },
+            {
+              "annotated_tactic": [
+                "\"ext\"",
+                "[]"
+              ],
+              "state_after": "case h\n\ud835\udd5c : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : RCLike \ud835\udd5c\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : F \u2192 \ud835\udd5c\nf' x : F\ns : Set F\nL : Filter F\ng : \ud835\udd5c \u2192 \ud835\udd5c\ng' u : \ud835\udd5c\nL' : Filter \ud835\udd5c\nh : HasGradientAtFilter g g' u L'\n\u22a2 (ContinuousLinearMap.smulRight 1 ((starRingEnd \ud835\udd5c) g')) 1 = ((toDual \ud835\udd5c \ud835\udd5c) g') 1",
+              "state_before": "\ud835\udd5c : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : RCLike \ud835\udd5c\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : F \u2192 \ud835\udd5c\nf' x : F\ns : Set F\nL : Filter F\ng : \ud835\udd5c \u2192 \ud835\udd5c\ng' u : \ud835\udd5c\nL' : Filter \ud835\udd5c\nh : HasGradientAtFilter g g' u L'\n\u22a2 ContinuousLinearMap.smulRight 1 ((starRingEnd \ud835\udd5c) g') = (toDual \ud835\udd5c \ud835\udd5c) g'",
+              "tactic": "ext"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h\n\ud835\udd5c : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : RCLike \ud835\udd5c\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : F \u2192 \ud835\udd5c\nf' x : F\ns : Set F\nL : Filter F\ng : \ud835\udd5c \u2192 \ud835\udd5c\ng' u : \ud835\udd5c\nL' : Filter \ud835\udd5c\nh : HasGradientAtFilter g g' u L'\n\u22a2 (ContinuousLinearMap.smulRight 1 ((starRingEnd \ud835\udd5c) g')) 1 = ((toDual \ud835\udd5c \ud835\udd5c) g') 1",
+              "tactic": "simp"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasGradientAtFilter.hasDerivAtFilter'",
+        "id": "HasGradientAtFilter.hasDerivAtFilter'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            190,
+            53
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasGradientAtFilter.hasDerivAtFilter'",
+          "start": [
+            189,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasGradientAtFilter.isBigO_sub",
+        "id": "HasGradientAtFilter.isBigO_sub",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            235,
+            33
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasGradientAtFilter.isBigO_sub",
+          "start": [
+            233,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasGradientAtFilter.tendsto_nhds",
+        "id": "HasGradientAtFilter.tendsto_nhds",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            328,
+            20
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasGradientAtFilter.tendsto_nhds",
+          "start": [
+            326,
+            8
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasGradientWithinAt.congr_mono",
+        "id": "HasGradientWithinAt.congr_mono",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            267,
+            42
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasGradientWithinAt.congr_mono",
+          "start": [
+            265,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasGradientWithinAt.congr_of_eventuallyEq",
+        "id": "HasGradientWithinAt.congr_of_eventuallyEq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            279,
+            52
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasGradientWithinAt.congr_of_eventuallyEq",
+          "start": [
+            277,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasGradientWithinAt.congr_of_eventuallyEq_of_mem",
+        "id": "HasGradientWithinAt.congr_of_eventuallyEq_of_mem",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            283,
+            54
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasGradientWithinAt.congr_of_eventuallyEq_of_mem",
+          "start": [
+            281,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasGradientWithinAt.congr_of_mem",
+        "id": "HasGradientWithinAt.congr_of_mem",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            275,
+            23
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasGradientWithinAt.congr_of_mem",
+          "start": [
+            273,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasGradientWithinAt.continuousWithinAt",
+        "id": "HasGradientWithinAt.continuousWithinAt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            332,
+            49
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasGradientWithinAt.continuousWithinAt",
+          "start": [
+            330,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasGradientWithinAt.differentiableWithinAt",
+        "id": "HasGradientWithinAt.differentiableWithinAt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            135,
+            45
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "HasGradientWithinAt.differentiableWithinAt",
+          "start": [
+            133,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "gradient_const'",
+        "id": "gradient_const'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            318,
+            37
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "gradient_const'",
+          "start": [
+            317,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "gradient_eq",
+        "id": "gradient_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            150,
+            33
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "gradient_eq",
+          "start": [
+            149,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "gradient_eq_deriv'",
+        "id": "gradient_eq_deriv'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            201,
+            68
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "gradient_eq_deriv'",
+          "start": [
+            201,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "hasGradientAtFilter_iff_isLittleO",
+        "id": "hasGradientAtFilter_iff_isLittleO",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            212,
+            37
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "hasGradientAtFilter_iff_isLittleO",
+          "start": [
+            209,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "hasGradientAt_const",
+        "id": "hasGradientAt_const",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            311,
+            34
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "hasGradientAt_const",
+          "start": [
+            310,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "hasGradientAt_iff_hasFDerivAt",
+        "id": "hasGradientAt_iff_hasFDerivAt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            96,
+            10
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "hasGradientAt_iff_hasFDerivAt",
+          "start": [
+            94,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "hasGradientAt_iff_isLittleO",
+        "id": "hasGradientAt_iff_isLittleO",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            226,
+            36
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "hasGradientAt_iff_isLittleO",
+          "start": [
+            224,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "hasGradientAt_iff_isLittleO_nhds_zero",
+        "id": "hasGradientAt_iff_isLittleO_nhds_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            247,
+            38
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "hasGradientAt_iff_isLittleO_nhds_zero",
+          "start": [
+            245,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "hasGradientAt_iff_tendsto",
+        "id": "hasGradientAt_iff_tendsto",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            231,
+            32
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "hasGradientAt_iff_tendsto",
+          "start": [
+            228,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "hasGradientWithinAt_congr_set",
+        "id": "hasGradientWithinAt_congr_set",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            243,
+            32
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "hasGradientWithinAt_congr_set",
+          "start": [
+            241,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "hasGradientWithinAt_congr_set'",
+        "id": "hasGradientWithinAt_congr_set'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            239,
+            35
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "hasGradientWithinAt_congr_set'",
+          "start": [
+            237,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "hasGradientWithinAt_const",
+        "id": "hasGradientWithinAt_const",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            308,
+            34
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "hasGradientWithinAt_const",
+          "start": [
+            307,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "hasGradientWithinAt_iff_hasFDerivWithinAt",
+        "id": "hasGradientWithinAt_iff_hasFDerivWithinAt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            88,
+            10
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "hasGradientWithinAt_iff_hasFDerivWithinAt",
+          "start": [
+            86,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "hasGradientWithinAt_iff_isLittleO",
+        "id": "hasGradientWithinAt_iff_isLittleO",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            217,
+            36
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "hasGradientWithinAt_iff_isLittleO",
+          "start": [
+            214,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "hasGradientWithinAt_iff_tendsto",
+        "id": "hasGradientWithinAt_iff_tendsto",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            222,
+            32
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+          "full_name": "hasGradientWithinAt_iff_tendsto",
+          "start": [
+            219,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Gradient/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.eq_implicitFunction",
+        "id": "HasStrictFDerivAt.eq_implicitFunction",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            476,
+            39
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "HasStrictFDerivAt.eq_implicitFunction",
+          "start": [
+            472,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.eq_implicitFunctionOfComplemented",
+        "id": "HasStrictFDerivAt.eq_implicitFunctionOfComplemented",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            337,
+            85
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "HasStrictFDerivAt.eq_implicitFunctionOfComplemented",
+          "start": [
+            333,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.implicitToPartialHomeomorphOfComplemented_apply",
+        "id": "HasStrictFDerivAt.implicitToPartialHomeomorphOfComplemented_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            289,
+            6
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "HasStrictFDerivAt.implicitToPartialHomeomorphOfComplemented_apply",
+          "start": [
+            285,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.implicitToPartialHomeomorphOfComplemented_fst",
+        "id": "HasStrictFDerivAt.implicitToPartialHomeomorphOfComplemented_fst",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            282,
+            6
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "HasStrictFDerivAt.implicitToPartialHomeomorphOfComplemented_fst",
+          "start": [
+            279,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.implicitToPartialHomeomorph_apply_ker",
+        "id": "HasStrictFDerivAt.implicitToPartialHomeomorph_apply_ker",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            421,
+            57
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "HasStrictFDerivAt.implicitToPartialHomeomorph_apply_ker",
+          "start": [
+            417,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.implicitToPartialHomeomorph_fst",
+        "id": "HasStrictFDerivAt.implicitToPartialHomeomorph_fst",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            413,
+            6
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "HasStrictFDerivAt.implicitToPartialHomeomorph_fst",
+          "start": [
+            411,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.implicitToPartialHomeomorph_self",
+        "id": "HasStrictFDerivAt.implicitToPartialHomeomorph_self",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            428,
+            52
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "HasStrictFDerivAt.implicitToPartialHomeomorph_self",
+          "start": [
+            425,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.map_implicitFunctionOfComplemented_eq",
+        "id": "HasStrictFDerivAt.map_implicitFunctionOfComplemented_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            328,
+            41
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "HasStrictFDerivAt.map_implicitFunctionOfComplemented_eq",
+          "start": [
+            322,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.map_implicitFunction_eq",
+        "id": "HasStrictFDerivAt.map_implicitFunction_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            460,
+            43
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "HasStrictFDerivAt.map_implicitFunction_eq",
+          "start": [
+            457,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.mem_implicitToPartialHomeomorphOfComplemented_source",
+        "id": "HasStrictFDerivAt.mem_implicitToPartialHomeomorphOfComplemented_source",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            310,
+            59
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "HasStrictFDerivAt.mem_implicitToPartialHomeomorphOfComplemented_source",
+          "start": [
+            307,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.mem_implicitToPartialHomeomorph_source",
+        "id": "HasStrictFDerivAt.mem_implicitToPartialHomeomorph_source",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            434,
+            59
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "HasStrictFDerivAt.mem_implicitToPartialHomeomorph_source",
+          "start": [
+            431,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.mem_implicitToPartialHomeomorph_target",
+        "id": "HasStrictFDerivAt.mem_implicitToPartialHomeomorph_target",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            440,
+            58
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "HasStrictFDerivAt.mem_implicitToPartialHomeomorph_target",
+          "start": [
+            437,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.to_implicitFunction",
+        "id": "HasStrictFDerivAt.to_implicitFunction",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            482,
+            39
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "HasStrictFDerivAt.to_implicitFunction",
+          "start": [
+            479,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'swap'",
+        "full_name": "HasStrictFDerivAt.to_implicitFunctionOfComplemented",
+        "id": "HasStrictFDerivAt.to_implicitFunctionOfComplemented",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            366,
+            68
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "HasStrictFDerivAt.to_implicitFunctionOfComplemented",
+          "start": [
+            349,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"convert (<a>implicitFunctionDataOfComplemented<\\/a> f f' hf hf' hker).<a>implicitFunction_hasStrictFDerivAt<\\/a>\\n    (<a>ker<\\/a> f').<a>subtypeL<\\/a> _ _\"",
+                "[{\"full_name\":\"HasStrictFDerivAt.implicitFunctionDataOfComplemented\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Implicit.lean\",\"def_pos\":[248,5],\"def_end_pos\":[248,39]},{\"full_name\":\"ImplicitFunctionData.implicitFunction_hasStrictFDerivAt\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Implicit.lean\",\"def_pos\":[201,9],\"def_end_pos\":[201,43]},{\"full_name\":\"LinearMap.ker\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Submodule\\/Ker.lean\",\"def_pos\":[60,5],\"def_end_pos\":[60,8]},{\"full_name\":\"Submodule.subtypeL\",\"def_path\":\"Mathlib\\/Topology\\/Algebra\\/Module\\/Basic.lean\",\"def_pos\":[1065,5],\"def_end_pos\":[1065,30]}]"
+              ],
+              "state_after": "case h.e'_11\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\n\u22a2 0 =\n    (implicitFunctionDataOfComplemented f f' hf hf' hker).rightFun\n      (implicitFunctionDataOfComplemented f f' hf hf' hker).pt\n\ncase convert_1\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\n\u22a2 (implicitFunctionDataOfComplemented f f' hf hf' hker).rightDeriv.comp (LinearMap.ker f').subtypeL =\n    ContinuousLinearMap.id \ud835\udd5c \u21a5(LinearMap.ker f')\n\ncase convert_2\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\n\u22a2 (implicitFunctionDataOfComplemented f f' hf hf' hker).leftDeriv.comp (LinearMap.ker f').subtypeL = 0",
+              "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\n\u22a2 HasStrictFDerivAt (implicitFunctionOfComplemented f f' hf hf' hker (f a)) (LinearMap.ker f').subtypeL 0",
+              "tactic": "convert (implicitFunctionDataOfComplemented f f' hf hf' hker).implicitFunction_hasStrictFDerivAt\n  (ker f').subtypeL _ _"
+            },
+            {
+              "annotated_tactic": [
+                "\"swap\"",
+                "[]"
+              ],
+              "state_after": "case convert_1\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\n\u22a2 (implicitFunctionDataOfComplemented f f' hf hf' hker).rightDeriv.comp (LinearMap.ker f').subtypeL =\n    ContinuousLinearMap.id \ud835\udd5c \u21a5(LinearMap.ker f')\n\ncase h.e'_11\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\n\u22a2 0 =\n    (implicitFunctionDataOfComplemented f f' hf hf' hker).rightFun\n      (implicitFunctionDataOfComplemented f f' hf hf' hker).pt\n\ncase convert_2\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\n\u22a2 (implicitFunctionDataOfComplemented f f' hf hf' hker).leftDeriv.comp (LinearMap.ker f').subtypeL = 0",
+              "state_before": "case h.e'_11\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\n\u22a2 0 =\n    (implicitFunctionDataOfComplemented f f' hf hf' hker).rightFun\n      (implicitFunctionDataOfComplemented f f' hf hf' hker).pt\n\ncase convert_1\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\n\u22a2 (implicitFunctionDataOfComplemented f f' hf hf' hker).rightDeriv.comp (LinearMap.ker f').subtypeL =\n    ContinuousLinearMap.id \ud835\udd5c \u21a5(LinearMap.ker f')\n\ncase convert_2\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\n\u22a2 (implicitFunctionDataOfComplemented f f' hf hf' hker).leftDeriv.comp (LinearMap.ker f').subtypeL = 0",
+              "tactic": "swap"
+            },
+            {
+              "annotated_tactic": [
+                "\"swap\"",
+                "[]"
+              ],
+              "state_after": "case convert_2\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\n\u22a2 (implicitFunctionDataOfComplemented f f' hf hf' hker).leftDeriv.comp (LinearMap.ker f').subtypeL = 0\n\ncase h.e'_11\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\n\u22a2 0 =\n    (implicitFunctionDataOfComplemented f f' hf hf' hker).rightFun\n      (implicitFunctionDataOfComplemented f f' hf hf' hker).pt",
+              "state_before": "case h.e'_11\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\n\u22a2 0 =\n    (implicitFunctionDataOfComplemented f f' hf hf' hker).rightFun\n      (implicitFunctionDataOfComplemented f f' hf hf' hker).pt\n\ncase convert_2\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\n\u22a2 (implicitFunctionDataOfComplemented f f' hf hf' hker).leftDeriv.comp (LinearMap.ker f').subtypeL = 0",
+              "tactic": "swap"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>implicitFunctionDataOfComplemented<\\/a>, <a>map_sub<\\/a>, <a>sub_self<\\/a>]\"",
+                "[{\"full_name\":\"HasStrictFDerivAt.implicitFunctionDataOfComplemented\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Implicit.lean\",\"def_pos\":[248,5],\"def_end_pos\":[248,39]},{\"full_name\":\"map_sub\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[461,3],\"def_end_pos\":[461,14]},{\"full_name\":\"sub_self\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[1003,30],\"def_end_pos\":[1003,38]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.e'_11\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\n\u22a2 0 =\n    (implicitFunctionDataOfComplemented f f' hf hf' hker).rightFun\n      (implicitFunctionDataOfComplemented f f' hf hf' hker).pt",
+              "tactic": "simp only [implicitFunctionDataOfComplemented, map_sub, sub_self]"
+            },
+            {
+              "annotated_tactic": [
+                "\"ext\"",
+                "[]"
+              ],
+              "state_after": "case convert_1.h.a\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\nx\u271d : \u21a5(LinearMap.ker f')\n\u22a2 \u2191(((implicitFunctionDataOfComplemented f f' hf hf' hker).rightDeriv.comp (LinearMap.ker f').subtypeL) x\u271d) =\n    \u2191((ContinuousLinearMap.id \ud835\udd5c \u21a5(LinearMap.ker f')) x\u271d)",
+              "state_before": "case convert_1\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\n\u22a2 (implicitFunctionDataOfComplemented f f' hf hf' hker).rightDeriv.comp (LinearMap.ker f').subtypeL =\n    ContinuousLinearMap.id \ud835\udd5c \u21a5(LinearMap.ker f')",
+              "tactic": "ext"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>Classical.choose_spec<\\/a> hker, <a>implicitFunctionDataOfComplemented<\\/a>,\\n      <a>ContinuousLinearMap.comp_apply<\\/a>, <a>Submodule.coe_subtypeL'<\\/a>, <a>Submodule.coeSubtype<\\/a>,\\n      <a>ContinuousLinearMap.id_apply<\\/a>]\"",
+                "[{\"full_name\":\"Classical.choose_spec\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Classical.lean\",\"def_pos\":[28,9],\"def_end_pos\":[28,20]},{\"full_name\":\"HasStrictFDerivAt.implicitFunctionDataOfComplemented\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Implicit.lean\",\"def_pos\":[248,5],\"def_end_pos\":[248,39]},{\"full_name\":\"ContinuousLinearMap.comp_apply\",\"def_path\":\"Mathlib\\/Topology\\/Algebra\\/Module\\/Basic.lean\",\"def_pos\":[799,9],\"def_end_pos\":[799,19]},{\"full_name\":\"Submodule.coe_subtypeL'\",\"def_path\":\"Mathlib\\/Topology\\/Algebra\\/Module\\/Basic.lean\",\"def_pos\":[1079,9],\"def_end_pos\":[1079,39]},{\"full_name\":\"Submodule.coeSubtype\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Submodule\\/LinearMap.lean\",\"def_pos\":[84,9],\"def_end_pos\":[84,19]},{\"full_name\":\"ContinuousLinearMap.id_apply\",\"def_path\":\"Mathlib\\/Topology\\/Algebra\\/Module\\/Basic.lean\",\"def_pos\":[682,9],\"def_end_pos\":[682,17]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case convert_1.h.a\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\nx\u271d : \u21a5(LinearMap.ker f')\n\u22a2 \u2191(((implicitFunctionDataOfComplemented f f' hf hf' hker).rightDeriv.comp (LinearMap.ker f').subtypeL) x\u271d) =\n    \u2191((ContinuousLinearMap.id \ud835\udd5c \u21a5(LinearMap.ker f')) x\u271d)",
+              "tactic": "simp only [Classical.choose_spec hker, implicitFunctionDataOfComplemented,\n  ContinuousLinearMap.comp_apply, Submodule.coe_subtypeL', Submodule.coeSubtype,\n  ContinuousLinearMap.id_apply]"
+            },
+            {
+              "annotated_tactic": [
+                "\"ext\"",
+                "[]"
+              ],
+              "state_after": "case convert_2.h\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\nx\u271d : \u21a5(LinearMap.ker f')\n\u22a2 ((implicitFunctionDataOfComplemented f f' hf hf' hker).leftDeriv.comp (LinearMap.ker f').subtypeL) x\u271d = 0 x\u271d",
+              "state_before": "case convert_2\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\n\u22a2 (implicitFunctionDataOfComplemented f f' hf hf' hker).leftDeriv.comp (LinearMap.ker f').subtypeL = 0",
+              "tactic": "ext"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [(<a>ContinuousLinearMap.comp_apply<\\/a>), <a>Submodule.coe_subtypeL'<\\/a>, <a>Submodule.coeSubtype<\\/a>,\\n      <a>LinearMap.map_coe_ker<\\/a>, (<a>ContinuousLinearMap.zero_apply<\\/a>)]\"",
+                "[{\"full_name\":\"ContinuousLinearMap.comp_apply\",\"def_path\":\"Mathlib\\/Topology\\/Algebra\\/Module\\/Basic.lean\",\"def_pos\":[799,9],\"def_end_pos\":[799,19]},{\"full_name\":\"Submodule.coe_subtypeL'\",\"def_path\":\"Mathlib\\/Topology\\/Algebra\\/Module\\/Basic.lean\",\"def_pos\":[1079,9],\"def_end_pos\":[1079,39]},{\"full_name\":\"Submodule.coeSubtype\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Submodule\\/LinearMap.lean\",\"def_pos\":[84,9],\"def_end_pos\":[84,19]},{\"full_name\":\"LinearMap.map_coe_ker\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Submodule\\/Ker.lean\",\"def_pos\":[75,9],\"def_end_pos\":[75,20]},{\"full_name\":\"ContinuousLinearMap.zero_apply\",\"def_path\":\"Mathlib\\/Topology\\/Algebra\\/Module\\/Basic.lean\",\"def_pos\":[633,9],\"def_end_pos\":[633,19]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case convert_2.h\n\ud835\udd5c : Type u_1\ninst\u271d\u2076 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : CompleteSpace E\nF : Type u_3\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nhf' : range f' = \u22a4\nhker : (LinearMap.ker f').ClosedComplemented\nx\u271d : \u21a5(LinearMap.ker f')\n\u22a2 ((implicitFunctionDataOfComplemented f f' hf hf' hker).leftDeriv.comp (LinearMap.ker f').subtypeL) x\u271d = 0 x\u271d",
+              "tactic": "simp only [(ContinuousLinearMap.comp_apply), Submodule.coe_subtypeL', Submodule.coeSubtype,\n  LinearMap.map_coe_ker, (ContinuousLinearMap.zero_apply)]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ImplicitFunctionData.hasStrictFDerivAt",
+        "id": "ImplicitFunctionData.hasStrictFDerivAt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            139,
+            42
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "ImplicitFunctionData.hasStrictFDerivAt",
+          "start": [
+            133,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ImplicitFunctionData.implicitFunction_apply_image",
+        "id": "ImplicitFunctionData.implicitFunction_apply_image",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            193,
+            46
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "ImplicitFunctionData.implicitFunction_apply_image",
+          "start": [
+            191,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ImplicitFunctionData.left_map_implicitFunction",
+        "id": "ImplicitFunctionData.left_map_implicitFunction",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            183,
+            63
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "ImplicitFunctionData.left_map_implicitFunction",
+          "start": [
+            181,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ImplicitFunctionData.map_pt_mem_toPartialHomeomorph_target",
+        "id": "ImplicitFunctionData.map_pt_mem_toPartialHomeomorph_target",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            173,
+            74
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "ImplicitFunctionData.map_pt_mem_toPartialHomeomorph_target",
+          "start": [
+            171,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ImplicitFunctionData.prodFun_apply",
+        "id": "ImplicitFunctionData.prodFun_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            130,
+            6
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "ImplicitFunctionData.prodFun_apply",
+          "start": [
+            129,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ImplicitFunctionData.prod_map_implicitFunction",
+        "id": "ImplicitFunctionData.prod_map_implicitFunction",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            178,
+            70
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "ImplicitFunctionData.prod_map_implicitFunction",
+          "start": [
+            176,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ImplicitFunctionData.pt_mem_toPartialHomeomorph_source",
+        "id": "ImplicitFunctionData.pt_mem_toPartialHomeomorph_source",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            168,
+            53
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "ImplicitFunctionData.pt_mem_toPartialHomeomorph_source",
+          "start": [
+            167,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ImplicitFunctionData.right_map_implicitFunction",
+        "id": "ImplicitFunctionData.right_map_implicitFunction",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            188,
+            63
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "ImplicitFunctionData.right_map_implicitFunction",
+          "start": [
+            186,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ImplicitFunctionData.toPartialHomeomorph_apply",
+        "id": "ImplicitFunctionData.toPartialHomeomorph_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            164,
+            6
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "ImplicitFunctionData.toPartialHomeomorph_apply",
+          "start": [
+            163,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ImplicitFunctionData.toPartialHomeomorph_coe",
+        "id": "ImplicitFunctionData.toPartialHomeomorph_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            160,
+            6
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/Implicit.lean",
+          "full_name": "ImplicitFunctionData.toPartialHomeomorph_coe",
+          "start": [
+            159,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/Implicit.lean"
+      }
+    ],
+    "input_proofs": 82,
+    "input_units": 2,
+    "proofs": 22,
+    "published_proofs": 21,
+    "published_transitions": 37,
+    "replay_failures": [],
+    "transitions": 40,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+        "proof_id": "mathlib:gradient_eq_deriv",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              181,
+              100
+            ],
+            "file_path": "Mathlib/Analysis/Calculus/Gradient/Basic.lean",
+            "full_name": "gradient_eq_deriv",
+            "start": [
+              178,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"by_cases h : <a>DifferentiableAt<\\/a> \\ud835\\udd5c g u\"",
+                  "[{\"full_name\":\"DifferentiableAt\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/FDeriv\\/Basic.lean\",\"def_pos\":[178,5],\"def_end_pos\":[178,21]}]"
+                ],
+                "state_after": "case pos\n\ud835\udd5c : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : RCLike \ud835\udd5c\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : F \u2192 \ud835\udd5c\nf' x : F\ns : Set F\nL : Filter F\ng : \ud835\udd5c \u2192 \ud835\udd5c\ng' u : \ud835\udd5c\nL' : Filter \ud835\udd5c\nh : DifferentiableAt \ud835\udd5c g u\n\u22a2 \u2207 g u = (starRingEnd \ud835\udd5c) (deriv g u)\n\ncase neg\n\ud835\udd5c : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : RCLike \ud835\udd5c\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : F \u2192 \ud835\udd5c\nf' x : F\ns : Set F\nL : Filter F\ng : \ud835\udd5c \u2192 \ud835\udd5c\ng' u : \ud835\udd5c\nL' : Filter \ud835\udd5c\nh : \u00acDifferentiableAt \ud835\udd5c g u\n\u22a2 \u2207 g u = (starRingEnd \ud835\udd5c) (deriv g u)",
+                "state_before": "\ud835\udd5c : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : RCLike \ud835\udd5c\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : F \u2192 \ud835\udd5c\nf' x : F\ns : Set F\nL : Filter F\ng : \ud835\udd5c \u2192 \ud835\udd5c\ng' u : \ud835\udd5c\nL' : Filter \ud835\udd5c\n\u22a2 \u2207 g u = (starRingEnd \ud835\udd5c) (deriv g u)",
+                "tactic": "by_cases h : DifferentiableAt \ud835\udd5c g u"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [h.hasGradientAt.hasDerivAt.deriv, <a>RCLike.conj_conj<\\/a>]\"",
+                  "[{\"full_name\":\"RCLike.conj_conj\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[416,7],\"def_end_pos\":[416,23]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case pos\n\ud835\udd5c : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : RCLike \ud835\udd5c\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : F \u2192 \ud835\udd5c\nf' x : F\ns : Set F\nL : Filter F\ng : \ud835\udd5c \u2192 \ud835\udd5c\ng' u : \ud835\udd5c\nL' : Filter \ud835\udd5c\nh : DifferentiableAt \ud835\udd5c g u\n\u22a2 \u2207 g u = (starRingEnd \ud835\udd5c) (deriv g u)",
+                "tactic": "rw [h.hasGradientAt.hasDerivAt.deriv, RCLike.conj_conj]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>gradient_eq_zero_of_not_differentiableAt<\\/a> h, <a>deriv_zero_of_not_differentiableAt<\\/a> h, <a>map_zero<\\/a>]\"",
+                  "[{\"full_name\":\"gradient_eq_zero_of_not_differentiableAt\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Gradient\\/Basic.lean\",\"def_pos\":[110,9],\"def_end_pos\":[110,49]},{\"full_name\":\"deriv_zero_of_not_differentiableAt\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Deriv\\/Basic.lean\",\"def_pos\":[246,9],\"def_end_pos\":[246,43]},{\"full_name\":\"map_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[203,3],\"def_end_pos\":[203,14]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case neg\n\ud835\udd5c : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : RCLike \ud835\udd5c\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \ud835\udd5c F\ninst\u271d : CompleteSpace F\nf : F \u2192 \ud835\udd5c\nf' x : F\ns : Set F\nL : Filter F\ng : \ud835\udd5c \u2192 \ud835\udd5c\ng' u : \ud835\udd5c\nL' : Filter \ud835\udd5c\nh : \u00acDifferentiableAt \ud835\udd5c g u\n\u22a2 \u2207 g u = (starRingEnd \ud835\udd5c) (deriv g u)",
+                "tactic": "rw [gradient_eq_zero_of_not_differentiableAt h, deriv_zero_of_not_differentiableAt h, map_zero]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "gradient_eq_deriv"
+      }
+    ],
+    "validation_rejected_proofs": 1,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000422-0000-ca1d405c44575c77.parquet",
+      "sha256": "ca1d405c44575c77e763c76758304096efb330b50223357c747165dd0b919fed",
+      "bytes": 202934,
+      "rows": 29,
+      "revision": "eef9f30926b0307521cf3967e66e7df66c40bfc5"
+    },
+    {
+      "path": "data/dev/mathlib-000422-0000-b653667f6afb2bbc.parquet",
+      "sha256": "b653667f6afb2bbc772f20b86a2cbf26dbb517ac44cf661316f053e9a962c0e2",
+      "bytes": 56640,
+      "rows": 1,
+      "revision": "eef9f30926b0307521cf3967e66e7df66c40bfc5"
+    },
+    {
+      "path": "data/internal_test/mathlib-000422-0000-31e0af4091325f6d.parquet",
+      "sha256": "31e0af4091325f6dd2ec024136a0d904ad88ea899ffaa0be8395a3862a730d36",
+      "bytes": 89284,
+      "rows": 7,
+      "revision": "eef9f30926b0307521cf3967e66e7df66c40bfc5"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:DifferentiableAt.hasGradientAt",
+    "mathlib:DifferentiableWithinAt.hasGradientWithinAt",
+    "mathlib:Filter.EventuallyEq.gradient_eq",
+    "mathlib:Filter.EventuallyEq.hasGradientAtFilter_iff",
+    "mathlib:HasDerivAt.hasGradientAt",
+    "mathlib:HasGradientAt.hasDerivAt",
+    "mathlib:HasGradientAtFilter.congr_of_eventuallyEq",
+    "mathlib:HasGradientWithinAt.congr",
+    "mathlib:HasStrictFDerivAt.implicitFunctionOfComplemented_apply_image",
+    "mathlib:HasStrictFDerivAt.implicitFunction_apply_image",
+    "mathlib:HasStrictFDerivAt.implicitToPartialHomeomorphOfComplemented_apply_ker",
+    "mathlib:HasStrictFDerivAt.implicitToPartialHomeomorphOfComplemented_self",
+    "mathlib:HasStrictFDerivAt.mem_implicitToPartialHomeomorphOfComplemented_target",
+    "mathlib:HasStrictFDerivAt.tendsto_implicitFunction",
+    "mathlib:ImplicitFunctionData.implicitFunction_hasStrictFDerivAt",
+    "mathlib:gradient_const",
+    "mathlib:gradient_eq_zero_of_not_differentiableAt",
+    "mathlib:hasFDerivAt_iff_hasGradientAt",
+    "mathlib:hasFDerivWithinAt_iff_hasGradientWithinAt",
+    "mathlib:hasGradientAtFilter_const",
+    "mathlib:hasGradientWithinAt_univ"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Gradient/Basic.lean\",null,null,\"DifferentiableAt.hasGradientAt\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Gradient/Basic.lean\",null,null,\"DifferentiableWithinAt.hasGradientWithinAt\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Gradient/Basic.lean\",null,null,\"Filter.EventuallyEq.gradient_eq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Gradient/Basic.lean\",null,null,\"Filter.EventuallyEq.hasGradientAtFilter_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Gradient/Basic.lean\",null,null,\"HasDerivAt.hasGradientAt\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Gradient/Basic.lean\",null,null,\"HasGradientAt.hasDerivAt\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Gradient/Basic.lean\",null,null,\"HasGradientAtFilter.congr_of_eventuallyEq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Gradient/Basic.lean\",null,null,\"HasGradientWithinAt.congr\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Gradient/Basic.lean\",null,null,\"gradient_const\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Gradient/Basic.lean\",null,null,\"gradient_eq_zero_of_not_differentiableAt\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Gradient/Basic.lean\",null,null,\"hasFDerivAt_iff_hasGradientAt\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Gradient/Basic.lean\",null,null,\"hasFDerivWithinAt_iff_hasGradientWithinAt\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Gradient/Basic.lean\",null,null,\"hasGradientAtFilter_const\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Gradient/Basic.lean\",null,null,\"hasGradientWithinAt_univ\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Implicit.lean\",null,null,\"HasStrictFDerivAt.implicitFunctionOfComplemented_apply_image\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Implicit.lean\",null,null,\"HasStrictFDerivAt.implicitFunction_apply_image\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Implicit.lean\",null,null,\"HasStrictFDerivAt.implicitToPartialHomeomorphOfComplemented_apply_ker\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Implicit.lean\",null,null,\"HasStrictFDerivAt.implicitToPartialHomeomorphOfComplemented_self\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Implicit.lean\",null,null,\"HasStrictFDerivAt.mem_implicitToPartialHomeomorphOfComplemented_target\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Implicit.lean\",null,null,\"HasStrictFDerivAt.tendsto_implicitFunction\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Implicit.lean\",null,null,\"ImplicitFunctionData.implicitFunction_hasStrictFDerivAt\"]"
+  ]
+}

manifests/batches/mathlib/000424.json

@@ -0,0 +1,485 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000424",
+  "batch_fingerprint": "0846056cb6f9cb872a9e2d65ddb5381ab0251eafcc25988506107bed23c1cd2c",
+  "evidence": {
+    "batch_fingerprint": "0846056cb6f9cb872a9e2d65ddb5381ab0251eafcc25988506107bed23c1cd2c",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictDerivAt.map_nhds_eq",
+        "id": "HasStrictDerivAt.map_nhds_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            35,
+            56
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/Deriv.lean",
+          "full_name": "HasStrictDerivAt.map_nhds_eq",
+          "start": [
+            34,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/Deriv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictDerivAt.to_localInverse",
+        "id": "HasStrictDerivAt.to_localInverse",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            39,
+            51
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/Deriv.lean",
+          "full_name": "HasStrictDerivAt.to_localInverse",
+          "start": [
+            38,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/Deriv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictDerivAt.to_local_left_inverse",
+        "id": "HasStrictDerivAt.to_local_left_inverse",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            44,
+            60
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/Deriv.lean",
+          "full_name": "HasStrictDerivAt.to_local_left_inverse",
+          "start": [
+            42,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/Deriv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "isOpenMap_of_hasStrictDerivAt",
+        "id": "isOpenMap_of_hasStrictDerivAt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            54,
+            66
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/Deriv.lean",
+          "full_name": "isOpenMap_of_hasStrictDerivAt",
+          "start": [
+            52,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/Deriv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.eventually_left_inverse",
+        "id": "HasStrictFDerivAt.eventually_left_inverse",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            165,
+            87
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean",
+          "full_name": "HasStrictFDerivAt.eventually_left_inverse",
+          "start": [
+            163,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.eventually_right_inverse",
+        "id": "HasStrictFDerivAt.eventually_right_inverse",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            176,
+            89
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean",
+          "full_name": "HasStrictFDerivAt.eventually_right_inverse",
+          "start": [
+            174,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.image_mem_toPartialHomeomorph_target",
+        "id": "HasStrictFDerivAt.image_mem_toPartialHomeomorph_target",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            140,
+            74
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean",
+          "full_name": "HasStrictFDerivAt.image_mem_toPartialHomeomorph_target",
+          "start": [
+            138,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.localInverse_apply_image",
+        "id": "HasStrictFDerivAt.localInverse_apply_image",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            171,
+            42
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean",
+          "full_name": "HasStrictFDerivAt.localInverse_apply_image",
+          "start": [
+            169,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.localInverse_continuousAt",
+        "id": "HasStrictFDerivAt.localInverse_continuousAt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            181,
+            87
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean",
+          "full_name": "HasStrictFDerivAt.localInverse_continuousAt",
+          "start": [
+            179,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.localInverse_def",
+        "id": "HasStrictFDerivAt.localInverse_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            160,
+            6
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean",
+          "full_name": "HasStrictFDerivAt.localInverse_def",
+          "start": [
+            158,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.localInverse_tendsto",
+        "id": "HasStrictFDerivAt.localInverse_tendsto",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            186,
+            76
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean",
+          "full_name": "HasStrictFDerivAt.localInverse_tendsto",
+          "start": [
+            184,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.localInverse_unique",
+        "id": "HasStrictFDerivAt.localInverse_unique",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            192,
+            78
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean",
+          "full_name": "HasStrictFDerivAt.localInverse_unique",
+          "start": [
+            189,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.map_nhds_eq_of_equiv",
+        "id": "HasStrictFDerivAt.map_nhds_eq_of_equiv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            145,
+            75
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean",
+          "full_name": "HasStrictFDerivAt.map_nhds_eq_of_equiv",
+          "start": [
+            143,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean"
+      },
+      {
+        "error": "no internal trace for tactic \"simp [hc, half_pos, inv_pos, f'symm_pos]\"",
+        "full_name": "HasStrictFDerivAt.map_nhds_eq_of_surj",
+        "id": "HasStrictFDerivAt.map_nhds_eq_of_surj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            96,
+            29
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean",
+          "full_name": "HasStrictFDerivAt.map_nhds_eq_of_surj",
+          "start": [
+            86,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"let f'symm := f'.nonlinearRightInverseOfSurjective h\"",
+                "[]"
+              ],
+              "state_after": "\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2079 : NormedAddCommGroup E\ninst\u271d\u2078 : NormedSpace \ud835\udd5c E\nF : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup F\ninst\u271d\u2076 : NormedSpace \ud835\udd5c F\nG : Type u_4\ninst\u271d\u2075 : NormedAddCommGroup G\ninst\u271d\u2074 : NormedSpace \ud835\udd5c G\nG' : Type u_5\ninst\u271d\u00b3 : NormedAddCommGroup G'\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c G'\n\u03b5 : \u211d\ninst\u271d\u00b9 : CompleteSpace E\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nh : LinearMap.range f' = \u22a4\nf'symm : f'.NonlinearRightInverse := f'.nonlinearRightInverseOfSurjective h\n\u22a2 map f (\ud835\udcdd a) = \ud835\udcdd (f a)",
+              "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2079 : NormedAddCommGroup E\ninst\u271d\u2078 : NormedSpace \ud835\udd5c E\nF : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup F\ninst\u271d\u2076 : NormedSpace \ud835\udd5c F\nG : Type u_4\ninst\u271d\u2075 : NormedAddCommGroup G\ninst\u271d\u2074 : NormedSpace \ud835\udd5c G\nG' : Type u_5\ninst\u271d\u00b3 : NormedAddCommGroup G'\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c G'\n\u03b5 : \u211d\ninst\u271d\u00b9 : CompleteSpace E\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nh : LinearMap.range f' = \u22a4\n\u22a2 map f (\ud835\udcdd a) = \ud835\udcdd (f a)",
+              "tactic": "let f'symm := f'.nonlinearRightInverseOfSurjective h"
+            },
+            {
+              "annotated_tactic": [
+                "\"set c : \\u211d\\u22650 := f'symm.nnnorm\\u207b\\u00b9 \\/ 2 with hc\"",
+                "[]"
+              ],
+              "state_after": "\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2079 : NormedAddCommGroup E\ninst\u271d\u2078 : NormedSpace \ud835\udd5c E\nF : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup F\ninst\u271d\u2076 : NormedSpace \ud835\udd5c F\nG : Type u_4\ninst\u271d\u2075 : NormedAddCommGroup G\ninst\u271d\u2074 : NormedSpace \ud835\udd5c G\nG' : Type u_5\ninst\u271d\u00b3 : NormedAddCommGroup G'\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c G'\n\u03b5 : \u211d\ninst\u271d\u00b9 : CompleteSpace E\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nh : LinearMap.range f' = \u22a4\nf'symm : f'.NonlinearRightInverse := f'.nonlinearRightInverseOfSurjective h\nc : \u211d\u22650 := f'symm.nnnorm\u207b\u00b9 / 2\nhc : c = f'symm.nnnorm\u207b\u00b9 / 2\n\u22a2 map f (\ud835\udcdd a) = \ud835\udcdd (f a)",
+              "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2079 : NormedAddCommGroup E\ninst\u271d\u2078 : NormedSpace \ud835\udd5c E\nF : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup F\ninst\u271d\u2076 : NormedSpace \ud835\udd5c F\nG : Type u_4\ninst\u271d\u2075 : NormedAddCommGroup G\ninst\u271d\u2074 : NormedSpace \ud835\udd5c G\nG' : Type u_5\ninst\u271d\u00b3 : NormedAddCommGroup G'\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c G'\n\u03b5 : \u211d\ninst\u271d\u00b9 : CompleteSpace E\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nh : LinearMap.range f' = \u22a4\nf'symm : f'.NonlinearRightInverse := f'.nonlinearRightInverseOfSurjective h\n\u22a2 map f (\ud835\udcdd a) = \ud835\udcdd (f a)",
+              "tactic": "set c : \u211d\u22650 := f'symm.nnnorm\u207b\u00b9 / 2 with hc"
+            },
+            {
+              "annotated_tactic": [
+                "\"have f'symm_pos : 0 < f'symm.nnnorm := f'.nonlinearRightInverseOfSurjective_nnnorm_pos h\"",
+                "[]"
+              ],
+              "state_after": "\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2079 : NormedAddCommGroup E\ninst\u271d\u2078 : NormedSpace \ud835\udd5c E\nF : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup F\ninst\u271d\u2076 : NormedSpace \ud835\udd5c F\nG : Type u_4\ninst\u271d\u2075 : NormedAddCommGroup G\ninst\u271d\u2074 : NormedSpace \ud835\udd5c G\nG' : Type u_5\ninst\u271d\u00b3 : NormedAddCommGroup G'\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c G'\n\u03b5 : \u211d\ninst\u271d\u00b9 : CompleteSpace E\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nh : LinearMap.range f' = \u22a4\nf'symm : f'.NonlinearRightInverse := f'.nonlinearRightInverseOfSurjective h\nc : \u211d\u22650 := f'symm.nnnorm\u207b\u00b9 / 2\nhc : c = f'symm.nnnorm\u207b\u00b9 / 2\nf'symm_pos : 0 < f'symm.nnnorm\n\u22a2 map f (\ud835\udcdd a) = \ud835\udcdd (f a)",
+              "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2079 : NormedAddCommGroup E\ninst\u271d\u2078 : NormedSpace \ud835\udd5c E\nF : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup F\ninst\u271d\u2076 : NormedSpace \ud835\udd5c F\nG : Type u_4\ninst\u271d\u2075 : NormedAddCommGroup G\ninst\u271d\u2074 : NormedSpace \ud835\udd5c G\nG' : Type u_5\ninst\u271d\u00b3 : NormedAddCommGroup G'\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c G'\n\u03b5 : \u211d\ninst\u271d\u00b9 : CompleteSpace E\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nh : LinearMap.range f' = \u22a4\nf'symm : f'.NonlinearRightInverse := f'.nonlinearRightInverseOfSurjective h\nc : \u211d\u22650 := f'symm.nnnorm\u207b\u00b9 / 2\nhc : c = f'symm.nnnorm\u207b\u00b9 / 2\n\u22a2 map f (\ud835\udcdd a) = \ud835\udcdd (f a)",
+              "tactic": "have f'symm_pos : 0 < f'symm.nnnorm := f'.nonlinearRightInverseOfSurjective_nnnorm_pos h"
+            },
+            {
+              "annotated_tactic": [
+                "\"have cpos : 0 < c := by simp [hc, <a>half_pos<\\/a>, <a>inv_pos<\\/a>, f'symm_pos]\"",
+                "[{\"full_name\":\"half_pos\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Field\\/Basic.lean\",\"def_pos\":[445,9],\"def_end_pos\":[445,17]},{\"full_name\":\"inv_pos\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Field\\/Defs.lean\",\"def_pos\":[47,15],\"def_end_pos\":[47,22]}]"
+              ],
+              "state_after": "\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2079 : NormedAddCommGroup E\ninst\u271d\u2078 : NormedSpace \ud835\udd5c E\nF : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup F\ninst\u271d\u2076 : NormedSpace \ud835\udd5c F\nG : Type u_4\ninst\u271d\u2075 : NormedAddCommGroup G\ninst\u271d\u2074 : NormedSpace \ud835\udd5c G\nG' : Type u_5\ninst\u271d\u00b3 : NormedAddCommGroup G'\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c G'\n\u03b5 : \u211d\ninst\u271d\u00b9 : CompleteSpace E\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nh : LinearMap.range f' = \u22a4\nf'symm : f'.NonlinearRightInverse := f'.nonlinearRightInverseOfSurjective h\nc : \u211d\u22650 := f'symm.nnnorm\u207b\u00b9 / 2\nhc : c = f'symm.nnnorm\u207b\u00b9 / 2\nf'symm_pos : 0 < f'symm.nnnorm\ncpos : 0 < c\n\u22a2 map f (\ud835\udcdd a) = \ud835\udcdd (f a)",
+              "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2079 : NormedAddCommGroup E\ninst\u271d\u2078 : NormedSpace \ud835\udd5c E\nF : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup F\ninst\u271d\u2076 : NormedSpace \ud835\udd5c F\nG : Type u_4\ninst\u271d\u2075 : NormedAddCommGroup G\ninst\u271d\u2074 : NormedSpace \ud835\udd5c G\nG' : Type u_5\ninst\u271d\u00b3 : NormedAddCommGroup G'\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c G'\n\u03b5 : \u211d\ninst\u271d\u00b9 : CompleteSpace E\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nh : LinearMap.range f' = \u22a4\nf'symm : f'.NonlinearRightInverse := f'.nonlinearRightInverseOfSurjective h\nc : \u211d\u22650 := f'symm.nnnorm\u207b\u00b9 / 2\nhc : c = f'symm.nnnorm\u207b\u00b9 / 2\nf'symm_pos : 0 < f'symm.nnnorm\n\u22a2 map f (\ud835\udcdd a) = \ud835\udcdd (f a)",
+              "tactic": "have cpos : 0 < c := by simp [hc, half_pos, inv_pos, f'symm_pos]"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8s, s_nhds, hs\\u27e9 : \\u2203 s \\u2208 \\ud835\\udcdd a, <a>ApproximatesLinearOn<\\/a> f f' s c :=\\n    hf.approximates_deriv_on_nhds (<a>Or.inr<\\/a> cpos)\"",
+                "[{\"full_name\":\"ApproximatesLinearOn\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/InverseFunctionTheorem\\/ApproximatesLinearOn.lean\",\"def_pos\":[71,5],\"def_end_pos\":[71,25]},{\"full_name\":\"Or.inr\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[536,5],\"def_end_pos\":[536,8]}]"
+              ],
+              "state_after": "case intro.intro\n\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2079 : NormedAddCommGroup E\ninst\u271d\u2078 : NormedSpace \ud835\udd5c E\nF : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup F\ninst\u271d\u2076 : NormedSpace \ud835\udd5c F\nG : Type u_4\ninst\u271d\u2075 : NormedAddCommGroup G\ninst\u271d\u2074 : NormedSpace \ud835\udd5c G\nG' : Type u_5\ninst\u271d\u00b3 : NormedAddCommGroup G'\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c G'\n\u03b5 : \u211d\ninst\u271d\u00b9 : CompleteSpace E\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nh : LinearMap.range f' = \u22a4\nf'symm : f'.NonlinearRightInverse := f'.nonlinearRightInverseOfSurjective h\nc : \u211d\u22650 := f'symm.nnnorm\u207b\u00b9 / 2\nhc : c = f'symm.nnnorm\u207b\u00b9 / 2\nf'symm_pos : 0 < f'symm.nnnorm\ncpos : 0 < c\ns : Set E\ns_nhds : s \u2208 \ud835\udcdd a\nhs : ApproximatesLinearOn f f' s c\n\u22a2 map f (\ud835\udcdd a) = \ud835\udcdd (f a)",
+              "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2079 : NormedAddCommGroup E\ninst\u271d\u2078 : NormedSpace \ud835\udd5c E\nF : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup F\ninst\u271d\u2076 : NormedSpace \ud835\udd5c F\nG : Type u_4\ninst\u271d\u2075 : NormedAddCommGroup G\ninst\u271d\u2074 : NormedSpace \ud835\udd5c G\nG' : Type u_5\ninst\u271d\u00b3 : NormedAddCommGroup G'\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c G'\n\u03b5 : \u211d\ninst\u271d\u00b9 : CompleteSpace E\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nh : LinearMap.range f' = \u22a4\nf'symm : f'.NonlinearRightInverse := f'.nonlinearRightInverseOfSurjective h\nc : \u211d\u22650 := f'symm.nnnorm\u207b\u00b9 / 2\nhc : c = f'symm.nnnorm\u207b\u00b9 / 2\nf'symm_pos : 0 < f'symm.nnnorm\ncpos : 0 < c\n\u22a2 map f (\ud835\udcdd a) = \ud835\udcdd (f a)",
+              "tactic": "obtain \u27e8s, s_nhds, hs\u27e9 : \u2203 s \u2208 \ud835\udcdd a, ApproximatesLinearOn f f' s c :=\n  hf.approximates_deriv_on_nhds (Or.inr cpos)"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply hs.map_nhds_eq f'symm s_nhds (<a>Or.inr<\\/a> (<a>NNReal.half_lt_self<\\/a> _))\"",
+                "[{\"full_name\":\"Or.inr\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[536,5],\"def_end_pos\":[536,8]},{\"full_name\":\"NNReal.half_lt_self\",\"def_path\":\"Mathlib\\/Data\\/NNReal\\/Basic.lean\",\"def_pos\":[1008,16],\"def_end_pos\":[1008,28]}]"
+              ],
+              "state_after": "\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2079 : NormedAddCommGroup E\ninst\u271d\u2078 : NormedSpace \ud835\udd5c E\nF : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup F\ninst\u271d\u2076 : NormedSpace \ud835\udd5c F\nG : Type u_4\ninst\u271d\u2075 : NormedAddCommGroup G\ninst\u271d\u2074 : NormedSpace \ud835\udd5c G\nG' : Type u_5\ninst\u271d\u00b3 : NormedAddCommGroup G'\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c G'\n\u03b5 : \u211d\ninst\u271d\u00b9 : CompleteSpace E\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nh : LinearMap.range f' = \u22a4\nf'symm : f'.NonlinearRightInverse := f'.nonlinearRightInverseOfSurjective h\nc : \u211d\u22650 := f'symm.nnnorm\u207b\u00b9 / 2\nhc : c = f'symm.nnnorm\u207b\u00b9 / 2\nf'symm_pos : 0 < f'symm.nnnorm\ncpos : 0 < c\ns : Set E\ns_nhds : s \u2208 \ud835\udcdd a\nhs : ApproximatesLinearOn f f' s c\n\u22a2 f'symm.nnnorm\u207b\u00b9 \u2260 0",
+              "state_before": "case intro.intro\n\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2079 : NormedAddCommGroup E\ninst\u271d\u2078 : NormedSpace \ud835\udd5c E\nF : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup F\ninst\u271d\u2076 : NormedSpace \ud835\udd5c F\nG : Type u_4\ninst\u271d\u2075 : NormedAddCommGroup G\ninst\u271d\u2074 : NormedSpace \ud835\udd5c G\nG' : Type u_5\ninst\u271d\u00b3 : NormedAddCommGroup G'\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c G'\n\u03b5 : \u211d\ninst\u271d\u00b9 : CompleteSpace E\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nh : LinearMap.range f' = \u22a4\nf'symm : f'.NonlinearRightInverse := f'.nonlinearRightInverseOfSurjective h\nc : \u211d\u22650 := f'symm.nnnorm\u207b\u00b9 / 2\nhc : c = f'symm.nnnorm\u207b\u00b9 / 2\nf'symm_pos : 0 < f'symm.nnnorm\ncpos : 0 < c\ns : Set E\ns_nhds : s \u2208 \ud835\udcdd a\nhs : ApproximatesLinearOn f f' s c\n\u22a2 map f (\ud835\udcdd a) = \ud835\udcdd (f a)",
+              "tactic": "apply hs.map_nhds_eq f'symm s_nhds (Or.inr (NNReal.half_lt_self _))"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [<a>ne_of_gt<\\/a> f'symm_pos]\"",
+                "[{\"full_name\":\"ne_of_gt\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[104,9],\"def_end_pos\":[104,17]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2079 : NormedAddCommGroup E\ninst\u271d\u2078 : NormedSpace \ud835\udd5c E\nF : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup F\ninst\u271d\u2076 : NormedSpace \ud835\udd5c F\nG : Type u_4\ninst\u271d\u2075 : NormedAddCommGroup G\ninst\u271d\u2074 : NormedSpace \ud835\udd5c G\nG' : Type u_5\ninst\u271d\u00b3 : NormedAddCommGroup G'\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c G'\n\u03b5 : \u211d\ninst\u271d\u00b9 : CompleteSpace E\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nh : LinearMap.range f' = \u22a4\nf'symm : f'.NonlinearRightInverse := f'.nonlinearRightInverseOfSurjective h\nc : \u211d\u22650 := f'symm.nnnorm\u207b\u00b9 / 2\nhc : c = f'symm.nnnorm\u207b\u00b9 / 2\nf'symm_pos : 0 < f'symm.nnnorm\ncpos : 0 < c\ns : Set E\ns_nhds : s \u2208 \ud835\udcdd a\nhs : ApproximatesLinearOn f f' s c\n\u22a2 f'symm.nnnorm\u207b\u00b9 \u2260 0",
+              "tactic": "simp [ne_of_gt f'symm_pos]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [hc, <a>half_pos<\\/a>, <a>inv_pos<\\/a>, f'symm_pos]\"",
+                "[{\"full_name\":\"half_pos\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Field\\/Basic.lean\",\"def_pos\":[445,9],\"def_end_pos\":[445,17]},{\"full_name\":\"inv_pos\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Field\\/Defs.lean\",\"def_pos\":[47,15],\"def_end_pos\":[47,22]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u00b9\u2070 : NontriviallyNormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2079 : NormedAddCommGroup E\ninst\u271d\u2078 : NormedSpace \ud835\udd5c E\nF : Type u_3\ninst\u271d\u2077 : NormedAddCommGroup F\ninst\u271d\u2076 : NormedSpace \ud835\udd5c F\nG : Type u_4\ninst\u271d\u2075 : NormedAddCommGroup G\ninst\u271d\u2074 : NormedSpace \ud835\udd5c G\nG' : Type u_5\ninst\u271d\u00b3 : NormedAddCommGroup G'\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c G'\n\u03b5 : \u211d\ninst\u271d\u00b9 : CompleteSpace E\ninst\u271d : CompleteSpace F\nf : E \u2192 F\nf' : E \u2192L[\ud835\udd5c] F\na : E\nhf : HasStrictFDerivAt f f' a\nh : LinearMap.range f' = \u22a4\nf'symm : f'.NonlinearRightInverse := f'.nonlinearRightInverseOfSurjective h\nc : \u211d\u22650 := f'symm.nnnorm\u207b\u00b9 / 2\nhc : c = f'symm.nnnorm\u207b\u00b9 / 2\nf'symm_pos : 0 < f'symm.nnnorm\n\u22a2 0 < c",
+              "tactic": "simp [hc, half_pos, inv_pos, f'symm_pos]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.mem_toPartialHomeomorph_source",
+        "id": "HasStrictFDerivAt.mem_toPartialHomeomorph_source",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            135,
+            63
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean",
+          "full_name": "HasStrictFDerivAt.mem_toPartialHomeomorph_source",
+          "start": [
+            133,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HasStrictFDerivAt.toPartialHomeomorph_coe",
+        "id": "HasStrictFDerivAt.toPartialHomeomorph_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            130,
+            6
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean",
+          "full_name": "HasStrictFDerivAt.toPartialHomeomorph_coe",
+          "start": [
+            128,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "isOpenMap_of_hasStrictFDerivAt_equiv",
+        "id": "isOpenMap_of_hasStrictFDerivAt_equiv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            218,
+            66
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean",
+          "full_name": "isOpenMap_of_hasStrictFDerivAt_equiv",
+          "start": [
+            216,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean"
+      }
+    ],
+    "input_proofs": 19,
+    "input_units": 2,
+    "proofs": 2,
+    "published_proofs": 2,
+    "published_transitions": 4,
+    "replay_failures": [],
+    "transitions": 4,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000424-0000-744ba3be07640002.parquet",
+      "sha256": "744ba3be076400027b7cd62bc81d18b0ee3ae6eefb9b652a0f1031e5262e0949",
+      "bytes": 74963,
+      "rows": 4,
+      "revision": "eef9f30926b0307521cf3967e66e7df66c40bfc5"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:HasStrictFDerivAt.approximates_deriv_on_open_nhds",
+    "mathlib:HasStrictFDerivAt.to_localInverse"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean\",null,null,\"HasStrictFDerivAt.approximates_deriv_on_open_nhds\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean\",null,null,\"HasStrictFDerivAt.to_localInverse\"]"
+  ]
+}

manifests/batches/mathlib/000425.json

@@ -0,0 +1,448 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000425",
+  "batch_fingerprint": "655950426052f1ca22eae62d29c91946fe8657e31c23766556b24af5102c31dd",
+  "evidence": {
+    "batch_fingerprint": "655950426052f1ca22eae62d29c91946fe8657e31c23766556b24af5102c31dd",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "no internal trace for tactic 'simp_rw [g, \u2190 uf hx, Pi.sub_apply, add_sub_cancel]'",
+        "full_name": "ApproximatesLinearOn.exists_homeomorph_extension",
+        "id": "ApproximatesLinearOn.exists_homeomorph_extension",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            47,
+            35
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FiniteDimensional.lean",
+          "full_name": "ApproximatesLinearOn.exists_homeomorph_extension",
+          "start": [
+            27,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8u, hu, uf\\u27e9 :\\n    \\u2203 u : E \\u2192 F, <a>LipschitzWith<\\/a> (<a>lipschitzExtensionConstant<\\/a> F * c) u \\u2227 <a>EqOn<\\/a> (f - \\u21d1f') u s :=\\n    hf.lipschitzOnWith.extend_finite_dimension\"",
+                "[{\"full_name\":\"LipschitzWith\",\"def_path\":\"Mathlib\\/Topology\\/EMetricSpace\\/Lipschitz.lean\",\"def_pos\":[52,5],\"def_end_pos\":[52,18]},{\"full_name\":\"lipschitzExtensionConstant\",\"def_path\":\"Mathlib\\/Analysis\\/NormedSpace\\/FiniteDimension.lean\",\"def_pos\":[183,17],\"def_end_pos\":[183,43]},{\"full_name\":\"Set.EqOn\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Defs.lean\",\"def_pos\":[263,5],\"def_end_pos\":[263,9]}]"
+              ],
+              "state_after": "case intro.intro\nE : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\n\u22a2 \u2203 g, EqOn f (\u21d1g) s",
+              "state_before": "E : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\n\u22a2 \u2203 g, EqOn f (\u21d1g) s",
+              "tactic": "obtain \u27e8u, hu, uf\u27e9 :\n  \u2203 u : E \u2192 F, LipschitzWith (lipschitzExtensionConstant F * c) u \u2227 EqOn (f - \u21d1f') u s :=\n  hf.lipschitzOnWith.extend_finite_dimension"
+            },
+            {
+              "annotated_tactic": [
+                "\"let g : E \\u2192 F := fun x => f' x + u x\"",
+                "[]"
+              ],
+              "state_after": "case intro.intro\nE : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\ng : E \u2192 F := fun x => f' x + u x\n\u22a2 \u2203 g, EqOn f (\u21d1g) s",
+              "state_before": "case intro.intro\nE : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\n\u22a2 \u2203 g, EqOn f (\u21d1g) s",
+              "tactic": "let g : E \u2192 F := fun x => f' x + u x"
+            },
+            {
+              "annotated_tactic": [
+                "\"have fg : <a>EqOn<\\/a> f g s := fun x hx => by simp_rw [g, \\u2190 uf hx, <a>Pi.sub_apply<\\/a>, <a>add_sub_cancel<\\/a>]\"",
+                "[{\"full_name\":\"Set.EqOn\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Defs.lean\",\"def_pos\":[263,5],\"def_end_pos\":[263,9]},{\"full_name\":\"Pi.sub_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[195,3],\"def_end_pos\":[195,14]},{\"full_name\":\"add_sub_cancel\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[1330,3],\"def_end_pos\":[1330,14]}]"
+              ],
+              "state_after": "case intro.intro\nE : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\ng : E \u2192 F := fun x => f' x + u x\nfg : EqOn f g s\n\u22a2 \u2203 g, EqOn f (\u21d1g) s",
+              "state_before": "case intro.intro\nE : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\ng : E \u2192 F := fun x => f' x + u x\n\u22a2 \u2203 g, EqOn f (\u21d1g) s",
+              "tactic": "have fg : EqOn f g s := fun x hx => by simp_rw [g, \u2190 uf hx, Pi.sub_apply, add_sub_cancel]"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hg : <a>ApproximatesLinearOn<\\/a> g (f' : E \\u2192L[\\u211d] F) <a>univ<\\/a> (<a>lipschitzExtensionConstant<\\/a> F * c) := by\\n    apply <a>LipschitzOnWith.approximatesLinearOn<\\/a>\\n    rw [<a>lipschitzOn_univ<\\/a>]\\n    convert hu\\n    ext x\\n    simp only [g, <a>add_sub_cancel_left<\\/a>, <a>ContinuousLinearEquiv.coe_coe<\\/a>, <a>Pi.sub_apply<\\/a>]\"",
+                "[{\"full_name\":\"ApproximatesLinearOn\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/InverseFunctionTheorem\\/ApproximatesLinearOn.lean\",\"def_pos\":[71,5],\"def_end_pos\":[71,25]},{\"full_name\":\"Set.univ\",\"def_path\":\"Mathlib\\/Init\\/Set.lean\",\"def_pos\":[153,5],\"def_end_pos\":[153,9]},{\"full_name\":\"lipschitzExtensionConstant\",\"def_path\":\"Mathlib\\/Analysis\\/NormedSpace\\/FiniteDimension.lean\",\"def_pos\":[183,17],\"def_end_pos\":[183,43]},{\"full_name\":\"LipschitzOnWith.approximatesLinearOn\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/InverseFunctionTheorem\\/ApproximatesLinearOn.lean\",\"def_pos\":[108,25],\"def_end_pos\":[108,68]},{\"full_name\":\"lipschitzOn_univ\",\"def_path\":\"Mathlib\\/Topology\\/EMetricSpace\\/Lipschitz.lean\",\"def_pos\":[82,9],\"def_end_pos\":[82,25]},{\"full_name\":\"add_sub_cancel_left\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[1325,3],\"def_end_pos\":[1325,14]},{\"full_name\":\"ContinuousLinearEquiv.coe_coe\",\"def_path\":\"Mathlib\\/Topology\\/Algebra\\/Module\\/Basic.lean\",\"def_pos\":[1905,9],\"def_end_pos\":[1905,16]},{\"full_name\":\"Pi.sub_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[195,3],\"def_end_pos\":[195,14]}]"
+              ],
+              "state_after": "case intro.intro\nE : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\ng : E \u2192 F := fun x => f' x + u x\nfg : EqOn f g s\nhg : ApproximatesLinearOn g (\u2191f') univ (lipschitzExtensionConstant F * c)\n\u22a2 \u2203 g, EqOn f (\u21d1g) s",
+              "state_before": "case intro.intro\nE : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\ng : E \u2192 F := fun x => f' x + u x\nfg : EqOn f g s\n\u22a2 \u2203 g, EqOn f (\u21d1g) s",
+              "tactic": "have hg : ApproximatesLinearOn g (f' : E \u2192L[\u211d] F) univ (lipschitzExtensionConstant F * c) := by\n  apply LipschitzOnWith.approximatesLinearOn\n  rw [lipschitzOn_univ]\n  convert hu\n  ext x\n  simp only [g, add_sub_cancel_left, ContinuousLinearEquiv.coe_coe, Pi.sub_apply]"
+            },
+            {
+              "annotated_tactic": [
+                "\"haveI : <a>FiniteDimensional<\\/a> \\u211d E := f'.symm.finiteDimensional\"",
+                "[{\"full_name\":\"FiniteDimensional\",\"def_path\":\"Mathlib\\/LinearAlgebra\\/FiniteDimensional.lean\",\"def_pos\":[79,8],\"def_end_pos\":[79,25]}]"
+              ],
+              "state_after": "case intro.intro\nE : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\ng : E \u2192 F := fun x => f' x + u x\nfg : EqOn f g s\nhg : ApproximatesLinearOn g (\u2191f') univ (lipschitzExtensionConstant F * c)\nthis : FiniteDimensional \u211d E\n\u22a2 \u2203 g, EqOn f (\u21d1g) s",
+              "state_before": "case intro.intro\nE : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\ng : E \u2192 F := fun x => f' x + u x\nfg : EqOn f g s\nhg : ApproximatesLinearOn g (\u2191f') univ (lipschitzExtensionConstant F * c)\n\u22a2 \u2203 g, EqOn f (\u21d1g) s",
+              "tactic": "haveI : FiniteDimensional \u211d E := f'.symm.finiteDimensional"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact \\u27e8hg.toHomeomorph g hc, fg\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case intro.intro\nE : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\ng : E \u2192 F := fun x => f' x + u x\nfg : EqOn f g s\nhg : ApproximatesLinearOn g (\u2191f') univ (lipschitzExtensionConstant F * c)\nthis : FiniteDimensional \u211d E\n\u22a2 \u2203 g, EqOn f (\u21d1g) s",
+              "tactic": "exact \u27e8hg.toHomeomorph g hc, fg\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp_rw [g, \\u2190 uf hx, <a>Pi.sub_apply<\\/a>, <a>add_sub_cancel<\\/a>]\"",
+                "[{\"full_name\":\"Pi.sub_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[195,3],\"def_end_pos\":[195,14]},{\"full_name\":\"add_sub_cancel\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[1330,3],\"def_end_pos\":[1330,14]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "E : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\ng : E \u2192 F := fun x => f' x + u x\nx : E\nhx : x \u2208 s\n\u22a2 f x = g x",
+              "tactic": "simp_rw [g, \u2190 uf hx, Pi.sub_apply, add_sub_cancel]"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>LipschitzOnWith.approximatesLinearOn<\\/a>\"",
+                "[{\"full_name\":\"LipschitzOnWith.approximatesLinearOn\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/InverseFunctionTheorem\\/ApproximatesLinearOn.lean\",\"def_pos\":[108,25],\"def_end_pos\":[108,68]}]"
+              ],
+              "state_after": "case a\nE : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\ng : E \u2192 F := fun x => f' x + u x\nfg : EqOn f g s\n\u22a2 LipschitzOnWith (lipschitzExtensionConstant F * c) (g - \u21d1\u2191f') univ",
+              "state_before": "E : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\ng : E \u2192 F := fun x => f' x + u x\nfg : EqOn f g s\n\u22a2 ApproximatesLinearOn g (\u2191f') univ (lipschitzExtensionConstant F * c)",
+              "tactic": "apply LipschitzOnWith.approximatesLinearOn"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>lipschitzOn_univ<\\/a>]\"",
+                "[{\"full_name\":\"lipschitzOn_univ\",\"def_path\":\"Mathlib\\/Topology\\/EMetricSpace\\/Lipschitz.lean\",\"def_pos\":[82,9],\"def_end_pos\":[82,25]}]"
+              ],
+              "state_after": "case a\nE : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\ng : E \u2192 F := fun x => f' x + u x\nfg : EqOn f g s\n\u22a2 LipschitzWith (lipschitzExtensionConstant F * c) (g - \u21d1\u2191f')",
+              "state_before": "case a\nE : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\ng : E \u2192 F := fun x => f' x + u x\nfg : EqOn f g s\n\u22a2 LipschitzOnWith (lipschitzExtensionConstant F * c) (g - \u21d1\u2191f') univ",
+              "tactic": "rw [lipschitzOn_univ]"
+            },
+            {
+              "annotated_tactic": [
+                "\"convert hu\"",
+                "[]"
+              ],
+              "state_after": "case h.e'_6\nE : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\ng : E \u2192 F := fun x => f' x + u x\nfg : EqOn f g s\n\u22a2 g - \u21d1\u2191f' = u",
+              "state_before": "case a\nE : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\ng : E \u2192 F := fun x => f' x + u x\nfg : EqOn f g s\n\u22a2 LipschitzWith (lipschitzExtensionConstant F * c) (g - \u21d1\u2191f')",
+              "tactic": "convert hu"
+            },
+            {
+              "annotated_tactic": [
+                "\"ext x\"",
+                "[]"
+              ],
+              "state_after": "case h.e'_6.h\nE : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\ng : E \u2192 F := fun x => f' x + u x\nfg : EqOn f g s\nx : E\n\u22a2 (g - \u21d1\u2191f') x = u x",
+              "state_before": "case h.e'_6\nE : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\ng : E \u2192 F := fun x => f' x + u x\nfg : EqOn f g s\n\u22a2 g - \u21d1\u2191f' = u",
+              "tactic": "ext x"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [g, <a>add_sub_cancel_left<\\/a>, <a>ContinuousLinearEquiv.coe_coe<\\/a>, <a>Pi.sub_apply<\\/a>]\"",
+                "[{\"full_name\":\"add_sub_cancel_left\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[1325,3],\"def_end_pos\":[1325,14]},{\"full_name\":\"ContinuousLinearEquiv.coe_coe\",\"def_path\":\"Mathlib\\/Topology\\/Algebra\\/Module\\/Basic.lean\",\"def_pos\":[1905,9],\"def_end_pos\":[1905,16]},{\"full_name\":\"Pi.sub_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[195,3],\"def_end_pos\":[195,14]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.e'_6.h\nE : Type u_1\ninst\u271d\u2074 : NormedAddCommGroup E\ninst\u271d\u00b3 : NormedSpace \u211d E\nF : Type u_2\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : NormedSpace \u211d F\ninst\u271d : FiniteDimensional \u211d F\ns : Set E\nf : E \u2192 F\nf' : E \u2243L[\u211d] F\nc : \u211d\u22650\nhf : ApproximatesLinearOn f (\u2191f') s c\nhc : Subsingleton E \u2228 lipschitzExtensionConstant F * c < \u2016\u2191f'.symm\u2016\u208a\u207b\u00b9\nu : E \u2192 F\nhu : LipschitzWith (lipschitzExtensionConstant F * c) u\nuf : EqOn (f - \u21d1f') u s\ng : E \u2192 F := fun x => f' x + u x\nfg : EqOn f g s\nx : E\n\u22a2 (g - \u21d1\u2191f') x = u x",
+              "tactic": "simp only [g, add_sub_cancel_left, ContinuousLinearEquiv.coe_coe, Pi.sub_apply]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FiniteDimensional.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ContDiff.continuous_iteratedDeriv",
+        "id": "ContDiff.continuous_iteratedDeriv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            275,
+            43
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/IteratedDeriv/Defs.lean",
+          "full_name": "ContDiff.continuous_iteratedDeriv",
+          "start": [
+            273,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/IteratedDeriv/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ContDiff.differentiable_iteratedDeriv",
+        "id": "ContDiff.differentiable_iteratedDeriv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            280,
+            43
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/IteratedDeriv/Defs.lean",
+          "full_name": "ContDiff.differentiable_iteratedDeriv",
+          "start": [
+            278,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/IteratedDeriv/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "contDiff_of_differentiable_iteratedDeriv",
+        "id": "contDiff_of_differentiable_iteratedDeriv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            270,
+            96
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/IteratedDeriv/Defs.lean",
+          "full_name": "contDiff_of_differentiable_iteratedDeriv",
+          "start": [
+            268,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/IteratedDeriv/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "iteratedDerivWithin_eq_iteratedFDerivWithin",
+        "id": "iteratedDerivWithin_eq_iteratedFDerivWithin",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            79,
+            6
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/IteratedDeriv/Defs.lean",
+          "full_name": "iteratedDerivWithin_eq_iteratedFDerivWithin",
+          "start": [
+            77,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/IteratedDeriv/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "iteratedDeriv_eq_iteratedFDeriv",
+        "id": "iteratedDeriv_eq_iteratedFDeriv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            216,
+            6
+          ],
+          "file_path": "Mathlib/Analysis/Calculus/IteratedDeriv/Defs.lean",
+          "full_name": "iteratedDeriv_eq_iteratedFDeriv",
+          "start": [
+            214,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Analysis/Calculus/IteratedDeriv/Defs.lean"
+      }
+    ],
+    "input_proofs": 32,
+    "input_units": 2,
+    "proofs": 26,
+    "published_proofs": 24,
+    "published_transitions": 44,
+    "replay_failures": [],
+    "transitions": 51,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Analysis/Calculus/IteratedDeriv/Defs.lean",
+        "proof_id": "mathlib:contDiffOn_of_continuousOn_differentiableOn_deriv",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              134,
+              99
+            ],
+            "file_path": "Mathlib/Analysis/Calculus/IteratedDeriv/Defs.lean",
+            "full_name": "contDiffOn_of_continuousOn_differentiableOn_deriv",
+            "start": [
+              128,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"apply <a>contDiffOn_of_continuousOn_differentiableOn<\\/a>\"",
+                  "[{\"full_name\":\"contDiffOn_of_continuousOn_differentiableOn\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/ContDiff\\/Defs.lean\",\"def_pos\":[1086,9],\"def_end_pos\":[1086,52]}]"
+                ],
+                "state_after": "case Hcont\n\ud835\udd5c : Type u_1\ninst\u271d\u2074 : NontriviallyNormedField \ud835\udd5c\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\nE : Type u_3\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nn\u271d : \u2115\nf : \ud835\udd5c \u2192 F\ns : Set \ud835\udd5c\nx : \ud835\udd5c\nn : \u2115\u221e\nHcont : \u2200 (m : \u2115), \u2191m \u2264 n \u2192 ContinuousOn (fun x => iteratedDerivWithin m f s x) s\nHdiff : \u2200 (m : \u2115), \u2191m < n \u2192 DifferentiableOn \ud835\udd5c (fun x => iteratedDerivWithin m f s x) s\n\u22a2 \u2200 (m : \u2115), \u2191m \u2264 n \u2192 ContinuousOn (fun x => iteratedFDerivWithin \ud835\udd5c m f s x) s\n\ncase Hdiff\n\ud835\udd5c : Type u_1\ninst\u271d\u2074 : NontriviallyNormedField \ud835\udd5c\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\nE : Type u_3\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nn\u271d : \u2115\nf : \ud835\udd5c \u2192 F\ns : Set \ud835\udd5c\nx : \ud835\udd5c\nn : \u2115\u221e\nHcont : \u2200 (m : \u2115), \u2191m \u2264 n \u2192 ContinuousOn (fun x => iteratedDerivWithin m f s x) s\nHdiff : \u2200 (m : \u2115), \u2191m < n \u2192 DifferentiableOn \ud835\udd5c (fun x => iteratedDerivWithin m f s x) s\n\u22a2 \u2200 (m : \u2115), \u2191m < n \u2192 DifferentiableOn \ud835\udd5c (fun x => iteratedFDerivWithin \ud835\udd5c m f s x) s",
+                "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u2074 : NontriviallyNormedField \ud835\udd5c\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\nE : Type u_3\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nn\u271d : \u2115\nf : \ud835\udd5c \u2192 F\ns : Set \ud835\udd5c\nx : \ud835\udd5c\nn : \u2115\u221e\nHcont : \u2200 (m : \u2115), \u2191m \u2264 n \u2192 ContinuousOn (fun x => iteratedDerivWithin m f s x) s\nHdiff : \u2200 (m : \u2115), \u2191m < n \u2192 DifferentiableOn \ud835\udd5c (fun x => iteratedDerivWithin m f s x) s\n\u22a2 ContDiffOn \ud835\udd5c n f s",
+                "tactic": "apply contDiffOn_of_continuousOn_differentiableOn"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simpa only [<a>iteratedFDerivWithin_eq_equiv_comp<\\/a>, <a>LinearIsometryEquiv.comp_continuousOn_iff<\\/a>]\"",
+                  "[{\"full_name\":\"iteratedFDerivWithin_eq_equiv_comp\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/IteratedDeriv\\/Defs.lean\",\"def_pos\":[91,9],\"def_end_pos\":[91,43]},{\"full_name\":\"LinearIsometryEquiv.comp_continuousOn_iff\",\"def_path\":\"Mathlib\\/Analysis\\/NormedSpace\\/LinearIsometry.lean\",\"def_pos\":[1079,9],\"def_end_pos\":[1079,30]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case Hcont\n\ud835\udd5c : Type u_1\ninst\u271d\u2074 : NontriviallyNormedField \ud835\udd5c\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\nE : Type u_3\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nn\u271d : \u2115\nf : \ud835\udd5c \u2192 F\ns : Set \ud835\udd5c\nx : \ud835\udd5c\nn : \u2115\u221e\nHcont : \u2200 (m : \u2115), \u2191m \u2264 n \u2192 ContinuousOn (fun x => iteratedDerivWithin m f s x) s\nHdiff : \u2200 (m : \u2115), \u2191m < n \u2192 DifferentiableOn \ud835\udd5c (fun x => iteratedDerivWithin m f s x) s\n\u22a2 \u2200 (m : \u2115), \u2191m \u2264 n \u2192 ContinuousOn (fun x => iteratedFDerivWithin \ud835\udd5c m f s x) s",
+                "tactic": "simpa only [iteratedFDerivWithin_eq_equiv_comp, LinearIsometryEquiv.comp_continuousOn_iff]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simpa only [<a>iteratedFDerivWithin_eq_equiv_comp<\\/a>, <a>LinearIsometryEquiv.comp_differentiableOn_iff<\\/a>]\"",
+                  "[{\"full_name\":\"iteratedFDerivWithin_eq_equiv_comp\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/IteratedDeriv\\/Defs.lean\",\"def_pos\":[91,9],\"def_end_pos\":[91,43]},{\"full_name\":\"LinearIsometryEquiv.comp_differentiableOn_iff\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/FDeriv\\/Equiv.lean\",\"def_pos\":[334,9],\"def_end_pos\":[334,34]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case Hdiff\n\ud835\udd5c : Type u_1\ninst\u271d\u2074 : NontriviallyNormedField \ud835\udd5c\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\nE : Type u_3\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nn\u271d : \u2115\nf : \ud835\udd5c \u2192 F\ns : Set \ud835\udd5c\nx : \ud835\udd5c\nn : \u2115\u221e\nHcont : \u2200 (m : \u2115), \u2191m \u2264 n \u2192 ContinuousOn (fun x => iteratedDerivWithin m f s x) s\nHdiff : \u2200 (m : \u2115), \u2191m < n \u2192 DifferentiableOn \ud835\udd5c (fun x => iteratedDerivWithin m f s x) s\n\u22a2 \u2200 (m : \u2115), \u2191m < n \u2192 DifferentiableOn \ud835\udd5c (fun x => iteratedFDerivWithin \ud835\udd5c m f s x) s",
+                "tactic": "simpa only [iteratedFDerivWithin_eq_equiv_comp, LinearIsometryEquiv.comp_differentiableOn_iff]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "contDiffOn_of_continuousOn_differentiableOn_deriv"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Analysis/Calculus/IteratedDeriv/Defs.lean",
+        "proof_id": "mathlib:iteratedDerivWithin_eq_iterate",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              201,
+              56
+            ],
+            "file_path": "Mathlib/Analysis/Calculus/IteratedDeriv/Defs.lean",
+            "full_name": "iteratedDerivWithin_eq_iterate",
+            "start": [
+              196,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"induction' n with n IH generalizing x\"",
+                  "[]"
+                ],
+                "state_after": "case zero\n\ud835\udd5c : Type u_1\ninst\u271d\u2074 : NontriviallyNormedField \ud835\udd5c\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\nE : Type u_3\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nn : \u2115\nf : \ud835\udd5c \u2192 F\ns : Set \ud835\udd5c\nx\u271d : \ud835\udd5c\nhs : UniqueDiffOn \ud835\udd5c s\nx : \ud835\udd5c\nhx : x \u2208 s\n\u22a2 iteratedDerivWithin 0 f s x = (fun g => derivWithin g s)^[0] f x\n\ncase succ\n\ud835\udd5c : Type u_1\ninst\u271d\u2074 : NontriviallyNormedField \ud835\udd5c\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\nE : Type u_3\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nn\u271d : \u2115\nf : \ud835\udd5c \u2192 F\ns : Set \ud835\udd5c\nx\u271d : \ud835\udd5c\nhs : UniqueDiffOn \ud835\udd5c s\nn : \u2115\nIH : \u2200 {x : \ud835\udd5c}, x \u2208 s \u2192 iteratedDerivWithin n f s x = (fun g => derivWithin g s)^[n] f x\nx : \ud835\udd5c\nhx : x \u2208 s\n\u22a2 iteratedDerivWithin (n + 1) f s x = (fun g => derivWithin g s)^[n + 1] f x",
+                "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u2074 : NontriviallyNormedField \ud835\udd5c\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\nE : Type u_3\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nn : \u2115\nf : \ud835\udd5c \u2192 F\ns : Set \ud835\udd5c\nx\u271d x : \ud835\udd5c\nhs : UniqueDiffOn \ud835\udd5c s\nhx : x \u2208 s\n\u22a2 iteratedDerivWithin n f s x = (fun g => derivWithin g s)^[n] f x",
+                "tactic": "induction' n with n IH generalizing x"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case zero\n\ud835\udd5c : Type u_1\ninst\u271d\u2074 : NontriviallyNormedField \ud835\udd5c\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\nE : Type u_3\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nn : \u2115\nf : \ud835\udd5c \u2192 F\ns : Set \ud835\udd5c\nx\u271d : \ud835\udd5c\nhs : UniqueDiffOn \ud835\udd5c s\nx : \ud835\udd5c\nhx : x \u2208 s\n\u22a2 iteratedDerivWithin 0 f s x = (fun g => derivWithin g s)^[0] f x",
+                "tactic": "simp"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>iteratedDerivWithin_succ<\\/a> (hs x hx), <a>Function.iterate_succ'<\\/a>]\"",
+                  "[{\"full_name\":\"iteratedDerivWithin_succ\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/IteratedDeriv\\/Defs.lean\",\"def_pos\":[184,9],\"def_end_pos\":[184,33]},{\"full_name\":\"Function.iterate_succ'\",\"def_path\":\"Mathlib\\/Logic\\/Function\\/Iterate.lean\",\"def_pos\":[187,9],\"def_end_pos\":[187,22]}]"
+                ],
+                "state_after": "case succ\n\ud835\udd5c : Type u_1\ninst\u271d\u2074 : NontriviallyNormedField \ud835\udd5c\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\nE : Type u_3\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nn\u271d : \u2115\nf : \ud835\udd5c \u2192 F\ns : Set \ud835\udd5c\nx\u271d : \ud835\udd5c\nhs : UniqueDiffOn \ud835\udd5c s\nn : \u2115\nIH : \u2200 {x : \ud835\udd5c}, x \u2208 s \u2192 iteratedDerivWithin n f s x = (fun g => derivWithin g s)^[n] f x\nx : \ud835\udd5c\nhx : x \u2208 s\n\u22a2 derivWithin (iteratedDerivWithin n f s) s x = ((fun g => derivWithin g s) \u2218 (fun g => derivWithin g s)^[n]) f x",
+                "state_before": "case succ\n\ud835\udd5c : Type u_1\ninst\u271d\u2074 : NontriviallyNormedField \ud835\udd5c\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\nE : Type u_3\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nn\u271d : \u2115\nf : \ud835\udd5c \u2192 F\ns : Set \ud835\udd5c\nx\u271d : \ud835\udd5c\nhs : UniqueDiffOn \ud835\udd5c s\nn : \u2115\nIH : \u2200 {x : \ud835\udd5c}, x \u2208 s \u2192 iteratedDerivWithin n f s x = (fun g => derivWithin g s)^[n] f x\nx : \ud835\udd5c\nhx : x \u2208 s\n\u22a2 iteratedDerivWithin (n + 1) f s x = (fun g => derivWithin g s)^[n + 1] f x",
+                "tactic": "rw [iteratedDerivWithin_succ (hs x hx), Function.iterate_succ']"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact <a>derivWithin_congr<\\/a> (fun y hy => IH hy) (IH hx)\"",
+                  "[{\"full_name\":\"derivWithin_congr\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Deriv\\/Basic.lean\",\"def_pos\":[645,9],\"def_end_pos\":[645,26]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case succ\n\ud835\udd5c : Type u_1\ninst\u271d\u2074 : NontriviallyNormedField \ud835\udd5c\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c F\nE : Type u_3\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nn\u271d : \u2115\nf : \ud835\udd5c \u2192 F\ns : Set \ud835\udd5c\nx\u271d : \ud835\udd5c\nhs : UniqueDiffOn \ud835\udd5c s\nn : \u2115\nIH : \u2200 {x : \ud835\udd5c}, x \u2208 s \u2192 iteratedDerivWithin n f s x = (fun g => derivWithin g s)^[n] f x\nx : \ud835\udd5c\nhx : x \u2208 s\n\u22a2 derivWithin (iteratedDerivWithin n f s) s x = ((fun g => derivWithin g s) \u2218 (fun g => derivWithin g s)^[n]) f x",
+                "tactic": "exact derivWithin_congr (fun y hy => IH hy) (IH hx)"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "iteratedDerivWithin_eq_iterate"
+      }
+    ],
+    "validation_rejected_proofs": 2,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000425-0000-1a10c1d5b47ac763.parquet",
+      "sha256": "1a10c1d5b47ac76319bff04a6a63d864e3fedbc02179d4176077164a1f50afad",
+      "bytes": 217493,
+      "rows": 40,
+      "revision": "eef9f30926b0307521cf3967e66e7df66c40bfc5"
+    },
+    {
+      "path": "data/internal_test/mathlib-000425-0000-38b1b05f4db694fd.parquet",
+      "sha256": "38b1b05f4db694fd20066d580079abcd18b37e449fd6d80af7cb5a6fa6c97260",
+      "bytes": 61384,
+      "rows": 4,
+      "revision": "eef9f30926b0307521cf3967e66e7df66c40bfc5"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:ContDiffOn.continuousOn_iteratedDerivWithin",
+    "mathlib:ContDiffOn.differentiableOn_iteratedDerivWithin",
+    "mathlib:ContDiffWithinAt.differentiableWithinAt_iteratedDerivWithin",
+    "mathlib:contDiffOn_iff_continuousOn_differentiableOn_deriv",
+    "mathlib:contDiffOn_of_differentiableOn_deriv",
+    "mathlib:contDiff_iff_iteratedDeriv",
+    "mathlib:iteratedDerivWithin_eq_equiv_comp",
+    "mathlib:iteratedDerivWithin_one",
+    "mathlib:iteratedDerivWithin_succ",
+    "mathlib:iteratedDerivWithin_succ'",
+    "mathlib:iteratedDerivWithin_univ",
+    "mathlib:iteratedDerivWithin_zero",
+    "mathlib:iteratedDeriv_eq_equiv_comp",
+    "mathlib:iteratedDeriv_eq_iterate",
+    "mathlib:iteratedDeriv_one",
+    "mathlib:iteratedDeriv_succ",
+    "mathlib:iteratedDeriv_succ'",
+    "mathlib:iteratedDeriv_zero",
+    "mathlib:iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod",
+    "mathlib:iteratedFDerivWithin_eq_equiv_comp",
+    "mathlib:iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod",
+    "mathlib:iteratedFDeriv_eq_equiv_comp",
+    "mathlib:norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin",
+    "mathlib:norm_iteratedFDeriv_eq_norm_iteratedDeriv"
+  ],
+  "proof_keys": [
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manifests/batches/numina/001182.json

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manifests/batches/numina/001183.json

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manifests/batches/numina/001185.json

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manifests/batches/numina/001187.json

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