Record 32 verified HPC batch manifests

manifests/batches/mathlib/001188.json

@@ -0,0 +1,759 @@
+{
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+        "source_file": "Mathlib/GroupTheory/GroupAction/ConjAct.lean"
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+      },
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+      },
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+      }
+    ],
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+    "validation_failures": [],
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+  },
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+    "mathlib:smul_ite_zero",
+    "mathlib:smul_neg",
+    "mathlib:smul_sub"
+  ],
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+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Defs.lean\",null,null,\"smul_neg\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Defs.lean\",null,null,\"smul_sub\"]"
+  ]
+}

manifests/batches/mathlib/001189.json

@@ -0,0 +1,443 @@
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+      },
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+      },
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+      },
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+      },
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+      },
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+        "error": "theorem has no selected tactic transitions",
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+        "id": "DomMulAct.symm_mk_mul",
+        "reason": "import_failure",
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+      },
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+      },
+      {
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+      }
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+    "input_units": 2,
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+    "zero_transition_proofs": 0
+  },
+  "shards": [],
+  "proof_ids": [],
+  "proof_keys": []
+}

manifests/batches/mathlib/001190.json

@@ -0,0 +1,376 @@
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+            46,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Embedding.lean",
+          "full_name": "Function.Embedding.coe_smul",
+          "start": [
+            45,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Embedding.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.Embedding.smul_apply",
+        "id": "Function.Embedding.smul_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            40,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Embedding.lean",
+          "full_name": "Function.Embedding.smul_apply",
+          "start": [
+            39,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Embedding.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.Embedding.smul_def",
+        "id": "Function.Embedding.smul_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            34,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Embedding.lean",
+          "full_name": "Function.Embedding.smul_def",
+          "start": [
+            32,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Embedding.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.fixedBy_one_eq_univ",
+        "id": "MulAction.fixedBy_one_eq_univ",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            92,
+            43
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/FixedPoints.lean",
+          "full_name": "MulAction.fixedBy_one_eq_univ",
+          "start": [
+            91,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/FixedPoints.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.minimalPeriod_eq_one_iff_fixedBy",
+        "id": "MulAction.minimalPeriod_eq_one_iff_fixedBy",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            78,
+            46
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/FixedPoints.lean",
+          "full_name": "MulAction.minimalPeriod_eq_one_iff_fixedBy",
+          "start": [
+            76,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/FixedPoints.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rw [a_fixed]'",
+        "full_name": "MulAction.set_mem_fixedBy_of_movedBy_subset",
+        "id": "MulAction.set_mem_fixedBy_of_movedBy_subset",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            172,
+            64
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/FixedPoints.lean",
+          "full_name": "MulAction.set_mem_fixedBy_of_movedBy_subset",
+          "start": [
+            161,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>fixedBy_inv<\\/a>]\"",
+                "[{\"full_name\":\"MulAction.fixedBy_inv\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/FixedPoints.lean\",\"def_pos\":[60,9],\"def_end_pos\":[60,20]}]"
+              ],
+              "state_after": "\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\n\u22a2 s \u2208 fixedBy (Set \u03b1) g\u207b\u00b9",
+              "state_before": "\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\n\u22a2 s \u2208 fixedBy (Set \u03b1) g",
+              "tactic": "rw [\u2190 fixedBy_inv]"
+            },
+            {
+              "annotated_tactic": [
+                "\"ext a\"",
+                "[]"
+              ],
+              "state_after": "case h\n\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\n\u22a2 a \u2208 g\u207b\u00b9 \u2022 s \u2194 a \u2208 s",
+              "state_before": "\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\n\u22a2 s \u2208 fixedBy (Set \u03b1) g\u207b\u00b9",
+              "tactic": "ext a"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Set.mem_inv_smul_set_iff<\\/a>]\"",
+                "[{\"full_name\":\"Set.mem_inv_smul_set_iff\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Pointwise\\/SMul.lean\",\"def_pos\":[906,9],\"def_end_pos\":[906,29]}]"
+              ],
+              "state_after": "case h\n\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\n\u22a2 g \u2022 a \u2208 s \u2194 a \u2208 s",
+              "state_before": "case h\n\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\n\u22a2 a \u2208 g\u207b\u00b9 \u2022 s \u2194 a \u2208 s",
+              "tactic": "rw [Set.mem_inv_smul_set_iff]"
+            },
+            {
+              "annotated_tactic": [
+                "\"by_cases a \\u2208 <a>fixedBy<\\/a> \\u03b1 g\"",
+                "[{\"full_name\":\"MulAction.fixedBy\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Basic.lean\",\"def_pos\":[155,5],\"def_end_pos\":[155,12]}]"
+              ],
+              "state_after": "case pos\n\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\nh\u271d : a \u2208 fixedBy \u03b1 g\n\u22a2 g \u2022 a \u2208 s \u2194 a \u2208 s\n\ncase neg\n\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\nh\u271d : a \u2209 fixedBy \u03b1 g\n\u22a2 g \u2022 a \u2208 s \u2194 a \u2208 s",
+              "state_before": "case h\n\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\n\u22a2 g \u2022 a \u2208 s \u2194 a \u2208 s",
+              "tactic": "by_cases a \u2208 fixedBy \u03b1 g"
+            },
+            {
+              "annotated_tactic": [
+                "\"case pos a_fixed =>\\n    rw [a_fixed]\"",
+                "[]"
+              ],
+              "state_after": "case neg\n\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\nh\u271d : a \u2209 fixedBy \u03b1 g\n\u22a2 g \u2022 a \u2208 s \u2194 a \u2208 s",
+              "state_before": "case pos\n\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\nh\u271d : a \u2208 fixedBy \u03b1 g\n\u22a2 g \u2022 a \u2208 s \u2194 a \u2208 s\n\ncase neg\n\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\nh\u271d : a \u2209 fixedBy \u03b1 g\n\u22a2 g \u2022 a \u2208 s \u2194 a \u2208 s",
+              "tactic": "case pos a_fixed =>\n  rw [a_fixed]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [a_fixed]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\na_fixed : a \u2208 fixedBy \u03b1 g\n\u22a2 g \u2022 a \u2208 s \u2194 a \u2208 s",
+              "tactic": "rw [a_fixed]"
+            },
+            {
+              "annotated_tactic": [
+                "\"constructor <;> (intro; apply s_subset)\"",
+                "[]"
+              ],
+              "state_after": "case mp.a\n\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\na_moved : a \u2209 fixedBy \u03b1 g\na\u271d : g \u2022 a \u2208 s\n\u22a2 a \u2208 (fixedBy \u03b1 g)\u1d9c\n\ncase mpr.a\n\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\na_moved : a \u2209 fixedBy \u03b1 g\na\u271d : a \u2208 s\n\u22a2 g \u2022 a \u2208 (fixedBy \u03b1 g)\u1d9c",
+              "state_before": "\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\na_moved : a \u2209 fixedBy \u03b1 g\n\u22a2 g \u2022 a \u2208 s \u2194 a \u2208 s",
+              "tactic": "constructor <;> (intro; apply s_subset)"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro\"",
+                "[]"
+              ],
+              "state_after": "case mpr\n\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\na_moved : a \u2209 fixedBy \u03b1 g\na\u271d : a \u2208 s\n\u22a2 g \u2022 a \u2208 s",
+              "state_before": "case mpr\n\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\na_moved : a \u2209 fixedBy \u03b1 g\n\u22a2 a \u2208 s \u2192 g \u2022 a \u2208 s",
+              "tactic": "intro"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply s_subset\"",
+                "[]"
+              ],
+              "state_after": "case mpr.a\n\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\na_moved : a \u2209 fixedBy \u03b1 g\na\u271d : a \u2208 s\n\u22a2 g \u2022 a \u2208 (fixedBy \u03b1 g)\u1d9c",
+              "state_before": "case mpr\n\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\na_moved : a \u2209 fixedBy \u03b1 g\na\u271d : a \u2208 s\n\u22a2 g \u2022 a \u2208 s",
+              "tactic": "apply s_subset"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact a_moved\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case mp.a\n\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\na_moved : a \u2209 fixedBy \u03b1 g\na\u271d : g \u2022 a \u2208 s\n\u22a2 a \u2208 (fixedBy \u03b1 g)\u1d9c",
+              "tactic": "exact a_moved"
+            },
+            {
+              "annotated_tactic": [
+                "\"rwa [<a>Set.mem_compl_iff<\\/a>, <a>smul_mem_fixedBy_iff_mem_fixedBy<\\/a>]\"",
+                "[{\"full_name\":\"Set.mem_compl_iff\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Defs.lean\",\"def_pos\":[87,17],\"def_end_pos\":[87,30]},{\"full_name\":\"MulAction.smul_mem_fixedBy_iff_mem_fixedBy\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/FixedPoints.lean\",\"def_pos\":[65,9],\"def_end_pos\":[65,41]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case mpr.a\n\u03b1 : Type u_1\nG : Type u_2\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : MulAction G \u03b1\nM : Type u_3\ninst\u271d\u00b9 : Monoid M\ninst\u271d : MulAction M \u03b1\ns : Set \u03b1\ng : G\ns_subset : (fixedBy \u03b1 g)\u1d9c \u2286 s\na : \u03b1\na_moved : a \u2209 fixedBy \u03b1 g\na\u271d : a \u2208 s\n\u22a2 g \u2022 a \u2208 (fixedBy \u03b1 g)\u1d9c",
+              "tactic": "rwa [Set.mem_compl_iff, smul_mem_fixedBy_iff_mem_fixedBy]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/FixedPoints.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.smul_mem_of_set_mem_fixedBy",
+        "id": "MulAction.smul_mem_of_set_mem_fixedBy",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            129,
+            79
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/FixedPoints.lean",
+          "full_name": "MulAction.smul_mem_of_set_mem_fixedBy",
+          "start": [
+            128,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/FixedPoints.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.smul_subset_of_set_mem_fixedBy",
+        "id": "MulAction.smul_subset_of_set_mem_fixedBy",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            152,
+            74
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/FixedPoints.lean",
+          "full_name": "MulAction.smul_subset_of_set_mem_fixedBy",
+          "start": [
+            150,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/FixedPoints.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.smul_zpow_fixedBy_eq_of_commute",
+        "id": "MulAction.smul_zpow_fixedBy_eq_of_commute",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            207,
+            80
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/FixedPoints.lean",
+          "full_name": "MulAction.smul_zpow_fixedBy_eq_of_commute",
+          "start": [
+            205,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/FixedPoints.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.smul_zpow_movedBy_eq_of_commute",
+        "id": "MulAction.smul_zpow_movedBy_eq_of_commute",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
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+  ]
+}

manifests/batches/mathlib/001191.json

@@ -0,0 +1,1048 @@
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+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            244,
+            40
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "MulAction.bijective\u2080",
+          "start": [
+            243,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.injective",
+        "id": "MulAction.injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            145,
+            36
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "MulAction.injective",
+          "start": [
+            144,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.injective\u2080",
+        "id": "MulAction.injective\u2080",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            248,
+            38
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "MulAction.injective\u2080",
+          "start": [
+            247,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.surjective",
+        "id": "MulAction.surjective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            151,
+            37
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "MulAction.surjective",
+          "start": [
+            150,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.surjective\u2080",
+        "id": "MulAction.surjective\u2080",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            252,
+            39
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "MulAction.surjective\u2080",
+          "start": [
+            251,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.toPerm_injective",
+        "id": "MulAction.toPerm_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            58,
+            95
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "MulAction.toPerm_injective",
+          "start": [
+            56,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "eq_inv_smul_iff",
+        "id": "eq_inv_smul_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            110,
+            37
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "eq_inv_smul_iff",
+          "start": [
+            109,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "eq_inv_smul_iff\u2080",
+        "id": "eq_inv_smul_iff\u2080",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            221,
+            52
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "eq_inv_smul_iff\u2080",
+          "start": [
+            220,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "invOf_smul_eq_iff",
+        "id": "invOf_smul_eq_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            189,
+            44
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "invOf_smul_eq_iff",
+          "start": [
+            188,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "invOf_smul_smul",
+        "id": "invOf_smul_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            181,
+            81
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "invOf_smul_smul",
+          "start": [
+            181,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "inv_smul_eq_iff",
+        "id": "inv_smul_eq_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            104,
+            37
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "inv_smul_eq_iff",
+          "start": [
+            103,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "inv_smul_smul\u2080",
+        "id": "inv_smul_smul\u2080",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            208,
+            35
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "inv_smul_smul\u2080",
+          "start": [
+            207,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "isUnit_smul_iff",
+        "id": "isUnit_smul_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            420,
+            59
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "isUnit_smul_iff",
+          "start": [
+            418,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "smul_eq_iff_eq_invOf_smul",
+        "id": "smul_eq_iff_eq_invOf_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            192,
+            52
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "smul_eq_iff_eq_invOf_smul",
+          "start": [
+            191,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "smul_eq_iff_eq_inv_smul",
+        "id": "smul_eq_iff_eq_inv_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            169,
+            50
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "smul_eq_iff_eq_inv_smul",
+          "start": [
+            168,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "smul_invOf_smul",
+        "id": "smul_invOf_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            184,
+            84
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "smul_invOf_smul",
+          "start": [
+            184,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "smul_inv_smul\u2080",
+        "id": "smul_inv_smul\u2080",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            213,
+            35
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "smul_inv_smul\u2080",
+          "start": [
+            212,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "smul_left_cancel",
+        "id": "smul_left_cancel",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            157,
+            26
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "smul_left_cancel",
+          "start": [
+            156,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "smul_left_cancel_iff",
+        "id": "smul_left_cancel_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            163,
+            33
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "smul_left_cancel_iff",
+          "start": [
+            162,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "smul_ne_zero_iff_ne",
+        "id": "smul_ne_zero_iff_ne",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            306,
+            37
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+          "full_name": "smul_ne_zero_iff_ne",
+          "start": [
+            305,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Group.lean"
+      }
+    ],
+    "input_proofs": 52,
+    "input_units": 2,
+    "proofs": 9,
+    "published_proofs": 8,
+    "published_transitions": 12,
+    "replay_failures": [],
+    "transitions": 14,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+        "proof_id": "mathlib:inv_smul_eq_iff\u2080",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              217,
+              83
+            ],
+            "file_path": "Mathlib/GroupTheory/GroupAction/Group.lean",
+            "full_name": "inv_smul_eq_iff\u2080",
+            "start": [
+              216,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"rw [\\u2190 h, <a>smul_inv_smul\\u2080<\\/a> ha]\"",
+                  "[{\"full_name\":\"smul_inv_smul\\u2080\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Group.lean\",\"def_pos\":[212,9],\"def_end_pos\":[212,23]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\ninst\u271d\u00b9 : GroupWithZero \u03b1\ninst\u271d : MulAction \u03b1 \u03b2\na\u271d a : \u03b1\nha : a \u2260 0\nx y : \u03b2\nh : a\u207b\u00b9 \u2022 x = y\n\u22a2 x = a \u2022 y",
+                "tactic": "rw [\u2190 h, smul_inv_smul\u2080 ha]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [h, <a>inv_smul_smul\\u2080<\\/a> ha]\"",
+                  "[{\"full_name\":\"inv_smul_smul\\u2080\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Group.lean\",\"def_pos\":[207,9],\"def_end_pos\":[207,23]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\ninst\u271d\u00b9 : GroupWithZero \u03b1\ninst\u271d : MulAction \u03b1 \u03b2\na\u271d a : \u03b1\nha : a \u2260 0\nx y : \u03b2\nh : x = a \u2022 y\n\u22a2 a\u207b\u00b9 \u2022 x = y",
+                "tactic": "rw [h, inv_smul_smul\u2080 ha]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "inv_smul_eq_iff\u2080"
+      }
+    ],
+    "validation_rejected_proofs": 1,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001191-0000-1cb6bc444294e68e.parquet",
+      "sha256": "1cb6bc444294e68e3504136e19ff13ef1716d685ca8547509678c5b2f6fa5e1e",
+      "bytes": 60871,
+      "rows": 11,
+      "revision": "906b7b88e1251d7543db52f3953c29ea18db26ce"
+    },
+    {
+      "path": "data/dev/mathlib-001191-0000-fcec9e1dc0fcb274.parquet",
+      "sha256": "fcec9e1dc0fcb27404136468f70c68426e9cec00ed23acfdcde5b586e104f6aa",
+      "bytes": 42661,
+      "rows": 1,
+      "revision": "906b7b88e1251d7543db52f3953c29ea18db26ce"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Commute.smul_left_iff",
+    "mathlib:inv_smul_smul",
+    "mathlib:mem_fixingSubgroup_compl_iff_movedBy_subset",
+    "mathlib:mem_fixingSubgroup_iff_subset_fixedBy",
+    "mathlib:orbit_fixingSubgroup_compl_subset",
+    "mathlib:smul_eq_zero_iff_eq",
+    "mathlib:smul_inv",
+    "mathlib:smul_zpow"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/FixingSubgroup.lean\",null,null,\"mem_fixingSubgroup_compl_iff_movedBy_subset\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/FixingSubgroup.lean\",null,null,\"mem_fixingSubgroup_iff_subset_fixedBy\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/FixingSubgroup.lean\",null,null,\"orbit_fixingSubgroup_compl_subset\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Group.lean\",null,null,\"Commute.smul_left_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Group.lean\",null,null,\"inv_smul_smul\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Group.lean\",null,null,\"smul_eq_zero_iff_eq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Group.lean\",null,null,\"smul_inv\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Group.lean\",null,null,\"smul_zpow\"]"
+  ]
+}

manifests/batches/mathlib/001192.json

@@ -0,0 +1,1132 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001192",
+  "batch_fingerprint": "7b5e44634a0681321bb99ea8cc8bebbe9b3a8865da1750ca593313c6e455be56",
+  "evidence": {
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+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistribMulActionHom.coe_fn_coe",
+        "id": "DistribMulActionHom.coe_fn_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            451,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "DistribMulActionHom.coe_fn_coe",
+          "start": [
+            450,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistribMulActionHom.coe_fn_coe'",
+        "id": "DistribMulActionHom.coe_fn_coe'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
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+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "DistribMulActionHom.coe_fn_coe'",
+          "start": [
+            455,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistribMulActionHom.coe_one",
+        "id": "DistribMulActionHom.coe_one",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            531,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "DistribMulActionHom.coe_one",
+          "start": [
+            530,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistribMulActionHom.coe_zero",
+        "id": "DistribMulActionHom.coe_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            526,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "DistribMulActionHom.coe_zero",
+          "start": [
+            525,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistribMulActionHom.comp_apply",
+        "id": "DistribMulActionHom.comp_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            556,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "DistribMulActionHom.comp_apply",
+          "start": [
+            554,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistribMulActionHom.comp_assoc",
+        "id": "DistribMulActionHom.comp_assoc",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            576,
+            19
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "DistribMulActionHom.comp_assoc",
+          "start": [
+            570,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistribMulActionHom.congr_fun",
+        "id": "DistribMulActionHom.congr_fun",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            469,
+            25
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "DistribMulActionHom.congr_fun",
+          "start": [
+            468,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistribMulActionHom.ext",
+        "id": "DistribMulActionHom.ext",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            461,
+            19
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "DistribMulActionHom.ext",
+          "start": [
+            460,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistribMulActionHom.ext_iff",
+        "id": "DistribMulActionHom.ext_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            465,
+            19
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "DistribMulActionHom.ext_iff",
+          "start": [
+            464,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistribMulActionHom.ext_ring_iff",
+        "id": "DistribMulActionHom.ext_ring_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            606,
+            31
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "DistribMulActionHom.ext_ring_iff",
+          "start": [
+            605,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistribMulActionHom.map_add",
+        "id": "DistribMulActionHom.map_add",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            488,
+            16
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "DistribMulActionHom.map_add",
+          "start": [
+            487,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistribMulActionHom.map_neg",
+        "id": "DistribMulActionHom.map_neg",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            492,
+            14
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "DistribMulActionHom.map_neg",
+          "start": [
+            491,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistribMulActionHom.map_smul\u2091",
+        "id": "DistribMulActionHom.map_smul\u2091",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            500,
+            19
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "DistribMulActionHom.map_smul\u2091",
+          "start": [
+            499,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistribMulActionHom.map_sub",
+        "id": "DistribMulActionHom.map_sub",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            496,
+            16
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "DistribMulActionHom.map_sub",
+          "start": [
+            495,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistribMulActionHom.map_zero",
+        "id": "DistribMulActionHom.map_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            484,
+            13
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "DistribMulActionHom.map_zero",
+          "start": [
+            483,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistribMulActionHom.one_apply",
+        "id": "DistribMulActionHom.one_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            539,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "DistribMulActionHom.one_apply",
+          "start": [
+            538,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistribMulActionHom.toFun_eq_coe",
+        "id": "DistribMulActionHom.toFun_eq_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            446,
+            59
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "DistribMulActionHom.toFun_eq_coe",
+          "start": [
+            446,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistribMulActionHom.zero_apply",
+        "id": "DistribMulActionHom.zero_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            535,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "DistribMulActionHom.zero_apply",
+          "start": [
+            534,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulActionHom.comp_apply",
+        "id": "MulActionHom.comp_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            231,
+            32
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulActionHom.comp_apply",
+          "start": [
+            229,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulActionHom.comp_assoc",
+        "id": "MulActionHom.comp_assoc",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            253,
+            19
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulActionHom.comp_assoc",
+          "start": [
+            247,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulActionHom.congr_fun",
+        "id": "MulActionHom.congr_fun",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            172,
+            25
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulActionHom.congr_fun",
+          "start": [
+            170,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulActionHom.ext",
+        "id": "MulActionHom.ext",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            162,
+            19
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulActionHom.ext",
+          "start": [
+            160,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulActionHom.ext_iff",
+        "id": "MulActionHom.ext_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            167,
+            19
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulActionHom.ext_iff",
+          "start": [
+            165,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulActionHom.id_apply",
+        "id": "MulActionHom.id_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            205,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulActionHom.id_apply",
+          "start": [
+            203,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulActionHom.inverse'_inverse'",
+        "id": "MulActionHom.inverse'_inverse'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            294,
+            19
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulActionHom.inverse'_inverse'",
+          "start": [
+            289,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulActionHom.ofEq_apply",
+        "id": "MulActionHom.ofEq_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            189,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulActionHom.ofEq_apply",
+          "start": [
+            187,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulActionHom.ofEq_coe",
+        "id": "MulActionHom.ofEq_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            183,
+            38
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulActionHom.ofEq_coe",
+          "start": [
+            182,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulSemiringActionHom.coe_fn_coe",
+        "id": "MulSemiringActionHom.coe_fn_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            735,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulSemiringActionHom.coe_fn_coe",
+          "start": [
+            734,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulSemiringActionHom.coe_fn_coe'",
+        "id": "MulSemiringActionHom.coe_fn_coe'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            740,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulSemiringActionHom.coe_fn_coe'",
+          "start": [
+            739,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulSemiringActionHom.comp_apply",
+        "id": "MulSemiringActionHom.comp_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            819,
+            32
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulSemiringActionHom.comp_apply",
+          "start": [
+            818,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulSemiringActionHom.ext",
+        "id": "MulSemiringActionHom.ext",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            745,
+            19
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulSemiringActionHom.ext",
+          "start": [
+            744,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulSemiringActionHom.ext_iff",
+        "id": "MulSemiringActionHom.ext_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            749,
+            19
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulSemiringActionHom.ext_iff",
+          "start": [
+            748,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulSemiringActionHom.id_apply",
+        "id": "MulSemiringActionHom.id_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            798,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulSemiringActionHom.id_apply",
+          "start": [
+            797,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulSemiringActionHom.map_add",
+        "id": "MulSemiringActionHom.map_add",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            757,
+            16
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulSemiringActionHom.map_add",
+          "start": [
+            756,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulSemiringActionHom.map_mul",
+        "id": "MulSemiringActionHom.map_mul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            773,
+            16
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulSemiringActionHom.map_mul",
+          "start": [
+            772,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulSemiringActionHom.map_neg",
+        "id": "MulSemiringActionHom.map_neg",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            761,
+            14
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulSemiringActionHom.map_neg",
+          "start": [
+            760,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulSemiringActionHom.map_one",
+        "id": "MulSemiringActionHom.map_one",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            769,
+            12
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulSemiringActionHom.map_one",
+          "start": [
+            768,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulSemiringActionHom.map_smul",
+        "id": "MulSemiringActionHom.map_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            782,
+            19
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulSemiringActionHom.map_smul",
+          "start": [
+            780,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulSemiringActionHom.map_smul\u209b\u2097",
+        "id": "MulSemiringActionHom.map_smul\u209b\u2097",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            777,
+            19
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulSemiringActionHom.map_smul\u209b\u2097",
+          "start": [
+            776,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulSemiringActionHom.map_sub",
+        "id": "MulSemiringActionHom.map_sub",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            765,
+            16
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulSemiringActionHom.map_sub",
+          "start": [
+            764,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulSemiringActionHom.map_zero",
+        "id": "MulSemiringActionHom.map_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            753,
+            13
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "MulSemiringActionHom.map_zero",
+          "start": [
+            752,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "map_smul",
+        "id": "map_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            114,
+            19
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Hom.lean",
+          "full_name": "map_smul",
+          "start": [
+            111,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulOpposite.op_smul_eq_op_smul_op",
+        "id": "MulOpposite.op_smul_eq_op_smul_op",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            73,
+            64
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Opposite.lean",
+          "full_name": "MulOpposite.op_smul_eq_op_smul_op",
+          "start": [
+            72,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Opposite.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulOpposite.smul_eq_mul_unop",
+        "id": "MulOpposite.smul_eq_mul_unop",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            181,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Opposite.lean",
+          "full_name": "MulOpposite.smul_eq_mul_unop",
+          "start": [
+            180,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Opposite.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulOpposite.unop_smul_eq_unop_smul_unop",
+        "id": "MulOpposite.unop_smul_eq_unop_smul_unop",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            77,
+            87
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Opposite.lean",
+          "full_name": "MulOpposite.unop_smul_eq_unop_smul_unop",
+          "start": [
+            76,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Opposite.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "op_smul_eq_mul",
+        "id": "op_smul_eq_mul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            175,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Opposite.lean",
+          "full_name": "op_smul_eq_mul",
+          "start": [
+            174,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Opposite.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "op_smul_mul",
+        "id": "op_smul_mul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            149,
+            53
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Opposite.lean",
+          "full_name": "op_smul_mul",
+          "start": [
+            148,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Opposite.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "op_smul_op_smul",
+        "id": "op_smul_op_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            145,
+            54
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Opposite.lean",
+          "full_name": "op_smul_op_smul",
+          "start": [
+            144,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Opposite.lean"
+      }
+    ],
+    "input_proofs": 62,
+    "input_units": 2,
+    "proofs": 14,
+    "published_proofs": 14,
+    "published_transitions": 23,
+    "replay_failures": [],
+    "transitions": 23,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001192-0000-9e443178ad8efd7f.parquet",
+      "sha256": "9e443178ad8efd7fb15b405ef14aa7af6e6d5034d70025ee823b089e966896c6",
+      "bytes": 107584,
+      "rows": 19,
+      "revision": "906b7b88e1251d7543db52f3953c29ea18db26ce"
+    },
+    {
+      "path": "data/dev/mathlib-001192-0000-d73a030b147df29f.parquet",
+      "sha256": "d73a030b147df29fa7de367fb3508578e746f30ea6c28a89801e165ee2116b4a",
+      "bytes": 43096,
+      "rows": 2,
+      "revision": "906b7b88e1251d7543db52f3953c29ea18db26ce"
+    },
+    {
+      "path": "data/internal_test/mathlib-001192-0000-da672c57597c8ccd.parquet",
+      "sha256": "da672c57597c8ccd20eb917af34018711855fae5c48196d01c2a67fa9522a904",
+      "bytes": 43076,
+      "rows": 2,
+      "revision": "906b7b88e1251d7543db52f3953c29ea18db26ce"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:DistribMulActionHom.comp_id",
+    "mathlib:DistribMulActionHom.ext_ring",
+    "mathlib:DistribMulActionHom.id_apply",
+    "mathlib:DistribMulActionHom.id_comp",
+    "mathlib:DistribMulActionHom.toAddMonoidHom_injective",
+    "mathlib:DistribMulActionHom.toMulActionHom_injective",
+    "mathlib:IsScalarTower.smulHomClass",
+    "mathlib:MulActionHom.comp_id",
+    "mathlib:MulActionHom.comp_inverse'",
+    "mathlib:MulActionHom.id_comp",
+    "mathlib:MulActionHom.inverse'_comp",
+    "mathlib:MulActionHom.inverse_eq_inverse'",
+    "mathlib:MulSemiringActionHom.comp_id",
+    "mathlib:MulSemiringActionHom.id_comp"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Hom.lean\",null,null,\"DistribMulActionHom.comp_id\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Hom.lean\",null,null,\"DistribMulActionHom.ext_ring\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Hom.lean\",null,null,\"DistribMulActionHom.id_apply\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Hom.lean\",null,null,\"DistribMulActionHom.id_comp\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Hom.lean\",null,null,\"DistribMulActionHom.toAddMonoidHom_injective\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Hom.lean\",null,null,\"DistribMulActionHom.toMulActionHom_injective\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Hom.lean\",null,null,\"IsScalarTower.smulHomClass\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Hom.lean\",null,null,\"MulActionHom.comp_id\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Hom.lean\",null,null,\"MulActionHom.comp_inverse'\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Hom.lean\",null,null,\"MulActionHom.id_comp\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Hom.lean\",null,null,\"MulActionHom.inverse'_comp\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Hom.lean\",null,null,\"MulActionHom.inverse_eq_inverse'\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Hom.lean\",null,null,\"MulSemiringActionHom.comp_id\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Hom.lean\",null,null,\"MulSemiringActionHom.id_comp\"]"
+  ]
+}

manifests/batches/mathlib/001193.json

@@ -0,0 +1,315 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001193",
+  "batch_fingerprint": "05ced3fee4d130edee98d6eb18c99ad080988342f29ef163a1dd04eba3a82f48",
+  "evidence": {
+    "batch_fingerprint": "05ced3fee4d130edee98d6eb18c99ad080988342f29ef163a1dd04eba3a82f48",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Option.smul_def",
+        "id": "Option.smul_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            39,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Option.lean",
+          "full_name": "Option.smul_def",
+          "start": [
+            38,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Option.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Option.smul_none",
+        "id": "Option.smul_none",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            45,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Option.lean",
+          "full_name": "Option.smul_none",
+          "start": [
+            44,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Option.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Option.smul_some",
+        "id": "Option.smul_some",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            51,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Option.lean",
+          "full_name": "Option.smul_some",
+          "start": [
+            50,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Option.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.le_period",
+        "id": "MulAction.le_period",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            34,
+            58
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Period.lean",
+          "full_name": "MulAction.le_period",
+          "start": [
+            31,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Period.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.period_le_exponent",
+        "id": "MulAction.period_le_exponent",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            112,
+            50
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Period.lean",
+          "full_name": "MulAction.period_le_exponent",
+          "start": [
+            110,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Period.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.period_le_of_fixed",
+        "id": "MulAction.period_le_of_fixed",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            40,
+            59
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Period.lean",
+          "full_name": "MulAction.period_le_of_fixed",
+          "start": [
+            38,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Period.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.period_le_orderOf",
+        "id": "MulAction.period_le_orderOf",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            98,
+            51
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Period.lean",
+          "full_name": "MulAction.period_le_orderOf",
+          "start": [
+            96,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Period.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.period_one",
+        "id": "MulAction.period_one",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            68,
+            90
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Period.lean",
+          "full_name": "MulAction.period_one",
+          "start": [
+            68,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Period.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.period_pos_of_exponent_pos",
+        "id": "MulAction.period_pos_of_exponent_pos",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            107,
+            58
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Period.lean",
+          "full_name": "MulAction.period_pos_of_exponent_pos",
+          "start": [
+            105,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Period.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.period_pos_of_fixed",
+        "id": "MulAction.period_pos_of_fixed",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            46,
+            60
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Period.lean",
+          "full_name": "MulAction.period_pos_of_fixed",
+          "start": [
+            44,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Period.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.period_pos_of_orderOf_pos",
+        "id": "MulAction.period_pos_of_orderOf_pos",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            93,
+            59
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Period.lean",
+          "full_name": "MulAction.period_pos_of_orderOf_pos",
+          "start": [
+            91,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Period.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.pow_smul_ne_of_lt_period",
+        "id": "MulAction.pow_smul_ne_of_lt_period",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            59,
+            63
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Period.lean",
+          "full_name": "MulAction.pow_smul_ne_of_lt_period",
+          "start": [
+            57,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Period.lean"
+      }
+    ],
+    "input_proofs": 17,
+    "input_units": 2,
+    "proofs": 5,
+    "published_proofs": 5,
+    "published_transitions": 8,
+    "replay_failures": [],
+    "transitions": 8,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001193-0000-213797fd8e1cedbb.parquet",
+      "sha256": "213797fd8e1cedbbc77e2b65ca5efbab1ac6630b7d9b3dae7de31f1b1338847e",
+      "bytes": 49694,
+      "rows": 7,
+      "revision": "906b7b88e1251d7543db52f3953c29ea18db26ce"
+    },
+    {
+      "path": "data/internal_test/mathlib-001193-0000-ccbf1e5c9013e2a7.parquet",
+      "sha256": "ccbf1e5c9013e2a7416378650611f03092a466b8894e084a94216c797ba17f49",
+      "bytes": 31922,
+      "rows": 1,
+      "revision": "906b7b88e1251d7543db52f3953c29ea18db26ce"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:MulAction.period_bounded_of_exponent_pos",
+    "mathlib:MulAction.period_dvd_exponent",
+    "mathlib:MulAction.period_dvd_orderOf",
+    "mathlib:MulAction.period_eq_one_iff",
+    "mathlib:MulAction.period_inv"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Period.lean\",null,null,\"MulAction.period_bounded_of_exponent_pos\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Period.lean\",null,null,\"MulAction.period_dvd_exponent\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Period.lean\",null,null,\"MulAction.period_dvd_orderOf\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Period.lean\",null,null,\"MulAction.period_eq_one_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Period.lean\",null,null,\"MulAction.period_inv\"]"
+  ]
+}

manifests/batches/mathlib/001194.json

@@ -0,0 +1,682 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001194",
+  "batch_fingerprint": "4b8d2eedf4144ebae49177d81e8170480fb6b1cda035a02267d36b924b23b54f",
+  "evidence": {
+    "batch_fingerprint": "4b8d2eedf4144ebae49177d81e8170480fb6b1cda035a02267d36b924b23b54f",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.update_smul",
+        "id": "Function.update_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            249,
+            76
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Pi.lean",
+          "full_name": "Function.update_smul",
+          "start": [
+            247,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Pi.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'have :=\\n  congr_fun (h <| Function.update (fun j => Classical.choice (\u2039\u2200 i, Nonempty (f i)\u203a j)) i a)\\n    i'",
+        "full_name": "Pi.faithfulSMul_at",
+        "id": "Pi.faithfulSMul_at",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            116,
+            26
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Pi.lean",
+          "full_name": "Pi.faithfulSMul_at",
+          "start": [
+            108,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"classical\\n        have :=\\n          <a>congr_fun<\\/a> (h <| <a>Function.update<\\/a> (fun j => <a>Classical.choice<\\/a> (\\u2039\\u2200 i, Nonempty (f i)\\u203a j)) i a)\\n            i\\n        simpa using this\"",
+                "[{\"full_name\":\"congr_fun\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Logic.lean\",\"def_pos\":[78,7],\"def_end_pos\":[78,16]},{\"full_name\":\"Function.update\",\"def_path\":\"Mathlib\\/Logic\\/Function\\/Basic.lean\",\"def_pos\":[553,5],\"def_end_pos\":[553,11]},{\"full_name\":\"Classical.choice\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[735,7],\"def_end_pos\":[735,23]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "I : Type u\nf : I \u2192 Type v\nx y : (i : I) \u2192 f i\ni\u271d : I\n\u03b1 : Type u_1\ninst\u271d\u00b2 : (i : I) \u2192 SMul \u03b1 (f i)\ninst\u271d\u00b9 : \u2200 (i : I), Nonempty (f i)\ni : I\ninst\u271d : FaithfulSMul \u03b1 (f i)\nm\u2081\u271d m\u2082\u271d : \u03b1\nh : \u2200 (a : (i : I) \u2192 f i), m\u2081\u271d \u2022 a = m\u2082\u271d \u2022 a\na : f i\n\u22a2 m\u2081\u271d \u2022 a = m\u2082\u271d \u2022 a",
+              "tactic": "classical\n  have :=\n    congr_fun (h <| Function.update (fun j => Classical.choice (\u2039\u2200 i, Nonempty (f i)\u203a j)) i a)\n      i\n  simpa using this"
+            },
+            {
+              "annotated_tactic": [
+                "\"have :=\\n          <a>congr_fun<\\/a> (h <| <a>Function.update<\\/a> (fun j => <a>Classical.choice<\\/a> (\\u2039\\u2200 i, Nonempty (f i)\\u203a j)) i a)\\n            i\"",
+                "[{\"full_name\":\"congr_fun\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Logic.lean\",\"def_pos\":[78,7],\"def_end_pos\":[78,16]},{\"full_name\":\"Function.update\",\"def_path\":\"Mathlib\\/Logic\\/Function\\/Basic.lean\",\"def_pos\":[553,5],\"def_end_pos\":[553,11]},{\"full_name\":\"Classical.choice\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[735,7],\"def_end_pos\":[735,23]}]"
+              ],
+              "state_after": "I : Type u\nf : I \u2192 Type v\nx y : (i : I) \u2192 f i\ni\u271d : I\n\u03b1 : Type u_1\ninst\u271d\u00b2 : (i : I) \u2192 SMul \u03b1 (f i)\ninst\u271d\u00b9 : \u2200 (i : I), Nonempty (f i)\ni : I\ninst\u271d : FaithfulSMul \u03b1 (f i)\nm\u2081\u271d m\u2082\u271d : \u03b1\nh : \u2200 (a : (i : I) \u2192 f i), m\u2081\u271d \u2022 a = m\u2082\u271d \u2022 a\na : f i\nthis :\n  (m\u2081\u271d \u2022 Function.update (fun j => Classical.choice \u22ef) i a) i =\n    (m\u2082\u271d \u2022 Function.update (fun j => Classical.choice \u22ef) i a) i\n\u22a2 m\u2081\u271d \u2022 a = m\u2082\u271d \u2022 a",
+              "state_before": "I : Type u\nf : I \u2192 Type v\nx y : (i : I) \u2192 f i\ni\u271d : I\n\u03b1 : Type u_1\ninst\u271d\u00b2 : (i : I) \u2192 SMul \u03b1 (f i)\ninst\u271d\u00b9 : \u2200 (i : I), Nonempty (f i)\ni : I\ninst\u271d : FaithfulSMul \u03b1 (f i)\nm\u2081\u271d m\u2082\u271d : \u03b1\nh : \u2200 (a : (i : I) \u2192 f i), m\u2081\u271d \u2022 a = m\u2082\u271d \u2022 a\na : f i\n\u22a2 m\u2081\u271d \u2022 a = m\u2082\u271d \u2022 a",
+              "tactic": "have :=\n  congr_fun (h <| Function.update (fun j => Classical.choice (\u2039\u2200 i, Nonempty (f i)\u203a j)) i a)\n    i"
+            },
+            {
+              "annotated_tactic": [
+                "\"simpa using this\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "I : Type u\nf : I \u2192 Type v\nx y : (i : I) \u2192 f i\ni\u271d : I\n\u03b1 : Type u_1\ninst\u271d\u00b2 : (i : I) \u2192 SMul \u03b1 (f i)\ninst\u271d\u00b9 : \u2200 (i : I), Nonempty (f i)\ni : I\ninst\u271d : FaithfulSMul \u03b1 (f i)\nm\u2081\u271d m\u2082\u271d : \u03b1\nh : \u2200 (a : (i : I) \u2192 f i), m\u2081\u271d \u2022 a = m\u2082\u271d \u2022 a\na : f i\nthis :\n  (m\u2081\u271d \u2022 Function.update (fun j => Classical.choice \u22ef) i a) i =\n    (m\u2082\u271d \u2022 Function.update (fun j => Classical.choice \u22ef) i a) i\n\u22a2 m\u2081\u271d \u2022 a = m\u2082\u271d \u2022 a",
+              "tactic": "simpa using this"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Pi.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Pi.single_smul",
+        "id": "Pi.single_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            183,
+            74
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Pi.lean",
+          "full_name": "Pi.single_smul",
+          "start": [
+            181,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Pi.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Pi.single_smul'",
+        "id": "Pi.single_smul'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            191,
+            38
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Pi.lean",
+          "full_name": "Pi.single_smul'",
+          "start": [
+            189,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Pi.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Pi.single_smul\u2080",
+        "id": "Pi.single_smul\u2080",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            197,
+            85
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Pi.lean",
+          "full_name": "Pi.single_smul\u2080",
+          "start": [
+            194,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Pi.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Pi.smul_apply'",
+        "id": "Pi.smul_apply'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            47,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Pi.lean",
+          "full_name": "Pi.smul_apply'",
+          "start": [
+            45,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Pi.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.piecewise_smul",
+        "id": "Set.piecewise_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            260,
+            49
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Pi.lean",
+          "full_name": "Set.piecewise_smul",
+          "start": [
+            258,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Pi.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Group.preimage_smul_set",
+        "id": "Group.preimage_smul_set",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            151,
+            56
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Pointwise.lean",
+          "full_name": "Group.preimage_smul_set",
+          "start": [
+            145,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Pointwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Group.preimage_smul_set\u209b\u2097",
+        "id": "Group.preimage_smul_set\u209b\u2097",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            118,
+            75
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Pointwise.lean",
+          "full_name": "Group.preimage_smul_set\u209b\u2097",
+          "start": [
+            112,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Pointwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MonoidHom.preimage_smul_set\u209b\u2097",
+        "id": "MonoidHom.preimage_smul_set\u209b\u2097",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            100,
+            62
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Pointwise.lean",
+          "full_name": "MonoidHom.preimage_smul_set\u209b\u2097",
+          "start": [
+            96,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Pointwise.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'intro x'",
+        "full_name": "MulAction.smul_bijective_of_is_unit",
+        "id": "MulAction.smul_bijective_of_is_unit",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            41,
+            37
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Pointwise.lean",
+          "full_name": "MulAction.smul_bijective_of_is_unit",
+          "start": [
+            33,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"lift m to M\\u02e3 using hm\"",
+                "[]"
+              ],
+              "state_after": "case intro\nM : Type u_1\ninst\u271d\u00b9 : Monoid M\n\u03b1 : Type u_2\ninst\u271d : MulAction M \u03b1\nm : M\u02e3\n\u22a2 Function.Bijective fun a => \u2191m \u2022 a",
+              "state_before": "M : Type u_1\ninst\u271d\u00b9 : Monoid M\n\u03b1 : Type u_2\ninst\u271d : MulAction M \u03b1\nm : M\nhm : IsUnit m\n\u22a2 Function.Bijective fun a => m \u2022 a",
+              "tactic": "lift m to M\u02e3 using hm"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Function.bijective_iff_has_inverse<\\/a>]\"",
+                "[{\"full_name\":\"Function.bijective_iff_has_inverse\",\"def_path\":\"Mathlib\\/Logic\\/Function\\/Basic.lean\",\"def_pos\":[518,9],\"def_end_pos\":[518,34]}]"
+              ],
+              "state_after": "case intro\nM : Type u_1\ninst\u271d\u00b9 : Monoid M\n\u03b1 : Type u_2\ninst\u271d : MulAction M \u03b1\nm : M\u02e3\n\u22a2 \u2203 g, (Function.LeftInverse g fun a => \u2191m \u2022 a) \u2227 Function.RightInverse g fun a => \u2191m \u2022 a",
+              "state_before": "case intro\nM : Type u_1\ninst\u271d\u00b9 : Monoid M\n\u03b1 : Type u_2\ninst\u271d : MulAction M \u03b1\nm : M\u02e3\n\u22a2 Function.Bijective fun a => \u2191m \u2022 a",
+              "tactic": "rw [Function.bijective_iff_has_inverse]"
+            },
+            {
+              "annotated_tactic": [
+                "\"use fun a \\u21a6 m\\u207b\\u00b9 \\u2022 a\"",
+                "[]"
+              ],
+              "state_after": "case h\nM : Type u_1\ninst\u271d\u00b9 : Monoid M\n\u03b1 : Type u_2\ninst\u271d : MulAction M \u03b1\nm : M\u02e3\n\u22a2 (Function.LeftInverse (fun a => m\u207b\u00b9 \u2022 a) fun a => \u2191m \u2022 a) \u2227 Function.RightInverse (fun a => m\u207b\u00b9 \u2022 a) fun a => \u2191m \u2022 a",
+              "state_before": "case intro\nM : Type u_1\ninst\u271d\u00b9 : Monoid M\n\u03b1 : Type u_2\ninst\u271d : MulAction M \u03b1\nm : M\u02e3\n\u22a2 \u2203 g, (Function.LeftInverse g fun a => \u2191m \u2022 a) \u2227 Function.RightInverse g fun a => \u2191m \u2022 a",
+              "tactic": "use fun a \u21a6 m\u207b\u00b9 \u2022 a"
+            },
+            {
+              "annotated_tactic": [
+                "\"constructor\"",
+                "[]"
+              ],
+              "state_after": "case h.left\nM : Type u_1\ninst\u271d\u00b9 : Monoid M\n\u03b1 : Type u_2\ninst\u271d : MulAction M \u03b1\nm : M\u02e3\n\u22a2 Function.LeftInverse (fun a => m\u207b\u00b9 \u2022 a) fun a => \u2191m \u2022 a\n\ncase h.right\nM : Type u_1\ninst\u271d\u00b9 : Monoid M\n\u03b1 : Type u_2\ninst\u271d : MulAction M \u03b1\nm : M\u02e3\n\u22a2 Function.RightInverse (fun a => m\u207b\u00b9 \u2022 a) fun a => \u2191m \u2022 a",
+              "state_before": "case h\nM : Type u_1\ninst\u271d\u00b9 : Monoid M\n\u03b1 : Type u_2\ninst\u271d : MulAction M \u03b1\nm : M\u02e3\n\u22a2 (Function.LeftInverse (fun a => m\u207b\u00b9 \u2022 a) fun a => \u2191m \u2022 a) \u2227 Function.RightInverse (fun a => m\u207b\u00b9 \u2022 a) fun a => \u2191m \u2022 a",
+              "tactic": "constructor"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro x\"",
+                "[]"
+              ],
+              "state_after": "case h.left\nM : Type u_1\ninst\u271d\u00b9 : Monoid M\n\u03b1 : Type u_2\ninst\u271d : MulAction M \u03b1\nm : M\u02e3\nx : \u03b1\n\u22a2 (fun a => m\u207b\u00b9 \u2022 a) ((fun a => \u2191m \u2022 a) x) = x",
+              "state_before": "case h.left\nM : Type u_1\ninst\u271d\u00b9 : Monoid M\n\u03b1 : Type u_2\ninst\u271d : MulAction M \u03b1\nm : M\u02e3\n\u22a2 Function.LeftInverse (fun a => m\u207b\u00b9 \u2022 a) fun a => \u2191m \u2022 a",
+              "tactic": "intro x"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [\\u2190 <a>Units.smul_def<\\/a>]\"",
+                "[{\"full_name\":\"Units.smul_def\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Units.lean\",\"def_pos\":[37,9],\"def_end_pos\":[37,17]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.left\nM : Type u_1\ninst\u271d\u00b9 : Monoid M\n\u03b1 : Type u_2\ninst\u271d : MulAction M \u03b1\nm : M\u02e3\nx : \u03b1\n\u22a2 (fun a => m\u207b\u00b9 \u2022 a) ((fun a => \u2191m \u2022 a) x) = x",
+              "tactic": "simp [\u2190 Units.smul_def]"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro x\"",
+                "[]"
+              ],
+              "state_after": "case h.right\nM : Type u_1\ninst\u271d\u00b9 : Monoid M\n\u03b1 : Type u_2\ninst\u271d : MulAction M \u03b1\nm : M\u02e3\nx : \u03b1\n\u22a2 (fun a => \u2191m \u2022 a) ((fun a => m\u207b\u00b9 \u2022 a) x) = x",
+              "state_before": "case h.right\nM : Type u_1\ninst\u271d\u00b9 : Monoid M\n\u03b1 : Type u_2\ninst\u271d : MulAction M \u03b1\nm : M\u02e3\n\u22a2 Function.RightInverse (fun a => m\u207b\u00b9 \u2022 a) fun a => \u2191m \u2022 a",
+              "tactic": "intro x"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [\\u2190 <a>Units.smul_def<\\/a>]\"",
+                "[{\"full_name\":\"Units.smul_def\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Units.lean\",\"def_pos\":[37,9],\"def_end_pos\":[37,17]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.right\nM : Type u_1\ninst\u271d\u00b9 : Monoid M\n\u03b1 : Type u_2\ninst\u271d : MulAction M \u03b1\nm : M\u02e3\nx : \u03b1\n\u22a2 (fun a => \u2191m \u2022 a) ((fun a => m\u207b\u00b9 \u2022 a) x) = x",
+              "tactic": "simp [\u2190 Units.smul_def]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Pointwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "image_smul_set",
+        "id": "image_smul_set",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            131,
+            31
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Pointwise.lean",
+          "full_name": "image_smul_set",
+          "start": [
+            129,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Pointwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "preimage_smul_set",
+        "id": "preimage_smul_set",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            142,
+            47
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Pointwise.lean",
+          "full_name": "preimage_smul_set",
+          "start": [
+            140,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Pointwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "preimage_smul_set\u209b\u2097",
+        "id": "preimage_smul_set\u209b\u2097",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            109,
+            55
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Pointwise.lean",
+          "full_name": "preimage_smul_set\u209b\u2097",
+          "start": [
+            103,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Pointwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "smul_preimage_set_le",
+        "id": "smul_preimage_set_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            136,
+            37
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Pointwise.lean",
+          "full_name": "smul_preimage_set_le",
+          "start": [
+            134,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Pointwise.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rw [map_smul\u209b\u2097]'",
+        "full_name": "smul_preimage_set_le\u209b\u2097",
+        "id": "smul_preimage_set_le\u209b\u2097",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            67,
+            38
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Pointwise.lean",
+          "full_name": "smul_preimage_set_le\u209b\u2097",
+          "start": [
+            64,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rintro x \\u27e8y, hy, rfl\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "case intro.intro\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\ny : M\nhy : y \u2208 \u21d1h \u207b\u00b9' t\n\u22a2 (fun x => c \u2022 x) y \u2208 \u21d1h \u207b\u00b9' (\u03c3 c \u2022 t)",
+              "state_before": "R : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\n\u22a2 c \u2022 \u21d1h \u207b\u00b9' t \u2286 \u21d1h \u207b\u00b9' (\u03c3 c \u2022 t)",
+              "tactic": "rintro x \u27e8y, hy, rfl\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact \\u27e8h y, hy, by rw [<a>map_smul\\u209b\\u2097<\\/a>]\\u27e9\"",
+                "[{\"full_name\":\"MulActionSemiHomClass.map_smul\\u209b\\u2097\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Hom.lean\",\"def_pos\":[94,3],\"def_end_pos\":[94,13]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case intro.intro\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\ny : M\nhy : y \u2208 \u21d1h \u207b\u00b9' t\n\u22a2 (fun x => c \u2022 x) y \u2208 \u21d1h \u207b\u00b9' (\u03c3 c \u2022 t)",
+              "tactic": "exact \u27e8h y, hy, by rw [map_smul\u209b\u2097]\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>map_smul\\u209b\\u2097<\\/a>]\"",
+                "[{\"full_name\":\"MulActionSemiHomClass.map_smul\\u209b\\u2097\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Hom.lean\",\"def_pos\":[94,3],\"def_end_pos\":[94,13]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\ny : M\nhy : y \u2208 \u21d1h \u207b\u00b9' t\n\u22a2 (fun x => \u03c3 c \u2022 x) (h y) = h ((fun x => c \u2022 x) y)",
+              "tactic": "rw [map_smul\u209b\u2097]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Pointwise.lean"
+      }
+    ],
+    "input_proofs": 20,
+    "input_units": 2,
+    "proofs": 4,
+    "published_proofs": 2,
+    "published_transitions": 4,
+    "replay_failures": [],
+    "transitions": 16,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/GroupTheory/GroupAction/Pointwise.lean",
+        "proof_id": "mathlib:preimage_smul_set\u209b\u2097'",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              84,
+              45
+            ],
+            "file_path": "Mathlib/GroupTheory/GroupAction/Pointwise.lean",
+            "full_name": "preimage_smul_set\u209b\u2097'",
+            "start": [
+              72,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"apply <a>le_antisymm<\\/a>\"",
+                  "[{\"full_name\":\"le_antisymm\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[188,9],\"def_end_pos\":[188,20]}]"
+                ],
+                "state_after": "case a\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : Function.Surjective fun m => c \u2022 m\nhc' : Function.Injective fun n => \u03c3 c \u2022 n\n\u22a2 \u21d1h \u207b\u00b9' (\u03c3 c \u2022 t) \u2264 c \u2022 \u21d1h \u207b\u00b9' t\n\ncase a\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : Function.Surjective fun m => c \u2022 m\nhc' : Function.Injective fun n => \u03c3 c \u2022 n\n\u22a2 c \u2022 \u21d1h \u207b\u00b9' t \u2264 \u21d1h \u207b\u00b9' (\u03c3 c \u2022 t)",
+                "state_before": "R : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : Function.Surjective fun m => c \u2022 m\nhc' : Function.Injective fun n => \u03c3 c \u2022 n\n\u22a2 \u21d1h \u207b\u00b9' (\u03c3 c \u2022 t) = c \u2022 \u21d1h \u207b\u00b9' t",
+                "tactic": "apply le_antisymm"
+              },
+              {
+                "annotated_tactic": [
+                  "\"intro m\"",
+                  "[]"
+                ],
+                "state_after": "case a\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : Function.Surjective fun m => c \u2022 m\nhc' : Function.Injective fun n => \u03c3 c \u2022 n\nm : M\n\u22a2 m \u2208 \u21d1h \u207b\u00b9' (\u03c3 c \u2022 t) \u2192 m \u2208 c \u2022 \u21d1h \u207b\u00b9' t",
+                "state_before": "case a\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : Function.Surjective fun m => c \u2022 m\nhc' : Function.Injective fun n => \u03c3 c \u2022 n\n\u22a2 \u21d1h \u207b\u00b9' (\u03c3 c \u2022 t) \u2264 c \u2022 \u21d1h \u207b\u00b9' t",
+                "tactic": "intro m"
+              },
+              {
+                "annotated_tactic": [
+                  "\"obtain \\u27e8m', rfl\\u27e9 := hc m\"",
+                  "[]"
+                ],
+                "state_after": "case a.intro\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : Function.Surjective fun m => c \u2022 m\nhc' : Function.Injective fun n => \u03c3 c \u2022 n\nm' : M\n\u22a2 (fun m => c \u2022 m) m' \u2208 \u21d1h \u207b\u00b9' (\u03c3 c \u2022 t) \u2192 (fun m => c \u2022 m) m' \u2208 c \u2022 \u21d1h \u207b\u00b9' t",
+                "state_before": "case a\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : Function.Surjective fun m => c \u2022 m\nhc' : Function.Injective fun n => \u03c3 c \u2022 n\nm : M\n\u22a2 m \u2208 \u21d1h \u207b\u00b9' (\u03c3 c \u2022 t) \u2192 m \u2208 c \u2022 \u21d1h \u207b\u00b9' t",
+                "tactic": "obtain \u27e8m', rfl\u27e9 := hc m"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rintro \\u27e8n, hn, hn'\\u27e9\"",
+                  "[]"
+                ],
+                "state_after": "case a.intro.intro.intro\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : Function.Surjective fun m => c \u2022 m\nhc' : Function.Injective fun n => \u03c3 c \u2022 n\nm' : M\nn : N\nhn : n \u2208 t\nhn' : (fun x => \u03c3 c \u2022 x) n = h ((fun m => c \u2022 m) m')\n\u22a2 (fun m => c \u2022 m) m' \u2208 c \u2022 \u21d1h \u207b\u00b9' t",
+                "state_before": "case a.intro\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : Function.Surjective fun m => c \u2022 m\nhc' : Function.Injective fun n => \u03c3 c \u2022 n\nm' : M\n\u22a2 (fun m => c \u2022 m) m' \u2208 \u21d1h \u207b\u00b9' (\u03c3 c \u2022 t) \u2192 (fun m => c \u2022 m) m' \u2208 c \u2022 \u21d1h \u207b\u00b9' t",
+                "tactic": "rintro \u27e8n, hn, hn'\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"refine \\u27e8m', ?_, <a>rfl<\\/a>\\u27e9\"",
+                  "[{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]}]"
+                ],
+                "state_after": "case a.intro.intro.intro\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : Function.Surjective fun m => c \u2022 m\nhc' : Function.Injective fun n => \u03c3 c \u2022 n\nm' : M\nn : N\nhn : n \u2208 t\nhn' : (fun x => \u03c3 c \u2022 x) n = h ((fun m => c \u2022 m) m')\n\u22a2 m' \u2208 \u21d1h \u207b\u00b9' t",
+                "state_before": "case a.intro.intro.intro\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : Function.Surjective fun m => c \u2022 m\nhc' : Function.Injective fun n => \u03c3 c \u2022 n\nm' : M\nn : N\nhn : n \u2208 t\nhn' : (fun x => \u03c3 c \u2022 x) n = h ((fun m => c \u2022 m) m')\n\u22a2 (fun m => c \u2022 m) m' \u2208 c \u2022 \u21d1h \u207b\u00b9' t",
+                "tactic": "refine \u27e8m', ?_, rfl\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>map_smul\\u209b\\u2097<\\/a>] at hn'\"",
+                  "[{\"full_name\":\"MulActionSemiHomClass.map_smul\\u209b\\u2097\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Hom.lean\",\"def_pos\":[94,3],\"def_end_pos\":[94,13]}]"
+                ],
+                "state_after": "case a.intro.intro.intro\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : Function.Surjective fun m => c \u2022 m\nhc' : Function.Injective fun n => \u03c3 c \u2022 n\nm' : M\nn : N\nhn : n \u2208 t\nhn' : (fun x => \u03c3 c \u2022 x) n = \u03c3 c \u2022 h m'\n\u22a2 m' \u2208 \u21d1h \u207b\u00b9' t",
+                "state_before": "case a.intro.intro.intro\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : Function.Surjective fun m => c \u2022 m\nhc' : Function.Injective fun n => \u03c3 c \u2022 n\nm' : M\nn : N\nhn : n \u2208 t\nhn' : (fun x => \u03c3 c \u2022 x) n = h ((fun m => c \u2022 m) m')\n\u22a2 m' \u2208 \u21d1h \u207b\u00b9' t",
+                "tactic": "rw [map_smul\u209b\u2097] at hn'"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>mem_preimage<\\/a>, \\u2190 hc' hn']\"",
+                  "[{\"full_name\":\"Set.mem_preimage\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Defs.lean\",\"def_pos\":[120,9],\"def_end_pos\":[120,21]}]"
+                ],
+                "state_after": "case a.intro.intro.intro\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : Function.Surjective fun m => c \u2022 m\nhc' : Function.Injective fun n => \u03c3 c \u2022 n\nm' : M\nn : N\nhn : n \u2208 t\nhn' : (fun x => \u03c3 c \u2022 x) n = \u03c3 c \u2022 h m'\n\u22a2 n \u2208 t",
+                "state_before": "case a.intro.intro.intro\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : Function.Surjective fun m => c \u2022 m\nhc' : Function.Injective fun n => \u03c3 c \u2022 n\nm' : M\nn : N\nhn : n \u2208 t\nhn' : (fun x => \u03c3 c \u2022 x) n = \u03c3 c \u2022 h m'\n\u22a2 m' \u2208 \u21d1h \u207b\u00b9' t",
+                "tactic": "rw [mem_preimage, \u2190 hc' hn']"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact hn\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case a.intro.intro.intro\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : Function.Surjective fun m => c \u2022 m\nhc' : Function.Injective fun n => \u03c3 c \u2022 n\nm' : M\nn : N\nhn : n \u2208 t\nhn' : (fun x => \u03c3 c \u2022 x) n = \u03c3 c \u2022 h m'\n\u22a2 n \u2208 t",
+                "tactic": "exact hn"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact <a>smul_preimage_set_le\\u209b\\u2097<\\/a> M N \\u03c3 h c t\"",
+                  "[{\"full_name\":\"smul_preimage_set_le\\u209b\\u2097\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Pointwise.lean\",\"def_pos\":[64,9],\"def_end_pos\":[64,31]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case a\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : Function.Surjective fun m => c \u2022 m\nhc' : Function.Injective fun n => \u03c3 c \u2022 n\n\u22a2 c \u2022 \u21d1h \u207b\u00b9' t \u2264 \u21d1h \u207b\u00b9' (\u03c3 c \u2022 t)",
+                "tactic": "exact smul_preimage_set_le\u209b\u2097 M N \u03c3 h c t"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "preimage_smul_set\u209b\u2097'"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/GroupTheory/GroupAction/Pointwise.lean",
+        "proof_id": "mathlib:preimage_smul_set\u209b\u2097_of_units",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              91,
+              62
+            ],
+            "file_path": "Mathlib/GroupTheory/GroupAction/Pointwise.lean",
+            "full_name": "preimage_smul_set\u209b\u2097_of_units",
+            "start": [
+              87,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"apply <a>preimage_smul_set\\u209b\\u2097'<\\/a>\"",
+                  "[{\"full_name\":\"preimage_smul_set\\u209b\\u2097'\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Pointwise.lean\",\"def_pos\":[72,9],\"def_end_pos\":[72,29]}]"
+                ],
+                "state_after": "case hc\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : IsUnit c\nhc' : IsUnit (\u03c3 c)\n\u22a2 Function.Surjective fun m => c \u2022 m\n\ncase hc'\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : IsUnit c\nhc' : IsUnit (\u03c3 c)\n\u22a2 Function.Injective fun n => \u03c3 c \u2022 n",
+                "state_before": "R : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : IsUnit c\nhc' : IsUnit (\u03c3 c)\n\u22a2 \u21d1h \u207b\u00b9' (\u03c3 c \u2022 t) = c \u2022 \u21d1h \u207b\u00b9' t",
+                "tactic": "apply preimage_smul_set\u209b\u2097'"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact (<a>MulAction.smul_bijective_of_is_unit<\\/a> hc).<a>surjective<\\/a>\"",
+                  "[{\"full_name\":\"MulAction.smul_bijective_of_is_unit\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Pointwise.lean\",\"def_pos\":[33,9],\"def_end_pos\":[33,44]},{\"full_name\":\"Function.Bijective.surjective\",\"def_path\":\"Mathlib\\/Logic\\/Function\\/Basic.lean\",\"def_pos\":[82,19],\"def_end_pos\":[82,39]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case hc\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : IsUnit c\nhc' : IsUnit (\u03c3 c)\n\u22a2 Function.Surjective fun m => c \u2022 m",
+                "tactic": "exact (MulAction.smul_bijective_of_is_unit hc).surjective"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact (<a>MulAction.smul_bijective_of_is_unit<\\/a> hc').<a>injective<\\/a>\"",
+                  "[{\"full_name\":\"MulAction.smul_bijective_of_is_unit\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Pointwise.lean\",\"def_pos\":[33,9],\"def_end_pos\":[33,44]},{\"full_name\":\"Function.Bijective.injective\",\"def_path\":\"Mathlib\\/Logic\\/Function\\/Basic.lean\",\"def_pos\":[80,19],\"def_end_pos\":[80,38]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case hc'\nR : Type u_1\nS : Type u_2\nM : Type u_3\nM\u2081 : Type u_4\nM\u2082 : Type u_5\nN : Type u_6\ninst\u271d\u2077 : Monoid R\ninst\u271d\u2076 : Monoid S\n\u03c3 : R \u2192 S\ninst\u271d\u2075 : MulAction R M\ninst\u271d\u2074 : MulAction S N\ninst\u271d\u00b3 : MulAction R M\u2081\ninst\u271d\u00b2 : MulAction R M\u2082\nF : Type u_7\nh : F\ninst\u271d\u00b9 : FunLike F M N\ninst\u271d : MulActionSemiHomClass F \u03c3 M N\nc : R\ns : Set M\nt : Set N\nhc : IsUnit c\nhc' : IsUnit (\u03c3 c)\n\u22a2 Function.Injective fun n => \u03c3 c \u2022 n",
+                "tactic": "exact (MulAction.smul_bijective_of_is_unit hc').injective"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "preimage_smul_set\u209b\u2097_of_units"
+      }
+    ],
+    "validation_rejected_proofs": 2,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001194-0000-dc6b2eb43a569ee0.parquet",
+      "sha256": "dc6b2eb43a569ee04de16d6b51470e920f4554f18459b6cd49f7ddff2cf49897",
+      "bytes": 59307,
+      "rows": 4,
+      "revision": "906b7b88e1251d7543db52f3953c29ea18db26ce"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Function.extend_smul",
+    "mathlib:image_smul_set\u209b\u2097"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Pi.lean\",null,null,\"Function.extend_smul\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Pointwise.lean\",null,null,\"image_smul_set\u209b\u2097\"]"
+  ]
+}

manifests/batches/mathlib/001195.json

@@ -0,0 +1,888 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001195",
+  "batch_fingerprint": "0e91c9ab2281201e8ba5b00c331da2fee803bd09c5c4c9be6d768d1c4dce94b3",
+  "evidence": {
+    "batch_fingerprint": "0e91c9ab2281201e8ba5b00c331da2fee803bd09c5c4c9be6d768d1c4dce94b3",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Prod.pow_def",
+        "id": "Prod.pow_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            111,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Prod.lean",
+          "full_name": "Prod.pow_def",
+          "start": [
+            110,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Prod.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Prod.pow_fst",
+        "id": "Prod.pow_fst",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            93,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Prod.lean",
+          "full_name": "Prod.pow_fst",
+          "start": [
+            92,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Prod.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Prod.pow_mk",
+        "id": "Prod.pow_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            106,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Prod.lean",
+          "full_name": "Prod.pow_mk",
+          "start": [
+            105,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Prod.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Prod.pow_snd",
+        "id": "Prod.pow_snd",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            98,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Prod.lean",
+          "full_name": "Prod.pow_snd",
+          "start": [
+            97,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Prod.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Prod.pow_swap",
+        "id": "Prod.pow_swap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            116,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Prod.lean",
+          "full_name": "Prod.pow_swap",
+          "start": [
+            115,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Prod.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Prod.smul_def",
+        "id": "Prod.smul_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            66,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Prod.lean",
+          "full_name": "Prod.smul_def",
+          "start": [
+            65,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Prod.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Prod.smul_fst",
+        "id": "Prod.smul_fst",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            48,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Prod.lean",
+          "full_name": "Prod.smul_fst",
+          "start": [
+            47,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Prod.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Prod.smul_mk",
+        "id": "Prod.smul_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            60,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Prod.lean",
+          "full_name": "Prod.smul_mk",
+          "start": [
+            59,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Prod.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Prod.smul_snd",
+        "id": "Prod.smul_snd",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            54,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Prod.lean",
+          "full_name": "Prod.smul_snd",
+          "start": [
+            53,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Prod.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Prod.smul_swap",
+        "id": "Prod.smul_swap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            72,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Prod.lean",
+          "full_name": "Prod.smul_swap",
+          "start": [
+            71,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Prod.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.Quotient.coe_smul_out'",
+        "id": "MulAction.Quotient.coe_smul_out'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            116,
+            30
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Quotient.lean",
+          "full_name": "MulAction.Quotient.coe_smul_out'",
+          "start": [
+            115,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Quotient.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.Quotient.smul_coe",
+        "id": "MulAction.Quotient.smul_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            103,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Quotient.lean",
+          "full_name": "MulAction.Quotient.smul_coe",
+          "start": [
+            101,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Quotient.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.Quotient.smul_mk",
+        "id": "MulAction.Quotient.smul_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            96,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Quotient.lean",
+          "full_name": "MulAction.Quotient.smul_mk",
+          "start": [
+            94,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Quotient.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.card_eq_sum_card_group_div_card_stabilizer",
+        "id": "MulAction.card_eq_sum_card_group_div_card_stabilizer",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            296,
+            67
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Quotient.lean",
+          "full_name": "MulAction.card_eq_sum_card_group_div_card_stabilizer",
+          "start": [
+            293,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Quotient.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'have : \u2200 \u03c9 : \u03a9, Fintype.card \u03b1 / Fintype.card (stabilizer \u03b1 (\u03c6 \u03c9)) =\\n    Fintype.card (\u03b1 \u29f8 stabilizer \u03b1 (\u03c6 \u03c9)) := by\\n  intro \u03c9\\n  rw [Fintype.card_congr (@Subgroup.groupEquivQuotientProdSubgroup \u03b1 _ (stabilizer \u03b1 <| \u03c6 \u03c9)),\\n    Fintype.card_prod, Nat.mul_div_cancel]\\n  exact Fintype.card_pos_iff.mpr (by infer_instance)'",
+        "full_name": "MulAction.card_eq_sum_card_group_div_card_stabilizer'",
+        "id": "MulAction.card_eq_sum_card_group_div_card_stabilizer'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            277,
+            75
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Quotient.lean",
+          "full_name": "MulAction.card_eq_sum_card_group_div_card_stabilizer'",
+          "start": [
+            266,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"classical\\n    have : \\u2200 \\u03c9 : \\u03a9, <a>Fintype.card<\\/a> \\u03b1 \\/ <a>Fintype.card<\\/a> (<a>stabilizer<\\/a> \\u03b1 (\\u03c6 \\u03c9)) =\\n        <a>Fintype.card<\\/a> (\\u03b1 \\u29f8 <a>stabilizer<\\/a> \\u03b1 (\\u03c6 \\u03c9)) := by\\n      intro \\u03c9\\n      rw [<a>Fintype.card_congr<\\/a> (@<a>Subgroup.groupEquivQuotientProdSubgroup<\\/a> \\u03b1 _ (<a>stabilizer<\\/a> \\u03b1 <| \\u03c6 \\u03c9)),\\n        <a>Fintype.card_prod<\\/a>, <a>Nat.mul_div_cancel<\\/a>]\\n      exact Fintype.card_pos_iff.mpr (by infer_instance)\\n    simp_rw [this, \\u2190 <a>Fintype.card_sigma<\\/a>,\\n      <a>Fintype.card_congr<\\/a> (<a>selfEquivSigmaOrbitsQuotientStabilizer'<\\/a> \\u03b1 \\u03b2 h\\u03c6)]\"",
+                "[{\"full_name\":\"Fintype.card\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[63,5],\"def_end_pos\":[63,9]},{\"full_name\":\"Fintype.card\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[63,5],\"def_end_pos\":[63,9]},{\"full_name\":\"MulAction.stabilizer\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Basic.lean\",\"def_pos\":[705,5],\"def_end_pos\":[705,15]},{\"full_name\":\"Fintype.card\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[63,5],\"def_end_pos\":[63,9]},{\"full_name\":\"MulAction.stabilizer\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Basic.lean\",\"def_pos\":[705,5],\"def_end_pos\":[705,15]},{\"full_name\":\"Fintype.card_congr\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[151,9],\"def_end_pos\":[151,19]},{\"full_name\":\"Subgroup.groupEquivQuotientProdSubgroup\",\"def_path\":\"Mathlib\\/GroupTheory\\/Coset.lean\",\"def_pos\":[587,19],\"def_end_pos\":[587,49]},{\"full_name\":\"MulAction.stabilizer\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Basic.lean\",\"def_pos\":[705,5],\"def_end_pos\":[705,15]},{\"full_name\":\"Fintype.card_prod\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Prod.lean\",\"def_pos\":[59,9],\"def_end_pos\":[59,26]},{\"full_name\":\"Nat.mul_div_cancel\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Div.lean\",\"def_pos\":[349,19],\"def_end_pos\":[349,33]},{\"full_name\":\"Fintype.card_sigma\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/BigOperators.lean\",\"def_pos\":[138,22],\"def_end_pos\":[138,32]},{\"full_name\":\"Fintype.card_congr\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[151,9],\"def_end_pos\":[151,19]},{\"full_name\":\"MulAction.selfEquivSigmaOrbitsQuotientStabilizer'\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Quotient.lean\",\"def_pos\":[248,19],\"def_end_pos\":[248,58]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\ninst\u271d\u2076 inst\u271d\u2075 : Group \u03b1\ninst\u271d\u2074 : MulAction \u03b1 \u03b2\nx : \u03b2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : Fintype (Quotient (orbitRel \u03b1 \u03b2))\ninst\u271d : (b : \u03b2) \u2192 Fintype \u21a5(stabilizer \u03b1 b)\n\u03c6 : Quotient (orbitRel \u03b1 \u03b2) \u2192 \u03b2\nh\u03c6 : LeftInverse Quotient.mk'' \u03c6\n\u22a2 Fintype.card \u03b2 = \u2211 \u03c9 : Quotient (orbitRel \u03b1 \u03b2), Fintype.card \u03b1 / Fintype.card \u21a5(stabilizer \u03b1 (\u03c6 \u03c9))",
+              "tactic": "classical\n  have : \u2200 \u03c9 : \u03a9, Fintype.card \u03b1 / Fintype.card (stabilizer \u03b1 (\u03c6 \u03c9)) =\n      Fintype.card (\u03b1 \u29f8 stabilizer \u03b1 (\u03c6 \u03c9)) := by\n    intro \u03c9\n    rw [Fintype.card_congr (@Subgroup.groupEquivQuotientProdSubgroup \u03b1 _ (stabilizer \u03b1 <| \u03c6 \u03c9)),\n      Fintype.card_prod, Nat.mul_div_cancel]\n    exact Fintype.card_pos_iff.mpr (by infer_instance)\n  simp_rw [this, \u2190 Fintype.card_sigma,\n    Fintype.card_congr (selfEquivSigmaOrbitsQuotientStabilizer' \u03b1 \u03b2 h\u03c6)]"
+            },
+            {
+              "annotated_tactic": [
+                "\"have : \\u2200 \\u03c9 : \\u03a9, <a>Fintype.card<\\/a> \\u03b1 \\/ <a>Fintype.card<\\/a> (<a>stabilizer<\\/a> \\u03b1 (\\u03c6 \\u03c9)) =\\n        <a>Fintype.card<\\/a> (\\u03b1 \\u29f8 <a>stabilizer<\\/a> \\u03b1 (\\u03c6 \\u03c9)) := by\\n      intro \\u03c9\\n      rw [<a>Fintype.card_congr<\\/a> (@<a>Subgroup.groupEquivQuotientProdSubgroup<\\/a> \\u03b1 _ (<a>stabilizer<\\/a> \\u03b1 <| \\u03c6 \\u03c9)),\\n        <a>Fintype.card_prod<\\/a>, <a>Nat.mul_div_cancel<\\/a>]\\n      exact Fintype.card_pos_iff.mpr (by infer_instance)\"",
+                "[{\"full_name\":\"Fintype.card\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[63,5],\"def_end_pos\":[63,9]},{\"full_name\":\"Fintype.card\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[63,5],\"def_end_pos\":[63,9]},{\"full_name\":\"MulAction.stabilizer\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Basic.lean\",\"def_pos\":[705,5],\"def_end_pos\":[705,15]},{\"full_name\":\"Fintype.card\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[63,5],\"def_end_pos\":[63,9]},{\"full_name\":\"MulAction.stabilizer\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Basic.lean\",\"def_pos\":[705,5],\"def_end_pos\":[705,15]},{\"full_name\":\"Fintype.card_congr\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[151,9],\"def_end_pos\":[151,19]},{\"full_name\":\"Subgroup.groupEquivQuotientProdSubgroup\",\"def_path\":\"Mathlib\\/GroupTheory\\/Coset.lean\",\"def_pos\":[587,19],\"def_end_pos\":[587,49]},{\"full_name\":\"MulAction.stabilizer\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Basic.lean\",\"def_pos\":[705,5],\"def_end_pos\":[705,15]},{\"full_name\":\"Fintype.card_prod\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Prod.lean\",\"def_pos\":[59,9],\"def_end_pos\":[59,26]},{\"full_name\":\"Nat.mul_div_cancel\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Div.lean\",\"def_pos\":[349,19],\"def_end_pos\":[349,33]}]"
+              ],
+              "state_after": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\ninst\u271d\u2076 inst\u271d\u2075 : Group \u03b1\ninst\u271d\u2074 : MulAction \u03b1 \u03b2\nx : \u03b2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : Fintype (Quotient (orbitRel \u03b1 \u03b2))\ninst\u271d : (b : \u03b2) \u2192 Fintype \u21a5(stabilizer \u03b1 b)\n\u03c6 : Quotient (orbitRel \u03b1 \u03b2) \u2192 \u03b2\nh\u03c6 : LeftInverse Quotient.mk'' \u03c6\nthis :\n  \u2200 (\u03c9 : Quotient (orbitRel \u03b1 \u03b2)),\n    Fintype.card \u03b1 / Fintype.card \u21a5(stabilizer \u03b1 (\u03c6 \u03c9)) = Fintype.card (\u03b1 \u29f8 stabilizer \u03b1 (\u03c6 \u03c9))\n\u22a2 Fintype.card \u03b2 = \u2211 \u03c9 : Quotient (orbitRel \u03b1 \u03b2), Fintype.card \u03b1 / Fintype.card \u21a5(stabilizer \u03b1 (\u03c6 \u03c9))",
+              "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\ninst\u271d\u2076 inst\u271d\u2075 : Group \u03b1\ninst\u271d\u2074 : MulAction \u03b1 \u03b2\nx : \u03b2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : Fintype (Quotient (orbitRel \u03b1 \u03b2))\ninst\u271d : (b : \u03b2) \u2192 Fintype \u21a5(stabilizer \u03b1 b)\n\u03c6 : Quotient (orbitRel \u03b1 \u03b2) \u2192 \u03b2\nh\u03c6 : LeftInverse Quotient.mk'' \u03c6\n\u22a2 Fintype.card \u03b2 = \u2211 \u03c9 : Quotient (orbitRel \u03b1 \u03b2), Fintype.card \u03b1 / Fintype.card \u21a5(stabilizer \u03b1 (\u03c6 \u03c9))",
+              "tactic": "have : \u2200 \u03c9 : \u03a9, Fintype.card \u03b1 / Fintype.card (stabilizer \u03b1 (\u03c6 \u03c9)) =\n    Fintype.card (\u03b1 \u29f8 stabilizer \u03b1 (\u03c6 \u03c9)) := by\n  intro \u03c9\n  rw [Fintype.card_congr (@Subgroup.groupEquivQuotientProdSubgroup \u03b1 _ (stabilizer \u03b1 <| \u03c6 \u03c9)),\n    Fintype.card_prod, Nat.mul_div_cancel]\n  exact Fintype.card_pos_iff.mpr (by infer_instance)"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp_rw [this, \\u2190 <a>Fintype.card_sigma<\\/a>,\\n      <a>Fintype.card_congr<\\/a> (<a>selfEquivSigmaOrbitsQuotientStabilizer'<\\/a> \\u03b1 \\u03b2 h\\u03c6)]\"",
+                "[{\"full_name\":\"Fintype.card_sigma\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/BigOperators.lean\",\"def_pos\":[138,22],\"def_end_pos\":[138,32]},{\"full_name\":\"Fintype.card_congr\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[151,9],\"def_end_pos\":[151,19]},{\"full_name\":\"MulAction.selfEquivSigmaOrbitsQuotientStabilizer'\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Quotient.lean\",\"def_pos\":[248,19],\"def_end_pos\":[248,58]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\ninst\u271d\u2076 inst\u271d\u2075 : Group \u03b1\ninst\u271d\u2074 : MulAction \u03b1 \u03b2\nx : \u03b2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : Fintype (Quotient (orbitRel \u03b1 \u03b2))\ninst\u271d : (b : \u03b2) \u2192 Fintype \u21a5(stabilizer \u03b1 b)\n\u03c6 : Quotient (orbitRel \u03b1 \u03b2) \u2192 \u03b2\nh\u03c6 : LeftInverse Quotient.mk'' \u03c6\nthis :\n  \u2200 (\u03c9 : Quotient (orbitRel \u03b1 \u03b2)),\n    Fintype.card \u03b1 / Fintype.card \u21a5(stabilizer \u03b1 (\u03c6 \u03c9)) = Fintype.card (\u03b1 \u29f8 stabilizer \u03b1 (\u03c6 \u03c9))\n\u22a2 Fintype.card \u03b2 = \u2211 \u03c9 : Quotient (orbitRel \u03b1 \u03b2), Fintype.card \u03b1 / Fintype.card \u21a5(stabilizer \u03b1 (\u03c6 \u03c9))",
+              "tactic": "simp_rw [this, \u2190 Fintype.card_sigma,\n  Fintype.card_congr (selfEquivSigmaOrbitsQuotientStabilizer' \u03b1 \u03b2 h\u03c6)]"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro \\u03c9\"",
+                "[]"
+              ],
+              "state_after": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\ninst\u271d\u2076 inst\u271d\u2075 : Group \u03b1\ninst\u271d\u2074 : MulAction \u03b1 \u03b2\nx : \u03b2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : Fintype (Quotient (orbitRel \u03b1 \u03b2))\ninst\u271d : (b : \u03b2) \u2192 Fintype \u21a5(stabilizer \u03b1 b)\n\u03c6 : Quotient (orbitRel \u03b1 \u03b2) \u2192 \u03b2\nh\u03c6 : LeftInverse Quotient.mk'' \u03c6\n\u03c9 : Quotient (orbitRel \u03b1 \u03b2)\n\u22a2 Fintype.card \u03b1 / Fintype.card \u21a5(stabilizer \u03b1 (\u03c6 \u03c9)) = Fintype.card (\u03b1 \u29f8 stabilizer \u03b1 (\u03c6 \u03c9))",
+              "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\ninst\u271d\u2076 inst\u271d\u2075 : Group \u03b1\ninst\u271d\u2074 : MulAction \u03b1 \u03b2\nx : \u03b2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : Fintype (Quotient (orbitRel \u03b1 \u03b2))\ninst\u271d : (b : \u03b2) \u2192 Fintype \u21a5(stabilizer \u03b1 b)\n\u03c6 : Quotient (orbitRel \u03b1 \u03b2) \u2192 \u03b2\nh\u03c6 : LeftInverse Quotient.mk'' \u03c6\n\u22a2 \u2200 (\u03c9 : Quotient (orbitRel \u03b1 \u03b2)),\n    Fintype.card \u03b1 / Fintype.card \u21a5(stabilizer \u03b1 (\u03c6 \u03c9)) = Fintype.card (\u03b1 \u29f8 stabilizer \u03b1 (\u03c6 \u03c9))",
+              "tactic": "intro \u03c9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Fintype.card_congr<\\/a> (@<a>Subgroup.groupEquivQuotientProdSubgroup<\\/a> \\u03b1 _ (<a>stabilizer<\\/a> \\u03b1 <| \\u03c6 \\u03c9)),\\n        <a>Fintype.card_prod<\\/a>, <a>Nat.mul_div_cancel<\\/a>]\"",
+                "[{\"full_name\":\"Fintype.card_congr\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[151,9],\"def_end_pos\":[151,19]},{\"full_name\":\"Subgroup.groupEquivQuotientProdSubgroup\",\"def_path\":\"Mathlib\\/GroupTheory\\/Coset.lean\",\"def_pos\":[587,19],\"def_end_pos\":[587,49]},{\"full_name\":\"MulAction.stabilizer\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Basic.lean\",\"def_pos\":[705,5],\"def_end_pos\":[705,15]},{\"full_name\":\"Fintype.card_prod\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Prod.lean\",\"def_pos\":[59,9],\"def_end_pos\":[59,26]},{\"full_name\":\"Nat.mul_div_cancel\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Div.lean\",\"def_pos\":[349,19],\"def_end_pos\":[349,33]}]"
+              ],
+              "state_after": "case H\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\ninst\u271d\u2076 inst\u271d\u2075 : Group \u03b1\ninst\u271d\u2074 : MulAction \u03b1 \u03b2\nx : \u03b2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : Fintype (Quotient (orbitRel \u03b1 \u03b2))\ninst\u271d : (b : \u03b2) \u2192 Fintype \u21a5(stabilizer \u03b1 b)\n\u03c6 : Quotient (orbitRel \u03b1 \u03b2) \u2192 \u03b2\nh\u03c6 : LeftInverse Quotient.mk'' \u03c6\n\u03c9 : Quotient (orbitRel \u03b1 \u03b2)\n\u22a2 0 < Fintype.card \u21a5(stabilizer \u03b1 (\u03c6 \u03c9))",
+              "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\ninst\u271d\u2076 inst\u271d\u2075 : Group \u03b1\ninst\u271d\u2074 : MulAction \u03b1 \u03b2\nx : \u03b2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : Fintype (Quotient (orbitRel \u03b1 \u03b2))\ninst\u271d : (b : \u03b2) \u2192 Fintype \u21a5(stabilizer \u03b1 b)\n\u03c6 : Quotient (orbitRel \u03b1 \u03b2) \u2192 \u03b2\nh\u03c6 : LeftInverse Quotient.mk'' \u03c6\n\u03c9 : Quotient (orbitRel \u03b1 \u03b2)\n\u22a2 Fintype.card \u03b1 / Fintype.card \u21a5(stabilizer \u03b1 (\u03c6 \u03c9)) = Fintype.card (\u03b1 \u29f8 stabilizer \u03b1 (\u03c6 \u03c9))",
+              "tactic": "rw [Fintype.card_congr (@Subgroup.groupEquivQuotientProdSubgroup \u03b1 _ (stabilizer \u03b1 <| \u03c6 \u03c9)),\n  Fintype.card_prod, Nat.mul_div_cancel]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact Fintype.card_pos_iff.mpr (by infer_instance)\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case H\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\ninst\u271d\u2076 inst\u271d\u2075 : Group \u03b1\ninst\u271d\u2074 : MulAction \u03b1 \u03b2\nx : \u03b2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : Fintype (Quotient (orbitRel \u03b1 \u03b2))\ninst\u271d : (b : \u03b2) \u2192 Fintype \u21a5(stabilizer \u03b1 b)\n\u03c6 : Quotient (orbitRel \u03b1 \u03b2) \u2192 \u03b2\nh\u03c6 : LeftInverse Quotient.mk'' \u03c6\n\u03c9 : Quotient (orbitRel \u03b1 \u03b2)\n\u22a2 0 < Fintype.card \u21a5(stabilizer \u03b1 (\u03c6 \u03c9))",
+              "tactic": "exact Fintype.card_pos_iff.mpr (by infer_instance)"
+            },
+            {
+              "annotated_tactic": [
+                "\"infer_instance\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\ninst\u271d\u2076 inst\u271d\u2075 : Group \u03b1\ninst\u271d\u2074 : MulAction \u03b1 \u03b2\nx : \u03b2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : Fintype (Quotient (orbitRel \u03b1 \u03b2))\ninst\u271d : (b : \u03b2) \u2192 Fintype \u21a5(stabilizer \u03b1 b)\n\u03c6 : Quotient (orbitRel \u03b1 \u03b2) \u2192 \u03b2\nh\u03c6 : LeftInverse Quotient.mk'' \u03c6\n\u03c9 : Quotient (orbitRel \u03b1 \u03b2)\n\u22a2 Nonempty \u21a5(stabilizer \u03b1 (\u03c6 \u03c9))",
+              "tactic": "infer_instance"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Quotient.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.ofQuotientStabilizer_mem_orbit",
+        "id": "MulAction.ofQuotientStabilizer_mem_orbit",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            168,
+            44
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Quotient.lean",
+          "full_name": "MulAction.ofQuotientStabilizer_mem_orbit",
+          "start": [
+            167,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Quotient.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.ofQuotientStabilizer_mk",
+        "id": "MulAction.ofQuotientStabilizer_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            162,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Quotient.lean",
+          "full_name": "MulAction.ofQuotientStabilizer_mk",
+          "start": [
+            161,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Quotient.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.ofQuotientStabilizer_smul",
+        "id": "MulAction.ofQuotientStabilizer_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            175,
+            51
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Quotient.lean",
+          "full_name": "MulAction.ofQuotientStabilizer_smul",
+          "start": [
+            173,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Quotient.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.orbitEquivQuotientStabilizer_symm_apply",
+        "id": "MulAction.orbitEquivQuotientStabilizer_symm_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            220,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Quotient.lean",
+          "full_name": "MulAction.orbitEquivQuotientStabilizer_symm_apply",
+          "start": [
+            218,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Quotient.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulActionHom.toQuotient_apply",
+        "id": "MulActionHom.toQuotient_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            138,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Quotient.lean",
+          "full_name": "MulActionHom.toQuotient_apply",
+          "start": [
+            136,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Quotient.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Subgroup.quotientCenterEmbedding_apply",
+        "id": "Subgroup.quotientCenterEmbedding_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            408,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Quotient.lean",
+          "full_name": "Subgroup.quotientCenterEmbedding_apply",
+          "start": [
+            406,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Quotient.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Subgroup.quotientCentralizerEmbedding_apply",
+        "id": "Subgroup.quotientCentralizerEmbedding_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            394,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Quotient.lean",
+          "full_name": "Subgroup.quotientCentralizerEmbedding_apply",
+          "start": [
+            392,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Quotient.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rw [mul_comm, Nat.card_eq_zero_of_infinite, Nat.card_eq_zero_of_infinite, zero_mul]'",
+        "full_name": "card_comm_eq_card_conjClasses_mul_card",
+        "id": "card_comm_eq_card_conjClasses_mul_card",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            430,
+            47
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Quotient.lean",
+          "full_name": "card_comm_eq_card_conjClasses_mul_card",
+          "start": [
+            417,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rcases <a>fintypeOrInfinite<\\/a> G\"",
+                "[{\"full_name\":\"fintypeOrInfinite\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[994,19],\"def_end_pos\":[994,36]}]"
+              ],
+              "state_after": "case inl\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Fintype G\n\u22a2 Nat.card { p // Commute p.1 p.2 } = Nat.card (ConjClasses G) * Nat.card G\n\ncase inr\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Infinite G\n\u22a2 Nat.card { p // Commute p.1 p.2 } = Nat.card (ConjClasses G) * Nat.card G",
+              "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\n\u22a2 Nat.card { p // Commute p.1 p.2 } = Nat.card (ConjClasses G) * Nat.card G",
+              "tactic": "rcases fintypeOrInfinite G"
+            },
+            {
+              "annotated_tactic": [
+                "\"swap\"",
+                "[]"
+              ],
+              "state_after": "case inr\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Infinite G\n\u22a2 Nat.card { p // Commute p.1 p.2 } = Nat.card (ConjClasses G) * Nat.card G\n\ncase inl\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Fintype G\n\u22a2 Nat.card { p // Commute p.1 p.2 } = Nat.card (ConjClasses G) * Nat.card G",
+              "state_before": "case inl\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Fintype G\n\u22a2 Nat.card { p // Commute p.1 p.2 } = Nat.card (ConjClasses G) * Nat.card G\n\ncase inr\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Infinite G\n\u22a2 Nat.card { p // Commute p.1 p.2 } = Nat.card (ConjClasses G) * Nat.card G",
+              "tactic": "swap"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>Nat.card_eq_fintype_card<\\/a>]\"",
+                "[{\"full_name\":\"Nat.card_eq_fintype_card\",\"def_path\":\"Mathlib\\/SetTheory\\/Cardinal\\/Finite.lean\",\"def_pos\":[40,9],\"def_end_pos\":[40,29]}]"
+              ],
+              "state_after": "case inl\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Fintype G\n\u22a2 card { p // Commute p.1 p.2 } = card (ConjClasses G) * card G",
+              "state_before": "case inl\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Fintype G\n\u22a2 Nat.card { p // Commute p.1 p.2 } = Nat.card (ConjClasses G) * Nat.card G",
+              "tactic": "simp only [Nat.card_eq_fintype_card]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>card_congr<\\/a> (<a>Equiv.subtypeProdEquivSigmaSubtype<\\/a> <a>Commute<\\/a>), <a>card_sigma<\\/a>,\\n    <a>sum_equiv<\\/a> ConjAct.toConjAct.toEquiv (fun a \\u21a6 <a>card<\\/a> { b \\/\\/ <a>Commute<\\/a> a b })\\n      (fun g \\u21a6 <a>card<\\/a> (<a>MulAction.fixedBy<\\/a> G g))\\n      fun g \\u21a6 <a>card_congr'<\\/a> <| <a>congr_arg<\\/a> _ <| <a>funext<\\/a> fun h \\u21a6 mul_inv_eq_iff_eq_mul.symm.eq,\\n    <a>MulAction.sum_card_fixedBy_eq_card_orbits_mul_card_group<\\/a>]\"",
+                "[{\"full_name\":\"Fintype.card_congr\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[151,9],\"def_end_pos\":[151,19]},{\"full_name\":\"Equiv.subtypeProdEquivSigmaSubtype\",\"def_path\":\"Mathlib\\/Logic\\/Equiv\\/Basic.lean\",\"def_pos\":[1392,5],\"def_end_pos\":[1392,33]},{\"full_name\":\"Commute\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Commute\\/Defs.lean\",\"def_pos\":[37,5],\"def_end_pos\":[37,12]},{\"full_name\":\"Fintype.card_sigma\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/BigOperators.lean\",\"def_pos\":[138,22],\"def_end_pos\":[138,32]},{\"full_name\":\"Fintype.sum_equiv\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Finset.lean\",\"def_pos\":[2269,3],\"def_end_pos\":[2269,14]},{\"full_name\":\"Fintype.card\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[63,5],\"def_end_pos\":[63,9]},{\"full_name\":\"Commute\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Commute\\/Defs.lean\",\"def_pos\":[37,5],\"def_end_pos\":[37,12]},{\"full_name\":\"Fintype.card\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[63,5],\"def_end_pos\":[63,9]},{\"full_name\":\"MulAction.fixedBy\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Basic.lean\",\"def_pos\":[155,5],\"def_end_pos\":[155,12]},{\"full_name\":\"Fintype.card_congr'\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[156,9],\"def_end_pos\":[156,20]},{\"full_name\":\"congr_arg\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Logic.lean\",\"def_pos\":[76,7],\"def_end_pos\":[76,16]},{\"full_name\":\"funext\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1817,9],\"def_end_pos\":[1817,15]},{\"full_name\":\"MulAction.sum_card_fixedBy_eq_card_orbits_mul_card_group\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Quotient.lean\",\"def_pos\":[333,9],\"def_end_pos\":[333,55]}]"
+              ],
+              "state_after": "case inl\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Fintype G\n\u22a2 card (Quotient (MulAction.orbitRel (ConjAct G) G)) * card (ConjAct G) = card (ConjClasses G) * card G",
+              "state_before": "case inl\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Fintype G\n\u22a2 card { p // Commute p.1 p.2 } = card (ConjClasses G) * card G",
+              "tactic": "rw [card_congr (Equiv.subtypeProdEquivSigmaSubtype Commute), card_sigma,\n  sum_equiv ConjAct.toConjAct.toEquiv (fun a \u21a6 card { b // Commute a b })\n    (fun g \u21a6 card (MulAction.fixedBy G g))\n    fun g \u21a6 card_congr' <| congr_arg _ <| funext fun h \u21a6 mul_inv_eq_iff_eq_mul.symm.eq,\n  MulAction.sum_card_fixedBy_eq_card_orbits_mul_card_group]"
+            },
+            {
+              "annotated_tactic": [
+                "\"congr 1\"",
+                "[]"
+              ],
+              "state_after": "case inl.e_a\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Fintype G\n\u22a2 card (Quotient (MulAction.orbitRel (ConjAct G) G)) = card (ConjClasses G)",
+              "state_before": "case inl\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Fintype G\n\u22a2 card (Quotient (MulAction.orbitRel (ConjAct G) G)) * card (ConjAct G) = card (ConjClasses G) * card G",
+              "tactic": "congr 1"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>card_congr'<\\/a>\"",
+                "[{\"full_name\":\"Fintype.card_congr'\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[156,9],\"def_end_pos\":[156,20]}]"
+              ],
+              "state_after": "case inl.e_a.h\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Fintype G\n\u22a2 Quotient (MulAction.orbitRel (ConjAct G) G) = ConjClasses G",
+              "state_before": "case inl.e_a\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Fintype G\n\u22a2 card (Quotient (MulAction.orbitRel (ConjAct G) G)) = card (ConjClasses G)",
+              "tactic": "apply card_congr'"
+            },
+            {
+              "annotated_tactic": [
+                "\"congr\"",
+                "[]"
+              ],
+              "state_after": "case inl.e_a.h.e_s\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Fintype G\n\u22a2 MulAction.orbitRel (ConjAct G) G = IsConj.setoid G",
+              "state_before": "case inl.e_a.h\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Fintype G\n\u22a2 Quotient (MulAction.orbitRel (ConjAct G) G) = ConjClasses G",
+              "tactic": "congr"
+            },
+            {
+              "annotated_tactic": [
+                "\"ext\"",
+                "[]"
+              ],
+              "state_after": "case inl.e_a.h.e_s.H\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Fintype G\na\u271d b\u271d : G\n\u22a2 (MulAction.orbitRel (ConjAct G) G).Rel a\u271d b\u271d \u2194 (IsConj.setoid G).Rel a\u271d b\u271d",
+              "state_before": "case inl.e_a.h.e_s\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Fintype G\n\u22a2 MulAction.orbitRel (ConjAct G) G = IsConj.setoid G",
+              "tactic": "ext"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact (<a>Setoid.comm'<\\/a> _).<a>trans<\\/a> isConj_iff.symm\"",
+                "[{\"full_name\":\"Setoid.comm'\",\"def_path\":\"Mathlib\\/Data\\/Setoid\\/Basic.lean\",\"def_pos\":[90,9],\"def_end_pos\":[90,14]},{\"full_name\":\"Iff.trans\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[803,9],\"def_end_pos\":[803,18]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inl.e_a.h.e_s.H\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Fintype G\na\u271d b\u271d : G\n\u22a2 (MulAction.orbitRel (ConjAct G) G).Rel a\u271d b\u271d \u2194 (IsConj.setoid G).Rel a\u271d b\u271d",
+              "tactic": "exact (Setoid.comm' _).trans isConj_iff.symm"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>mul_comm<\\/a>, <a>Nat.card_eq_zero_of_infinite<\\/a>, <a>Nat.card_eq_zero_of_infinite<\\/a>, <a>zero_mul<\\/a>]\"",
+                "[{\"full_name\":\"mul_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[332,9],\"def_end_pos\":[332,17]},{\"full_name\":\"Nat.card_eq_zero_of_infinite\",\"def_path\":\"Mathlib\\/SetTheory\\/Cardinal\\/Finite.lean\",\"def_pos\":[61,15],\"def_end_pos\":[61,39]},{\"full_name\":\"Nat.card_eq_zero_of_infinite\",\"def_path\":\"Mathlib\\/SetTheory\\/Cardinal\\/Finite.lean\",\"def_pos\":[61,15],\"def_end_pos\":[61,39]},{\"full_name\":\"MulZeroClass.zero_mul\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Defs.lean\",\"def_pos\":[37,3],\"def_end_pos\":[37,11]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inr\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nval\u271d : Infinite G\n\u22a2 Nat.card { p // Commute p.1 p.2 } = Nat.card (ConjClasses G) * Nat.card G",
+              "tactic": "rw [mul_comm, Nat.card_eq_zero_of_infinite, Nat.card_eq_zero_of_infinite, zero_mul]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Quotient.lean"
+      }
+    ],
+    "input_proofs": 31,
+    "input_units": 2,
+    "proofs": 8,
+    "published_proofs": 6,
+    "published_transitions": 9,
+    "replay_failures": [],
+    "transitions": 23,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/GroupTheory/GroupAction/Quotient.lean",
+        "proof_id": "mathlib:ConjClasses.card_carrier",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              359,
+              49
+            ],
+            "file_path": "Mathlib/GroupTheory/GroupAction/Quotient.lean",
+            "full_name": "ConjClasses.card_carrier",
+            "start": [
+              351,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>Fintype.card_congr<\\/a> <| <a>ConjAct.toConjAct<\\/a> (G := G) |>.<a>toEquiv<\\/a>]\"",
+                  "[{\"full_name\":\"Fintype.card_congr\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[151,9],\"def_end_pos\":[151,19]},{\"full_name\":\"ConjAct.toConjAct\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/ConjAct.lean\",\"def_pos\":[80,5],\"def_end_pos\":[80,14]},{\"full_name\":\"MulEquiv.toEquiv\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Equiv\\/Basic.lean\",\"def_pos\":[101,14],\"def_end_pos\":[101,30]}]"
+                ],
+                "state_after": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : Fintype G\ng : G\ninst\u271d\u00b9 : Fintype \u2191(ConjClasses.mk g).carrier\ninst\u271d : Fintype \u21a5(MulAction.stabilizer (ConjAct G) g)\n\u22a2 Fintype.card \u2191(ConjClasses.mk g).carrier =\n    Fintype.card (ConjAct G) / Fintype.card \u21a5(MulAction.stabilizer (ConjAct G) g)",
+                "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : Fintype G\ng : G\ninst\u271d\u00b9 : Fintype \u2191(ConjClasses.mk g).carrier\ninst\u271d : Fintype \u21a5(MulAction.stabilizer (ConjAct G) g)\n\u22a2 Fintype.card \u2191(ConjClasses.mk g).carrier = Fintype.card G / Fintype.card \u21a5(MulAction.stabilizer (ConjAct G) g)",
+                "tactic": "rw [Fintype.card_congr <| ConjAct.toConjAct (G := G) |>.toEquiv]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [\\u2190 <a>MulAction.card_orbit_mul_card_stabilizer_eq_card_group<\\/a> (<a>ConjAct<\\/a> G) g, <a>Nat.mul_div_cancel<\\/a>]\"",
+                  "[{\"full_name\":\"MulAction.card_orbit_mul_card_stabilizer_eq_card_group\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Quotient.lean\",\"def_pos\":[210,9],\"def_end_pos\":[210,53]},{\"full_name\":\"ConjAct\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/ConjAct.lean\",\"def_pos\":[40,5],\"def_end_pos\":[40,12]},{\"full_name\":\"Nat.mul_div_cancel\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Div.lean\",\"def_pos\":[349,19],\"def_end_pos\":[349,33]}]"
+                ],
+                "state_after": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : Fintype G\ng : G\ninst\u271d\u00b9 : Fintype \u2191(ConjClasses.mk g).carrier\ninst\u271d : Fintype \u21a5(MulAction.stabilizer (ConjAct G) g)\n\u22a2 Fintype.card \u2191(ConjClasses.mk g).carrier = Fintype.card \u2191(MulAction.orbit (ConjAct G) g)\n\ncase H\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : Fintype G\ng : G\ninst\u271d\u00b9 : Fintype \u2191(ConjClasses.mk g).carrier\ninst\u271d : Fintype \u21a5(MulAction.stabilizer (ConjAct G) g)\n\u22a2 0 < Fintype.card \u21a5(MulAction.stabilizer (ConjAct G) g)",
+                "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : Fintype G\ng : G\ninst\u271d\u00b9 : Fintype \u2191(ConjClasses.mk g).carrier\ninst\u271d : Fintype \u21a5(MulAction.stabilizer (ConjAct G) g)\n\u22a2 Fintype.card \u2191(ConjClasses.mk g).carrier =\n    Fintype.card (ConjAct G) / Fintype.card \u21a5(MulAction.stabilizer (ConjAct G) g)",
+                "tactic": "rw [\u2190 MulAction.card_orbit_mul_card_stabilizer_eq_card_group (ConjAct G) g, Nat.mul_div_cancel]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp_rw [<a>ConjAct.orbit_eq_carrier_conjClasses<\\/a>]\"",
+                  "[{\"full_name\":\"ConjAct.orbit_eq_carrier_conjClasses\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/ConjAct.lean\",\"def_pos\":[315,9],\"def_end_pos\":[315,37]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : Fintype G\ng : G\ninst\u271d\u00b9 : Fintype \u2191(ConjClasses.mk g).carrier\ninst\u271d : Fintype \u21a5(MulAction.stabilizer (ConjAct G) g)\n\u22a2 Fintype.card \u2191(ConjClasses.mk g).carrier = Fintype.card \u2191(MulAction.orbit (ConjAct G) g)",
+                "tactic": "simp_rw [ConjAct.orbit_eq_carrier_conjClasses]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact Fintype.card_pos_iff.mpr <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": "case H\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : Fintype G\ng : G\ninst\u271d\u00b9 : Fintype \u2191(ConjClasses.mk g).carrier\ninst\u271d : Fintype \u21a5(MulAction.stabilizer (ConjAct G) g)\n\u22a2 0 < Fintype.card \u21a5(MulAction.stabilizer (ConjAct G) g)",
+                "tactic": "exact Fintype.card_pos_iff.mpr inferInstance"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "ConjClasses.card_carrier"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/GroupTheory/GroupAction/Quotient.lean",
+        "proof_id": "mathlib:Subgroup.normalCore_eq_ker",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              375,
+              91
+            ],
+            "file_path": "Mathlib/GroupTheory/GroupAction/Quotient.lean",
+            "full_name": "Subgroup.normalCore_eq_ker",
+            "start": [
+              365,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"apply <a>le_antisymm<\\/a>\"",
+                  "[{\"full_name\":\"le_antisymm\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[188,9],\"def_end_pos\":[188,20]}]"
+                ],
+                "state_after": "case a\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\n\u22a2 H.normalCore \u2264 (MulAction.toPermHom G (G \u29f8 H)).ker\n\ncase a\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\n\u22a2 (MulAction.toPermHom G (G \u29f8 H)).ker \u2264 H.normalCore",
+                "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\n\u22a2 H.normalCore = (MulAction.toPermHom G (G \u29f8 H)).ker",
+                "tactic": "apply le_antisymm"
+              },
+              {
+                "annotated_tactic": [
+                  "\"intro g hg\"",
+                  "[]"
+                ],
+                "state_after": "case a\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\ng : G\nhg : g \u2208 H.normalCore\n\u22a2 g \u2208 (MulAction.toPermHom G (G \u29f8 H)).ker",
+                "state_before": "case a\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\n\u22a2 H.normalCore \u2264 (MulAction.toPermHom G (G \u29f8 H)).ker",
+                "tactic": "intro g hg"
+              },
+              {
+                "annotated_tactic": [
+                  "\"apply <a>Equiv.Perm.ext<\\/a>\"",
+                  "[{\"full_name\":\"Equiv.Perm.ext\",\"def_path\":\"Mathlib\\/Logic\\/Equiv\\/Defs.lean\",\"def_pos\":[140,16],\"def_end_pos\":[140,24]}]"
+                ],
+                "state_after": "case a.H\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\ng : G\nhg : g \u2208 H.normalCore\n\u22a2 \u2200 (x : G \u29f8 H), ((MulAction.toPermHom G (G \u29f8 H)) g) x = 1 x",
+                "state_before": "case a\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\ng : G\nhg : g \u2208 H.normalCore\n\u22a2 g \u2208 (MulAction.toPermHom G (G \u29f8 H)).ker",
+                "tactic": "apply Equiv.Perm.ext"
+              },
+              {
+                "annotated_tactic": [
+                  "\"refine fun q \\u21a6 <a>QuotientGroup.induction_on<\\/a> q ?_\"",
+                  "[{\"full_name\":\"QuotientGroup.induction_on\",\"def_path\":\"Mathlib\\/GroupTheory\\/Coset.lean\",\"def_pos\":[458,9],\"def_end_pos\":[458,21]}]"
+                ],
+                "state_after": "case a.H\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\ng : G\nhg : g \u2208 H.normalCore\nq : G \u29f8 H\n\u22a2 \u2200 (z : G), ((MulAction.toPermHom G (G \u29f8 H)) g) \u2191z = 1 \u2191z",
+                "state_before": "case a.H\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\ng : G\nhg : g \u2208 H.normalCore\n\u22a2 \u2200 (x : G \u29f8 H), ((MulAction.toPermHom G (G \u29f8 H)) g) x = 1 x",
+                "tactic": "refine fun q \u21a6 QuotientGroup.induction_on q ?_"
+              },
+              {
+                "annotated_tactic": [
+                  "\"refine fun g' => (<a>MulAction.Quotient.smul_mk<\\/a> H g g').<a>trans<\\/a> (QuotientGroup.eq.mpr ?_)\"",
+                  "[{\"full_name\":\"MulAction.Quotient.smul_mk\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Quotient.lean\",\"def_pos\":[94,9],\"def_end_pos\":[94,25]},{\"full_name\":\"Eq.trans\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[335,9],\"def_end_pos\":[335,17]}]"
+                ],
+                "state_after": "case a.H\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\ng : G\nhg : g \u2208 H.normalCore\nq : G \u29f8 H\ng' : G\n\u22a2 (g \u2022 g')\u207b\u00b9 * g' \u2208 H",
+                "state_before": "case a.H\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\ng : G\nhg : g \u2208 H.normalCore\nq : G \u29f8 H\n\u22a2 \u2200 (z : G), ((MulAction.toPermHom G (G \u29f8 H)) g) \u2191z = 1 \u2191z",
+                "tactic": "refine fun g' => (MulAction.Quotient.smul_mk H g g').trans (QuotientGroup.eq.mpr ?_)"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>smul_eq_mul<\\/a>, <a>mul_inv_rev<\\/a>, \\u2190 <a>inv_inv<\\/a> g', <a>inv_inv<\\/a>]\"",
+                  "[{\"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_inv_rev\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1153,9],\"def_end_pos\":[1153,20]},{\"full_name\":\"inv_inv\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[870,9],\"def_end_pos\":[870,16]},{\"full_name\":\"inv_inv\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[870,9],\"def_end_pos\":[870,16]}]"
+                ],
+                "state_after": "case a.H\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\ng : G\nhg : g \u2208 H.normalCore\nq : G \u29f8 H\ng' : G\n\u22a2 g'\u207b\u00b9 * g\u207b\u00b9 * g'\u207b\u00b9\u207b\u00b9 \u2208 H",
+                "state_before": "case a.H\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\ng : G\nhg : g \u2208 H.normalCore\nq : G \u29f8 H\ng' : G\n\u22a2 (g \u2022 g')\u207b\u00b9 * g' \u2208 H",
+                "tactic": "rw [smul_eq_mul, mul_inv_rev, \u2190 inv_inv g', inv_inv]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact H.normalCore.inv_mem hg g'\\u207b\\u00b9\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case a.H\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\ng : G\nhg : g \u2208 H.normalCore\nq : G \u29f8 H\ng' : G\n\u22a2 g'\u207b\u00b9 * g\u207b\u00b9 * g'\u207b\u00b9\u207b\u00b9 \u2208 H",
+                "tactic": "exact H.normalCore.inv_mem hg g'\u207b\u00b9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"refine (Subgroup.normal_le_normalCore.mpr fun g hg => ?_)\"",
+                  "[]"
+                ],
+                "state_after": "case a\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\ng : G\nhg : g \u2208 (MulAction.toPermHom G (G \u29f8 H)).ker\n\u22a2 g \u2208 H",
+                "state_before": "case a\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\n\u22a2 (MulAction.toPermHom G (G \u29f8 H)).ker \u2264 H.normalCore",
+                "tactic": "refine (Subgroup.normal_le_normalCore.mpr fun g hg => ?_)"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [\\u2190 H.inv_mem_iff, \\u2190 <a>mul_one<\\/a> g\\u207b\\u00b9, \\u2190 <a>QuotientGroup.eq<\\/a>, \\u2190 <a>mul_one<\\/a> g]\"",
+                  "[{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"QuotientGroup.eq\",\"def_path\":\"Mathlib\\/GroupTheory\\/Coset.lean\",\"def_pos\":[496,19],\"def_end_pos\":[496,21]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]}]"
+                ],
+                "state_after": "case a\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\ng : G\nhg : g \u2208 (MulAction.toPermHom G (G \u29f8 H)).ker\n\u22a2 \u2191(g * 1) = \u21911",
+                "state_before": "case a\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\ng : G\nhg : g \u2208 (MulAction.toPermHom G (G \u29f8 H)).ker\n\u22a2 g \u2208 H",
+                "tactic": "rw [\u2190 H.inv_mem_iff, \u2190 mul_one g\u207b\u00b9, \u2190 QuotientGroup.eq, \u2190 mul_one g]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact (<a>MulAction.Quotient.smul_mk<\\/a> H g 1).symm.trans (Equiv.Perm.ext_iff.mp hg (1 : G))\"",
+                  "[{\"full_name\":\"MulAction.Quotient.smul_mk\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Quotient.lean\",\"def_pos\":[94,9],\"def_end_pos\":[94,25]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case a\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nG : Type u_1\ninst\u271d : Group G\nH : Subgroup G\ng : G\nhg : g \u2208 (MulAction.toPermHom G (G \u29f8 H)).ker\n\u22a2 \u2191(g * 1) = \u21911",
+                "tactic": "exact (MulAction.Quotient.smul_mk H g 1).symm.trans (Equiv.Perm.ext_iff.mp hg (1 : G))"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Subgroup.normalCore_eq_ker"
+      }
+    ],
+    "validation_rejected_proofs": 2,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001195-0000-1edd8d2c9170a8f0.parquet",
+      "sha256": "1edd8d2c9170a8f0fde1fb76cdcc2e7873f8f587a27d39044a9024361108b521",
+      "bytes": 63400,
+      "rows": 9,
+      "revision": "906b7b88e1251d7543db52f3953c29ea18db26ce"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:MulAction.Quotient.mk_smul_out'",
+    "mathlib:MulAction.injective_ofQuotientStabilizer",
+    "mathlib:MulAction.stabilizer_quotient",
+    "mathlib:MulAction.sum_card_fixedBy_eq_card_orbits_mul_card_group",
+    "mathlib:Prod.smul_zero_mk",
+    "mathlib:QuotientGroup.out'_conj_pow_minimalPeriod_mem"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Prod.lean\",null,null,\"Prod.smul_zero_mk\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Quotient.lean\",null,null,\"MulAction.Quotient.mk_smul_out'\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Quotient.lean\",null,null,\"MulAction.injective_ofQuotientStabilizer\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Quotient.lean\",null,null,\"MulAction.stabilizer_quotient\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Quotient.lean\",null,null,\"MulAction.sum_card_fixedBy_eq_card_orbits_mul_card_group\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Quotient.lean\",null,null,\"QuotientGroup.out'_conj_pow_minimalPeriod_mem\"]"
+  ]
+}

manifests/batches/mathlib/001196.json

@@ -0,0 +1,704 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001196",
+  "batch_fingerprint": "4fe2435523fa7049b0fcdec997572777a3ae09c97ee5e49436a35a54ae775ad6",
+  "evidence": {
+    "batch_fingerprint": "4fe2435523fa7049b0fcdec997572777a3ae09c97ee5e49436a35a54ae775ad6",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Sigma.FaithfulSMul'",
+        "id": "Sigma.FaithfulSMul'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            69,
+            89
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Sigma.lean",
+          "full_name": "Sigma.FaithfulSMul'",
+          "start": [
+            68,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Sigma.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Sigma.smul_def",
+        "id": "Sigma.smul_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            37,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Sigma.lean",
+          "full_name": "Sigma.smul_def",
+          "start": [
+            36,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Sigma.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Sigma.smul_mk",
+        "id": "Sigma.smul_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            43,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Sigma.lean",
+          "full_name": "Sigma.smul_mk",
+          "start": [
+            42,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Sigma.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "AddSubgroupClass.zsmulMemClass",
+        "id": "AddSubgroupClass.zsmulMemClass",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            77,
+            37
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "AddSubgroupClass.zsmulMemClass",
+          "start": [
+            74,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "AddSubmonoidClass.nsmulMemClass",
+        "id": "AddSubmonoidClass.nsmulMemClass",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            72,
+            37
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "AddSubmonoidClass.nsmulMemClass",
+          "start": [
+            69,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SMulMemClass.ofIsScalarTower",
+        "id": "SMulMemClass.ofIsScalarTower",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            100,
+            81
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SMulMemClass.ofIsScalarTower",
+          "start": [
+            97,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SetLike.mk_smul_mk",
+        "id": "SetLike.mk_smul_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            122,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SetLike.mk_smul_mk",
+          "start": [
+            121,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SetLike.mk_smul_of_tower_mk",
+        "id": "SetLike.mk_smul_of_tower_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            158,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SetLike.mk_smul_of_tower_mk",
+          "start": [
+            156,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SetLike.smul_def",
+        "id": "SetLike.smul_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            128,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SetLike.smul_def",
+          "start": [
+            127,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SetLike.smul_of_tower_def",
+        "id": "SetLike.smul_of_tower_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            163,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SetLike.smul_of_tower_def",
+          "start": [
+            161,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SetLike.val_smul",
+        "id": "SetLike.val_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            114,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SetLike.val_smul",
+          "start": [
+            113,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SetLike.val_smul_of_tower",
+        "id": "SetLike.val_smul_of_tower",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            153,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SetLike.val_smul_of_tower",
+          "start": [
+            152,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.SMulMemClass.coeSubtype",
+        "id": "SubMulAction.SMulMemClass.coeSubtype",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            283,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SubMulAction.SMulMemClass.coeSubtype",
+          "start": [
+            282,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.coe_copy",
+        "id": "SubMulAction.coe_copy",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            205,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SubMulAction.coe_copy",
+          "start": [
+            204,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.copy_eq",
+        "id": "SubMulAction.copy_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            209,
+            27
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SubMulAction.copy_eq",
+          "start": [
+            208,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.ext",
+        "id": "SubMulAction.ext",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            193,
+            16
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SubMulAction.ext",
+          "start": [
+            192,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.inclusion.coe_eq",
+        "id": "SubMulAction.inclusion.coe_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            475,
+            38
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SubMulAction.inclusion.coe_eq",
+          "start": [
+            474,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.inclusion.toFun_eq_coe",
+        "id": "SubMulAction.inclusion.toFun_eq_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            472,
+            43
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SubMulAction.inclusion.toFun_eq_coe",
+          "start": [
+            471,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.inclusion_injective",
+        "id": "SubMulAction.inclusion_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            484,
+            24
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SubMulAction.inclusion_injective",
+          "start": [
+            482,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.mem_carrier",
+        "id": "SubMulAction.mem_carrier",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            188,
+            10
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SubMulAction.mem_carrier",
+          "start": [
+            187,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.smul_mem",
+        "id": "SubMulAction.smul_mem",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            231,
+            18
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SubMulAction.smul_mem",
+          "start": [
+            230,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.smul_mem_iff",
+        "id": "SubMulAction.smul_mem_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            453,
+            35
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SubMulAction.smul_mem_iff",
+          "start": [
+            452,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.smul_mem_iff'",
+        "id": "SubMulAction.smul_mem_iff'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            322,
+            82
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SubMulAction.smul_mem_iff'",
+          "start": [
+            320,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.subtype_apply",
+        "id": "SubMulAction.subtype_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            256,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SubMulAction.subtype_apply",
+          "start": [
+            255,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.subtype_eq_val",
+        "id": "SubMulAction.subtype_eq_val",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            260,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SubMulAction.subtype_eq_val",
+          "start": [
+            259,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.val_image_orbit",
+        "id": "SubMulAction.val_image_orbit",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            353,
+            28
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SubMulAction.val_image_orbit",
+          "start": [
+            351,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.val_neg",
+        "id": "SubMulAction.val_neg",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            439,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SubMulAction.val_neg",
+          "start": [
+            438,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.val_smul_of_tower",
+        "id": "SubMulAction.val_smul_of_tower",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
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+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SubMulAction.val_smul_of_tower",
+          "start": [
+            315,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.zero_mem",
+        "id": "SubMulAction.zero_mem",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            405,
+            40
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean",
+          "full_name": "SubMulAction.zero_mem",
+          "start": [
+            403,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction.lean"
+      }
+    ],
+    "input_proofs": 38,
+    "input_units": 2,
+    "proofs": 9,
+    "published_proofs": 9,
+    "published_transitions": 16,
+    "replay_failures": [],
+    "transitions": 16,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001196-0000-49b286c17c95fec3.parquet",
+      "sha256": "49b286c17c95fec3d7faeef37d5514de2037872b9984cb83f35a25e79ebba801",
+      "bytes": 67402,
+      "rows": 13,
+      "revision": "906b7b88e1251d7543db52f3953c29ea18db26ce"
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+      "rows": 1,
+      "revision": "906b7b88e1251d7543db52f3953c29ea18db26ce"
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+      "rows": 2,
+      "revision": "906b7b88e1251d7543db52f3953c29ea18db26ce"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:SetLike.forall_smul_mem_iff",
+    "mathlib:SubMulAction.mem_orbit_subMul_iff",
+    "mathlib:SubMulAction.neg_mem",
+    "mathlib:SubMulAction.neg_mem_iff",
+    "mathlib:SubMulAction.orbitRel_of_subMul",
+    "mathlib:SubMulAction.smul_of_tower_mem",
+    "mathlib:SubMulAction.stabilizer_of_subMul",
+    "mathlib:SubMulAction.stabilizer_of_subMul.submonoid",
+    "mathlib:SubMulAction.val_preimage_orbit"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/SubMulAction.lean\",null,null,\"SetLike.forall_smul_mem_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/SubMulAction.lean\",null,null,\"SubMulAction.mem_orbit_subMul_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/SubMulAction.lean\",null,null,\"SubMulAction.neg_mem\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/SubMulAction.lean\",null,null,\"SubMulAction.neg_mem_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/SubMulAction.lean\",null,null,\"SubMulAction.orbitRel_of_subMul\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/SubMulAction.lean\",null,null,\"SubMulAction.smul_of_tower_mem\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/SubMulAction.lean\",null,null,\"SubMulAction.stabilizer_of_subMul\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/SubMulAction.lean\",null,null,\"SubMulAction.stabilizer_of_subMul.submonoid\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/SubMulAction.lean\",null,null,\"SubMulAction.val_preimage_orbit\"]"
+  ]
+}

manifests/batches/mathlib/001197.json

@@ -0,0 +1,310 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001197",
+  "batch_fingerprint": "13369d81f9b25012aa223772879aee0821fde4bd3d09757b344b2a024073bb1f",
+  "evidence": {
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+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.coe_mul",
+        "id": "SubMulAction.coe_mul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
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+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction/Pointwise.lean",
+          "full_name": "SubMulAction.coe_mul",
+          "start": [
+            62,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction/Pointwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.coe_one",
+        "id": "SubMulAction.coe_one",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
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+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction/Pointwise.lean",
+          "full_name": "SubMulAction.coe_one",
+          "start": [
+            36,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction/Pointwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.mem_mul",
+        "id": "SubMulAction.mem_mul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
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+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction/Pointwise.lean",
+          "full_name": "SubMulAction.mem_mul",
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+          "traced_tactics": [],
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+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction/Pointwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.mem_one",
+        "id": "SubMulAction.mem_one",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
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+          "full_name": "SubMulAction.mem_one",
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+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction/Pointwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SubMulAction.subset_coe_one",
+        "id": "SubMulAction.subset_coe_one",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
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+            36
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction/Pointwise.lean",
+          "full_name": "SubMulAction.subset_coe_one",
+          "start": [
+            45,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/SubMulAction/Pointwise.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Sum.smul_def",
+        "id": "Sum.smul_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            39,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Sum.lean",
+          "full_name": "Sum.smul_def",
+          "start": [
+            38,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Sum.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Sum.smul_inl",
+        "id": "Sum.smul_inl",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            45,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Sum.lean",
+          "full_name": "Sum.smul_inl",
+          "start": [
+            44,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Sum.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Sum.smul_inr",
+        "id": "Sum.smul_inr",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            51,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Sum.lean",
+          "full_name": "Sum.smul_inr",
+          "start": [
+            50,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Sum.lean"
+      }
+    ],
+    "input_proofs": 11,
+    "input_units": 2,
+    "proofs": 3,
+    "published_proofs": 1,
+    "published_transitions": 1,
+    "replay_failures": [],
+    "transitions": 6,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction/Pointwise.lean",
+        "proof_id": "mathlib:SubMulAction.coe_pow",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              120,
+              83
+            ],
+            "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction/Pointwise.lean",
+            "full_name": "SubMulAction.coe_pow",
+            "start": [
+              116,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>pow_one<\\/a>, <a>pow_one<\\/a>]\"",
+                  "[{\"full_name\":\"pow_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[663,7],\"def_end_pos\":[663,14]},{\"full_name\":\"pow_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[663,7],\"def_end_pos\":[663,14]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "R : Type u_1\nM : Type u_2\ninst\u271d\u2074 : Monoid R\ninst\u271d\u00b3 : MulAction R M\ninst\u271d\u00b2 : Monoid M\ninst\u271d\u00b9 : IsScalarTower R M M\ninst\u271d : SMulCommClass R M M\np : SubMulAction R M\nx\u271d : 1 \u2260 0\n\u22a2 \u2191(p ^ 1) = \u2191p ^ 1",
+                "tactic": "rw [pow_one, pow_one]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>pow_succ<\\/a> _ (n + 1), <a>pow_succ<\\/a> _ (n + 1), <a>coe_mul<\\/a>, coe_pow _ n.succ_ne_zero]\"",
+                  "[{\"full_name\":\"pow_succ\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[657,9],\"def_end_pos\":[657,17]},{\"full_name\":\"pow_succ\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[657,9],\"def_end_pos\":[657,17]},{\"full_name\":\"SubMulAction.coe_mul\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/SubMulAction\\/Pointwise.lean\",\"def_pos\":[62,9],\"def_end_pos\":[62,16]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "R : Type u_1\nM : Type u_2\ninst\u271d\u2074 : Monoid R\ninst\u271d\u00b3 : MulAction R M\ninst\u271d\u00b2 : Monoid M\ninst\u271d\u00b9 : IsScalarTower R M M\ninst\u271d : SMulCommClass R M M\np : SubMulAction R M\nn : \u2115\nx\u271d : n + 2 \u2260 0\n\u22a2 \u2191(p ^ (n + 2)) = \u2191p ^ (n + 2)",
+                "tactic": "rw [pow_succ _ (n + 1), pow_succ _ (n + 1), coe_mul, coe_pow _ n.succ_ne_zero]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "SubMulAction.coe_pow"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction/Pointwise.lean",
+        "proof_id": "mathlib:SubMulAction.subset_coe_pow",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              127,
+              69
+            ],
+            "file_path": "Mathlib/GroupTheory/GroupAction/SubMulAction/Pointwise.lean",
+            "full_name": "SubMulAction.subset_coe_pow",
+            "start": [
+              123,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>pow_zero<\\/a>, <a>pow_zero<\\/a>]\"",
+                  "[{\"full_name\":\"pow_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[651,9],\"def_end_pos\":[651,17]},{\"full_name\":\"pow_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[651,9],\"def_end_pos\":[651,17]}]"
+                ],
+                "state_after": "R : Type u_1\nM : Type u_2\ninst\u271d\u2074 : Monoid R\ninst\u271d\u00b3 : MulAction R M\ninst\u271d\u00b2 : Monoid M\ninst\u271d\u00b9 : IsScalarTower R M M\ninst\u271d : SMulCommClass R M M\np : SubMulAction R M\n\u22a2 1 \u2286 \u21911",
+                "state_before": "R : Type u_1\nM : Type u_2\ninst\u271d\u2074 : Monoid R\ninst\u271d\u00b3 : MulAction R M\ninst\u271d\u00b2 : Monoid M\ninst\u271d\u00b9 : IsScalarTower R M M\ninst\u271d : SMulCommClass R M M\np : SubMulAction R M\n\u22a2 \u2191p ^ 0 \u2286 \u2191(p ^ 0)",
+                "tactic": "rw [pow_zero, pow_zero]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact <a>subset_coe_one<\\/a>\"",
+                  "[{\"full_name\":\"SubMulAction.subset_coe_one\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/SubMulAction\\/Pointwise.lean\",\"def_pos\":[45,9],\"def_end_pos\":[45,23]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "R : Type u_1\nM : Type u_2\ninst\u271d\u2074 : Monoid R\ninst\u271d\u00b3 : MulAction R M\ninst\u271d\u00b2 : Monoid M\ninst\u271d\u00b9 : IsScalarTower R M M\ninst\u271d : SMulCommClass R M M\np : SubMulAction R M\n\u22a2 1 \u2286 \u21911",
+                "tactic": "exact subset_coe_one"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [\\u2190 <a>Nat.succ_eq_add_one<\\/a>, <a>coe_pow<\\/a> _ n.succ_ne_zero]\"",
+                  "[{\"full_name\":\"Nat.succ_eq_add_one\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[154,17],\"def_end_pos\":[154,32]},{\"full_name\":\"SubMulAction.coe_pow\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/SubMulAction\\/Pointwise.lean\",\"def_pos\":[116,9],\"def_end_pos\":[116,16]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "R : Type u_1\nM : Type u_2\ninst\u271d\u2074 : Monoid R\ninst\u271d\u00b3 : MulAction R M\ninst\u271d\u00b2 : Monoid M\ninst\u271d\u00b9 : IsScalarTower R M M\ninst\u271d : SMulCommClass R M M\np : SubMulAction R M\nn : \u2115\n\u22a2 \u2191p ^ (n + 1) \u2286 \u2191(p ^ (n + 1))",
+                "tactic": "rw [\u2190 Nat.succ_eq_add_one, coe_pow _ n.succ_ne_zero]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "SubMulAction.subset_coe_pow"
+      }
+    ],
+    "validation_rejected_proofs": 2,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001197-0000-44fc1fe9ffc793a7.parquet",
+      "sha256": "44fc1fe9ffc793a78a25de2cc452129c68fc6bf729559edc9b39d6268c700e44",
+      "bytes": 33769,
+      "rows": 1,
+      "revision": "906b7b88e1251d7543db52f3953c29ea18db26ce"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Sum.smul_swap"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/GroupAction/Sum.lean\",null,null,\"Sum.smul_swap\"]"
+  ]
+}

manifests/batches/mathlib/001198.json

@@ -0,0 +1,223 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001198",
+  "batch_fingerprint": "f737b12b67d2f1e033a93cedf43ce09233b57e2a4fa88831a7106ff22c40dad0",
+  "evidence": {
+    "batch_fingerprint": "f737b12b67d2f1e033a93cedf43ce09233b57e2a4fa88831a7106ff22c40dad0",
+    "batch_outcome": "all_inputs_failed_with_evidence",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.Supports.mono",
+        "id": "MulAction.Supports.mono",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            47,
+            32
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Support.lean",
+          "full_name": "MulAction.Supports.mono",
+          "start": [
+            46,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Support.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "MulAction.supports_of_mem",
+        "id": "MulAction.supports_of_mem",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            39,
+            73
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Support.lean",
+          "full_name": "MulAction.supports_of_mem",
+          "start": [
+            39,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Support.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsUnit.inv_smul",
+        "id": "IsUnit.inv_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            54,
+            16
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Units.lean",
+          "full_name": "IsUnit.inv_smul",
+          "start": [
+            53,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Units.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsUnit.smul",
+        "id": "IsUnit.smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            165,
+            35
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Units.lean",
+          "full_name": "IsUnit.smul",
+          "start": [
+            162,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Units.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Units.smul_def",
+        "id": "Units.smul_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            38,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Units.lean",
+          "full_name": "Units.smul_def",
+          "start": [
+            37,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Units.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Units.smul_inv",
+        "id": "Units.smul_inv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            123,
+            10
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Units.lean",
+          "full_name": "Units.smul_inv",
+          "start": [
+            121,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Units.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Units.smul_isUnit",
+        "id": "Units.smul_isUnit",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            50,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Units.lean",
+          "full_name": "Units.smul_isUnit",
+          "start": [
+            48,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Units.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Units.smul_mk_apply",
+        "id": "Units.smul_mk_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            45,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Units.lean",
+          "full_name": "Units.smul_mk_apply",
+          "start": [
+            43,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Units.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Units.val_smul",
+        "id": "Units.val_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            116,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/GroupAction/Units.lean",
+          "full_name": "Units.val_smul",
+          "start": [
+            114,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/GroupAction/Units.lean"
+      }
+    ],
+    "input_proofs": 9,
+    "input_units": 2,
+    "proofs": 0,
+    "published_proofs": 0,
+    "published_transitions": 0,
+    "replay_failures": [],
+    "transitions": 0,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [],
+  "proof_ids": [],
+  "proof_keys": []
+}

manifests/batches/mathlib/001217.json

@@ -0,0 +1,1201 @@
+{
+  "format": "leangpt-parquet-v2",
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+  "batch_fingerprint": "e00da9b7e119593337aaabf7a20db6a88b119826bafc3c4513f5a779afeb5ef4",
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+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsKleinFour.card_four'",
+        "id": "IsKleinFour.card_four'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            86,
+            65
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/KleinFour.lean",
+          "full_name": "IsKleinFour.card_four'",
+          "start": [
+            83,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/KleinFour.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rw [card_insert_of_not_mem]'",
+        "full_name": "IsKleinFour.eq_finset_univ",
+        "id": "IsKleinFour.eq_finset_univ",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            116,
+            18
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/KleinFour.lean",
+          "full_name": "IsKleinFour.eq_finset_univ",
+          "start": [
+            109,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"apply <a>Finset.eq_univ_of_card<\\/a>\"",
+                "[{\"full_name\":\"Finset.eq_univ_of_card\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[254,9],\"def_end_pos\":[254,31]}]"
+              ],
+              "state_after": "case hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 {x * y, x, y, 1}.card = Fintype.card G",
+              "state_before": "G : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 {x * y, x, y, 1} = univ",
+              "tactic": "apply Finset.eq_univ_of_card"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>card_four'<\\/a>]\"",
+                "[{\"full_name\":\"IsKleinFour.card_four'\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/KleinFour.lean\",\"def_pos\":[84,7],\"def_end_pos\":[84,17]}]"
+              ],
+              "state_after": "case hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 {x * y, x, y, 1}.card = 4",
+              "state_before": "case hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 {x * y, x, y, 1}.card = Fintype.card G",
+              "tactic": "rw [card_four']"
+            },
+            {
+              "annotated_tactic": [
+                "\"repeat rw [<a>card_insert_of_not_mem<\\/a>]\"",
+                "[{\"full_name\":\"Finset.card_insert_of_not_mem\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[108,9],\"def_end_pos\":[108,31]}]"
+              ],
+              "state_after": "case hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 {1}.card + 1 + 1 + 1 = 4\n\ncase hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 y \u2209 {1}\n\ncase hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 x \u2209 {y, 1}\n\ncase hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 x * y \u2209 {x, y, 1}",
+              "state_before": "case hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 {x * y, x, y, 1}.card = 4",
+              "tactic": "repeat rw [card_insert_of_not_mem]"
+            },
+            {
+              "annotated_tactic": [
+                "\"on_goal 4 => simpa using <a>mul_not_mem_of_exponent_two<\\/a> (by simp) hx hy hxy\"",
+                "[{\"full_name\":\"mul_not_mem_of_exponent_two\",\"def_path\":\"Mathlib\\/GroupTheory\\/Exponent.lean\",\"def_pos\":[701,7],\"def_end_pos\":[701,34]}]"
+              ],
+              "state_after": "case hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 {1}.card + 1 + 1 + 1 = 4\n\ncase hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 y \u2209 {1}\n\ncase hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 x \u2209 {y, 1}",
+              "state_before": "case hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 {1}.card + 1 + 1 + 1 = 4\n\ncase hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 y \u2209 {1}\n\ncase hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 x \u2209 {y, 1}\n\ncase hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 x * y \u2209 {x, y, 1}",
+              "tactic": "on_goal 4 => simpa using mul_not_mem_of_exponent_two (by simp) hx hy hxy"
+            },
+            {
+              "annotated_tactic": [
+                "\"all_goals aesop\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 {1}.card + 1 + 1 + 1 = 4\n\ncase hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 y \u2209 {1}\n\ncase hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 x \u2209 {y, 1}",
+              "tactic": "all_goals aesop"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>card_insert_of_not_mem<\\/a>]\"",
+                "[{\"full_name\":\"Finset.card_insert_of_not_mem\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[108,9],\"def_end_pos\":[108,31]}]"
+              ],
+              "state_after": "case hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 {1}.card + 1 + 1 + 1 = 4\n\ncase hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 y \u2209 {1}\n\ncase hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 x \u2209 {y, 1}\n\ncase hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 x * y \u2209 {x, y, 1}",
+              "state_before": "case hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 {y, 1}.card + 1 + 1 = 4\n\ncase hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 x \u2209 {y, 1}\n\ncase hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 x * y \u2209 {x, y, 1}",
+              "tactic": "rw [card_insert_of_not_mem]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simpa using <a>mul_not_mem_of_exponent_two<\\/a> (by simp) hx hy hxy\"",
+                "[{\"full_name\":\"mul_not_mem_of_exponent_two\",\"def_path\":\"Mathlib\\/GroupTheory\\/Exponent.lean\",\"def_pos\":[701,7],\"def_end_pos\":[701,34]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 x * y \u2209 {x, y, 1}",
+              "tactic": "simpa using mul_not_mem_of_exponent_two (by simp) hx hy hxy"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "G : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 Monoid.exponent G = 2",
+              "tactic": "simp"
+            },
+            {
+              "annotated_tactic": [
+                "\"aesop\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case hs\nG : Type u_1\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : IsKleinFour G\ninst\u271d\u00b9 : Fintype G\ninst\u271d : DecidableEq G\nx y : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\n\u22a2 x \u2209 {y, 1}",
+              "tactic": "aesop"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/KleinFour.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'let _ := Fintype.ofFinite G'",
+        "full_name": "IsKleinFour.eq_mul_of_ne_all",
+        "id": "IsKleinFour.eq_mul_of_ne_all",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            124,
+            70
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/KleinFour.lean",
+          "full_name": "IsKleinFour.eq_mul_of_ne_all",
+          "start": [
+            118,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"classical\\n  let _ := <a>Fintype.ofFinite<\\/a> G\\n  apply <a>eq_of_not_mem_of_mem_insert<\\/a> <| (<a>eq_finset_univ<\\/a> hx hy hxy).<a>symm<\\/a> \\u25b8 <a>mem_univ<\\/a> _\\n  simpa only [<a>mem_singleton<\\/a>, <a>mem_insert<\\/a>, <a>not_or<\\/a>] using \\u27e8hzx, hzy, hz\\u27e9\"",
+                "[{\"full_name\":\"Fintype.ofFinite\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[449,19],\"def_end_pos\":[449,35]},{\"full_name\":\"Finset.eq_of_not_mem_of_mem_insert\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[1129,9],\"def_end_pos\":[1129,36]},{\"full_name\":\"IsKleinFour.eq_finset_univ\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/KleinFour.lean\",\"def_pos\":[110,7],\"def_end_pos\":[110,21]},{\"full_name\":\"Eq.symm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[323,9],\"def_end_pos\":[323,16]},{\"full_name\":\"Finset.mem_univ\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Basic.lean\",\"def_pos\":[75,9],\"def_end_pos\":[75,17]},{\"full_name\":\"Finset.mem_singleton\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[680,9],\"def_end_pos\":[680,22]},{\"full_name\":\"Finset.mem_insert\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[1113,9],\"def_end_pos\":[1113,19]},{\"full_name\":\"not_or\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/PropLemmas.lean\",\"def_pos\":[134,17],\"def_end_pos\":[134,23]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "G : Type u_1\ninst\u271d\u00b9 : Group G\ninst\u271d : IsKleinFour G\nx y z : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\nhz : z \u2260 1\nhzx : z \u2260 x\nhzy : z \u2260 y\n\u22a2 z = x * y",
+              "tactic": "classical\nlet _ := Fintype.ofFinite G\napply eq_of_not_mem_of_mem_insert <| (eq_finset_univ hx hy hxy).symm \u25b8 mem_univ _\nsimpa only [mem_singleton, mem_insert, not_or] using \u27e8hzx, hzy, hz\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"let _ := <a>Fintype.ofFinite<\\/a> G\"",
+                "[{\"full_name\":\"Fintype.ofFinite\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[449,19],\"def_end_pos\":[449,35]}]"
+              ],
+              "state_after": "G : Type u_1\ninst\u271d\u00b9 : Group G\ninst\u271d : IsKleinFour G\nx y z : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\nhz : z \u2260 1\nhzx : z \u2260 x\nhzy : z \u2260 y\nx\u271d : Fintype G := Fintype.ofFinite G\n\u22a2 z = x * y",
+              "state_before": "G : Type u_1\ninst\u271d\u00b9 : Group G\ninst\u271d : IsKleinFour G\nx y z : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\nhz : z \u2260 1\nhzx : z \u2260 x\nhzy : z \u2260 y\n\u22a2 z = x * y",
+              "tactic": "let _ := Fintype.ofFinite G"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>eq_of_not_mem_of_mem_insert<\\/a> <| (<a>eq_finset_univ<\\/a> hx hy hxy).<a>symm<\\/a> \\u25b8 <a>mem_univ<\\/a> _\"",
+                "[{\"full_name\":\"Finset.eq_of_not_mem_of_mem_insert\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[1129,9],\"def_end_pos\":[1129,36]},{\"full_name\":\"IsKleinFour.eq_finset_univ\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/KleinFour.lean\",\"def_pos\":[110,7],\"def_end_pos\":[110,21]},{\"full_name\":\"Eq.symm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[323,9],\"def_end_pos\":[323,16]},{\"full_name\":\"Finset.mem_univ\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Basic.lean\",\"def_pos\":[75,9],\"def_end_pos\":[75,17]}]"
+              ],
+              "state_after": "G : Type u_1\ninst\u271d\u00b9 : Group G\ninst\u271d : IsKleinFour G\nx y z : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\nhz : z \u2260 1\nhzx : z \u2260 x\nhzy : z \u2260 y\nx\u271d : Fintype G := Fintype.ofFinite G\n\u22a2 z \u2209 {x, y, 1}",
+              "state_before": "G : Type u_1\ninst\u271d\u00b9 : Group G\ninst\u271d : IsKleinFour G\nx y z : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\nhz : z \u2260 1\nhzx : z \u2260 x\nhzy : z \u2260 y\nx\u271d : Fintype G := Fintype.ofFinite G\n\u22a2 z = x * y",
+              "tactic": "apply eq_of_not_mem_of_mem_insert <| (eq_finset_univ hx hy hxy).symm \u25b8 mem_univ _"
+            },
+            {
+              "annotated_tactic": [
+                "\"simpa only [<a>mem_singleton<\\/a>, <a>mem_insert<\\/a>, <a>not_or<\\/a>] using \\u27e8hzx, hzy, hz\\u27e9\"",
+                "[{\"full_name\":\"Finset.mem_singleton\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[680,9],\"def_end_pos\":[680,22]},{\"full_name\":\"Finset.mem_insert\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[1113,9],\"def_end_pos\":[1113,19]},{\"full_name\":\"not_or\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/PropLemmas.lean\",\"def_pos\":[134,17],\"def_end_pos\":[134,23]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "G : Type u_1\ninst\u271d\u00b9 : Group G\ninst\u271d : IsKleinFour G\nx y z : G\nhx : x \u2260 1\nhy : y \u2260 1\nhxy : x \u2260 y\nhz : z \u2260 1\nhzx : z \u2260 x\nhzy : z \u2260 y\nx\u271d : Fintype G := Fintype.ofFinite G\n\u22a2 z \u2209 {x, y, 1}",
+              "tactic": "simpa only [mem_singleton, mem_insert, not_or] using \u27e8hzx, hzy, hz\u27e9"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/KleinFour.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'let _inst\u2081 := Fintype.ofFinite G\u2081'",
+        "full_name": "IsKleinFour.nonempty_mulEquiv",
+        "id": "IsKleinFour.nonempty_mulEquiv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            165,
+            80
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/KleinFour.lean",
+          "full_name": "IsKleinFour.nonempty_mulEquiv",
+          "start": [
+            159,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"classical\\n  let _inst\\u2081 := <a>Fintype.ofFinite<\\/a> G\\u2081\\n  let _inst\\u2081 := <a>Fintype.ofFinite<\\/a> G\\u2082\\n  exact \\u27e8<a>mulEquiv<\\/a> ((<a>Fintype.equivOfCardEq<\\/a> <| by simp).<a>setValue<\\/a> 1 1) <| by simp\\u27e9\"",
+                "[{\"full_name\":\"Fintype.ofFinite\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[449,19],\"def_end_pos\":[449,35]},{\"full_name\":\"Fintype.ofFinite\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[449,19],\"def_end_pos\":[449,35]},{\"full_name\":\"IsKleinFour.mulEquiv\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/KleinFour.lean\",\"def_pos\":[156,5],\"def_end_pos\":[156,13]},{\"full_name\":\"Fintype.equivOfCardEq\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[199,19],\"def_end_pos\":[199,32]},{\"full_name\":\"Equiv.setValue\",\"def_path\":\"Mathlib\\/Logic\\/Equiv\\/Basic.lean\",\"def_pos\":[1769,5],\"def_end_pos\":[1769,13]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "G : Type u_1\ninst\u271d\u2075 : Group G\ninst\u271d\u2074 : IsKleinFour G\nG\u2081 : Type u_2\nG\u2082 : Type u_3\ninst\u271d\u00b3 : Group G\u2081\ninst\u271d\u00b2 : Group G\u2082\ninst\u271d\u00b9 : IsKleinFour G\u2081\ninst\u271d : IsKleinFour G\u2082\n\u22a2 Nonempty (G\u2081 \u2243* G\u2082)",
+              "tactic": "classical\nlet _inst\u2081 := Fintype.ofFinite G\u2081\nlet _inst\u2081 := Fintype.ofFinite G\u2082\nexact \u27e8mulEquiv ((Fintype.equivOfCardEq <| by simp).setValue 1 1) <| by simp\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"let _inst\\u2081 := <a>Fintype.ofFinite<\\/a> G\\u2081\"",
+                "[{\"full_name\":\"Fintype.ofFinite\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[449,19],\"def_end_pos\":[449,35]}]"
+              ],
+              "state_after": "G : Type u_1\ninst\u271d\u2075 : Group G\ninst\u271d\u2074 : IsKleinFour G\nG\u2081 : Type u_2\nG\u2082 : Type u_3\ninst\u271d\u00b3 : Group G\u2081\ninst\u271d\u00b2 : Group G\u2082\ninst\u271d\u00b9 : IsKleinFour G\u2081\ninst\u271d : IsKleinFour G\u2082\n_inst\u2081 : Fintype G\u2081 := Fintype.ofFinite G\u2081\n\u22a2 Nonempty (G\u2081 \u2243* G\u2082)",
+              "state_before": "G : Type u_1\ninst\u271d\u2075 : Group G\ninst\u271d\u2074 : IsKleinFour G\nG\u2081 : Type u_2\nG\u2082 : Type u_3\ninst\u271d\u00b3 : Group G\u2081\ninst\u271d\u00b2 : Group G\u2082\ninst\u271d\u00b9 : IsKleinFour G\u2081\ninst\u271d : IsKleinFour G\u2082\n\u22a2 Nonempty (G\u2081 \u2243* G\u2082)",
+              "tactic": "let _inst\u2081 := Fintype.ofFinite G\u2081"
+            },
+            {
+              "annotated_tactic": [
+                "\"let _inst\\u2081 := <a>Fintype.ofFinite<\\/a> G\\u2082\"",
+                "[{\"full_name\":\"Fintype.ofFinite\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[449,19],\"def_end_pos\":[449,35]}]"
+              ],
+              "state_after": "G : Type u_1\ninst\u271d\u2075 : Group G\ninst\u271d\u2074 : IsKleinFour G\nG\u2081 : Type u_2\nG\u2082 : Type u_3\ninst\u271d\u00b3 : Group G\u2081\ninst\u271d\u00b2 : Group G\u2082\ninst\u271d\u00b9 : IsKleinFour G\u2081\ninst\u271d : IsKleinFour G\u2082\n_inst\u2081\u271d : Fintype G\u2081 := Fintype.ofFinite G\u2081\n_inst\u2081 : Fintype G\u2082 := Fintype.ofFinite G\u2082\n\u22a2 Nonempty (G\u2081 \u2243* G\u2082)",
+              "state_before": "G : Type u_1\ninst\u271d\u2075 : Group G\ninst\u271d\u2074 : IsKleinFour G\nG\u2081 : Type u_2\nG\u2082 : Type u_3\ninst\u271d\u00b3 : Group G\u2081\ninst\u271d\u00b2 : Group G\u2082\ninst\u271d\u00b9 : IsKleinFour G\u2081\ninst\u271d : IsKleinFour G\u2082\n_inst\u2081 : Fintype G\u2081 := Fintype.ofFinite G\u2081\n\u22a2 Nonempty (G\u2081 \u2243* G\u2082)",
+              "tactic": "let _inst\u2081 := Fintype.ofFinite G\u2082"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact \\u27e8<a>mulEquiv<\\/a> ((<a>Fintype.equivOfCardEq<\\/a> <| by simp).<a>setValue<\\/a> 1 1) <| by simp\\u27e9\"",
+                "[{\"full_name\":\"IsKleinFour.mulEquiv\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/KleinFour.lean\",\"def_pos\":[156,5],\"def_end_pos\":[156,13]},{\"full_name\":\"Fintype.equivOfCardEq\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[199,19],\"def_end_pos\":[199,32]},{\"full_name\":\"Equiv.setValue\",\"def_path\":\"Mathlib\\/Logic\\/Equiv\\/Basic.lean\",\"def_pos\":[1769,5],\"def_end_pos\":[1769,13]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "G : Type u_1\ninst\u271d\u2075 : Group G\ninst\u271d\u2074 : IsKleinFour G\nG\u2081 : Type u_2\nG\u2082 : Type u_3\ninst\u271d\u00b3 : Group G\u2081\ninst\u271d\u00b2 : Group G\u2082\ninst\u271d\u00b9 : IsKleinFour G\u2081\ninst\u271d : IsKleinFour G\u2082\n_inst\u2081\u271d : Fintype G\u2081 := Fintype.ofFinite G\u2081\n_inst\u2081 : Fintype G\u2082 := Fintype.ofFinite G\u2082\n\u22a2 Nonempty (G\u2081 \u2243* G\u2082)",
+              "tactic": "exact \u27e8mulEquiv ((Fintype.equivOfCardEq <| by simp).setValue 1 1) <| by simp\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "G : Type u_1\ninst\u271d\u2075 : Group G\ninst\u271d\u2074 : IsKleinFour G\nG\u2081 : Type u_2\nG\u2082 : Type u_3\ninst\u271d\u00b3 : Group G\u2081\ninst\u271d\u00b2 : Group G\u2082\ninst\u271d\u00b9 : IsKleinFour G\u2081\ninst\u271d : IsKleinFour G\u2082\n_inst\u2081\u271d : Fintype G\u2081 := Fintype.ofFinite G\u2081\n_inst\u2081 : Fintype G\u2082 := Fintype.ofFinite G\u2082\n\u22a2 Fintype.card G\u2081 = Fintype.card G\u2082",
+              "tactic": "simp"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "G : Type u_1\ninst\u271d\u2075 : Group G\ninst\u271d\u2074 : IsKleinFour G\nG\u2081 : Type u_2\nG\u2082 : Type u_3\ninst\u271d\u00b3 : Group G\u2081\ninst\u271d\u00b2 : Group G\u2082\ninst\u271d\u00b9 : IsKleinFour G\u2081\ninst\u271d : IsKleinFour G\u2082\n_inst\u2081\u271d : Fintype G\u2081 := Fintype.ofFinite G\u2081\n_inst\u2081 : Fintype G\u2082 := Fintype.ofFinite G\u2082\n\u22a2 ((Fintype.equivOfCardEq \u22ef).setValue 1 1) 1 = 1",
+              "tactic": "simp"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/KleinFour.lean"
+      },
+      {
+        "full_name": "QuaternionGroup.a_mul_a",
+        "id": "QuaternionGroup.a_mul_a",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            113,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean",
+          "full_name": "QuaternionGroup.a_mul_a",
+          "start": [
+            112,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean"
+      },
+      {
+        "full_name": "QuaternionGroup.a_mul_xa",
+        "id": "QuaternionGroup.a_mul_xa",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            118,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean",
+          "full_name": "QuaternionGroup.a_mul_xa",
+          "start": [
+            117,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean"
+      },
+      {
+        "full_name": "QuaternionGroup.a_one_pow",
+        "id": "QuaternionGroup.a_one_pow",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            185,
+            14
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean",
+          "full_name": "QuaternionGroup.a_one_pow",
+          "start": [
+            180,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"induction' k with k IH\"",
+                "[]"
+              ],
+              "state_after": "case zero\nn : \u2115\n\u22a2 a 1 ^ 0 = a \u21910\n\ncase succ\nn k : \u2115\nIH : a 1 ^ k = a \u2191k\n\u22a2 a 1 ^ (k + 1) = a \u2191(k + 1)",
+              "state_before": "n k : \u2115\n\u22a2 a 1 ^ k = a \u2191k",
+              "tactic": "induction' k with k IH"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Nat.cast_zero<\\/a>]\"",
+                "[{\"full_name\":\"Nat.cast_zero\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Defs.lean\",\"def_pos\":[127,9],\"def_end_pos\":[127,18]}]"
+              ],
+              "state_after": "case zero\nn : \u2115\n\u22a2 a 1 ^ 0 = a 0",
+              "state_before": "case zero\nn : \u2115\n\u22a2 a 1 ^ 0 = a \u21910",
+              "tactic": "rw [Nat.cast_zero]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rfl\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case zero\nn : \u2115\n\u22a2 a 1 ^ 0 = a 0",
+              "tactic": "rfl"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>pow_succ<\\/a>, IH, <a>a_mul_a<\\/a>]\"",
+                "[{\"full_name\":\"pow_succ\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[657,9],\"def_end_pos\":[657,17]},{\"full_name\":\"QuaternionGroup.a_mul_a\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[112,9],\"def_end_pos\":[112,16]}]"
+              ],
+              "state_after": "case succ\nn k : \u2115\nIH : a 1 ^ k = a \u2191k\n\u22a2 a (\u2191k + 1) = a \u2191(k + 1)",
+              "state_before": "case succ\nn k : \u2115\nIH : a 1 ^ k = a \u2191k\n\u22a2 a 1 ^ (k + 1) = a \u2191(k + 1)",
+              "tactic": "rw [pow_succ, IH, a_mul_a]"
+            },
+            {
+              "annotated_tactic": [
+                "\"congr 1\"",
+                "[]"
+              ],
+              "state_after": "case succ.e_a\nn k : \u2115\nIH : a 1 ^ k = a \u2191k\n\u22a2 \u2191k + 1 = \u2191(k + 1)",
+              "state_before": "case succ\nn k : \u2115\nIH : a 1 ^ k = a \u2191k\n\u22a2 a (\u2191k + 1) = a \u2191(k + 1)",
+              "tactic": "congr 1"
+            },
+            {
+              "annotated_tactic": [
+                "\"norm_cast\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case succ.e_a\nn k : \u2115\nIH : a 1 ^ k = a \u2191k\n\u22a2 \u2191k + 1 = \u2191(k + 1)",
+              "tactic": "norm_cast"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean"
+      },
+      {
+        "full_name": "QuaternionGroup.a_one_pow_n",
+        "id": "QuaternionGroup.a_one_pow_n",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            192,
+            28
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean",
+          "full_name": "QuaternionGroup.a_one_pow_n",
+          "start": [
+            189,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [<a>a_one_pow<\\/a>, <a>one_def<\\/a>]\"",
+                "[{\"full_name\":\"QuaternionGroup.a_one_pow\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[180,9],\"def_end_pos\":[180,18]},{\"full_name\":\"QuaternionGroup.one_def\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[131,9],\"def_end_pos\":[131,16]}]"
+              ],
+              "state_after": "n : \u2115\n\u22a2 a \u2191(2 * n) = a 0",
+              "state_before": "n : \u2115\n\u22a2 a 1 ^ (2 * n) = 1",
+              "tactic": "rw [a_one_pow, one_def]"
+            },
+            {
+              "annotated_tactic": [
+                "\"congr 1\"",
+                "[]"
+              ],
+              "state_after": "case e_a\nn : \u2115\n\u22a2 \u2191(2 * n) = 0",
+              "state_before": "n : \u2115\n\u22a2 a \u2191(2 * n) = a 0",
+              "tactic": "congr 1"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>ZMod.natCast_self<\\/a> _\"",
+                "[{\"full_name\":\"ZMod.natCast_self\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Basic.lean\",\"def_pos\":[143,9],\"def_end_pos\":[143,21]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case e_a\nn : \u2115\n\u22a2 \u2191(2 * n) = 0",
+              "tactic": "exact ZMod.natCast_self _"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean"
+      },
+      {
+        "full_name": "QuaternionGroup.card",
+        "id": "QuaternionGroup.card",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            176,
+            7
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean",
+          "full_name": "QuaternionGroup.card",
+          "start": [
+            174,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 Fintype.card_eq.mpr \\u27e8<a>fintypeHelper<\\/a>\\u27e9, <a>Fintype.card_sum<\\/a>, <a>ZMod.card<\\/a>, <a>two_mul<\\/a>]\"",
+                "[{\"full_name\":\"_private.Mathlib.GroupTheory.SpecificGroups.Quaternion.0.QuaternionGroup.fintypeHelper\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[135,13],\"def_end_pos\":[135,26]},{\"full_name\":\"Fintype.card_sum\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Sum.lean\",\"def_pos\":[36,9],\"def_end_pos\":[36,25]},{\"full_name\":\"ZMod.card\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Defs.lean\",\"def_pos\":[124,9],\"def_end_pos\":[124,13]},{\"full_name\":\"two_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[179,9],\"def_end_pos\":[179,16]}]"
+              ],
+              "state_after": "n : \u2115\ninst\u271d : NeZero n\n\u22a2 n + n + (n + n) = 4 * n",
+              "state_before": "n : \u2115\ninst\u271d : NeZero n\n\u22a2 Fintype.card (QuaternionGroup n) = 4 * n",
+              "tactic": "rw [\u2190 Fintype.card_eq.mpr \u27e8fintypeHelper\u27e9, Fintype.card_sum, ZMod.card, two_mul]"
+            },
+            {
+              "annotated_tactic": [
+                "\"ring\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "n : \u2115\ninst\u271d : NeZero n\n\u22a2 n + n + (n + n) = 4 * n",
+              "tactic": "ring"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean"
+      },
+      {
+        "full_name": "QuaternionGroup.exponent",
+        "id": "QuaternionGroup.exponent",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            281,
+            32
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean",
+          "full_name": "QuaternionGroup.exponent",
+          "start": [
+            262,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>normalize_eq<\\/a> 2, \\u2190 <a>lcm_mul_left<\\/a>, <a>normalize_eq<\\/a>]\"",
+                "[{\"full_name\":\"normalize_eq\",\"def_path\":\"Mathlib\\/Algebra\\/GCDMonoid\\/Basic.lean\",\"def_pos\":[986,9],\"def_end_pos\":[986,21]},{\"full_name\":\"lcm_mul_left\",\"def_path\":\"Mathlib\\/Algebra\\/GCDMonoid\\/Basic.lean\",\"def_pos\":[863,9],\"def_end_pos\":[863,21]},{\"full_name\":\"normalize_eq\",\"def_path\":\"Mathlib\\/Algebra\\/GCDMonoid\\/Basic.lean\",\"def_pos\":[986,9],\"def_end_pos\":[986,21]}]"
+              ],
+              "state_after": "n : \u2115\n\u22a2 Monoid.exponent (QuaternionGroup n) = lcm (2 * n) (2 * 2)",
+              "state_before": "n : \u2115\n\u22a2 Monoid.exponent (QuaternionGroup n) = 2 * lcm n 2",
+              "tactic": "rw [\u2190 normalize_eq 2, \u2190 lcm_mul_left, normalize_eq]"
+            },
+            {
+              "annotated_tactic": [
+                "\"norm_num\"",
+                "[]"
+              ],
+              "state_after": "n : \u2115\n\u22a2 Monoid.exponent (QuaternionGroup n) = lcm (2 * n) 4",
+              "state_before": "n : \u2115\n\u22a2 Monoid.exponent (QuaternionGroup n) = lcm (2 * n) (2 * 2)",
+              "tactic": "norm_num"
+            },
+            {
+              "annotated_tactic": [
+                "\"cases' <a>eq_zero_or_neZero<\\/a> n with hn hn\"",
+                "[{\"full_name\":\"eq_zero_or_neZero\",\"def_path\":\"Mathlib\\/Algebra\\/NeZero.lean\",\"def_pos\":[48,9],\"def_end_pos\":[48,26]}]"
+              ],
+              "state_after": "case inl\nn : \u2115\nhn : n = 0\n\u22a2 Monoid.exponent (QuaternionGroup n) = lcm (2 * n) 4\n\ncase inr\nn : \u2115\nhn : NeZero n\n\u22a2 Monoid.exponent (QuaternionGroup n) = lcm (2 * n) 4",
+              "state_before": "n : \u2115\n\u22a2 Monoid.exponent (QuaternionGroup n) = lcm (2 * n) 4",
+              "tactic": "cases' eq_zero_or_neZero n with hn hn"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Nat.dvd_antisymm<\\/a>\"",
+                "[{\"full_name\":\"Nat.dvd_antisymm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Dvd.lean\",\"def_pos\":[57,19],\"def_end_pos\":[57,31]}]"
+              ],
+              "state_after": "case inr.a\nn : \u2115\nhn : NeZero n\n\u22a2 Monoid.exponent (QuaternionGroup n) \u2223 lcm (2 * n) 4\n\ncase inr.a\nn : \u2115\nhn : NeZero n\n\u22a2 lcm (2 * n) 4 \u2223 Monoid.exponent (QuaternionGroup n)",
+              "state_before": "case inr\nn : \u2115\nhn : NeZero n\n\u22a2 Monoid.exponent (QuaternionGroup n) = lcm (2 * n) 4",
+              "tactic": "apply Nat.dvd_antisymm"
+            },
+            {
+              "annotated_tactic": [
+                "\"subst hn\"",
+                "[]"
+              ],
+              "state_after": "case inl\n\n\u22a2 Monoid.exponent (QuaternionGroup 0) = lcm (2 * 0) 4",
+              "state_before": "case inl\nn : \u2115\nhn : n = 0\n\u22a2 Monoid.exponent (QuaternionGroup n) = lcm (2 * n) 4",
+              "tactic": "subst hn"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>lcm_zero_left<\\/a>, <a>mul_zero<\\/a>]\"",
+                "[{\"full_name\":\"GCDMonoid.lcm_zero_left\",\"def_path\":\"Mathlib\\/Algebra\\/GCDMonoid\\/Basic.lean\",\"def_pos\":[288,3],\"def_end_pos\":[288,16]},{\"full_name\":\"MulZeroClass.mul_zero\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Defs.lean\",\"def_pos\":[39,3],\"def_end_pos\":[39,11]}]"
+              ],
+              "state_after": "case inl\n\n\u22a2 Monoid.exponent (QuaternionGroup 0) = 0",
+              "state_before": "case inl\n\n\u22a2 Monoid.exponent (QuaternionGroup 0) = lcm (2 * 0) 4",
+              "tactic": "simp only [lcm_zero_left, mul_zero]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>Monoid.exponent_eq_zero_of_order_zero<\\/a> <a>orderOf_a_one<\\/a>\"",
+                "[{\"full_name\":\"Monoid.exponent_eq_zero_of_order_zero\",\"def_path\":\"Mathlib\\/GroupTheory\\/Exponent.lean\",\"def_pos\":[135,9],\"def_end_pos\":[135,39]},{\"full_name\":\"QuaternionGroup.orderOf_a_one\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[235,9],\"def_end_pos\":[235,22]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inl\n\n\u22a2 Monoid.exponent (QuaternionGroup 0) = 0",
+              "tactic": "exact Monoid.exponent_eq_zero_of_order_zero orderOf_a_one"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Monoid.exponent_dvd_of_forall_pow_eq_one<\\/a>\"",
+                "[{\"full_name\":\"Monoid.exponent_dvd_of_forall_pow_eq_one\",\"def_path\":\"Mathlib\\/GroupTheory\\/Exponent.lean\",\"def_pos\":[235,11],\"def_end_pos\":[235,44]}]"
+              ],
+              "state_after": "case inr.a.a\nn : \u2115\nhn : NeZero n\n\u22a2 \u2200 (g : QuaternionGroup n), g ^ lcm (2 * n) 4 = 1",
+              "state_before": "case inr.a\nn : \u2115\nhn : NeZero n\n\u22a2 Monoid.exponent (QuaternionGroup n) \u2223 lcm (2 * n) 4",
+              "tactic": "apply Monoid.exponent_dvd_of_forall_pow_eq_one"
+            },
+            {
+              "annotated_tactic": [
+                "\"rintro (m | m)\"",
+                "[]"
+              ],
+              "state_after": "case inr.a.a.a\nn : \u2115\nhn : NeZero n\nm : ZMod (2 * n)\n\u22a2 a m ^ lcm (2 * n) 4 = 1\n\ncase inr.a.a.xa\nn : \u2115\nhn : NeZero n\nm : ZMod (2 * n)\n\u22a2 xa m ^ lcm (2 * n) 4 = 1",
+              "state_before": "case inr.a.a\nn : \u2115\nhn : NeZero n\n\u22a2 \u2200 (g : QuaternionGroup n), g ^ lcm (2 * n) 4 = 1",
+              "tactic": "rintro (m | m)"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>orderOf_dvd_iff_pow_eq_one<\\/a>, <a>orderOf_a<\\/a>]\"",
+                "[{\"full_name\":\"orderOf_dvd_iff_pow_eq_one\",\"def_path\":\"Mathlib\\/GroupTheory\\/OrderOfElement.lean\",\"def_pos\":[272,9],\"def_end_pos\":[272,35]},{\"full_name\":\"QuaternionGroup.orderOf_a\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[256,9],\"def_end_pos\":[256,18]}]"
+              ],
+              "state_after": "case inr.a.a.a\nn : \u2115\nhn : NeZero n\nm : ZMod (2 * n)\n\u22a2 2 * n / (2 * n).gcd m.val \u2223 lcm (2 * n) 4",
+              "state_before": "case inr.a.a.a\nn : \u2115\nhn : NeZero n\nm : ZMod (2 * n)\n\u22a2 a m ^ lcm (2 * n) 4 = 1",
+              "tactic": "rw [\u2190 orderOf_dvd_iff_pow_eq_one, orderOf_a]"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine <a>Nat.dvd_trans<\\/a> \\u27e8<a>gcd<\\/a> (2 * n) m.val, ?_\\u27e9 (<a>dvd_lcm_left<\\/a> (2 * n) 4)\"",
+                "[{\"full_name\":\"Nat.dvd_trans\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Dvd.lean\",\"def_pos\":[19,19],\"def_end_pos\":[19,28]},{\"full_name\":\"GCDMonoid.gcd\",\"def_path\":\"Mathlib\\/Algebra\\/GCDMonoid\\/Basic.lean\",\"def_pos\":[276,3],\"def_end_pos\":[276,6]},{\"full_name\":\"dvd_lcm_left\",\"def_path\":\"Mathlib\\/Algebra\\/GCDMonoid\\/Basic.lean\",\"def_pos\":[756,9],\"def_end_pos\":[756,21]}]"
+              ],
+              "state_after": "case inr.a.a.a\nn : \u2115\nhn : NeZero n\nm : ZMod (2 * n)\n\u22a2 2 * n = 2 * n / (2 * n).gcd m.val * gcd (2 * n) m.val",
+              "state_before": "case inr.a.a.a\nn : \u2115\nhn : NeZero n\nm : ZMod (2 * n)\n\u22a2 2 * n / (2 * n).gcd m.val \u2223 lcm (2 * n) 4",
+              "tactic": "refine Nat.dvd_trans \u27e8gcd (2 * n) m.val, ?_\u27e9 (dvd_lcm_left (2 * n) 4)"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact (<a>Nat.div_mul_cancel<\\/a> (<a>Nat.gcd_dvd_left<\\/a> (2 * n) m.val)).<a>symm<\\/a>\"",
+                "[{\"full_name\":\"Nat.div_mul_cancel\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Dvd.lean\",\"def_pos\":[91,19],\"def_end_pos\":[91,33]},{\"full_name\":\"Nat.gcd_dvd_left\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Gcd.lean\",\"def_pos\":[86,9],\"def_end_pos\":[86,21]},{\"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 inr.a.a.a\nn : \u2115\nhn : NeZero n\nm : ZMod (2 * n)\n\u22a2 2 * n = 2 * n / (2 * n).gcd m.val * gcd (2 * n) m.val",
+              "tactic": "exact (Nat.div_mul_cancel (Nat.gcd_dvd_left (2 * n) m.val)).symm"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>orderOf_dvd_iff_pow_eq_one<\\/a>, <a>orderOf_xa<\\/a>]\"",
+                "[{\"full_name\":\"orderOf_dvd_iff_pow_eq_one\",\"def_path\":\"Mathlib\\/GroupTheory\\/OrderOfElement.lean\",\"def_pos\":[272,9],\"def_end_pos\":[272,35]},{\"full_name\":\"QuaternionGroup.orderOf_xa\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[211,9],\"def_end_pos\":[211,19]}]"
+              ],
+              "state_after": "case inr.a.a.xa\nn : \u2115\nhn : NeZero n\nm : ZMod (2 * n)\n\u22a2 4 \u2223 lcm (2 * n) 4",
+              "state_before": "case inr.a.a.xa\nn : \u2115\nhn : NeZero n\nm : ZMod (2 * n)\n\u22a2 xa m ^ lcm (2 * n) 4 = 1",
+              "tactic": "rw [\u2190 orderOf_dvd_iff_pow_eq_one, orderOf_xa]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>dvd_lcm_right<\\/a> (2 * n) 4\"",
+                "[{\"full_name\":\"dvd_lcm_right\",\"def_path\":\"Mathlib\\/Algebra\\/GCDMonoid\\/Basic.lean\",\"def_pos\":[760,9],\"def_end_pos\":[760,22]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inr.a.a.xa\nn : \u2115\nhn : NeZero n\nm : ZMod (2 * n)\n\u22a2 4 \u2223 lcm (2 * n) 4",
+              "tactic": "exact dvd_lcm_right (2 * n) 4"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>lcm_dvd<\\/a>\"",
+                "[{\"full_name\":\"lcm_dvd\",\"def_path\":\"Mathlib\\/Algebra\\/GCDMonoid\\/Basic.lean\",\"def_pos\":[764,9],\"def_end_pos\":[764,16]}]"
+              ],
+              "state_after": "case inr.a.hab\nn : \u2115\nhn : NeZero n\n\u22a2 2 * n \u2223 Monoid.exponent (QuaternionGroup n)\n\ncase inr.a.hcb\nn : \u2115\nhn : NeZero n\n\u22a2 4 \u2223 Monoid.exponent (QuaternionGroup n)",
+              "state_before": "case inr.a\nn : \u2115\nhn : NeZero n\n\u22a2 lcm (2 * n) 4 \u2223 Monoid.exponent (QuaternionGroup n)",
+              "tactic": "apply lcm_dvd"
+            },
+            {
+              "annotated_tactic": [
+                "\"convert <a>Monoid.order_dvd_exponent<\\/a> (<a>a<\\/a> 1)\"",
+                "[{\"full_name\":\"Monoid.order_dvd_exponent\",\"def_path\":\"Mathlib\\/GroupTheory\\/Exponent.lean\",\"def_pos\":[207,9],\"def_end_pos\":[207,27]},{\"full_name\":\"QuaternionGroup.a\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[54,5],\"def_end_pos\":[54,6]}]"
+              ],
+              "state_after": "case h.e'_3\nn : \u2115\nhn : NeZero n\n\u22a2 2 * n = orderOf (a 1)",
+              "state_before": "case inr.a.hab\nn : \u2115\nhn : NeZero n\n\u22a2 2 * n \u2223 Monoid.exponent (QuaternionGroup n)",
+              "tactic": "convert Monoid.order_dvd_exponent (a 1)"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact orderOf_a_one.symm\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.e'_3\nn : \u2115\nhn : NeZero n\n\u22a2 2 * n = orderOf (a 1)",
+              "tactic": "exact orderOf_a_one.symm"
+            },
+            {
+              "annotated_tactic": [
+                "\"convert <a>Monoid.order_dvd_exponent<\\/a> (<a>xa<\\/a> (0 : <a>ZMod<\\/a> (2 * n)))\"",
+                "[{\"full_name\":\"Monoid.order_dvd_exponent\",\"def_path\":\"Mathlib\\/GroupTheory\\/Exponent.lean\",\"def_pos\":[207,9],\"def_end_pos\":[207,27]},{\"full_name\":\"QuaternionGroup.xa\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[55,5],\"def_end_pos\":[55,7]},{\"full_name\":\"ZMod\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Defs.lean\",\"def_pos\":[95,5],\"def_end_pos\":[95,9]}]"
+              ],
+              "state_after": "case h.e'_3\nn : \u2115\nhn : NeZero n\n\u22a2 4 = orderOf (xa 0)",
+              "state_before": "case inr.a.hcb\nn : \u2115\nhn : NeZero n\n\u22a2 4 \u2223 Monoid.exponent (QuaternionGroup n)",
+              "tactic": "convert Monoid.order_dvd_exponent (xa (0 : ZMod (2 * n)))"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact (<a>orderOf_xa<\\/a> 0).<a>symm<\\/a>\"",
+                "[{\"full_name\":\"QuaternionGroup.orderOf_xa\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[211,9],\"def_end_pos\":[211,19]},{\"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'_3\nn : \u2115\nhn : NeZero n\n\u22a2 4 = orderOf (xa 0)",
+              "tactic": "exact (orderOf_xa 0).symm"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean"
+      },
+      {
+        "full_name": "QuaternionGroup.one_def",
+        "id": "QuaternionGroup.one_def",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            132,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean",
+          "full_name": "QuaternionGroup.one_def",
+          "start": [
+            131,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean"
+      },
+      {
+        "full_name": "QuaternionGroup.orderOf_a",
+        "id": "QuaternionGroup.orderOf_a",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            259,
+            47
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean",
+          "full_name": "QuaternionGroup.orderOf_a",
+          "start": [
+            256,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"conv_lhs => rw [\\u2190 <a>ZMod.natCast_zmod_val<\\/a> i]\"",
+                "[{\"full_name\":\"ZMod.natCast_zmod_val\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Basic.lean\",\"def_pos\":[209,9],\"def_end_pos\":[209,25]}]"
+              ],
+              "state_after": "n : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\n\u22a2 orderOf (a \u2191i.val) = 2 * n / (2 * n).gcd i.val",
+              "state_before": "n : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\n\u22a2 orderOf (a i) = 2 * n / (2 * n).gcd i.val",
+              "tactic": "conv_lhs => rw [\u2190 ZMod.natCast_zmod_val i]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>a_one_pow<\\/a>, <a>orderOf_pow<\\/a>, <a>orderOf_a_one<\\/a>]\"",
+                "[{\"full_name\":\"QuaternionGroup.a_one_pow\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[180,9],\"def_end_pos\":[180,18]},{\"full_name\":\"orderOf_pow\",\"def_path\":\"Mathlib\\/GroupTheory\\/OrderOfElement.lean\",\"def_pos\":[873,9],\"def_end_pos\":[873,20]},{\"full_name\":\"QuaternionGroup.orderOf_a_one\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[235,9],\"def_end_pos\":[235,22]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "n : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\n\u22a2 orderOf (a \u2191i.val) = 2 * n / (2 * n).gcd i.val",
+              "tactic": "rw [\u2190 a_one_pow, orderOf_pow, orderOf_a_one]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean"
+      },
+      {
+        "full_name": "QuaternionGroup.orderOf_a_one",
+        "id": "QuaternionGroup.orderOf_a_one",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            251,
+            42
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean",
+          "full_name": "QuaternionGroup.orderOf_a_one",
+          "start": [
+            235,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"cases' <a>eq_zero_or_neZero<\\/a> n with hn hn\"",
+                "[{\"full_name\":\"eq_zero_or_neZero\",\"def_path\":\"Mathlib\\/Algebra\\/NeZero.lean\",\"def_pos\":[48,9],\"def_end_pos\":[48,26]}]"
+              ],
+              "state_after": "case inl\nn : \u2115\nhn : n = 0\n\u22a2 orderOf (a 1) = 2 * n\n\ncase inr\nn : \u2115\nhn : NeZero n\n\u22a2 orderOf (a 1) = 2 * n",
+              "state_before": "n : \u2115\n\u22a2 orderOf (a 1) = 2 * n",
+              "tactic": "cases' eq_zero_or_neZero n with hn hn"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply (<a>Nat.le_of_dvd<\\/a>\\n    (<a>NeZero.pos<\\/a> _) (<a>orderOf_dvd_of_pow_eq_one<\\/a> (@<a>a_one_pow_n<\\/a> n))).lt_or_eq.resolve_left\"",
+                "[{\"full_name\":\"Nat.le_of_dvd\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Dvd.lean\",\"def_pos\":[46,9],\"def_end_pos\":[46,18]},{\"full_name\":\"NeZero.pos\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Canonical\\/Defs.lean\",\"def_pos\":[297,9],\"def_end_pos\":[297,12]},{\"full_name\":\"orderOf_dvd_of_pow_eq_one\",\"def_path\":\"Mathlib\\/GroupTheory\\/OrderOfElement.lean\",\"def_pos\":[266,9],\"def_end_pos\":[266,34]},{\"full_name\":\"QuaternionGroup.a_one_pow_n\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[189,9],\"def_end_pos\":[189,20]}]"
+              ],
+              "state_after": "case inr\nn : \u2115\nhn : NeZero n\n\u22a2 \u00acorderOf (a 1) < 2 * n",
+              "state_before": "case inr\nn : \u2115\nhn : NeZero n\n\u22a2 orderOf (a 1) = 2 * n",
+              "tactic": "apply (Nat.le_of_dvd\n  (NeZero.pos _) (orderOf_dvd_of_pow_eq_one (@a_one_pow_n n))).lt_or_eq.resolve_left"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro h\"",
+                "[]"
+              ],
+              "state_after": "case inr\nn : \u2115\nhn : NeZero n\nh : orderOf (a 1) < 2 * n\n\u22a2 False",
+              "state_before": "case inr\nn : \u2115\nhn : NeZero n\n\u22a2 \u00acorderOf (a 1) < 2 * n",
+              "tactic": "intro h"
+            },
+            {
+              "annotated_tactic": [
+                "\"have h1 : (<a>a<\\/a> 1 : <a>QuaternionGroup<\\/a> n) ^ <a>orderOf<\\/a> (<a>a<\\/a> 1) = 1 := <a>pow_orderOf_eq_one<\\/a> _\"",
+                "[{\"full_name\":\"QuaternionGroup.a\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[54,5],\"def_end_pos\":[54,6]},{\"full_name\":\"QuaternionGroup\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[53,11],\"def_end_pos\":[53,26]},{\"full_name\":\"orderOf\",\"def_path\":\"Mathlib\\/GroupTheory\\/OrderOfElement.lean\",\"def_pos\":[155,19],\"def_end_pos\":[155,26]},{\"full_name\":\"QuaternionGroup.a\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[54,5],\"def_end_pos\":[54,6]},{\"full_name\":\"pow_orderOf_eq_one\",\"def_path\":\"Mathlib\\/GroupTheory\\/OrderOfElement.lean\",\"def_pos\":[177,9],\"def_end_pos\":[177,27]}]"
+              ],
+              "state_after": "case inr\nn : \u2115\nhn : NeZero n\nh : orderOf (a 1) < 2 * n\nh1 : a 1 ^ orderOf (a 1) = 1\n\u22a2 False",
+              "state_before": "case inr\nn : \u2115\nhn : NeZero n\nh : orderOf (a 1) < 2 * n\n\u22a2 False",
+              "tactic": "have h1 : (a 1 : QuaternionGroup n) ^ orderOf (a 1) = 1 := pow_orderOf_eq_one _"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>a_one_pow<\\/a>] at h1\"",
+                "[{\"full_name\":\"QuaternionGroup.a_one_pow\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[180,9],\"def_end_pos\":[180,18]}]"
+              ],
+              "state_after": "case inr\nn : \u2115\nhn : NeZero n\nh : orderOf (a 1) < 2 * n\nh1 : a \u2191(orderOf (a 1)) = 1\n\u22a2 False",
+              "state_before": "case inr\nn : \u2115\nhn : NeZero n\nh : orderOf (a 1) < 2 * n\nh1 : a 1 ^ orderOf (a 1) = 1\n\u22a2 False",
+              "tactic": "rw [a_one_pow] at h1"
+            },
+            {
+              "annotated_tactic": [
+                "\"injection h1 with h2\"",
+                "[]"
+              ],
+              "state_after": "case inr\nn : \u2115\nhn : NeZero n\nh : orderOf (a 1) < 2 * n\nh2 : \u2191(orderOf (a 1)) = 0\n\u22a2 False",
+              "state_before": "case inr\nn : \u2115\nhn : NeZero n\nh : orderOf (a 1) < 2 * n\nh1 : a \u2191(orderOf (a 1)) = 1\n\u22a2 False",
+              "tactic": "injection h1 with h2"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>ZMod.val_eq_zero<\\/a>, <a>ZMod.val_natCast<\\/a>, <a>Nat.mod_eq_of_lt<\\/a> h] at h2\"",
+                "[{\"full_name\":\"ZMod.val_eq_zero\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Basic.lean\",\"def_pos\":[1039,9],\"def_end_pos\":[1039,20]},{\"full_name\":\"ZMod.val_natCast\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Basic.lean\",\"def_pos\":[84,9],\"def_end_pos\":[84,20]},{\"full_name\":\"Nat.mod_eq_of_lt\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Div.lean\",\"def_pos\":[131,9],\"def_end_pos\":[131,21]}]"
+              ],
+              "state_after": "case inr\nn : \u2115\nhn : NeZero n\nh : orderOf (a 1) < 2 * n\nh2 : orderOf (a 1) = 0\n\u22a2 False",
+              "state_before": "case inr\nn : \u2115\nhn : NeZero n\nh : orderOf (a 1) < 2 * n\nh2 : \u2191(orderOf (a 1)) = 0\n\u22a2 False",
+              "tactic": "rw [\u2190 ZMod.val_eq_zero, ZMod.val_natCast, Nat.mod_eq_of_lt h] at h2"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>absurd<\\/a> h2.symm (<a>orderOf_pos<\\/a> _).<a>ne<\\/a>\"",
+                "[{\"full_name\":\"absurd\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[246,21],\"def_end_pos\":[246,27]},{\"full_name\":\"orderOf_pos\",\"def_path\":\"Mathlib\\/GroupTheory\\/OrderOfElement.lean\",\"def_pos\":[864,7],\"def_end_pos\":[864,18]},{\"full_name\":\"LT.lt.ne\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[147,7],\"def_end_pos\":[147,15]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inr\nn : \u2115\nhn : NeZero n\nh : orderOf (a 1) < 2 * n\nh2 : orderOf (a 1) = 0\n\u22a2 False",
+              "tactic": "exact absurd h2.symm (orderOf_pos _).ne"
+            },
+            {
+              "annotated_tactic": [
+                "\"subst hn\"",
+                "[]"
+              ],
+              "state_after": "case inl\n\n\u22a2 orderOf (a 1) = 2 * 0",
+              "state_before": "case inl\nn : \u2115\nhn : n = 0\n\u22a2 orderOf (a 1) = 2 * n",
+              "tactic": "subst hn"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp_rw [<a>mul_zero<\\/a>, <a>orderOf_eq_zero_iff'<\\/a>]\"",
+                "[{\"full_name\":\"MulZeroClass.mul_zero\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Defs.lean\",\"def_pos\":[39,3],\"def_end_pos\":[39,11]},{\"full_name\":\"orderOf_eq_zero_iff'\",\"def_path\":\"Mathlib\\/GroupTheory\\/OrderOfElement.lean\",\"def_pos\":[197,9],\"def_end_pos\":[197,29]}]"
+              ],
+              "state_after": "case inl\n\n\u22a2 \u2200 (n : \u2115), 0 < n \u2192 QuaternionGroup.a 1 ^ n \u2260 1",
+              "state_before": "case inl\n\n\u22a2 orderOf (a 1) = 2 * 0",
+              "tactic": "simp_rw [mul_zero, orderOf_eq_zero_iff']"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro n h\"",
+                "[]"
+              ],
+              "state_after": "case inl\nn : \u2115\nh : 0 < n\n\u22a2 a 1 ^ n \u2260 1",
+              "state_before": "case inl\n\n\u22a2 \u2200 (n : \u2115), 0 < n \u2192 QuaternionGroup.a 1 ^ n \u2260 1",
+              "tactic": "intro n h"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>one_def<\\/a>, <a>a_one_pow<\\/a>]\"",
+                "[{\"full_name\":\"QuaternionGroup.one_def\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[131,9],\"def_end_pos\":[131,16]},{\"full_name\":\"QuaternionGroup.a_one_pow\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[180,9],\"def_end_pos\":[180,18]}]"
+              ],
+              "state_after": "case inl\nn : \u2115\nh : 0 < n\n\u22a2 a \u2191n \u2260 a 0",
+              "state_before": "case inl\nn : \u2115\nh : 0 < n\n\u22a2 a 1 ^ n \u2260 1",
+              "tactic": "rw [one_def, a_one_pow]"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>mt<\\/a> a.inj\"",
+                "[{\"full_name\":\"mt\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[647,9],\"def_end_pos\":[647,11]}]"
+              ],
+              "state_after": "case inl\nn : \u2115\nh : 0 < n\n\u22a2 \u00ac\u2191n = 0",
+              "state_before": "case inl\nn : \u2115\nh : 0 < n\n\u22a2 a \u2191n \u2260 a 0",
+              "tactic": "apply mt a.inj"
+            },
+            {
+              "annotated_tactic": [
+                "\"haveI : <a>CharZero<\\/a> (<a>ZMod<\\/a> (2 * 0)) := <a>ZMod.charZero<\\/a>\"",
+                "[{\"full_name\":\"CharZero\",\"def_path\":\"Mathlib\\/Algebra\\/CharZero\\/Defs.lean\",\"def_pos\":[42,7],\"def_end_pos\":[42,15]},{\"full_name\":\"ZMod\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Defs.lean\",\"def_pos\":[95,5],\"def_end_pos\":[95,9]},{\"full_name\":\"ZMod.charZero\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Basic.lean\",\"def_pos\":[39,10],\"def_end_pos\":[39,18]}]"
+              ],
+              "state_after": "case inl\nn : \u2115\nh : 0 < n\nthis : CharZero (ZMod (2 * 0))\n\u22a2 \u00ac\u2191n = 0",
+              "state_before": "case inl\nn : \u2115\nh : 0 < n\n\u22a2 \u00ac\u2191n = 0",
+              "tactic": "haveI : CharZero (ZMod (2 * 0)) := ZMod.charZero"
+            },
+            {
+              "annotated_tactic": [
+                "\"simpa using h.ne'\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inl\nn : \u2115\nh : 0 < n\nthis : CharZero (ZMod (2 * 0))\n\u22a2 \u00ac\u2191n = 0",
+              "tactic": "simpa using h.ne'"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean"
+      },
+      {
+        "full_name": "QuaternionGroup.orderOf_xa",
+        "id": "QuaternionGroup.orderOf_xa",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            222,
+            13
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean",
+          "full_name": "QuaternionGroup.orderOf_xa",
+          "start": [
+            211,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"change _ = 2 ^ 2\"",
+                "[]"
+              ],
+              "state_after": "n : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\n\u22a2 orderOf (xa i) = 2 ^ 2",
+              "state_before": "n : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\n\u22a2 orderOf (xa i) = 4",
+              "tactic": "change _ = 2 ^ 2"
+            },
+            {
+              "annotated_tactic": [
+                "\"haveI : <a>Fact<\\/a> (<a>Nat.Prime<\\/a> 2) := <a>Fact.mk<\\/a> <a>Nat.prime_two<\\/a>\"",
+                "[{\"full_name\":\"Fact\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[114,7],\"def_end_pos\":[114,11]},{\"full_name\":\"Nat.Prime\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Prime.lean\",\"def_pos\":[45,5],\"def_end_pos\":[45,10]},{\"full_name\":\"Fact.mk\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[114,7],\"def_end_pos\":[114,11]},{\"full_name\":\"Nat.prime_two\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Prime.lean\",\"def_pos\":[170,9],\"def_end_pos\":[170,18]}]"
+              ],
+              "state_after": "n : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\nthis : Fact (Nat.Prime 2)\n\u22a2 orderOf (xa i) = 2 ^ 2",
+              "state_before": "n : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\n\u22a2 orderOf (xa i) = 2 ^ 2",
+              "tactic": "haveI : Fact (Nat.Prime 2) := Fact.mk Nat.prime_two"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>orderOf_eq_prime_pow<\\/a>\"",
+                "[{\"full_name\":\"orderOf_eq_prime_pow\",\"def_path\":\"Mathlib\\/GroupTheory\\/OrderOfElement.lean\",\"def_pos\":[536,9],\"def_end_pos\":[536,29]}]"
+              ],
+              "state_after": "case hnot\nn : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\nthis : Fact (Nat.Prime 2)\n\u22a2 \u00acxa i ^ 2 ^ 1 = 1\n\ncase hfin\nn : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\nthis : Fact (Nat.Prime 2)\n\u22a2 xa i ^ 2 ^ (1 + 1) = 1",
+              "state_before": "n : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\nthis : Fact (Nat.Prime 2)\n\u22a2 orderOf (xa i) = 2 ^ 2",
+              "tactic": "apply orderOf_eq_prime_pow"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro h\"",
+                "[]"
+              ],
+              "state_after": "case hnot\nn : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\nthis : Fact (Nat.Prime 2)\nh : xa i ^ 2 ^ 1 = 1\n\u22a2 False",
+              "state_before": "case hnot\nn : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\nthis : Fact (Nat.Prime 2)\n\u22a2 \u00acxa i ^ 2 ^ 1 = 1",
+              "tactic": "intro h"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>pow_one<\\/a>, <a>xa_sq<\\/a>] at h\"",
+                "[{\"full_name\":\"pow_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[663,7],\"def_end_pos\":[663,14]},{\"full_name\":\"QuaternionGroup.xa_sq\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[196,9],\"def_end_pos\":[196,14]}]"
+              ],
+              "state_after": "case hnot\nn : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\nthis : Fact (Nat.Prime 2)\nh : a \u2191n = 1\n\u22a2 False",
+              "state_before": "case hnot\nn : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\nthis : Fact (Nat.Prime 2)\nh : xa i ^ 2 ^ 1 = 1\n\u22a2 False",
+              "tactic": "simp only [pow_one, xa_sq] at h"
+            },
+            {
+              "annotated_tactic": [
+                "\"injection h with h'\"",
+                "[]"
+              ],
+              "state_after": "case hnot\nn : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\nthis : Fact (Nat.Prime 2)\nh' : \u2191n = 0\n\u22a2 False",
+              "state_before": "case hnot\nn : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\nthis : Fact (Nat.Prime 2)\nh : a \u2191n = 1\n\u22a2 False",
+              "tactic": "injection h with h'"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply_fun <a>ZMod.val<\\/a> at h'\"",
+                "[{\"full_name\":\"ZMod.val\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Basic.lean\",\"def_pos\":[47,5],\"def_end_pos\":[47,8]}]"
+              ],
+              "state_after": "case hnot\nn : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\nthis : Fact (Nat.Prime 2)\nh' : (\u2191n).val = ZMod.val 0\n\u22a2 False",
+              "state_before": "case hnot\nn : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\nthis : Fact (Nat.Prime 2)\nh' : \u2191n = 0\n\u22a2 False",
+              "tactic": "apply_fun ZMod.val at h'"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>ZMod.val_natCast<\\/a>, <a>ZMod.val_zero<\\/a>, <a>Nat.zero_div<\\/a>, <a>Nat.mod_mul_left_div_self<\\/a>,\\n      <a>Nat.div_self<\\/a> (<a>NeZero.pos<\\/a> n)] at h'\"",
+                "[{\"full_name\":\"ZMod.val_natCast\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Basic.lean\",\"def_pos\":[84,9],\"def_end_pos\":[84,20]},{\"full_name\":\"ZMod.val_zero\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Basic.lean\",\"def_pos\":[63,9],\"def_end_pos\":[63,17]},{\"full_name\":\"Nat.zero_div\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Div.lean\",\"def_pos\":[213,27],\"def_end_pos\":[213,35]},{\"full_name\":\"Nat.mod_mul_left_div_self\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Mod.lean\",\"def_pos\":[57,9],\"def_end_pos\":[57,30]},{\"full_name\":\"Nat.div_self\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Div.lean\",\"def_pos\":[373,19],\"def_end_pos\":[373,27]},{\"full_name\":\"NeZero.pos\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Canonical\\/Defs.lean\",\"def_pos\":[297,9],\"def_end_pos\":[297,12]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case hnot\nn : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\nthis : Fact (Nat.Prime 2)\nh' : (\u2191n).val / n = ZMod.val 0 / n\n\u22a2 False",
+              "tactic": "simp only [ZMod.val_natCast, ZMod.val_zero, Nat.zero_div, Nat.mod_mul_left_div_self,\n  Nat.div_self (NeZero.pos n)] at h'"
+            },
+            {
+              "annotated_tactic": [
+                "\"norm_num\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case hfin\nn : \u2115\ninst\u271d : NeZero n\ni : ZMod (2 * n)\nthis : Fact (Nat.Prime 2)\n\u22a2 xa i ^ 2 ^ (1 + 1) = 1",
+              "tactic": "norm_num"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean"
+      },
+      {
+        "full_name": "QuaternionGroup.quaternionGroup_one_isCyclic",
+        "id": "QuaternionGroup.quaternionGroup_one_isCyclic",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            229,
+            23
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean",
+          "full_name": "QuaternionGroup.quaternionGroup_one_isCyclic",
+          "start": [
+            226,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"apply <a>isCyclic_of_orderOf_eq_card<\\/a>\"",
+                "[{\"full_name\":\"isCyclic_of_orderOf_eq_card\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Cyclic.lean\",\"def_pos\":[124,9],\"def_end_pos\":[124,36]}]"
+              ],
+              "state_after": "case hx\nn : \u2115\n\u22a2 orderOf ?x = Fintype.card (QuaternionGroup 1)\n\ncase x\nn : \u2115\n\u22a2 QuaternionGroup 1",
+              "state_before": "n : \u2115\n\u22a2 IsCyclic (QuaternionGroup 1)",
+              "tactic": "apply isCyclic_of_orderOf_eq_card"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>card<\\/a>, <a>mul_one<\\/a>]\"",
+                "[{\"full_name\":\"QuaternionGroup.card\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[174,9],\"def_end_pos\":[174,13]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]}]"
+              ],
+              "state_after": "case hx\nn : \u2115\n\u22a2 orderOf ?x = 4",
+              "state_before": "case hx\nn : \u2115\n\u22a2 orderOf ?x = Fintype.card (QuaternionGroup 1)",
+              "tactic": "rw [card, mul_one]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>orderOf_xa<\\/a> 0\"",
+                "[{\"full_name\":\"QuaternionGroup.orderOf_xa\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[211,9],\"def_end_pos\":[211,19]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case hx\nn : \u2115\n\u22a2 orderOf ?x = 4",
+              "tactic": "exact orderOf_xa 0"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean"
+      },
+      {
+        "full_name": "QuaternionGroup.xa_mul_a",
+        "id": "QuaternionGroup.xa_mul_a",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            123,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean",
+          "full_name": "QuaternionGroup.xa_mul_a",
+          "start": [
+            122,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean"
+      },
+      {
+        "full_name": "QuaternionGroup.xa_mul_xa",
+        "id": "QuaternionGroup.xa_mul_xa",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            128,
+            6
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean",
+          "full_name": "QuaternionGroup.xa_mul_xa",
+          "start": [
+            127,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean"
+      },
+      {
+        "full_name": "QuaternionGroup.xa_pow_four",
+        "id": "QuaternionGroup.xa_pow_four",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            205,
+            17
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean",
+          "full_name": "QuaternionGroup.xa_pow_four",
+          "start": [
+            200,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [<a>pow_succ<\\/a>, <a>pow_succ<\\/a>, <a>sq<\\/a>, <a>xa_mul_xa<\\/a>, <a>a_mul_xa<\\/a>, <a>xa_mul_xa<\\/a>,\\n    <a>add_sub_cancel_right<\\/a>, <a>add_sub_assoc<\\/a>, <a>sub_sub_cancel<\\/a>]\"",
+                "[{\"full_name\":\"pow_succ\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[657,9],\"def_end_pos\":[657,17]},{\"full_name\":\"pow_succ\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[657,9],\"def_end_pos\":[657,17]},{\"full_name\":\"sq\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[684,41],\"def_end_pos\":[684,43]},{\"full_name\":\"QuaternionGroup.xa_mul_xa\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[127,9],\"def_end_pos\":[127,18]},{\"full_name\":\"QuaternionGroup.a_mul_xa\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[117,9],\"def_end_pos\":[117,17]},{\"full_name\":\"QuaternionGroup.xa_mul_xa\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[127,9],\"def_end_pos\":[127,18]},{\"full_name\":\"add_sub_cancel_right\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[1008,3],\"def_end_pos\":[1008,14]},{\"full_name\":\"add_sub_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[455,3],\"def_end_pos\":[455,14]},{\"full_name\":\"sub_sub_cancel\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[1304,3],\"def_end_pos\":[1304,14]}]"
+              ],
+              "state_after": "n : \u2115\ni : ZMod (2 * n)\n\u22a2 a (\u2191n + \u2191n) = 1",
+              "state_before": "n : \u2115\ni : ZMod (2 * n)\n\u22a2 xa i ^ 4 = 1",
+              "tactic": "rw [pow_succ, pow_succ, sq, xa_mul_xa, a_mul_xa, xa_mul_xa,\n  add_sub_cancel_right, add_sub_assoc, sub_sub_cancel]"
+            },
+            {
+              "annotated_tactic": [
+                "\"norm_cast\"",
+                "[]"
+              ],
+              "state_after": "n : \u2115\ni : ZMod (2 * n)\n\u22a2 a \u2191(n + n) = 1",
+              "state_before": "n : \u2115\ni : ZMod (2 * n)\n\u22a2 a (\u2191n + \u2191n) = 1",
+              "tactic": "norm_cast"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>two_mul<\\/a>]\"",
+                "[{\"full_name\":\"two_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[179,9],\"def_end_pos\":[179,16]}]"
+              ],
+              "state_after": "n : \u2115\ni : ZMod (2 * n)\n\u22a2 a \u2191(2 * n) = 1",
+              "state_before": "n : \u2115\ni : ZMod (2 * n)\n\u22a2 a \u2191(n + n) = 1",
+              "tactic": "rw [\u2190 two_mul]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [<a>one_def<\\/a>]\"",
+                "[{\"full_name\":\"QuaternionGroup.one_def\",\"def_path\":\"Mathlib\\/GroupTheory\\/SpecificGroups\\/Quaternion.lean\",\"def_pos\":[131,9],\"def_end_pos\":[131,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "n : \u2115\ni : ZMod (2 * n)\n\u22a2 a \u2191(2 * n) = 1",
+              "tactic": "simp [one_def]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean"
+      },
+      {
+        "full_name": "QuaternionGroup.xa_sq",
+        "id": "QuaternionGroup.xa_sq",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            196,
+            66
+          ],
+          "file_path": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean",
+          "full_name": "QuaternionGroup.xa_sq",
+          "start": [
+            196,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"simp [<a>sq<\\/a>]\"",
+                "[{\"full_name\":\"sq\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[684,41],\"def_end_pos\":[684,43]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "n : \u2115\ni : ZMod (2 * n)\n\u22a2 xa i ^ 2 = a \u2191n",
+              "tactic": "simp [sq]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/GroupTheory/SpecificGroups/Quaternion.lean"
+      }
+    ],
+    "input_proofs": 21,
+    "input_units": 2,
+    "proofs": 2,
+    "published_proofs": 2,
+    "published_transitions": 2,
+    "replay_failures": [],
+    "transitions": 2,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001217-0000-1b6f91a2db987e5b.parquet",
+      "sha256": "1b6f91a2db987e5b4c2dea1a9eddcf7d10766f566e79fbb32a57d174d0ba0e26",
+      "bytes": 29970,
+      "rows": 2,
+      "revision": "906b7b88e1251d7543db52f3953c29ea18db26ce"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:IsKleinFour.inv_eq_self",
+    "mathlib:IsKleinFour.mul_self"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/SpecificGroups/KleinFour.lean\",null,null,\"IsKleinFour.inv_eq_self\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/GroupTheory/SpecificGroups/KleinFour.lean\",null,null,\"IsKleinFour.mul_self\"]"
+  ]
+}