Record 15 verified HPC batch manifests

manifests/batches/mathlib/000720.json

@@ -0,0 +1,181 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000720",
+  "batch_fingerprint": "789310406a8b23c791e52161e0ff52e8cb5ac42fd9f9924dba9481c9bace5b1b",
+  "evidence": {
+    "batch_fingerprint": "789310406a8b23c791e52161e0ff52e8cb5ac42fd9f9924dba9481c9bace5b1b",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Localization.homEquiv_symm_apply",
+        "id": "CategoryTheory.Localization.homEquiv_symm_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            130,
+            58
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/HomEquiv.lean",
+          "full_name": "CategoryTheory.Localization.homEquiv_symm_apply",
+          "start": [
+            128,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/HomEquiv.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'refine Functor.IsLocalization.of_equivalence_source W\u2082.Q W\u2082 (\u03a6.functor \u22d9 W\u2082.Q) W\u2081\\n  (Functor.asEquivalence \u03a6.functor).symm ?_ (\u03a6.inverts W\u2082.Q)\\n  ((Functor.associator _ _ _).symm \u226a\u226b isoWhiskerRight ((Equivalence.unitIso _).symm) _ \u226a\u226b\\n    Functor.leftUnitor _)'",
+        "full_name": "CategoryTheory.LocalizerMorphism.IsLocalizedEquivalence.of_equivalence",
+        "id": "CategoryTheory.LocalizerMorphism.IsLocalizedEquivalence.of_equivalence",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            175,
+            74
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/LocalizerMorphism.lean",
+          "full_name": "CategoryTheory.LocalizerMorphism.IsLocalizedEquivalence.of_equivalence",
+          "start": [
+            161,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"haveI : <a>Functor.IsLocalization<\\/a> (\\u03a6.functor \\u22d9 <a>MorphismProperty.Q<\\/a> W\\u2082) W\\u2081 := by\\n    refine <a>Functor.IsLocalization.of_equivalence_source<\\/a> W\\u2082.Q W\\u2082 (\\u03a6.functor \\u22d9 W\\u2082.Q) W\\u2081\\n      (<a>Functor.asEquivalence<\\/a> \\u03a6.functor).<a>symm<\\/a> ?_ (\\u03a6.inverts W\\u2082.Q)\\n      ((<a>Functor.associator<\\/a> _ _ _).<a>symm<\\/a> \\u226a\\u226b <a>isoWhiskerRight<\\/a> ((<a>Equivalence.unitIso<\\/a> _).<a>symm<\\/a>) _ \\u226a\\u226b\\n        <a>Functor.leftUnitor<\\/a> _)\\n    erw [W\\u2081.isoClosure.inverseImage_equivalence_functor_eq_map_inverse\\n      W\\u2081.isoClosure_respectsIso \\u03a6.functor.asEquivalence]\\n    rw [<a>MorphismProperty.map_isoClosure<\\/a>]\\n    exact h\"",
+                "[{\"full_name\":\"CategoryTheory.Functor.IsLocalization\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Localization\\/Predicate.lean\",\"def_pos\":[50,7],\"def_end_pos\":[50,21]},{\"full_name\":\"CategoryTheory.MorphismProperty.Q\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Localization\\/Construction.lean\",\"def_pos\":[112,5],\"def_end_pos\":[112,6]},{\"full_name\":\"CategoryTheory.Functor.IsLocalization.of_equivalence_source\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Localization\\/Equivalence.lean\",\"def_pos\":[67,7],\"def_end_pos\":[67,28]},{\"full_name\":\"CategoryTheory.Functor.asEquivalence\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Equivalence.lean\",\"def_pos\":[580,19],\"def_end_pos\":[580,32]},{\"full_name\":\"CategoryTheory.Equivalence.symm\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Equivalence.lean\",\"def_pos\":[290,5],\"def_end_pos\":[290,9]},{\"full_name\":\"CategoryTheory.Functor.associator\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Whiskering.lean\",\"def_pos\":[280,5],\"def_end_pos\":[280,15]},{\"full_name\":\"CategoryTheory.Iso.symm\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[94,5],\"def_end_pos\":[94,9]},{\"full_name\":\"CategoryTheory.isoWhiskerRight\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Whiskering.lean\",\"def_pos\":[191,5],\"def_end_pos\":[191,20]},{\"full_name\":\"CategoryTheory.Equivalence.unitIso\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Equivalence.lean\",\"def_pos\":[87,3],\"def_end_pos\":[87,10]},{\"full_name\":\"CategoryTheory.Iso.symm\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[94,5],\"def_end_pos\":[94,9]},{\"full_name\":\"CategoryTheory.Functor.leftUnitor\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Whiskering.lean\",\"def_pos\":[252,5],\"def_end_pos\":[252,15]},{\"full_name\":\"CategoryTheory.MorphismProperty.map_isoClosure\",\"def_path\":\"Mathlib\\/CategoryTheory\\/MorphismProperty\\/Basic.lean\",\"def_pos\":[208,7],\"def_end_pos\":[208,21]}]"
+              ],
+              "state_after": "C\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nC\u2083 : Type u\u2083\nD\u2081 : Type u\u2084\nD\u2082 : Type u\u2085\nD\u2083 : Type u\u2086\ninst\u271d\u2078 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2077 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2076 : Category.{v\u2083, u\u2083} C\u2083\ninst\u271d\u2075 : Category.{v\u2084, u\u2084} D\u2081\ninst\u271d\u2074 : Category.{v\u2085, u\u2085} D\u2082\ninst\u271d\u00b3 : Category.{v\u2086, u\u2085} D\u2082\nW\u2081 : MorphismProperty C\u2081\nW\u2082 : MorphismProperty C\u2082\nW\u2083 : MorphismProperty C\u2083\n\u03a6 : LocalizerMorphism W\u2081 W\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\ninst\u271d\u00b2 : L\u2081.IsLocalization W\u2081\nL\u2082 : C\u2082 \u2964 D\u2082\ninst\u271d\u00b9 : L\u2082.IsLocalization W\u2082\nG : D\u2081 \u2964 D\u2082\ninst\u271d : \u03a6.functor.IsEquivalence\nh : W\u2082 \u2264 W\u2081.map \u03a6.functor\nthis : (\u03a6.functor \u22d9 W\u2082.Q).IsLocalization W\u2081\n\u22a2 \u03a6.IsLocalizedEquivalence",
+              "state_before": "C\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nC\u2083 : Type u\u2083\nD\u2081 : Type u\u2084\nD\u2082 : Type u\u2085\nD\u2083 : Type u\u2086\ninst\u271d\u2078 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2077 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2076 : Category.{v\u2083, u\u2083} C\u2083\ninst\u271d\u2075 : Category.{v\u2084, u\u2084} D\u2081\ninst\u271d\u2074 : Category.{v\u2085, u\u2085} D\u2082\ninst\u271d\u00b3 : Category.{v\u2086, u\u2085} D\u2082\nW\u2081 : MorphismProperty C\u2081\nW\u2082 : MorphismProperty C\u2082\nW\u2083 : MorphismProperty C\u2083\n\u03a6 : LocalizerMorphism W\u2081 W\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\ninst\u271d\u00b2 : L\u2081.IsLocalization W\u2081\nL\u2082 : C\u2082 \u2964 D\u2082\ninst\u271d\u00b9 : L\u2082.IsLocalization W\u2082\nG : D\u2081 \u2964 D\u2082\ninst\u271d : \u03a6.functor.IsEquivalence\nh : W\u2082 \u2264 W\u2081.map \u03a6.functor\n\u22a2 \u03a6.IsLocalizedEquivalence",
+              "tactic": "haveI : Functor.IsLocalization (\u03a6.functor \u22d9 MorphismProperty.Q W\u2082) W\u2081 := by\n  refine Functor.IsLocalization.of_equivalence_source W\u2082.Q W\u2082 (\u03a6.functor \u22d9 W\u2082.Q) W\u2081\n    (Functor.asEquivalence \u03a6.functor).symm ?_ (\u03a6.inverts W\u2082.Q)\n    ((Functor.associator _ _ _).symm \u226a\u226b isoWhiskerRight ((Equivalence.unitIso _).symm) _ \u226a\u226b\n      Functor.leftUnitor _)\n  erw [W\u2081.isoClosure.inverseImage_equivalence_functor_eq_map_inverse\n    W\u2081.isoClosure_respectsIso \u03a6.functor.asEquivalence]\n  rw [MorphismProperty.map_isoClosure]\n  exact h"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>IsLocalizedEquivalence.of_isLocalization_of_isLocalization<\\/a> \\u03a6 W\\u2082.Q\"",
+                "[{\"full_name\":\"CategoryTheory.LocalizerMorphism.IsLocalizedEquivalence.of_isLocalization_of_isLocalization\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Localization\\/LocalizerMorphism.lean\",\"def_pos\":[154,7],\"def_end_pos\":[154,65]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nC\u2083 : Type u\u2083\nD\u2081 : Type u\u2084\nD\u2082 : Type u\u2085\nD\u2083 : Type u\u2086\ninst\u271d\u2078 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2077 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2076 : Category.{v\u2083, u\u2083} C\u2083\ninst\u271d\u2075 : Category.{v\u2084, u\u2084} D\u2081\ninst\u271d\u2074 : Category.{v\u2085, u\u2085} D\u2082\ninst\u271d\u00b3 : Category.{v\u2086, u\u2085} D\u2082\nW\u2081 : MorphismProperty C\u2081\nW\u2082 : MorphismProperty C\u2082\nW\u2083 : MorphismProperty C\u2083\n\u03a6 : LocalizerMorphism W\u2081 W\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\ninst\u271d\u00b2 : L\u2081.IsLocalization W\u2081\nL\u2082 : C\u2082 \u2964 D\u2082\ninst\u271d\u00b9 : L\u2082.IsLocalization W\u2082\nG : D\u2081 \u2964 D\u2082\ninst\u271d : \u03a6.functor.IsEquivalence\nh : W\u2082 \u2264 W\u2081.map \u03a6.functor\nthis : (\u03a6.functor \u22d9 W\u2082.Q).IsLocalization W\u2081\n\u22a2 \u03a6.IsLocalizedEquivalence",
+              "tactic": "exact IsLocalizedEquivalence.of_isLocalization_of_isLocalization \u03a6 W\u2082.Q"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine <a>Functor.IsLocalization.of_equivalence_source<\\/a> W\\u2082.Q W\\u2082 (\\u03a6.functor \\u22d9 W\\u2082.Q) W\\u2081\\n      (<a>Functor.asEquivalence<\\/a> \\u03a6.functor).<a>symm<\\/a> ?_ (\\u03a6.inverts W\\u2082.Q)\\n      ((<a>Functor.associator<\\/a> _ _ _).<a>symm<\\/a> \\u226a\\u226b <a>isoWhiskerRight<\\/a> ((<a>Equivalence.unitIso<\\/a> _).<a>symm<\\/a>) _ \\u226a\\u226b\\n        <a>Functor.leftUnitor<\\/a> _)\"",
+                "[{\"full_name\":\"CategoryTheory.Functor.IsLocalization.of_equivalence_source\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Localization\\/Equivalence.lean\",\"def_pos\":[67,7],\"def_end_pos\":[67,28]},{\"full_name\":\"CategoryTheory.Functor.asEquivalence\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Equivalence.lean\",\"def_pos\":[580,19],\"def_end_pos\":[580,32]},{\"full_name\":\"CategoryTheory.Equivalence.symm\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Equivalence.lean\",\"def_pos\":[290,5],\"def_end_pos\":[290,9]},{\"full_name\":\"CategoryTheory.Functor.associator\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Whiskering.lean\",\"def_pos\":[280,5],\"def_end_pos\":[280,15]},{\"full_name\":\"CategoryTheory.Iso.symm\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[94,5],\"def_end_pos\":[94,9]},{\"full_name\":\"CategoryTheory.isoWhiskerRight\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Whiskering.lean\",\"def_pos\":[191,5],\"def_end_pos\":[191,20]},{\"full_name\":\"CategoryTheory.Equivalence.unitIso\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Equivalence.lean\",\"def_pos\":[87,3],\"def_end_pos\":[87,10]},{\"full_name\":\"CategoryTheory.Iso.symm\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[94,5],\"def_end_pos\":[94,9]},{\"full_name\":\"CategoryTheory.Functor.leftUnitor\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Whiskering.lean\",\"def_pos\":[252,5],\"def_end_pos\":[252,15]}]"
+              ],
+              "state_after": "C\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nC\u2083 : Type u\u2083\nD\u2081 : Type u\u2084\nD\u2082 : Type u\u2085\nD\u2083 : Type u\u2086\ninst\u271d\u2078 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2077 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2076 : Category.{v\u2083, u\u2083} C\u2083\ninst\u271d\u2075 : Category.{v\u2084, u\u2084} D\u2081\ninst\u271d\u2074 : Category.{v\u2085, u\u2085} D\u2082\ninst\u271d\u00b3 : Category.{v\u2086, u\u2085} D\u2082\nW\u2081 : MorphismProperty C\u2081\nW\u2082 : MorphismProperty C\u2082\nW\u2083 : MorphismProperty C\u2083\n\u03a6 : LocalizerMorphism W\u2081 W\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\ninst\u271d\u00b2 : L\u2081.IsLocalization W\u2081\nL\u2082 : C\u2082 \u2964 D\u2082\ninst\u271d\u00b9 : L\u2082.IsLocalization W\u2082\nG : D\u2081 \u2964 D\u2082\ninst\u271d : \u03a6.functor.IsEquivalence\nh : W\u2082 \u2264 W\u2081.map \u03a6.functor\n\u22a2 W\u2082 \u2264 W\u2081.isoClosure.inverseImage \u03a6.functor.asEquivalence.symm.functor",
+              "state_before": "C\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nC\u2083 : Type u\u2083\nD\u2081 : Type u\u2084\nD\u2082 : Type u\u2085\nD\u2083 : Type u\u2086\ninst\u271d\u2078 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2077 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2076 : Category.{v\u2083, u\u2083} C\u2083\ninst\u271d\u2075 : Category.{v\u2084, u\u2084} D\u2081\ninst\u271d\u2074 : Category.{v\u2085, u\u2085} D\u2082\ninst\u271d\u00b3 : Category.{v\u2086, u\u2085} D\u2082\nW\u2081 : MorphismProperty C\u2081\nW\u2082 : MorphismProperty C\u2082\nW\u2083 : MorphismProperty C\u2083\n\u03a6 : LocalizerMorphism W\u2081 W\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\ninst\u271d\u00b2 : L\u2081.IsLocalization W\u2081\nL\u2082 : C\u2082 \u2964 D\u2082\ninst\u271d\u00b9 : L\u2082.IsLocalization W\u2082\nG : D\u2081 \u2964 D\u2082\ninst\u271d : \u03a6.functor.IsEquivalence\nh : W\u2082 \u2264 W\u2081.map \u03a6.functor\n\u22a2 (\u03a6.functor \u22d9 W\u2082.Q).IsLocalization W\u2081",
+              "tactic": "refine Functor.IsLocalization.of_equivalence_source W\u2082.Q W\u2082 (\u03a6.functor \u22d9 W\u2082.Q) W\u2081\n  (Functor.asEquivalence \u03a6.functor).symm ?_ (\u03a6.inverts W\u2082.Q)\n  ((Functor.associator _ _ _).symm \u226a\u226b isoWhiskerRight ((Equivalence.unitIso _).symm) _ \u226a\u226b\n    Functor.leftUnitor _)"
+            },
+            {
+              "annotated_tactic": [
+                "\"erw [W\\u2081.isoClosure.inverseImage_equivalence_functor_eq_map_inverse\\n      W\\u2081.isoClosure_respectsIso \\u03a6.functor.asEquivalence]\"",
+                "[]"
+              ],
+              "state_after": "C\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nC\u2083 : Type u\u2083\nD\u2081 : Type u\u2084\nD\u2082 : Type u\u2085\nD\u2083 : Type u\u2086\ninst\u271d\u2078 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2077 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2076 : Category.{v\u2083, u\u2083} C\u2083\ninst\u271d\u2075 : Category.{v\u2084, u\u2084} D\u2081\ninst\u271d\u2074 : Category.{v\u2085, u\u2085} D\u2082\ninst\u271d\u00b3 : Category.{v\u2086, u\u2085} D\u2082\nW\u2081 : MorphismProperty C\u2081\nW\u2082 : MorphismProperty C\u2082\nW\u2083 : MorphismProperty C\u2083\n\u03a6 : LocalizerMorphism W\u2081 W\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\ninst\u271d\u00b2 : L\u2081.IsLocalization W\u2081\nL\u2082 : C\u2082 \u2964 D\u2082\ninst\u271d\u00b9 : L\u2082.IsLocalization W\u2082\nG : D\u2081 \u2964 D\u2082\ninst\u271d : \u03a6.functor.IsEquivalence\nh : W\u2082 \u2264 W\u2081.map \u03a6.functor\n\u22a2 W\u2082 \u2264 W\u2081.isoClosure.map \u03a6.functor.asEquivalence.functor",
+              "state_before": "C\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nC\u2083 : Type u\u2083\nD\u2081 : Type u\u2084\nD\u2082 : Type u\u2085\nD\u2083 : Type u\u2086\ninst\u271d\u2078 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2077 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2076 : Category.{v\u2083, u\u2083} C\u2083\ninst\u271d\u2075 : Category.{v\u2084, u\u2084} D\u2081\ninst\u271d\u2074 : Category.{v\u2085, u\u2085} D\u2082\ninst\u271d\u00b3 : Category.{v\u2086, u\u2085} D\u2082\nW\u2081 : MorphismProperty C\u2081\nW\u2082 : MorphismProperty C\u2082\nW\u2083 : MorphismProperty C\u2083\n\u03a6 : LocalizerMorphism W\u2081 W\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\ninst\u271d\u00b2 : L\u2081.IsLocalization W\u2081\nL\u2082 : C\u2082 \u2964 D\u2082\ninst\u271d\u00b9 : L\u2082.IsLocalization W\u2082\nG : D\u2081 \u2964 D\u2082\ninst\u271d : \u03a6.functor.IsEquivalence\nh : W\u2082 \u2264 W\u2081.map \u03a6.functor\n\u22a2 W\u2082 \u2264 W\u2081.isoClosure.inverseImage \u03a6.functor.asEquivalence.symm.functor",
+              "tactic": "erw [W\u2081.isoClosure.inverseImage_equivalence_functor_eq_map_inverse\n  W\u2081.isoClosure_respectsIso \u03a6.functor.asEquivalence]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>MorphismProperty.map_isoClosure<\\/a>]\"",
+                "[{\"full_name\":\"CategoryTheory.MorphismProperty.map_isoClosure\",\"def_path\":\"Mathlib\\/CategoryTheory\\/MorphismProperty\\/Basic.lean\",\"def_pos\":[208,7],\"def_end_pos\":[208,21]}]"
+              ],
+              "state_after": "C\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nC\u2083 : Type u\u2083\nD\u2081 : Type u\u2084\nD\u2082 : Type u\u2085\nD\u2083 : Type u\u2086\ninst\u271d\u2078 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2077 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2076 : Category.{v\u2083, u\u2083} C\u2083\ninst\u271d\u2075 : Category.{v\u2084, u\u2084} D\u2081\ninst\u271d\u2074 : Category.{v\u2085, u\u2085} D\u2082\ninst\u271d\u00b3 : Category.{v\u2086, u\u2085} D\u2082\nW\u2081 : MorphismProperty C\u2081\nW\u2082 : MorphismProperty C\u2082\nW\u2083 : MorphismProperty C\u2083\n\u03a6 : LocalizerMorphism W\u2081 W\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\ninst\u271d\u00b2 : L\u2081.IsLocalization W\u2081\nL\u2082 : C\u2082 \u2964 D\u2082\ninst\u271d\u00b9 : L\u2082.IsLocalization W\u2082\nG : D\u2081 \u2964 D\u2082\ninst\u271d : \u03a6.functor.IsEquivalence\nh : W\u2082 \u2264 W\u2081.map \u03a6.functor\n\u22a2 W\u2082 \u2264 W\u2081.map \u03a6.functor.asEquivalence.functor",
+              "state_before": "C\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nC\u2083 : Type u\u2083\nD\u2081 : Type u\u2084\nD\u2082 : Type u\u2085\nD\u2083 : Type u\u2086\ninst\u271d\u2078 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2077 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2076 : Category.{v\u2083, u\u2083} C\u2083\ninst\u271d\u2075 : Category.{v\u2084, u\u2084} D\u2081\ninst\u271d\u2074 : Category.{v\u2085, u\u2085} D\u2082\ninst\u271d\u00b3 : Category.{v\u2086, u\u2085} D\u2082\nW\u2081 : MorphismProperty C\u2081\nW\u2082 : MorphismProperty C\u2082\nW\u2083 : MorphismProperty C\u2083\n\u03a6 : LocalizerMorphism W\u2081 W\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\ninst\u271d\u00b2 : L\u2081.IsLocalization W\u2081\nL\u2082 : C\u2082 \u2964 D\u2082\ninst\u271d\u00b9 : L\u2082.IsLocalization W\u2082\nG : D\u2081 \u2964 D\u2082\ninst\u271d : \u03a6.functor.IsEquivalence\nh : W\u2082 \u2264 W\u2081.map \u03a6.functor\n\u22a2 W\u2082 \u2264 W\u2081.isoClosure.map \u03a6.functor.asEquivalence.functor",
+              "tactic": "rw [MorphismProperty.map_isoClosure]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact h\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nC\u2083 : Type u\u2083\nD\u2081 : Type u\u2084\nD\u2082 : Type u\u2085\nD\u2083 : Type u\u2086\ninst\u271d\u2078 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2077 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2076 : Category.{v\u2083, u\u2083} C\u2083\ninst\u271d\u2075 : Category.{v\u2084, u\u2084} D\u2081\ninst\u271d\u2074 : Category.{v\u2085, u\u2085} D\u2082\ninst\u271d\u00b3 : Category.{v\u2086, u\u2085} D\u2082\nW\u2081 : MorphismProperty C\u2081\nW\u2082 : MorphismProperty C\u2082\nW\u2083 : MorphismProperty C\u2083\n\u03a6 : LocalizerMorphism W\u2081 W\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\ninst\u271d\u00b2 : L\u2081.IsLocalization W\u2081\nL\u2082 : C\u2082 \u2964 D\u2082\ninst\u271d\u00b9 : L\u2082.IsLocalization W\u2082\nG : D\u2081 \u2964 D\u2082\ninst\u271d : \u03a6.functor.IsEquivalence\nh : W\u2082 \u2264 W\u2081.map \u03a6.functor\n\u22a2 W\u2082 \u2264 W\u2081.map \u03a6.functor.asEquivalence.functor",
+              "tactic": "exact h"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/LocalizerMorphism.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.LocalizerMorphism.isEquivalence_iff",
+        "id": "CategoryTheory.LocalizerMorphism.isEquivalence_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            124,
+            53
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/LocalizerMorphism.lean",
+          "full_name": "CategoryTheory.LocalizerMorphism.isEquivalence_iff",
+          "start": [
+            122,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/LocalizerMorphism.lean"
+      }
+    ],
+    "input_proofs": 16,
+    "input_units": 2,
+    "proofs": 13,
+    "published_proofs": 13,
+    "published_transitions": 24,
+    "replay_failures": [],
+    "transitions": 24,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000720-0000-e6386e482ee65199.parquet",
+      "sha256": "e6386e482ee65199611488c697e35099da9c9c12948bd3ffaaab08f881fb5b8d",
+      "bytes": 165585,
+      "rows": 24,
+      "revision": "a498fa87b358e6eb392b8a125474b05531d1b03e"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:CategoryTheory.Localization.homEquiv_comp",
+    "mathlib:CategoryTheory.Localization.homEquiv_eq",
+    "mathlib:CategoryTheory.Localization.homEquiv_id",
+    "mathlib:CategoryTheory.Localization.homEquiv_isoOfHom_inv",
+    "mathlib:CategoryTheory.Localization.homEquiv_map",
+    "mathlib:CategoryTheory.Localization.homEquiv_refl",
+    "mathlib:CategoryTheory.Localization.homEquiv_trans",
+    "mathlib:CategoryTheory.LocalizerMorphism.IsLocalizedEquivalence.mk'",
+    "mathlib:CategoryTheory.LocalizerMorphism.IsLocalizedEquivalence.of_isLocalization_of_isLocalization",
+    "mathlib:CategoryTheory.LocalizerMorphism.homMap_comp",
+    "mathlib:CategoryTheory.LocalizerMorphism.homMap_homMap",
+    "mathlib:CategoryTheory.LocalizerMorphism.homMap_id",
+    "mathlib:CategoryTheory.LocalizerMorphism.homMap_map"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Localization/HomEquiv.lean\",null,null,\"CategoryTheory.Localization.homEquiv_comp\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Localization/HomEquiv.lean\",null,null,\"CategoryTheory.Localization.homEquiv_eq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Localization/HomEquiv.lean\",null,null,\"CategoryTheory.Localization.homEquiv_id\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Localization/HomEquiv.lean\",null,null,\"CategoryTheory.Localization.homEquiv_isoOfHom_inv\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Localization/HomEquiv.lean\",null,null,\"CategoryTheory.Localization.homEquiv_map\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Localization/HomEquiv.lean\",null,null,\"CategoryTheory.Localization.homEquiv_refl\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Localization/HomEquiv.lean\",null,null,\"CategoryTheory.Localization.homEquiv_trans\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Localization/HomEquiv.lean\",null,null,\"CategoryTheory.LocalizerMorphism.homMap_comp\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Localization/HomEquiv.lean\",null,null,\"CategoryTheory.LocalizerMorphism.homMap_homMap\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Localization/HomEquiv.lean\",null,null,\"CategoryTheory.LocalizerMorphism.homMap_id\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Localization/HomEquiv.lean\",null,null,\"CategoryTheory.LocalizerMorphism.homMap_map\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Localization/LocalizerMorphism.lean\",null,null,\"CategoryTheory.LocalizerMorphism.IsLocalizedEquivalence.mk'\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Localization/LocalizerMorphism.lean\",null,null,\"CategoryTheory.LocalizerMorphism.IsLocalizedEquivalence.of_isLocalization_of_isLocalization\"]"
+  ]
+}

manifests/batches/mathlib/000721.json

@@ -0,0 +1,706 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000721",
+  "batch_fingerprint": "64bbe3818d2da82fbae63b41482f0dd8929740eafaf555171f49e994af95d347",
+  "evidence": {
+    "batch_fingerprint": "64bbe3818d2da82fbae63b41482f0dd8929740eafaf555171f49e994af95d347",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.AreEqualizedByLocalization.map_eq",
+        "id": "CategoryTheory.AreEqualizedByLocalization.map_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            519,
+            47
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/Predicate.lean",
+          "full_name": "CategoryTheory.AreEqualizedByLocalization.map_eq",
+          "start": [
+            518,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/Predicate.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.AreEqualizedByLocalization.mk",
+        "id": "CategoryTheory.AreEqualizedByLocalization.mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            513,
+            47
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/Predicate.lean",
+          "full_name": "CategoryTheory.AreEqualizedByLocalization.mk",
+          "start": [
+            511,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/Predicate.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Functor.IsLocalization.for_id",
+        "id": "CategoryTheory.Functor.IsLocalization.for_id",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            134,
+            63
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/Predicate.lean",
+          "full_name": "CategoryTheory.Functor.IsLocalization.for_id",
+          "start": [
+            132,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/Predicate.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rw [\u2190 MorphismProperty.IsInvertedBy.iff_of_iso W e]'",
+        "full_name": "CategoryTheory.Functor.IsLocalization.of_equivalence_target",
+        "id": "CategoryTheory.Functor.IsLocalization.of_equivalence_target",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            431,
+            57
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/Predicate.lean",
+          "full_name": "CategoryTheory.Functor.IsLocalization.of_equivalence_target",
+          "start": [
+            421,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"have h : W.IsInvertedBy L' := by\\n    rw [\\u2190 <a>MorphismProperty.IsInvertedBy.iff_of_iso<\\/a> W e]\\n    exact <a>MorphismProperty.IsInvertedBy.of_comp<\\/a> W L (<a>Localization.inverts<\\/a> L W) eq.functor\"",
+                "[{\"full_name\":\"CategoryTheory.MorphismProperty.IsInvertedBy.iff_of_iso\",\"def_path\":\"Mathlib\\/CategoryTheory\\/MorphismProperty\\/IsInvertedBy.lean\",\"def_pos\":[127,9],\"def_end_pos\":[127,32]},{\"full_name\":\"CategoryTheory.MorphismProperty.IsInvertedBy.of_comp\",\"def_path\":\"Mathlib\\/CategoryTheory\\/MorphismProperty\\/IsInvertedBy.lean\",\"def_pos\":[41,9],\"def_end_pos\":[41,16]},{\"full_name\":\"CategoryTheory.Localization.inverts\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Localization\\/Predicate.lean\",\"def_pos\":[143,9],\"def_end_pos\":[143,16]}]"
+              ],
+              "state_after": "C : Type u_1\nD : Type u_2\ninst\u271d\u2074 : Category.{u_6, u_1} C\ninst\u271d\u00b3 : Category.{u_7, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE\u271d : Type u_3\ninst\u271d\u00b2 : Category.{?u.60259, u_3} E\u271d\nE : Type u_4\ninst\u271d\u00b9 : Category.{u_5, u_4} E\nL' : C \u2964 E\neq : D \u224c E\ninst\u271d : L.IsLocalization W\ne : L \u22d9 eq.functor \u2245 L'\nh : W.IsInvertedBy L'\n\u22a2 L'.IsLocalization W",
+              "state_before": "C : Type u_1\nD : Type u_2\ninst\u271d\u2074 : Category.{u_6, u_1} C\ninst\u271d\u00b3 : Category.{u_7, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE\u271d : Type u_3\ninst\u271d\u00b2 : Category.{?u.60259, u_3} E\u271d\nE : Type u_4\ninst\u271d\u00b9 : Category.{u_5, u_4} E\nL' : C \u2964 E\neq : D \u224c E\ninst\u271d : L.IsLocalization W\ne : L \u22d9 eq.functor \u2245 L'\n\u22a2 L'.IsLocalization W",
+              "tactic": "have h : W.IsInvertedBy L' := by\n  rw [\u2190 MorphismProperty.IsInvertedBy.iff_of_iso W e]\n  exact MorphismProperty.IsInvertedBy.of_comp W L (Localization.inverts L W) eq.functor"
+            },
+            {
+              "annotated_tactic": [
+                "\"let F\\u2081 := <a>Localization.Construction.lift<\\/a> L (<a>Localization.inverts<\\/a> L W)\"",
+                "[{\"full_name\":\"CategoryTheory.Localization.Construction.lift\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Localization\\/Construction.lean\",\"def_pos\":[167,5],\"def_end_pos\":[167,9]},{\"full_name\":\"CategoryTheory.Localization.inverts\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Localization\\/Predicate.lean\",\"def_pos\":[143,9],\"def_end_pos\":[143,16]}]"
+              ],
+              "state_after": "C : Type u_1\nD : Type u_2\ninst\u271d\u2074 : Category.{u_6, u_1} C\ninst\u271d\u00b3 : Category.{u_7, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE\u271d : Type u_3\ninst\u271d\u00b2 : Category.{?u.60259, u_3} E\u271d\nE : Type u_4\ninst\u271d\u00b9 : Category.{u_5, u_4} E\nL' : C \u2964 E\neq : D \u224c E\ninst\u271d : L.IsLocalization W\ne : L \u22d9 eq.functor \u2245 L'\nh : W.IsInvertedBy L'\nF\u2081 : W.Localization \u2964 D := Construction.lift L \u22ef\n\u22a2 L'.IsLocalization W",
+              "state_before": "C : Type u_1\nD : Type u_2\ninst\u271d\u2074 : Category.{u_6, u_1} C\ninst\u271d\u00b3 : Category.{u_7, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE\u271d : Type u_3\ninst\u271d\u00b2 : Category.{?u.60259, u_3} E\u271d\nE : Type u_4\ninst\u271d\u00b9 : Category.{u_5, u_4} E\nL' : C \u2964 E\neq : D \u224c E\ninst\u271d : L.IsLocalization W\ne : L \u22d9 eq.functor \u2245 L'\nh : W.IsInvertedBy L'\n\u22a2 L'.IsLocalization W",
+              "tactic": "let F\u2081 := Localization.Construction.lift L (Localization.inverts L W)"
+            },
+            {
+              "annotated_tactic": [
+                "\"let F\\u2082 := <a>Localization.Construction.lift<\\/a> L' h\"",
+                "[{\"full_name\":\"CategoryTheory.Localization.Construction.lift\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Localization\\/Construction.lean\",\"def_pos\":[167,5],\"def_end_pos\":[167,9]}]"
+              ],
+              "state_after": "C : Type u_1\nD : Type u_2\ninst\u271d\u2074 : Category.{u_6, u_1} C\ninst\u271d\u00b3 : Category.{u_7, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE\u271d : Type u_3\ninst\u271d\u00b2 : Category.{?u.60259, u_3} E\u271d\nE : Type u_4\ninst\u271d\u00b9 : Category.{u_5, u_4} E\nL' : C \u2964 E\neq : D \u224c E\ninst\u271d : L.IsLocalization W\ne : L \u22d9 eq.functor \u2245 L'\nh : W.IsInvertedBy L'\nF\u2081 : W.Localization \u2964 D := Construction.lift L \u22ef\nF\u2082 : W.Localization \u2964 E := Construction.lift L' h\n\u22a2 L'.IsLocalization W",
+              "state_before": "C : Type u_1\nD : Type u_2\ninst\u271d\u2074 : Category.{u_6, u_1} C\ninst\u271d\u00b3 : Category.{u_7, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE\u271d : Type u_3\ninst\u271d\u00b2 : Category.{?u.60259, u_3} E\u271d\nE : Type u_4\ninst\u271d\u00b9 : Category.{u_5, u_4} E\nL' : C \u2964 E\neq : D \u224c E\ninst\u271d : L.IsLocalization W\ne : L \u22d9 eq.functor \u2245 L'\nh : W.IsInvertedBy L'\nF\u2081 : W.Localization \u2964 D := Construction.lift L \u22ef\n\u22a2 L'.IsLocalization W",
+              "tactic": "let F\u2082 := Localization.Construction.lift L' h"
+            },
+            {
+              "annotated_tactic": [
+                "\"let e' : F\\u2081 \\u22d9 eq.functor \\u2245 F\\u2082 := <a>liftNatIso<\\/a> W.Q W (L \\u22d9 eq.functor) L' _ _ e\"",
+                "[{\"full_name\":\"CategoryTheory.Localization.liftNatIso\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Localization\\/Predicate.lean\",\"def_pos\":[368,5],\"def_end_pos\":[368,15]}]"
+              ],
+              "state_after": "C : Type u_1\nD : Type u_2\ninst\u271d\u2074 : Category.{u_6, u_1} C\ninst\u271d\u00b3 : Category.{u_7, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE\u271d : Type u_3\ninst\u271d\u00b2 : Category.{?u.60259, u_3} E\u271d\nE : Type u_4\ninst\u271d\u00b9 : Category.{u_5, u_4} E\nL' : C \u2964 E\neq : D \u224c E\ninst\u271d : L.IsLocalization W\ne : L \u22d9 eq.functor \u2245 L'\nh : W.IsInvertedBy L'\nF\u2081 : W.Localization \u2964 D := Construction.lift L \u22ef\nF\u2082 : W.Localization \u2964 E := Construction.lift L' h\ne' : F\u2081 \u22d9 eq.functor \u2245 F\u2082 := liftNatIso W.Q W (L \u22d9 eq.functor) L' (F\u2081 \u22d9 eq.functor) F\u2082 e\n\u22a2 L'.IsLocalization W",
+              "state_before": "C : Type u_1\nD : Type u_2\ninst\u271d\u2074 : Category.{u_6, u_1} C\ninst\u271d\u00b3 : Category.{u_7, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE\u271d : Type u_3\ninst\u271d\u00b2 : Category.{?u.60259, u_3} E\u271d\nE : Type u_4\ninst\u271d\u00b9 : Category.{u_5, u_4} E\nL' : C \u2964 E\neq : D \u224c E\ninst\u271d : L.IsLocalization W\ne : L \u22d9 eq.functor \u2245 L'\nh : W.IsInvertedBy L'\nF\u2081 : W.Localization \u2964 D := Construction.lift L \u22ef\nF\u2082 : W.Localization \u2964 E := Construction.lift L' h\n\u22a2 L'.IsLocalization W",
+              "tactic": "let e' : F\u2081 \u22d9 eq.functor \u2245 F\u2082 := liftNatIso W.Q W (L \u22d9 eq.functor) L' _ _ e"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact\\n    { inverts := h\\n      isEquivalence := <a>Functor.isEquivalence_of_iso<\\/a> e' }\"",
+                "[{\"full_name\":\"CategoryTheory.Functor.isEquivalence_of_iso\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Equivalence.lean\",\"def_pos\":[629,7],\"def_end_pos\":[629,27]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C : Type u_1\nD : Type u_2\ninst\u271d\u2074 : Category.{u_6, u_1} C\ninst\u271d\u00b3 : Category.{u_7, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE\u271d : Type u_3\ninst\u271d\u00b2 : Category.{?u.60259, u_3} E\u271d\nE : Type u_4\ninst\u271d\u00b9 : Category.{u_5, u_4} E\nL' : C \u2964 E\neq : D \u224c E\ninst\u271d : L.IsLocalization W\ne : L \u22d9 eq.functor \u2245 L'\nh : W.IsInvertedBy L'\nF\u2081 : W.Localization \u2964 D := Construction.lift L \u22ef\nF\u2082 : W.Localization \u2964 E := Construction.lift L' h\ne' : F\u2081 \u22d9 eq.functor \u2245 F\u2082 := liftNatIso W.Q W (L \u22d9 eq.functor) L' (F\u2081 \u22d9 eq.functor) F\u2082 e\n\u22a2 L'.IsLocalization W",
+              "tactic": "exact\n  { inverts := h\n    isEquivalence := Functor.isEquivalence_of_iso e' }"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>MorphismProperty.IsInvertedBy.iff_of_iso<\\/a> W e]\"",
+                "[{\"full_name\":\"CategoryTheory.MorphismProperty.IsInvertedBy.iff_of_iso\",\"def_path\":\"Mathlib\\/CategoryTheory\\/MorphismProperty\\/IsInvertedBy.lean\",\"def_pos\":[127,9],\"def_end_pos\":[127,32]}]"
+              ],
+              "state_after": "C : Type u_1\nD : Type u_2\ninst\u271d\u2074 : Category.{u_6, u_1} C\ninst\u271d\u00b3 : Category.{u_7, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE\u271d : Type u_3\ninst\u271d\u00b2 : Category.{?u.60259, u_3} E\u271d\nE : Type u_4\ninst\u271d\u00b9 : Category.{u_5, u_4} E\nL' : C \u2964 E\neq : D \u224c E\ninst\u271d : L.IsLocalization W\ne : L \u22d9 eq.functor \u2245 L'\n\u22a2 W.IsInvertedBy (L \u22d9 eq.functor)",
+              "state_before": "C : Type u_1\nD : Type u_2\ninst\u271d\u2074 : Category.{u_6, u_1} C\ninst\u271d\u00b3 : Category.{u_7, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE\u271d : Type u_3\ninst\u271d\u00b2 : Category.{?u.60259, u_3} E\u271d\nE : Type u_4\ninst\u271d\u00b9 : Category.{u_5, u_4} E\nL' : C \u2964 E\neq : D \u224c E\ninst\u271d : L.IsLocalization W\ne : L \u22d9 eq.functor \u2245 L'\n\u22a2 W.IsInvertedBy L'",
+              "tactic": "rw [\u2190 MorphismProperty.IsInvertedBy.iff_of_iso W e]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>MorphismProperty.IsInvertedBy.of_comp<\\/a> W L (<a>Localization.inverts<\\/a> L W) eq.functor\"",
+                "[{\"full_name\":\"CategoryTheory.MorphismProperty.IsInvertedBy.of_comp\",\"def_path\":\"Mathlib\\/CategoryTheory\\/MorphismProperty\\/IsInvertedBy.lean\",\"def_pos\":[41,9],\"def_end_pos\":[41,16]},{\"full_name\":\"CategoryTheory.Localization.inverts\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Localization\\/Predicate.lean\",\"def_pos\":[143,9],\"def_end_pos\":[143,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C : Type u_1\nD : Type u_2\ninst\u271d\u2074 : Category.{u_6, u_1} C\ninst\u271d\u00b3 : Category.{u_7, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE\u271d : Type u_3\ninst\u271d\u00b2 : Category.{?u.60259, u_3} E\u271d\nE : Type u_4\ninst\u271d\u00b9 : Category.{u_5, u_4} E\nL' : C \u2964 E\neq : D \u224c E\ninst\u271d : L.IsLocalization W\ne : L \u22d9 eq.functor \u2245 L'\n\u22a2 W.IsInvertedBy (L \u22d9 eq.functor)",
+              "tactic": "exact MorphismProperty.IsInvertedBy.of_comp W L (Localization.inverts L W) eq.functor"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/Predicate.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Localization.faithful_whiskeringLeft",
+        "id": "CategoryTheory.Localization.faithful_whiskeringLeft",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            275,
+            58
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/Predicate.lean",
+          "full_name": "CategoryTheory.Localization.faithful_whiskeringLeft",
+          "start": [
+            274,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/Predicate.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Localization.full_whiskeringLeft",
+        "id": "CategoryTheory.Localization.full_whiskeringLeft",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            272,
+            54
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/Predicate.lean",
+          "full_name": "CategoryTheory.Localization.full_whiskeringLeft",
+          "start": [
+            271,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/Predicate.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Localization.inverts",
+        "id": "CategoryTheory.Localization.inverts",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            144,
+            47
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/Predicate.lean",
+          "full_name": "CategoryTheory.Localization.inverts",
+          "start": [
+            143,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/Predicate.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Localization.isoOfHom_hom_inv_id",
+        "id": "CategoryTheory.Localization.isoOfHom_hom_inv_id",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            158,
+            33
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/Predicate.lean",
+          "full_name": "CategoryTheory.Localization.isoOfHom_hom_inv_id",
+          "start": [
+            155,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/Predicate.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Localization.isoOfHom_inv_hom_id",
+        "id": "CategoryTheory.Localization.isoOfHom_inv_hom_id",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            163,
+            33
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/Predicate.lean",
+          "full_name": "CategoryTheory.Localization.isoOfHom_inv_hom_id",
+          "start": [
+            160,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/Predicate.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Localization.liftNatTrans_app",
+        "id": "CategoryTheory.Localization.liftNatTrans_app",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            344,
+            70
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/Predicate.lean",
+          "full_name": "CategoryTheory.Localization.liftNatTrans_app",
+          "start": [
+            340,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/Predicate.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Localization.uniq_symm",
+        "id": "CategoryTheory.Localization.uniq_symm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            458,
+            62
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/Predicate.lean",
+          "full_name": "CategoryTheory.Localization.uniq_symm",
+          "start": [
+            458,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/Predicate.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Localization.whiskeringLeftFunctor'_eq",
+        "id": "CategoryTheory.Localization.whiskeringLeftFunctor'_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            250,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/Predicate.lean",
+          "full_name": "CategoryTheory.Localization.whiskeringLeftFunctor'_eq",
+          "start": [
+            248,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/Predicate.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Localization.whiskeringLeftFunctor'_obj",
+        "id": "CategoryTheory.Localization.whiskeringLeftFunctor'_obj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            256,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/Predicate.lean",
+          "full_name": "CategoryTheory.Localization.whiskeringLeftFunctor'_obj",
+          "start": [
+            255,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/Predicate.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'let e := Localization.compUniqFunctor W.Q L W'",
+        "full_name": "CategoryTheory.areEqualizedByLocalization_iff",
+        "id": "CategoryTheory.areEqualizedByLocalization_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            507,
+            11
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/Predicate.lean",
+          "full_name": "CategoryTheory.areEqualizedByLocalization_iff",
+          "start": [
+            494,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"dsimp [<a>AreEqualizedByLocalization<\\/a>]\"",
+                "[{\"full_name\":\"CategoryTheory.AreEqualizedByLocalization\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Localization\\/Predicate.lean\",\"def_pos\":[492,5],\"def_end_pos\":[492,31]}]"
+              ],
+              "state_after": "C : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\n\u22a2 W.Q.map f = W.Q.map g \u2194 L.map f = L.map g",
+              "state_before": "C : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\n\u22a2 AreEqualizedByLocalization W f g \u2194 L.map f = L.map g",
+              "tactic": "dsimp [AreEqualizedByLocalization]"
+            },
+            {
+              "annotated_tactic": [
+                "\"constructor\"",
+                "[]"
+              ],
+              "state_after": "case mp\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\n\u22a2 W.Q.map f = W.Q.map g \u2192 L.map f = L.map g\n\ncase mpr\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\n\u22a2 L.map f = L.map g \u2192 W.Q.map f = W.Q.map g",
+              "state_before": "C : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\n\u22a2 W.Q.map f = W.Q.map g \u2194 L.map f = L.map g",
+              "tactic": "constructor"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro h\"",
+                "[]"
+              ],
+              "state_after": "case mp\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\nh : W.Q.map f = W.Q.map g\n\u22a2 L.map f = L.map g",
+              "state_before": "case mp\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\n\u22a2 W.Q.map f = W.Q.map g \u2192 L.map f = L.map g",
+              "tactic": "intro h"
+            },
+            {
+              "annotated_tactic": [
+                "\"let e := <a>Localization.compUniqFunctor<\\/a> W.Q L W\"",
+                "[{\"full_name\":\"CategoryTheory.Localization.compUniqFunctor\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Localization\\/Predicate.lean\",\"def_pos\":[462,5],\"def_end_pos\":[462,20]}]"
+              ],
+              "state_after": "case mp\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\nh : W.Q.map f = W.Q.map g\ne : W.Q \u22d9 (Localization.uniq W.Q L W).functor \u2245 L := Localization.compUniqFunctor W.Q L W\n\u22a2 L.map f = L.map g",
+              "state_before": "case mp\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\nh : W.Q.map f = W.Q.map g\n\u22a2 L.map f = L.map g",
+              "tactic": "let e := Localization.compUniqFunctor W.Q L W"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>NatIso.naturality_1<\\/a> e f, \\u2190 <a>NatIso.naturality_1<\\/a> e g]\"",
+                "[{\"full_name\":\"CategoryTheory.NatIso.naturality_1\",\"def_path\":\"Mathlib\\/CategoryTheory\\/NatIso.lean\",\"def_pos\":[168,9],\"def_end_pos\":[168,21]},{\"full_name\":\"CategoryTheory.NatIso.naturality_1\",\"def_path\":\"Mathlib\\/CategoryTheory\\/NatIso.lean\",\"def_pos\":[168,9],\"def_end_pos\":[168,21]}]"
+              ],
+              "state_after": "case mp\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\nh : W.Q.map f = W.Q.map g\ne : W.Q \u22d9 (Localization.uniq W.Q L W).functor \u2245 L := Localization.compUniqFunctor W.Q L W\n\u22a2 e.inv.app X \u226b (W.Q \u22d9 (Localization.uniq W.Q L W).functor).map f \u226b e.hom.app Y =\n    e.inv.app X \u226b (W.Q \u22d9 (Localization.uniq W.Q L W).functor).map g \u226b e.hom.app Y",
+              "state_before": "case mp\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\nh : W.Q.map f = W.Q.map g\ne : W.Q \u22d9 (Localization.uniq W.Q L W).functor \u2245 L := Localization.compUniqFunctor W.Q L W\n\u22a2 L.map f = L.map g",
+              "tactic": "rw [\u2190 NatIso.naturality_1 e f, \u2190 NatIso.naturality_1 e g]"
+            },
+            {
+              "annotated_tactic": [
+                "\"dsimp\"",
+                "[]"
+              ],
+              "state_after": "case mp\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\nh : W.Q.map f = W.Q.map g\ne : W.Q \u22d9 (Localization.uniq W.Q L W).functor \u2245 L := Localization.compUniqFunctor W.Q L W\n\u22a2 e.inv.app X \u226b (Localization.uniq W.Q L W).functor.map (W.Q.map f) \u226b e.hom.app Y =\n    e.inv.app X \u226b (Localization.uniq W.Q L W).functor.map (W.Q.map g) \u226b e.hom.app Y",
+              "state_before": "case mp\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\nh : W.Q.map f = W.Q.map g\ne : W.Q \u22d9 (Localization.uniq W.Q L W).functor \u2245 L := Localization.compUniqFunctor W.Q L W\n\u22a2 e.inv.app X \u226b (W.Q \u22d9 (Localization.uniq W.Q L W).functor).map f \u226b e.hom.app Y =\n    e.inv.app X \u226b (W.Q \u22d9 (Localization.uniq W.Q L W).functor).map g \u226b e.hom.app Y",
+              "tactic": "dsimp"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [h]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case mp\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\nh : W.Q.map f = W.Q.map g\ne : W.Q \u22d9 (Localization.uniq W.Q L W).functor \u2245 L := Localization.compUniqFunctor W.Q L W\n\u22a2 e.inv.app X \u226b (Localization.uniq W.Q L W).functor.map (W.Q.map f) \u226b e.hom.app Y =\n    e.inv.app X \u226b (Localization.uniq W.Q L W).functor.map (W.Q.map g) \u226b e.hom.app Y",
+              "tactic": "rw [h]"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro h\"",
+                "[]"
+              ],
+              "state_after": "case mpr\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\nh : L.map f = L.map g\n\u22a2 W.Q.map f = W.Q.map g",
+              "state_before": "case mpr\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\n\u22a2 L.map f = L.map g \u2192 W.Q.map f = W.Q.map g",
+              "tactic": "intro h"
+            },
+            {
+              "annotated_tactic": [
+                "\"let e := <a>Localization.compUniqFunctor<\\/a> L W.Q W\"",
+                "[{\"full_name\":\"CategoryTheory.Localization.compUniqFunctor\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Localization\\/Predicate.lean\",\"def_pos\":[462,5],\"def_end_pos\":[462,20]}]"
+              ],
+              "state_after": "case mpr\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\nh : L.map f = L.map g\ne : L \u22d9 (Localization.uniq L W.Q W).functor \u2245 W.Q := Localization.compUniqFunctor L W.Q W\n\u22a2 W.Q.map f = W.Q.map g",
+              "state_before": "case mpr\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\nh : L.map f = L.map g\n\u22a2 W.Q.map f = W.Q.map g",
+              "tactic": "let e := Localization.compUniqFunctor L W.Q W"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>NatIso.naturality_1<\\/a> e f, \\u2190 <a>NatIso.naturality_1<\\/a> e g]\"",
+                "[{\"full_name\":\"CategoryTheory.NatIso.naturality_1\",\"def_path\":\"Mathlib\\/CategoryTheory\\/NatIso.lean\",\"def_pos\":[168,9],\"def_end_pos\":[168,21]},{\"full_name\":\"CategoryTheory.NatIso.naturality_1\",\"def_path\":\"Mathlib\\/CategoryTheory\\/NatIso.lean\",\"def_pos\":[168,9],\"def_end_pos\":[168,21]}]"
+              ],
+              "state_after": "case mpr\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\nh : L.map f = L.map g\ne : L \u22d9 (Localization.uniq L W.Q W).functor \u2245 W.Q := Localization.compUniqFunctor L W.Q W\n\u22a2 e.inv.app X \u226b (L \u22d9 (Localization.uniq L W.Q W).functor).map f \u226b e.hom.app Y =\n    e.inv.app X \u226b (L \u22d9 (Localization.uniq L W.Q W).functor).map g \u226b e.hom.app Y",
+              "state_before": "case mpr\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\nh : L.map f = L.map g\ne : L \u22d9 (Localization.uniq L W.Q W).functor \u2245 W.Q := Localization.compUniqFunctor L W.Q W\n\u22a2 W.Q.map f = W.Q.map g",
+              "tactic": "rw [\u2190 NatIso.naturality_1 e f, \u2190 NatIso.naturality_1 e g]"
+            },
+            {
+              "annotated_tactic": [
+                "\"dsimp\"",
+                "[]"
+              ],
+              "state_after": "case mpr\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\nh : L.map f = L.map g\ne : L \u22d9 (Localization.uniq L W.Q W).functor \u2245 W.Q := Localization.compUniqFunctor L W.Q W\n\u22a2 e.inv.app X \u226b (Localization.uniq L W.Q W).functor.map (L.map f) \u226b e.hom.app Y =\n    e.inv.app X \u226b (Localization.uniq L W.Q W).functor.map (L.map g) \u226b e.hom.app Y",
+              "state_before": "case mpr\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\nh : L.map f = L.map g\ne : L \u22d9 (Localization.uniq L W.Q W).functor \u2245 W.Q := Localization.compUniqFunctor L W.Q W\n\u22a2 e.inv.app X \u226b (L \u22d9 (Localization.uniq L W.Q W).functor).map f \u226b e.hom.app Y =\n    e.inv.app X \u226b (L \u22d9 (Localization.uniq L W.Q W).functor).map g \u226b e.hom.app Y",
+              "tactic": "dsimp"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [h]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case mpr\nC : Type u_1\nD : Type u_2\ninst\u271d\u00b3 : Category.{u_4, u_1} C\ninst\u271d\u00b2 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d\u00b9 : Category.{?u.72622, u_3} E\nX Y : C\nf g : X \u27f6 Y\ninst\u271d : L.IsLocalization W\nh : L.map f = L.map g\ne : L \u22d9 (Localization.uniq L W.Q W).functor \u2245 W.Q := Localization.compUniqFunctor L W.Q W\n\u22a2 e.inv.app X \u226b (Localization.uniq L W.Q W).functor.map (L.map f) \u226b e.hom.app Y =\n    e.inv.app X \u226b (Localization.uniq L W.Q W).functor.map (L.map g) \u226b e.hom.app Y",
+              "tactic": "rw [h]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/Predicate.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Localization.Construction.prodIsLocalization",
+        "id": "CategoryTheory.Localization.Construction.prodIsLocalization",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            111,
+            52
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/Prod.lean",
+          "full_name": "CategoryTheory.Localization.Construction.prodIsLocalization",
+          "start": [
+            107,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/Prod.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_fac\u2081",
+        "id": "CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_fac\u2081",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            54,
+            23
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/Prod.lean",
+          "full_name": "CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_fac\u2081",
+          "start": [
+            52,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/Prod.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'apply Construction.uniq'",
+        "full_name": "CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_uniq",
+        "id": "CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_uniq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            90,
+            63
+          ],
+          "file_path": "Mathlib/CategoryTheory/Localization/Prod.lean",
+          "full_name": "CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_uniq",
+          "start": [
+            81,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"apply <a>Functor.curry_obj_injective<\\/a>\"",
+                "[{\"full_name\":\"CategoryTheory.Functor.curry_obj_injective\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Currying.lean\",\"def_pos\":[125,7],\"def_end_pos\":[125,26]}]"
+              ],
+              "state_after": "case h\nC\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nD\u2081 : Type u\u2083\nD\u2082 : Type u\u2084\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2075 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2074 : Category.{v\u2083, u\u2083} D\u2081\ninst\u271d\u00b3 : Category.{v\u2084, u\u2084} D\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\nW\u2081 : MorphismProperty C\u2081\ninst\u271d\u00b2 : W\u2081.ContainsIdentities\nL\u2082 : C\u2082 \u2964 D\u2082\nW\u2082 : MorphismProperty C\u2082\ninst\u271d\u00b9 : W\u2082.ContainsIdentities\nE : Type u\u2085\ninst\u271d : Category.{v\u2085, u\u2085} E\nF : C\u2081 \u00d7 C\u2082 \u2964 E\nhF : (W\u2081.prod W\u2082).IsInvertedBy F\nF\u2081 F\u2082 : W\u2081.Localization \u00d7 W\u2082.Localization \u2964 E\nh : W\u2081.Q.prod W\u2082.Q \u22d9 F\u2081 = W\u2081.Q.prod W\u2082.Q \u22d9 F\u2082\n\u22a2 curry.obj F\u2081 = curry.obj F\u2082",
+              "state_before": "C\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nD\u2081 : Type u\u2083\nD\u2082 : Type u\u2084\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2075 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2074 : Category.{v\u2083, u\u2083} D\u2081\ninst\u271d\u00b3 : Category.{v\u2084, u\u2084} D\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\nW\u2081 : MorphismProperty C\u2081\ninst\u271d\u00b2 : W\u2081.ContainsIdentities\nL\u2082 : C\u2082 \u2964 D\u2082\nW\u2082 : MorphismProperty C\u2082\ninst\u271d\u00b9 : W\u2082.ContainsIdentities\nE : Type u\u2085\ninst\u271d : Category.{v\u2085, u\u2085} E\nF : C\u2081 \u00d7 C\u2082 \u2964 E\nhF : (W\u2081.prod W\u2082).IsInvertedBy F\nF\u2081 F\u2082 : W\u2081.Localization \u00d7 W\u2082.Localization \u2964 E\nh : W\u2081.Q.prod W\u2082.Q \u22d9 F\u2081 = W\u2081.Q.prod W\u2082.Q \u22d9 F\u2082\n\u22a2 F\u2081 = F\u2082",
+              "tactic": "apply Functor.curry_obj_injective"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Construction.uniq<\\/a>\"",
+                "[{\"full_name\":\"CategoryTheory.Localization.Construction.uniq\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Localization\\/Construction.lean\",\"def_pos\":[192,9],\"def_end_pos\":[192,13]}]"
+              ],
+              "state_after": "case h.h\nC\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nD\u2081 : Type u\u2083\nD\u2082 : Type u\u2084\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2075 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2074 : Category.{v\u2083, u\u2083} D\u2081\ninst\u271d\u00b3 : Category.{v\u2084, u\u2084} D\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\nW\u2081 : MorphismProperty C\u2081\ninst\u271d\u00b2 : W\u2081.ContainsIdentities\nL\u2082 : C\u2082 \u2964 D\u2082\nW\u2082 : MorphismProperty C\u2082\ninst\u271d\u00b9 : W\u2082.ContainsIdentities\nE : Type u\u2085\ninst\u271d : Category.{v\u2085, u\u2085} E\nF : C\u2081 \u00d7 C\u2082 \u2964 E\nhF : (W\u2081.prod W\u2082).IsInvertedBy F\nF\u2081 F\u2082 : W\u2081.Localization \u00d7 W\u2082.Localization \u2964 E\nh : W\u2081.Q.prod W\u2082.Q \u22d9 F\u2081 = W\u2081.Q.prod W\u2082.Q \u22d9 F\u2082\n\u22a2 W\u2081.Q \u22d9 curry.obj F\u2081 = W\u2081.Q \u22d9 curry.obj F\u2082",
+              "state_before": "case h\nC\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nD\u2081 : Type u\u2083\nD\u2082 : Type u\u2084\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2075 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2074 : Category.{v\u2083, u\u2083} D\u2081\ninst\u271d\u00b3 : Category.{v\u2084, u\u2084} D\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\nW\u2081 : MorphismProperty C\u2081\ninst\u271d\u00b2 : W\u2081.ContainsIdentities\nL\u2082 : C\u2082 \u2964 D\u2082\nW\u2082 : MorphismProperty C\u2082\ninst\u271d\u00b9 : W\u2082.ContainsIdentities\nE : Type u\u2085\ninst\u271d : Category.{v\u2085, u\u2085} E\nF : C\u2081 \u00d7 C\u2082 \u2964 E\nhF : (W\u2081.prod W\u2082).IsInvertedBy F\nF\u2081 F\u2082 : W\u2081.Localization \u00d7 W\u2082.Localization \u2964 E\nh : W\u2081.Q.prod W\u2082.Q \u22d9 F\u2081 = W\u2081.Q.prod W\u2082.Q \u22d9 F\u2082\n\u22a2 curry.obj F\u2081 = curry.obj F\u2082",
+              "tactic": "apply Construction.uniq"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Functor.flip_injective<\\/a>\"",
+                "[{\"full_name\":\"CategoryTheory.Functor.flip_injective\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Currying.lean\",\"def_pos\":[138,7],\"def_end_pos\":[138,21]}]"
+              ],
+              "state_after": "case h.h.h\nC\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nD\u2081 : Type u\u2083\nD\u2082 : Type u\u2084\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2075 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2074 : Category.{v\u2083, u\u2083} D\u2081\ninst\u271d\u00b3 : Category.{v\u2084, u\u2084} D\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\nW\u2081 : MorphismProperty C\u2081\ninst\u271d\u00b2 : W\u2081.ContainsIdentities\nL\u2082 : C\u2082 \u2964 D\u2082\nW\u2082 : MorphismProperty C\u2082\ninst\u271d\u00b9 : W\u2082.ContainsIdentities\nE : Type u\u2085\ninst\u271d : Category.{v\u2085, u\u2085} E\nF : C\u2081 \u00d7 C\u2082 \u2964 E\nhF : (W\u2081.prod W\u2082).IsInvertedBy F\nF\u2081 F\u2082 : W\u2081.Localization \u00d7 W\u2082.Localization \u2964 E\nh : W\u2081.Q.prod W\u2082.Q \u22d9 F\u2081 = W\u2081.Q.prod W\u2082.Q \u22d9 F\u2082\n\u22a2 (W\u2081.Q \u22d9 curry.obj F\u2081).flip = (W\u2081.Q \u22d9 curry.obj F\u2082).flip",
+              "state_before": "case h.h\nC\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nD\u2081 : Type u\u2083\nD\u2082 : Type u\u2084\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2075 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2074 : Category.{v\u2083, u\u2083} D\u2081\ninst\u271d\u00b3 : Category.{v\u2084, u\u2084} D\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\nW\u2081 : MorphismProperty C\u2081\ninst\u271d\u00b2 : W\u2081.ContainsIdentities\nL\u2082 : C\u2082 \u2964 D\u2082\nW\u2082 : MorphismProperty C\u2082\ninst\u271d\u00b9 : W\u2082.ContainsIdentities\nE : Type u\u2085\ninst\u271d : Category.{v\u2085, u\u2085} E\nF : C\u2081 \u00d7 C\u2082 \u2964 E\nhF : (W\u2081.prod W\u2082).IsInvertedBy F\nF\u2081 F\u2082 : W\u2081.Localization \u00d7 W\u2082.Localization \u2964 E\nh : W\u2081.Q.prod W\u2082.Q \u22d9 F\u2081 = W\u2081.Q.prod W\u2082.Q \u22d9 F\u2082\n\u22a2 W\u2081.Q \u22d9 curry.obj F\u2081 = W\u2081.Q \u22d9 curry.obj F\u2082",
+              "tactic": "apply Functor.flip_injective"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Construction.uniq<\\/a>\"",
+                "[{\"full_name\":\"CategoryTheory.Localization.Construction.uniq\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Localization\\/Construction.lean\",\"def_pos\":[192,9],\"def_end_pos\":[192,13]}]"
+              ],
+              "state_after": "case h.h.h.h\nC\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nD\u2081 : Type u\u2083\nD\u2082 : Type u\u2084\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2075 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2074 : Category.{v\u2083, u\u2083} D\u2081\ninst\u271d\u00b3 : Category.{v\u2084, u\u2084} D\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\nW\u2081 : MorphismProperty C\u2081\ninst\u271d\u00b2 : W\u2081.ContainsIdentities\nL\u2082 : C\u2082 \u2964 D\u2082\nW\u2082 : MorphismProperty C\u2082\ninst\u271d\u00b9 : W\u2082.ContainsIdentities\nE : Type u\u2085\ninst\u271d : Category.{v\u2085, u\u2085} E\nF : C\u2081 \u00d7 C\u2082 \u2964 E\nhF : (W\u2081.prod W\u2082).IsInvertedBy F\nF\u2081 F\u2082 : W\u2081.Localization \u00d7 W\u2082.Localization \u2964 E\nh : W\u2081.Q.prod W\u2082.Q \u22d9 F\u2081 = W\u2081.Q.prod W\u2082.Q \u22d9 F\u2082\n\u22a2 W\u2082.Q \u22d9 (W\u2081.Q \u22d9 curry.obj F\u2081).flip = W\u2082.Q \u22d9 (W\u2081.Q \u22d9 curry.obj F\u2082).flip",
+              "state_before": "case h.h.h\nC\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nD\u2081 : Type u\u2083\nD\u2082 : Type u\u2084\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2075 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2074 : Category.{v\u2083, u\u2083} D\u2081\ninst\u271d\u00b3 : Category.{v\u2084, u\u2084} D\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\nW\u2081 : MorphismProperty C\u2081\ninst\u271d\u00b2 : W\u2081.ContainsIdentities\nL\u2082 : C\u2082 \u2964 D\u2082\nW\u2082 : MorphismProperty C\u2082\ninst\u271d\u00b9 : W\u2082.ContainsIdentities\nE : Type u\u2085\ninst\u271d : Category.{v\u2085, u\u2085} E\nF : C\u2081 \u00d7 C\u2082 \u2964 E\nhF : (W\u2081.prod W\u2082).IsInvertedBy F\nF\u2081 F\u2082 : W\u2081.Localization \u00d7 W\u2082.Localization \u2964 E\nh : W\u2081.Q.prod W\u2082.Q \u22d9 F\u2081 = W\u2081.Q.prod W\u2082.Q \u22d9 F\u2082\n\u22a2 (W\u2081.Q \u22d9 curry.obj F\u2081).flip = (W\u2081.Q \u22d9 curry.obj F\u2082).flip",
+              "tactic": "apply Construction.uniq"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Functor.flip_injective<\\/a>\"",
+                "[{\"full_name\":\"CategoryTheory.Functor.flip_injective\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Currying.lean\",\"def_pos\":[138,7],\"def_end_pos\":[138,21]}]"
+              ],
+              "state_after": "case h.h.h.h.h\nC\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nD\u2081 : Type u\u2083\nD\u2082 : Type u\u2084\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2075 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2074 : Category.{v\u2083, u\u2083} D\u2081\ninst\u271d\u00b3 : Category.{v\u2084, u\u2084} D\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\nW\u2081 : MorphismProperty C\u2081\ninst\u271d\u00b2 : W\u2081.ContainsIdentities\nL\u2082 : C\u2082 \u2964 D\u2082\nW\u2082 : MorphismProperty C\u2082\ninst\u271d\u00b9 : W\u2082.ContainsIdentities\nE : Type u\u2085\ninst\u271d : Category.{v\u2085, u\u2085} E\nF : C\u2081 \u00d7 C\u2082 \u2964 E\nhF : (W\u2081.prod W\u2082).IsInvertedBy F\nF\u2081 F\u2082 : W\u2081.Localization \u00d7 W\u2082.Localization \u2964 E\nh : W\u2081.Q.prod W\u2082.Q \u22d9 F\u2081 = W\u2081.Q.prod W\u2082.Q \u22d9 F\u2082\n\u22a2 (W\u2082.Q \u22d9 (W\u2081.Q \u22d9 curry.obj F\u2081).flip).flip = (W\u2082.Q \u22d9 (W\u2081.Q \u22d9 curry.obj F\u2082).flip).flip",
+              "state_before": "case h.h.h.h\nC\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nD\u2081 : Type u\u2083\nD\u2082 : Type u\u2084\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2075 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2074 : Category.{v\u2083, u\u2083} D\u2081\ninst\u271d\u00b3 : Category.{v\u2084, u\u2084} D\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\nW\u2081 : MorphismProperty C\u2081\ninst\u271d\u00b2 : W\u2081.ContainsIdentities\nL\u2082 : C\u2082 \u2964 D\u2082\nW\u2082 : MorphismProperty C\u2082\ninst\u271d\u00b9 : W\u2082.ContainsIdentities\nE : Type u\u2085\ninst\u271d : Category.{v\u2085, u\u2085} E\nF : C\u2081 \u00d7 C\u2082 \u2964 E\nhF : (W\u2081.prod W\u2082).IsInvertedBy F\nF\u2081 F\u2082 : W\u2081.Localization \u00d7 W\u2082.Localization \u2964 E\nh : W\u2081.Q.prod W\u2082.Q \u22d9 F\u2081 = W\u2081.Q.prod W\u2082.Q \u22d9 F\u2082\n\u22a2 W\u2082.Q \u22d9 (W\u2081.Q \u22d9 curry.obj F\u2081).flip = W\u2082.Q \u22d9 (W\u2081.Q \u22d9 curry.obj F\u2082).flip",
+              "tactic": "apply Functor.flip_injective"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Functor.uncurry_obj_injective<\\/a>\"",
+                "[{\"full_name\":\"CategoryTheory.Functor.uncurry_obj_injective\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Currying.lean\",\"def_pos\":[132,7],\"def_end_pos\":[132,28]}]"
+              ],
+              "state_after": "case h.h.h.h.h.h\nC\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nD\u2081 : Type u\u2083\nD\u2082 : Type u\u2084\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2075 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2074 : Category.{v\u2083, u\u2083} D\u2081\ninst\u271d\u00b3 : Category.{v\u2084, u\u2084} D\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\nW\u2081 : MorphismProperty C\u2081\ninst\u271d\u00b2 : W\u2081.ContainsIdentities\nL\u2082 : C\u2082 \u2964 D\u2082\nW\u2082 : MorphismProperty C\u2082\ninst\u271d\u00b9 : W\u2082.ContainsIdentities\nE : Type u\u2085\ninst\u271d : Category.{v\u2085, u\u2085} E\nF : C\u2081 \u00d7 C\u2082 \u2964 E\nhF : (W\u2081.prod W\u2082).IsInvertedBy F\nF\u2081 F\u2082 : W\u2081.Localization \u00d7 W\u2082.Localization \u2964 E\nh : W\u2081.Q.prod W\u2082.Q \u22d9 F\u2081 = W\u2081.Q.prod W\u2082.Q \u22d9 F\u2082\n\u22a2 uncurry.obj (W\u2082.Q \u22d9 (W\u2081.Q \u22d9 curry.obj F\u2081).flip).flip = uncurry.obj (W\u2082.Q \u22d9 (W\u2081.Q \u22d9 curry.obj F\u2082).flip).flip",
+              "state_before": "case h.h.h.h.h\nC\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nD\u2081 : Type u\u2083\nD\u2082 : Type u\u2084\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2075 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2074 : Category.{v\u2083, u\u2083} D\u2081\ninst\u271d\u00b3 : Category.{v\u2084, u\u2084} D\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\nW\u2081 : MorphismProperty C\u2081\ninst\u271d\u00b2 : W\u2081.ContainsIdentities\nL\u2082 : C\u2082 \u2964 D\u2082\nW\u2082 : MorphismProperty C\u2082\ninst\u271d\u00b9 : W\u2082.ContainsIdentities\nE : Type u\u2085\ninst\u271d : Category.{v\u2085, u\u2085} E\nF : C\u2081 \u00d7 C\u2082 \u2964 E\nhF : (W\u2081.prod W\u2082).IsInvertedBy F\nF\u2081 F\u2082 : W\u2081.Localization \u00d7 W\u2082.Localization \u2964 E\nh : W\u2081.Q.prod W\u2082.Q \u22d9 F\u2081 = W\u2081.Q.prod W\u2082.Q \u22d9 F\u2082\n\u22a2 (W\u2082.Q \u22d9 (W\u2081.Q \u22d9 curry.obj F\u2081).flip).flip = (W\u2082.Q \u22d9 (W\u2081.Q \u22d9 curry.obj F\u2082).flip).flip",
+              "tactic": "apply Functor.uncurry_obj_injective"
+            },
+            {
+              "annotated_tactic": [
+                "\"simpa only [<a>Functor.uncurry_obj_curry_obj_flip_flip<\\/a>] using h\"",
+                "[{\"full_name\":\"CategoryTheory.Functor.uncurry_obj_curry_obj_flip_flip\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Currying.lean\",\"def_pos\":[142,7],\"def_end_pos\":[142,38]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.h.h.h.h.h\nC\u2081 : Type u\u2081\nC\u2082 : Type u\u2082\nD\u2081 : Type u\u2083\nD\u2082 : Type u\u2084\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\u2081\ninst\u271d\u2075 : Category.{v\u2082, u\u2082} C\u2082\ninst\u271d\u2074 : Category.{v\u2083, u\u2083} D\u2081\ninst\u271d\u00b3 : Category.{v\u2084, u\u2084} D\u2082\nL\u2081 : C\u2081 \u2964 D\u2081\nW\u2081 : MorphismProperty C\u2081\ninst\u271d\u00b2 : W\u2081.ContainsIdentities\nL\u2082 : C\u2082 \u2964 D\u2082\nW\u2082 : MorphismProperty C\u2082\ninst\u271d\u00b9 : W\u2082.ContainsIdentities\nE : Type u\u2085\ninst\u271d : Category.{v\u2085, u\u2085} E\nF : C\u2081 \u00d7 C\u2082 \u2964 E\nhF : (W\u2081.prod W\u2082).IsInvertedBy F\nF\u2081 F\u2082 : W\u2081.Localization \u00d7 W\u2082.Localization \u2964 E\nh : W\u2081.Q.prod W\u2082.Q \u22d9 F\u2081 = W\u2081.Q.prod W\u2082.Q \u22d9 F\u2082\n\u22a2 uncurry.obj (W\u2082.Q \u22d9 (W\u2081.Q \u22d9 curry.obj F\u2081).flip).flip = uncurry.obj (W\u2082.Q \u22d9 (W\u2081.Q \u22d9 curry.obj F\u2082).flip).flip",
+              "tactic": "simpa only [Functor.uncurry_obj_curry_obj_flip_flip] using h"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Localization/Prod.lean"
+      }
+    ],
+    "input_proofs": 26,
+    "input_units": 2,
+    "proofs": 9,
+    "published_proofs": 8,
+    "published_transitions": 17,
+    "replay_failures": [],
+    "transitions": 19,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/CategoryTheory/Localization/Predicate.lean",
+        "proof_id": "mathlib:CategoryTheory.Functor.IsLocalization.mk'",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              129,
+              97
+            ],
+            "file_path": "Mathlib/CategoryTheory/Localization/Predicate.lean",
+            "full_name": "CategoryTheory.Functor.IsLocalization.mk'",
+            "start": [
+              121,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"simp only [\\u2190 <a>Functor.assoc<\\/a>, <a>Localization.Construction.fac<\\/a>, h\\u2082.fac, <a>Functor.comp_id<\\/a>]\"",
+                  "[{\"full_name\":\"CategoryTheory.Functor.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Whiskering.lean\",\"def_pos\":[288,19],\"def_end_pos\":[288,24]},{\"full_name\":\"CategoryTheory.Localization.Construction.fac\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Localization\\/Construction.lean\",\"def_pos\":[183,9],\"def_end_pos\":[183,12]},{\"full_name\":\"CategoryTheory.Functor.comp_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Basic.lean\",\"def_pos\":[129,19],\"def_end_pos\":[129,26]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "C : Type u_1\nD : Type u_2\ninst\u271d\u00b2 : Category.{u_4, u_1} C\ninst\u271d\u00b9 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d : Category.{?u.5160, u_3} E\nh\u2081 : Localization.StrictUniversalPropertyFixedTarget L W D\nh\u2082 : Localization.StrictUniversalPropertyFixedTarget L W W.Localization\n\u22a2 W.Q \u22d9 \ud835\udfed W.Localization = W.Q \u22d9 Localization.Construction.lift L \u22ef \u22d9 h\u2082.lift W.Q \u22ef",
+                "tactic": "simp only [\u2190 Functor.assoc, Localization.Construction.fac, h\u2082.fac, Functor.comp_id]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp only [\\u2190 <a>Functor.assoc<\\/a>, h\\u2082.fac, <a>Localization.Construction.fac<\\/a>, <a>Functor.comp_id<\\/a>]\"",
+                  "[{\"full_name\":\"CategoryTheory.Functor.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Whiskering.lean\",\"def_pos\":[288,19],\"def_end_pos\":[288,24]},{\"full_name\":\"CategoryTheory.Localization.Construction.fac\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Localization\\/Construction.lean\",\"def_pos\":[183,9],\"def_end_pos\":[183,12]},{\"full_name\":\"CategoryTheory.Functor.comp_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Basic.lean\",\"def_pos\":[129,19],\"def_end_pos\":[129,26]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "C : Type u_1\nD : Type u_2\ninst\u271d\u00b2 : Category.{u_4, u_1} C\ninst\u271d\u00b9 : Category.{u_5, u_2} D\nL : C \u2964 D\nW : MorphismProperty C\nE : Type u_3\ninst\u271d : Category.{?u.5160, u_3} E\nh\u2081 : Localization.StrictUniversalPropertyFixedTarget L W D\nh\u2082 : Localization.StrictUniversalPropertyFixedTarget L W W.Localization\n\u22a2 L \u22d9 h\u2082.lift W.Q \u22ef \u22d9 Localization.Construction.lift L \u22ef = L \u22d9 \ud835\udfed D",
+                "tactic": "simp only [\u2190 Functor.assoc, h\u2082.fac, Localization.Construction.fac, Functor.comp_id]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "CategoryTheory.Functor.IsLocalization.mk'"
+      }
+    ],
+    "validation_rejected_proofs": 1,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000721-0000-a304ae081f9b45e3.parquet",
+      "sha256": "a304ae081f9b45e3b0aec2ab6880afcbf331149ac0eaf8d890cdde0c9c0c7af4",
+      "bytes": 102579,
+      "rows": 17,
+      "revision": "a498fa87b358e6eb392b8a125474b05531d1b03e"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:CategoryTheory.Functor.IsLocalization.of_isEquivalence",
+    "mathlib:CategoryTheory.Functor.IsLocalization.of_iso",
+    "mathlib:CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_fac",
+    "mathlib:CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prod_fac\u2082",
+    "mathlib:CategoryTheory.Localization.comp_liftNatTrans",
+    "mathlib:CategoryTheory.Localization.isoOfHom_id_inv",
+    "mathlib:CategoryTheory.Localization.liftNatTrans_id",
+    "mathlib:CategoryTheory.Localization.natTrans_ext"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Localization/Predicate.lean\",null,null,\"CategoryTheory.Functor.IsLocalization.of_isEquivalence\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Localization/Predicate.lean\",null,null,\"CategoryTheory.Functor.IsLocalization.of_iso\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Localization/Predicate.lean\",null,null,\"CategoryTheory.Localization.comp_liftNatTrans\"]",
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+  ]
+}

manifests/batches/mathlib/000723.json

@@ -0,0 +1,517 @@
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Adjunction.lean"
+      },
+      {
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+        "id": "CategoryTheory.Monad.left_comparison",
+        "reason": "import_failure",
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Adjunction.lean"
+      },
+      {
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+      },
+      {
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Algebra.lean"
+      },
+      {
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+        "id": "CategoryTheory.Comonad.Coalgebra.comp_f",
+        "reason": "import_failure",
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+          "full_name": "CategoryTheory.Comonad.Coalgebra.comp_f",
+          "start": [
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+            1
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Algebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Comonad.Coalgebra.id_eq_id",
+        "id": "CategoryTheory.Comonad.Coalgebra.id_eq_id",
+        "reason": "import_failure",
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Algebra.lean"
+      },
+      {
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+        "id": "CategoryTheory.Comonad.Coalgebra.id_f",
+        "reason": "import_failure",
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+        },
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+      },
+      {
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+        "id": "CategoryTheory.Comonad.algebra_epi_of_epi",
+        "reason": "import_failure",
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+          "full_name": "CategoryTheory.Comonad.algebra_epi_of_epi",
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+            1
+          ],
+          "traced_tactics": [],
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Algebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Comonad.algebra_mono_of_mono",
+        "id": "CategoryTheory.Comonad.algebra_mono_of_mono",
+        "reason": "import_failure",
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+          "full_name": "CategoryTheory.Comonad.algebra_mono_of_mono",
+          "start": [
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+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Algebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Monad.Algebra.Hom.ext'",
+        "id": "CategoryTheory.Monad.Algebra.Hom.ext'",
+        "reason": "import_failure",
+        "selection": {
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+          "full_name": "CategoryTheory.Monad.Algebra.Hom.ext'",
+          "start": [
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+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Algebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Monad.Algebra.comp_eq_comp",
+        "id": "CategoryTheory.Monad.Algebra.comp_eq_comp",
+        "reason": "import_failure",
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+          "file_path": "Mathlib/CategoryTheory/Monad/Algebra.lean",
+          "full_name": "CategoryTheory.Monad.Algebra.comp_eq_comp",
+          "start": [
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+            1
+          ],
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Algebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Monad.Algebra.comp_f",
+        "id": "CategoryTheory.Monad.Algebra.comp_f",
+        "reason": "import_failure",
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+          "file_path": "Mathlib/CategoryTheory/Monad/Algebra.lean",
+          "full_name": "CategoryTheory.Monad.Algebra.comp_f",
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+            1
+          ],
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+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Algebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Monad.Algebra.id_eq_id",
+        "id": "CategoryTheory.Monad.Algebra.id_eq_id",
+        "reason": "import_failure",
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+          "full_name": "CategoryTheory.Monad.Algebra.id_eq_id",
+          "start": [
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+            1
+          ],
+          "traced_tactics": [],
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Algebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
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+        "id": "CategoryTheory.Monad.Algebra.id_f",
+        "reason": "import_failure",
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+          "full_name": "CategoryTheory.Monad.Algebra.id_f",
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+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Algebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Monad.algebra_epi_of_epi",
+        "id": "CategoryTheory.Monad.algebra_epi_of_epi",
+        "reason": "import_failure",
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+          "full_name": "CategoryTheory.Monad.algebra_epi_of_epi",
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+            1
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+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Algebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Monad.algebra_equiv_of_iso_monads_comp_forget",
+        "id": "CategoryTheory.Monad.algebra_equiv_of_iso_monads_comp_forget",
+        "reason": "import_failure",
+        "selection": {
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+          "end": [
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+          "file_path": "Mathlib/CategoryTheory/Monad/Algebra.lean",
+          "full_name": "CategoryTheory.Monad.algebra_equiv_of_iso_monads_comp_forget",
+          "start": [
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+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Algebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Monad.algebra_mono_of_mono",
+        "id": "CategoryTheory.Monad.algebra_mono_of_mono",
+        "reason": "import_failure",
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+          "end": [
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+          "file_path": "Mathlib/CategoryTheory/Monad/Algebra.lean",
+          "full_name": "CategoryTheory.Monad.algebra_mono_of_mono",
+          "start": [
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+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Algebra.lean"
+      }
+    ],
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+    "input_units": 2,
+    "proofs": 3,
+    "published_proofs": 1,
+    "published_transitions": 1,
+    "replay_failures": [],
+    "transitions": 7,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/CategoryTheory/Monad/Algebra.lean",
+        "proof_id": "mathlib:CategoryTheory.Comonad.coalgebra_iso_of_iso",
+        "provenance": {
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+            "full_name": "CategoryTheory.Comonad.coalgebra_iso_of_iso",
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+                "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\nG : Comonad C\nA B : G.Coalgebra\nf : A \u27f6 B\ninst\u271d : IsIso f.f\n\u22a2 B.a \u226b G.map (inv f.f) = inv f.f \u226b A.a",
+                "tactic": "rw [IsIso.eq_inv_comp f.f, \u2190 f.h_assoc]"
+              },
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+                "state_after": "no goals",
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+                "tactic": "simp"
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+              {
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+                  "\"aesop_cat\"",
+                  "[]"
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+                "state_after": "no goals",
+                "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\nG : Comonad C\nA B : G.Coalgebra\nf : A \u27f6 B\ninst\u271d : IsIso f.f\n\u22a2 f \u226b { f := inv f.f, h := \u22ef } = \ud835\udfd9 A \u2227 { f := inv f.f, h := \u22ef } \u226b f = \ud835\udfd9 B",
+                "tactic": "aesop_cat"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "CategoryTheory.Comonad.coalgebra_iso_of_iso"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/CategoryTheory/Monad/Algebra.lean",
+        "proof_id": "mathlib:CategoryTheory.Monad.algebra_iso_of_iso",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
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+              21
+            ],
+            "file_path": "Mathlib/CategoryTheory/Monad/Algebra.lean",
+            "full_name": "CategoryTheory.Monad.algebra_iso_of_iso",
+            "start": [
+              200,
+              1
+            ],
+            "traced_tactics": [
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+                ],
+                "state_after": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\nT : Monad C\nA B : T.Algebra\nf : A \u27f6 B\ninst\u271d : IsIso f.f\n\u22a2 T.map (inv f.f) \u226b T.map f.f \u226b B.a = B.a",
+                "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\nT : Monad C\nA B : T.Algebra\nf : A \u27f6 B\ninst\u271d : IsIso f.f\n\u22a2 T.map (inv f.f) \u226b A.a = B.a \u226b inv f.f",
+                "tactic": "rw [IsIso.eq_comp_inv f.f, Category.assoc, \u2190 f.h]"
+              },
+              {
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+                "state_after": "no goals",
+                "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\nT : Monad C\nA B : T.Algebra\nf : A \u27f6 B\ninst\u271d : IsIso f.f\n\u22a2 T.map (inv f.f) \u226b T.map f.f \u226b B.a = B.a",
+                "tactic": "simp"
+              },
+              {
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+                  "\"aesop_cat\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\nT : Monad C\nA B : T.Algebra\nf : A \u27f6 B\ninst\u271d : IsIso f.f\n\u22a2 f \u226b { f := inv f.f, h := \u22ef } = \ud835\udfd9 A \u2227 { f := inv f.f, h := \u22ef } \u226b f = \ud835\udfd9 B",
+                "tactic": "aesop_cat"
+              }
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+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "CategoryTheory.Monad.algebra_iso_of_iso"
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+}

manifests/batches/mathlib/000724.json

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+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Coequalizer.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Monad.beckCoequalizer_desc",
+        "id": "CategoryTheory.Monad.beckCoequalizer_desc",
+        "reason": "import_failure",
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+          "full_name": "CategoryTheory.Monad.beckCoequalizer_desc",
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Coequalizer.lean"
+      },
+      {
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+        "full_name": "CategoryTheory.Monad.beckCofork_\u03c0",
+        "id": "CategoryTheory.Monad.beckCofork_\u03c0",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            118,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monad/Coequalizer.lean",
+          "full_name": "CategoryTheory.Monad.beckCofork_\u03c0",
+          "start": [
+            117,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Coequalizer.lean"
+      }
+    ],
+    "input_proofs": 16,
+    "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/000725.json

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+          "file_path": "Mathlib/CategoryTheory/Monad/Limits.lean",
+          "full_name": "CategoryTheory.Monad.hasLimit_of_comp_forget_hasLimit",
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+          "traced_tactics": [],
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Limits.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.hasColimits_of_reflective",
+        "id": "CategoryTheory.hasColimits_of_reflective",
+        "reason": "import_failure",
+        "selection": {
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+          "end": [
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+          "file_path": "Mathlib/CategoryTheory/Monad/Limits.lean",
+          "full_name": "CategoryTheory.hasColimits_of_reflective",
+          "start": [
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+            1
+          ],
+          "traced_tactics": [],
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Limits.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.hasLimit_of_reflective",
+        "id": "CategoryTheory.hasLimit_of_reflective",
+        "reason": "import_failure",
+        "selection": {
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+          "full_name": "CategoryTheory.hasLimit_of_reflective",
+          "start": [
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+            1
+          ],
+          "traced_tactics": [],
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Limits.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.hasLimitsOfShape_of_reflective",
+        "id": "CategoryTheory.hasLimitsOfShape_of_reflective",
+        "reason": "import_failure",
+        "selection": {
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+          "end": [
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+          "file_path": "Mathlib/CategoryTheory/Monad/Limits.lean",
+          "full_name": "CategoryTheory.hasLimitsOfShape_of_reflective",
+          "start": [
+            356,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Limits.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.hasLimits_of_reflective",
+        "id": "CategoryTheory.hasLimits_of_reflective",
+        "reason": "import_failure",
+        "selection": {
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+          "end": [
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+          ],
+          "file_path": "Mathlib/CategoryTheory/Monad/Limits.lean",
+          "full_name": "CategoryTheory.hasLimits_of_reflective",
+          "start": [
+            362,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monad/Limits.lean"
+      }
+    ],
+    "input_proofs": 9,
+    "input_units": 2,
+    "proofs": 1,
+    "published_proofs": 1,
+    "published_transitions": 5,
+    "replay_failures": [],
+    "transitions": 5,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000725-0000-6790ef03eb839c70.parquet",
+      "sha256": "6790ef03eb839c7010d0774fb374da7669bed2e1d0bec23720abf912cac7c405",
+      "bytes": 71825,
+      "rows": 5,
+      "revision": "a498fa87b358e6eb392b8a125474b05531d1b03e"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:CategoryTheory.hasColimitsOfShape_of_reflective"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Monad/Limits.lean\",null,null,\"CategoryTheory.hasColimitsOfShape_of_reflective\"]"
+  ]
+}

manifests/batches/mathlib/000728.json

@@ -0,0 +1,569 @@
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+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
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+        "id": "CategoryTheory.MonoidalCategory.leftAssocTensor_map",
+        "reason": "import_failure",
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+          "full_name": "CategoryTheory.MonoidalCategory.leftAssocTensor_map",
+          "start": [
+            826,
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+          ],
+          "traced_tactics": [],
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Category.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
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+        "id": "CategoryTheory.MonoidalCategory.leftAssocTensor_obj",
+        "reason": "import_failure",
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+          "full_name": "CategoryTheory.MonoidalCategory.leftAssocTensor_obj",
+          "start": [
+            821,
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+          ],
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Category.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.MonoidalCategory.rightAssocTensor_map",
+        "id": "CategoryTheory.MonoidalCategory.rightAssocTensor_map",
+        "reason": "import_failure",
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+          "full_name": "CategoryTheory.MonoidalCategory.rightAssocTensor_map",
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+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.MonoidalCategory.rightAssocTensor_obj",
+        "id": "CategoryTheory.MonoidalCategory.rightAssocTensor_obj",
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+          ],
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Category.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.MonoidalCategory.tensorHom_def'",
+        "id": "CategoryTheory.MonoidalCategory.tensorHom_def'",
+        "reason": "import_failure",
+        "selection": {
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+          "full_name": "CategoryTheory.MonoidalCategory.tensorHom_def'",
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+            283,
+            1
+          ],
+          "traced_tactics": [],
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Category.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.MonoidalCategory.tensorLeftTensor_hom_app",
+        "id": "CategoryTheory.MonoidalCategory.tensorLeftTensor_hom_app",
+        "reason": "import_failure",
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+          "full_name": "CategoryTheory.MonoidalCategory.tensorLeftTensor_hom_app",
+          "start": [
+            920,
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+          ],
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Category.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.MonoidalCategory.tensorRightTensor_hom_app",
+        "id": "CategoryTheory.MonoidalCategory.tensorRightTensor_hom_app",
+        "reason": "import_failure",
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+          ],
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Category.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.MonoidalCategory.whiskerLeftIso_refl",
+        "id": "CategoryTheory.MonoidalCategory.whiskerLeftIso_refl",
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+          "full_name": "CategoryTheory.MonoidalCategory.whiskerLeftIso_refl",
+          "start": [
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+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Category.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.MonoidalCategory.whiskerLeftIso_symm",
+        "id": "CategoryTheory.MonoidalCategory.whiskerLeftIso_symm",
+        "reason": "import_failure",
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+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Category.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
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+        },
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+      },
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+      },
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+      },
+      {
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+    "validation_failures": [
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+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/CategoryTheory/Monoidal/Cartesian/Comon_.lean",
+        "proof_id": "mathlib:comul_eq_diag",
+        "provenance": {
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+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
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+            "full_name": "comul_eq_diag",
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+            ],
+            "traced_tactics": [
+              {
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+                "state_before": "C : Type u\ninst\u271d\u00b2 : Category.{v, u} C\ninst\u271d\u00b9 : HasTerminal C\ninst\u271d : HasBinaryProducts C\nA : Comon_ C\n\u22a2 A.comul = diag A.X",
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+              },
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+                ],
+                "state_after": "no goals",
+                "state_before": "case w\u2081\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\ninst\u271d\u00b9 : HasTerminal C\ninst\u271d : HasBinaryProducts C\nA : Comon_ C\n\u22a2 A.comul \u226b prod.fst = diag A.X \u226b prod.fst",
+                "tactic": "simpa using A.comul_counit =\u226b prod.fst"
+              },
+              {
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+                ],
+                "state_after": "no goals",
+                "state_before": "case w\u2082\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\ninst\u271d\u00b9 : HasTerminal C\ninst\u271d : HasBinaryProducts C\nA : Comon_ C\n\u22a2 A.comul \u226b prod.snd = diag A.X \u226b prod.snd",
+                "tactic": "simpa using A.counit_comul =\u226b prod.snd"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "comul_eq_diag"
+      }
+    ],
+    "validation_rejected_proofs": 1,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
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+      "sha256": "d2846e5ed1b13bc4ec83cbcc98ac3106a0fd3643c116b2fd8a07a425afd1c386",
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+      "rows": 103,
+      "revision": "a498fa87b358e6eb392b8a125474b05531d1b03e"
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+    {
+      "path": "data/dev/mathlib-000728-0000-917dcb3a2055d2e6.parquet",
+      "sha256": "917dcb3a2055d2e6f25c4cb5659f8ce690819dd54ea494e425672ff6dc065e5b",
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+      "rows": 8,
+      "revision": "a498fa87b358e6eb392b8a125474b05531d1b03e"
+    },
+    {
+      "path": "data/internal_test/mathlib-000728-0000-3867c6e763c3577f.parquet",
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+      "rows": 8,
+      "revision": "a498fa87b358e6eb392b8a125474b05531d1b03e"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:CategoryTheory.MonoidalCategory.associator_conjugation",
+    "mathlib:CategoryTheory.MonoidalCategory.associator_inv_conjugation",
+    "mathlib:CategoryTheory.MonoidalCategory.associator_inv_naturality",
+    "mathlib:CategoryTheory.MonoidalCategory.associator_inv_naturality_left",
+    "mathlib:CategoryTheory.MonoidalCategory.associator_inv_naturality_middle",
+    "mathlib:CategoryTheory.MonoidalCategory.associator_inv_naturality_right",
+    "mathlib:CategoryTheory.MonoidalCategory.associator_naturality_left",
+    "mathlib:CategoryTheory.MonoidalCategory.associator_naturality_middle",
+    "mathlib:CategoryTheory.MonoidalCategory.associator_naturality_right",
+    "mathlib:CategoryTheory.MonoidalCategory.comp_tensor_id",
+    "mathlib:CategoryTheory.MonoidalCategory.comp_whiskerRight",
+    "mathlib:CategoryTheory.MonoidalCategory.dite_tensor",
+    "mathlib:CategoryTheory.MonoidalCategory.dite_whiskerRight",
+    "mathlib:CategoryTheory.MonoidalCategory.eqToHom_whiskerRight",
+    "mathlib:CategoryTheory.MonoidalCategory.hom_inv_id_tensor",
+    "mathlib:CategoryTheory.MonoidalCategory.hom_inv_id_tensor'",
+    "mathlib:CategoryTheory.MonoidalCategory.hom_inv_whiskerRight",
+    "mathlib:CategoryTheory.MonoidalCategory.hom_inv_whiskerRight'",
+    "mathlib:CategoryTheory.MonoidalCategory.id_tensorHom",
+    "mathlib:CategoryTheory.MonoidalCategory.id_tensor_associator_inv_naturality",
+    "mathlib:CategoryTheory.MonoidalCategory.id_tensor_associator_naturality",
+    "mathlib:CategoryTheory.MonoidalCategory.id_tensor_comp",
+    "mathlib:CategoryTheory.MonoidalCategory.id_tensor_comp_tensor_id",
+    "mathlib:CategoryTheory.MonoidalCategory.id_whiskerLeft",
+    "mathlib:CategoryTheory.MonoidalCategory.id_whiskerLeft_symm",
+    "mathlib:CategoryTheory.MonoidalCategory.inv_hom_id_tensor'",
+    "mathlib:CategoryTheory.MonoidalCategory.inv_hom_whiskerRight",
+    "mathlib:CategoryTheory.MonoidalCategory.inv_hom_whiskerRight'",
+    "mathlib:CategoryTheory.MonoidalCategory.inv_tensor",
+    "mathlib:CategoryTheory.MonoidalCategory.inv_whiskerLeft",
+    "mathlib:CategoryTheory.MonoidalCategory.inv_whiskerRight",
+    "mathlib:CategoryTheory.MonoidalCategory.leftUnitor_inv_naturality",
+    "mathlib:CategoryTheory.MonoidalCategory.leftUnitor_inv_whiskerRight",
+    "mathlib:CategoryTheory.MonoidalCategory.leftUnitor_tensor",
+    "mathlib:CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv",
+    "mathlib:CategoryTheory.MonoidalCategory.leftUnitor_whiskerRight",
+    "mathlib:CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_hom_hom",
+    "mathlib:CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_inv_hom",
+    "mathlib:CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_hom",
+    "mathlib:CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_inv",
+    "mathlib:CategoryTheory.MonoidalCategory.pentagon_inv",
+    "mathlib:CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_hom",
+    "mathlib:CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_inv",
+    "mathlib:CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_hom_inv",
+    "mathlib:CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_inv_inv",
+    "mathlib:CategoryTheory.MonoidalCategory.prodMonoidal_leftUnitor_hom_fst",
+    "mathlib:CategoryTheory.MonoidalCategory.prodMonoidal_leftUnitor_hom_snd",
+    "mathlib:CategoryTheory.MonoidalCategory.prodMonoidal_leftUnitor_inv_fst",
+    "mathlib:CategoryTheory.MonoidalCategory.prodMonoidal_leftUnitor_inv_snd",
+    "mathlib:CategoryTheory.MonoidalCategory.prodMonoidal_rightUnitor_hom_fst",
+    "mathlib:CategoryTheory.MonoidalCategory.prodMonoidal_rightUnitor_hom_snd",
+    "mathlib:CategoryTheory.MonoidalCategory.prodMonoidal_rightUnitor_inv_fst",
+    "mathlib:CategoryTheory.MonoidalCategory.prodMonoidal_rightUnitor_inv_snd",
+    "mathlib:CategoryTheory.MonoidalCategory.rightUnitor_inv_naturality",
+    "mathlib:CategoryTheory.MonoidalCategory.rightUnitor_tensor",
+    "mathlib:CategoryTheory.MonoidalCategory.rightUnitor_tensor_inv",
+    "mathlib:CategoryTheory.MonoidalCategory.tensorHom_id",
+    "mathlib:CategoryTheory.MonoidalCategory.tensorLeftTensor_inv_app",
+    "mathlib:CategoryTheory.MonoidalCategory.tensorRightTensor_inv_app",
+    "mathlib:CategoryTheory.MonoidalCategory.tensor_dite",
+    "mathlib:CategoryTheory.MonoidalCategory.tensor_hom_inv_id",
+    "mathlib:CategoryTheory.MonoidalCategory.tensor_hom_inv_id'",
+    "mathlib:CategoryTheory.MonoidalCategory.tensor_id_comp_id_tensor",
+    "mathlib:CategoryTheory.MonoidalCategory.tensor_inv_hom_id",
+    "mathlib:CategoryTheory.MonoidalCategory.tensor_inv_hom_id'",
+    "mathlib:CategoryTheory.MonoidalCategory.tensor_left_iff",
+    "mathlib:CategoryTheory.MonoidalCategory.tensor_right_iff",
+    "mathlib:CategoryTheory.MonoidalCategory.tensor_whiskerLeft",
+    "mathlib:CategoryTheory.MonoidalCategory.tensor_whiskerLeft_symm",
+    "mathlib:CategoryTheory.MonoidalCategory.triangle_assoc_comp_left_inv",
+    "mathlib:CategoryTheory.MonoidalCategory.triangle_assoc_comp_right",
+    "mathlib:CategoryTheory.MonoidalCategory.triangle_assoc_comp_right_inv",
+    "mathlib:CategoryTheory.MonoidalCategory.whiskerLeft_comp",
+    "mathlib:CategoryTheory.MonoidalCategory.whiskerLeft_dite",
+    "mathlib:CategoryTheory.MonoidalCategory.whiskerLeft_eqToHom",
+    "mathlib:CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv",
+    "mathlib:CategoryTheory.MonoidalCategory.whiskerLeft_hom_inv'",
+    "mathlib:CategoryTheory.MonoidalCategory.whiskerLeft_iff",
+    "mathlib:CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom",
+    "mathlib:CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom'",
+    "mathlib:CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor",
+    "mathlib:CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_inv",
+    "mathlib:CategoryTheory.MonoidalCategory.whiskerRight_id",
+    "mathlib:CategoryTheory.MonoidalCategory.whiskerRight_id_symm",
+    "mathlib:CategoryTheory.MonoidalCategory.whiskerRight_iff",
+    "mathlib:CategoryTheory.MonoidalCategory.whiskerRight_tensor",
+    "mathlib:CategoryTheory.MonoidalCategory.whiskerRight_tensor_symm",
+    "mathlib:CategoryTheory.MonoidalCategory.whisker_assoc",
+    "mathlib:CategoryTheory.MonoidalCategory.whisker_assoc_symm",
+    "mathlib:CategoryTheory.MonoidalCategory.whisker_exchange"
+  ],
+  "proof_keys": [
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+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Monoidal/Category.lean\",null,null,\"CategoryTheory.MonoidalCategory.whiskerRight_tensor_symm\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Monoidal/Category.lean\",null,null,\"CategoryTheory.MonoidalCategory.whisker_assoc\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Monoidal/Category.lean\",null,null,\"CategoryTheory.MonoidalCategory.whisker_assoc_symm\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Monoidal/Category.lean\",null,null,\"CategoryTheory.MonoidalCategory.whisker_exchange\"]"
+  ]
+}

manifests/batches/mathlib/000729.json

@@ -0,0 +1,488 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000729",
+  "batch_fingerprint": "be4381178188efd1e1228ec589b90fc09020f7a1e30f26cd99e4d02f0f8cfee4",
+  "evidence": {
+    "batch_fingerprint": "be4381178188efd1e1228ec589b90fc09020f7a1e30f26cd99e4d02f0f8cfee4",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Center.associator_hom_f",
+        "id": "CategoryTheory.Center.associator_hom_f",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            297,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Center.lean",
+          "full_name": "CategoryTheory.Center.associator_hom_f",
+          "start": [
+            296,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Center.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Center.comp_f",
+        "id": "CategoryTheory.Center.comp_f",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            112,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Center.lean",
+          "full_name": "CategoryTheory.Center.comp_f",
+          "start": [
+            111,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Center.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Center.id_f",
+        "id": "CategoryTheory.Center.id_f",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            107,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Center.lean",
+          "full_name": "CategoryTheory.Center.id_f",
+          "start": [
+            106,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Center.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Center.leftUnitor_hom_f",
+        "id": "CategoryTheory.Center.leftUnitor_hom_f",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            308,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Center.lean",
+          "full_name": "CategoryTheory.Center.leftUnitor_hom_f",
+          "start": [
+            307,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Center.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Center.rightUnitor_hom_f",
+        "id": "CategoryTheory.Center.rightUnitor_hom_f",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            319,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Center.lean",
+          "full_name": "CategoryTheory.Center.rightUnitor_hom_f",
+          "start": [
+            318,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Center.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Center.tensorUnit_\u03b2",
+        "id": "CategoryTheory.Center.tensorUnit_\u03b2",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            292,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Center.lean",
+          "full_name": "CategoryTheory.Center.tensorUnit_\u03b2",
+          "start": [
+            291,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Center.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Center.tensor_f",
+        "id": "CategoryTheory.Center.tensor_f",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            287,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Center.lean",
+          "full_name": "CategoryTheory.Center.tensor_f",
+          "start": [
+            286,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Center.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Center.tensor_fst",
+        "id": "CategoryTheory.Center.tensor_fst",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            265,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Center.lean",
+          "full_name": "CategoryTheory.Center.tensor_fst",
+          "start": [
+            264,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Center.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Center.tensor_\u03b2",
+        "id": "CategoryTheory.Center.tensor_\u03b2",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            274,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Center.lean",
+          "full_name": "CategoryTheory.Center.tensor_\u03b2",
+          "start": [
+            269,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Center.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'coherence'",
+        "full_name": "CategoryTheory.Center.whiskerLeft_comm",
+        "id": "CategoryTheory.Center.whiskerLeft_comm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            179,
+            49
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Center.lean",
+          "full_name": "CategoryTheory.Center.whiskerLeft_comm",
+          "start": [
+            166,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"dsimp only [<a>tensorObj_fst<\\/a>, <a>tensorObj_snd_\\u03b2<\\/a>, <a>Iso.trans_hom<\\/a>, <a>whiskerLeftIso_hom<\\/a>,\\n    <a>Iso.symm_hom<\\/a>, <a>whiskerRightIso_hom<\\/a>]\"",
+                "[{\"full_name\":\"CategoryTheory.Center.tensorObj_fst\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Center.lean\",\"def_pos\":[132,3],\"def_end_pos\":[132,8]},{\"full_name\":\"CategoryTheory.Center.tensorObj_snd_\\u03b2\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Center.lean\",\"def_pos\":[132,3],\"def_end_pos\":[132,8]},{\"full_name\":\"CategoryTheory.Iso.trans_hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[149,10],\"def_end_pos\":[149,15]},{\"full_name\":\"CategoryTheory.MonoidalCategory.whiskerLeftIso_hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Category.lean\",\"def_pos\":[337,3],\"def_end_pos\":[337,8]},{\"full_name\":\"CategoryTheory.Iso.symm_hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[100,9],\"def_end_pos\":[100,17]},{\"full_name\":\"CategoryTheory.MonoidalCategory.whiskerRightIso_hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Category.lean\",\"def_pos\":[365,3],\"def_end_pos\":[365,9]}]"
+              ],
+              "state_after": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX Y\u2081 Y\u2082 : Center C\nf : Y\u2081 \u27f6 Y\u2082\nU : C\n\u22a2 (X.fst \u25c1 f.f) \u25b7 U \u226b\n      (\u03b1_ X.fst Y\u2082.fst U).hom \u226b\n        X.fst \u25c1 (Y\u2082.snd.\u03b2 U).hom \u226b (\u03b1_ X.fst U Y\u2082.fst).inv \u226b (X.snd.\u03b2 U).hom \u25b7 Y\u2082.fst \u226b (\u03b1_ U X.fst Y\u2082.fst).hom =\n    ((\u03b1_ X.fst Y\u2081.fst U).hom \u226b\n        X.fst \u25c1 (Y\u2081.snd.\u03b2 U).hom \u226b (\u03b1_ X.fst U Y\u2081.fst).inv \u226b (X.snd.\u03b2 U).hom \u25b7 Y\u2081.fst \u226b (\u03b1_ U X.fst Y\u2081.fst).hom) \u226b\n      U \u25c1 X.fst \u25c1 f.f",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX Y\u2081 Y\u2082 : Center C\nf : Y\u2081 \u27f6 Y\u2082\nU : C\n\u22a2 (X.fst \u25c1 f.f) \u25b7 U \u226b ((X.tensorObj Y\u2082).snd.\u03b2 U).hom = ((X.tensorObj Y\u2081).snd.\u03b2 U).hom \u226b U \u25c1 X.fst \u25c1 f.f",
+              "tactic": "dsimp only [tensorObj_fst, tensorObj_snd_\u03b2, Iso.trans_hom, whiskerLeftIso_hom,\n  Iso.symm_hom, whiskerRightIso_hom]"
+            },
+            {
+              "annotated_tactic": [
+                "\"calc\\n    _ = \\ud835\\udfd9 _ \\u2297\\u226b\\n      X.fst \\u25c1 (f.f \\u25b7 U \\u226b (<a>HalfBraiding.\\u03b2<\\/a> Y\\u2082.snd U).<a>hom<\\/a>) \\u2297\\u226b\\n        (<a>HalfBraiding.\\u03b2<\\/a> X.snd U).<a>hom<\\/a> \\u25b7 Y\\u2082.fst \\u2297\\u226b \\ud835\\udfd9 _ := by coherence\\n    _ = \\ud835\\udfd9 _ \\u2297\\u226b\\n      X.fst \\u25c1 (<a>HalfBraiding.\\u03b2<\\/a> Y\\u2081.snd U).<a>hom<\\/a> \\u2297\\u226b\\n        ((X.fst \\u2297 U) \\u25c1 f.f \\u226b (<a>HalfBraiding.\\u03b2<\\/a> X.snd U).<a>hom<\\/a> \\u25b7 Y\\u2082.fst) \\u2297\\u226b \\ud835\\udfd9 _ := by\\n      rw [f.comm]; coherence\\n    _ = _ := by rw [<a>whisker_exchange<\\/a>]; coherence\"",
+                "[{\"full_name\":\"CategoryTheory.HalfBraiding.\\u03b2\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Center.lean\",\"def_pos\":[56,3],\"def_end_pos\":[56,4]},{\"full_name\":\"CategoryTheory.Iso.hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[53,3],\"def_end_pos\":[53,6]},{\"full_name\":\"CategoryTheory.HalfBraiding.\\u03b2\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Center.lean\",\"def_pos\":[56,3],\"def_end_pos\":[56,4]},{\"full_name\":\"CategoryTheory.Iso.hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[53,3],\"def_end_pos\":[53,6]},{\"full_name\":\"CategoryTheory.HalfBraiding.\\u03b2\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Center.lean\",\"def_pos\":[56,3],\"def_end_pos\":[56,4]},{\"full_name\":\"CategoryTheory.Iso.hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[53,3],\"def_end_pos\":[53,6]},{\"full_name\":\"CategoryTheory.HalfBraiding.\\u03b2\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Center.lean\",\"def_pos\":[56,3],\"def_end_pos\":[56,4]},{\"full_name\":\"CategoryTheory.Iso.hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[53,3],\"def_end_pos\":[53,6]},{\"full_name\":\"CategoryTheory.MonoidalCategory.whisker_exchange\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Category.lean\",\"def_pos\":[278,9],\"def_end_pos\":[278,25]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX Y\u2081 Y\u2082 : Center C\nf : Y\u2081 \u27f6 Y\u2082\nU : C\n\u22a2 (X.fst \u25c1 f.f) \u25b7 U \u226b\n      (\u03b1_ X.fst Y\u2082.fst U).hom \u226b\n        X.fst \u25c1 (Y\u2082.snd.\u03b2 U).hom \u226b (\u03b1_ X.fst U Y\u2082.fst).inv \u226b (X.snd.\u03b2 U).hom \u25b7 Y\u2082.fst \u226b (\u03b1_ U X.fst Y\u2082.fst).hom =\n    ((\u03b1_ X.fst Y\u2081.fst U).hom \u226b\n        X.fst \u25c1 (Y\u2081.snd.\u03b2 U).hom \u226b (\u03b1_ X.fst U Y\u2081.fst).inv \u226b (X.snd.\u03b2 U).hom \u25b7 Y\u2081.fst \u226b (\u03b1_ U X.fst Y\u2081.fst).hom) \u226b\n      U \u25c1 X.fst \u25c1 f.f",
+              "tactic": "calc\n  _ = \ud835\udfd9 _ \u2297\u226b\n    X.fst \u25c1 (f.f \u25b7 U \u226b (HalfBraiding.\u03b2 Y\u2082.snd U).hom) \u2297\u226b\n      (HalfBraiding.\u03b2 X.snd U).hom \u25b7 Y\u2082.fst \u2297\u226b \ud835\udfd9 _ := by coherence\n  _ = \ud835\udfd9 _ \u2297\u226b\n    X.fst \u25c1 (HalfBraiding.\u03b2 Y\u2081.snd U).hom \u2297\u226b\n      ((X.fst \u2297 U) \u25c1 f.f \u226b (HalfBraiding.\u03b2 X.snd U).hom \u25b7 Y\u2082.fst) \u2297\u226b \ud835\udfd9 _ := by\n    rw [f.comm]; coherence\n  _ = _ := by rw [whisker_exchange]; coherence"
+            },
+            {
+              "annotated_tactic": [
+                "\"coherence\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX Y\u2081 Y\u2082 : Center C\nf : Y\u2081 \u27f6 Y\u2082\nU : C\n\u22a2 (X.fst \u25c1 f.f) \u25b7 U \u226b\n      (\u03b1_ X.fst Y\u2082.fst U).hom \u226b\n        X.fst \u25c1 (Y\u2082.snd.\u03b2 U).hom \u226b (\u03b1_ X.fst U Y\u2082.fst).inv \u226b (X.snd.\u03b2 U).hom \u25b7 Y\u2082.fst \u226b (\u03b1_ U X.fst Y\u2082.fst).hom =\n    \ud835\udfd9 ((X.fst \u2297 Y\u2081.fst) \u2297 U) \u2297\u226b\n      X.fst \u25c1 (f.f \u25b7 U \u226b (Y\u2082.snd.\u03b2 U).hom) \u2297\u226b (X.snd.\u03b2 U).hom \u25b7 Y\u2082.fst \u2297\u226b \ud835\udfd9 (U \u2297 X.fst \u2297 Y\u2082.fst)",
+              "tactic": "coherence"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [f.comm]\"",
+                "[]"
+              ],
+              "state_after": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX Y\u2081 Y\u2082 : Center C\nf : Y\u2081 \u27f6 Y\u2082\nU : C\n\u22a2 \ud835\udfd9 ((X.fst \u2297 Y\u2081.fst) \u2297 U) \u2297\u226b\n      X.fst \u25c1 ((Y\u2081.snd.\u03b2 U).hom \u226b U \u25c1 f.f) \u2297\u226b (X.snd.\u03b2 U).hom \u25b7 Y\u2082.fst \u2297\u226b \ud835\udfd9 (U \u2297 X.fst \u2297 Y\u2082.fst) =\n    \ud835\udfd9 ((X.fst \u2297 Y\u2081.fst) \u2297 U) \u2297\u226b\n      X.fst \u25c1 (Y\u2081.snd.\u03b2 U).hom \u2297\u226b ((X.fst \u2297 U) \u25c1 f.f \u226b (X.snd.\u03b2 U).hom \u25b7 Y\u2082.fst) \u2297\u226b \ud835\udfd9 (U \u2297 X.fst \u2297 Y\u2082.fst)",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX Y\u2081 Y\u2082 : Center C\nf : Y\u2081 \u27f6 Y\u2082\nU : C\n\u22a2 \ud835\udfd9 ((X.fst \u2297 Y\u2081.fst) \u2297 U) \u2297\u226b\n      X.fst \u25c1 (f.f \u25b7 U \u226b (Y\u2082.snd.\u03b2 U).hom) \u2297\u226b (X.snd.\u03b2 U).hom \u25b7 Y\u2082.fst \u2297\u226b \ud835\udfd9 (U \u2297 X.fst \u2297 Y\u2082.fst) =\n    \ud835\udfd9 ((X.fst \u2297 Y\u2081.fst) \u2297 U) \u2297\u226b\n      X.fst \u25c1 (Y\u2081.snd.\u03b2 U).hom \u2297\u226b ((X.fst \u2297 U) \u25c1 f.f \u226b (X.snd.\u03b2 U).hom \u25b7 Y\u2082.fst) \u2297\u226b \ud835\udfd9 (U \u2297 X.fst \u2297 Y\u2082.fst)",
+              "tactic": "rw [f.comm]"
+            },
+            {
+              "annotated_tactic": [
+                "\"coherence\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX Y\u2081 Y\u2082 : Center C\nf : Y\u2081 \u27f6 Y\u2082\nU : C\n\u22a2 \ud835\udfd9 ((X.fst \u2297 Y\u2081.fst) \u2297 U) \u2297\u226b\n      X.fst \u25c1 ((Y\u2081.snd.\u03b2 U).hom \u226b U \u25c1 f.f) \u2297\u226b (X.snd.\u03b2 U).hom \u25b7 Y\u2082.fst \u2297\u226b \ud835\udfd9 (U \u2297 X.fst \u2297 Y\u2082.fst) =\n    \ud835\udfd9 ((X.fst \u2297 Y\u2081.fst) \u2297 U) \u2297\u226b\n      X.fst \u25c1 (Y\u2081.snd.\u03b2 U).hom \u2297\u226b ((X.fst \u2297 U) \u25c1 f.f \u226b (X.snd.\u03b2 U).hom \u25b7 Y\u2082.fst) \u2297\u226b \ud835\udfd9 (U \u2297 X.fst \u2297 Y\u2082.fst)",
+              "tactic": "coherence"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>whisker_exchange<\\/a>]\"",
+                "[{\"full_name\":\"CategoryTheory.MonoidalCategory.whisker_exchange\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Category.lean\",\"def_pos\":[278,9],\"def_end_pos\":[278,25]}]"
+              ],
+              "state_after": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX Y\u2081 Y\u2082 : Center C\nf : Y\u2081 \u27f6 Y\u2082\nU : C\n\u22a2 \ud835\udfd9 ((X.fst \u2297 Y\u2081.fst) \u2297 U) \u2297\u226b\n      X.fst \u25c1 (Y\u2081.snd.\u03b2 U).hom \u2297\u226b ((X.snd.\u03b2 U).hom \u25b7 Y\u2081.fst \u226b (U \u2297 X.fst) \u25c1 f.f) \u2297\u226b \ud835\udfd9 (U \u2297 X.fst \u2297 Y\u2082.fst) =\n    ((\u03b1_ X.fst Y\u2081.fst U).hom \u226b\n        X.fst \u25c1 (Y\u2081.snd.\u03b2 U).hom \u226b (\u03b1_ X.fst U Y\u2081.fst).inv \u226b (X.snd.\u03b2 U).hom \u25b7 Y\u2081.fst \u226b (\u03b1_ U X.fst Y\u2081.fst).hom) \u226b\n      U \u25c1 X.fst \u25c1 f.f",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX Y\u2081 Y\u2082 : Center C\nf : Y\u2081 \u27f6 Y\u2082\nU : C\n\u22a2 \ud835\udfd9 ((X.fst \u2297 Y\u2081.fst) \u2297 U) \u2297\u226b\n      X.fst \u25c1 (Y\u2081.snd.\u03b2 U).hom \u2297\u226b ((X.fst \u2297 U) \u25c1 f.f \u226b (X.snd.\u03b2 U).hom \u25b7 Y\u2082.fst) \u2297\u226b \ud835\udfd9 (U \u2297 X.fst \u2297 Y\u2082.fst) =\n    ((\u03b1_ X.fst Y\u2081.fst U).hom \u226b\n        X.fst \u25c1 (Y\u2081.snd.\u03b2 U).hom \u226b (\u03b1_ X.fst U Y\u2081.fst).inv \u226b (X.snd.\u03b2 U).hom \u25b7 Y\u2081.fst \u226b (\u03b1_ U X.fst Y\u2081.fst).hom) \u226b\n      U \u25c1 X.fst \u25c1 f.f",
+              "tactic": "rw [whisker_exchange]"
+            },
+            {
+              "annotated_tactic": [
+                "\"coherence\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX Y\u2081 Y\u2082 : Center C\nf : Y\u2081 \u27f6 Y\u2082\nU : C\n\u22a2 \ud835\udfd9 ((X.fst \u2297 Y\u2081.fst) \u2297 U) \u2297\u226b\n      X.fst \u25c1 (Y\u2081.snd.\u03b2 U).hom \u2297\u226b ((X.snd.\u03b2 U).hom \u25b7 Y\u2081.fst \u226b (U \u2297 X.fst) \u25c1 f.f) \u2297\u226b \ud835\udfd9 (U \u2297 X.fst \u2297 Y\u2082.fst) =\n    ((\u03b1_ X.fst Y\u2081.fst U).hom \u226b\n        X.fst \u25c1 (Y\u2081.snd.\u03b2 U).hom \u226b (\u03b1_ X.fst U Y\u2081.fst).inv \u226b (X.snd.\u03b2 U).hom \u25b7 Y\u2081.fst \u226b (\u03b1_ U X.fst Y\u2081.fst).hom) \u226b\n      U \u25c1 X.fst \u25c1 f.f",
+              "tactic": "coherence"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Center.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Center.whiskerLeft_f",
+        "id": "CategoryTheory.Center.whiskerLeft_f",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            279,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Center.lean",
+          "full_name": "CategoryTheory.Center.whiskerLeft_f",
+          "start": [
+            278,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Center.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'coherence'",
+        "full_name": "CategoryTheory.Center.whiskerRight_comm",
+        "id": "CategoryTheory.Center.whiskerRight_comm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            201,
+            39
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Center.lean",
+          "full_name": "CategoryTheory.Center.whiskerRight_comm",
+          "start": [
+            188,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"dsimp only [<a>tensorObj_fst<\\/a>, <a>tensorObj_snd_\\u03b2<\\/a>, <a>Iso.trans_hom<\\/a>, <a>whiskerLeftIso_hom<\\/a>,\\n    <a>Iso.symm_hom<\\/a>, <a>whiskerRightIso_hom<\\/a>]\"",
+                "[{\"full_name\":\"CategoryTheory.Center.tensorObj_fst\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Center.lean\",\"def_pos\":[132,3],\"def_end_pos\":[132,8]},{\"full_name\":\"CategoryTheory.Center.tensorObj_snd_\\u03b2\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Center.lean\",\"def_pos\":[132,3],\"def_end_pos\":[132,8]},{\"full_name\":\"CategoryTheory.Iso.trans_hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[149,10],\"def_end_pos\":[149,15]},{\"full_name\":\"CategoryTheory.MonoidalCategory.whiskerLeftIso_hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Category.lean\",\"def_pos\":[337,3],\"def_end_pos\":[337,8]},{\"full_name\":\"CategoryTheory.Iso.symm_hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[100,9],\"def_end_pos\":[100,17]},{\"full_name\":\"CategoryTheory.MonoidalCategory.whiskerRightIso_hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Category.lean\",\"def_pos\":[365,3],\"def_end_pos\":[365,9]}]"
+              ],
+              "state_after": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX\u2081 X\u2082 : Center C\nf : X\u2081 \u27f6 X\u2082\nY : Center C\nU : C\n\u22a2 f.f \u25b7 Y.fst \u25b7 U \u226b\n      (\u03b1_ X\u2082.fst Y.fst U).hom \u226b\n        X\u2082.fst \u25c1 (Y.snd.\u03b2 U).hom \u226b (\u03b1_ X\u2082.fst U Y.fst).inv \u226b (X\u2082.snd.\u03b2 U).hom \u25b7 Y.fst \u226b (\u03b1_ U X\u2082.fst Y.fst).hom =\n    ((\u03b1_ X\u2081.fst Y.fst U).hom \u226b\n        X\u2081.fst \u25c1 (Y.snd.\u03b2 U).hom \u226b (\u03b1_ X\u2081.fst U Y.fst).inv \u226b (X\u2081.snd.\u03b2 U).hom \u25b7 Y.fst \u226b (\u03b1_ U X\u2081.fst Y.fst).hom) \u226b\n      U \u25c1 f.f \u25b7 Y.fst",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX\u2081 X\u2082 : Center C\nf : X\u2081 \u27f6 X\u2082\nY : Center C\nU : C\n\u22a2 f.f \u25b7 Y.fst \u25b7 U \u226b ((X\u2082.tensorObj Y).snd.\u03b2 U).hom = ((X\u2081.tensorObj Y).snd.\u03b2 U).hom \u226b U \u25c1 f.f \u25b7 Y.fst",
+              "tactic": "dsimp only [tensorObj_fst, tensorObj_snd_\u03b2, Iso.trans_hom, whiskerLeftIso_hom,\n  Iso.symm_hom, whiskerRightIso_hom]"
+            },
+            {
+              "annotated_tactic": [
+                "\"calc\\n    _ = \\ud835\\udfd9 _ \\u2297\\u226b\\n      (f.f \\u25b7 (Y.fst \\u2297 U) \\u226b X\\u2082.fst \\u25c1 (<a>HalfBraiding.\\u03b2<\\/a> Y.snd U).<a>hom<\\/a>) \\u2297\\u226b\\n        (<a>HalfBraiding.\\u03b2<\\/a> X\\u2082.snd U).<a>hom<\\/a> \\u25b7 Y.fst \\u2297\\u226b \\ud835\\udfd9 _ := by coherence\\n    _ = \\ud835\\udfd9 _ \\u2297\\u226b\\n      X\\u2081.fst \\u25c1 (<a>HalfBraiding.\\u03b2<\\/a> Y.snd U).<a>hom<\\/a> \\u2297\\u226b\\n        (f.f \\u25b7 U \\u226b (<a>HalfBraiding.\\u03b2<\\/a> X\\u2082.snd U).<a>hom<\\/a>) \\u25b7 Y.fst \\u2297\\u226b \\ud835\\udfd9 _ := by\\n      rw [\\u2190 <a>whisker_exchange<\\/a>]; coherence\\n    _ = _ := by rw [f.comm]; coherence\"",
+                "[{\"full_name\":\"CategoryTheory.HalfBraiding.\\u03b2\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Center.lean\",\"def_pos\":[56,3],\"def_end_pos\":[56,4]},{\"full_name\":\"CategoryTheory.Iso.hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[53,3],\"def_end_pos\":[53,6]},{\"full_name\":\"CategoryTheory.HalfBraiding.\\u03b2\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Center.lean\",\"def_pos\":[56,3],\"def_end_pos\":[56,4]},{\"full_name\":\"CategoryTheory.Iso.hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[53,3],\"def_end_pos\":[53,6]},{\"full_name\":\"CategoryTheory.HalfBraiding.\\u03b2\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Center.lean\",\"def_pos\":[56,3],\"def_end_pos\":[56,4]},{\"full_name\":\"CategoryTheory.Iso.hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[53,3],\"def_end_pos\":[53,6]},{\"full_name\":\"CategoryTheory.HalfBraiding.\\u03b2\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Center.lean\",\"def_pos\":[56,3],\"def_end_pos\":[56,4]},{\"full_name\":\"CategoryTheory.Iso.hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[53,3],\"def_end_pos\":[53,6]},{\"full_name\":\"CategoryTheory.MonoidalCategory.whisker_exchange\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Category.lean\",\"def_pos\":[278,9],\"def_end_pos\":[278,25]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX\u2081 X\u2082 : Center C\nf : X\u2081 \u27f6 X\u2082\nY : Center C\nU : C\n\u22a2 f.f \u25b7 Y.fst \u25b7 U \u226b\n      (\u03b1_ X\u2082.fst Y.fst U).hom \u226b\n        X\u2082.fst \u25c1 (Y.snd.\u03b2 U).hom \u226b (\u03b1_ X\u2082.fst U Y.fst).inv \u226b (X\u2082.snd.\u03b2 U).hom \u25b7 Y.fst \u226b (\u03b1_ U X\u2082.fst Y.fst).hom =\n    ((\u03b1_ X\u2081.fst Y.fst U).hom \u226b\n        X\u2081.fst \u25c1 (Y.snd.\u03b2 U).hom \u226b (\u03b1_ X\u2081.fst U Y.fst).inv \u226b (X\u2081.snd.\u03b2 U).hom \u25b7 Y.fst \u226b (\u03b1_ U X\u2081.fst Y.fst).hom) \u226b\n      U \u25c1 f.f \u25b7 Y.fst",
+              "tactic": "calc\n  _ = \ud835\udfd9 _ \u2297\u226b\n    (f.f \u25b7 (Y.fst \u2297 U) \u226b X\u2082.fst \u25c1 (HalfBraiding.\u03b2 Y.snd U).hom) \u2297\u226b\n      (HalfBraiding.\u03b2 X\u2082.snd U).hom \u25b7 Y.fst \u2297\u226b \ud835\udfd9 _ := by coherence\n  _ = \ud835\udfd9 _ \u2297\u226b\n    X\u2081.fst \u25c1 (HalfBraiding.\u03b2 Y.snd U).hom \u2297\u226b\n      (f.f \u25b7 U \u226b (HalfBraiding.\u03b2 X\u2082.snd U).hom) \u25b7 Y.fst \u2297\u226b \ud835\udfd9 _ := by\n    rw [\u2190 whisker_exchange]; coherence\n  _ = _ := by rw [f.comm]; coherence"
+            },
+            {
+              "annotated_tactic": [
+                "\"coherence\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX\u2081 X\u2082 : Center C\nf : X\u2081 \u27f6 X\u2082\nY : Center C\nU : C\n\u22a2 f.f \u25b7 Y.fst \u25b7 U \u226b\n      (\u03b1_ X\u2082.fst Y.fst U).hom \u226b\n        X\u2082.fst \u25c1 (Y.snd.\u03b2 U).hom \u226b (\u03b1_ X\u2082.fst U Y.fst).inv \u226b (X\u2082.snd.\u03b2 U).hom \u25b7 Y.fst \u226b (\u03b1_ U X\u2082.fst Y.fst).hom =\n    \ud835\udfd9 ((X\u2081.fst \u2297 Y.fst) \u2297 U) \u2297\u226b\n      (f.f \u25b7 (Y.fst \u2297 U) \u226b X\u2082.fst \u25c1 (Y.snd.\u03b2 U).hom) \u2297\u226b (X\u2082.snd.\u03b2 U).hom \u25b7 Y.fst \u2297\u226b \ud835\udfd9 (U \u2297 X\u2082.fst \u2297 Y.fst)",
+              "tactic": "coherence"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>whisker_exchange<\\/a>]\"",
+                "[{\"full_name\":\"CategoryTheory.MonoidalCategory.whisker_exchange\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Category.lean\",\"def_pos\":[278,9],\"def_end_pos\":[278,25]}]"
+              ],
+              "state_after": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX\u2081 X\u2082 : Center C\nf : X\u2081 \u27f6 X\u2082\nY : Center C\nU : C\n\u22a2 \ud835\udfd9 ((X\u2081.fst \u2297 Y.fst) \u2297 U) \u2297\u226b\n      (X\u2081.fst \u25c1 (Y.snd.\u03b2 U).hom \u226b f.f \u25b7 (U \u2297 Y.fst)) \u2297\u226b (X\u2082.snd.\u03b2 U).hom \u25b7 Y.fst \u2297\u226b \ud835\udfd9 (U \u2297 X\u2082.fst \u2297 Y.fst) =\n    \ud835\udfd9 ((X\u2081.fst \u2297 Y.fst) \u2297 U) \u2297\u226b\n      X\u2081.fst \u25c1 (Y.snd.\u03b2 U).hom \u2297\u226b (f.f \u25b7 U \u226b (X\u2082.snd.\u03b2 U).hom) \u25b7 Y.fst \u2297\u226b \ud835\udfd9 (U \u2297 X\u2082.fst \u2297 Y.fst)",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX\u2081 X\u2082 : Center C\nf : X\u2081 \u27f6 X\u2082\nY : Center C\nU : C\n\u22a2 \ud835\udfd9 ((X\u2081.fst \u2297 Y.fst) \u2297 U) \u2297\u226b\n      (f.f \u25b7 (Y.fst \u2297 U) \u226b X\u2082.fst \u25c1 (Y.snd.\u03b2 U).hom) \u2297\u226b (X\u2082.snd.\u03b2 U).hom \u25b7 Y.fst \u2297\u226b \ud835\udfd9 (U \u2297 X\u2082.fst \u2297 Y.fst) =\n    \ud835\udfd9 ((X\u2081.fst \u2297 Y.fst) \u2297 U) \u2297\u226b\n      X\u2081.fst \u25c1 (Y.snd.\u03b2 U).hom \u2297\u226b (f.f \u25b7 U \u226b (X\u2082.snd.\u03b2 U).hom) \u25b7 Y.fst \u2297\u226b \ud835\udfd9 (U \u2297 X\u2082.fst \u2297 Y.fst)",
+              "tactic": "rw [\u2190 whisker_exchange]"
+            },
+            {
+              "annotated_tactic": [
+                "\"coherence\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX\u2081 X\u2082 : Center C\nf : X\u2081 \u27f6 X\u2082\nY : Center C\nU : C\n\u22a2 \ud835\udfd9 ((X\u2081.fst \u2297 Y.fst) \u2297 U) \u2297\u226b\n      (X\u2081.fst \u25c1 (Y.snd.\u03b2 U).hom \u226b f.f \u25b7 (U \u2297 Y.fst)) \u2297\u226b (X\u2082.snd.\u03b2 U).hom \u25b7 Y.fst \u2297\u226b \ud835\udfd9 (U \u2297 X\u2082.fst \u2297 Y.fst) =\n    \ud835\udfd9 ((X\u2081.fst \u2297 Y.fst) \u2297 U) \u2297\u226b\n      X\u2081.fst \u25c1 (Y.snd.\u03b2 U).hom \u2297\u226b (f.f \u25b7 U \u226b (X\u2082.snd.\u03b2 U).hom) \u25b7 Y.fst \u2297\u226b \ud835\udfd9 (U \u2297 X\u2082.fst \u2297 Y.fst)",
+              "tactic": "coherence"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [f.comm]\"",
+                "[]"
+              ],
+              "state_after": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX\u2081 X\u2082 : Center C\nf : X\u2081 \u27f6 X\u2082\nY : Center C\nU : C\n\u22a2 \ud835\udfd9 ((X\u2081.fst \u2297 Y.fst) \u2297 U) \u2297\u226b\n      X\u2081.fst \u25c1 (Y.snd.\u03b2 U).hom \u2297\u226b ((X\u2081.snd.\u03b2 U).hom \u226b U \u25c1 f.f) \u25b7 Y.fst \u2297\u226b \ud835\udfd9 (U \u2297 X\u2082.fst \u2297 Y.fst) =\n    ((\u03b1_ X\u2081.fst Y.fst U).hom \u226b\n        X\u2081.fst \u25c1 (Y.snd.\u03b2 U).hom \u226b (\u03b1_ X\u2081.fst U Y.fst).inv \u226b (X\u2081.snd.\u03b2 U).hom \u25b7 Y.fst \u226b (\u03b1_ U X\u2081.fst Y.fst).hom) \u226b\n      U \u25c1 f.f \u25b7 Y.fst",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX\u2081 X\u2082 : Center C\nf : X\u2081 \u27f6 X\u2082\nY : Center C\nU : C\n\u22a2 \ud835\udfd9 ((X\u2081.fst \u2297 Y.fst) \u2297 U) \u2297\u226b\n      X\u2081.fst \u25c1 (Y.snd.\u03b2 U).hom \u2297\u226b (f.f \u25b7 U \u226b (X\u2082.snd.\u03b2 U).hom) \u25b7 Y.fst \u2297\u226b \ud835\udfd9 (U \u2297 X\u2082.fst \u2297 Y.fst) =\n    ((\u03b1_ X\u2081.fst Y.fst U).hom \u226b\n        X\u2081.fst \u25c1 (Y.snd.\u03b2 U).hom \u226b (\u03b1_ X\u2081.fst U Y.fst).inv \u226b (X\u2081.snd.\u03b2 U).hom \u25b7 Y.fst \u226b (\u03b1_ U X\u2081.fst Y.fst).hom) \u226b\n      U \u25c1 f.f \u25b7 Y.fst",
+              "tactic": "rw [f.comm]"
+            },
+            {
+              "annotated_tactic": [
+                "\"coherence\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nX\u2081 X\u2082 : Center C\nf : X\u2081 \u27f6 X\u2082\nY : Center C\nU : C\n\u22a2 \ud835\udfd9 ((X\u2081.fst \u2297 Y.fst) \u2297 U) \u2297\u226b\n      X\u2081.fst \u25c1 (Y.snd.\u03b2 U).hom \u2297\u226b ((X\u2081.snd.\u03b2 U).hom \u226b U \u25c1 f.f) \u25b7 Y.fst \u2297\u226b \ud835\udfd9 (U \u2297 X\u2082.fst \u2297 Y.fst) =\n    ((\u03b1_ X\u2081.fst Y.fst U).hom \u226b\n        X\u2081.fst \u25c1 (Y.snd.\u03b2 U).hom \u226b (\u03b1_ X\u2081.fst U Y.fst).inv \u226b (X\u2081.snd.\u03b2 U).hom \u25b7 Y.fst \u226b (\u03b1_ U X\u2081.fst Y.fst).hom) \u226b\n      U \u25c1 f.f \u25b7 Y.fst",
+              "tactic": "coherence"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Center.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CategoryTheory.Center.whiskerRight_f",
+        "id": "CategoryTheory.Center.whiskerRight_f",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            283,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Center.lean",
+          "full_name": "CategoryTheory.Center.whiskerRight_f",
+          "start": [
+            282,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Center.lean"
+      }
+    ],
+    "input_proofs": 26,
+    "input_units": 2,
+    "proofs": 13,
+    "published_proofs": 13,
+    "published_transitions": 21,
+    "replay_failures": [],
+    "transitions": 21,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000729-0000-2e6bfc343a374bc5.parquet",
+      "sha256": "2e6bfc343a374bc5ce3c7c94646d4b47894413067c9df98544565bfe6943758d",
+      "bytes": 71309,
+      "rows": 14,
+      "revision": "a498fa87b358e6eb392b8a125474b05531d1b03e"
+    },
+    {
+      "path": "data/dev/mathlib-000729-0000-a79640b4b44159be.parquet",
+      "sha256": "a79640b4b44159beae2b35ddf2d714efaca56725ce23cf44b4c55d73fad43086",
+      "bytes": 49932,
+      "rows": 3,
+      "revision": "a498fa87b358e6eb392b8a125474b05531d1b03e"
+    },
+    {
+      "path": "data/internal_test/mathlib-000729-0000-e031a439ec9d0441.parquet",
+      "sha256": "e031a439ec9d044101f11b1f39bc708985ed62fb0733309160d045fa86e66ee9",
+      "bytes": 50427,
+      "rows": 4,
+      "revision": "a498fa87b358e6eb392b8a125474b05531d1b03e"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:CategoryTheory.Center.associator_inv_f",
+    "mathlib:CategoryTheory.Center.ext",
+    "mathlib:CategoryTheory.Center.leftUnitor_inv_f",
+    "mathlib:CategoryTheory.Center.rightUnitor_inv_f",
+    "mathlib:CategoryTheory.MonoidalCategory.id_tensor_rightUnitor_inv",
+    "mathlib:CategoryTheory.MonoidalCategory.leftUnitor_tensor'",
+    "mathlib:CategoryTheory.MonoidalCategory.leftUnitor_tensor''",
+    "mathlib:CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv'",
+    "mathlib:CategoryTheory.MonoidalCategory.pentagon_hom_inv",
+    "mathlib:CategoryTheory.MonoidalCategory.pentagon_inv_hom",
+    "mathlib:CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom",
+    "mathlib:CategoryTheory.MonoidalCategory.unitors_equal",
+    "mathlib:CategoryTheory.MonoidalCategory.unitors_inv_equal"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Monoidal/Center.lean\",null,null,\"CategoryTheory.Center.associator_inv_f\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Monoidal/Center.lean\",null,null,\"CategoryTheory.Center.ext\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Monoidal/Center.lean\",null,null,\"CategoryTheory.Center.leftUnitor_inv_f\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Monoidal/Center.lean\",null,null,\"CategoryTheory.Center.rightUnitor_inv_f\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Monoidal/CoherenceLemmas.lean\",null,null,\"CategoryTheory.MonoidalCategory.id_tensor_rightUnitor_inv\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Monoidal/CoherenceLemmas.lean\",null,null,\"CategoryTheory.MonoidalCategory.leftUnitor_tensor'\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Monoidal/CoherenceLemmas.lean\",null,null,\"CategoryTheory.MonoidalCategory.leftUnitor_tensor''\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Monoidal/CoherenceLemmas.lean\",null,null,\"CategoryTheory.MonoidalCategory.leftUnitor_tensor_inv'\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Monoidal/CoherenceLemmas.lean\",null,null,\"CategoryTheory.MonoidalCategory.pentagon_hom_inv\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Monoidal/CoherenceLemmas.lean\",null,null,\"CategoryTheory.MonoidalCategory.pentagon_inv_hom\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Monoidal/CoherenceLemmas.lean\",null,null,\"CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Monoidal/CoherenceLemmas.lean\",null,null,\"CategoryTheory.MonoidalCategory.unitors_equal\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Monoidal/CoherenceLemmas.lean\",null,null,\"CategoryTheory.MonoidalCategory.unitors_inv_equal\"]"
+  ]
+}

manifests/batches/mathlib/000730.json

@@ -0,0 +1,547 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000730",
+  "batch_fingerprint": "4452138ca20d06a0ec23abd3a2e6260b5789eeaa3b4344156ee8792f3fc269ad",
+  "evidence": {
+    "batch_fingerprint": "4452138ca20d06a0ec23abd3a2e6260b5789eeaa3b4344156ee8792f3fc269ad",
+    "batch_outcome": "all_inputs_failed_with_evidence",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CommMon_.comp'",
+        "id": "CommMon_.comp'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            76,
+            99
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/CommMon_.lean",
+          "full_name": "CommMon_.comp'",
+          "start": [
+            74,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/CommMon_.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CommMon_.comp_hom",
+        "id": "CommMon_.comp_hom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            59,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/CommMon_.lean",
+          "full_name": "CommMon_.comp_hom",
+          "start": [
+            57,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/CommMon_.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CommMon_.forget\u2082_Mon_map_hom",
+        "id": "CommMon_.forget\u2082_Mon_map_hom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            106,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/CommMon_.lean",
+          "full_name": "CommMon_.forget\u2082_Mon_map_hom",
+          "start": [
+            105,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/CommMon_.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CommMon_.forget\u2082_Mon_obj_mul",
+        "id": "CommMon_.forget\u2082_Mon_obj_mul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            100,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/CommMon_.lean",
+          "full_name": "CommMon_.forget\u2082_Mon_obj_mul",
+          "start": [
+            99,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/CommMon_.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CommMon_.forget\u2082_Mon_obj_one",
+        "id": "CommMon_.forget\u2082_Mon_obj_one",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            94,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/CommMon_.lean",
+          "full_name": "CommMon_.forget\u2082_Mon_obj_one",
+          "start": [
+            93,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/CommMon_.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CommMon_.hom_ext",
+        "id": "CommMon_.hom_ext",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            67,
+            21
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/CommMon_.lean",
+          "full_name": "CommMon_.hom_ext",
+          "start": [
+            65,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/CommMon_.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CommMon_.id_hom",
+        "id": "CommMon_.id_hom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            52,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/CommMon_.lean",
+          "full_name": "CommMon_.id_hom",
+          "start": [
+            51,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/CommMon_.lean"
+      },
+      {
+        "full_name": "Comon_.comp_hom'",
+        "id": "Comon_.comp_hom'",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            118,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Comon_.lean",
+          "full_name": "Comon_.comp_hom'",
+          "start": [
+            117,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Comon_.lean"
+      },
+      {
+        "full_name": "Comon_.comul_assoc_flip",
+        "id": "Comon_.comul_assoc_flip",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            82,
+            23
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Comon_.lean",
+          "full_name": "Comon_.comul_assoc_flip",
+          "start": [
+            80,
+            12
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"simp [\\u2190 <a>comul_assoc<\\/a>]\"",
+                "[{\"full_name\":\"Comon_.comul_assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Comon_.lean\",\"def_pos\":[47,3],\"def_end_pos\":[47,14]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nM : Comon_ C\n\u22a2 M.comul \u226b M.comul \u25b7 M.X = M.comul \u226b M.X \u25c1 M.comul \u226b (\u03b1_ M.X M.X M.X).inv",
+              "tactic": "simp [\u2190 comul_assoc]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Comon_.lean"
+      },
+      {
+        "full_name": "Comon_.comul_counit_hom",
+        "id": "Comon_.comul_counit_hom",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            78,
+            70
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Comon_.lean",
+          "full_name": "Comon_.comul_counit_hom",
+          "start": [
+            77,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [<a>rightUnitor_inv_naturality<\\/a>, <a>tensorHom_def'<\\/a>, <a>comul_counit_assoc<\\/a>]\"",
+                "[{\"full_name\":\"CategoryTheory.MonoidalCategory.rightUnitor_inv_naturality\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Category.lean\",\"def_pos\":[504,9],\"def_end_pos\":[504,35]},{\"full_name\":\"CategoryTheory.MonoidalCategory.tensorHom_def'\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Category.lean\",\"def_pos\":[283,9],\"def_end_pos\":[283,23]},{\"full_name\":\"Comon_.comul_counit_assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Comon_.lean\",\"def_pos\":[49,12],\"def_end_pos\":[49,34]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nM : Comon_ C\nZ : C\nf : M.X \u27f6 Z\n\u22a2 M.comul \u226b (f \u2297 M.counit) = f \u226b (\u03c1_ Z).inv",
+              "tactic": "rw [rightUnitor_inv_naturality, tensorHom_def', comul_counit_assoc]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Comon_.lean"
+      },
+      {
+        "full_name": "Comon_.counit_comul_hom",
+        "id": "Comon_.counit_comul_hom",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            74,
+            68
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Comon_.lean",
+          "full_name": "Comon_.counit_comul_hom",
+          "start": [
+            73,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [<a>leftUnitor_inv_naturality<\\/a>, <a>tensorHom_def<\\/a>, <a>counit_comul_assoc<\\/a>]\"",
+                "[{\"full_name\":\"CategoryTheory.MonoidalCategory.leftUnitor_inv_naturality\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Category.lean\",\"def_pos\":[494,9],\"def_end_pos\":[494,34]},{\"full_name\":\"CategoryTheory.MonoidalCategory.tensorHom_def\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Category.lean\",\"def_pos\":[159,3],\"def_end_pos\":[159,16]},{\"full_name\":\"Comon_.counit_comul_assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Comon_.lean\",\"def_pos\":[49,12],\"def_end_pos\":[49,34]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b9 : Category.{v\u2081, u\u2081} C\ninst\u271d : MonoidalCategory C\nM : Comon_ C\nZ : C\nf : M.X \u27f6 Z\n\u22a2 M.comul \u226b (M.counit \u2297 f) = f \u226b (\u03bb_ Z).inv",
+              "tactic": "rw [leftUnitor_inv_naturality, tensorHom_def, counit_comul_assoc]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Comon_.lean"
+      },
+      {
+        "full_name": "Comon_.ext",
+        "id": "Comon_.ext",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            112,
+            93
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Comon_.lean",
+          "full_name": "Comon_.ext",
+          "start": [
+            112,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Comon_.lean"
+      },
+      {
+        "full_name": "Comon_.forgetMonoidal_toFunctor",
+        "id": "Comon_.forgetMonoidal_toFunctor",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            286,
+            90
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Comon_.lean",
+          "full_name": "Comon_.forgetMonoidal_toFunctor",
+          "start": [
+            286,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Comon_.lean"
+      },
+      {
+        "full_name": "Comon_.forgetMonoidal_\u03b5",
+        "id": "Comon_.forgetMonoidal_\u03b5",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            287,
+            74
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Comon_.lean",
+          "full_name": "Comon_.forgetMonoidal_\u03b5",
+          "start": [
+            287,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Comon_.lean"
+      },
+      {
+        "full_name": "Comon_.forgetMonoidal_\u03bc",
+        "id": "Comon_.forgetMonoidal_\u03bc",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            288,
+            100
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Comon_.lean",
+          "full_name": "Comon_.forgetMonoidal_\u03bc",
+          "start": [
+            288,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Comon_.lean"
+      },
+      {
+        "full_name": "Comon_.id_hom'",
+        "id": "Comon_.id_hom'",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            114,
+            76
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Comon_.lean",
+          "full_name": "Comon_.id_hom'",
+          "start": [
+            114,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Comon_.lean"
+      },
+      {
+        "full_name": "Comon_.tensorObj_X",
+        "id": "Comon_.tensorObj_X",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            251,
+            68
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Comon_.lean",
+          "full_name": "Comon_.tensorObj_X",
+          "start": [
+            251,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Comon_.lean"
+      },
+      {
+        "full_name": "Comon_.tensorObj_comul",
+        "id": "Comon_.tensorObj_comul",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            278,
+            54
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Comon_.lean",
+          "full_name": "Comon_.tensorObj_comul",
+          "start": [
+            271,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [<a>tensorObj_comul'<\\/a>]\"",
+                "[{\"full_name\":\"Comon_.tensorObj_comul'\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Comon_.lean\",\"def_pos\":[261,9],\"def_end_pos\":[261,25]}]"
+              ],
+              "state_after": "C : Type u\u2081\ninst\u271d\u00b2 : Category.{v\u2081, u\u2081} C\ninst\u271d\u00b9 : MonoidalCategory C\nM : Comon_ C\ninst\u271d : BraidedCategory C\nA B : Comon_ C\n\u22a2 (A.comul \u2297 B.comul) \u226b (tensor_\u03bc C\u1d52\u1d56 ({ unop := A.X }, { unop := B.X }) ({ unop := A.X }, { unop := B.X })).unop =\n    (A.comul \u2297 B.comul) \u226b tensor_\u03bc C (A.X, A.X) (B.X, B.X)",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b2 : Category.{v\u2081, u\u2081} C\ninst\u271d\u00b9 : MonoidalCategory C\nM : Comon_ C\ninst\u271d : BraidedCategory C\nA B : Comon_ C\n\u22a2 (A \u2297 B).comul = (A.comul \u2297 B.comul) \u226b tensor_\u03bc C (A.X, A.X) (B.X, B.X)",
+              "tactic": "rw [tensorObj_comul']"
+            },
+            {
+              "annotated_tactic": [
+                "\"congr\"",
+                "[]"
+              ],
+              "state_after": "case e_a.e_f\nC : Type u\u2081\ninst\u271d\u00b2 : Category.{v\u2081, u\u2081} C\ninst\u271d\u00b9 : MonoidalCategory C\nM : Comon_ C\ninst\u271d : BraidedCategory C\nA B : Comon_ C\n\u22a2 tensor_\u03bc C\u1d52\u1d56 ({ unop := A.X }, { unop := B.X }) ({ unop := A.X }, { unop := B.X }) =\n    {\n      unop :=\n        (\u03b1_ (A.X, A.X).1 (A.X, A.X).2 ((B.X, B.X).1 \u2297 (B.X, B.X).2)).hom \u226b\n          (A.X, A.X).1 \u25c1 (\u03b1_ (A.X, A.X).2 (B.X, B.X).1 (B.X, B.X).2).inv \u226b\n            (A.X, A.X).1 \u25c1 (\u03b2_ (A.X, A.X).2 (B.X, B.X).1).hom \u25b7 (B.X, B.X).2 \u226b\n              (A.X, A.X).1 \u25c1 (\u03b1_ (B.X, B.X).1 (A.X, A.X).2 (B.X, B.X).2).hom \u226b\n                (\u03b1_ (A.X, A.X).1 (B.X, B.X).1 ((A.X, A.X).2 \u2297 (B.X, B.X).2)).inv }",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b2 : Category.{v\u2081, u\u2081} C\ninst\u271d\u00b9 : MonoidalCategory C\nM : Comon_ C\ninst\u271d : BraidedCategory C\nA B : Comon_ C\n\u22a2 (A.comul \u2297 B.comul) \u226b (tensor_\u03bc C\u1d52\u1d56 ({ unop := A.X }, { unop := B.X }) ({ unop := A.X }, { unop := B.X })).unop =\n    (A.comul \u2297 B.comul) \u226b tensor_\u03bc C (A.X, A.X) (B.X, B.X)",
+              "tactic": "congr"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>tensor_\\u03bc<\\/a>, <a>unop_tensorObj<\\/a>, <a>unop_op<\\/a>]\"",
+                "[{\"full_name\":\"CategoryTheory.tensor_\\u03bc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Braided\\/Basic.lean\",\"def_pos\":[538,5],\"def_end_pos\":[538,13]},{\"full_name\":\"CategoryTheory.unop_tensorObj\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Opposite.lean\",\"def_pos\":[196,15],\"def_end_pos\":[196,29]},{\"full_name\":\"Opposite.unop_op\",\"def_path\":\"Mathlib\\/Data\\/Opposite.lean\",\"def_pos\":[66,9],\"def_end_pos\":[66,16]}]"
+              ],
+              "state_after": "case e_a.e_f\nC : Type u\u2081\ninst\u271d\u00b2 : Category.{v\u2081, u\u2081} C\ninst\u271d\u00b9 : MonoidalCategory C\nM : Comon_ C\ninst\u271d : BraidedCategory C\nA B : Comon_ C\n\u22a2 (\u03b1_ { unop := A.X } { unop := B.X } ({ unop := A.X } \u2297 { unop := B.X })).hom \u226b\n      { unop := A.X } \u25c1 (\u03b1_ { unop := B.X } { unop := A.X } { unop := B.X }).inv \u226b\n        { unop := A.X } \u25c1 (\u03b2_ { unop := B.X } { unop := A.X }).hom \u25b7 { unop := B.X } \u226b\n          { unop := A.X } \u25c1 (\u03b1_ { unop := A.X } { unop := B.X } { unop := B.X }).hom \u226b\n            (\u03b1_ { unop := A.X } { unop := A.X } ({ unop := B.X } \u2297 { unop := B.X })).inv =\n    {\n      unop :=\n        (\u03b1_ A.X A.X (B.X \u2297 B.X)).hom \u226b\n          A.X \u25c1 (\u03b1_ A.X B.X B.X).inv \u226b\n            A.X \u25c1 (\u03b2_ A.X B.X).hom \u25b7 B.X \u226b A.X \u25c1 (\u03b1_ B.X A.X B.X).hom \u226b (\u03b1_ A.X B.X (A.X \u2297 B.X)).inv }",
+              "state_before": "case e_a.e_f\nC : Type u\u2081\ninst\u271d\u00b2 : Category.{v\u2081, u\u2081} C\ninst\u271d\u00b9 : MonoidalCategory C\nM : Comon_ C\ninst\u271d : BraidedCategory C\nA B : Comon_ C\n\u22a2 tensor_\u03bc C\u1d52\u1d56 ({ unop := A.X }, { unop := B.X }) ({ unop := A.X }, { unop := B.X }) =\n    {\n      unop :=\n        (\u03b1_ (A.X, A.X).1 (A.X, A.X).2 ((B.X, B.X).1 \u2297 (B.X, B.X).2)).hom \u226b\n          (A.X, A.X).1 \u25c1 (\u03b1_ (A.X, A.X).2 (B.X, B.X).1 (B.X, B.X).2).inv \u226b\n            (A.X, A.X).1 \u25c1 (\u03b2_ (A.X, A.X).2 (B.X, B.X).1).hom \u25b7 (B.X, B.X).2 \u226b\n              (A.X, A.X).1 \u25c1 (\u03b1_ (B.X, B.X).1 (A.X, A.X).2 (B.X, B.X).2).hom \u226b\n                (\u03b1_ (A.X, A.X).1 (B.X, B.X).1 ((A.X, A.X).2 \u2297 (B.X, B.X).2)).inv }",
+              "tactic": "simp only [tensor_\u03bc, unop_tensorObj, unop_op]"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Quiver.Hom.unop_inj<\\/a>\"",
+                "[{\"full_name\":\"Quiver.Hom.unop_inj\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Opposites.lean\",\"def_pos\":[42,9],\"def_end_pos\":[42,28]}]"
+              ],
+              "state_after": "case e_a.e_f.a\nC : Type u\u2081\ninst\u271d\u00b2 : Category.{v\u2081, u\u2081} C\ninst\u271d\u00b9 : MonoidalCategory C\nM : Comon_ C\ninst\u271d : BraidedCategory C\nA B : Comon_ C\n\u22a2 ((\u03b1_ { unop := A.X } { unop := B.X } ({ unop := A.X } \u2297 { unop := B.X })).hom \u226b\n        { unop := A.X } \u25c1 (\u03b1_ { unop := B.X } { unop := A.X } { unop := B.X }).inv \u226b\n          { unop := A.X } \u25c1 (\u03b2_ { unop := B.X } { unop := A.X }).hom \u25b7 { unop := B.X } \u226b\n            { unop := A.X } \u25c1 (\u03b1_ { unop := A.X } { unop := B.X } { unop := B.X }).hom \u226b\n              (\u03b1_ { unop := A.X } { unop := A.X } ({ unop := B.X } \u2297 { unop := B.X })).inv).unop =\n    Quiver.Hom.unop\n      {\n        unop :=\n          (\u03b1_ A.X A.X (B.X \u2297 B.X)).hom \u226b\n            A.X \u25c1 (\u03b1_ A.X B.X B.X).inv \u226b\n              A.X \u25c1 (\u03b2_ A.X B.X).hom \u25b7 B.X \u226b A.X \u25c1 (\u03b1_ B.X A.X B.X).hom \u226b (\u03b1_ A.X B.X (A.X \u2297 B.X)).inv }",
+              "state_before": "case e_a.e_f\nC : Type u\u2081\ninst\u271d\u00b2 : Category.{v\u2081, u\u2081} C\ninst\u271d\u00b9 : MonoidalCategory C\nM : Comon_ C\ninst\u271d : BraidedCategory C\nA B : Comon_ C\n\u22a2 (\u03b1_ { unop := A.X } { unop := B.X } ({ unop := A.X } \u2297 { unop := B.X })).hom \u226b\n      { unop := A.X } \u25c1 (\u03b1_ { unop := B.X } { unop := A.X } { unop := B.X }).inv \u226b\n        { unop := A.X } \u25c1 (\u03b2_ { unop := B.X } { unop := A.X }).hom \u25b7 { unop := B.X } \u226b\n          { unop := A.X } \u25c1 (\u03b1_ { unop := A.X } { unop := B.X } { unop := B.X }).hom \u226b\n            (\u03b1_ { unop := A.X } { unop := A.X } ({ unop := B.X } \u2297 { unop := B.X })).inv =\n    {\n      unop :=\n        (\u03b1_ A.X A.X (B.X \u2297 B.X)).hom \u226b\n          A.X \u25c1 (\u03b1_ A.X B.X B.X).inv \u226b\n            A.X \u25c1 (\u03b2_ A.X B.X).hom \u25b7 B.X \u226b A.X \u25c1 (\u03b1_ B.X A.X B.X).hom \u226b (\u03b1_ A.X B.X (A.X \u2297 B.X)).inv }",
+              "tactic": "apply Quiver.Hom.unop_inj"
+            },
+            {
+              "annotated_tactic": [
+                "\"dsimp [<a>op_tensorObj<\\/a>, <a>op_associator<\\/a>]\"",
+                "[{\"full_name\":\"CategoryTheory.op_tensorObj\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Opposite.lean\",\"def_pos\":[195,15],\"def_end_pos\":[195,27]},{\"full_name\":\"CategoryTheory.op_associator\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Monoidal\\/Opposite.lean\",\"def_pos\":[216,15],\"def_end_pos\":[216,28]}]"
+              ],
+              "state_after": "case e_a.e_f.a\nC : Type u\u2081\ninst\u271d\u00b2 : Category.{v\u2081, u\u2081} C\ninst\u271d\u00b9 : MonoidalCategory C\nM : Comon_ C\ninst\u271d : BraidedCategory C\nA B : Comon_ C\n\u22a2 ((((\u03b1_ A.X A.X (B.X \u2297 B.X)).hom \u226b A.X \u25c1 (\u03b1_ A.X B.X B.X).inv) \u226b A.X \u25c1 (\u03b2_ A.X B.X).hom \u25b7 B.X) \u226b\n        A.X \u25c1 (\u03b1_ B.X A.X B.X).hom) \u226b\n      (\u03b1_ A.X B.X (A.X \u2297 B.X)).inv =\n    (\u03b1_ A.X A.X (B.X \u2297 B.X)).hom \u226b\n      A.X \u25c1 (\u03b1_ A.X B.X B.X).inv \u226b\n        A.X \u25c1 (\u03b2_ A.X B.X).hom \u25b7 B.X \u226b A.X \u25c1 (\u03b1_ B.X A.X B.X).hom \u226b (\u03b1_ A.X B.X (A.X \u2297 B.X)).inv",
+              "state_before": "case e_a.e_f.a\nC : Type u\u2081\ninst\u271d\u00b2 : Category.{v\u2081, u\u2081} C\ninst\u271d\u00b9 : MonoidalCategory C\nM : Comon_ C\ninst\u271d : BraidedCategory C\nA B : Comon_ C\n\u22a2 ((\u03b1_ { unop := A.X } { unop := B.X } ({ unop := A.X } \u2297 { unop := B.X })).hom \u226b\n        { unop := A.X } \u25c1 (\u03b1_ { unop := B.X } { unop := A.X } { unop := B.X }).inv \u226b\n          { unop := A.X } \u25c1 (\u03b2_ { unop := B.X } { unop := A.X }).hom \u25b7 { unop := B.X } \u226b\n            { unop := A.X } \u25c1 (\u03b1_ { unop := A.X } { unop := B.X } { unop := B.X }).hom \u226b\n              (\u03b1_ { unop := A.X } { unop := A.X } ({ unop := B.X } \u2297 { unop := B.X })).inv).unop =\n    Quiver.Hom.unop\n      {\n        unop :=\n          (\u03b1_ A.X A.X (B.X \u2297 B.X)).hom \u226b\n            A.X \u25c1 (\u03b1_ A.X B.X B.X).inv \u226b\n              A.X \u25c1 (\u03b2_ A.X B.X).hom \u25b7 B.X \u226b A.X \u25c1 (\u03b1_ B.X A.X B.X).hom \u226b (\u03b1_ A.X B.X (A.X \u2297 B.X)).inv }",
+              "tactic": "dsimp [op_tensorObj, op_associator]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Category.assoc<\\/a>, <a>Category.assoc<\\/a>, <a>Category.assoc<\\/a>]\"",
+                "[{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case e_a.e_f.a\nC : Type u\u2081\ninst\u271d\u00b2 : Category.{v\u2081, u\u2081} C\ninst\u271d\u00b9 : MonoidalCategory C\nM : Comon_ C\ninst\u271d : BraidedCategory C\nA B : Comon_ C\n\u22a2 ((((\u03b1_ A.X A.X (B.X \u2297 B.X)).hom \u226b A.X \u25c1 (\u03b1_ A.X B.X B.X).inv) \u226b A.X \u25c1 (\u03b2_ A.X B.X).hom \u25b7 B.X) \u226b\n        A.X \u25c1 (\u03b1_ B.X A.X B.X).hom) \u226b\n      (\u03b1_ A.X B.X (A.X \u2297 B.X)).inv =\n    (\u03b1_ A.X A.X (B.X \u2297 B.X)).hom \u226b\n      A.X \u25c1 (\u03b1_ A.X B.X B.X).inv \u226b\n        A.X \u25c1 (\u03b2_ A.X B.X).hom \u25b7 B.X \u226b A.X \u25c1 (\u03b1_ B.X A.X B.X).hom \u226b (\u03b1_ A.X B.X (A.X \u2297 B.X)).inv",
+              "tactic": "rw [Category.assoc, Category.assoc, Category.assoc]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Comon_.lean"
+      },
+      {
+        "full_name": "Comon_.tensorObj_comul'",
+        "id": "Comon_.tensorObj_comul'",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            264,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Comon_.lean",
+          "full_name": "Comon_.tensorObj_comul'",
+          "start": [
+            261,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rfl\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C : Type u\u2081\ninst\u271d\u00b2 : Category.{v\u2081, u\u2081} C\ninst\u271d\u00b9 : MonoidalCategory C\nM : Comon_ C\ninst\u271d : BraidedCategory C\nA B : Comon_ C\n\u22a2 (A \u2297 B).comul =\n    (A.comul \u2297 B.comul) \u226b (tensor_\u03bc C\u1d52\u1d56 ({ unop := A.X }, { unop := B.X }) ({ unop := A.X }, { unop := B.X })).unop",
+              "tactic": "rfl"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Comon_.lean"
+      },
+      {
+        "full_name": "Comon_.tensorObj_counit",
+        "id": "Comon_.tensorObj_counit",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            254,
+            6
+          ],
+          "file_path": "Mathlib/CategoryTheory/Monoidal/Comon_.lean",
+          "full_name": "Comon_.tensorObj_counit",
+          "start": [
+            253,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/CategoryTheory/Monoidal/Comon_.lean"
+      }
+    ],
+    "input_proofs": 20,
+    "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/numina/001481.json

@@ -0,0 +1,51 @@
+{
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+    "proofs": 5,
+    "published_proofs": 5,
+    "published_transitions": 22,
+    "replay_failures": [],
+    "trace_mode": "bundle",
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+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
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+    {
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+    "numina:1356d3a6-113b-53dc-bd11-461fe7923419",
+    "numina:4debfe05-d174-5ed1-b8d0-9512ab8c8fed",
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manifests/batches/numina/001483.json

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manifests/batches/numina/001484.json

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manifests/batches/numina/001485.json

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manifests/batches/numina/001486.json

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manifests/batches/numina/001488.json

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