Record 30 verified HPC batch manifests

manifests/batches/mathlib/001346.json

@@ -0,0 +1,698 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001346",
+  "batch_fingerprint": "0105c2be0add4649a133d59b40d793dda22758962b0fe4f7896546087ff157fd",
+  "evidence": {
+    "batch_fingerprint": "0105c2be0add4649a133d59b40d793dda22758962b0fe4f7896546087ff157fd",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Classical.nonempty_pi",
+        "id": "Classical.nonempty_pi",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            131,
+            44
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "Classical.nonempty_pi",
+          "start": [
+            130,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.Surjective.nonempty",
+        "id": "Function.Surjective.nonempty",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            142,
+            6
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "Function.Surjective.nonempty",
+          "start": [
+            138,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Nonempty.congr",
+        "id": "Nonempty.congr",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            115,
+            35
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "Nonempty.congr",
+          "start": [
+            114,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Nonempty.elim_to_inhabited",
+        "id": "Nonempty.elim_to_inhabited",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            120,
+            29
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "Nonempty.elim_to_inhabited",
+          "start": [
+            118,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Nonempty.exists",
+        "id": "Nonempty.exists",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            33,
+            58
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "Nonempty.exists",
+          "start": [
+            32,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Nonempty.forall",
+        "id": "Nonempty.forall",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            28,
+            44
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "Nonempty.forall",
+          "start": [
+            27,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Nonempty.imp",
+        "id": "Nonempty.imp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            46,
+            18
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "Nonempty.imp",
+          "start": [
+            45,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Nonempty.map",
+        "id": "Nonempty.map",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            106,
+            17
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "Nonempty.map",
+          "start": [
+            105,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Nonempty.map2",
+        "id": "Nonempty.map2",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            111,
+            24
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "Nonempty.map2",
+          "start": [
+            109,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "exists_true_iff_nonempty",
+        "id": "exists_true_iff_nonempty",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            37,
+            54
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "exists_true_iff_nonempty",
+          "start": [
+            36,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "nonempty_Prop",
+        "id": "nonempty_Prop",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            42,
+            38
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "nonempty_Prop",
+          "start": [
+            41,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "nonempty_plift",
+        "id": "nonempty_plift",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            82,
+            46
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "nonempty_plift",
+          "start": [
+            81,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "nonempty_pprod",
+        "id": "nonempty_pprod",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            64,
+            66
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "nonempty_pprod",
+          "start": [
+            63,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "nonempty_prod",
+        "id": "nonempty_prod",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            176,
+            66
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "nonempty_prod",
+          "start": [
+            175,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "nonempty_psigma",
+        "id": "nonempty_psigma",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            54,
+            62
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "nonempty_psigma",
+          "start": [
+            53,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "nonempty_psum",
+        "id": "nonempty_psum",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            77,
+            33
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "nonempty_psum",
+          "start": [
+            68,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "nonempty_sigma",
+        "id": "nonempty_sigma",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            158,
+            62
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "nonempty_sigma",
+          "start": [
+            157,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "nonempty_subtype",
+        "id": "nonempty_subtype",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            59,
+            58
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "nonempty_subtype",
+          "start": [
+            58,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "nonempty_sum",
+        "id": "nonempty_sum",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            171,
+            32
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "nonempty_sum",
+          "start": [
+            162,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "nonempty_ulift",
+        "id": "nonempty_ulift",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            181,
+            46
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "nonempty_ulift",
+          "start": [
+            180,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "not_nonempty_iff_imp_false",
+        "id": "not_nonempty_iff_imp_false",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            49,
+            15
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "not_nonempty_iff_imp_false",
+          "start": [
+            48,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "subsingleton_of_not_nonempty",
+        "id": "subsingleton_of_not_nonempty",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            135,
+            60
+          ],
+          "file_path": "Mathlib/Logic/Nonempty.lean",
+          "full_name": "subsingleton_of_not_nonempty",
+          "start": [
+            134,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nonempty.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.Injective.nontrivial",
+        "id": "Function.Injective.nontrivial",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            66,
+            24
+          ],
+          "file_path": "Mathlib/Logic/Nontrivial/Basic.lean",
+          "full_name": "Function.Injective.nontrivial",
+          "start": [
+            63,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nontrivial/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Subsingleton.eq_one",
+        "id": "Subsingleton.eq_one",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            116,
+            24
+          ],
+          "file_path": "Mathlib/Logic/Nontrivial/Basic.lean",
+          "full_name": "Subsingleton.eq_one",
+          "start": [
+            115,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nontrivial/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Subsingleton.le",
+        "id": "Subsingleton.le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            111,
+            35
+          ],
+          "file_path": "Mathlib/Logic/Nontrivial/Basic.lean",
+          "full_name": "Subsingleton.le",
+          "start": [
+            110,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nontrivial/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "nontrivial_iff_lt",
+        "id": "nontrivial_iff_lt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            38,
+            74
+          ],
+          "file_path": "Mathlib/Logic/Nontrivial/Basic.lean",
+          "full_name": "nontrivial_iff_lt",
+          "start": [
+            37,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nontrivial/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "nontrivial_of_lt",
+        "id": "nontrivial_of_lt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            29,
+            23
+          ],
+          "file_path": "Mathlib/Logic/Nontrivial/Basic.lean",
+          "full_name": "nontrivial_of_lt",
+          "start": [
+            28,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nontrivial/Basic.lean"
+      }
+    ],
+    "input_proofs": 31,
+    "input_units": 2,
+    "proofs": 4,
+    "published_proofs": 3,
+    "published_transitions": 5,
+    "replay_failures": [],
+    "transitions": 9,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Logic/Nontrivial/Basic.lean",
+        "proof_id": "mathlib:Function.Injective.exists_ne",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              76,
+              18
+            ],
+            "file_path": "Mathlib/Logic/Nontrivial/Basic.lean",
+            "full_name": "Function.Injective.exists_ne",
+            "start": [
+              71,
+              11
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"rcases <a>exists_pair_ne<\\/a> \\u03b1 with \\u27e8x\\u2081, x\\u2082, hx\\u27e9\"",
+                  "[{\"full_name\":\"exists_pair_ne\",\"def_path\":\"Mathlib\\/Logic\\/Nontrivial\\/Defs.lean\",\"def_pos\":[40,9],\"def_end_pos\":[40,23]}]"
+                ],
+                "state_after": "case intro.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : Nontrivial \u03b1\nf : \u03b1 \u2192 \u03b2\nhf : Injective f\ny : \u03b2\nx\u2081 x\u2082 : \u03b1\nhx : x\u2081 \u2260 x\u2082\n\u22a2 \u2203 x, f x \u2260 y",
+                "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : Nontrivial \u03b1\nf : \u03b1 \u2192 \u03b2\nhf : Injective f\ny : \u03b2\n\u22a2 \u2203 x, f x \u2260 y",
+                "tactic": "rcases exists_pair_ne \u03b1 with \u27e8x\u2081, x\u2082, hx\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"by_cases h:f x\\u2082 = y\"",
+                  "[]"
+                ],
+                "state_after": "case pos\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : Nontrivial \u03b1\nf : \u03b1 \u2192 \u03b2\nhf : Injective f\ny : \u03b2\nx\u2081 x\u2082 : \u03b1\nhx : x\u2081 \u2260 x\u2082\nh : f x\u2082 = y\n\u22a2 \u2203 x, f x \u2260 y\n\ncase neg\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : Nontrivial \u03b1\nf : \u03b1 \u2192 \u03b2\nhf : Injective f\ny : \u03b2\nx\u2081 x\u2082 : \u03b1\nhx : x\u2081 \u2260 x\u2082\nh : \u00acf x\u2082 = y\n\u22a2 \u2203 x, f x \u2260 y",
+                "state_before": "case intro.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : Nontrivial \u03b1\nf : \u03b1 \u2192 \u03b2\nhf : Injective f\ny : \u03b2\nx\u2081 x\u2082 : \u03b1\nhx : x\u2081 \u2260 x\u2082\n\u22a2 \u2203 x, f x \u2260 y",
+                "tactic": "by_cases h:f x\u2082 = y"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact \\u27e8x\\u2081, (hf.ne_iff' h).2 hx\\u27e9\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case pos\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : Nontrivial \u03b1\nf : \u03b1 \u2192 \u03b2\nhf : Injective f\ny : \u03b2\nx\u2081 x\u2082 : \u03b1\nhx : x\u2081 \u2260 x\u2082\nh : f x\u2082 = y\n\u22a2 \u2203 x, f x \u2260 y",
+                "tactic": "exact \u27e8x\u2081, (hf.ne_iff' h).2 hx\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact \\u27e8x\\u2082, h\\u27e9\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case neg\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : Nontrivial \u03b1\nf : \u03b1 \u2192 \u03b2\nhf : Injective f\ny : \u03b2\nx\u2081 x\u2082 : \u03b1\nhx : x\u2081 \u2260 x\u2082\nh : \u00acf x\u2082 = y\n\u22a2 \u2203 x, f x \u2260 y",
+                "tactic": "exact \u27e8x\u2082, h\u27e9"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Function.Injective.exists_ne"
+      }
+    ],
+    "validation_rejected_proofs": 1,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001346-0000-191a6c3f79d8ecad.parquet",
+      "sha256": "191a6c3f79d8ecad4e62df9a31034e140e8223f332385370a74eef86447fb12f",
+      "bytes": 56591,
+      "rows": 5,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Pi.nontrivial_at",
+    "mathlib:Subtype.nontrivial_iff_exists_ne",
+    "mathlib:exists_pair_lt"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Nontrivial/Basic.lean\",null,null,\"Pi.nontrivial_at\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Nontrivial/Basic.lean\",null,null,\"Subtype.nontrivial_iff_exists_ne\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Nontrivial/Basic.lean\",null,null,\"exists_pair_lt\"]"
+  ]
+}

manifests/batches/mathlib/001347.json

@@ -0,0 +1,582 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001347",
+  "batch_fingerprint": "1792268372ad6aad0581b4b375c3bd9c682661d7304d11d4fd4c274ea99d9771",
+  "evidence": {
+    "batch_fingerprint": "1792268372ad6aad0581b4b375c3bd9c682661d7304d11d4fd4c274ea99d9771",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "exists_ne",
+        "id": "exists_ne",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            53,
+            79
+          ],
+          "file_path": "Mathlib/Logic/Nontrivial/Defs.lean",
+          "full_name": "exists_ne",
+          "start": [
+            53,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nontrivial/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "exists_pair_ne",
+        "id": "exists_pair_ne",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            41,
+            28
+          ],
+          "file_path": "Mathlib/Logic/Nontrivial/Defs.lean",
+          "full_name": "exists_pair_ne",
+          "start": [
+            40,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nontrivial/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "false_of_nontrivial_of_subsingleton",
+        "id": "false_of_nontrivial_of_subsingleton",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            105,
+            23
+          ],
+          "file_path": "Mathlib/Logic/Nontrivial/Defs.lean",
+          "full_name": "false_of_nontrivial_of_subsingleton",
+          "start": [
+            104,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nontrivial/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "nontrivial_iff",
+        "id": "nontrivial_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            37,
+            42
+          ],
+          "file_path": "Mathlib/Logic/Nontrivial/Defs.lean",
+          "full_name": "nontrivial_iff",
+          "start": [
+            36,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nontrivial/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "nontrivial_iff_exists_ne",
+        "id": "nontrivial_iff_exists_ne",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            62,
+            68
+          ],
+          "file_path": "Mathlib/Logic/Nontrivial/Defs.lean",
+          "full_name": "nontrivial_iff_exists_ne",
+          "start": [
+            61,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nontrivial/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "nontrivial_of_ne",
+        "id": "nontrivial_of_ne",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            58,
+            14
+          ],
+          "file_path": "Mathlib/Logic/Nontrivial/Defs.lean",
+          "full_name": "nontrivial_of_ne",
+          "start": [
+            57,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nontrivial/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "not_nontrivial",
+        "id": "not_nontrivial",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            88,
+            47
+          ],
+          "file_path": "Mathlib/Logic/Nontrivial/Defs.lean",
+          "full_name": "not_nontrivial",
+          "start": [
+            87,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nontrivial/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "not_subsingleton",
+        "id": "not_subsingleton",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            92,
+            32
+          ],
+          "file_path": "Mathlib/Logic/Nontrivial/Defs.lean",
+          "full_name": "not_subsingleton",
+          "start": [
+            91,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Nontrivial/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.Bijective.pairwise_comp_iff",
+        "id": "Function.Bijective.pairwise_comp_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            64,
+            96
+          ],
+          "file_path": "Mathlib/Logic/Pairwise.lean",
+          "full_name": "Function.Bijective.pairwise_comp_iff",
+          "start": [
+            62,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Pairwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.injective_iff_pairwise_ne",
+        "id": "Function.injective_iff_pairwise_ne",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            49,
+            46
+          ],
+          "file_path": "Mathlib/Logic/Pairwise.lean",
+          "full_name": "Function.injective_iff_pairwise_ne",
+          "start": [
+            48,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Pairwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Pairwise.comp_of_injective",
+        "id": "Pairwise.comp_of_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            57,
+            28
+          ],
+          "file_path": "Mathlib/Logic/Pairwise.lean",
+          "full_name": "Pairwise.comp_of_injective",
+          "start": [
+            55,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Pairwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Pairwise.mono",
+        "id": "Pairwise.mono",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            38,
+            31
+          ],
+          "file_path": "Mathlib/Logic/Pairwise.lean",
+          "full_name": "Pairwise.mono",
+          "start": [
+            37,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Pairwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Pairwise.of_comp_of_surjective",
+        "id": "Pairwise.of_comp_of_surjective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            60,
+            68
+          ],
+          "file_path": "Mathlib/Logic/Pairwise.lean",
+          "full_name": "Pairwise.of_comp_of_surjective",
+          "start": [
+            59,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Pairwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Pairwise.set_pairwise",
+        "id": "Pairwise.set_pairwise",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            102,
+            98
+          ],
+          "file_path": "Mathlib/Logic/Pairwise.lean",
+          "full_name": "Pairwise.set_pairwise",
+          "start": [
+            102,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Pairwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Reflexive.set_pairwise_iff",
+        "id": "Reflexive.set_pairwise_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            93,
+            9
+          ],
+          "file_path": "Mathlib/Logic/Pairwise.lean",
+          "full_name": "Reflexive.set_pairwise_iff",
+          "start": [
+            90,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Pairwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.Pairwise.eq",
+        "id": "Set.Pairwise.eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            87,
+            42
+          ],
+          "file_path": "Mathlib/Logic/Pairwise.lean",
+          "full_name": "Set.Pairwise.eq",
+          "start": [
+            86,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Pairwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.Pairwise.imp",
+        "id": "Set.Pairwise.imp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            83,
+            41
+          ],
+          "file_path": "Mathlib/Logic/Pairwise.lean",
+          "full_name": "Set.Pairwise.imp",
+          "start": [
+            82,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Pairwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.Pairwise.imp_on",
+        "id": "Set.Pairwise.imp_on",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            79,
+            54
+          ],
+          "file_path": "Mathlib/Logic/Pairwise.lean",
+          "full_name": "Set.Pairwise.imp_on",
+          "start": [
+            77,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Pairwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.Pairwise.on_injective",
+        "id": "Set.Pairwise.on_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            97,
+            71
+          ],
+          "file_path": "Mathlib/Logic/Pairwise.lean",
+          "full_name": "Set.Pairwise.on_injective",
+          "start": [
+            96,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Pairwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.pairwise_of_forall",
+        "id": "Set.pairwise_of_forall",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            74,
+            25
+          ],
+          "file_path": "Mathlib/Logic/Pairwise.lean",
+          "full_name": "Set.pairwise_of_forall",
+          "start": [
+            73,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Pairwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Subsingleton.pairwise",
+        "id": "Subsingleton.pairwise",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            46,
+            60
+          ],
+          "file_path": "Mathlib/Logic/Pairwise.lean",
+          "full_name": "Subsingleton.pairwise",
+          "start": [
+            45,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Pairwise.lean"
+      }
+    ],
+    "input_proofs": 25,
+    "input_units": 2,
+    "proofs": 4,
+    "published_proofs": 3,
+    "published_transitions": 4,
+    "replay_failures": [],
+    "transitions": 9,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Logic/Nontrivial/Defs.lean",
+        "proof_id": "mathlib:Decidable.exists_ne",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              50,
+              26
+            ],
+            "file_path": "Mathlib/Logic/Nontrivial/Defs.lean",
+            "full_name": "Decidable.exists_ne",
+            "start": [
+              45,
+              11
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"rcases <a>exists_pair_ne<\\/a> \\u03b1 with \\u27e8y, y', h\\u27e9\"",
+                  "[{\"full_name\":\"exists_pair_ne\",\"def_path\":\"Mathlib\\/Logic\\/Nontrivial\\/Defs.lean\",\"def_pos\":[40,9],\"def_end_pos\":[40,23]}]"
+                ],
+                "state_after": "case intro.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : Nontrivial \u03b1\ninst\u271d : DecidableEq \u03b1\nx y y' : \u03b1\nh : y \u2260 y'\n\u22a2 \u2203 y, y \u2260 x",
+                "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : Nontrivial \u03b1\ninst\u271d : DecidableEq \u03b1\nx : \u03b1\n\u22a2 \u2203 y, y \u2260 x",
+                "tactic": "rcases exists_pair_ne \u03b1 with \u27e8y, y', h\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"by_cases hx:x = y\"",
+                  "[]"
+                ],
+                "state_after": "case pos\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : Nontrivial \u03b1\ninst\u271d : DecidableEq \u03b1\nx y y' : \u03b1\nh : y \u2260 y'\nhx : x = y\n\u22a2 \u2203 y, y \u2260 x\n\ncase neg\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : Nontrivial \u03b1\ninst\u271d : DecidableEq \u03b1\nx y y' : \u03b1\nh : y \u2260 y'\nhx : \u00acx = y\n\u22a2 \u2203 y, y \u2260 x",
+                "state_before": "case intro.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : Nontrivial \u03b1\ninst\u271d : DecidableEq \u03b1\nx y y' : \u03b1\nh : y \u2260 y'\n\u22a2 \u2203 y, y \u2260 x",
+                "tactic": "by_cases hx:x = y"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [\\u2190 hx] at h\"",
+                  "[]"
+                ],
+                "state_after": "case pos\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : Nontrivial \u03b1\ninst\u271d : DecidableEq \u03b1\nx y y' : \u03b1\nh : x \u2260 y'\nhx : x = y\n\u22a2 \u2203 y, y \u2260 x",
+                "state_before": "case pos\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : Nontrivial \u03b1\ninst\u271d : DecidableEq \u03b1\nx y y' : \u03b1\nh : y \u2260 y'\nhx : x = y\n\u22a2 \u2203 y, y \u2260 x",
+                "tactic": "rw [\u2190 hx] at h"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact \\u27e8y', h.symm\\u27e9\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case pos\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : Nontrivial \u03b1\ninst\u271d : DecidableEq \u03b1\nx y y' : \u03b1\nh : x \u2260 y'\nhx : x = y\n\u22a2 \u2203 y, y \u2260 x",
+                "tactic": "exact \u27e8y', h.symm\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact \\u27e8y, <a>Ne.symm<\\/a> hx\\u27e9\"",
+                  "[{\"full_name\":\"Ne.symm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[704,9],\"def_end_pos\":[704,16]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case neg\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : Nontrivial \u03b1\ninst\u271d : DecidableEq \u03b1\nx y y' : \u03b1\nh : y \u2260 y'\nhx : \u00acx = y\n\u22a2 \u2203 y, y \u2260 x",
+                "tactic": "exact \u27e8y, Ne.symm hx\u27e9"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Decidable.exists_ne"
+      }
+    ],
+    "validation_rejected_proofs": 1,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001347-0000-551fe9917ed024be.parquet",
+      "sha256": "551fe9917ed024be5b1841177f97388f722b932c38e4c233b40d113cb997ded1",
+      "bytes": 51912,
+      "rows": 3,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    },
+    {
+      "path": "data/internal_test/mathlib-001347-0000-aa53ae4b2cd713c9.parquet",
+      "sha256": "aa53ae4b2cd713c98fa871173a26e05245c00e27884ebc200c723d9db4a9be5d",
+      "bytes": 41488,
+      "rows": 1,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:not_nontrivial_iff_subsingleton",
+    "mathlib:not_subsingleton_iff_nontrivial",
+    "mathlib:subsingleton_iff"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Nontrivial/Defs.lean\",null,null,\"not_nontrivial_iff_subsingleton\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Nontrivial/Defs.lean\",null,null,\"not_subsingleton_iff_nontrivial\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Nontrivial/Defs.lean\",null,null,\"subsingleton_iff\"]"
+  ]
+}

manifests/batches/mathlib/001349.json

@@ -0,0 +1,285 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001349",
+  "batch_fingerprint": "b25ae4fd46777f245057f407425701c3653eb45c1f161ee941de1bb74179ca01",
+  "evidence": {
+    "batch_fingerprint": "b25ae4fd46777f245057f407425701c3653eb45c1f161ee941de1bb74179ca01",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "small_of_injective",
+        "id": "small_of_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            29,
+            37
+          ],
+          "file_path": "Mathlib/Logic/Small/Basic.lean",
+          "full_name": "small_of_injective",
+          "start": [
+            27,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Small/Basic.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rw [Function.comp_apply, ha, Function.leftInverse_invFun hg]'",
+        "full_name": "small_of_injective_of_exists",
+        "id": "small_of_injective_of_exists",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            54,
+            19
+          ],
+          "file_path": "Mathlib/Logic/Small/Basic.lean",
+          "full_name": "small_of_injective_of_exists",
+          "start": [
+            46,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"by_cases h\\u03b2 : <a>Nonempty<\\/a> \\u03b2\"",
+                "[{\"full_name\":\"Nonempty\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[709,17],\"def_end_pos\":[709,25]}]"
+              ],
+              "state_after": "case pos\n\u03b1 : Type v\n\u03b2 : Type w\n\u03b3 : Type v'\ninst\u271d : Small.{u, v} \u03b1\nf : \u03b1 \u2192 \u03b3\ng : \u03b2 \u2192 \u03b3\nhg : Function.Injective g\nh : \u2200 (b : \u03b2), \u2203 a, f a = g b\nh\u03b2 : Nonempty \u03b2\n\u22a2 Small.{u, w} \u03b2\n\ncase neg\n\u03b1 : Type v\n\u03b2 : Type w\n\u03b3 : Type v'\ninst\u271d : Small.{u, v} \u03b1\nf : \u03b1 \u2192 \u03b3\ng : \u03b2 \u2192 \u03b3\nhg : Function.Injective g\nh : \u2200 (b : \u03b2), \u2203 a, f a = g b\nh\u03b2 : \u00acNonempty \u03b2\n\u22a2 Small.{u, w} \u03b2",
+              "state_before": "\u03b1 : Type v\n\u03b2 : Type w\n\u03b3 : Type v'\ninst\u271d : Small.{u, v} \u03b1\nf : \u03b1 \u2192 \u03b3\ng : \u03b2 \u2192 \u03b3\nhg : Function.Injective g\nh : \u2200 (b : \u03b2), \u2203 a, f a = g b\n\u22a2 Small.{u, w} \u03b2",
+              "tactic": "by_cases h\u03b2 : Nonempty \u03b2"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine <a>small_of_surjective<\\/a> (f := <a>Function.invFun<\\/a> g \\u2218 f) (fun b => ?_)\"",
+                "[{\"full_name\":\"small_of_surjective\",\"def_path\":\"Mathlib\\/Logic\\/Small\\/Basic.lean\",\"def_pos\":[32,9],\"def_end_pos\":[32,28]},{\"full_name\":\"Function.invFun\",\"def_path\":\"Mathlib\\/Logic\\/Function\\/Basic.lean\",\"def_pos\":[437,19],\"def_end_pos\":[437,25]}]"
+              ],
+              "state_after": "case pos\n\u03b1 : Type v\n\u03b2 : Type w\n\u03b3 : Type v'\ninst\u271d : Small.{u, v} \u03b1\nf : \u03b1 \u2192 \u03b3\ng : \u03b2 \u2192 \u03b3\nhg : Function.Injective g\nh : \u2200 (b : \u03b2), \u2203 a, f a = g b\nh\u03b2 : Nonempty \u03b2\nb : \u03b2\n\u22a2 \u2203 a, (Function.invFun g \u2218 f) a = b",
+              "state_before": "case pos\n\u03b1 : Type v\n\u03b2 : Type w\n\u03b3 : Type v'\ninst\u271d : Small.{u, v} \u03b1\nf : \u03b1 \u2192 \u03b3\ng : \u03b2 \u2192 \u03b3\nhg : Function.Injective g\nh : \u2200 (b : \u03b2), \u2203 a, f a = g b\nh\u03b2 : Nonempty \u03b2\n\u22a2 Small.{u, w} \u03b2",
+              "tactic": "refine small_of_surjective (f := Function.invFun g \u2218 f) (fun b => ?_)"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8a, ha\\u27e9 := h b\"",
+                "[]"
+              ],
+              "state_after": "case pos.intro\n\u03b1 : Type v\n\u03b2 : Type w\n\u03b3 : Type v'\ninst\u271d : Small.{u, v} \u03b1\nf : \u03b1 \u2192 \u03b3\ng : \u03b2 \u2192 \u03b3\nhg : Function.Injective g\nh : \u2200 (b : \u03b2), \u2203 a, f a = g b\nh\u03b2 : Nonempty \u03b2\nb : \u03b2\na : \u03b1\nha : f a = g b\n\u22a2 \u2203 a, (Function.invFun g \u2218 f) a = b",
+              "state_before": "case pos\n\u03b1 : Type v\n\u03b2 : Type w\n\u03b3 : Type v'\ninst\u271d : Small.{u, v} \u03b1\nf : \u03b1 \u2192 \u03b3\ng : \u03b2 \u2192 \u03b3\nhg : Function.Injective g\nh : \u2200 (b : \u03b2), \u2203 a, f a = g b\nh\u03b2 : Nonempty \u03b2\nb : \u03b2\n\u22a2 \u2203 a, (Function.invFun g \u2218 f) a = b",
+              "tactic": "obtain \u27e8a, ha\u27e9 := h b"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact \\u27e8a, by rw [<a>Function.comp_apply<\\/a>, ha, <a>Function.leftInverse_invFun<\\/a> hg]\\u27e9\"",
+                "[{\"full_name\":\"Function.comp_apply\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[35,17],\"def_end_pos\":[35,36]},{\"full_name\":\"Function.leftInverse_invFun\",\"def_path\":\"Mathlib\\/Logic\\/Function\\/Basic.lean\",\"def_pos\":[466,9],\"def_end_pos\":[466,27]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case pos.intro\n\u03b1 : Type v\n\u03b2 : Type w\n\u03b3 : Type v'\ninst\u271d : Small.{u, v} \u03b1\nf : \u03b1 \u2192 \u03b3\ng : \u03b2 \u2192 \u03b3\nhg : Function.Injective g\nh : \u2200 (b : \u03b2), \u2203 a, f a = g b\nh\u03b2 : Nonempty \u03b2\nb : \u03b2\na : \u03b1\nha : f a = g b\n\u22a2 \u2203 a, (Function.invFun g \u2218 f) a = b",
+              "tactic": "exact \u27e8a, by rw [Function.comp_apply, ha, Function.leftInverse_invFun hg]\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Function.comp_apply<\\/a>, ha, <a>Function.leftInverse_invFun<\\/a> hg]\"",
+                "[{\"full_name\":\"Function.comp_apply\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[35,17],\"def_end_pos\":[35,36]},{\"full_name\":\"Function.leftInverse_invFun\",\"def_path\":\"Mathlib\\/Logic\\/Function\\/Basic.lean\",\"def_pos\":[466,9],\"def_end_pos\":[466,27]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type v\n\u03b2 : Type w\n\u03b3 : Type v'\ninst\u271d : Small.{u, v} \u03b1\nf : \u03b1 \u2192 \u03b3\ng : \u03b2 \u2192 \u03b3\nhg : Function.Injective g\nh : \u2200 (b : \u03b2), \u2203 a, f a = g b\nh\u03b2 : Nonempty \u03b2\nb : \u03b2\na : \u03b1\nha : f a = g b\n\u22a2 (Function.invFun g \u2218 f) a = b",
+              "tactic": "rw [Function.comp_apply, ha, Function.leftInverse_invFun hg]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>not_nonempty_iff<\\/a>] at h\\u03b2\"",
+                "[{\"full_name\":\"not_nonempty_iff\",\"def_path\":\"Mathlib\\/Logic\\/IsEmpty.lean\",\"def_pos\":[144,9],\"def_end_pos\":[144,25]}]"
+              ],
+              "state_after": "case neg\n\u03b1 : Type v\n\u03b2 : Type w\n\u03b3 : Type v'\ninst\u271d : Small.{u, v} \u03b1\nf : \u03b1 \u2192 \u03b3\ng : \u03b2 \u2192 \u03b3\nhg : Function.Injective g\nh : \u2200 (b : \u03b2), \u2203 a, f a = g b\nh\u03b2 : IsEmpty \u03b2\n\u22a2 Small.{u, w} \u03b2",
+              "state_before": "case neg\n\u03b1 : Type v\n\u03b2 : Type w\n\u03b3 : Type v'\ninst\u271d : Small.{u, v} \u03b1\nf : \u03b1 \u2192 \u03b3\ng : \u03b2 \u2192 \u03b3\nhg : Function.Injective g\nh : \u2200 (b : \u03b2), \u2203 a, f a = g b\nh\u03b2 : \u00acNonempty \u03b2\n\u22a2 Small.{u, w} \u03b2",
+              "tactic": "simp only [not_nonempty_iff] at h\u03b2"
+            },
+            {
+              "annotated_tactic": [
+                "\"infer_instance\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case neg\n\u03b1 : Type v\n\u03b2 : Type w\n\u03b3 : Type v'\ninst\u271d : Small.{u, v} \u03b1\nf : \u03b1 \u2192 \u03b3\ng : \u03b2 \u2192 \u03b3\nhg : Function.Injective g\nh : \u2200 (b : \u03b2), \u2203 a, f a = g b\nh\u03b2 : IsEmpty \u03b2\n\u22a2 Small.{u, w} \u03b2",
+              "tactic": "infer_instance"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Small/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "small_of_surjective",
+        "id": "small_of_surjective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            34,
+            53
+          ],
+          "file_path": "Mathlib/Logic/Small/Basic.lean",
+          "full_name": "small_of_surjective",
+          "start": [
+            32,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Small/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "small_congr",
+        "id": "small_congr",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            106,
+            66
+          ],
+          "file_path": "Mathlib/Logic/Small/Defs.lean",
+          "full_name": "small_congr",
+          "start": [
+            105,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Small/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "small_lift",
+        "id": "small_lift",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            80,
+            46
+          ],
+          "file_path": "Mathlib/Logic/Small/Defs.lean",
+          "full_name": "small_lift",
+          "start": [
+            78,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Small/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "small_map",
+        "id": "small_map",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            75,
+            24
+          ],
+          "file_path": "Mathlib/Logic/Small/Defs.lean",
+          "full_name": "small_map",
+          "start": [
+            73,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Small/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "small_max",
+        "id": "small_max",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            85,
+            22
+          ],
+          "file_path": "Mathlib/Logic/Small/Defs.lean",
+          "full_name": "small_max",
+          "start": [
+            84,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Small/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "small_type",
+        "id": "small_type",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            98,
+            30
+          ],
+          "file_path": "Mathlib/Logic/Small/Defs.lean",
+          "full_name": "small_type",
+          "start": [
+            97,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Small/Defs.lean"
+      }
+    ],
+    "input_proofs": 10,
+    "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-001349-0000-ca17dc82263f8dca.parquet",
+      "sha256": "ca17dc82263f8dca2f48569922c3a207a7dafdb971ee80b23e797ece27e2bd38",
+      "bytes": 29597,
+      "rows": 1,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    },
+    {
+      "path": "data/internal_test/mathlib-001349-0000-3d2a17dd4df705be.parquet",
+      "sha256": "3d2a17dd4df705be46773b51f35d21e2c9fa174adf06ff4624d29cfaf7807bb6",
+      "bytes": 43727,
+      "rows": 3,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Shrink.ext",
+    "mathlib:not_small_type"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Small/Defs.lean\",null,null,\"Shrink.ext\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Small/Defs.lean\",null,null,\"not_small_type\"]"
+  ]
+}

manifests/batches/mathlib/001350.json

@@ -0,0 +1,136 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001350",
+  "batch_fingerprint": "ab19637a6c1c2c2ea51ded2511716bffdfe71f3b3e7348f902d2ec462488e8b5",
+  "evidence": {
+    "batch_fingerprint": "ab19637a6c1c2c2ea51ded2511716bffdfe71f3b3e7348f902d2ec462488e8b5",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "equivShrink_symm_one",
+        "id": "equivShrink_symm_one",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            31,
+            37
+          ],
+          "file_path": "Mathlib/Logic/Small/Group.lean",
+          "full_name": "equivShrink_symm_one",
+          "start": [
+            29,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Small/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "equivShrink_symm_zero",
+        "id": "equivShrink_symm_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            27,
+            37
+          ],
+          "file_path": "Mathlib/Logic/Small/Group.lean",
+          "full_name": "equivShrink_symm_zero",
+          "start": [
+            25,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Small/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "small_subset",
+        "id": "small_subset",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            17,
+            78
+          ],
+          "file_path": "Mathlib/Logic/Small/Set.lean",
+          "full_name": "small_subset",
+          "start": [
+            15,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Small/Set.lean"
+      }
+    ],
+    "input_proofs": 14,
+    "input_units": 2,
+    "proofs": 11,
+    "published_proofs": 11,
+    "published_transitions": 22,
+    "replay_failures": [],
+    "transitions": 22,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001350-0000-58113f5c644384c0.parquet",
+      "sha256": "58113f5c644384c0cb684ccd4bfae44aec80202dece38c8d5daaffcf4051763b",
+      "bytes": 52844,
+      "rows": 14,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    },
+    {
+      "path": "data/dev/mathlib-001350-0000-0333bf433686dabd.parquet",
+      "sha256": "0333bf433686dabd736eaaa23aaf21cf167333985a3eb75d1b932675ca5bcd96",
+      "bytes": 39341,
+      "rows": 2,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    },
+    {
+      "path": "data/internal_test/mathlib-001350-0000-27963a4d74869110.parquet",
+      "sha256": "27963a4d74869110be2481635c6327d2226d05053af3f93332d984437affac14",
+      "bytes": 43497,
+      "rows": 6,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:equivShrink_add",
+    "mathlib:equivShrink_div",
+    "mathlib:equivShrink_inv",
+    "mathlib:equivShrink_mul",
+    "mathlib:equivShrink_neg",
+    "mathlib:equivShrink_sub",
+    "mathlib:equivShrink_symm_add",
+    "mathlib:equivShrink_symm_div",
+    "mathlib:equivShrink_symm_inv",
+    "mathlib:equivShrink_symm_mul",
+    "mathlib:equivShrink_symm_neg"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Small/Group.lean\",null,null,\"equivShrink_add\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Small/Group.lean\",null,null,\"equivShrink_div\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Small/Group.lean\",null,null,\"equivShrink_inv\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Small/Group.lean\",null,null,\"equivShrink_mul\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Small/Group.lean\",null,null,\"equivShrink_neg\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Small/Group.lean\",null,null,\"equivShrink_sub\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Small/Group.lean\",null,null,\"equivShrink_symm_add\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Small/Group.lean\",null,null,\"equivShrink_symm_div\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Small/Group.lean\",null,null,\"equivShrink_symm_inv\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Small/Group.lean\",null,null,\"equivShrink_symm_mul\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Small/Group.lean\",null,null,\"equivShrink_symm_neg\"]"
+  ]
+}

manifests/batches/mathlib/001351.json

@@ -0,0 +1,457 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001351",
+  "batch_fingerprint": "18e1c019142d21dc9e8aa43d8c2f999e56bf6d6d67ae391b36b7e7e11cc816ce",
+  "evidence": {
+    "batch_fingerprint": "18e1c019142d21dc9e8aa43d8c2f999e56bf6d6d67ae391b36b7e7e11cc816ce",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.Injective.subsingleton",
+        "id": "Function.Injective.subsingleton",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            208,
+            42
+          ],
+          "file_path": "Mathlib/Logic/Unique.lean",
+          "full_name": "Function.Injective.subsingleton",
+          "start": [
+            207,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Unique.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.Surjective.subsingleton",
+        "id": "Function.Surjective.subsingleton",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            214,
+            64
+          ],
+          "file_path": "Mathlib/Logic/Unique.lean",
+          "full_name": "Function.Surjective.subsingleton",
+          "start": [
+            213,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Unique.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Option.subsingleton_iff_isEmpty",
+        "id": "Option.subsingleton_iff_isEmpty",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            270,
+            81
+          ],
+          "file_path": "Mathlib/Logic/Unique.lean",
+          "full_name": "Option.subsingleton_iff_isEmpty",
+          "start": [
+            267,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Unique.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "PUnit.default_eq_unit",
+        "id": "PUnit.default_eq_unit",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            97,
+            6
+          ],
+          "file_path": "Mathlib/Logic/Unique.lean",
+          "full_name": "PUnit.default_eq_unit",
+          "start": [
+            96,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Unique.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Pi.default_apply",
+        "id": "Pi.default_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            177,
+            6
+          ],
+          "file_path": "Mathlib/Logic/Unique.lean",
+          "full_name": "Pi.default_apply",
+          "start": [
+            175,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Unique.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Pi.default_def",
+        "id": "Pi.default_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            172,
+            6
+          ],
+          "file_path": "Mathlib/Logic/Unique.lean",
+          "full_name": "Pi.default_def",
+          "start": [
+            170,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Unique.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Unique.default_eq",
+        "id": "Unique.default_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            126,
+            18
+          ],
+          "file_path": "Mathlib/Logic/Unique.lean",
+          "full_name": "Unique.default_eq",
+          "start": [
+            125,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Unique.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Unique.eq_default",
+        "id": "Unique.eq_default",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            122,
+            11
+          ],
+          "file_path": "Mathlib/Logic/Unique.lean",
+          "full_name": "Unique.eq_default",
+          "start": [
+            121,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Unique.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Unique.exists_iff",
+        "id": "Unique.exists_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            138,
+            58
+          ],
+          "file_path": "Mathlib/Logic/Unique.lean",
+          "full_name": "Unique.exists_iff",
+          "start": [
+            137,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Unique.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "eq_const_of_subsingleton",
+        "id": "eq_const_of_subsingleton",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            190,
+            45
+          ],
+          "file_path": "Mathlib/Logic/Unique.lean",
+          "full_name": "eq_const_of_subsingleton",
+          "start": [
+            188,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Unique.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "eq_const_of_unique",
+        "id": "eq_const_of_unique",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            193,
+            30
+          ],
+          "file_path": "Mathlib/Logic/Unique.lean",
+          "full_name": "eq_const_of_unique",
+          "start": [
+            192,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Unique.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "uniqueElim_const",
+        "id": "uniqueElim_const",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            253,
+            6
+          ],
+          "file_path": "Mathlib/Logic/Unique.lean",
+          "full_name": "uniqueElim_const",
+          "start": [
+            251,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Unique.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "uniqueElim_default",
+        "id": "uniqueElim_default",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            248,
+            6
+          ],
+          "file_path": "Mathlib/Logic/Unique.lean",
+          "full_name": "uniqueElim_default",
+          "start": [
+            247,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/Unique.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Small.trans_univLE",
+        "id": "Small.trans_univLE",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            50,
+            19
+          ],
+          "file_path": "Mathlib/Logic/UnivLE.lean",
+          "full_name": "Small.trans_univLE",
+          "start": [
+            46,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/UnivLE.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "UnivLE.trans",
+        "id": "UnivLE.trans",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            53,
+            31
+          ],
+          "file_path": "Mathlib/Logic/UnivLE.lean",
+          "full_name": "UnivLE.trans",
+          "start": [
+            52,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/UnivLE.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "univLE_max",
+        "id": "univLE_max",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            44,
+            68
+          ],
+          "file_path": "Mathlib/Logic/UnivLE.lean",
+          "full_name": "univLE_max",
+          "start": [
+            44,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Logic/UnivLE.lean"
+      }
+    ],
+    "input_proofs": 22,
+    "input_units": 2,
+    "proofs": 6,
+    "published_proofs": 5,
+    "published_transitions": 9,
+    "replay_failures": [],
+    "transitions": 12,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Logic/Unique.lean",
+        "proof_id": "mathlib:unique_iff_subsingleton_and_nonempty",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              164,
+              54
+            ],
+            "file_path": "Mathlib/Logic/Unique.lean",
+            "full_name": "unique_iff_subsingleton_and_nonempty",
+            "start": [
+              161,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"constructor <;> exact <a>inferInstance<\\/a>\"",
+                  "[{\"full_name\":\"inferInstance\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[99,8],\"def_end_pos\":[99,21]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "\u03b1 : Sort u\nx\u271d : Nonempty (Unique \u03b1)\nu : Unique \u03b1\n\u22a2 Subsingleton \u03b1 \u2227 Nonempty \u03b1",
+                "tactic": "constructor <;> exact inferInstance"
+              },
+              {
+                "annotated_tactic": [
+                  "\"inhabit \\u03b1\"",
+                  "[]"
+                ],
+                "state_after": "\u03b1 : Sort u\nx\u271d : Subsingleton \u03b1 \u2227 Nonempty \u03b1\nhs : Subsingleton \u03b1\nhn : Nonempty \u03b1\ninhabited_h : Inhabited \u03b1\n\u22a2 Unique \u03b1",
+                "state_before": "\u03b1 : Sort u\nx\u271d : Subsingleton \u03b1 \u2227 Nonempty \u03b1\nhs : Subsingleton \u03b1\nhn : Nonempty \u03b1\n\u22a2 Unique \u03b1",
+                "tactic": "inhabit \u03b1"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact <a>Unique.mk'<\\/a> \\u03b1\"",
+                  "[{\"full_name\":\"Unique.mk'\",\"def_path\":\"Mathlib\\/Logic\\/Unique.lean\",\"def_pos\":[155,8],\"def_end_pos\":[155,11]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "\u03b1 : Sort u\nx\u271d : Subsingleton \u03b1 \u2227 Nonempty \u03b1\nhs : Subsingleton \u03b1\nhn : Nonempty \u03b1\ninhabited_h : Inhabited \u03b1\n\u22a2 Unique \u03b1",
+                "tactic": "exact Unique.mk' \u03b1"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "unique_iff_subsingleton_and_nonempty"
+      }
+    ],
+    "validation_rejected_proofs": 1,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001351-0000-527077bbaa358b54.parquet",
+      "sha256": "527077bbaa358b542dda309362ccc633b4c6f52adecbdbb9018ffcad9d6193b2",
+      "bytes": 43347,
+      "rows": 7,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    },
+    {
+      "path": "data/internal_test/mathlib-001351-0000-3895ac29605f8274.parquet",
+      "sha256": "3895ac29605f8274f1fbaa83d7484362cc11a63f70142f66a8b7adc09467fe15",
+      "bytes": 38678,
+      "rows": 2,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Unique.bijective",
+    "mathlib:Unique.forall_iff",
+    "mathlib:Unique.subsingleton_unique'",
+    "mathlib:heq_const_of_unique",
+    "mathlib:unique_subtype_iff_exists_unique"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Unique.lean\",null,null,\"Unique.bijective\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Unique.lean\",null,null,\"Unique.forall_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Unique.lean\",null,null,\"Unique.subsingleton_unique'\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Unique.lean\",null,null,\"heq_const_of_unique\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Logic/Unique.lean\",null,null,\"unique_subtype_iff_exists_unique\"]"
+  ]
+}

manifests/batches/mathlib/001353.json

@@ -0,0 +1,947 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001353",
+  "batch_fingerprint": "476bc7e8e1d9e349be1b5a74d08a729db94e661d8218aae6c8e4cd6863dd7d15",
+  "evidence": {
+    "batch_fingerprint": "476bc7e8e1d9e349be1b5a74d08a729db94e661d8218aae6c8e4cd6863dd7d15",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "AEMeasurable.apply_continuousLinearMap",
+        "id": "AEMeasurable.apply_continuousLinearMap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            91,
+            68
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean",
+          "full_name": "AEMeasurable.apply_continuousLinearMap",
+          "start": [
+            89,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ContinuousLinearMap.measurable",
+        "id": "ContinuousLinearMap.measurable",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            31,
+            26
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean",
+          "full_name": "ContinuousLinearMap.measurable",
+          "start": [
+            30,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ContinuousLinearMap.measurable_apply",
+        "id": "ContinuousLinearMap.measurable_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            59,
+            38
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean",
+          "full_name": "ContinuousLinearMap.measurable_apply",
+          "start": [
+            57,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ContinuousLinearMap.measurable_apply'",
+        "id": "ContinuousLinearMap.measurable_apply'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            65,
+            47
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean",
+          "full_name": "ContinuousLinearMap.measurable_apply'",
+          "start": [
+            63,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ContinuousLinearMap.measurable_coe",
+        "id": "ContinuousLinearMap.measurable_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            71,
+            42
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean",
+          "full_name": "ContinuousLinearMap.measurable_coe",
+          "start": [
+            69,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ContinuousLinearMap.measurable_comp",
+        "id": "ContinuousLinearMap.measurable_comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            37,
+            27
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean",
+          "full_name": "ContinuousLinearMap.measurable_comp",
+          "start": [
+            35,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Measurable.apply_continuousLinearMap",
+        "id": "Measurable.apply_continuousLinearMap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            85,
+            55
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean",
+          "full_name": "Measurable.apply_continuousLinearMap",
+          "start": [
+            83,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "aemeasurable_smul_const",
+        "id": "aemeasurable_smul_const",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            109,
+            75
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean",
+          "full_name": "aemeasurable_smul_const",
+          "start": [
+            107,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "measurable_smul_const",
+        "id": "measurable_smul_const",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            104,
+            73
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean",
+          "full_name": "measurable_smul_const",
+          "start": [
+            102,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "AEMeasurable.edist",
+        "id": "AEMeasurable.edist",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            200,
+            46
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "AEMeasurable.edist",
+          "start": [
+            198,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "AEMeasurable.ennnorm",
+        "id": "AEMeasurable.ennnorm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            285,
+            42
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "AEMeasurable.ennnorm",
+          "start": [
+            283,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "AEMeasurable.nnnorm",
+        "id": "AEMeasurable.nnnorm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            269,
+            41
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "AEMeasurable.nnnorm",
+          "start": [
+            267,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "AEMeasurable.norm",
+        "id": "AEMeasurable.norm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            253,
+            39
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "AEMeasurable.norm",
+          "start": [
+            251,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Measurable.dist",
+        "id": "Measurable.dist",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            87,
+            43
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "Measurable.dist",
+          "start": [
+            85,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Measurable.edist",
+        "id": "Measurable.edist",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            194,
+            44
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "Measurable.edist",
+          "start": [
+            192,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Measurable.ennnorm",
+        "id": "Measurable.ennnorm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            279,
+            31
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "Measurable.ennnorm",
+          "start": [
+            278,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Measurable.infDist",
+        "id": "Measurable.infDist",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            61,
+            29
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "Measurable.infDist",
+          "start": [
+            59,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Measurable.infEdist",
+        "id": "Measurable.infEdist",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            135,
+            30
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "Measurable.infEdist",
+          "start": [
+            133,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Measurable.infNndist",
+        "id": "Measurable.infNndist",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            72,
+            31
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "Measurable.infNndist",
+          "start": [
+            70,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Measurable.nndist",
+        "id": "Measurable.nndist",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            98,
+            45
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "Measurable.nndist",
+          "start": [
+            96,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Measurable.nnnorm",
+        "id": "Measurable.nnnorm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            263,
+            28
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "Measurable.nnnorm",
+          "start": [
+            262,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Measurable.norm",
+        "id": "Measurable.norm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            247,
+            26
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "Measurable.norm",
+          "start": [
+            246,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "measurableSet_ball",
+        "id": "measurableSet_ball",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            45,
+            35
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "measurableSet_ball",
+          "start": [
+            44,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "measurableSet_closedBall",
+        "id": "measurableSet_closedBall",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            50,
+            37
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "measurableSet_closedBall",
+          "start": [
+            49,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "measurable_dist",
+        "id": "measurable_dist",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            81,
+            29
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "measurable_dist",
+          "start": [
+            80,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "measurable_edist",
+        "id": "measurable_edist",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            188,
+            30
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "measurable_edist",
+          "start": [
+            187,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "measurable_edist_left",
+        "id": "measurable_edist_left",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            124,
+            52
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "measurable_edist_left",
+          "start": [
+            123,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "measurable_edist_right",
+        "id": "measurable_edist_right",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            119,
+            52
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "measurable_edist_right",
+          "start": [
+            118,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "measurable_ennnorm",
+        "id": "measurable_ennnorm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            274,
+            39
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "measurable_ennnorm",
+          "start": [
+            273,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "measurable_infDist",
+        "id": "measurable_infDist",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            55,
+            39
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "measurable_infDist",
+          "start": [
+            54,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "measurable_infEdist",
+        "id": "measurable_infEdist",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            129,
+            33
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "measurable_infEdist",
+          "start": [
+            128,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "measurable_infNndist",
+        "id": "measurable_infNndist",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            66,
+            41
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "measurable_infNndist",
+          "start": [
+            65,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "measurable_nndist",
+        "id": "measurable_nndist",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            92,
+            31
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "measurable_nndist",
+          "start": [
+            91,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "measurable_nnnorm",
+        "id": "measurable_nnnorm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            258,
+            31
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "measurable_nnnorm",
+          "start": [
+            257,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "measurable_norm",
+        "id": "measurable_norm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            242,
+            29
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "measurable_norm",
+          "start": [
+            241,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rw [closure_eq_iInter_cthickening]'",
+        "full_name": "tendsto_measure_cthickening",
+        "id": "tendsto_measure_cthickening",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            155,
+            43
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "tendsto_measure_cthickening",
+          "start": [
+            142,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"have A : <a>Tendsto<\\/a> (fun r => \\u03bc (<a>cthickening<\\/a> r s)) (\\ud835\\udcdd[<a>Ioi<\\/a> 0] 0) (\\ud835\\udcdd (\\u03bc (<a>closure<\\/a> s))) := by\\n    rw [<a>closure_eq_iInter_cthickening<\\/a>]\\n    exact\\n      <a>tendsto_measure_biInter_gt<\\/a> (fun r _ => isClosed_cthickening.measurableSet)\\n        (fun i j _ ij => <a>cthickening_mono<\\/a> ij _) hs\"",
+                "[{\"full_name\":\"Filter.Tendsto\",\"def_path\":\"Mathlib\\/Order\\/Filter\\/Basic.lean\",\"def_pos\":[2991,5],\"def_end_pos\":[2991,12]},{\"full_name\":\"Metric.cthickening\",\"def_path\":\"Mathlib\\/Topology\\/MetricSpace\\/Thickening.lean\",\"def_pos\":[195,5],\"def_end_pos\":[195,16]},{\"full_name\":\"Set.Ioi\",\"def_path\":\"Mathlib\\/Order\\/Interval\\/Set\\/Basic.lean\",\"def_pos\":[79,5],\"def_end_pos\":[79,8]},{\"full_name\":\"closure\",\"def_path\":\"Mathlib\\/Topology\\/Defs\\/Basic.lean\",\"def_pos\":[116,5],\"def_end_pos\":[116,12]},{\"full_name\":\"Metric.closure_eq_iInter_cthickening\",\"def_path\":\"Mathlib\\/Topology\\/MetricSpace\\/Thickening.lean\",\"def_pos\":[557,9],\"def_end_pos\":[557,38]},{\"full_name\":\"MeasureTheory.tendsto_measure_biInter_gt\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Measure\\/MeasureSpace.lean\",\"def_pos\":[610,9],\"def_end_pos\":[610,35]},{\"full_name\":\"Metric.cthickening_mono\",\"def_path\":\"Mathlib\\/Topology\\/MetricSpace\\/Thickening.lean\",\"def_pos\":[258,9],\"def_end_pos\":[258,25]}]"
+              ],
+              "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\n\u03b9 : Sort y\ns\u271d t u : Set \u03b1\ninst\u271d\u00b3 : PseudoEMetricSpace \u03b1\ninst\u271d\u00b2 : MeasurableSpace \u03b1\ninst\u271d\u00b9 : OpensMeasurableSpace \u03b1\ninst\u271d : MeasurableSpace \u03b2\nx : \u03b1\n\u03b5 : \u211d\u22650\u221e\n\u03bc : Measure \u03b1\ns : Set \u03b1\nhs : \u2203 R > 0, \u03bc (cthickening R s) \u2260 \u22a4\nA : Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[>] 0) (\ud835\udcdd (\u03bc (closure s)))\n\u22a2 Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd 0) (\ud835\udcdd (\u03bc (closure s)))",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\n\u03b9 : Sort y\ns\u271d t u : Set \u03b1\ninst\u271d\u00b3 : PseudoEMetricSpace \u03b1\ninst\u271d\u00b2 : MeasurableSpace \u03b1\ninst\u271d\u00b9 : OpensMeasurableSpace \u03b1\ninst\u271d : MeasurableSpace \u03b2\nx : \u03b1\n\u03b5 : \u211d\u22650\u221e\n\u03bc : Measure \u03b1\ns : Set \u03b1\nhs : \u2203 R > 0, \u03bc (cthickening R s) \u2260 \u22a4\n\u22a2 Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd 0) (\ud835\udcdd (\u03bc (closure s)))",
+              "tactic": "have A : Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[Ioi 0] 0) (\ud835\udcdd (\u03bc (closure s))) := by\n  rw [closure_eq_iInter_cthickening]\n  exact\n    tendsto_measure_biInter_gt (fun r _ => isClosed_cthickening.measurableSet)\n      (fun i j _ ij => cthickening_mono ij _) hs"
+            },
+            {
+              "annotated_tactic": [
+                "\"have B : <a>Tendsto<\\/a> (fun r => \\u03bc (<a>cthickening<\\/a> r s)) (\\ud835\\udcdd[<a>Iic<\\/a> 0] 0) (\\ud835\\udcdd (\\u03bc (<a>closure<\\/a> s))) := by\\n    apply <a>Tendsto.congr'<\\/a> _ <a>tendsto_const_nhds<\\/a>\\n    filter_upwards [<a>self_mem_nhdsWithin<\\/a> (\\u03b1 := \\u211d)] with _ hr\\n    rw [<a>cthickening_of_nonpos<\\/a> hr]\"",
+                "[{\"full_name\":\"Filter.Tendsto\",\"def_path\":\"Mathlib\\/Order\\/Filter\\/Basic.lean\",\"def_pos\":[2991,5],\"def_end_pos\":[2991,12]},{\"full_name\":\"Metric.cthickening\",\"def_path\":\"Mathlib\\/Topology\\/MetricSpace\\/Thickening.lean\",\"def_pos\":[195,5],\"def_end_pos\":[195,16]},{\"full_name\":\"Set.Iic\",\"def_path\":\"Mathlib\\/Order\\/Interval\\/Set\\/Basic.lean\",\"def_pos\":[64,5],\"def_end_pos\":[64,8]},{\"full_name\":\"closure\",\"def_path\":\"Mathlib\\/Topology\\/Defs\\/Basic.lean\",\"def_pos\":[116,5],\"def_end_pos\":[116,12]},{\"full_name\":\"Filter.Tendsto.congr'\",\"def_path\":\"Mathlib\\/Order\\/Filter\\/Basic.lean\",\"def_pos\":[3075,9],\"def_end_pos\":[3075,23]},{\"full_name\":\"tendsto_const_nhds\",\"def_path\":\"Mathlib\\/Topology\\/Basic.lean\",\"def_pos\":[991,9],\"def_end_pos\":[991,27]},{\"full_name\":\"self_mem_nhdsWithin\",\"def_path\":\"Mathlib\\/Topology\\/ContinuousOn.lean\",\"def_pos\":[147,9],\"def_end_pos\":[147,28]},{\"full_name\":\"Metric.cthickening_of_nonpos\",\"def_path\":\"Mathlib\\/Topology\\/MetricSpace\\/Thickening.lean\",\"def_pos\":[241,9],\"def_end_pos\":[241,30]}]"
+              ],
+              "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\n\u03b9 : Sort y\ns\u271d t u : Set \u03b1\ninst\u271d\u00b3 : PseudoEMetricSpace \u03b1\ninst\u271d\u00b2 : MeasurableSpace \u03b1\ninst\u271d\u00b9 : OpensMeasurableSpace \u03b1\ninst\u271d : MeasurableSpace \u03b2\nx : \u03b1\n\u03b5 : \u211d\u22650\u221e\n\u03bc : Measure \u03b1\ns : Set \u03b1\nhs : \u2203 R > 0, \u03bc (cthickening R s) \u2260 \u22a4\nA : Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[>] 0) (\ud835\udcdd (\u03bc (closure s)))\nB : Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[\u2264] 0) (\ud835\udcdd (\u03bc (closure s)))\n\u22a2 Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd 0) (\ud835\udcdd (\u03bc (closure s)))",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\n\u03b9 : Sort y\ns\u271d t u : Set \u03b1\ninst\u271d\u00b3 : PseudoEMetricSpace \u03b1\ninst\u271d\u00b2 : MeasurableSpace \u03b1\ninst\u271d\u00b9 : OpensMeasurableSpace \u03b1\ninst\u271d : MeasurableSpace \u03b2\nx : \u03b1\n\u03b5 : \u211d\u22650\u221e\n\u03bc : Measure \u03b1\ns : Set \u03b1\nhs : \u2203 R > 0, \u03bc (cthickening R s) \u2260 \u22a4\nA : Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[>] 0) (\ud835\udcdd (\u03bc (closure s)))\n\u22a2 Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd 0) (\ud835\udcdd (\u03bc (closure s)))",
+              "tactic": "have B : Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[Iic 0] 0) (\ud835\udcdd (\u03bc (closure s))) := by\n  apply Tendsto.congr' _ tendsto_const_nhds\n  filter_upwards [self_mem_nhdsWithin (\u03b1 := \u211d)] with _ hr\n  rw [cthickening_of_nonpos hr]"
+            },
+            {
+              "annotated_tactic": [
+                "\"convert B.sup A\"",
+                "[]"
+              ],
+              "state_after": "case h.e'_4\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\n\u03b9 : Sort y\ns\u271d t u : Set \u03b1\ninst\u271d\u00b3 : PseudoEMetricSpace \u03b1\ninst\u271d\u00b2 : MeasurableSpace \u03b1\ninst\u271d\u00b9 : OpensMeasurableSpace \u03b1\ninst\u271d : MeasurableSpace \u03b2\nx : \u03b1\n\u03b5 : \u211d\u22650\u221e\n\u03bc : Measure \u03b1\ns : Set \u03b1\nhs : \u2203 R > 0, \u03bc (cthickening R s) \u2260 \u22a4\nA : Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[>] 0) (\ud835\udcdd (\u03bc (closure s)))\nB : Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[\u2264] 0) (\ud835\udcdd (\u03bc (closure s)))\n\u22a2 \ud835\udcdd 0 = \ud835\udcdd[\u2264] 0 \u2294 \ud835\udcdd[>] 0",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\n\u03b9 : Sort y\ns\u271d t u : Set \u03b1\ninst\u271d\u00b3 : PseudoEMetricSpace \u03b1\ninst\u271d\u00b2 : MeasurableSpace \u03b1\ninst\u271d\u00b9 : OpensMeasurableSpace \u03b1\ninst\u271d : MeasurableSpace \u03b2\nx : \u03b1\n\u03b5 : \u211d\u22650\u221e\n\u03bc : Measure \u03b1\ns : Set \u03b1\nhs : \u2203 R > 0, \u03bc (cthickening R s) \u2260 \u22a4\nA : Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[>] 0) (\ud835\udcdd (\u03bc (closure s)))\nB : Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[\u2264] 0) (\ud835\udcdd (\u03bc (closure s)))\n\u22a2 Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd 0) (\ud835\udcdd (\u03bc (closure s)))",
+              "tactic": "convert B.sup A"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact (<a>nhds_left_sup_nhds_right'<\\/a> 0).<a>symm<\\/a>\"",
+                "[{\"full_name\":\"nhds_left_sup_nhds_right'\",\"def_path\":\"Mathlib\\/Topology\\/Order\\/LeftRight.lean\",\"def_pos\":[119,9],\"def_end_pos\":[119,34]},{\"full_name\":\"Eq.symm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[323,9],\"def_end_pos\":[323,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.e'_4\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\n\u03b9 : Sort y\ns\u271d t u : Set \u03b1\ninst\u271d\u00b3 : PseudoEMetricSpace \u03b1\ninst\u271d\u00b2 : MeasurableSpace \u03b1\ninst\u271d\u00b9 : OpensMeasurableSpace \u03b1\ninst\u271d : MeasurableSpace \u03b2\nx : \u03b1\n\u03b5 : \u211d\u22650\u221e\n\u03bc : Measure \u03b1\ns : Set \u03b1\nhs : \u2203 R > 0, \u03bc (cthickening R s) \u2260 \u22a4\nA : Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[>] 0) (\ud835\udcdd (\u03bc (closure s)))\nB : Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[\u2264] 0) (\ud835\udcdd (\u03bc (closure s)))\n\u22a2 \ud835\udcdd 0 = \ud835\udcdd[\u2264] 0 \u2294 \ud835\udcdd[>] 0",
+              "tactic": "exact (nhds_left_sup_nhds_right' 0).symm"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>closure_eq_iInter_cthickening<\\/a>]\"",
+                "[{\"full_name\":\"Metric.closure_eq_iInter_cthickening\",\"def_path\":\"Mathlib\\/Topology\\/MetricSpace\\/Thickening.lean\",\"def_pos\":[557,9],\"def_end_pos\":[557,38]}]"
+              ],
+              "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\n\u03b9 : Sort y\ns\u271d t u : Set \u03b1\ninst\u271d\u00b3 : PseudoEMetricSpace \u03b1\ninst\u271d\u00b2 : MeasurableSpace \u03b1\ninst\u271d\u00b9 : OpensMeasurableSpace \u03b1\ninst\u271d : MeasurableSpace \u03b2\nx : \u03b1\n\u03b5 : \u211d\u22650\u221e\n\u03bc : Measure \u03b1\ns : Set \u03b1\nhs : \u2203 R > 0, \u03bc (cthickening R s) \u2260 \u22a4\n\u22a2 Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[>] 0) (\ud835\udcdd (\u03bc (\u22c2 \u03b4, \u22c2 (_ : 0 < \u03b4), cthickening \u03b4 s)))",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\n\u03b9 : Sort y\ns\u271d t u : Set \u03b1\ninst\u271d\u00b3 : PseudoEMetricSpace \u03b1\ninst\u271d\u00b2 : MeasurableSpace \u03b1\ninst\u271d\u00b9 : OpensMeasurableSpace \u03b1\ninst\u271d : MeasurableSpace \u03b2\nx : \u03b1\n\u03b5 : \u211d\u22650\u221e\n\u03bc : Measure \u03b1\ns : Set \u03b1\nhs : \u2203 R > 0, \u03bc (cthickening R s) \u2260 \u22a4\n\u22a2 Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[>] 0) (\ud835\udcdd (\u03bc (closure s)))",
+              "tactic": "rw [closure_eq_iInter_cthickening]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact\\n      <a>tendsto_measure_biInter_gt<\\/a> (fun r _ => isClosed_cthickening.measurableSet)\\n        (fun i j _ ij => <a>cthickening_mono<\\/a> ij _) hs\"",
+                "[{\"full_name\":\"MeasureTheory.tendsto_measure_biInter_gt\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Measure\\/MeasureSpace.lean\",\"def_pos\":[610,9],\"def_end_pos\":[610,35]},{\"full_name\":\"Metric.cthickening_mono\",\"def_path\":\"Mathlib\\/Topology\\/MetricSpace\\/Thickening.lean\",\"def_pos\":[258,9],\"def_end_pos\":[258,25]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\n\u03b9 : Sort y\ns\u271d t u : Set \u03b1\ninst\u271d\u00b3 : PseudoEMetricSpace \u03b1\ninst\u271d\u00b2 : MeasurableSpace \u03b1\ninst\u271d\u00b9 : OpensMeasurableSpace \u03b1\ninst\u271d : MeasurableSpace \u03b2\nx : \u03b1\n\u03b5 : \u211d\u22650\u221e\n\u03bc : Measure \u03b1\ns : Set \u03b1\nhs : \u2203 R > 0, \u03bc (cthickening R s) \u2260 \u22a4\n\u22a2 Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[>] 0) (\ud835\udcdd (\u03bc (\u22c2 \u03b4, \u22c2 (_ : 0 < \u03b4), cthickening \u03b4 s)))",
+              "tactic": "exact\n  tendsto_measure_biInter_gt (fun r _ => isClosed_cthickening.measurableSet)\n    (fun i j _ ij => cthickening_mono ij _) hs"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Tendsto.congr'<\\/a> _ <a>tendsto_const_nhds<\\/a>\"",
+                "[{\"full_name\":\"Filter.Tendsto.congr'\",\"def_path\":\"Mathlib\\/Order\\/Filter\\/Basic.lean\",\"def_pos\":[3075,9],\"def_end_pos\":[3075,23]},{\"full_name\":\"tendsto_const_nhds\",\"def_path\":\"Mathlib\\/Topology\\/Basic.lean\",\"def_pos\":[991,9],\"def_end_pos\":[991,27]}]"
+              ],
+              "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\n\u03b9 : Sort y\ns\u271d t u : Set \u03b1\ninst\u271d\u00b3 : PseudoEMetricSpace \u03b1\ninst\u271d\u00b2 : MeasurableSpace \u03b1\ninst\u271d\u00b9 : OpensMeasurableSpace \u03b1\ninst\u271d : MeasurableSpace \u03b2\nx : \u03b1\n\u03b5 : \u211d\u22650\u221e\n\u03bc : Measure \u03b1\ns : Set \u03b1\nhs : \u2203 R > 0, \u03bc (cthickening R s) \u2260 \u22a4\nA : Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[>] 0) (\ud835\udcdd (\u03bc (closure s)))\n\u22a2 (fun x => \u03bc (closure s)) =\u1da0[\ud835\udcdd[\u2264] 0] fun r => \u03bc (cthickening r s)",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\n\u03b9 : Sort y\ns\u271d t u : Set \u03b1\ninst\u271d\u00b3 : PseudoEMetricSpace \u03b1\ninst\u271d\u00b2 : MeasurableSpace \u03b1\ninst\u271d\u00b9 : OpensMeasurableSpace \u03b1\ninst\u271d : MeasurableSpace \u03b2\nx : \u03b1\n\u03b5 : \u211d\u22650\u221e\n\u03bc : Measure \u03b1\ns : Set \u03b1\nhs : \u2203 R > 0, \u03bc (cthickening R s) \u2260 \u22a4\nA : Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[>] 0) (\ud835\udcdd (\u03bc (closure s)))\n\u22a2 Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[\u2264] 0) (\ud835\udcdd (\u03bc (closure s)))",
+              "tactic": "apply Tendsto.congr' _ tendsto_const_nhds"
+            },
+            {
+              "annotated_tactic": [
+                "\"filter_upwards [<a>self_mem_nhdsWithin<\\/a> (\\u03b1 := \\u211d)] with _ hr\"",
+                "[{\"full_name\":\"self_mem_nhdsWithin\",\"def_path\":\"Mathlib\\/Topology\\/ContinuousOn.lean\",\"def_pos\":[147,9],\"def_end_pos\":[147,28]}]"
+              ],
+              "state_after": "case h\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\n\u03b9 : Sort y\ns\u271d t u : Set \u03b1\ninst\u271d\u00b3 : PseudoEMetricSpace \u03b1\ninst\u271d\u00b2 : MeasurableSpace \u03b1\ninst\u271d\u00b9 : OpensMeasurableSpace \u03b1\ninst\u271d : MeasurableSpace \u03b2\nx : \u03b1\n\u03b5 : \u211d\u22650\u221e\n\u03bc : Measure \u03b1\ns : Set \u03b1\nhs : \u2203 R > 0, \u03bc (cthickening R s) \u2260 \u22a4\nA : Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[>] 0) (\ud835\udcdd (\u03bc (closure s)))\na\u271d : \u211d\nhr : a\u271d \u2208 Iic 0\n\u22a2 \u03bc (closure s) = \u03bc (cthickening a\u271d s)",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\n\u03b9 : Sort y\ns\u271d t u : Set \u03b1\ninst\u271d\u00b3 : PseudoEMetricSpace \u03b1\ninst\u271d\u00b2 : MeasurableSpace \u03b1\ninst\u271d\u00b9 : OpensMeasurableSpace \u03b1\ninst\u271d : MeasurableSpace \u03b2\nx : \u03b1\n\u03b5 : \u211d\u22650\u221e\n\u03bc : Measure \u03b1\ns : Set \u03b1\nhs : \u2203 R > 0, \u03bc (cthickening R s) \u2260 \u22a4\nA : Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[>] 0) (\ud835\udcdd (\u03bc (closure s)))\n\u22a2 (fun x => \u03bc (closure s)) =\u1da0[\ud835\udcdd[\u2264] 0] fun r => \u03bc (cthickening r s)",
+              "tactic": "filter_upwards [self_mem_nhdsWithin (\u03b1 := \u211d)] with _ hr"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>cthickening_of_nonpos<\\/a> hr]\"",
+                "[{\"full_name\":\"Metric.cthickening_of_nonpos\",\"def_path\":\"Mathlib\\/Topology\\/MetricSpace\\/Thickening.lean\",\"def_pos\":[241,9],\"def_end_pos\":[241,30]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\n\u03b9 : Sort y\ns\u271d t u : Set \u03b1\ninst\u271d\u00b3 : PseudoEMetricSpace \u03b1\ninst\u271d\u00b2 : MeasurableSpace \u03b1\ninst\u271d\u00b9 : OpensMeasurableSpace \u03b1\ninst\u271d : MeasurableSpace \u03b2\nx : \u03b1\n\u03b5 : \u211d\u22650\u221e\n\u03bc : Measure \u03b1\ns : Set \u03b1\nhs : \u2203 R > 0, \u03bc (cthickening R s) \u2260 \u22a4\nA : Tendsto (fun r => \u03bc (cthickening r s)) (\ud835\udcdd[>] 0) (\ud835\udcdd (\u03bc (closure s)))\na\u271d : \u211d\nhr : a\u271d \u2208 Iic 0\n\u22a2 \u03bc (closure s) = \u03bc (cthickening a\u271d s)",
+              "tactic": "rw [cthickening_of_nonpos hr]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "tendsto_measure_cthickening_of_isCompact",
+        "id": "tendsto_measure_cthickening_of_isCompact",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            212,
+            77
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean",
+          "full_name": "tendsto_measure_cthickening_of_isCompact",
+          "start": [
+            207,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean"
+      }
+    ],
+    "input_proofs": 42,
+    "input_units": 2,
+    "proofs": 5,
+    "published_proofs": 5,
+    "published_transitions": 13,
+    "replay_failures": [],
+    "transitions": 13,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001353-0000-963b37b02ece2c90.parquet",
+      "sha256": "963b37b02ece2c9069ec5ff9995e45e4a7890e4b8b0485b9b0bd4678a035a4e8",
+      "bytes": 81787,
+      "rows": 11,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    },
+    {
+      "path": "data/internal_test/mathlib-001353-0000-e26be5c8bea3c581.parquet",
+      "sha256": "e26be5c8bea3c58129951a9d81569695292a3b4364080481cb928c7a9a77875e",
+      "bytes": 55112,
+      "rows": 2,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:exists_borelSpace_of_countablyGenerated_of_separatesPoints",
+    "mathlib:exists_opensMeasurableSpace_of_countablySeparated",
+    "mathlib:tendsto_measure_cthickening_of_isClosed",
+    "mathlib:tendsto_measure_thickening",
+    "mathlib:tendsto_measure_thickening_of_isClosed"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean\",null,null,\"exists_borelSpace_of_countablyGenerated_of_separatesPoints\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean\",null,null,\"exists_opensMeasurableSpace_of_countablySeparated\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean\",null,null,\"tendsto_measure_cthickening_of_isClosed\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean\",null,null,\"tendsto_measure_thickening\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Constructions/BorelSpace/Metric.lean\",null,null,\"tendsto_measure_thickening_of_isClosed\"]"
+  ]
+}

manifests/batches/mathlib/001356.json

@@ -0,0 +1,446 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001356",
+  "batch_fingerprint": "712c7ea64eb81e04ffca70beb8098b10a591674f38f45a11fa16c976ebc612dd",
+  "evidence": {
+    "batch_fingerprint": "712c7ea64eb81e04ffca70beb8098b10a591674f38f45a11fa16c976ebc612dd",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "EventuallyMeasurable.congr",
+        "id": "EventuallyMeasurable.congr",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            112,
+            21
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/EventuallyMeasurable.lean",
+          "full_name": "EventuallyMeasurable.congr",
+          "start": [
+            109,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/EventuallyMeasurable.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "EventuallyMeasurableSpace.measurable_le",
+        "id": "EventuallyMeasurableSpace.measurable_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            60,
+            41
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/EventuallyMeasurable.lean",
+          "full_name": "EventuallyMeasurableSpace.measurable_le",
+          "start": [
+            59,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/EventuallyMeasurable.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Measurable.comp_eventuallyMeasurable",
+        "id": "Measurable.comp_eventuallyMeasurable",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            105,
+            13
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/EventuallyMeasurable.lean",
+          "full_name": "Measurable.comp_eventuallyMeasurable",
+          "start": [
+            103,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/EventuallyMeasurable.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Measurable.eventuallyMeasurable",
+        "id": "Measurable.eventuallyMeasurable",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            101,
+            48
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/EventuallyMeasurable.lean",
+          "full_name": "Measurable.eventuallyMeasurable",
+          "start": [
+            100,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/EventuallyMeasurable.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Measurable.eventuallyMeasurable_of_eventuallyEq",
+        "id": "Measurable.eventuallyMeasurable_of_eventuallyEq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            117,
+            36
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/EventuallyMeasurable.lean",
+          "full_name": "Measurable.eventuallyMeasurable_of_eventuallyEq",
+          "start": [
+            115,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/EventuallyMeasurable.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasurableSet.eventuallyMeasurableSet",
+        "id": "MeasurableSet.eventuallyMeasurableSet",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            57,
+            33
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/EventuallyMeasurable.lean",
+          "full_name": "MeasurableSet.eventuallyMeasurableSet",
+          "start": [
+            55,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/EventuallyMeasurable.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "eventuallyMeasurableSet_of_mem_filter",
+        "id": "eventuallyMeasurableSet_of_mem_filter",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            63,
+            55
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/EventuallyMeasurable.lean",
+          "full_name": "eventuallyMeasurableSet_of_mem_filter",
+          "start": [
+            62,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/EventuallyMeasurable.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rw [LinearOrderedField.smul_Ioo r.2.out, smul_zero, smul_eq_mul, mul_one]'",
+        "full_name": "MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd",
+        "id": "MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            125,
+            56
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/HaarToSphere.lean",
+          "full_name": "MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd",
+          "start": [
+            108,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"nontriviality E\"",
+                "[]"
+              ],
+              "state_after": "E : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\na\u271d : Nontrivial E\n\u22a2 MeasurePreserving (\u21d1(homeomorphUnitSphereProd E)) (comap Subtype.val \u03bc) (\u03bc.toSphere.prod (volumeIoiPow (dim E - 1)))",
+              "state_before": "E : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\n\u22a2 MeasurePreserving (\u21d1(homeomorphUnitSphereProd E)) (comap Subtype.val \u03bc) (\u03bc.toSphere.prod (volumeIoiPow (dim E - 1)))",
+              "tactic": "nontriviality E"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine \\u27e8(<a>homeomorphUnitSphereProd<\\/a> E).<a>measurable<\\/a>, .symm ?_\\u27e9\"",
+                "[{\"full_name\":\"homeomorphUnitSphereProd\",\"def_path\":\"Mathlib\\/Analysis\\/NormedSpace\\/SphereNormEquiv.lean\",\"def_pos\":[28,19],\"def_end_pos\":[28,43]},{\"full_name\":\"Homeomorph.measurable\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/BorelSpace\\/Basic.lean\",\"def_pos\":[566,19],\"def_end_pos\":[566,40]}]"
+              ],
+              "state_after": "E : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\na\u271d : Nontrivial E\n\u22a2 \u03bc.toSphere.prod (volumeIoiPow (dim E - 1)) = map (\u21d1(homeomorphUnitSphereProd E)) (comap Subtype.val \u03bc)",
+              "state_before": "E : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\na\u271d : Nontrivial E\n\u22a2 MeasurePreserving (\u21d1(homeomorphUnitSphereProd E)) (comap Subtype.val \u03bc) (\u03bc.toSphere.prod (volumeIoiPow (dim E - 1)))",
+              "tactic": "refine \u27e8(homeomorphUnitSphereProd E).measurable, .symm ?_\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine <a>prod_eq_generateFrom<\\/a> <a>generateFrom_measurableSet<\\/a>\\n    ((<a>borel_eq_generateFrom_Iio<\\/a> _).symm.trans BorelSpace.measurable_eq.symm)\\n    <a>isPiSystem_measurableSet<\\/a> <a>isPiSystem_Iio<\\/a>\\n    \\u03bc.toSphere.toFiniteSpanningSetsIn (<a>finiteSpanningSetsIn_volumeIoiPow_range_Iio<\\/a> _)\\n    fun s hs \\u21a6 <a>forall_mem_range<\\/a>.2 fun r \\u21a6 ?_\"",
+                "[{\"full_name\":\"MeasureTheory.Measure.prod_eq_generateFrom\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/Prod\\/Basic.lean\",\"def_pos\":[631,9],\"def_end_pos\":[631,29]},{\"full_name\":\"MeasurableSpace.generateFrom_measurableSet\",\"def_path\":\"Mathlib\\/MeasureTheory\\/MeasurableSpace\\/Defs.lean\",\"def_pos\":[402,9],\"def_end_pos\":[402,35]},{\"full_name\":\"borel_eq_generateFrom_Iio\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/BorelSpace\\/Order.lean\",\"def_pos\":[54,9],\"def_end_pos\":[54,34]},{\"full_name\":\"MeasurableSpace.isPiSystem_measurableSet\",\"def_path\":\"Mathlib\\/MeasureTheory\\/PiSystem.lean\",\"def_pos\":[73,9],\"def_end_pos\":[73,33]},{\"full_name\":\"isPiSystem_Iio\",\"def_path\":\"Mathlib\\/MeasureTheory\\/PiSystem.lean\",\"def_pos\":[137,9],\"def_end_pos\":[137,23]},{\"full_name\":\"MeasureTheory.Measure.finiteSpanningSetsIn_volumeIoiPow_range_Iio\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/HaarToSphere.lean\",\"def_pos\":[95,5],\"def_end_pos\":[95,48]},{\"full_name\":\"Set.forall_mem_range\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Image.lean\",\"def_pos\":[662,9],\"def_end_pos\":[662,25]}]"
+              ],
+              "state_after": "E : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\na\u271d : Nontrivial E\ns : Set \u2191(sphere 0 1)\nhs : s \u2208 {s | MeasurableSet s}\nr : \u2191(Ioi 0)\n\u22a2 (map (\u21d1(homeomorphUnitSphereProd E)) (comap Subtype.val \u03bc)) (s \u00d7\u02e2 Iio r) =\n    \u03bc.toSphere s * (volumeIoiPow (dim E - 1)) (Iio r)",
+              "state_before": "E : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\na\u271d : Nontrivial E\n\u22a2 \u03bc.toSphere.prod (volumeIoiPow (dim E - 1)) = map (\u21d1(homeomorphUnitSphereProd E)) (comap Subtype.val \u03bc)",
+              "tactic": "refine prod_eq_generateFrom generateFrom_measurableSet\n  ((borel_eq_generateFrom_Iio _).symm.trans BorelSpace.measurable_eq.symm)\n  isPiSystem_measurableSet isPiSystem_Iio\n  \u03bc.toSphere.toFiniteSpanningSetsIn (finiteSpanningSetsIn_volumeIoiPow_range_Iio _)\n  fun s hs \u21a6 forall_mem_range.2 fun r \u21a6 ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"have : <a>Ioo<\\/a> (0 : \\u211d) r = r.1 \\u2022 <a>Ioo<\\/a> (0 : \\u211d) 1 := by\\n    rw [<a>LinearOrderedField.smul_Ioo<\\/a> r.2.<a>out<\\/a>, <a>smul_zero<\\/a>, <a>smul_eq_mul<\\/a>, <a>mul_one<\\/a>]\"",
+                "[{\"full_name\":\"Set.Ioo\",\"def_path\":\"Mathlib\\/Order\\/Interval\\/Set\\/Basic.lean\",\"def_pos\":[44,5],\"def_end_pos\":[44,8]},{\"full_name\":\"Set.Ioo\",\"def_path\":\"Mathlib\\/Order\\/Interval\\/Set\\/Basic.lean\",\"def_pos\":[44,5],\"def_end_pos\":[44,8]},{\"full_name\":\"LinearOrderedField.smul_Ioo\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Pointwise.lean\",\"def_pos\":[183,9],\"def_end_pos\":[183,17]},{\"full_name\":\"Membership.mem.out\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[237,9],\"def_end_pos\":[237,34]},{\"full_name\":\"smul_zero\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Defs.lean\",\"def_pos\":[66,9],\"def_end_pos\":[66,18]},{\"full_name\":\"smul_eq_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[89,7],\"def_end_pos\":[89,18]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]}]"
+              ],
+              "state_after": "E : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\na\u271d : Nontrivial E\ns : Set \u2191(sphere 0 1)\nhs : s \u2208 {s | MeasurableSet s}\nr : \u2191(Ioi 0)\nthis : Ioo 0 \u2191r = \u2191r \u2022 Ioo 0 1\n\u22a2 (map (\u21d1(homeomorphUnitSphereProd E)) (comap Subtype.val \u03bc)) (s \u00d7\u02e2 Iio r) =\n    \u03bc.toSphere s * (volumeIoiPow (dim E - 1)) (Iio r)",
+              "state_before": "E : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\na\u271d : Nontrivial E\ns : Set \u2191(sphere 0 1)\nhs : s \u2208 {s | MeasurableSet s}\nr : \u2191(Ioi 0)\n\u22a2 (map (\u21d1(homeomorphUnitSphereProd E)) (comap Subtype.val \u03bc)) (s \u00d7\u02e2 Iio r) =\n    \u03bc.toSphere s * (volumeIoiPow (dim E - 1)) (Iio r)",
+              "tactic": "have : Ioo (0 : \u211d) r = r.1 \u2022 Ioo (0 : \u211d) 1 := by\n  rw [LinearOrderedField.smul_Ioo r.2.out, smul_zero, smul_eq_mul, mul_one]"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hpos : 0 < dim E := <a>FiniteDimensional.finrank_pos<\\/a>\"",
+                "[{\"full_name\":\"FiniteDimensional.finrank_pos\",\"def_path\":\"Mathlib\\/LinearAlgebra\\/Dimension\\/Finite.lean\",\"def_pos\":[424,9],\"def_end_pos\":[424,38]}]"
+              ],
+              "state_after": "E : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\na\u271d : Nontrivial E\ns : Set \u2191(sphere 0 1)\nhs : s \u2208 {s | MeasurableSet s}\nr : \u2191(Ioi 0)\nthis : Ioo 0 \u2191r = \u2191r \u2022 Ioo 0 1\nhpos : 0 < dim E\n\u22a2 (map (\u21d1(homeomorphUnitSphereProd E)) (comap Subtype.val \u03bc)) (s \u00d7\u02e2 Iio r) =\n    \u03bc.toSphere s * (volumeIoiPow (dim E - 1)) (Iio r)",
+              "state_before": "E : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\na\u271d : Nontrivial E\ns : Set \u2191(sphere 0 1)\nhs : s \u2208 {s | MeasurableSet s}\nr : \u2191(Ioi 0)\nthis : Ioo 0 \u2191r = \u2191r \u2022 Ioo 0 1\n\u22a2 (map (\u21d1(homeomorphUnitSphereProd E)) (comap Subtype.val \u03bc)) (s \u00d7\u02e2 Iio r) =\n    \u03bc.toSphere s * (volumeIoiPow (dim E - 1)) (Iio r)",
+              "tactic": "have hpos : 0 < dim E := FiniteDimensional.finrank_pos"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [(<a>Homeomorph.measurableEmbedding<\\/a> _).<a>map_apply<\\/a>, <a>toSphere_apply'<\\/a> _ hs, <a>volumeIoiPow_apply_Iio<\\/a>,\\n    <a>comap_subtype_coe_apply<\\/a> (<a>measurableSet_singleton<\\/a> _).<a>compl<\\/a>, <a>toSphere_apply_aux<\\/a>, this,\\n    <a>smul_assoc<\\/a>, \\u03bc.addHaar_smul_of_nonneg r.2.out.le, <a>Nat.sub_add_cancel<\\/a> hpos, <a>Nat.cast_pred<\\/a> hpos,\\n    <a>sub_add_cancel<\\/a>, <a>mul_right_comm<\\/a>, \\u2190 <a>ENNReal.ofReal_natCast<\\/a>, \\u2190 <a>ENNReal.ofReal_mul<\\/a>, <a>mul_div_cancel\\u2080<\\/a>]\"",
+                "[{\"full_name\":\"Homeomorph.measurableEmbedding\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/BorelSpace\\/Basic.lean\",\"def_pos\":[577,7],\"def_end_pos\":[577,37]},{\"full_name\":\"MeasurableEmbedding.map_apply\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Measure\\/MeasureSpace.lean\",\"def_pos\":[2160,16],\"def_end_pos\":[2160,25]},{\"full_name\":\"MeasureTheory.Measure.toSphere_apply'\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/HaarToSphere.lean\",\"def_pos\":[55,9],\"def_end_pos\":[55,24]},{\"full_name\":\"MeasureTheory.Measure.volumeIoiPow_apply_Iio\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/HaarToSphere.lean\",\"def_pos\":[82,7],\"def_end_pos\":[82,29]},{\"full_name\":\"comap_subtype_coe_apply\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Measure\\/Restrict.lean\",\"def_pos\":[945,9],\"def_end_pos\":[945,32]},{\"full_name\":\"MeasurableSingletonClass.measurableSet_singleton\",\"def_path\":\"Mathlib\\/MeasureTheory\\/MeasurableSpace\\/Defs.lean\",\"def_pos\":[275,3],\"def_end_pos\":[275,26]},{\"full_name\":\"MeasurableSet.compl\",\"def_path\":\"Mathlib\\/MeasureTheory\\/MeasurableSpace\\/Defs.lean\",\"def_pos\":[89,19],\"def_end_pos\":[89,38]},{\"full_name\":\"MeasureTheory.Measure.toSphere_apply_aux\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/HaarToSphere.lean\",\"def_pos\":[49,9],\"def_end_pos\":[49,27]},{\"full_name\":\"smul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[255,7],\"def_end_pos\":[255,17]},{\"full_name\":\"Nat.sub_add_cancel\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[893,27],\"def_end_pos\":[893,41]},{\"full_name\":\"Nat.cast_pred\",\"def_path\":\"Mathlib\\/Data\\/Int\\/Cast\\/Basic.lean\",\"def_pos\":[39,9],\"def_end_pos\":[39,18]},{\"full_name\":\"sub_add_cancel\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[997,3],\"def_end_pos\":[997,14]},{\"full_name\":\"mul_right_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[190,9],\"def_end_pos\":[190,23]},{\"full_name\":\"ENNReal.ofReal_natCast\",\"def_path\":\"Mathlib\\/Data\\/ENNReal\\/Basic.lean\",\"def_pos\":[559,26],\"def_end_pos\":[559,40]},{\"full_name\":\"ENNReal.ofReal_mul\",\"def_path\":\"Mathlib\\/Data\\/ENNReal\\/Real.lean\",\"def_pos\":[353,9],\"def_end_pos\":[353,19]},{\"full_name\":\"mul_div_cancel\\u2080\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Units\\/Basic.lean\",\"def_pos\":[516,7],\"def_end_pos\":[516,22]}]"
+              ],
+              "state_after": "case hb\nE : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\na\u271d : Nontrivial E\ns : Set \u2191(sphere 0 1)\nhs : s \u2208 {s | MeasurableSet s}\nr : \u2191(Ioi 0)\nthis : Ioo 0 \u2191r = \u2191r \u2022 Ioo 0 1\nhpos : 0 < dim E\n\u22a2 \u2191(dim E) \u2260 0\n\nE : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\na\u271d : Nontrivial E\ns : Set \u2191(sphere 0 1)\nhs : s \u2208 {s | MeasurableSet s}\nr : \u2191(Ioi 0)\nthis : Ioo 0 \u2191r = \u2191r \u2022 Ioo 0 1\nhpos : 0 < dim E\n\u22a2 0 \u2264 \u2191(dim E)",
+              "state_before": "E : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\na\u271d : Nontrivial E\ns : Set \u2191(sphere 0 1)\nhs : s \u2208 {s | MeasurableSet s}\nr : \u2191(Ioi 0)\nthis : Ioo 0 \u2191r = \u2191r \u2022 Ioo 0 1\nhpos : 0 < dim E\n\u22a2 (map (\u21d1(homeomorphUnitSphereProd E)) (comap Subtype.val \u03bc)) (s \u00d7\u02e2 Iio r) =\n    \u03bc.toSphere s * (volumeIoiPow (dim E - 1)) (Iio r)",
+              "tactic": "rw [(Homeomorph.measurableEmbedding _).map_apply, toSphere_apply' _ hs, volumeIoiPow_apply_Iio,\n  comap_subtype_coe_apply (measurableSet_singleton _).compl, toSphere_apply_aux, this,\n  smul_assoc, \u03bc.addHaar_smul_of_nonneg r.2.out.le, Nat.sub_add_cancel hpos, Nat.cast_pred hpos,\n  sub_add_cancel, mul_right_comm, \u2190 ENNReal.ofReal_natCast, \u2190 ENNReal.ofReal_mul, mul_div_cancel\u2080]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exacts [(<a>Nat.cast_pos<\\/a>.2 hpos).<a>ne'<\\/a>, <a>Nat.cast_nonneg<\\/a> _]\"",
+                "[{\"full_name\":\"Nat.cast_pos\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Order.lean\",\"def_pos\":[92,9],\"def_end_pos\":[92,17]},{\"full_name\":\"LT.lt.ne'\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[306,9],\"def_end_pos\":[306,12]},{\"full_name\":\"Nat.cast_nonneg\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Order.lean\",\"def_pos\":[50,9],\"def_end_pos\":[50,20]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case hb\nE : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\na\u271d : Nontrivial E\ns : Set \u2191(sphere 0 1)\nhs : s \u2208 {s | MeasurableSet s}\nr : \u2191(Ioi 0)\nthis : Ioo 0 \u2191r = \u2191r \u2022 Ioo 0 1\nhpos : 0 < dim E\n\u22a2 \u2191(dim E) \u2260 0\n\nE : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\na\u271d : Nontrivial E\ns : Set \u2191(sphere 0 1)\nhs : s \u2208 {s | MeasurableSet s}\nr : \u2191(Ioi 0)\nthis : Ioo 0 \u2191r = \u2191r \u2022 Ioo 0 1\nhpos : 0 < dim E\n\u22a2 0 \u2264 \u2191(dim E)",
+              "tactic": "exacts [(Nat.cast_pos.2 hpos).ne', Nat.cast_nonneg _]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>LinearOrderedField.smul_Ioo<\\/a> r.2.<a>out<\\/a>, <a>smul_zero<\\/a>, <a>smul_eq_mul<\\/a>, <a>mul_one<\\/a>]\"",
+                "[{\"full_name\":\"LinearOrderedField.smul_Ioo\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Pointwise.lean\",\"def_pos\":[183,9],\"def_end_pos\":[183,17]},{\"full_name\":\"Membership.mem.out\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[237,9],\"def_end_pos\":[237,34]},{\"full_name\":\"smul_zero\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Defs.lean\",\"def_pos\":[66,9],\"def_end_pos\":[66,18]},{\"full_name\":\"smul_eq_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[89,7],\"def_end_pos\":[89,18]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "E : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\na\u271d : Nontrivial E\ns : Set \u2191(sphere 0 1)\nhs : s \u2208 {s | MeasurableSet s}\nr : \u2191(Ioi 0)\n\u22a2 Ioo 0 \u2191r = \u2191r \u2022 Ioo 0 1",
+              "tactic": "rw [LinearOrderedField.smul_Ioo r.2.out, smul_zero, smul_eq_mul, mul_one]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/HaarToSphere.lean"
+      }
+    ],
+    "input_proofs": 15,
+    "input_units": 2,
+    "proofs": 7,
+    "published_proofs": 5,
+    "published_transitions": 8,
+    "replay_failures": [],
+    "transitions": 18,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/MeasureTheory/Constructions/HaarToSphere.lean",
+        "proof_id": "mathlib:MeasureTheory.Measure.volumeIoiPow_apply_Iio",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              91,
+              31
+            ],
+            "file_path": "Mathlib/MeasureTheory/Constructions/HaarToSphere.lean",
+            "full_name": "MeasureTheory.Measure.volumeIoiPow_apply_Iio",
+            "start": [
+              82,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"have hr\\u2080 : 0 \\u2264 x.1 := <a>le_of_lt<\\/a> x.2\"",
+                  "[{\"full_name\":\"le_of_lt\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[110,9],\"def_end_pos\":[110,17]}]"
+                ],
+                "state_after": "E : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\nn : \u2115\nx : \u2191(Ioi 0)\nhr\u2080 : 0 \u2264 \u2191x\n\u22a2 (volumeIoiPow n) (Iio x) = ENNReal.ofReal (\u2191x ^ (n + 1) / (\u2191n + 1))",
+                "state_before": "E : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\nn : \u2115\nx : \u2191(Ioi 0)\n\u22a2 (volumeIoiPow n) (Iio x) = ENNReal.ofReal (\u2191x ^ (n + 1) / (\u2191n + 1))",
+                "tactic": "have hr\u2080 : 0 \u2264 x.1 := le_of_lt x.2"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>volumeIoiPow<\\/a>, <a>withDensity_apply<\\/a> _ <a>measurableSet_Iio<\\/a>,\\n    <a>setLIntegral_subtype<\\/a> <a>measurableSet_Ioi<\\/a> _ fun a : \\u211d \\u21a6 .ofReal (a ^ n),\\n    <a>image_subtype_val_Ioi_Iio<\\/a>, <a>restrict_congr_set<\\/a> <a>Ioo_ae_eq_Ioc<\\/a>,\\n    \\u2190 <a>ofReal_integral_eq_lintegral_ofReal<\\/a> (<a>intervalIntegrable_pow<\\/a> _).1, \\u2190 <a>integral_of_le<\\/a> hr\\u2080]\"",
+                  "[{\"full_name\":\"MeasureTheory.Measure.volumeIoiPow\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/HaarToSphere.lean\",\"def_pos\":[79,5],\"def_end_pos\":[79,17]},{\"full_name\":\"MeasureTheory.withDensity_apply\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Measure\\/WithDensity.lean\",\"def_pos\":[39,9],\"def_end_pos\":[39,26]},{\"full_name\":\"measurableSet_Iio\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/BorelSpace\\/Order.lean\",\"def_pos\":[182,9],\"def_end_pos\":[182,26]},{\"full_name\":\"MeasureTheory.setLIntegral_subtype\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Integral\\/Lebesgue.lean\",\"def_pos\":[1578,9],\"def_end_pos\":[1578,29]},{\"full_name\":\"measurableSet_Ioi\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/BorelSpace\\/Order.lean\",\"def_pos\":[187,9],\"def_end_pos\":[187,26]},{\"full_name\":\"Set.image_subtype_val_Ioi_Iio\",\"def_path\":\"Mathlib\\/Order\\/Interval\\/Set\\/Image.lean\",\"def_pos\":[334,7],\"def_end_pos\":[334,32]},{\"full_name\":\"MeasureTheory.Measure.restrict_congr_set\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Measure\\/Restrict.lean\",\"def_pos\":[96,9],\"def_end_pos\":[96,27]},{\"full_name\":\"MeasureTheory.Ioo_ae_eq_Ioc\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Measure\\/Typeclasses.lean\",\"def_pos\":[433,9],\"def_end_pos\":[433,22]},{\"full_name\":\"MeasureTheory.ofReal_integral_eq_lintegral_ofReal\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Integral\\/Bochner.lean\",\"def_pos\":[1204,9],\"def_end_pos\":[1204,44]},{\"full_name\":\"intervalIntegral.intervalIntegrable_pow\",\"def_path\":\"Mathlib\\/Analysis\\/SpecialFunctions\\/Integrals.lean\",\"def_pos\":[54,9],\"def_end_pos\":[54,31]},{\"full_name\":\"intervalIntegral.integral_of_le\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Integral\\/IntervalIntegral.lean\",\"def_pos\":[487,9],\"def_end_pos\":[487,23]}]"
+                ],
+                "state_after": "E : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\nn : \u2115\nx : \u2191(Ioi 0)\nhr\u2080 : 0 \u2264 \u2191x\n\u22a2 ENNReal.ofReal (\u222b (x : \u211d) in 0 ..\u2191x, x ^ n) = ENNReal.ofReal (\u2191x ^ (n + 1) / (\u2191n + 1))\n\nE : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\nn : \u2115\nx : \u2191(Ioi 0)\nhr\u2080 : 0 \u2264 \u2191x\n\u22a2 0 \u2264\u1da0[ae (volume.restrict (Ioc 0 \u2191x))] fun x => x ^ n",
+                "state_before": "E : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\nn : \u2115\nx : \u2191(Ioi 0)\nhr\u2080 : 0 \u2264 \u2191x\n\u22a2 (volumeIoiPow n) (Iio x) = ENNReal.ofReal (\u2191x ^ (n + 1) / (\u2191n + 1))",
+                "tactic": "rw [volumeIoiPow, withDensity_apply _ measurableSet_Iio,\n  setLIntegral_subtype measurableSet_Ioi _ fun a : \u211d \u21a6 .ofReal (a ^ n),\n  image_subtype_val_Ioi_Iio, restrict_congr_set Ioo_ae_eq_Ioc,\n  \u2190 ofReal_integral_eq_lintegral_ofReal (intervalIntegrable_pow _).1, \u2190 integral_of_le hr\u2080]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "E : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\nn : \u2115\nx : \u2191(Ioi 0)\nhr\u2080 : 0 \u2264 \u2191x\n\u22a2 ENNReal.ofReal (\u222b (x : \u211d) in 0 ..\u2191x, x ^ n) = ENNReal.ofReal (\u2191x ^ (n + 1) / (\u2191n + 1))",
+                "tactic": "simp"
+              },
+              {
+                "annotated_tactic": [
+                  "\"filter_upwards [<a>ae_restrict_mem<\\/a> <a>measurableSet_Ioc<\\/a>] with y hy\"",
+                  "[{\"full_name\":\"MeasureTheory.ae_restrict_mem\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Measure\\/Restrict.lean\",\"def_pos\":[653,9],\"def_end_pos\":[653,24]},{\"full_name\":\"measurableSet_Ioc\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/BorelSpace\\/Order.lean\",\"def_pos\":[197,9],\"def_end_pos\":[197,26]}]"
+                ],
+                "state_after": "case h\nE : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\nn : \u2115\nx : \u2191(Ioi 0)\nhr\u2080 : 0 \u2264 \u2191x\ny : \u211d\nhy : y \u2208 Ioc 0 \u2191x\n\u22a2 0 y \u2264 y ^ n",
+                "state_before": "E : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\nn : \u2115\nx : \u2191(Ioi 0)\nhr\u2080 : 0 \u2264 \u2191x\n\u22a2 0 \u2264\u1da0[ae (volume.restrict (Ioc 0 \u2191x))] fun x => x ^ n",
+                "tactic": "filter_upwards [ae_restrict_mem measurableSet_Ioc] with y hy"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact <a>pow_nonneg<\\/a> hy.1.<a>le<\\/a> _\"",
+                  "[{\"full_name\":\"pow_nonneg\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Ring\\/Defs.lean\",\"def_pos\":[241,9],\"def_end_pos\":[241,19]},{\"full_name\":\"LT.lt.le\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[137,7],\"def_end_pos\":[137,15]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case h\nE : Type u_1\ninst\u271d\u2075 : NormedAddCommGroup E\ninst\u271d\u2074 : NormedSpace \u211d E\ninst\u271d\u00b3 : FiniteDimensional \u211d E\ninst\u271d\u00b2 : MeasurableSpace E\ninst\u271d\u00b9 : BorelSpace E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\nn : \u2115\nx : \u2191(Ioi 0)\nhr\u2080 : 0 \u2264 \u2191x\ny : \u211d\nhy : y \u2208 Ioc 0 \u2191x\n\u22a2 0 y \u2264 y ^ n",
+                "tactic": "exact pow_nonneg hy.1.le _"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "MeasureTheory.Measure.volumeIoiPow_apply_Iio"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/MeasureTheory/Constructions/HaarToSphere.lean",
+        "proof_id": "mathlib:MeasureTheory.integral_fun_norm_addHaar",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              150,
+              65
+            ],
+            "file_path": "Mathlib/MeasureTheory/Constructions/HaarToSphere.lean",
+            "full_name": "MeasureTheory.integral_fun_norm_addHaar",
+            "start": [
+              132,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>integral_subtype_comap<\\/a> (<a>measurableSet_singleton<\\/a> _).<a>compl<\\/a> fun x \\u21a6 f (\\u2016x\\u2016),\\n        <a>restrict_compl_singleton<\\/a>]\"",
+                  "[{\"full_name\":\"MeasureTheory.integral_subtype_comap\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Integral\\/Bochner.lean\",\"def_pos\":[1743,9],\"def_end_pos\":[1743,31]},{\"full_name\":\"MeasurableSingletonClass.measurableSet_singleton\",\"def_path\":\"Mathlib\\/MeasureTheory\\/MeasurableSpace\\/Defs.lean\",\"def_pos\":[275,3],\"def_end_pos\":[275,26]},{\"full_name\":\"MeasurableSet.compl\",\"def_path\":\"Mathlib\\/MeasureTheory\\/MeasurableSpace\\/Defs.lean\",\"def_pos\":[89,19],\"def_end_pos\":[89,38]},{\"full_name\":\"MeasureTheory.restrict_compl_singleton\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Measure\\/Typeclasses.lean\",\"def_pos\":[406,7],\"def_end_pos\":[406,31]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "E : Type u_1\ninst\u271d\u2078 : NormedAddCommGroup E\ninst\u271d\u2077 : NormedSpace \u211d E\ninst\u271d\u2076 : FiniteDimensional \u211d E\ninst\u271d\u2075 : MeasurableSpace E\ninst\u271d\u2074 : BorelSpace E\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \u211d F\ninst\u271d\u00b9 : Nontrivial E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\nf : \u211d \u2192 F\n\u22a2 \u222b (x : E), f \u2016x\u2016 \u2202\u03bc = \u222b (x : \u2191{0}\u1d9c), f \u2016\u2191x\u2016 \u2202Measure.comap Subtype.val \u03bc",
+                "tactic": "rw [integral_subtype_comap (measurableSet_singleton _).compl fun x \u21a6 f (\u2016x\u2016),\n  restrict_compl_singleton]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp only [<a>Measure.volumeIoiPow<\\/a>, <a>ENNReal.ofReal<\\/a>]\"",
+                  "[{\"full_name\":\"MeasureTheory.Measure.volumeIoiPow\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/HaarToSphere.lean\",\"def_pos\":[79,5],\"def_end_pos\":[79,17]},{\"full_name\":\"ENNReal.ofReal\",\"def_path\":\"Mathlib\\/Data\\/ENNReal\\/Basic.lean\",\"def_pos\":[198,29],\"def_end_pos\":[198,35]}]"
+                ],
+                "state_after": "E : Type u_1\ninst\u271d\u2078 : NormedAddCommGroup E\ninst\u271d\u2077 : NormedSpace \u211d E\ninst\u271d\u2076 : FiniteDimensional \u211d E\ninst\u271d\u2075 : MeasurableSpace E\ninst\u271d\u2074 : BorelSpace E\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \u211d F\ninst\u271d\u00b9 : Nontrivial E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\nf : \u211d \u2192 F\n\u22a2 ((\u03bc.toSphere univ).toReal \u2022\n      \u222b (x : \u2191(Ioi 0)), f \u2191x \u2202(Measure.comap Subtype.val volume).withDensity fun r => \u2191(\u2191r ^ (dim E - 1)).toNNReal) =\n    dim E \u2022 (\u03bc (ball 0 1)).toReal \u2022 \u222b (y : \u211d) in Ioi 0, y ^ (dim E - 1) \u2022 f y",
+                "state_before": "E : Type u_1\ninst\u271d\u2078 : NormedAddCommGroup E\ninst\u271d\u2077 : NormedSpace \u211d E\ninst\u271d\u2076 : FiniteDimensional \u211d E\ninst\u271d\u2075 : MeasurableSpace E\ninst\u271d\u2074 : BorelSpace E\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \u211d F\ninst\u271d\u00b9 : Nontrivial E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\nf : \u211d \u2192 F\n\u22a2 (\u03bc.toSphere univ).toReal \u2022 \u222b (x : \u2191(Ioi 0)), f \u2191x \u2202Measure.volumeIoiPow (dim E - 1) =\n    dim E \u2022 (\u03bc (ball 0 1)).toReal \u2022 \u222b (y : \u211d) in Ioi 0, y ^ (dim E - 1) \u2022 f y",
+                "tactic": "simp only [Measure.volumeIoiPow, ENNReal.ofReal]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>integral_withDensity_eq_integral_smul<\\/a>, \\u03bc.toSphere_apply_univ,\\n        <a>ENNReal.toReal_mul<\\/a>, <a>ENNReal.toReal_nat<\\/a>, \\u2190 <a>nsmul_eq_mul<\\/a>, <a>smul_assoc<\\/a>,\\n        <a>integral_subtype_comap<\\/a> <a>measurableSet_Ioi<\\/a> fun a \\u21a6 <a>Real.toNNReal<\\/a> (a ^ (dim E - 1)) \\u2022 f a,\\n        <a>setIntegral_congr<\\/a> <a>measurableSet_Ioi<\\/a> fun x hx \\u21a6 ?_]\"",
+                  "[{\"full_name\":\"integral_withDensity_eq_integral_smul\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Integral\\/SetIntegral.lean\",\"def_pos\":[1465,9],\"def_end_pos\":[1465,46]},{\"full_name\":\"ENNReal.toReal_mul\",\"def_path\":\"Mathlib\\/Data\\/ENNReal\\/Real.lean\",\"def_pos\":[425,9],\"def_end_pos\":[425,19]},{\"full_name\":\"ENNReal.toReal_nat\",\"def_path\":\"Mathlib\\/Data\\/ENNReal\\/Basic.lean\",\"def_pos\":[582,9],\"def_end_pos\":[582,19]},{\"full_name\":\"nsmul_eq_mul\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Basic.lean\",\"def_pos\":[81,15],\"def_end_pos\":[81,34]},{\"full_name\":\"smul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[255,7],\"def_end_pos\":[255,17]},{\"full_name\":\"MeasureTheory.integral_subtype_comap\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Integral\\/Bochner.lean\",\"def_pos\":[1743,9],\"def_end_pos\":[1743,31]},{\"full_name\":\"measurableSet_Ioi\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/BorelSpace\\/Order.lean\",\"def_pos\":[187,9],\"def_end_pos\":[187,26]},{\"full_name\":\"Real.toNNReal\",\"def_path\":\"Mathlib\\/Data\\/NNReal\\/Basic.lean\",\"def_pos\":[120,19],\"def_end_pos\":[120,39]},{\"full_name\":\"MeasureTheory.setIntegral_congr\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Integral\\/SetIntegral.lean\",\"def_pos\":[95,9],\"def_end_pos\":[95,26]},{\"full_name\":\"measurableSet_Ioi\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/BorelSpace\\/Order.lean\",\"def_pos\":[187,9],\"def_end_pos\":[187,26]}]"
+                ],
+                "state_after": "E : Type u_1\ninst\u271d\u2078 : NormedAddCommGroup E\ninst\u271d\u2077 : NormedSpace \u211d E\ninst\u271d\u2076 : FiniteDimensional \u211d E\ninst\u271d\u2075 : MeasurableSpace E\ninst\u271d\u2074 : BorelSpace E\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \u211d F\ninst\u271d\u00b9 : Nontrivial E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\nf : \u211d \u2192 F\nx : \u211d\nhx : x \u2208 Ioi 0\n\u22a2 (x ^ (dim E - 1)).toNNReal \u2022 f x = x ^ (dim E - 1) \u2022 f x\n\ncase f_meas\nE : Type u_1\ninst\u271d\u2078 : NormedAddCommGroup E\ninst\u271d\u2077 : NormedSpace \u211d E\ninst\u271d\u2076 : FiniteDimensional \u211d E\ninst\u271d\u2075 : MeasurableSpace E\ninst\u271d\u2074 : BorelSpace E\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \u211d F\ninst\u271d\u00b9 : Nontrivial E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\nf : \u211d \u2192 F\n\u22a2 Measurable fun r => (\u2191r ^ (dim E - 1)).toNNReal",
+                "state_before": "E : Type u_1\ninst\u271d\u2078 : NormedAddCommGroup E\ninst\u271d\u2077 : NormedSpace \u211d E\ninst\u271d\u2076 : FiniteDimensional \u211d E\ninst\u271d\u2075 : MeasurableSpace E\ninst\u271d\u2074 : BorelSpace E\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \u211d F\ninst\u271d\u00b9 : Nontrivial E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\nf : \u211d \u2192 F\n\u22a2 ((\u03bc.toSphere univ).toReal \u2022\n      \u222b (x : \u2191(Ioi 0)), f \u2191x \u2202(Measure.comap Subtype.val volume).withDensity fun r => \u2191(\u2191r ^ (dim E - 1)).toNNReal) =\n    dim E \u2022 (\u03bc (ball 0 1)).toReal \u2022 \u222b (y : \u211d) in Ioi 0, y ^ (dim E - 1) \u2022 f y",
+                "tactic": "rw [integral_withDensity_eq_integral_smul, \u03bc.toSphere_apply_univ,\n  ENNReal.toReal_mul, ENNReal.toReal_nat, \u2190 nsmul_eq_mul, smul_assoc,\n  integral_subtype_comap measurableSet_Ioi fun a \u21a6 Real.toNNReal (a ^ (dim E - 1)) \u2022 f a,\n  setIntegral_congr measurableSet_Ioi fun x hx \u21a6 ?_]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>NNReal.smul_def<\\/a>, <a>Real.coe_toNNReal<\\/a> _ (<a>pow_nonneg<\\/a> hx.out.le _)]\"",
+                  "[{\"full_name\":\"NNReal.smul_def\",\"def_path\":\"Mathlib\\/Data\\/NNReal\\/Basic.lean\",\"def_pos\":[245,9],\"def_end_pos\":[245,17]},{\"full_name\":\"Real.coe_toNNReal\",\"def_path\":\"Mathlib\\/Data\\/NNReal\\/Basic.lean\",\"def_pos\":[124,9],\"def_end_pos\":[124,33]},{\"full_name\":\"pow_nonneg\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Ring\\/Defs.lean\",\"def_pos\":[241,9],\"def_end_pos\":[241,19]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "E : Type u_1\ninst\u271d\u2078 : NormedAddCommGroup E\ninst\u271d\u2077 : NormedSpace \u211d E\ninst\u271d\u2076 : FiniteDimensional \u211d E\ninst\u271d\u2075 : MeasurableSpace E\ninst\u271d\u2074 : BorelSpace E\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \u211d F\ninst\u271d\u00b9 : Nontrivial E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\nf : \u211d \u2192 F\nx : \u211d\nhx : x \u2208 Ioi 0\n\u22a2 (x ^ (dim E - 1)).toNNReal \u2022 f x = x ^ (dim E - 1) \u2022 f x",
+                "tactic": "rw [NNReal.smul_def, Real.coe_toNNReal _ (pow_nonneg hx.out.le _)]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact (measurable_subtype_coe.pow_const _).<a>real_toNNReal<\\/a>\"",
+                  "[{\"full_name\":\"Measurable.real_toNNReal\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/BorelSpace\\/Real.lean\",\"def_pos\":[147,9],\"def_end_pos\":[147,33]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case f_meas\nE : Type u_1\ninst\u271d\u2078 : NormedAddCommGroup E\ninst\u271d\u2077 : NormedSpace \u211d E\ninst\u271d\u2076 : FiniteDimensional \u211d E\ninst\u271d\u2075 : MeasurableSpace E\ninst\u271d\u2074 : BorelSpace E\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup F\ninst\u271d\u00b2 : NormedSpace \u211d F\ninst\u271d\u00b9 : Nontrivial E\n\u03bc : Measure E\ninst\u271d : \u03bc.IsAddHaarMeasure\nf : \u211d \u2192 F\n\u22a2 Measurable fun r => (\u2191r ^ (dim E - 1)).toNNReal",
+                "tactic": "exact (measurable_subtype_coe.pow_const _).real_toNNReal"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "MeasureTheory.integral_fun_norm_addHaar"
+      }
+    ],
+    "validation_rejected_proofs": 2,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001356-0000-77bca5979d62c001.parquet",
+      "sha256": "77bca5979d62c001c19ac0a13cf2b6e87d3c902f48a63ee5a35b43d9b96af6a5",
+      "bytes": 54312,
+      "rows": 3,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    },
+    {
+      "path": "data/internal_test/mathlib-001356-0000-ca025fae524a6495.parquet",
+      "sha256": "ca025fae524a6495722989a49b568d772a4b541f384f8dfe20894644c65cf1a4",
+      "bytes": 63391,
+      "rows": 5,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:EventuallyMeasurableSet.congr",
+    "mathlib:MeasureTheory.Measure.toSphere_apply'",
+    "mathlib:MeasureTheory.Measure.toSphere_apply_aux",
+    "mathlib:MeasureTheory.Measure.toSphere_apply_univ",
+    "mathlib:MeasureTheory.Measure.toSphere_apply_univ'"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Constructions/EventuallyMeasurable.lean\",null,null,\"EventuallyMeasurableSet.congr\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Constructions/HaarToSphere.lean\",null,null,\"MeasureTheory.Measure.toSphere_apply'\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Constructions/HaarToSphere.lean\",null,null,\"MeasureTheory.Measure.toSphere_apply_aux\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Constructions/HaarToSphere.lean\",null,null,\"MeasureTheory.Measure.toSphere_apply_univ\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Constructions/HaarToSphere.lean\",null,null,\"MeasureTheory.Measure.toSphere_apply_univ'\"]"
+  ]
+}

manifests/batches/mathlib/001359.json

@@ -0,0 +1,459 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001359",
+  "batch_fingerprint": "0fb01706090a1116c35347acf944da6b07ed8a6f6c50827266ed0cb15549d75d",
+  "evidence": {
+    "batch_fingerprint": "0fb01706090a1116c35347acf944da6b07ed8a6f6c50827266ed0cb15549d75d",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "no internal trace for tactic 'have h_eq_union : cylinder J T = cylinder (I \u222a J) U := by\\n  rw [\u2190 inter_cylinder, h_eq, inter_self]'",
+        "full_name": "MeasureTheory.IsProjectiveMeasureFamily.congr_cylinder",
+        "id": "MeasureTheory.IsProjectiveMeasureFamily.congr_cylinder",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            102,
+            83
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/Projective.lean",
+          "full_name": "MeasureTheory.IsProjectiveMeasureFamily.congr_cylinder",
+          "start": [
+            87,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"let U := (fun f : \\u2200 i : (I \\u222a J : <a>Finset<\\/a> \\u03b9), \\u03b1 i\\n        \\u21a6 fun j : I \\u21a6 f \\u27e8j, <a>Finset.mem_union_left<\\/a> J j.prop\\u27e9) \\u207b\\u00b9' S \\u2229\\n      (fun f \\u21a6 fun j : J \\u21a6 f \\u27e8j, <a>Finset.mem_union_right<\\/a> I j.prop\\u27e9) \\u207b\\u00b9' T\"",
+                "[{\"full_name\":\"Finset\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[135,11],\"def_end_pos\":[135,17]},{\"full_name\":\"Finset.mem_union_left\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[1413,9],\"def_end_pos\":[1413,23]},{\"full_name\":\"Finset.mem_union_right\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[1417,9],\"def_end_pos\":[1417,24]}]"
+              ],
+              "state_after": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhS : MeasurableSet S\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nU : Set ((i : { x // x \u2208 I \u222a J }) \u2192 \u03b1 \u2191i) := (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' S \u2229 (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' T\n\u22a2 (P I) S = (P J) T",
+              "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhS : MeasurableSet S\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\n\u22a2 (P I) S = (P J) T",
+              "tactic": "let U := (fun f : \u2200 i : (I \u222a J : Finset \u03b9), \u03b1 i\n      \u21a6 fun j : I \u21a6 f \u27e8j, Finset.mem_union_left J j.prop\u27e9) \u207b\u00b9' S \u2229\n    (fun f \u21a6 fun j : J \u21a6 f \u27e8j, Finset.mem_union_right I j.prop\u27e9) \u207b\u00b9' T"
+            },
+            {
+              "annotated_tactic": [
+                "\"suffices P (I \\u222a J) U = P I S \\u2227 P (I \\u222a J) U = P J T from this.1.symm.trans this.2\"",
+                "[]"
+              ],
+              "state_after": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhS : MeasurableSet S\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nU : Set ((i : { x // x \u2208 I \u222a J }) \u2192 \u03b1 \u2191i) := (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' S \u2229 (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' T\n\u22a2 (P (I \u222a J)) U = (P I) S \u2227 (P (I \u222a J)) U = (P J) T",
+              "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhS : MeasurableSet S\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nU : Set ((i : { x // x \u2208 I \u222a J }) \u2192 \u03b1 \u2191i) := (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' S \u2229 (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' T\n\u22a2 (P I) S = (P J) T",
+              "tactic": "suffices P (I \u222a J) U = P I S \u2227 P (I \u222a J) U = P J T from this.1.symm.trans this.2"
+            },
+            {
+              "annotated_tactic": [
+                "\"constructor\"",
+                "[]"
+              ],
+              "state_after": "case left\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhS : MeasurableSet S\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nU : Set ((i : { x // x \u2208 I \u222a J }) \u2192 \u03b1 \u2191i) := (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' S \u2229 (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' T\n\u22a2 (P (I \u222a J)) U = (P I) S\n\ncase right\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhS : MeasurableSet S\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nU : Set ((i : { x // x \u2208 I \u222a J }) \u2192 \u03b1 \u2191i) := (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' S \u2229 (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' T\n\u22a2 (P (I \u222a J)) U = (P J) T",
+              "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhS : MeasurableSet S\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nU : Set ((i : { x // x \u2208 I \u222a J }) \u2192 \u03b1 \u2191i) := (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' S \u2229 (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' T\n\u22a2 (P (I \u222a J)) U = (P I) S \u2227 (P (I \u222a J)) U = (P J) T",
+              "tactic": "constructor"
+            },
+            {
+              "annotated_tactic": [
+                "\"have h_eq_union : <a>cylinder<\\/a> I S = <a>cylinder<\\/a> (I \\u222a J) U := by\\n      rw [\\u2190 <a>inter_cylinder<\\/a>, h_eq, <a>inter_self<\\/a>]\"",
+                "[{\"full_name\":\"MeasureTheory.cylinder\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/Cylinders.lean\",\"def_pos\":[152,5],\"def_end_pos\":[152,13]},{\"full_name\":\"MeasureTheory.cylinder\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/Cylinders.lean\",\"def_pos\":[152,5],\"def_end_pos\":[152,13]},{\"full_name\":\"MeasureTheory.inter_cylinder\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/Cylinders.lean\",\"def_pos\":[185,9],\"def_end_pos\":[185,23]},{\"full_name\":\"Set.inter_self\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[891,9],\"def_end_pos\":[891,19]}]"
+              ],
+              "state_after": "case left\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhS : MeasurableSet S\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nU : Set ((i : { x // x \u2208 I \u222a J }) \u2192 \u03b1 \u2191i) := (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' S \u2229 (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' T\nh_eq_union : cylinder I S = cylinder (I \u222a J) U\n\u22a2 (P (I \u222a J)) U = (P I) S",
+              "state_before": "case left\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhS : MeasurableSet S\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nU : Set ((i : { x // x \u2208 I \u222a J }) \u2192 \u03b1 \u2191i) := (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' S \u2229 (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' T\n\u22a2 (P (I \u222a J)) U = (P I) S",
+              "tactic": "have h_eq_union : cylinder I S = cylinder (I \u222a J) U := by\n  rw [\u2190 inter_cylinder, h_eq, inter_self]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact hP.congr_cylinder_of_subset hS h_eq_union.symm <a>Finset.subset_union_left<\\/a>\"",
+                "[{\"full_name\":\"Finset.subset_union_left\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[1438,9],\"def_end_pos\":[1438,26]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case left\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhS : MeasurableSet S\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nU : Set ((i : { x // x \u2208 I \u222a J }) \u2192 \u03b1 \u2191i) := (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' S \u2229 (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' T\nh_eq_union : cylinder I S = cylinder (I \u222a J) U\n\u22a2 (P (I \u222a J)) U = (P I) S",
+              "tactic": "exact hP.congr_cylinder_of_subset hS h_eq_union.symm Finset.subset_union_left"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>inter_cylinder<\\/a>, h_eq, <a>inter_self<\\/a>]\"",
+                "[{\"full_name\":\"MeasureTheory.inter_cylinder\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/Cylinders.lean\",\"def_pos\":[185,9],\"def_end_pos\":[185,23]},{\"full_name\":\"Set.inter_self\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[891,9],\"def_end_pos\":[891,19]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhS : MeasurableSet S\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nU : Set ((i : { x // x \u2208 I \u222a J }) \u2192 \u03b1 \u2191i) := (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' S \u2229 (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' T\n\u22a2 cylinder I S = cylinder (I \u222a J) U",
+              "tactic": "rw [\u2190 inter_cylinder, h_eq, inter_self]"
+            },
+            {
+              "annotated_tactic": [
+                "\"have h_eq_union : <a>cylinder<\\/a> J T = <a>cylinder<\\/a> (I \\u222a J) U := by\\n      rw [\\u2190 <a>inter_cylinder<\\/a>, h_eq, <a>inter_self<\\/a>]\"",
+                "[{\"full_name\":\"MeasureTheory.cylinder\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/Cylinders.lean\",\"def_pos\":[152,5],\"def_end_pos\":[152,13]},{\"full_name\":\"MeasureTheory.cylinder\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/Cylinders.lean\",\"def_pos\":[152,5],\"def_end_pos\":[152,13]},{\"full_name\":\"MeasureTheory.inter_cylinder\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/Cylinders.lean\",\"def_pos\":[185,9],\"def_end_pos\":[185,23]},{\"full_name\":\"Set.inter_self\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[891,9],\"def_end_pos\":[891,19]}]"
+              ],
+              "state_after": "case right\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhS : MeasurableSet S\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nU : Set ((i : { x // x \u2208 I \u222a J }) \u2192 \u03b1 \u2191i) := (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' S \u2229 (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' T\nh_eq_union : cylinder J T = cylinder (I \u222a J) U\n\u22a2 (P (I \u222a J)) U = (P J) T",
+              "state_before": "case right\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhS : MeasurableSet S\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nU : Set ((i : { x // x \u2208 I \u222a J }) \u2192 \u03b1 \u2191i) := (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' S \u2229 (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' T\n\u22a2 (P (I \u222a J)) U = (P J) T",
+              "tactic": "have h_eq_union : cylinder J T = cylinder (I \u222a J) U := by\n  rw [\u2190 inter_cylinder, h_eq, inter_self]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact hP.congr_cylinder_of_subset hT h_eq_union.symm <a>Finset.subset_union_right<\\/a>\"",
+                "[{\"full_name\":\"Finset.subset_union_right\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[1441,9],\"def_end_pos\":[1441,27]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case right\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhS : MeasurableSet S\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nU : Set ((i : { x // x \u2208 I \u222a J }) \u2192 \u03b1 \u2191i) := (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' S \u2229 (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' T\nh_eq_union : cylinder J T = cylinder (I \u222a J) U\n\u22a2 (P (I \u222a J)) U = (P J) T",
+              "tactic": "exact hP.congr_cylinder_of_subset hT h_eq_union.symm Finset.subset_union_right"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>inter_cylinder<\\/a>, h_eq, <a>inter_self<\\/a>]\"",
+                "[{\"full_name\":\"MeasureTheory.inter_cylinder\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/Cylinders.lean\",\"def_pos\":[185,9],\"def_end_pos\":[185,23]},{\"full_name\":\"Set.inter_self\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[891,9],\"def_end_pos\":[891,19]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhS : MeasurableSet S\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nU : Set ((i : { x // x \u2208 I \u222a J }) \u2192 \u03b1 \u2191i) := (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' S \u2229 (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' T\n\u22a2 cylinder J T = cylinder (I \u222a J) U",
+              "tactic": "rw [\u2190 inter_cylinder, h_eq, inter_self]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/Projective.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'suffices \u2200 I, P I univ = 0 by\\n  simp only [Measure.measure_univ_eq_zero] at this\\n  simp [this]'",
+        "full_name": "MeasureTheory.IsProjectiveMeasureFamily.congr_cylinder_of_subset",
+        "id": "MeasureTheory.IsProjectiveMeasureFamily.congr_cylinder_of_subset",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            85,
+            65
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/Projective.lean",
+          "full_name": "MeasureTheory.IsProjectiveMeasureFamily.congr_cylinder_of_subset",
+          "start": [
+            66,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"cases <a>isEmpty_or_nonempty<\\/a> (\\u2200 i, \\u03b1 i) with\\n  | <a>inl<\\/a> h =>\\n    suffices \\u2200 I, P I <a>univ<\\/a> = 0 by\\n      simp only [<a>Measure.measure_univ_eq_zero<\\/a>] at this\\n      simp [this]\\n    intro I\\n    simp only [<a>isEmpty_pi<\\/a>] at h\\n    obtain \\u27e8i, hi_empty\\u27e9 := h\\n    rw [<a>measure_univ_eq<\\/a> hP I {i}]\\n    have : (<a>univ<\\/a> : <a>Set<\\/a> ((j : {x \\/\\/ x \\u2208 ({i} : <a>Finset<\\/a> \\u03b9)}) \\u2192 \\u03b1 j)) = \\u2205 := by simp [hi_empty]\\n    simp [this]\\n  | <a>inr<\\/a> h =>\\n    have : S = (fun f : \\u2200 i : I, \\u03b1 i \\u21a6 fun j : J \\u21a6 f \\u27e8j, hJI j.prop\\u27e9) \\u207b\\u00b9' T :=\\n      <a>eq_of_cylinder_eq_of_subset<\\/a> h_eq hJI\\n    rw [hP I J hJI, <a>Measure.map_apply<\\/a> _ hT, this]\\n    exact <a>measurable_pi_lambda<\\/a> _ (fun _ \\u21a6 <a>measurable_pi_apply<\\/a> _)\"",
+                "[{\"full_name\":\"isEmpty_or_nonempty\",\"def_path\":\"Mathlib\\/Logic\\/IsEmpty.lean\",\"def_pos\":[221,9],\"def_end_pos\":[221,28]},{\"full_name\":\"Or.inl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[534,5],\"def_end_pos\":[534,8]},{\"full_name\":\"Set.univ\",\"def_path\":\"Mathlib\\/Init\\/Set.lean\",\"def_pos\":[153,5],\"def_end_pos\":[153,9]},{\"full_name\":\"MeasureTheory.Measure.measure_univ_eq_zero\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Measure\\/MeasureSpace.lean\",\"def_pos\":[1145,9],\"def_end_pos\":[1145,29]},{\"full_name\":\"isEmpty_pi\",\"def_path\":\"Mathlib\\/Logic\\/IsEmpty.lean\",\"def_pos\":[159,9],\"def_end_pos\":[159,19]},{\"full_name\":\"MeasureTheory.IsProjectiveMeasureFamily.measure_univ_eq\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/Projective.lean\",\"def_pos\":[60,7],\"def_end_pos\":[60,22]},{\"full_name\":\"Set.univ\",\"def_path\":\"Mathlib\\/Init\\/Set.lean\",\"def_pos\":[153,5],\"def_end_pos\":[153,9]},{\"full_name\":\"Set\",\"def_path\":\"Mathlib\\/Init\\/Set.lean\",\"def_pos\":[47,5],\"def_end_pos\":[47,8]},{\"full_name\":\"Finset\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[135,11],\"def_end_pos\":[135,17]},{\"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\":\"MeasureTheory.eq_of_cylinder_eq_of_subset\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/Cylinders.lean\",\"def_pos\":[217,9],\"def_end_pos\":[217,36]},{\"full_name\":\"MeasureTheory.Measure.map_apply\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Measure\\/MeasureSpace.lean\",\"def_pos\":[1291,9],\"def_end_pos\":[1291,18]},{\"full_name\":\"measurable_pi_lambda\",\"def_path\":\"Mathlib\\/MeasureTheory\\/MeasurableSpace\\/Basic.lean\",\"def_pos\":[924,9],\"def_end_pos\":[924,29]},{\"full_name\":\"measurable_pi_apply\",\"def_path\":\"Mathlib\\/MeasureTheory\\/MeasurableSpace\\/Basic.lean\",\"def_pos\":[913,9],\"def_end_pos\":[913,28]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nhJI : J \u2286 I\n\u22a2 (P I) S = (P J) T",
+              "tactic": "cases isEmpty_or_nonempty (\u2200 i, \u03b1 i) with\n| inl h =>\n  suffices \u2200 I, P I univ = 0 by\n    simp only [Measure.measure_univ_eq_zero] at this\n    simp [this]\n  intro I\n  simp only [isEmpty_pi] at h\n  obtain \u27e8i, hi_empty\u27e9 := h\n  rw [measure_univ_eq hP I {i}]\n  have : (univ : Set ((j : {x // x \u2208 ({i} : Finset \u03b9)}) \u2192 \u03b1 j)) = \u2205 := by simp [hi_empty]\n  simp [this]\n| inr h =>\n  have : S = (fun f : \u2200 i : I, \u03b1 i \u21a6 fun j : J \u21a6 f \u27e8j, hJI j.prop\u27e9) \u207b\u00b9' T :=\n    eq_of_cylinder_eq_of_subset h_eq hJI\n  rw [hP I J hJI, Measure.map_apply _ hT, this]\n  exact measurable_pi_lambda _ (fun _ \u21a6 measurable_pi_apply _)"
+            },
+            {
+              "annotated_tactic": [
+                "\"suffices \\u2200 I, P I <a>univ<\\/a> = 0 by\\n      simp only [<a>Measure.measure_univ_eq_zero<\\/a>] at this\\n      simp [this]\"",
+                "[{\"full_name\":\"Set.univ\",\"def_path\":\"Mathlib\\/Init\\/Set.lean\",\"def_pos\":[153,5],\"def_end_pos\":[153,9]},{\"full_name\":\"MeasureTheory.Measure.measure_univ_eq_zero\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Measure\\/MeasureSpace.lean\",\"def_pos\":[1145,9],\"def_end_pos\":[1145,29]}]"
+              ],
+              "state_after": "case inl\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nhJI : J \u2286 I\nh : IsEmpty ((i : \u03b9) \u2192 \u03b1 i)\n\u22a2 \u2200 (I : Finset \u03b9), (P I) univ = 0",
+              "state_before": "case inl\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nhJI : J \u2286 I\nh : IsEmpty ((i : \u03b9) \u2192 \u03b1 i)\n\u22a2 (P I) S = (P J) T",
+              "tactic": "suffices \u2200 I, P I univ = 0 by\n  simp only [Measure.measure_univ_eq_zero] at this\n  simp [this]"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro I\"",
+                "[]"
+              ],
+              "state_after": "case inl\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI\u271d J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I\u271d }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I\u271d S = cylinder J T\nhJI : J \u2286 I\u271d\nh : IsEmpty ((i : \u03b9) \u2192 \u03b1 i)\nI : Finset \u03b9\n\u22a2 (P I) univ = 0",
+              "state_before": "case inl\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nhJI : J \u2286 I\nh : IsEmpty ((i : \u03b9) \u2192 \u03b1 i)\n\u22a2 \u2200 (I : Finset \u03b9), (P I) univ = 0",
+              "tactic": "intro I"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>isEmpty_pi<\\/a>] at h\"",
+                "[{\"full_name\":\"isEmpty_pi\",\"def_path\":\"Mathlib\\/Logic\\/IsEmpty.lean\",\"def_pos\":[159,9],\"def_end_pos\":[159,19]}]"
+              ],
+              "state_after": "case inl\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI\u271d J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I\u271d }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I\u271d S = cylinder J T\nhJI : J \u2286 I\u271d\nI : Finset \u03b9\nh : \u2203 a, IsEmpty (\u03b1 a)\n\u22a2 (P I) univ = 0",
+              "state_before": "case inl\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI\u271d J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I\u271d }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I\u271d S = cylinder J T\nhJI : J \u2286 I\u271d\nh : IsEmpty ((i : \u03b9) \u2192 \u03b1 i)\nI : Finset \u03b9\n\u22a2 (P I) univ = 0",
+              "tactic": "simp only [isEmpty_pi] at h"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8i, hi_empty\\u27e9 := h\"",
+                "[]"
+              ],
+              "state_after": "case inl.intro\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI\u271d J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I\u271d }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I\u271d S = cylinder J T\nhJI : J \u2286 I\u271d\nI : Finset \u03b9\ni : \u03b9\nhi_empty : IsEmpty (\u03b1 i)\n\u22a2 (P I) univ = 0",
+              "state_before": "case inl\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI\u271d J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I\u271d }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I\u271d S = cylinder J T\nhJI : J \u2286 I\u271d\nI : Finset \u03b9\nh : \u2203 a, IsEmpty (\u03b1 a)\n\u22a2 (P I) univ = 0",
+              "tactic": "obtain \u27e8i, hi_empty\u27e9 := h"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>measure_univ_eq<\\/a> hP I {i}]\"",
+                "[{\"full_name\":\"MeasureTheory.IsProjectiveMeasureFamily.measure_univ_eq\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/Projective.lean\",\"def_pos\":[60,7],\"def_end_pos\":[60,22]}]"
+              ],
+              "state_after": "case inl.intro\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI\u271d J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I\u271d }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I\u271d S = cylinder J T\nhJI : J \u2286 I\u271d\nI : Finset \u03b9\ni : \u03b9\nhi_empty : IsEmpty (\u03b1 i)\n\u22a2 (P {i}) univ = 0",
+              "state_before": "case inl.intro\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI\u271d J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I\u271d }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I\u271d S = cylinder J T\nhJI : J \u2286 I\u271d\nI : Finset \u03b9\ni : \u03b9\nhi_empty : IsEmpty (\u03b1 i)\n\u22a2 (P I) univ = 0",
+              "tactic": "rw [measure_univ_eq hP I {i}]"
+            },
+            {
+              "annotated_tactic": [
+                "\"have : (<a>univ<\\/a> : <a>Set<\\/a> ((j : {x \\/\\/ x \\u2208 ({i} : <a>Finset<\\/a> \\u03b9)}) \\u2192 \\u03b1 j)) = \\u2205 := by simp [hi_empty]\"",
+                "[{\"full_name\":\"Set.univ\",\"def_path\":\"Mathlib\\/Init\\/Set.lean\",\"def_pos\":[153,5],\"def_end_pos\":[153,9]},{\"full_name\":\"Set\",\"def_path\":\"Mathlib\\/Init\\/Set.lean\",\"def_pos\":[47,5],\"def_end_pos\":[47,8]},{\"full_name\":\"Finset\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[135,11],\"def_end_pos\":[135,17]}]"
+              ],
+              "state_after": "case inl.intro\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI\u271d J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I\u271d }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I\u271d S = cylinder J T\nhJI : J \u2286 I\u271d\nI : Finset \u03b9\ni : \u03b9\nhi_empty : IsEmpty (\u03b1 i)\nthis : univ = \u2205\n\u22a2 (P {i}) univ = 0",
+              "state_before": "case inl.intro\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI\u271d J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I\u271d }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I\u271d S = cylinder J T\nhJI : J \u2286 I\u271d\nI : Finset \u03b9\ni : \u03b9\nhi_empty : IsEmpty (\u03b1 i)\n\u22a2 (P {i}) univ = 0",
+              "tactic": "have : (univ : Set ((j : {x // x \u2208 ({i} : Finset \u03b9)}) \u2192 \u03b1 j)) = \u2205 := by simp [hi_empty]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [this]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inl.intro\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI\u271d J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I\u271d }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I\u271d S = cylinder J T\nhJI : J \u2286 I\u271d\nI : Finset \u03b9\ni : \u03b9\nhi_empty : IsEmpty (\u03b1 i)\nthis : univ = \u2205\n\u22a2 (P {i}) univ = 0",
+              "tactic": "simp [this]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>Measure.measure_univ_eq_zero<\\/a>] at this\"",
+                "[{\"full_name\":\"MeasureTheory.Measure.measure_univ_eq_zero\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Measure\\/MeasureSpace.lean\",\"def_pos\":[1145,9],\"def_end_pos\":[1145,29]}]"
+              ],
+              "state_after": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nhJI : J \u2286 I\nh : IsEmpty ((i : \u03b9) \u2192 \u03b1 i)\nthis : \u2200 (I : Finset \u03b9), P I = 0\n\u22a2 (P I) S = (P J) T",
+              "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nhJI : J \u2286 I\nh : IsEmpty ((i : \u03b9) \u2192 \u03b1 i)\nthis : \u2200 (I : Finset \u03b9), (P I) univ = 0\n\u22a2 (P I) S = (P J) T",
+              "tactic": "simp only [Measure.measure_univ_eq_zero] at this"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [this]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nhJI : J \u2286 I\nh : IsEmpty ((i : \u03b9) \u2192 \u03b1 i)\nthis : \u2200 (I : Finset \u03b9), P I = 0\n\u22a2 (P I) S = (P J) T",
+              "tactic": "simp [this]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [hi_empty]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI\u271d J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I\u271d }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I\u271d S = cylinder J T\nhJI : J \u2286 I\u271d\nI : Finset \u03b9\ni : \u03b9\nhi_empty : IsEmpty (\u03b1 i)\n\u22a2 univ = \u2205",
+              "tactic": "simp [hi_empty]"
+            },
+            {
+              "annotated_tactic": [
+                "\"have : S = (fun f : \\u2200 i : I, \\u03b1 i \\u21a6 fun j : J \\u21a6 f \\u27e8j, hJI j.prop\\u27e9) \\u207b\\u00b9' T :=\\n      <a>eq_of_cylinder_eq_of_subset<\\/a> h_eq hJI\"",
+                "[{\"full_name\":\"MeasureTheory.eq_of_cylinder_eq_of_subset\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Constructions\\/Cylinders.lean\",\"def_pos\":[217,9],\"def_end_pos\":[217,36]}]"
+              ],
+              "state_after": "case inr\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nhJI : J \u2286 I\nh : Nonempty ((i : \u03b9) \u2192 \u03b1 i)\nthis : S = (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' T\n\u22a2 (P I) S = (P J) T",
+              "state_before": "case inr\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nhJI : J \u2286 I\nh : Nonempty ((i : \u03b9) \u2192 \u03b1 i)\n\u22a2 (P I) S = (P J) T",
+              "tactic": "have : S = (fun f : \u2200 i : I, \u03b1 i \u21a6 fun j : J \u21a6 f \u27e8j, hJI j.prop\u27e9) \u207b\u00b9' T :=\n  eq_of_cylinder_eq_of_subset h_eq hJI"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [hP I J hJI, <a>Measure.map_apply<\\/a> _ hT, this]\"",
+                "[{\"full_name\":\"MeasureTheory.Measure.map_apply\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Measure\\/MeasureSpace.lean\",\"def_pos\":[1291,9],\"def_end_pos\":[1291,18]}]"
+              ],
+              "state_after": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nhJI : J \u2286 I\nh : Nonempty ((i : \u03b9) \u2192 \u03b1 i)\nthis : S = (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' T\n\u22a2 Measurable fun x j => x \u27e8\u2191j, \u22ef\u27e9",
+              "state_before": "case inr\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nhJI : J \u2286 I\nh : Nonempty ((i : \u03b9) \u2192 \u03b1 i)\nthis : S = (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' T\n\u22a2 (P I) S = (P J) T",
+              "tactic": "rw [hP I J hJI, Measure.map_apply _ hT, this]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>measurable_pi_lambda<\\/a> _ (fun _ \\u21a6 <a>measurable_pi_apply<\\/a> _)\"",
+                "[{\"full_name\":\"measurable_pi_lambda\",\"def_path\":\"Mathlib\\/MeasureTheory\\/MeasurableSpace\\/Basic.lean\",\"def_pos\":[924,9],\"def_end_pos\":[924,29]},{\"full_name\":\"measurable_pi_apply\",\"def_path\":\"Mathlib\\/MeasureTheory\\/MeasurableSpace\\/Basic.lean\",\"def_pos\":[913,9],\"def_end_pos\":[913,28]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nS : Set ((i : { x // x \u2208 I }) \u2192 \u03b1 \u2191i)\nT : Set ((i : { x // x \u2208 J }) \u2192 \u03b1 \u2191i)\nhT : MeasurableSet T\nh_eq : cylinder I S = cylinder J T\nhJI : J \u2286 I\nh : Nonempty ((i : \u03b9) \u2192 \u03b1 i)\nthis : S = (fun f j => f \u27e8\u2191j, \u22ef\u27e9) \u207b\u00b9' T\n\u22a2 Measurable fun x j => x \u27e8\u2191j, \u22ef\u27e9",
+              "tactic": "exact measurable_pi_lambda _ (fun _ \u21a6 measurable_pi_apply _)"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/Projective.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rw [\u2190 hP.measure_univ_eq_of_subset I.subset_union_left,\\n  \u2190 hP.measure_univ_eq_of_subset (I.subset_union_right (s\u2082:= J))]'",
+        "full_name": "MeasureTheory.IsProjectiveMeasureFamily.measure_univ_eq",
+        "id": "MeasureTheory.IsProjectiveMeasureFamily.measure_univ_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            64,
+            68
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/Projective.lean",
+          "full_name": "MeasureTheory.IsProjectiveMeasureFamily.measure_univ_eq",
+          "start": [
+            60,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"classical\\n  rw [\\u2190 hP.measure_univ_eq_of_subset I.subset_union_left,\\n    \\u2190 hP.measure_univ_eq_of_subset (I.subset_union_right (s\\u2082:= J))]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI\u271d J\u271d : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nI J : Finset \u03b9\n\u22a2 (P I) univ = (P J) univ",
+              "tactic": "classical\nrw [\u2190 hP.measure_univ_eq_of_subset I.subset_union_left,\n  \u2190 hP.measure_univ_eq_of_subset (I.subset_union_right (s\u2082:= J))]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 hP.measure_univ_eq_of_subset I.subset_union_left,\\n    \\u2190 hP.measure_univ_eq_of_subset (I.subset_union_right (s\\u2082:= J))]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI\u271d J\u271d : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nI J : Finset \u03b9\n\u22a2 (P I) univ = (P J) univ",
+              "tactic": "rw [\u2190 hP.measure_univ_eq_of_subset I.subset_union_left,\n  \u2190 hP.measure_univ_eq_of_subset (I.subset_union_right (s\u2082:= J))]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/Projective.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rw [preimage_univ]'",
+        "full_name": "MeasureTheory.IsProjectiveMeasureFamily.measure_univ_eq_of_subset",
+        "id": "MeasureTheory.IsProjectiveMeasureFamily.measure_univ_eq_of_subset",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            58,
+            65
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/Projective.lean",
+          "full_name": "MeasureTheory.IsProjectiveMeasureFamily.measure_univ_eq_of_subset",
+          "start": [
+            49,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"have : (<a>univ<\\/a> : <a>Set<\\/a> (\\u2200 i : I, \\u03b1 i)) =\\n      (fun x : \\u2200 i : I, \\u03b1 i \\u21a6 fun i : J \\u21a6 x \\u27e8i, hJI i.2\\u27e9) \\u207b\\u00b9' (<a>univ<\\/a> : <a>Set<\\/a> (\\u2200 i : J, \\u03b1 i)) := by\\n    rw [<a>preimage_univ<\\/a>]\"",
+                "[{\"full_name\":\"Set.univ\",\"def_path\":\"Mathlib\\/Init\\/Set.lean\",\"def_pos\":[153,5],\"def_end_pos\":[153,9]},{\"full_name\":\"Set\",\"def_path\":\"Mathlib\\/Init\\/Set.lean\",\"def_pos\":[47,5],\"def_end_pos\":[47,8]},{\"full_name\":\"Set.univ\",\"def_path\":\"Mathlib\\/Init\\/Set.lean\",\"def_pos\":[153,5],\"def_end_pos\":[153,9]},{\"full_name\":\"Set\",\"def_path\":\"Mathlib\\/Init\\/Set.lean\",\"def_pos\":[47,5],\"def_end_pos\":[47,8]},{\"full_name\":\"Set.preimage_univ\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Image.lean\",\"def_pos\":[63,9],\"def_end_pos\":[63,22]}]"
+              ],
+              "state_after": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nhJI : J \u2286 I\nthis : univ = (fun x i => x \u27e8\u2191i, \u22ef\u27e9) \u207b\u00b9' univ\n\u22a2 (P I) univ = (P J) univ",
+              "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nhJI : J \u2286 I\n\u22a2 (P I) univ = (P J) univ",
+              "tactic": "have : (univ : Set (\u2200 i : I, \u03b1 i)) =\n    (fun x : \u2200 i : I, \u03b1 i \u21a6 fun i : J \u21a6 x \u27e8i, hJI i.2\u27e9) \u207b\u00b9' (univ : Set (\u2200 i : J, \u03b1 i)) := by\n  rw [preimage_univ]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [this, \\u2190 <a>Measure.map_apply<\\/a> _ <a>MeasurableSet.univ<\\/a>]\"",
+                "[{\"full_name\":\"MeasureTheory.Measure.map_apply\",\"def_path\":\"Mathlib\\/MeasureTheory\\/Measure\\/MeasureSpace.lean\",\"def_pos\":[1291,9],\"def_end_pos\":[1291,18]},{\"full_name\":\"MeasurableSet.univ\",\"def_path\":\"Mathlib\\/MeasureTheory\\/MeasurableSpace\\/Defs.lean\",\"def_pos\":[103,19],\"def_end_pos\":[103,37]}]"
+              ],
+              "state_after": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nhJI : J \u2286 I\nthis : univ = (fun x i => x \u27e8\u2191i, \u22ef\u27e9) \u207b\u00b9' univ\n\u22a2 (Measure.map (fun x i => x \u27e8\u2191i, \u22ef\u27e9) (P I)) univ = (P J) univ\n\n\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nhJI : J \u2286 I\nthis : univ = (fun x i => x \u27e8\u2191i, \u22ef\u27e9) \u207b\u00b9' univ\n\u22a2 Measurable fun x i => x \u27e8\u2191i, \u22ef\u27e9",
+              "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nhJI : J \u2286 I\nthis : univ = (fun x i => x \u27e8\u2191i, \u22ef\u27e9) \u207b\u00b9' univ\n\u22a2 (P I) univ = (P J) univ",
+              "tactic": "rw [this, \u2190 Measure.map_apply _ MeasurableSet.univ]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>preimage_univ<\\/a>]\"",
+                "[{\"full_name\":\"Set.preimage_univ\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Image.lean\",\"def_pos\":[63,9],\"def_end_pos\":[63,22]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nhJI : J \u2286 I\n\u22a2 univ = (fun x i => x \u27e8\u2191i, \u22ef\u27e9) \u207b\u00b9' univ",
+              "tactic": "rw [preimage_univ]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [hP I J hJI]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nhJI : J \u2286 I\nthis : univ = (fun x i => x \u27e8\u2191i, \u22ef\u27e9) \u207b\u00b9' univ\n\u22a2 (Measure.map (fun x i => x \u27e8\u2191i, \u22ef\u27e9) (P I)) univ = (P J) univ",
+              "tactic": "rw [hP I J hJI]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>measurable_pi_lambda<\\/a> _ (fun _ \\u21a6 <a>measurable_pi_apply<\\/a> _)\"",
+                "[{\"full_name\":\"measurable_pi_lambda\",\"def_path\":\"Mathlib\\/MeasureTheory\\/MeasurableSpace\\/Basic.lean\",\"def_pos\":[924,9],\"def_end_pos\":[924,29]},{\"full_name\":\"measurable_pi_apply\",\"def_path\":\"Mathlib\\/MeasureTheory\\/MeasurableSpace\\/Basic.lean\",\"def_pos\":[913,9],\"def_end_pos\":[913,28]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\ninst\u271d : (i : \u03b9) \u2192 MeasurableSpace (\u03b1 i)\nP : (J : Finset \u03b9) \u2192 Measure ((j : { x // x \u2208 J }) \u2192 \u03b1 \u2191j)\nI J : Finset \u03b9\nhP : IsProjectiveMeasureFamily P\nhJI : J \u2286 I\nthis : univ = (fun x i => x \u27e8\u2191i, \u22ef\u27e9) \u207b\u00b9' univ\n\u22a2 Measurable fun x i => x \u27e8\u2191i, \u22ef\u27e9",
+              "tactic": "exact measurable_pi_lambda _ (fun _ \u21a6 measurable_pi_apply _)"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/Projective.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "unitInterval.measurable_symm",
+        "id": "unitInterval.measurable_symm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            32,
+            72
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/UnitInterval.lean",
+          "full_name": "unitInterval.measurable_symm",
+          "start": [
+            32,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/UnitInterval.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "unitInterval.volume_def",
+        "id": "unitInterval.volume_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            24,
+            76
+          ],
+          "file_path": "Mathlib/MeasureTheory/Constructions/UnitInterval.lean",
+          "full_name": "unitInterval.volume_def",
+          "start": [
+            24,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Constructions/UnitInterval.lean"
+      }
+    ],
+    "input_proofs": 12,
+    "input_units": 2,
+    "proofs": 6,
+    "published_proofs": 6,
+    "published_transitions": 14,
+    "replay_failures": [],
+    "transitions": 14,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001359-0000-7367df361d1f59e3.parquet",
+      "sha256": "7367df361d1f59e3d81953eb36655511ec3675895c08bc65f15ec8445e3a5769",
+      "bytes": 73997,
+      "rows": 13,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    },
+    {
+      "path": "data/internal_test/mathlib-001359-0000-2a7439c10669ef59.parquet",
+      "sha256": "2a7439c10669ef59f50dafcc4dc76e7c6fc27ba16036d77f19e268fbe8bfdaf9",
+      "bytes": 44773,
+      "rows": 1,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:MeasureTheory.IsProjectiveLimit.isFiniteMeasure",
+    "mathlib:MeasureTheory.IsProjectiveLimit.isProbabilityMeasure",
+    "mathlib:MeasureTheory.IsProjectiveLimit.measure_cylinder",
+    "mathlib:MeasureTheory.IsProjectiveLimit.measure_univ_eq",
+    "mathlib:MeasureTheory.IsProjectiveLimit.measure_univ_unique",
+    "mathlib:MeasureTheory.IsProjectiveLimit.unique"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Constructions/Projective.lean\",null,null,\"MeasureTheory.IsProjectiveLimit.isFiniteMeasure\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Constructions/Projective.lean\",null,null,\"MeasureTheory.IsProjectiveLimit.isProbabilityMeasure\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Constructions/Projective.lean\",null,null,\"MeasureTheory.IsProjectiveLimit.measure_cylinder\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Constructions/Projective.lean\",null,null,\"MeasureTheory.IsProjectiveLimit.measure_univ_eq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Constructions/Projective.lean\",null,null,\"MeasureTheory.IsProjectiveLimit.measure_univ_unique\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Constructions/Projective.lean\",null,null,\"MeasureTheory.IsProjectiveLimit.unique\"]"
+  ]
+}

manifests/batches/mathlib/001367.json

@@ -0,0 +1,1346 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001367",
+  "batch_fingerprint": "991fe23f2b66be501cb7ea8c79c3dfc4ddc6bf7599779f5154425d910a7d5247",
+  "evidence": {
+    "batch_fingerprint": "991fe23f2b66be501cb7ea8c79c3dfc4ddc6bf7599779f5154425d910a7d5247",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ContinuousMap.coeFn_toAEEqFun",
+        "id": "ContinuousMap.coeFn_toAEEqFun",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            1001,
+            23
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "ContinuousMap.coeFn_toAEEqFun",
+          "start": [
+            1000,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.aemeasurable",
+        "id": "MeasureTheory.AEEqFun.aemeasurable",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            146,
+            28
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.aemeasurable",
+          "start": [
+            144,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.aestronglyMeasurable",
+        "id": "MeasureTheory.AEEqFun.aestronglyMeasurable",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            136,
+            44
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.aestronglyMeasurable",
+          "start": [
+            135,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.coeFn_compMeasurePreserving",
+        "id": "MeasureTheory.AEEqFun.coeFn_compMeasurePreserving",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            264,
+            39
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.coeFn_compMeasurePreserving",
+          "start": [
+            262,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.coeFn_const",
+        "id": "MeasureTheory.AEEqFun.coeFn_const",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            629,
+            15
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.coeFn_const",
+          "start": [
+            628,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.coeFn_div",
+        "id": "MeasureTheory.AEEqFun.coeFn_div",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            837,
+            22
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.coeFn_div",
+          "start": [
+            836,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.coeFn_inf",
+        "id": "MeasureTheory.AEEqFun.coeFn_inf",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            578,
+            22
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.coeFn_inf",
+          "start": [
+            577,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.coeFn_inv",
+        "id": "MeasureTheory.AEEqFun.coeFn_inv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            808,
+            19
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.coeFn_inv",
+          "start": [
+            807,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.coeFn_le",
+        "id": "MeasureTheory.AEEqFun.coeFn_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            527,
+            25
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.coeFn_le",
+          "start": [
+            526,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.coeFn_mul",
+        "id": "MeasureTheory.AEEqFun.coeFn_mul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            721,
+            22
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.coeFn_mul",
+          "start": [
+            720,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.coeFn_posPart",
+        "id": "MeasureTheory.AEEqFun.coeFn_posPart",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            978,
+            19
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.coeFn_posPart",
+          "start": [
+            977,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.coeFn_pow",
+        "id": "MeasureTheory.AEEqFun.coeFn_pow",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            757,
+            19
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.coeFn_pow",
+          "start": [
+            756,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.coeFn_smul",
+        "id": "MeasureTheory.AEEqFun.coeFn_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            681,
+            19
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.coeFn_smul",
+          "start": [
+            680,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.coeFn_sup",
+        "id": "MeasureTheory.AEEqFun.coeFn_sup",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            544,
+            22
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.coeFn_sup",
+          "start": [
+            543,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.coeFn_zpow",
+        "id": "MeasureTheory.AEEqFun.coeFn_zpow",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            862,
+            19
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.coeFn_zpow",
+          "start": [
+            861,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.compMeasurable_mk",
+        "id": "MeasureTheory.AEEqFun.compMeasurable_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            317,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.compMeasurable_mk",
+          "start": [
+            313,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.compMeasurePreserving_eq_mk",
+        "id": "MeasureTheory.AEEqFun.compMeasurePreserving_eq_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            260,
+            39
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.compMeasurePreserving_eq_mk",
+          "start": [
+            257,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.compMeasurePreserving_mk",
+        "id": "MeasureTheory.AEEqFun.compMeasurePreserving_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            255,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.compMeasurePreserving_mk",
+          "start": [
+            252,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.compMeasurePreserving_toGerm",
+        "id": "MeasureTheory.AEEqFun.compMeasurePreserving_toGerm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            465,
+            40
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.compMeasurePreserving_toGerm",
+          "start": [
+            461,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.compQuasiMeasurePreserving_mk",
+        "id": "MeasureTheory.AEEqFun.compQuasiMeasurePreserving_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            226,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.compQuasiMeasurePreserving_mk",
+          "start": [
+            223,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.comp_mk",
+        "id": "MeasureTheory.AEEqFun.comp_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            279,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.comp_mk",
+          "start": [
+            277,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.comp\u2082Measurable_eq_pair",
+        "id": "MeasureTheory.AEEqFun.comp\u2082Measurable_eq_pair",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            417,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.comp\u2082Measurable_eq_pair",
+          "start": [
+            415,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.comp\u2082Measurable_mk_mk",
+        "id": "MeasureTheory.AEEqFun.comp\u2082Measurable_mk_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            412,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.comp\u2082Measurable_mk_mk",
+          "start": [
+            407,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.comp\u2082_eq_pair",
+        "id": "MeasureTheory.AEEqFun.comp\u2082_eq_pair",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            376,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.comp\u2082_eq_pair",
+          "start": [
+            374,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.comp\u2082_mk_mk",
+        "id": "MeasureTheory.AEEqFun.comp\u2082_mk_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            371,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.comp\u2082_mk_mk",
+          "start": [
+            367,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.div_toGerm",
+        "id": "MeasureTheory.AEEqFun.div_toGerm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            843,
+            23
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.div_toGerm",
+          "start": [
+            842,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.induction_on",
+        "id": "MeasureTheory.AEEqFun.induction_on",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            185,
+            48
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.induction_on",
+          "start": [
+            184,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.induction_on\u2083",
+        "id": "MeasureTheory.AEEqFun.induction_on\u2083",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            201,
+            60
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.induction_on\u2083",
+          "start": [
+            196,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.inv_mk",
+        "id": "MeasureTheory.AEEqFun.inv_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            802,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.inv_mk",
+          "start": [
+            801,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.inv_toGerm",
+        "id": "MeasureTheory.AEEqFun.inv_toGerm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            814,
+            20
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.inv_toGerm",
+          "start": [
+            813,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.liftRel_mk_mk",
+        "id": "MeasureTheory.AEEqFun.liftRel_mk_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            507,
+            10
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.liftRel_mk_mk",
+          "start": [
+            505,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.lintegral_eq_zero_iff",
+        "id": "MeasureTheory.AEEqFun.lintegral_eq_zero_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            938,
+            91
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.lintegral_eq_zero_iff",
+          "start": [
+            937,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.lintegral_mk",
+        "id": "MeasureTheory.AEEqFun.lintegral_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            924,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.lintegral_mk",
+          "start": [
+            923,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.lintegral_mono",
+        "id": "MeasureTheory.AEEqFun.lintegral_mono",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            946,
+            63
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.lintegral_mono",
+          "start": [
+            945,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.lintegral_zero",
+        "id": "MeasureTheory.AEEqFun.lintegral_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            933,
+            17
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.lintegral_zero",
+          "start": [
+            932,
+            8
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.measurable",
+        "id": "MeasureTheory.AEEqFun.measurable",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            141,
+            39
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.measurable",
+          "start": [
+            139,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.mk_div",
+        "id": "MeasureTheory.AEEqFun.mk_div",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            831,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.mk_div",
+          "start": [
+            829,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.mk_eq_mk",
+        "id": "MeasureTheory.AEEqFun.mk_eq_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            157,
+            16
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.mk_eq_mk",
+          "start": [
+            156,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.mk_mul_mk",
+        "id": "MeasureTheory.AEEqFun.mk_mul_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            715,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.mk_mul_mk",
+          "start": [
+            713,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.mk_pow",
+        "id": "MeasureTheory.AEEqFun.mk_pow",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            753,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.mk_pow",
+          "start": [
+            750,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.mk_toGerm",
+        "id": "MeasureTheory.AEEqFun.mk_toGerm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            444,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.mk_toGerm",
+          "start": [
+            443,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.mk_zpow",
+        "id": "MeasureTheory.AEEqFun.mk_zpow",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            858,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.mk_zpow",
+          "start": [
+            856,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.mul_toGerm",
+        "id": "MeasureTheory.AEEqFun.mul_toGerm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            727,
+            23
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.mul_toGerm",
+          "start": [
+            726,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.one_def",
+        "id": "MeasureTheory.AEEqFun.one_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            646,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.one_def",
+          "start": [
+            645,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.one_toGerm",
+        "id": "MeasureTheory.AEEqFun.one_toGerm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            658,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.one_toGerm",
+          "start": [
+            657,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.pair_mk_mk",
+        "id": "MeasureTheory.AEEqFun.pair_mk_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            343,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.pair_mk_mk",
+          "start": [
+            341,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.posPart_mk",
+        "id": "MeasureTheory.AEEqFun.posPart_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            974,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.posPart_mk",
+          "start": [
+            970,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.pow_toGerm",
+        "id": "MeasureTheory.AEEqFun.pow_toGerm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            762,
+            20
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.pow_toGerm",
+          "start": [
+            761,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.quot_mk_eq_mk",
+        "id": "MeasureTheory.AEEqFun.quot_mk_eq_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            152,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.quot_mk_eq_mk",
+          "start": [
+            150,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.smul_mk",
+        "id": "MeasureTheory.AEEqFun.smul_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            677,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.smul_mk",
+          "start": [
+            675,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.smul_toGerm",
+        "id": "MeasureTheory.AEEqFun.smul_toGerm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            685,
+            20
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.smul_toGerm",
+          "start": [
+            684,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.stronglyMeasurable",
+        "id": "MeasureTheory.AEEqFun.stronglyMeasurable",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            132,
+            47
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.stronglyMeasurable",
+          "start": [
+            131,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MeasureTheory.AEEqFun.zpow_toGerm",
+        "id": "MeasureTheory.AEEqFun.zpow_toGerm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            867,
+            20
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun.lean",
+          "full_name": "MeasureTheory.AEEqFun.zpow_toGerm",
+          "start": [
+            866,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DomMulAct.mk_smul_mk_aeeqFun",
+        "id": "DomMulAct.mk_smul_mk_aeeqFun",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            50,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun/DomAct.lean",
+          "full_name": "DomMulAct.mk_smul_mk_aeeqFun",
+          "start": [
+            47,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun/DomAct.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DomMulAct.smul_aeeqFun_aeeq",
+        "id": "DomMulAct.smul_aeeqFun_aeeq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            44,
+            34
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun/DomAct.lean",
+          "full_name": "DomMulAct.smul_aeeqFun_aeeq",
+          "start": [
+            42,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun/DomAct.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DomMulAct.smul_aeeqFun_const",
+        "id": "DomMulAct.smul_aeeqFun_const",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            55,
+            6
+          ],
+          "file_path": "Mathlib/MeasureTheory/Function/AEEqFun/DomAct.lean",
+          "full_name": "DomMulAct.smul_aeeqFun_const",
+          "start": [
+            53,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/MeasureTheory/Function/AEEqFun/DomAct.lean"
+      }
+    ],
+    "input_proofs": 89,
+    "input_units": 2,
+    "proofs": 33,
+    "published_proofs": 33,
+    "published_transitions": 68,
+    "replay_failures": [],
+    "transitions": 68,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001367-0000-fc59594fa0481d05.parquet",
+      "sha256": "fc59594fa0481d052682bdcd0cf9dc6d7bc52ba16a6282bd2bf204ce391a43ea",
+      "bytes": 187468,
+      "rows": 50,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    },
+    {
+      "path": "data/dev/mathlib-001367-0000-2bde5afada110088.parquet",
+      "sha256": "2bde5afada11008867841a3423857a30336f3033c527931bdf1ff506aff1ec83",
+      "bytes": 60664,
+      "rows": 4,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    },
+    {
+      "path": "data/internal_test/mathlib-001367-0000-ffa06023828d995e.parquet",
+      "sha256": "ffa06023828d995e99eb8453797a9912cd80d4e73d09c102d489c730a421cb3c",
+      "bytes": 76778,
+      "rows": 14,
+      "revision": "713c98978a447a41255a0e12f4d34fc2750dd7a8"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:MeasureTheory.AEEqFun.coeFn_abs",
+    "mathlib:MeasureTheory.AEEqFun.coeFn_comp",
+    "mathlib:MeasureTheory.AEEqFun.coeFn_compMeasurable",
+    "mathlib:MeasureTheory.AEEqFun.coeFn_compQuasiMeasurePreserving",
+    "mathlib:MeasureTheory.AEEqFun.coeFn_comp\u2082",
+    "mathlib:MeasureTheory.AEEqFun.coeFn_comp\u2082Measurable",
+    "mathlib:MeasureTheory.AEEqFun.coeFn_mk",
+    "mathlib:MeasureTheory.AEEqFun.coeFn_pair",
+    "mathlib:MeasureTheory.AEEqFun.compMeasurable_eq_mk",
+    "mathlib:MeasureTheory.AEEqFun.compMeasurable_toGerm",
+    "mathlib:MeasureTheory.AEEqFun.compQuasiMeasurePreserving_eq_mk",
+    "mathlib:MeasureTheory.AEEqFun.compQuasiMeasurePreserving_toGerm",
+    "mathlib:MeasureTheory.AEEqFun.comp_compQuasiMeasurePreserving",
+    "mathlib:MeasureTheory.AEEqFun.comp_eq_mk",
+    "mathlib:MeasureTheory.AEEqFun.comp_toGerm",
+    "mathlib:MeasureTheory.AEEqFun.comp\u2082Measurable_eq_mk",
+    "mathlib:MeasureTheory.AEEqFun.comp\u2082Measurable_toGerm",
+    "mathlib:MeasureTheory.AEEqFun.comp\u2082_eq_mk",
+    "mathlib:MeasureTheory.AEEqFun.comp\u2082_toGerm",
+    "mathlib:MeasureTheory.AEEqFun.ext",
+    "mathlib:MeasureTheory.AEEqFun.ext_iff",
+    "mathlib:MeasureTheory.AEEqFun.inf_le_left",
+    "mathlib:MeasureTheory.AEEqFun.inf_le_right",
+    "mathlib:MeasureTheory.AEEqFun.le_inf",
+    "mathlib:MeasureTheory.AEEqFun.le_sup_left",
+    "mathlib:MeasureTheory.AEEqFun.le_sup_right",
+    "mathlib:MeasureTheory.AEEqFun.liftRel_iff_coeFn",
+    "mathlib:MeasureTheory.AEEqFun.lintegral_add",
+    "mathlib:MeasureTheory.AEEqFun.lintegral_coeFn",
+    "mathlib:MeasureTheory.AEEqFun.mk_coeFn",
+    "mathlib:MeasureTheory.AEEqFun.pair_eq_mk",
+    "mathlib:MeasureTheory.AEEqFun.sup_le",
+    "mathlib:MeasureTheory.AEEqFun.toGerm_eq"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.coeFn_abs\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.coeFn_comp\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.coeFn_compMeasurable\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.coeFn_compQuasiMeasurePreserving\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.coeFn_comp\u2082\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.coeFn_comp\u2082Measurable\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.coeFn_mk\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.coeFn_pair\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.compMeasurable_eq_mk\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.compMeasurable_toGerm\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.compQuasiMeasurePreserving_eq_mk\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.compQuasiMeasurePreserving_toGerm\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.comp_compQuasiMeasurePreserving\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.comp_eq_mk\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.comp_toGerm\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.comp\u2082Measurable_eq_mk\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.comp\u2082Measurable_toGerm\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.comp\u2082_eq_mk\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.comp\u2082_toGerm\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.ext\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.ext_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.inf_le_left\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.inf_le_right\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.le_inf\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.le_sup_left\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.le_sup_right\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.liftRel_iff_coeFn\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.lintegral_add\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.lintegral_coeFn\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.mk_coeFn\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.pair_eq_mk\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.sup_le\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/MeasureTheory/Function/AEEqFun.lean\",null,null,\"MeasureTheory.AEEqFun.toGerm_eq\"]"
+  ]
+}