Record 23 verified HPC batch manifests

manifests/batches/mathlib/001636.json

@@ -0,0 +1,609 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001636",
+  "batch_fingerprint": "9c6124f524d2663ab28916e8f78e931a0a74ba1baf65f7af1019bbcf174bda0c",
+  "evidence": {
+    "batch_fingerprint": "9c6124f524d2663ab28916e8f78e931a0a74ba1baf65f7af1019bbcf174bda0c",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Representation.apply_eq_self",
+        "id": "Representation.apply_eq_self",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            84,
+            27
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Basic.lean",
+          "full_name": "Representation.apply_eq_self",
+          "start": [
+            82,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Representation.asAlgebraHom_def",
+        "id": "Representation.asAlgebraHom_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            101,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Basic.lean",
+          "full_name": "Representation.asAlgebraHom_def",
+          "start": [
+            100,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Representation.asModuleEquiv_map_smul",
+        "id": "Representation.asModuleEquiv_map_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            154,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Basic.lean",
+          "full_name": "Representation.asModuleEquiv_map_smul",
+          "start": [
+            152,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Representation.dual_apply",
+        "id": "Representation.dual_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            491,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Basic.lean",
+          "full_name": "Representation.dual_apply",
+          "start": [
+            490,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Representation.linHom_apply",
+        "id": "Representation.linHom_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            466,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Basic.lean",
+          "full_name": "Representation.linHom_apply",
+          "start": [
+            465,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Representation.ofDistribMulAction_apply_apply",
+        "id": "Representation.ofDistribMulAction_apply_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            313,
+            48
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Basic.lean",
+          "full_name": "Representation.ofDistribMulAction_apply_apply",
+          "start": [
+            312,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Basic.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'intro h\u2081 h\u2082'",
+        "full_name": "Representation.ofMulAction_apply",
+        "id": "Representation.ofMulAction_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            343,
+            85
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Basic.lean",
+          "full_name": "Representation.ofMulAction_apply",
+          "start": [
+            335,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"conv_lhs => rw [\\u2190 <a>smul_inv_smul<\\/a> g h]\"",
+                "[{\"full_name\":\"smul_inv_smul\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Group.lean\",\"def_pos\":[35,9],\"def_end_pos\":[35,22]}]"
+              ],
+              "state_after": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2074 : CommSemiring k\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : AddCommMonoid V\ninst\u271d\u00b9 : Module k V\n\u03c1 : Representation k G V\nH : Type u_4\ninst\u271d : MulAction G H\ng : G\nf : H \u2192\u2080 k\nh : H\n\u22a2 (((ofMulAction k G H) g) f) (g \u2022 g\u207b\u00b9 \u2022 h) = f (g\u207b\u00b9 \u2022 h)",
+              "state_before": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2074 : CommSemiring k\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : AddCommMonoid V\ninst\u271d\u00b9 : Module k V\n\u03c1 : Representation k G V\nH : Type u_4\ninst\u271d : MulAction G H\ng : G\nf : H \u2192\u2080 k\nh : H\n\u22a2 (((ofMulAction k G H) g) f) h = f (g\u207b\u00b9 \u2022 h)",
+              "tactic": "conv_lhs => rw [\u2190 smul_inv_smul g h]"
+            },
+            {
+              "annotated_tactic": [
+                "\"let h' := g\\u207b\\u00b9 \\u2022 h\"",
+                "[]"
+              ],
+              "state_after": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2074 : CommSemiring k\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : AddCommMonoid V\ninst\u271d\u00b9 : Module k V\n\u03c1 : Representation k G V\nH : Type u_4\ninst\u271d : MulAction G H\ng : G\nf : H \u2192\u2080 k\nh : H\nh' : H := g\u207b\u00b9 \u2022 h\n\u22a2 (((ofMulAction k G H) g) f) (g \u2022 g\u207b\u00b9 \u2022 h) = f (g\u207b\u00b9 \u2022 h)",
+              "state_before": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2074 : CommSemiring k\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : AddCommMonoid V\ninst\u271d\u00b9 : Module k V\n\u03c1 : Representation k G V\nH : Type u_4\ninst\u271d : MulAction G H\ng : G\nf : H \u2192\u2080 k\nh : H\n\u22a2 (((ofMulAction k G H) g) f) (g \u2022 g\u207b\u00b9 \u2022 h) = f (g\u207b\u00b9 \u2022 h)",
+              "tactic": "let h' := g\u207b\u00b9 \u2022 h"
+            },
+            {
+              "annotated_tactic": [
+                "\"change <a>ofMulAction<\\/a> k G H g f (g \\u2022 h') = f h'\"",
+                "[{\"full_name\":\"Representation.ofMulAction\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Basic.lean\",\"def_pos\":[273,19],\"def_end_pos\":[273,30]}]"
+              ],
+              "state_after": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2074 : CommSemiring k\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : AddCommMonoid V\ninst\u271d\u00b9 : Module k V\n\u03c1 : Representation k G V\nH : Type u_4\ninst\u271d : MulAction G H\ng : G\nf : H \u2192\u2080 k\nh : H\nh' : H := g\u207b\u00b9 \u2022 h\n\u22a2 (((ofMulAction k G H) g) f) (g \u2022 h') = f h'",
+              "state_before": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2074 : CommSemiring k\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : AddCommMonoid V\ninst\u271d\u00b9 : Module k V\n\u03c1 : Representation k G V\nH : Type u_4\ninst\u271d : MulAction G H\ng : G\nf : H \u2192\u2080 k\nh : H\nh' : H := g\u207b\u00b9 \u2022 h\n\u22a2 (((ofMulAction k G H) g) f) (g \u2022 g\u207b\u00b9 \u2022 h) = f (g\u207b\u00b9 \u2022 h)",
+              "tactic": "change ofMulAction k G H g f (g \u2022 h') = f h'"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>ofMulAction_def<\\/a>, <a>Finsupp.lmapDomain_apply<\\/a>, <a>Finsupp.mapDomain_apply<\\/a>, hg]\"",
+                "[{\"full_name\":\"Representation.ofMulAction_def\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Basic.lean\",\"def_pos\":[286,9],\"def_end_pos\":[286,24]},{\"full_name\":\"Finsupp.lmapDomain_apply\",\"def_path\":\"Mathlib\\/LinearAlgebra\\/Finsupp.lean\",\"def_pos\":[566,9],\"def_end_pos\":[566,25]},{\"full_name\":\"Finsupp.mapDomain_apply\",\"def_path\":\"Mathlib\\/Data\\/Finsupp\\/Basic.lean\",\"def_pos\":[451,9],\"def_end_pos\":[451,24]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2074 : CommSemiring k\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : AddCommMonoid V\ninst\u271d\u00b9 : Module k V\n\u03c1 : Representation k G V\nH : Type u_4\ninst\u271d : MulAction G H\ng : G\nf : H \u2192\u2080 k\nh : H\nh' : H := g\u207b\u00b9 \u2022 h\nhg : Function.Injective fun x => g \u2022 x\n\u22a2 (((ofMulAction k G H) g) f) (g \u2022 h') = f h'",
+              "tactic": "simp only [ofMulAction_def, Finsupp.lmapDomain_apply, Finsupp.mapDomain_apply, hg]"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro h\\u2081 h\\u2082\"",
+                "[]"
+              ],
+              "state_after": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2074 : CommSemiring k\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : AddCommMonoid V\ninst\u271d\u00b9 : Module k V\n\u03c1 : Representation k G V\nH : Type u_4\ninst\u271d : MulAction G H\ng : G\nf : H \u2192\u2080 k\nh : H\nh' : H := g\u207b\u00b9 \u2022 h\nh\u2081 h\u2082 : H\n\u22a2 (fun x => g \u2022 x) h\u2081 = (fun x => g \u2022 x) h\u2082 \u2192 h\u2081 = h\u2082",
+              "state_before": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2074 : CommSemiring k\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : AddCommMonoid V\ninst\u271d\u00b9 : Module k V\n\u03c1 : Representation k G V\nH : Type u_4\ninst\u271d : MulAction G H\ng : G\nf : H \u2192\u2080 k\nh : H\nh' : H := g\u207b\u00b9 \u2022 h\n\u22a2 Function.Injective fun x => g \u2022 x",
+              "tactic": "intro h\u2081 h\u2082"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2074 : CommSemiring k\ninst\u271d\u00b3 : Group G\ninst\u271d\u00b2 : AddCommMonoid V\ninst\u271d\u00b9 : Module k V\n\u03c1 : Representation k G V\nH : Type u_4\ninst\u271d : MulAction G H\ng : G\nf : H \u2192\u2080 k\nh : H\nh' : H := g\u207b\u00b9 \u2022 h\nh\u2081 h\u2082 : H\n\u22a2 (fun x => g \u2022 x) h\u2081 = (fun x => g \u2022 x) h\u2082 \u2192 h\u2081 = h\u2082",
+              "tactic": "simp"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Representation.ofMulAction_def",
+        "id": "Representation.ofMulAction_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            287,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Basic.lean",
+          "full_name": "Representation.ofMulAction_def",
+          "start": [
+            286,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Basic.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'ext'",
+        "full_name": "Representation.ofMulAction_self_smul_eq_mul",
+        "id": "Representation.ofMulAction_self_smul_eq_mul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            366,
+            8
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Basic.lean",
+          "full_name": "Representation.ofMulAction_self_smul_eq_mul",
+          "start": [
+            351,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"show <a>asAlgebraHom<\\/a> (<a>ofMulAction<\\/a> k G G) _ _ = _\"",
+                "[{\"full_name\":\"Representation.asAlgebraHom\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Basic.lean\",\"def_pos\":[96,19],\"def_end_pos\":[96,31]},{\"full_name\":\"Representation.ofMulAction\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Basic.lean\",\"def_pos\":[273,19],\"def_end_pos\":[273,30]}]"
+              ],
+              "state_after": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u00b3 : CommSemiring k\ninst\u271d\u00b2 : Group G\ninst\u271d\u00b9 : AddCommMonoid V\ninst\u271d : Module k V\n\u03c1 : Representation k G V\nx : MonoidAlgebra k G\ny : (ofMulAction k G G).asModule\ng : G\n\u22a2 ((ofMulAction k G G).asAlgebraHom ((of k G) g)) y = (of k G) g * y",
+              "state_before": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u00b3 : CommSemiring k\ninst\u271d\u00b2 : Group G\ninst\u271d\u00b9 : AddCommMonoid V\ninst\u271d : Module k V\n\u03c1 : Representation k G V\nx : MonoidAlgebra k G\ny : (ofMulAction k G G).asModule\ng : G\n\u22a2 (fun z => z \u2022 y = z * y) ((of k G) g)",
+              "tactic": "show asAlgebraHom (ofMulAction k G G) _ _ = _"
+            },
+            {
+              "annotated_tactic": [
+                "\"ext\"",
+                "[]"
+              ],
+              "state_after": "case h\nk : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u00b3 : CommSemiring k\ninst\u271d\u00b2 : Group G\ninst\u271d\u00b9 : AddCommMonoid V\ninst\u271d : Module k V\n\u03c1 : Representation k G V\nx : MonoidAlgebra k G\ny : (ofMulAction k G G).asModule\ng a\u271d : G\n\u22a2 (((ofMulAction k G G).asAlgebraHom ((of k G) g)) y) a\u271d = ((of k G) g * y) a\u271d",
+              "state_before": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u00b3 : CommSemiring k\ninst\u271d\u00b2 : Group G\ninst\u271d\u00b9 : AddCommMonoid V\ninst\u271d : Module k V\n\u03c1 : Representation k G V\nx : MonoidAlgebra k G\ny : (ofMulAction k G G).asModule\ng : G\n\u22a2 ((ofMulAction k G G).asAlgebraHom ((of k G) g)) y = (of k G) g * y",
+              "tactic": "ext"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>MonoidAlgebra.of_apply<\\/a>, <a>asAlgebraHom_single<\\/a>, <a>one_smul<\\/a>,\\n        <a>ofMulAction_apply<\\/a>, <a>smul_eq_mul<\\/a>]\"",
+                "[{\"full_name\":\"MonoidAlgebra.of_apply\",\"def_path\":\"Mathlib\\/Algebra\\/MonoidAlgebra\\/Basic.lean\",\"def_pos\":[521,3],\"def_end_pos\":[521,8]},{\"full_name\":\"Representation.asAlgebraHom_single\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Basic.lean\",\"def_pos\":[105,9],\"def_end_pos\":[105,28]},{\"full_name\":\"one_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[453,7],\"def_end_pos\":[453,15]},{\"full_name\":\"Representation.ofMulAction_apply\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Basic.lean\",\"def_pos\":[335,9],\"def_end_pos\":[335,26]},{\"full_name\":\"smul_eq_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[89,7],\"def_end_pos\":[89,18]}]"
+              ],
+              "state_after": "case h\nk : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u00b3 : CommSemiring k\ninst\u271d\u00b2 : Group G\ninst\u271d\u00b9 : AddCommMonoid V\ninst\u271d : Module k V\n\u03c1 : Representation k G V\nx : MonoidAlgebra k G\ny : (ofMulAction k G G).asModule\ng a\u271d : G\n\u22a2 y (g\u207b\u00b9 * a\u271d) = (MonoidAlgebra.single g 1 * y) a\u271d",
+              "state_before": "case h\nk : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u00b3 : CommSemiring k\ninst\u271d\u00b2 : Group G\ninst\u271d\u00b9 : AddCommMonoid V\ninst\u271d : Module k V\n\u03c1 : Representation k G V\nx : MonoidAlgebra k G\ny : (ofMulAction k G G).asModule\ng a\u271d : G\n\u22a2 (((ofMulAction k G G).asAlgebraHom ((of k G) g)) y) a\u271d = ((of k G) g * y) a\u271d",
+              "tactic": "simp only [MonoidAlgebra.of_apply, asAlgebraHom_single, one_smul,\n  ofMulAction_apply, smul_eq_mul]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>MonoidAlgebra.single_mul_apply<\\/a>, <a>one_mul<\\/a>]\"",
+                "[{\"full_name\":\"MonoidAlgebra.single_mul_apply\",\"def_path\":\"Mathlib\\/Algebra\\/MonoidAlgebra\\/Basic.lean\",\"def_pos\":[1109,9],\"def_end_pos\":[1109,25]},{\"full_name\":\"one_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[477,9],\"def_end_pos\":[477,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h\nk : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u00b3 : CommSemiring k\ninst\u271d\u00b2 : Group G\ninst\u271d\u00b9 : AddCommMonoid V\ninst\u271d : Module k V\n\u03c1 : Representation k G V\nx : MonoidAlgebra k G\ny : (ofMulAction k G G).asModule\ng a\u271d : G\n\u22a2 y (g\u207b\u00b9 * a\u271d) = (MonoidAlgebra.single g 1 * y) a\u271d",
+              "tactic": "rw [MonoidAlgebra.single_mul_apply, one_mul]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [hx, hy, <a>add_mul<\\/a>, <a>add_smul<\\/a>]\"",
+                "[{\"full_name\":\"add_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[91,7],\"def_end_pos\":[91,14]},{\"full_name\":\"add_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Defs.lean\",\"def_pos\":[93,9],\"def_end_pos\":[93,17]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u00b3 : CommSemiring k\ninst\u271d\u00b2 : Group G\ninst\u271d\u00b9 : AddCommMonoid V\ninst\u271d : Module k V\n\u03c1 : Representation k G V\nx\u271d : MonoidAlgebra k G\ny\u271d : (ofMulAction k G G).asModule\nx y : MonoidAlgebra k G\nhx : (fun z => z \u2022 y\u271d = z * y\u271d) x\nhy : (fun z => z \u2022 y\u271d = z * y\u271d) y\n\u22a2 (fun z => z \u2022 y\u271d = z * y\u271d) (x + y)",
+              "tactic": "simp only [hx, hy, add_mul, add_smul]"
+            },
+            {
+              "annotated_tactic": [
+                "\"show <a>asAlgebraHom<\\/a> (<a>ofMulAction<\\/a> k G G) _ _ = _\"",
+                "[{\"full_name\":\"Representation.asAlgebraHom\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Basic.lean\",\"def_pos\":[96,19],\"def_end_pos\":[96,31]},{\"full_name\":\"Representation.ofMulAction\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Basic.lean\",\"def_pos\":[273,19],\"def_end_pos\":[273,30]}]"
+              ],
+              "state_after": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u00b3 : CommSemiring k\ninst\u271d\u00b2 : Group G\ninst\u271d\u00b9 : AddCommMonoid V\ninst\u271d : Module k V\n\u03c1 : Representation k G V\nx\u271d : MonoidAlgebra k G\ny : (ofMulAction k G G).asModule\nr : k\nx : MonoidAlgebra k G\nhx : (fun z => z \u2022 y = z * y) x\n\u22a2 ((ofMulAction k G G).asAlgebraHom (r \u2022 x)) y = r \u2022 x * y",
+              "state_before": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u00b3 : CommSemiring k\ninst\u271d\u00b2 : Group G\ninst\u271d\u00b9 : AddCommMonoid V\ninst\u271d : Module k V\n\u03c1 : Representation k G V\nx\u271d : MonoidAlgebra k G\ny : (ofMulAction k G G).asModule\nr : k\nx : MonoidAlgebra k G\nhx : (fun z => z \u2022 y = z * y) x\n\u22a2 (fun z => z \u2022 y = z * y) (r \u2022 x)",
+              "tactic": "show asAlgebraHom (ofMulAction k G G) _ _ = _"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>map_smul<\\/a>, <a>smul_apply<\\/a>, <a>Algebra.smul_mul_assoc<\\/a>]\"",
+                "[{\"full_name\":\"map_smul\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Hom.lean\",\"def_pos\":[111,9],\"def_end_pos\":[111,17]},{\"full_name\":\"LinearMap.smul_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/LinearMap\\/Defs.lean\",\"def_pos\":[831,9],\"def_end_pos\":[831,19]},{\"full_name\":\"Algebra.smul_mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Defs.lean\",\"def_pos\":[384,19],\"def_end_pos\":[384,33]}]"
+              ],
+              "state_after": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u00b3 : CommSemiring k\ninst\u271d\u00b2 : Group G\ninst\u271d\u00b9 : AddCommMonoid V\ninst\u271d : Module k V\n\u03c1 : Representation k G V\nx\u271d : MonoidAlgebra k G\ny : (ofMulAction k G G).asModule\nr : k\nx : MonoidAlgebra k G\nhx : (fun z => z \u2022 y = z * y) x\n\u22a2 r \u2022 ((ofMulAction k G G).asAlgebraHom x) y = r \u2022 (x * y)",
+              "state_before": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u00b3 : CommSemiring k\ninst\u271d\u00b2 : Group G\ninst\u271d\u00b9 : AddCommMonoid V\ninst\u271d : Module k V\n\u03c1 : Representation k G V\nx\u271d : MonoidAlgebra k G\ny : (ofMulAction k G G).asModule\nr : k\nx : MonoidAlgebra k G\nhx : (fun z => z \u2022 y = z * y) x\n\u22a2 ((ofMulAction k G G).asAlgebraHom (r \u2022 x)) y = r \u2022 x * y",
+              "tactic": "simp only [map_smul, smul_apply, Algebra.smul_mul_assoc]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 hx]\"",
+                "[]"
+              ],
+              "state_after": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u00b3 : CommSemiring k\ninst\u271d\u00b2 : Group G\ninst\u271d\u00b9 : AddCommMonoid V\ninst\u271d : Module k V\n\u03c1 : Representation k G V\nx\u271d : MonoidAlgebra k G\ny : (ofMulAction k G G).asModule\nr : k\nx : MonoidAlgebra k G\nhx : (fun z => z \u2022 y = z * y) x\n\u22a2 r \u2022 ((ofMulAction k G G).asAlgebraHom x) y = r \u2022 x \u2022 y",
+              "state_before": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u00b3 : CommSemiring k\ninst\u271d\u00b2 : Group G\ninst\u271d\u00b9 : AddCommMonoid V\ninst\u271d : Module k V\n\u03c1 : Representation k G V\nx\u271d : MonoidAlgebra k G\ny : (ofMulAction k G G).asModule\nr : k\nx : MonoidAlgebra k G\nhx : (fun z => z \u2022 y = z * y) x\n\u22a2 r \u2022 ((ofMulAction k G G).asAlgebraHom x) y = r \u2022 (x * y)",
+              "tactic": "rw [\u2190 hx]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rfl\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u00b3 : CommSemiring k\ninst\u271d\u00b2 : Group G\ninst\u271d\u00b9 : AddCommMonoid V\ninst\u271d : Module k V\n\u03c1 : Representation k G V\nx\u271d : MonoidAlgebra k G\ny : (ofMulAction k G G).asModule\nr : k\nx : MonoidAlgebra k G\nhx : (fun z => z \u2022 y = z * y) x\n\u22a2 r \u2022 ((ofMulAction k G G).asAlgebraHom x) y = r \u2022 x \u2022 y",
+              "tactic": "rfl"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Representation.ofMulAction_single",
+        "id": "Representation.ofMulAction_single",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            292,
+            27
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Basic.lean",
+          "full_name": "Representation.ofMulAction_single",
+          "start": [
+            290,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Representation.ofMulDistribMulAction_apply_apply",
+        "id": "Representation.ofMulDistribMulAction_apply_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            326,
+            81
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Basic.lean",
+          "full_name": "Representation.ofMulDistribMulAction_apply_apply",
+          "start": [
+            325,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Representation.tprod_apply",
+        "id": "Representation.tprod_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            412,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Basic.lean",
+          "full_name": "Representation.tprod_apply",
+          "start": [
+            411,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Representation.trivial_def",
+        "id": "Representation.trivial_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            71,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Basic.lean",
+          "full_name": "Representation.trivial_def",
+          "start": [
+            70,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "FdRep.char_dual",
+        "id": "FdRep.char_dual",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            95,
+            29
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Character.lean",
+          "full_name": "FdRep.char_dual",
+          "start": [
+            94,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Character.lean"
+      }
+    ],
+    "input_proofs": 34,
+    "input_units": 2,
+    "proofs": 20,
+    "published_proofs": 19,
+    "published_transitions": 38,
+    "replay_failures": [],
+    "transitions": 45,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/RepresentationTheory/Basic.lean",
+        "proof_id": "mathlib:Representation.ofModule_asAlgebraHom_apply_apply",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              233,
+              51
+            ],
+            "file_path": "Mathlib/RepresentationTheory/Basic.lean",
+            "full_name": "Representation.ofModule_asAlgebraHom_apply_apply",
+            "start": [
+              220,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"apply <a>MonoidAlgebra.induction_on<\\/a> r\"",
+                  "[{\"full_name\":\"MonoidAlgebra.induction_on\",\"def_path\":\"Mathlib\\/Algebra\\/MonoidAlgebra\\/Basic.lean\",\"def_pos\":[854,9],\"def_end_pos\":[854,21]}]"
+                ],
+                "state_after": "case hM\nk : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2075 : CommSemiring k\ninst\u271d\u2074 : Monoid G\ninst\u271d\u00b3 : AddCommMonoid V\ninst\u271d\u00b2 : Module k V\n\u03c1 : Representation k G V\nM : Type u_4\ninst\u271d\u00b9 : AddCommMonoid M\ninst\u271d : Module (MonoidAlgebra k G) M\nr : MonoidAlgebra k G\nm : RestrictScalars k (MonoidAlgebra k G) M\n\u22a2 \u2200 (g : G),\n    ((ofModule M).asAlgebraHom ((of k G) g)) m =\n      (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm\n        ((of k G) g \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)\n\ncase hadd\nk : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2075 : CommSemiring k\ninst\u271d\u2074 : Monoid G\ninst\u271d\u00b3 : AddCommMonoid V\ninst\u271d\u00b2 : Module k V\n\u03c1 : Representation k G V\nM : Type u_4\ninst\u271d\u00b9 : AddCommMonoid M\ninst\u271d : Module (MonoidAlgebra k G) M\nr : MonoidAlgebra k G\nm : RestrictScalars k (MonoidAlgebra k G) M\n\u22a2 \u2200 (f g : MonoidAlgebra k G),\n    ((ofModule M).asAlgebraHom f) m =\n        (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm\n          (f \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m) \u2192\n      ((ofModule M).asAlgebraHom g) m =\n          (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm\n            (g \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m) \u2192\n        ((ofModule M).asAlgebraHom (f + g)) m =\n          (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm\n            ((f + g) \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)\n\ncase hsmul\nk : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2075 : CommSemiring k\ninst\u271d\u2074 : Monoid G\ninst\u271d\u00b3 : AddCommMonoid V\ninst\u271d\u00b2 : Module k V\n\u03c1 : Representation k G V\nM : Type u_4\ninst\u271d\u00b9 : AddCommMonoid M\ninst\u271d : Module (MonoidAlgebra k G) M\nr : MonoidAlgebra k G\nm : RestrictScalars k (MonoidAlgebra k G) M\n\u22a2 \u2200 (r : k) (f : MonoidAlgebra k G),\n    ((ofModule M).asAlgebraHom f) m =\n        (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm\n          (f \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m) \u2192\n      ((ofModule M).asAlgebraHom (r \u2022 f)) m =\n        (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm\n          ((r \u2022 f) \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)",
+                "state_before": "k : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2075 : CommSemiring k\ninst\u271d\u2074 : Monoid G\ninst\u271d\u00b3 : AddCommMonoid V\ninst\u271d\u00b2 : Module k V\n\u03c1 : Representation k G V\nM : Type u_4\ninst\u271d\u00b9 : AddCommMonoid M\ninst\u271d : Module (MonoidAlgebra k G) M\nr : MonoidAlgebra k G\nm : RestrictScalars k (MonoidAlgebra k G) M\n\u22a2 ((ofModule M).asAlgebraHom r) m =\n    (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm (r \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)",
+                "tactic": "apply MonoidAlgebra.induction_on r"
+              },
+              {
+                "annotated_tactic": [
+                  "\"intro g\"",
+                  "[]"
+                ],
+                "state_after": "case hM\nk : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2075 : CommSemiring k\ninst\u271d\u2074 : Monoid G\ninst\u271d\u00b3 : AddCommMonoid V\ninst\u271d\u00b2 : Module k V\n\u03c1 : Representation k G V\nM : Type u_4\ninst\u271d\u00b9 : AddCommMonoid M\ninst\u271d : Module (MonoidAlgebra k G) M\nr : MonoidAlgebra k G\nm : RestrictScalars k (MonoidAlgebra k G) M\ng : G\n\u22a2 ((ofModule M).asAlgebraHom ((of k G) g)) m =\n    (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm\n      ((of k G) g \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)",
+                "state_before": "case hM\nk : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2075 : CommSemiring k\ninst\u271d\u2074 : Monoid G\ninst\u271d\u00b3 : AddCommMonoid V\ninst\u271d\u00b2 : Module k V\n\u03c1 : Representation k G V\nM : Type u_4\ninst\u271d\u00b9 : AddCommMonoid M\ninst\u271d : Module (MonoidAlgebra k G) M\nr : MonoidAlgebra k G\nm : RestrictScalars k (MonoidAlgebra k G) M\n\u22a2 \u2200 (g : G),\n    ((ofModule M).asAlgebraHom ((of k G) g)) m =\n      (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm\n        ((of k G) g \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)",
+                "tactic": "intro g"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp only [<a>one_smul<\\/a>, <a>MonoidAlgebra.lift_symm_apply<\\/a>, <a>MonoidAlgebra.of_apply<\\/a>,\\n      <a>Representation.asAlgebraHom_single<\\/a>, <a>Representation.ofModule<\\/a>, <a>AddEquiv.apply_eq_iff_eq<\\/a>,\\n      <a>RestrictScalars.lsmul_apply_apply<\\/a>]\"",
+                  "[{\"full_name\":\"one_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[453,7],\"def_end_pos\":[453,15]},{\"full_name\":\"MonoidAlgebra.lift_symm_apply\",\"def_path\":\"Mathlib\\/Algebra\\/MonoidAlgebra\\/Basic.lean\",\"def_pos\":[926,9],\"def_end_pos\":[926,24]},{\"full_name\":\"MonoidAlgebra.of_apply\",\"def_path\":\"Mathlib\\/Algebra\\/MonoidAlgebra\\/Basic.lean\",\"def_pos\":[521,3],\"def_end_pos\":[521,8]},{\"full_name\":\"Representation.asAlgebraHom_single\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Basic.lean\",\"def_pos\":[105,9],\"def_end_pos\":[105,28]},{\"full_name\":\"Representation.ofModule\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Basic.lean\",\"def_pos\":[194,19],\"def_end_pos\":[194,27]},{\"full_name\":\"AddEquiv.apply_eq_iff_eq\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Equiv\\/Basic.lean\",\"def_pos\":[424,3],\"def_end_pos\":[424,14]},{\"full_name\":\"RestrictScalars.lsmul_apply_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/RestrictScalars.lean\",\"def_pos\":[182,9],\"def_end_pos\":[182,42]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case hM\nk : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2075 : CommSemiring k\ninst\u271d\u2074 : Monoid G\ninst\u271d\u00b3 : AddCommMonoid V\ninst\u271d\u00b2 : Module k V\n\u03c1 : Representation k G V\nM : Type u_4\ninst\u271d\u00b9 : AddCommMonoid M\ninst\u271d : Module (MonoidAlgebra k G) M\nr : MonoidAlgebra k G\nm : RestrictScalars k (MonoidAlgebra k G) M\ng : G\n\u22a2 ((ofModule M).asAlgebraHom ((of k G) g)) m =\n    (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm\n      ((of k G) g \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)",
+                "tactic": "simp only [one_smul, MonoidAlgebra.lift_symm_apply, MonoidAlgebra.of_apply,\n  Representation.asAlgebraHom_single, Representation.ofModule, AddEquiv.apply_eq_iff_eq,\n  RestrictScalars.lsmul_apply_apply]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"intro f g fw gw\"",
+                  "[]"
+                ],
+                "state_after": "case hadd\nk : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2075 : CommSemiring k\ninst\u271d\u2074 : Monoid G\ninst\u271d\u00b3 : AddCommMonoid V\ninst\u271d\u00b2 : Module k V\n\u03c1 : Representation k G V\nM : Type u_4\ninst\u271d\u00b9 : AddCommMonoid M\ninst\u271d : Module (MonoidAlgebra k G) M\nr : MonoidAlgebra k G\nm : RestrictScalars k (MonoidAlgebra k G) M\nf g : MonoidAlgebra k G\nfw :\n  ((ofModule M).asAlgebraHom f) m =\n    (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm (f \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)\ngw :\n  ((ofModule M).asAlgebraHom g) m =\n    (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm (g \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)\n\u22a2 ((ofModule M).asAlgebraHom (f + g)) m =\n    (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm\n      ((f + g) \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)",
+                "state_before": "case hadd\nk : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2075 : CommSemiring k\ninst\u271d\u2074 : Monoid G\ninst\u271d\u00b3 : AddCommMonoid V\ninst\u271d\u00b2 : Module k V\n\u03c1 : Representation k G V\nM : Type u_4\ninst\u271d\u00b9 : AddCommMonoid M\ninst\u271d : Module (MonoidAlgebra k G) M\nr : MonoidAlgebra k G\nm : RestrictScalars k (MonoidAlgebra k G) M\n\u22a2 \u2200 (f g : MonoidAlgebra k G),\n    ((ofModule M).asAlgebraHom f) m =\n        (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm\n          (f \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m) \u2192\n      ((ofModule M).asAlgebraHom g) m =\n          (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm\n            (g \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m) \u2192\n        ((ofModule M).asAlgebraHom (f + g)) m =\n          (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm\n            ((f + g) \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)",
+                "tactic": "intro f g fw gw"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp only [fw, gw, <a>map_add<\\/a>, <a>add_smul<\\/a>, <a>LinearMap.add_apply<\\/a>]\"",
+                  "[{\"full_name\":\"map_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[308,3],\"def_end_pos\":[308,14]},{\"full_name\":\"add_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Defs.lean\",\"def_pos\":[93,9],\"def_end_pos\":[93,17]},{\"full_name\":\"LinearMap.add_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/LinearMap\\/Defs.lean\",\"def_pos\":[910,9],\"def_end_pos\":[910,18]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case hadd\nk : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2075 : CommSemiring k\ninst\u271d\u2074 : Monoid G\ninst\u271d\u00b3 : AddCommMonoid V\ninst\u271d\u00b2 : Module k V\n\u03c1 : Representation k G V\nM : Type u_4\ninst\u271d\u00b9 : AddCommMonoid M\ninst\u271d : Module (MonoidAlgebra k G) M\nr : MonoidAlgebra k G\nm : RestrictScalars k (MonoidAlgebra k G) M\nf g : MonoidAlgebra k G\nfw :\n  ((ofModule M).asAlgebraHom f) m =\n    (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm (f \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)\ngw :\n  ((ofModule M).asAlgebraHom g) m =\n    (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm (g \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)\n\u22a2 ((ofModule M).asAlgebraHom (f + g)) m =\n    (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm\n      ((f + g) \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)",
+                "tactic": "simp only [fw, gw, map_add, add_smul, LinearMap.add_apply]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"intro r f w\"",
+                  "[]"
+                ],
+                "state_after": "case hsmul\nk : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2075 : CommSemiring k\ninst\u271d\u2074 : Monoid G\ninst\u271d\u00b3 : AddCommMonoid V\ninst\u271d\u00b2 : Module k V\n\u03c1 : Representation k G V\nM : Type u_4\ninst\u271d\u00b9 : AddCommMonoid M\ninst\u271d : Module (MonoidAlgebra k G) M\nr\u271d : MonoidAlgebra k G\nm : RestrictScalars k (MonoidAlgebra k G) M\nr : k\nf : MonoidAlgebra k G\nw :\n  ((ofModule M).asAlgebraHom f) m =\n    (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm (f \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)\n\u22a2 ((ofModule M).asAlgebraHom (r \u2022 f)) m =\n    (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm\n      ((r \u2022 f) \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)",
+                "state_before": "case hsmul\nk : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2075 : CommSemiring k\ninst\u271d\u2074 : Monoid G\ninst\u271d\u00b3 : AddCommMonoid V\ninst\u271d\u00b2 : Module k V\n\u03c1 : Representation k G V\nM : Type u_4\ninst\u271d\u00b9 : AddCommMonoid M\ninst\u271d : Module (MonoidAlgebra k G) M\nr : MonoidAlgebra k G\nm : RestrictScalars k (MonoidAlgebra k G) M\n\u22a2 \u2200 (r : k) (f : MonoidAlgebra k G),\n    ((ofModule M).asAlgebraHom f) m =\n        (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm\n          (f \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m) \u2192\n      ((ofModule M).asAlgebraHom (r \u2022 f)) m =\n        (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm\n          ((r \u2022 f) \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)",
+                "tactic": "intro r f w"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp only [w, <a>AlgHom.map_smul<\\/a>, <a>LinearMap.smul_apply<\\/a>,\\n      <a>RestrictScalars.addEquiv_symm_map_smul_smul<\\/a>]\"",
+                  "[{\"full_name\":\"AlgHom.map_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Hom.lean\",\"def_pos\":[259,19],\"def_end_pos\":[259,27]},{\"full_name\":\"LinearMap.smul_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/LinearMap\\/Defs.lean\",\"def_pos\":[831,9],\"def_end_pos\":[831,19]},{\"full_name\":\"RestrictScalars.addEquiv_symm_map_smul_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/RestrictScalars.lean\",\"def_pos\":[175,9],\"def_end_pos\":[175,52]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case hsmul\nk : Type u_1\nG : Type u_2\nV : Type u_3\ninst\u271d\u2075 : CommSemiring k\ninst\u271d\u2074 : Monoid G\ninst\u271d\u00b3 : AddCommMonoid V\ninst\u271d\u00b2 : Module k V\n\u03c1 : Representation k G V\nM : Type u_4\ninst\u271d\u00b9 : AddCommMonoid M\ninst\u271d : Module (MonoidAlgebra k G) M\nr\u271d : MonoidAlgebra k G\nm : RestrictScalars k (MonoidAlgebra k G) M\nr : k\nf : MonoidAlgebra k G\nw :\n  ((ofModule M).asAlgebraHom f) m =\n    (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm (f \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)\n\u22a2 ((ofModule M).asAlgebraHom (r \u2022 f)) m =\n    (RestrictScalars.addEquiv k (MonoidAlgebra k G) M).symm\n      ((r \u2022 f) \u2022 (RestrictScalars.addEquiv k (MonoidAlgebra k G) M) m)",
+                "tactic": "simp only [w, AlgHom.map_smul, LinearMap.smul_apply,\n  RestrictScalars.addEquiv_symm_map_smul_smul]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Representation.ofModule_asAlgebraHom_apply_apply"
+      }
+    ],
+    "validation_rejected_proofs": 1,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001636-0000-06fd2dd307eed128.parquet",
+      "sha256": "06fd2dd307eed1283c81aa255f4dd0199049f0336c6653d3975bac8260f4f4ea",
+      "bytes": 348940,
+      "rows": 38,
+      "revision": "df8c9c479578582ca5384c5c62608ea4677707ca"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:FdRep.average_char_eq_finrank_invariants",
+    "mathlib:FdRep.char_conj",
+    "mathlib:FdRep.char_iso",
+    "mathlib:FdRep.char_linHom",
+    "mathlib:FdRep.char_mul_comm",
+    "mathlib:FdRep.char_one",
+    "mathlib:FdRep.char_orthonormal",
+    "mathlib:FdRep.char_tensor",
+    "mathlib:FdRep.char_tensor'",
+    "mathlib:Representation.asAlgebraHom_of",
+    "mathlib:Representation.asAlgebraHom_single_one",
+    "mathlib:Representation.asGroupHom_apply",
+    "mathlib:Representation.asModuleEquiv_symm_map_rho",
+    "mathlib:Representation.asModuleEquiv_symm_map_smul",
+    "mathlib:Representation.dualTensorHom_comm",
+    "mathlib:Representation.ofModule_asModule_act",
+    "mathlib:Representation.smul_ofModule_asModule",
+    "mathlib:Representation.smul_one_tprod_asModule",
+    "mathlib:Representation.smul_tprod_one_asModule"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Basic.lean\",null,null,\"Representation.asAlgebraHom_of\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Basic.lean\",null,null,\"Representation.asAlgebraHom_single_one\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Basic.lean\",null,null,\"Representation.asGroupHom_apply\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Basic.lean\",null,null,\"Representation.asModuleEquiv_symm_map_rho\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Basic.lean\",null,null,\"Representation.asModuleEquiv_symm_map_smul\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Basic.lean\",null,null,\"Representation.dualTensorHom_comm\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Basic.lean\",null,null,\"Representation.ofModule_asModule_act\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Basic.lean\",null,null,\"Representation.smul_ofModule_asModule\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Basic.lean\",null,null,\"Representation.smul_one_tprod_asModule\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Basic.lean\",null,null,\"Representation.smul_tprod_one_asModule\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Character.lean\",null,null,\"FdRep.average_char_eq_finrank_invariants\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Character.lean\",null,null,\"FdRep.char_conj\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Character.lean\",null,null,\"FdRep.char_iso\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Character.lean\",null,null,\"FdRep.char_linHom\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Character.lean\",null,null,\"FdRep.char_mul_comm\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Character.lean\",null,null,\"FdRep.char_one\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Character.lean\",null,null,\"FdRep.char_orthonormal\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Character.lean\",null,null,\"FdRep.char_tensor\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Character.lean\",null,null,\"FdRep.char_tensor'\"]"
+  ]
+}

manifests/batches/mathlib/001637.json

@@ -0,0 +1,262 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001637",
+  "batch_fingerprint": "8dac583683ce286fef2e63a904128f852732840ba7b12b3245135b9bcb1d281f",
+  "evidence": {
+    "batch_fingerprint": "8dac583683ce286fef2e63a904128f852732840ba7b12b3245135b9bcb1d281f",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "FdRep.dualTensorIsoLinHom_hom_hom",
+        "id": "FdRep.dualTensorIsoLinHom_hom_hom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            196,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/FdRep.lean",
+          "full_name": "FdRep.dualTensorIsoLinHom_hom_hom",
+          "start": [
+            195,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/FdRep.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "FdRep.finrank_hom_simple_simple",
+        "id": "FdRep.finrank_hom_simple_simple",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            136,
+            49
+          ],
+          "file_path": "Mathlib/RepresentationTheory/FdRep.lean",
+          "full_name": "FdRep.finrank_hom_simple_simple",
+          "start": [
+            134,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/FdRep.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "groupCohomology.inhomogeneousCochains.d_def",
+        "id": "groupCohomology.inhomogeneousCochains.d_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            209,
+            30
+          ],
+          "file_path": "Mathlib/RepresentationTheory/GroupCohomology/Basic.lean",
+          "full_name": "groupCohomology.inhomogeneousCochains.d_def",
+          "start": [
+            207,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/GroupCohomology/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "groupCohomology.linearYonedaObjResolution_d_apply",
+        "id": "groupCohomology.linearYonedaObjResolution_d_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            93,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/GroupCohomology/Basic.lean",
+          "full_name": "groupCohomology.linearYonedaObjResolution_d_apply",
+          "start": [
+            91,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/GroupCohomology/Basic.lean"
+      }
+    ],
+    "input_proofs": 7,
+    "input_units": 2,
+    "proofs": 3,
+    "published_proofs": 2,
+    "published_transitions": 5,
+    "replay_failures": [],
+    "transitions": 17,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/RepresentationTheory/GroupCohomology/Basic.lean",
+        "proof_id": "mathlib:inhomogeneousCochains.d_eq",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              169,
+              73
+            ],
+            "file_path": "Mathlib/RepresentationTheory/GroupCohomology/Basic.lean",
+            "full_name": "inhomogeneousCochains.d_eq",
+            "start": [
+              127,
+              21
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"ext f g\"",
+                  "[]"
+                ],
+                "state_after": "case h.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\n\u22a2 (d n A) f g =\n    ((diagonalHomEquiv n A).toModuleIso.inv \u226b\n        (linearYonedaObjResolution A).d n (n + 1) \u226b (diagonalHomEquiv (n + 1) A).toModuleIso.hom)\n      f g",
+                "state_before": "k G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\n\u22a2 d n A =\n    (diagonalHomEquiv n A).toModuleIso.inv \u226b\n      (linearYonedaObjResolution A).d n (n + 1) \u226b (diagonalHomEquiv (n + 1) A).toModuleIso.hom",
+                "tactic": "ext f g"
+              },
+              {
+                "annotated_tactic": [
+                  "\"change <a>d<\\/a> n A f g = <a>diagonalHomEquiv<\\/a> (n + 1) A\\n    ((<a>resolution<\\/a> k G).<a>d<\\/a> (n + 1) n \\u226b (<a>diagonalHomEquiv<\\/a> n A).<a>symm<\\/a> f) g\"",
+                  "[{\"full_name\":\"inhomogeneousCochains.d\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/GroupCohomology\\/Basic.lean\",\"def_pos\":[105,5],\"def_end_pos\":[105,6]},{\"full_name\":\"Rep.diagonalHomEquiv\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/GroupCohomology\\/Resolution.lean\",\"def_pos\":[328,19],\"def_end_pos\":[328,35]},{\"full_name\":\"groupCohomology.resolution\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/GroupCohomology\\/Resolution.lean\",\"def_pos\":[509,5],\"def_end_pos\":[509,31]},{\"full_name\":\"HomologicalComplex.d\",\"def_path\":\"Mathlib\\/Algebra\\/Homology\\/HomologicalComplex.lean\",\"def_pos\":[59,3],\"def_end_pos\":[59,4]},{\"full_name\":\"Rep.diagonalHomEquiv\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/GroupCohomology\\/Resolution.lean\",\"def_pos\":[328,19],\"def_end_pos\":[328,35]},{\"full_name\":\"LinearEquiv.symm\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Equiv.lean\",\"def_pos\":[282,5],\"def_end_pos\":[282,9]}]"
+                ],
+                "state_after": "case h.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\n\u22a2 (d n A) f g = (diagonalHomEquiv (n + 1) A) ((resolution k G).d (n + 1) n \u226b (diagonalHomEquiv n A).symm f) g",
+                "state_before": "case h.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\n\u22a2 (d n A) f g =\n    ((diagonalHomEquiv n A).toModuleIso.inv \u226b\n        (linearYonedaObjResolution A).d n (n + 1) \u226b (diagonalHomEquiv (n + 1) A).toModuleIso.hom)\n      f g",
+                "tactic": "change d n A f g = diagonalHomEquiv (n + 1) A\n  ((resolution k G).d (n + 1) n \u226b (diagonalHomEquiv n A).symm f) g"
+              },
+              {
+                "annotated_tactic": [
+                  "\"erw [<a>diagonalHomEquiv_apply<\\/a>, <a>Action.comp_hom<\\/a>, <a>ModuleCat.comp_def<\\/a>, <a>LinearMap.comp_apply<\\/a>,\\n    <a>resolution.d_eq<\\/a>]\"",
+                  "[{\"full_name\":\"Rep.diagonalHomEquiv_apply\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/GroupCohomology\\/Resolution.lean\",\"def_pos\":[344,9],\"def_end_pos\":[344,31]},{\"full_name\":\"Action.comp_hom\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Action\\/Basic.lean\",\"def_pos\":[144,9],\"def_end_pos\":[144,17]},{\"full_name\":\"ModuleCat.comp_def\",\"def_path\":\"Mathlib\\/Algebra\\/Category\\/ModuleCat\\/Basic.lean\",\"def_pos\":[227,9],\"def_end_pos\":[227,17]},{\"full_name\":\"LinearMap.comp_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/LinearMap\\/Defs.lean\",\"def_pos\":[552,9],\"def_end_pos\":[552,19]},{\"full_name\":\"groupCohomology.resolution.d_eq\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/GroupCohomology\\/Resolution.lean\",\"def_pos\":[558,9],\"def_end_pos\":[558,13]}]"
+                ],
+                "state_after": "case h.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\n\u22a2 (d n A) f g = ((diagonalHomEquiv n A).symm f).hom ((resolution.d k G (n + 1)) (Finsupp.single (Fin.partialProd g) 1))",
+                "state_before": "case h.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\n\u22a2 (d n A) f g = (diagonalHomEquiv (n + 1) A) ((resolution k G).d (n + 1) n \u226b (diagonalHomEquiv n A).symm f) g",
+                "tactic": "erw [diagonalHomEquiv_apply, Action.comp_hom, ModuleCat.comp_def, LinearMap.comp_apply,\n  resolution.d_eq]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"erw [<a>resolution.d_of<\\/a> (<a>Fin.partialProd<\\/a> g)]\"",
+                  "[{\"full_name\":\"groupCohomology.resolution.d_of\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/GroupCohomology\\/Resolution.lean\",\"def_pos\":[531,9],\"def_end_pos\":[531,13]},{\"full_name\":\"Fin.partialProd\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Fin.lean\",\"def_pos\":[233,5],\"def_end_pos\":[233,16]}]"
+                ],
+                "state_after": "case h.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\n\u22a2 (d n A) f g =\n    ((diagonalHomEquiv n A).symm f).hom\n      (\u2211 p : Fin (n + 1 + 1), Finsupp.single (Fin.partialProd g \u2218 p.succAbove) ((-1) ^ \u2191p))",
+                "state_before": "case h.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\n\u22a2 (d n A) f g = ((diagonalHomEquiv n A).symm f).hom ((resolution.d k G (n + 1)) (Finsupp.single (Fin.partialProd g) 1))",
+                "tactic": "erw [resolution.d_of (Fin.partialProd g)]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp only [<a>map_sum<\\/a>, \\u2190 <a>Finsupp.smul_single_one<\\/a> _ ((-1 : k) ^ _)]\"",
+                  "[{\"full_name\":\"map_sum\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Finset.lean\",\"def_pos\":[295,3],\"def_end_pos\":[295,14]},{\"full_name\":\"Finsupp.smul_single_one\",\"def_path\":\"Mathlib\\/Data\\/Finsupp\\/Basic.lean\",\"def_pos\":[1594,9],\"def_end_pos\":[1594,24]}]"
+                ],
+                "state_after": "case h.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\n\u22a2 (d n A) f g =\n    \u2211 x : Fin (n + 1 + 1),\n      ((diagonalHomEquiv n A).symm f).hom ((-1) ^ \u2191x \u2022 Finsupp.single (Fin.partialProd g \u2218 x.succAbove) 1)",
+                "state_before": "case h.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\n\u22a2 (d n A) f g =\n    ((diagonalHomEquiv n A).symm f).hom\n      (\u2211 p : Fin (n + 1 + 1), Finsupp.single (Fin.partialProd g \u2218 p.succAbove) ((-1) ^ \u2191p))",
+                "tactic": "simp only [map_sum, \u2190 Finsupp.smul_single_one _ ((-1 : k) ^ _)]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"erw [<a>d_apply<\\/a>, @<a>Fin.sum_univ_succ<\\/a> _ _ (n + 1), <a>Fin.val_zero<\\/a>, <a>pow_zero<\\/a>, <a>one_smul<\\/a>,\\n    <a>Fin.succAbove_zero<\\/a>, <a>diagonalHomEquiv_symm_apply<\\/a> f (<a>Fin.partialProd<\\/a> g \\u2218 @<a>Fin.succ<\\/a> (n + 1))]\"",
+                  "[{\"full_name\":\"inhomogeneousCochains.d_apply\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/GroupCohomology\\/Basic.lean\",\"def_pos\":[104,3],\"def_end_pos\":[104,8]},{\"full_name\":\"Fin.sum_univ_succ\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Fin.lean\",\"def_pos\":[78,3],\"def_end_pos\":[78,14]},{\"full_name\":\"Fin.val_zero\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[126,17],\"def_end_pos\":[126,25]},{\"full_name\":\"pow_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[651,9],\"def_end_pos\":[651,17]},{\"full_name\":\"one_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[453,7],\"def_end_pos\":[453,15]},{\"full_name\":\"Fin.succAbove_zero\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Basic.lean\",\"def_pos\":[1423,15],\"def_end_pos\":[1423,29]},{\"full_name\":\"Rep.diagonalHomEquiv_symm_apply\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/GroupCohomology\\/Resolution.lean\",\"def_pos\":[363,9],\"def_end_pos\":[363,36]},{\"full_name\":\"Fin.partialProd\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Fin.lean\",\"def_pos\":[233,5],\"def_end_pos\":[233,16]},{\"full_name\":\"Fin.succ\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Basic.lean\",\"def_pos\":[34,5],\"def_end_pos\":[34,9]}]"
+                ],
+                "state_after": "case h.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\n\u22a2 (A.\u03c1 (g 0)) (f fun i => g i.succ) + \u2211 j : Fin (n + 1), (-1) ^ (\u2191j + 1) \u2022 f (j.contractNth (fun x x_1 => x * x_1) g) =\n    (A.\u03c1 ((Fin.partialProd g \u2218 Fin.succ) 0))\n        (f fun i => ((Fin.partialProd g \u2218 Fin.succ) i.castSucc)\u207b\u00b9 * (Fin.partialProd g \u2218 Fin.succ) i.succ) +\n      \u2211 i : Fin (n + 1),\n        ((diagonalHomEquiv n A).symm f).hom ((-1) ^ \u2191i.succ \u2022 Finsupp.single (Fin.partialProd g \u2218 i.succ.succAbove) 1)",
+                "state_before": "case h.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\n\u22a2 (d n A) f g =\n    \u2211 x : Fin (n + 1 + 1),\n      ((diagonalHomEquiv n A).symm f).hom ((-1) ^ \u2191x \u2022 Finsupp.single (Fin.partialProd g \u2218 x.succAbove) 1)",
+                "tactic": "erw [d_apply, @Fin.sum_univ_succ _ _ (n + 1), Fin.val_zero, pow_zero, one_smul,\n  Fin.succAbove_zero, diagonalHomEquiv_symm_apply f (Fin.partialProd g \u2218 @Fin.succ (n + 1))]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp_rw [<a>Function.comp_apply<\\/a>, <a>Fin.partialProd_succ<\\/a>, <a>Fin.castSucc_zero<\\/a>,\\n    <a>Fin.partialProd_zero<\\/a>, <a>one_mul<\\/a>]\"",
+                  "[{\"full_name\":\"Function.comp_apply\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[35,17],\"def_end_pos\":[35,36]},{\"full_name\":\"Fin.partialProd_succ\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Fin.lean\",\"def_pos\":[244,9],\"def_end_pos\":[244,25]},{\"full_name\":\"Fin.castSucc_zero\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[404,17],\"def_end_pos\":[404,30]},{\"full_name\":\"Fin.partialProd_zero\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Fin.lean\",\"def_pos\":[239,9],\"def_end_pos\":[239,25]},{\"full_name\":\"one_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[477,9],\"def_end_pos\":[477,16]}]"
+                ],
+                "state_after": "case h.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\n\u22a2 (A.\u03c1 (g 0)) (f fun i => g i.succ) + \u2211 j : Fin (n + 1), (-1) ^ (\u2191j + 1) \u2022 f (j.contractNth (fun x x_1 => x * x_1) g) =\n    (A.\u03c1 (g 0))\n        (f fun i =>\n          (Fin.partialProd g i.castSucc.castSucc * g i.castSucc)\u207b\u00b9 * (Fin.partialProd g i.succ.castSucc * g i.succ)) +\n      \u2211 i : Fin (n + 1),\n        ((diagonalHomEquiv n A).symm f).hom ((-1) ^ \u2191i.succ \u2022 Finsupp.single (Fin.partialProd g \u2218 i.succ.succAbove) 1)",
+                "state_before": "case h.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\n\u22a2 (A.\u03c1 (g 0)) (f fun i => g i.succ) + \u2211 j : Fin (n + 1), (-1) ^ (\u2191j + 1) \u2022 f (j.contractNth (fun x x_1 => x * x_1) g) =\n    (A.\u03c1 ((Fin.partialProd g \u2218 Fin.succ) 0))\n        (f fun i => ((Fin.partialProd g \u2218 Fin.succ) i.castSucc)\u207b\u00b9 * (Fin.partialProd g \u2218 Fin.succ) i.succ) +\n      \u2211 i : Fin (n + 1),\n        ((diagonalHomEquiv n A).symm f).hom ((-1) ^ \u2191i.succ \u2022 Finsupp.single (Fin.partialProd g \u2218 i.succ.succAbove) 1)",
+                "tactic": "simp_rw [Function.comp_apply, Fin.partialProd_succ, Fin.castSucc_zero,\n  Fin.partialProd_zero, one_mul]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rcongr x\"",
+                  "[]"
+                ],
+                "state_after": "case h.h.e_a.h.e_6.h.e_a.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\nx : Fin n\n\u22a2 g x.succ = (Fin.partialProd g x.castSucc.castSucc * g x.castSucc)\u207b\u00b9 * (Fin.partialProd g x.succ.castSucc * g x.succ)\n\ncase h.h.e_a.e_f.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\nx : Fin (n + 1)\n\u22a2 (-1) ^ (\u2191x + 1) \u2022 f (x.contractNth (fun x x_1 => x * x_1) g) =\n    ((diagonalHomEquiv n A).symm f).hom ((-1) ^ \u2191x.succ \u2022 Finsupp.single (Fin.partialProd g \u2218 x.succ.succAbove) 1)",
+                "state_before": "case h.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\n\u22a2 (A.\u03c1 (g 0)) (f fun i => g i.succ) + \u2211 j : Fin (n + 1), (-1) ^ (\u2191j + 1) \u2022 f (j.contractNth (fun x x_1 => x * x_1) g) =\n    (A.\u03c1 (g 0))\n        (f fun i =>\n          (Fin.partialProd g i.castSucc.castSucc * g i.castSucc)\u207b\u00b9 * (Fin.partialProd g i.succ.castSucc * g i.succ)) +\n      \u2211 i : Fin (n + 1),\n        ((diagonalHomEquiv n A).symm f).hom ((-1) ^ \u2191i.succ \u2022 Finsupp.single (Fin.partialProd g \u2218 i.succ.succAbove) 1)",
+                "tactic": "rcongr x"
+              },
+              {
+                "annotated_tactic": [
+                  "\"have := <a>Fin.partialProd_right_inv<\\/a> g (<a>Fin.castSucc<\\/a> x)\"",
+                  "[{\"full_name\":\"Fin.partialProd_right_inv\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Fin.lean\",\"def_pos\":[268,9],\"def_end_pos\":[268,30]},{\"full_name\":\"Fin.castSucc\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Basic.lean\",\"def_pos\":[181,15],\"def_end_pos\":[181,23]}]"
+                ],
+                "state_after": "case h.h.e_a.h.e_6.h.e_a.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\nx : Fin n\nthis : (Fin.partialProd g x.castSucc.castSucc)\u207b\u00b9 * Fin.partialProd g x.castSucc.succ = g x.castSucc\n\u22a2 g x.succ = (Fin.partialProd g x.castSucc.castSucc * g x.castSucc)\u207b\u00b9 * (Fin.partialProd g x.succ.castSucc * g x.succ)",
+                "state_before": "case h.h.e_a.h.e_6.h.e_a.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\nx : Fin n\n\u22a2 g x.succ = (Fin.partialProd g x.castSucc.castSucc * g x.castSucc)\u207b\u00b9 * (Fin.partialProd g x.succ.castSucc * g x.succ)",
+                "tactic": "have := Fin.partialProd_right_inv g (Fin.castSucc x)"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp only [<a>mul_inv_rev<\\/a>, <a>Fin.castSucc_fin_succ<\\/a>] at this \\u22a2\"",
+                  "[{\"full_name\":\"mul_inv_rev\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1153,9],\"def_end_pos\":[1153,20]},{\"full_name\":\"Fin.castSucc_fin_succ\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[417,9],\"def_end_pos\":[417,26]}]"
+                ],
+                "state_after": "case h.h.e_a.h.e_6.h.e_a.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\nx : Fin n\nthis : (Fin.partialProd g x.castSucc.castSucc)\u207b\u00b9 * Fin.partialProd g x.castSucc.succ = g x.castSucc\n\u22a2 g x.succ =\n    (g x.castSucc)\u207b\u00b9 * (Fin.partialProd g x.castSucc.castSucc)\u207b\u00b9 * (Fin.partialProd g x.castSucc.succ * g x.succ)",
+                "state_before": "case h.h.e_a.h.e_6.h.e_a.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\nx : Fin n\nthis : (Fin.partialProd g x.castSucc.castSucc)\u207b\u00b9 * Fin.partialProd g x.castSucc.succ = g x.castSucc\n\u22a2 g x.succ = (Fin.partialProd g x.castSucc.castSucc * g x.castSucc)\u207b\u00b9 * (Fin.partialProd g x.succ.castSucc * g x.succ)",
+                "tactic": "simp only [mul_inv_rev, Fin.castSucc_fin_succ] at this \u22a2"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>mul_assoc<\\/a>, \\u2190 <a>mul_assoc<\\/a> _ _ (g x.succ), this, <a>inv_mul_cancel_left<\\/a>]\"",
+                  "[{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]},{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]},{\"full_name\":\"inv_mul_cancel_left\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1250,9],\"def_end_pos\":[1250,28]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case h.h.e_a.h.e_6.h.e_a.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\nx : Fin n\nthis : (Fin.partialProd g x.castSucc.castSucc)\u207b\u00b9 * Fin.partialProd g x.castSucc.succ = g x.castSucc\n\u22a2 g x.succ =\n    (g x.castSucc)\u207b\u00b9 * (Fin.partialProd g x.castSucc.castSucc)\u207b\u00b9 * (Fin.partialProd g x.castSucc.succ * g x.succ)",
+                "tactic": "rw [mul_assoc, \u2190 mul_assoc _ _ (g x.succ), this, inv_mul_cancel_left]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"erw [<a>map_smul<\\/a>, <a>diagonalHomEquiv_symm_partialProd_succ<\\/a>, <a>Fin.val_succ<\\/a>]\"",
+                  "[{\"full_name\":\"map_smul\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Hom.lean\",\"def_pos\":[111,9],\"def_end_pos\":[111,17]},{\"full_name\":\"Rep.diagonalHomEquiv_symm_partialProd_succ\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/GroupCohomology\\/Resolution.lean\",\"def_pos\":[401,9],\"def_end_pos\":[401,47]},{\"full_name\":\"Fin.val_succ\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[237,17],\"def_end_pos\":[237,25]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case h.h.e_a.e_f.h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\nn : \u2115\ninst\u271d : Group G\nA : Rep k G\nf : (Fin n \u2192 G) \u2192 CoeSort.coe A\ng : Fin (n + 1) \u2192 G\nx : Fin (n + 1)\n\u22a2 (-1) ^ (\u2191x + 1) \u2022 f (x.contractNth (fun x x_1 => x * x_1) g) =\n    ((diagonalHomEquiv n A).symm f).hom ((-1) ^ \u2191x.succ \u2022 Finsupp.single (Fin.partialProd g \u2218 x.succ.succAbove) 1)",
+                "tactic": "erw [map_smul, diagonalHomEquiv_symm_partialProd_succ, Fin.val_succ]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "inhomogeneousCochains.d_eq"
+      }
+    ],
+    "validation_rejected_proofs": 1,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001637-0000-3688294358a61160.parquet",
+      "sha256": "3688294358a611608b16bae77e5e55ef0e7ed66e04e30b2a17ec4d87c1a6442c",
+      "bytes": 91140,
+      "rows": 5,
+      "revision": "df8c9c479578582ca5384c5c62608ea4677707ca"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:FdRep.Iso.conj_\u03c1",
+    "mathlib:FdRep.forget\u2082_\u03c1"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/FdRep.lean\",null,null,\"FdRep.Iso.conj_\u03c1\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/FdRep.lean\",null,null,\"FdRep.forget\u2082_\u03c1\"]"
+  ]
+}

manifests/batches/mathlib/001640.json

@@ -0,0 +1,1264 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001640",
+  "batch_fingerprint": "a3f8fb40b9b8749e74f3317c9933fe8e2109a0c8502b9cfb71e64ef54eb91ed1",
+  "evidence": {
+    "batch_fingerprint": "a3f8fb40b9b8749e74f3317c9933fe8e2109a0c8502b9cfb71e64ef54eb91ed1",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LinearMap.conjugate_apply",
+        "id": "LinearMap.conjugate_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            75,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Maschke.lean",
+          "full_name": "LinearMap.conjugate_apply",
+          "start": [
+            73,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Maschke.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LinearMap.sumOfConjugatesEquivariant_apply",
+        "id": "LinearMap.sumOfConjugatesEquivariant_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            112,
+            30
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Maschke.lean",
+          "full_name": "LinearMap.sumOfConjugatesEquivariant_apply",
+          "start": [
+            110,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Maschke.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LinearMap.sumOfConjugates_apply",
+        "id": "LinearMap.sumOfConjugates_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            99,
+            28
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Maschke.lean",
+          "full_name": "LinearMap.sumOfConjugates_apply",
+          "start": [
+            98,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Maschke.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'simp only [hf, Submodule.restrictScalars_bot, LinearMap.ker_restrictScalars]'",
+        "full_name": "MonoidAlgebra.exists_leftInverse_of_injective",
+        "id": "MonoidAlgebra.exists_leftInverse_of_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            161,
+            71
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Maschke.lean",
+          "full_name": "MonoidAlgebra.exists_leftInverse_of_injective",
+          "start": [
+            150,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"let A := <a>MonoidAlgebra<\\/a> k G\"",
+                "[{\"full_name\":\"MonoidAlgebra\",\"def_path\":\"Mathlib\\/Algebra\\/MonoidAlgebra\\/Basic.lean\",\"def_pos\":[76,5],\"def_end_pos\":[76,18]}]"
+              ],
+              "state_after": "k : Type u\ninst\u271d\u2077 : Field k\nG : Type u\ninst\u271d\u2076 : Fintype G\ninst\u271d\u2075 : Invertible \u2191(Fintype.card G)\ninst\u271d\u2074 : Group G\nV : Type u\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : Module (MonoidAlgebra k G) V\nW : Type u\ninst\u271d\u00b9 : AddCommGroup W\ninst\u271d : Module (MonoidAlgebra k G) W\nf : V \u2192\u2097[MonoidAlgebra k G] W\nhf : LinearMap.ker f = \u22a5\nA : Type u := MonoidAlgebra k G\n\u22a2 \u2203 g, g \u2218\u2097 f = LinearMap.id",
+              "state_before": "k : Type u\ninst\u271d\u2077 : Field k\nG : Type u\ninst\u271d\u2076 : Fintype G\ninst\u271d\u2075 : Invertible \u2191(Fintype.card G)\ninst\u271d\u2074 : Group G\nV : Type u\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : Module (MonoidAlgebra k G) V\nW : Type u\ninst\u271d\u00b9 : AddCommGroup W\ninst\u271d : Module (MonoidAlgebra k G) W\nf : V \u2192\u2097[MonoidAlgebra k G] W\nhf : LinearMap.ker f = \u22a5\n\u22a2 \u2203 g, g \u2218\u2097 f = LinearMap.id",
+              "tactic": "let A := MonoidAlgebra k G"
+            },
+            {
+              "annotated_tactic": [
+                "\"letI : <a>Module<\\/a> k W := .compHom W (<a>algebraMap<\\/a> k A)\"",
+                "[{\"full_name\":\"Module\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Defs.lean\",\"def_pos\":[57,7],\"def_end_pos\":[57,13]},{\"full_name\":\"algebraMap\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Defs.lean\",\"def_pos\":[110,5],\"def_end_pos\":[110,15]}]"
+              ],
+              "state_after": "k : Type u\ninst\u271d\u2077 : Field k\nG : Type u\ninst\u271d\u2076 : Fintype G\ninst\u271d\u2075 : Invertible \u2191(Fintype.card G)\ninst\u271d\u2074 : Group G\nV : Type u\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : Module (MonoidAlgebra k G) V\nW : Type u\ninst\u271d\u00b9 : AddCommGroup W\ninst\u271d : Module (MonoidAlgebra k G) W\nf : V \u2192\u2097[MonoidAlgebra k G] W\nhf : LinearMap.ker f = \u22a5\nA : Type u := MonoidAlgebra k G\nthis : Module k W := Module.compHom W (algebraMap k A)\n\u22a2 \u2203 g, g \u2218\u2097 f = LinearMap.id",
+              "state_before": "k : Type u\ninst\u271d\u2077 : Field k\nG : Type u\ninst\u271d\u2076 : Fintype G\ninst\u271d\u2075 : Invertible \u2191(Fintype.card G)\ninst\u271d\u2074 : Group G\nV : Type u\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : Module (MonoidAlgebra k G) V\nW : Type u\ninst\u271d\u00b9 : AddCommGroup W\ninst\u271d : Module (MonoidAlgebra k G) W\nf : V \u2192\u2097[MonoidAlgebra k G] W\nhf : LinearMap.ker f = \u22a5\nA : Type u := MonoidAlgebra k G\n\u22a2 \u2203 g, g \u2218\u2097 f = LinearMap.id",
+              "tactic": "letI : Module k W := .compHom W (algebraMap k A)"
+            },
+            {
+              "annotated_tactic": [
+                "\"letI : <a>Module<\\/a> k V := .compHom V (<a>algebraMap<\\/a> k A)\"",
+                "[{\"full_name\":\"Module\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Defs.lean\",\"def_pos\":[57,7],\"def_end_pos\":[57,13]},{\"full_name\":\"algebraMap\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Defs.lean\",\"def_pos\":[110,5],\"def_end_pos\":[110,15]}]"
+              ],
+              "state_after": "k : Type u\ninst\u271d\u2077 : Field k\nG : Type u\ninst\u271d\u2076 : Fintype G\ninst\u271d\u2075 : Invertible \u2191(Fintype.card G)\ninst\u271d\u2074 : Group G\nV : Type u\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : Module (MonoidAlgebra k G) V\nW : Type u\ninst\u271d\u00b9 : AddCommGroup W\ninst\u271d : Module (MonoidAlgebra k G) W\nf : V \u2192\u2097[MonoidAlgebra k G] W\nhf : LinearMap.ker f = \u22a5\nA : Type u := MonoidAlgebra k G\nthis\u271d : Module k W := Module.compHom W (algebraMap k A)\nthis : Module k V := Module.compHom V (algebraMap k A)\n\u22a2 \u2203 g, g \u2218\u2097 f = LinearMap.id",
+              "state_before": "k : Type u\ninst\u271d\u2077 : Field k\nG : Type u\ninst\u271d\u2076 : Fintype G\ninst\u271d\u2075 : Invertible \u2191(Fintype.card G)\ninst\u271d\u2074 : Group G\nV : Type u\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : Module (MonoidAlgebra k G) V\nW : Type u\ninst\u271d\u00b9 : AddCommGroup W\ninst\u271d : Module (MonoidAlgebra k G) W\nf : V \u2192\u2097[MonoidAlgebra k G] W\nhf : LinearMap.ker f = \u22a5\nA : Type u := MonoidAlgebra k G\nthis : Module k W := Module.compHom W (algebraMap k A)\n\u22a2 \u2203 g, g \u2218\u2097 f = LinearMap.id",
+              "tactic": "letI : Module k V := .compHom V (algebraMap k A)"
+            },
+            {
+              "annotated_tactic": [
+                "\"have := <a>IsScalarTower.of_compHom<\\/a> k A W\"",
+                "[{\"full_name\":\"IsScalarTower.of_compHom\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Tower.lean\",\"def_pos\":[99,9],\"def_end_pos\":[99,19]}]"
+              ],
+              "state_after": "k : Type u\ninst\u271d\u2077 : Field k\nG : Type u\ninst\u271d\u2076 : Fintype G\ninst\u271d\u2075 : Invertible \u2191(Fintype.card G)\ninst\u271d\u2074 : Group G\nV : Type u\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : Module (MonoidAlgebra k G) V\nW : Type u\ninst\u271d\u00b9 : AddCommGroup W\ninst\u271d : Module (MonoidAlgebra k G) W\nf : V \u2192\u2097[MonoidAlgebra k G] W\nhf : LinearMap.ker f = \u22a5\nA : Type u := MonoidAlgebra k G\nthis\u271d\u00b9 : Module k W := Module.compHom W (algebraMap k A)\nthis\u271d : Module k V := Module.compHom V (algebraMap k A)\nthis : IsScalarTower k A W\n\u22a2 \u2203 g, g \u2218\u2097 f = LinearMap.id",
+              "state_before": "k : Type u\ninst\u271d\u2077 : Field k\nG : Type u\ninst\u271d\u2076 : Fintype G\ninst\u271d\u2075 : Invertible \u2191(Fintype.card G)\ninst\u271d\u2074 : Group G\nV : Type u\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : Module (MonoidAlgebra k G) V\nW : Type u\ninst\u271d\u00b9 : AddCommGroup W\ninst\u271d : Module (MonoidAlgebra k G) W\nf : V \u2192\u2097[MonoidAlgebra k G] W\nhf : LinearMap.ker f = \u22a5\nA : Type u := MonoidAlgebra k G\nthis\u271d : Module k W := Module.compHom W (algebraMap k A)\nthis : Module k V := Module.compHom V (algebraMap k A)\n\u22a2 \u2203 g, g \u2218\u2097 f = LinearMap.id",
+              "tactic": "have := IsScalarTower.of_compHom k A W"
+            },
+            {
+              "annotated_tactic": [
+                "\"have := <a>IsScalarTower.of_compHom<\\/a> k A V\"",
+                "[{\"full_name\":\"IsScalarTower.of_compHom\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Tower.lean\",\"def_pos\":[99,9],\"def_end_pos\":[99,19]}]"
+              ],
+              "state_after": "k : Type u\ninst\u271d\u2077 : Field k\nG : Type u\ninst\u271d\u2076 : Fintype G\ninst\u271d\u2075 : Invertible \u2191(Fintype.card G)\ninst\u271d\u2074 : Group G\nV : Type u\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : Module (MonoidAlgebra k G) V\nW : Type u\ninst\u271d\u00b9 : AddCommGroup W\ninst\u271d : Module (MonoidAlgebra k G) W\nf : V \u2192\u2097[MonoidAlgebra k G] W\nhf : LinearMap.ker f = \u22a5\nA : Type u := MonoidAlgebra k G\nthis\u271d\u00b2 : Module k W := Module.compHom W (algebraMap k A)\nthis\u271d\u00b9 : Module k V := Module.compHom V (algebraMap k A)\nthis\u271d : IsScalarTower k A W\nthis : IsScalarTower k A V\n\u22a2 \u2203 g, g \u2218\u2097 f = LinearMap.id",
+              "state_before": "k : Type u\ninst\u271d\u2077 : Field k\nG : Type u\ninst\u271d\u2076 : Fintype G\ninst\u271d\u2075 : Invertible \u2191(Fintype.card G)\ninst\u271d\u2074 : Group G\nV : Type u\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : Module (MonoidAlgebra k G) V\nW : Type u\ninst\u271d\u00b9 : AddCommGroup W\ninst\u271d : Module (MonoidAlgebra k G) W\nf : V \u2192\u2097[MonoidAlgebra k G] W\nhf : LinearMap.ker f = \u22a5\nA : Type u := MonoidAlgebra k G\nthis\u271d\u00b9 : Module k W := Module.compHom W (algebraMap k A)\nthis\u271d : Module k V := Module.compHom V (algebraMap k A)\nthis : IsScalarTower k A W\n\u22a2 \u2203 g, g \u2218\u2097 f = LinearMap.id",
+              "tactic": "have := IsScalarTower.of_compHom k A V"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8\\u03c6, h\\u03c6\\u27e9 := (f.restrictScalars k).<a>exists_leftInverse_of_injective<\\/a> <| by\\n    simp only [hf, <a>Submodule.restrictScalars_bot<\\/a>, <a>LinearMap.ker_restrictScalars<\\/a>]\"",
+                "[{\"full_name\":\"LinearMap.exists_leftInverse_of_injective\",\"def_path\":\"Mathlib\\/LinearAlgebra\\/Basis\\/VectorSpace.lean\",\"def_pos\":[206,9],\"def_end_pos\":[206,50]},{\"full_name\":\"Submodule.restrictScalars_bot\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Submodule\\/RestrictScalars.lean\",\"def_pos\":[101,9],\"def_end_pos\":[101,28]},{\"full_name\":\"LinearMap.ker_restrictScalars\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Basic.lean\",\"def_pos\":[489,9],\"def_end_pos\":[489,38]}]"
+              ],
+              "state_after": "case intro\nk : Type u\ninst\u271d\u2077 : Field k\nG : Type u\ninst\u271d\u2076 : Fintype G\ninst\u271d\u2075 : Invertible \u2191(Fintype.card G)\ninst\u271d\u2074 : Group G\nV : Type u\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : Module (MonoidAlgebra k G) V\nW : Type u\ninst\u271d\u00b9 : AddCommGroup W\ninst\u271d : Module (MonoidAlgebra k G) W\nf : V \u2192\u2097[MonoidAlgebra k G] W\nhf : LinearMap.ker f = \u22a5\nA : Type u := MonoidAlgebra k G\nthis\u271d\u00b2 : Module k W := Module.compHom W (algebraMap k A)\nthis\u271d\u00b9 : Module k V := Module.compHom V (algebraMap k A)\nthis\u271d : IsScalarTower k A W\nthis : IsScalarTower k A V\n\u03c6 : W \u2192\u2097[k] V\nh\u03c6 : \u03c6 \u2218\u2097 \u2191k f = LinearMap.id\n\u22a2 \u2203 g, g \u2218\u2097 f = LinearMap.id",
+              "state_before": "k : Type u\ninst\u271d\u2077 : Field k\nG : Type u\ninst\u271d\u2076 : Fintype G\ninst\u271d\u2075 : Invertible \u2191(Fintype.card G)\ninst\u271d\u2074 : Group G\nV : Type u\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : Module (MonoidAlgebra k G) V\nW : Type u\ninst\u271d\u00b9 : AddCommGroup W\ninst\u271d : Module (MonoidAlgebra k G) W\nf : V \u2192\u2097[MonoidAlgebra k G] W\nhf : LinearMap.ker f = \u22a5\nA : Type u := MonoidAlgebra k G\nthis\u271d\u00b2 : Module k W := Module.compHom W (algebraMap k A)\nthis\u271d\u00b9 : Module k V := Module.compHom V (algebraMap k A)\nthis\u271d : IsScalarTower k A W\nthis : IsScalarTower k A V\n\u22a2 \u2203 g, g \u2218\u2097 f = LinearMap.id",
+              "tactic": "obtain \u27e8\u03c6, h\u03c6\u27e9 := (f.restrictScalars k).exists_leftInverse_of_injective <| by\n  simp only [hf, Submodule.restrictScalars_bot, LinearMap.ker_restrictScalars]"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine \\u27e8\\u03c6.equivariantProjection G, <a>DFunLike.ext<\\/a> _ _ ?_\\u27e9\"",
+                "[{\"full_name\":\"DFunLike.ext\",\"def_path\":\"Mathlib\\/Data\\/FunLike\\/Basic.lean\",\"def_pos\":[201,9],\"def_end_pos\":[201,12]}]"
+              ],
+              "state_after": "case intro\nk : Type u\ninst\u271d\u2077 : Field k\nG : Type u\ninst\u271d\u2076 : Fintype G\ninst\u271d\u2075 : Invertible \u2191(Fintype.card G)\ninst\u271d\u2074 : Group G\nV : Type u\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : Module (MonoidAlgebra k G) V\nW : Type u\ninst\u271d\u00b9 : AddCommGroup W\ninst\u271d : Module (MonoidAlgebra k G) W\nf : V \u2192\u2097[MonoidAlgebra k G] W\nhf : LinearMap.ker f = \u22a5\nA : Type u := MonoidAlgebra k G\nthis\u271d\u00b2 : Module k W := Module.compHom W (algebraMap k A)\nthis\u271d\u00b9 : Module k V := Module.compHom V (algebraMap k A)\nthis\u271d : IsScalarTower k A W\nthis : IsScalarTower k A V\n\u03c6 : W \u2192\u2097[k] V\nh\u03c6 : \u03c6 \u2218\u2097 \u2191k f = LinearMap.id\n\u22a2 \u2200 (x : V), (LinearMap.equivariantProjection G \u03c6 \u2218\u2097 f) x = LinearMap.id x",
+              "state_before": "case intro\nk : Type u\ninst\u271d\u2077 : Field k\nG : Type u\ninst\u271d\u2076 : Fintype G\ninst\u271d\u2075 : Invertible \u2191(Fintype.card G)\ninst\u271d\u2074 : Group G\nV : Type u\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : Module (MonoidAlgebra k G) V\nW : Type u\ninst\u271d\u00b9 : AddCommGroup W\ninst\u271d : Module (MonoidAlgebra k G) W\nf : V \u2192\u2097[MonoidAlgebra k G] W\nhf : LinearMap.ker f = \u22a5\nA : Type u := MonoidAlgebra k G\nthis\u271d\u00b2 : Module k W := Module.compHom W (algebraMap k A)\nthis\u271d\u00b9 : Module k V := Module.compHom V (algebraMap k A)\nthis\u271d : IsScalarTower k A W\nthis : IsScalarTower k A V\n\u03c6 : W \u2192\u2097[k] V\nh\u03c6 : \u03c6 \u2218\u2097 \u2191k f = LinearMap.id\n\u22a2 \u2203 g, g \u2218\u2097 f = LinearMap.id",
+              "tactic": "refine \u27e8\u03c6.equivariantProjection G, DFunLike.ext _ _ ?_\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact \\u03c6.equivariantProjection_condition G _ <| <a>DFunLike.congr_fun<\\/a> h\\u03c6\"",
+                "[{\"full_name\":\"DFunLike.congr_fun\",\"def_path\":\"Mathlib\\/Data\\/FunLike\\/Basic.lean\",\"def_pos\":[209,19],\"def_end_pos\":[209,28]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case intro\nk : Type u\ninst\u271d\u2077 : Field k\nG : Type u\ninst\u271d\u2076 : Fintype G\ninst\u271d\u2075 : Invertible \u2191(Fintype.card G)\ninst\u271d\u2074 : Group G\nV : Type u\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : Module (MonoidAlgebra k G) V\nW : Type u\ninst\u271d\u00b9 : AddCommGroup W\ninst\u271d : Module (MonoidAlgebra k G) W\nf : V \u2192\u2097[MonoidAlgebra k G] W\nhf : LinearMap.ker f = \u22a5\nA : Type u := MonoidAlgebra k G\nthis\u271d\u00b2 : Module k W := Module.compHom W (algebraMap k A)\nthis\u271d\u00b9 : Module k V := Module.compHom V (algebraMap k A)\nthis\u271d : IsScalarTower k A W\nthis : IsScalarTower k A V\n\u03c6 : W \u2192\u2097[k] V\nh\u03c6 : \u03c6 \u2218\u2097 \u2191k f = LinearMap.id\n\u22a2 \u2200 (x : V), (LinearMap.equivariantProjection G \u03c6 \u2218\u2097 f) x = LinearMap.id x",
+              "tactic": "exact \u03c6.equivariantProjection_condition G _ <| DFunLike.congr_fun h\u03c6"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [hf, <a>Submodule.restrictScalars_bot<\\/a>, <a>LinearMap.ker_restrictScalars<\\/a>]\"",
+                "[{\"full_name\":\"Submodule.restrictScalars_bot\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Submodule\\/RestrictScalars.lean\",\"def_pos\":[101,9],\"def_end_pos\":[101,28]},{\"full_name\":\"LinearMap.ker_restrictScalars\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Basic.lean\",\"def_pos\":[489,9],\"def_end_pos\":[489,38]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "k : Type u\ninst\u271d\u2077 : Field k\nG : Type u\ninst\u271d\u2076 : Fintype G\ninst\u271d\u2075 : Invertible \u2191(Fintype.card G)\ninst\u271d\u2074 : Group G\nV : Type u\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : Module (MonoidAlgebra k G) V\nW : Type u\ninst\u271d\u00b9 : AddCommGroup W\ninst\u271d : Module (MonoidAlgebra k G) W\nf : V \u2192\u2097[MonoidAlgebra k G] W\nhf : LinearMap.ker f = \u22a5\nA : Type u := MonoidAlgebra k G\nthis\u271d\u00b2 : Module k W := Module.compHom W (algebraMap k A)\nthis\u271d\u00b9 : Module k V := Module.compHom V (algebraMap k A)\nthis\u271d : IsScalarTower k A W\nthis : IsScalarTower k A V\n\u22a2 LinearMap.ker (\u2191k f) = \u22a5",
+              "tactic": "simp only [hf, Submodule.restrictScalars_bot, LinearMap.ker_restrictScalars]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Maschke.lean"
+      },
+      {
+        "full_name": "Rep.Action_\u03c1_eq_\u03c1",
+        "id": "Rep.Action_\u03c1_eq_\u03c1",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            92,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.Action_\u03c1_eq_\u03c1",
+          "start": [
+            91,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.MonoidalCategory.braiding_hom_apply",
+        "id": "Rep.MonoidalCategory.braiding_hom_apply",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            160,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.MonoidalCategory.braiding_hom_apply",
+          "start": [
+            158,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.MonoidalCategory.braiding_inv_apply",
+        "id": "Rep.MonoidalCategory.braiding_inv_apply",
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+            6
+          ],
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+          "full_name": "Rep.MonoidalCategory.braiding_inv_apply",
+          "start": [
+            166,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.MonoidalClosed.linearHomEquivComm_hom",
+        "id": "Rep.MonoidalClosed.linearHomEquivComm_hom",
+        "reason": "missing_trace",
+        "selection": {
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+          "end": [
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+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.MonoidalClosed.linearHomEquivComm_hom",
+          "start": [
+            533,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.MonoidalClosed.linearHomEquivComm_symm_hom",
+        "id": "Rep.MonoidalClosed.linearHomEquivComm_symm_hom",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            548,
+            36
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.MonoidalClosed.linearHomEquivComm_symm_hom",
+          "start": [
+            545,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.MonoidalClosed.linearHomEquiv_hom",
+        "id": "Rep.MonoidalClosed.linearHomEquiv_hom",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            527,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.MonoidalClosed.linearHomEquiv_hom",
+          "start": [
+            525,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.MonoidalClosed.linearHomEquiv_symm_hom",
+        "id": "Rep.MonoidalClosed.linearHomEquiv_symm_hom",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            541,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.MonoidalClosed.linearHomEquiv_symm_hom",
+          "start": [
+            539,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.coe_of",
+        "id": "Rep.coe_of",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            81,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.coe_of",
+          "start": [
+            79,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.homEquiv_apply_hom",
+        "id": "Rep.homEquiv_apply_hom",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            456,
+            69
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.homEquiv_apply_hom",
+          "start": [
+            455,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.homEquiv_def",
+        "id": "Rep.homEquiv_def",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            485,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.homEquiv_def",
+          "start": [
+            484,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.homEquiv_symm_apply_hom",
+        "id": "Rep.homEquiv_symm_apply_hom",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            463,
+            84
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.homEquiv_symm_apply_hom",
+          "start": [
+            462,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.hom_comm_apply",
+        "id": "Rep.hom_comm_apply",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            120,
+            35
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.hom_comm_apply",
+          "start": [
+            118,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.ihom_coev_app_hom",
+        "id": "Rep.ihom_coev_app_hom",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            499,
+            52
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.ihom_coev_app_hom",
+          "start": [
+            497,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.ihom_ev_app_hom",
+        "id": "Rep.ihom_ev_app_hom",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            493,
+            11
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.ihom_ev_app_hom",
+          "start": [
+            490,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"ext\"",
+                "[]"
+              ],
+              "state_after": "case h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Group G\nA\u271d B\u271d C A B : Rep k G\nx\u271d : \u2191((ihom A \u22d9 tensorLeft A).obj B).V\n\u22a2 ((ihom.ev A).app B).hom x\u271d =\n    ((TensorProduct.uncurry k (CoeSort.coe A) (CoeSort.coe A \u2192\u2097[k] CoeSort.coe B) (CoeSort.coe B)) LinearMap.id.flip) x\u271d",
+              "state_before": "k G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Group G\nA\u271d B\u271d C A B : Rep k G\n\u22a2 ((ihom.ev A).app B).hom =\n    (TensorProduct.uncurry k (CoeSort.coe A) (CoeSort.coe A \u2192\u2097[k] CoeSort.coe B) (CoeSort.coe B)) LinearMap.id.flip",
+              "tactic": "ext"
+            },
+            {
+              "annotated_tactic": [
+                "\"rfl\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h\nk G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Group G\nA\u271d B\u271d C A B : Rep k G\nx\u271d : \u2191((ihom A \u22d9 tensorLeft A).obj B).V\n\u22a2 ((ihom.ev A).app B).hom x\u271d =\n    ((TensorProduct.uncurry k (CoeSort.coe A) (CoeSort.coe A \u2192\u2097[k] CoeSort.coe B) (CoeSort.coe B)) LinearMap.id.flip) x\u271d",
+              "tactic": "rfl"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.ihom_obj_\u03c1_apply",
+        "id": "Rep.ihom_obj_\u03c1_apply",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            412,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.ihom_obj_\u03c1_apply",
+          "start": [
+            410,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.ihom_obj_\u03c1_def",
+        "id": "Rep.ihom_obj_\u03c1_def",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            479,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.ihom_obj_\u03c1_def",
+          "start": [
+            478,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.leftRegularHomEquiv_symm_single",
+        "id": "Rep.leftRegularHomEquiv_symm_single",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            381,
+            17
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.leftRegularHomEquiv_symm_single",
+          "start": [
+            376,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"erw [<a>leftRegularHomEquiv_symm_apply<\\/a>, <a>leftRegularHom_hom<\\/a>, <a>Finsupp.lift_apply<\\/a>,\\n    <a>Finsupp.sum_single_index<\\/a>, <a>one_smul<\\/a>]\"",
+                "[{\"full_name\":\"Rep.leftRegularHomEquiv_symm_apply\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Rep.lean\",\"def_pos\":[355,3],\"def_end_pos\":[355,8]},{\"full_name\":\"Rep.leftRegularHom_hom\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Rep.lean\",\"def_pos\":[328,3],\"def_end_pos\":[328,8]},{\"full_name\":\"Finsupp.lift_apply\",\"def_path\":\"Mathlib\\/LinearAlgebra\\/Finsupp.lean\",\"def_pos\":[524,9],\"def_end_pos\":[524,19]},{\"full_name\":\"Finsupp.sum_single_index\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Finsupp.lean\",\"def_pos\":[68,3],\"def_end_pos\":[68,14]},{\"full_name\":\"one_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[453,7],\"def_end_pos\":[453,15]}]"
+              ],
+              "state_after": "k G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Monoid G\nX Y : Action (Type u) (MonCat.of G)\nf : X \u27f6 Y\nA : Rep k G\nx : CoeSort.coe A\ng : G\n\u22a2 0 \u2022 (A.\u03c1 g) x = 0",
+              "state_before": "k G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Monoid G\nX Y : Action (Type u) (MonCat.of G)\nf : X \u27f6 Y\nA : Rep k G\nx : CoeSort.coe A\ng : G\n\u22a2 (A.leftRegularHomEquiv.symm x).hom (Finsupp.single g 1) = (A.\u03c1 g) x",
+              "tactic": "erw [leftRegularHomEquiv_symm_apply, leftRegularHom_hom, Finsupp.lift_apply,\n  Finsupp.sum_single_index, one_smul]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>zero_smul<\\/a>]\"",
+                "[{\"full_name\":\"zero_smul\",\"def_path\":\"Mathlib\\/Algebra\\/SMulWithZero.lean\",\"def_pos\":[70,9],\"def_end_pos\":[70,18]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "k G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Monoid G\nX Y : Action (Type u) (MonCat.of G)\nf : X \u27f6 Y\nA : Rep k G\nx : CoeSort.coe A\ng : G\n\u22a2 0 \u2022 (A.\u03c1 g) x = 0",
+              "tactic": "rw [zero_smul]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.leftRegularHom_apply",
+        "id": "Rep.leftRegularHom_apply",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            349,
+            17
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.leftRegularHom_apply",
+          "start": [
+            344,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"erw [<a>leftRegularHom_hom<\\/a>, <a>Finsupp.lift_apply<\\/a>, <a>Finsupp.sum_single_index<\\/a>, <a>one_smul<\\/a>,\\n    A.\\u03c1.map_one, <a>LinearMap.one_apply<\\/a>]\"",
+                "[{\"full_name\":\"Rep.leftRegularHom_hom\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Rep.lean\",\"def_pos\":[328,3],\"def_end_pos\":[328,8]},{\"full_name\":\"Finsupp.lift_apply\",\"def_path\":\"Mathlib\\/LinearAlgebra\\/Finsupp.lean\",\"def_pos\":[524,9],\"def_end_pos\":[524,19]},{\"full_name\":\"Finsupp.sum_single_index\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Finsupp.lean\",\"def_pos\":[68,3],\"def_end_pos\":[68,14]},{\"full_name\":\"one_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[453,7],\"def_end_pos\":[453,15]},{\"full_name\":\"LinearMap.one_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/LinearMap\\/End.lean\",\"def_pos\":[58,9],\"def_end_pos\":[58,18]}]"
+              ],
+              "state_after": "k G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Monoid G\nX Y : Action (Type u) (MonCat.of G)\nf : X \u27f6 Y\nA : Rep k G\nx : CoeSort.coe A\n\u22a2 0 \u2022 (A.\u03c1 1) x = 0",
+              "state_before": "k G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Monoid G\nX Y : Action (Type u) (MonCat.of G)\nf : X \u27f6 Y\nA : Rep k G\nx : CoeSort.coe A\n\u22a2 (A.leftRegularHom x).hom (Finsupp.single 1 1) = x",
+              "tactic": "erw [leftRegularHom_hom, Finsupp.lift_apply, Finsupp.sum_single_index, one_smul,\n  A.\u03c1.map_one, LinearMap.one_apply]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>zero_smul<\\/a>]\"",
+                "[{\"full_name\":\"zero_smul\",\"def_path\":\"Mathlib\\/Algebra\\/SMulWithZero.lean\",\"def_pos\":[70,9],\"def_end_pos\":[70,18]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "k G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Monoid G\nX Y : Action (Type u) (MonCat.of G)\nf : X \u27f6 Y\nA : Rep k G\nx : CoeSort.coe A\n\u22a2 0 \u2022 (A.\u03c1 1) x = 0",
+              "tactic": "rw [zero_smul]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.linearization_map_hom",
+        "id": "Rep.linearization_map_hom",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            208,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.linearization_map_hom",
+          "start": [
+            207,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.linearization_map_hom_single",
+        "id": "Rep.linearization_map_hom_single",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            214,
+            27
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.linearization_map_hom_single",
+          "start": [
+            212,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.linearization_obj_\u03c1",
+        "id": "Rep.linearization_obj_\u03c1",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            188,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.linearization_obj_\u03c1",
+          "start": [
+            186,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.linearization_of",
+        "id": "Rep.linearization_of",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            195,
+            79
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.linearization_of",
+          "start": [
+            192,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [<a>linearization_obj_\\u03c1<\\/a>, <a>Finsupp.lmapDomain_apply<\\/a>, <a>Finsupp.mapDomain_single<\\/a>]\"",
+                "[{\"full_name\":\"Rep.linearization_obj_\\u03c1\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Rep.lean\",\"def_pos\":[186,9],\"def_end_pos\":[186,28]},{\"full_name\":\"Finsupp.lmapDomain_apply\",\"def_path\":\"Mathlib\\/LinearAlgebra\\/Finsupp.lean\",\"def_pos\":[566,9],\"def_end_pos\":[566,25]},{\"full_name\":\"Finsupp.mapDomain_single\",\"def_path\":\"Mathlib\\/Data\\/Finsupp\\/Basic.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,25]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "k G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Monoid G\nX : Action (Type u) (MonCat.of G)\ng : G\nx : X.V\n\u22a2 (((linearization k G).obj X).\u03c1 g) (Finsupp.single x 1) = Finsupp.single (X.\u03c1 g x) 1",
+              "tactic": "rw [linearization_obj_\u03c1, Finsupp.lmapDomain_apply, Finsupp.mapDomain_single]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.linearization_single",
+        "id": "Rep.linearization_single",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            202,
+            79
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.linearization_single",
+          "start": [
+            200,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [<a>linearization_obj_\\u03c1<\\/a>, <a>Finsupp.lmapDomain_apply<\\/a>, <a>Finsupp.mapDomain_single<\\/a>]\"",
+                "[{\"full_name\":\"Rep.linearization_obj_\\u03c1\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Rep.lean\",\"def_pos\":[186,9],\"def_end_pos\":[186,28]},{\"full_name\":\"Finsupp.lmapDomain_apply\",\"def_path\":\"Mathlib\\/LinearAlgebra\\/Finsupp.lean\",\"def_pos\":[566,9],\"def_end_pos\":[566,25]},{\"full_name\":\"Finsupp.mapDomain_single\",\"def_path\":\"Mathlib\\/Data\\/Finsupp\\/Basic.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,25]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "k G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Monoid G\nX : Action (Type u) (MonCat.of G)\ng : G\nx : X.V\nr : k\n\u22a2 (((linearization k G).obj X).\u03c1 g) (Finsupp.single x r) = Finsupp.single (X.\u03c1 g x) r",
+              "tactic": "rw [linearization_obj_\u03c1, Finsupp.lmapDomain_apply, Finsupp.mapDomain_single]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.linearization_\u03b5_hom",
+        "id": "Rep.linearization_\u03b5_hom",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            240,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.linearization_\u03b5_hom",
+          "start": [
+            239,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.linearization_\u03bc_hom",
+        "id": "Rep.linearization_\u03bc_hom",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            221,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.linearization_\u03bc_hom",
+          "start": [
+            219,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.linearization_\u03bc_inv_hom",
+        "id": "Rep.linearization_\u03bc_inv_hom",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            234,
+            96
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.linearization_\u03bc_inv_hom",
+          "start": [
+            226,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>Action.forget_map<\\/a>, <a>Functor.map_inv<\\/a>]\"",
+                "[{\"full_name\":\"Action.forget_map\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Action\\/Basic.lean\",\"def_pos\":[269,3],\"def_end_pos\":[269,8]},{\"full_name\":\"CategoryTheory.Functor.map_inv\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[651,9],\"def_end_pos\":[651,16]}]"
+              ],
+              "state_after": "k G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Monoid G\nX\u271d Y\u271d : Action (Type u) (MonCat.of G)\nf : X\u271d \u27f6 Y\u271d\nX Y : Action (Type u) (MonCat.of G)\n\u22a2 inv ((Action.forget (ModuleCat k) (MonCat.of G)).map ((linearization k G).\u03bc X Y)) =\n    \u2191(finsuppTensorFinsupp' k X.V Y.V).symm",
+              "state_before": "k G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Monoid G\nX\u271d Y\u271d : Action (Type u) (MonCat.of G)\nf : X\u271d \u27f6 Y\u271d\nX Y : Action (Type u) (MonCat.of G)\n\u22a2 (inv ((linearization k G).\u03bc X Y)).hom = \u2191(finsuppTensorFinsupp' k X.V Y.V).symm",
+              "tactic": "rw [\u2190 Action.forget_map, Functor.map_inv]"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>IsIso.inv_eq_of_hom_inv_id<\\/a>\"",
+                "[{\"full_name\":\"CategoryTheory.IsIso.inv_eq_of_hom_inv_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[366,9],\"def_end_pos\":[366,29]}]"
+              ],
+              "state_after": "case hom_inv_id\nk G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Monoid G\nX\u271d Y\u271d : Action (Type u) (MonCat.of G)\nf : X\u271d \u27f6 Y\u271d\nX Y : Action (Type u) (MonCat.of G)\n\u22a2 (Action.forget (ModuleCat k) (MonCat.of G)).map ((linearization k G).\u03bc X Y) \u226b\n      \u2191(finsuppTensorFinsupp' k X.V Y.V).symm =\n    \ud835\udfd9\n      ((Action.forget (ModuleCat k) (MonCat.of G)).obj\n        (MonoidalCategory.tensorObj ((linearization k G).obj X) ((linearization k G).obj Y)))",
+              "state_before": "k G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Monoid G\nX\u271d Y\u271d : Action (Type u) (MonCat.of G)\nf : X\u271d \u27f6 Y\u271d\nX Y : Action (Type u) (MonCat.of G)\n\u22a2 inv ((Action.forget (ModuleCat k) (MonCat.of G)).map ((linearization k G).\u03bc X Y)) =\n    \u2191(finsuppTensorFinsupp' k X.V Y.V).symm",
+              "tactic": "apply IsIso.inv_eq_of_hom_inv_id"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>LinearMap.ext<\\/a> fun x => <a>LinearEquiv.symm_apply_apply<\\/a> (<a>finsuppTensorFinsupp'<\\/a> k X.V Y.V) x\"",
+                "[{\"full_name\":\"LinearMap.ext\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/LinearMap\\/Defs.lean\",\"def_pos\":[244,9],\"def_end_pos\":[244,12]},{\"full_name\":\"LinearEquiv.symm_apply_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Equiv.lean\",\"def_pos\":[381,9],\"def_end_pos\":[381,25]},{\"full_name\":\"finsuppTensorFinsupp'\",\"def_path\":\"Mathlib\\/LinearAlgebra\\/DirectSum\\/Finsupp.lean\",\"def_pos\":[333,5],\"def_end_pos\":[333,26]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case hom_inv_id\nk G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Monoid G\nX\u271d Y\u271d : Action (Type u) (MonCat.of G)\nf : X\u271d \u27f6 Y\u271d\nX Y : Action (Type u) (MonCat.of G)\n\u22a2 (Action.forget (ModuleCat k) (MonCat.of G)).map ((linearization k G).\u03bc X Y) \u226b\n      \u2191(finsuppTensorFinsupp' k X.V Y.V).symm =\n    \ud835\udfd9\n      ((Action.forget (ModuleCat k) (MonCat.of G)).obj\n        (MonoidalCategory.tensorObj ((linearization k G).obj X) ((linearization k G).obj Y)))",
+              "tactic": "exact LinearMap.ext fun x => LinearEquiv.symm_apply_apply (finsuppTensorFinsupp' k X.V Y.V) x"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.ofDistribMulAction_\u03c1_apply_apply",
+        "id": "Rep.ofDistribMulAction_\u03c1_apply_apply",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            299,
+            52
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.ofDistribMulAction_\u03c1_apply_apply",
+          "start": [
+            298,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.ofModuleMonoidAlgebra_obj_coe",
+        "id": "Rep.ofModuleMonoidAlgebra_obj_coe",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            640,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.ofModuleMonoidAlgebra_obj_coe",
+          "start": [
+            638,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.ofModuleMonoidAlgebra_obj_\u03c1",
+        "id": "Rep.ofModuleMonoidAlgebra_obj_\u03c1",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            646,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.ofModuleMonoidAlgebra_obj_\u03c1",
+          "start": [
+            644,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.ofMulDistribMulAction_\u03c1_apply_apply",
+        "id": "Rep.ofMulDistribMulAction_\u03c1_apply_apply",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            315,
+            85
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.ofMulDistribMulAction_\u03c1_apply_apply",
+          "start": [
+            314,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.of_\u03c1",
+        "id": "Rep.of_\u03c1",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            87,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.of_\u03c1",
+          "start": [
+            86,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.of_\u03c1_apply",
+        "id": "Rep.of_\u03c1_apply",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            100,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.of_\u03c1_apply",
+          "start": [
+            98,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.to_Module_monoidAlgebra_map_aux",
+        "id": "Rep.to_Module_monoidAlgebra_map_aux",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            610,
+            97
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.to_Module_monoidAlgebra_map_aux",
+          "start": [
+            598,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"apply <a>MonoidAlgebra.induction_on<\\/a> r\"",
+                "[{\"full_name\":\"MonoidAlgebra.induction_on\",\"def_path\":\"Mathlib\\/Algebra\\/MonoidAlgebra\\/Basic.lean\",\"def_pos\":[854,9],\"def_end_pos\":[854,21]}]"
+              ],
+              "state_after": "case hM\nk\u271d G\u271d : Type u\ninst\u271d\u2077 : CommRing k\u271d\ninst\u271d\u2076 : Monoid G\u271d\nk : Type u_1\nG : Type u_2\ninst\u271d\u2075 : CommRing k\ninst\u271d\u2074 : Monoid G\nV : Type u_3\nW : Type u_4\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : AddCommGroup W\ninst\u271d\u00b9 : Module k V\ninst\u271d : Module k W\n\u03c1 : G \u2192* V \u2192\u2097[k] V\n\u03c3 : G \u2192* W \u2192\u2097[k] W\nf : V \u2192\u2097[k] W\nw : \u2200 (g : G), f \u2218\u2097 \u03c1 g = \u03c3 g \u2218\u2097 f\nr : MonoidAlgebra k G\nx : V\n\u22a2 \u2200 (g : G),\n    f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) ((MonoidAlgebra.of k G) g)) x) =\n      (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) ((MonoidAlgebra.of k G) g)) (f x)\n\ncase hadd\nk\u271d G\u271d : Type u\ninst\u271d\u2077 : CommRing k\u271d\ninst\u271d\u2076 : Monoid G\u271d\nk : Type u_1\nG : Type u_2\ninst\u271d\u2075 : CommRing k\ninst\u271d\u2074 : Monoid G\nV : Type u_3\nW : Type u_4\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : AddCommGroup W\ninst\u271d\u00b9 : Module k V\ninst\u271d : Module k W\n\u03c1 : G \u2192* V \u2192\u2097[k] V\n\u03c3 : G \u2192* W \u2192\u2097[k] W\nf : V \u2192\u2097[k] W\nw : \u2200 (g : G), f \u2218\u2097 \u03c1 g = \u03c3 g \u2218\u2097 f\nr : MonoidAlgebra k G\nx : V\n\u22a2 \u2200 (f_1 g : MonoidAlgebra k G),\n    f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) f_1) x) = (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) f_1) (f x) \u2192\n      f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) g) x) = (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) g) (f x) \u2192\n        f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) (f_1 + g)) x) =\n          (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) (f_1 + g)) (f x)\n\ncase hsmul\nk\u271d G\u271d : Type u\ninst\u271d\u2077 : CommRing k\u271d\ninst\u271d\u2076 : Monoid G\u271d\nk : Type u_1\nG : Type u_2\ninst\u271d\u2075 : CommRing k\ninst\u271d\u2074 : Monoid G\nV : Type u_3\nW : Type u_4\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : AddCommGroup W\ninst\u271d\u00b9 : Module k V\ninst\u271d : Module k W\n\u03c1 : G \u2192* V \u2192\u2097[k] V\n\u03c3 : G \u2192* W \u2192\u2097[k] W\nf : V \u2192\u2097[k] W\nw : \u2200 (g : G), f \u2218\u2097 \u03c1 g = \u03c3 g \u2218\u2097 f\nr : MonoidAlgebra k G\nx : V\n\u22a2 \u2200 (r : k) (f_1 : MonoidAlgebra k G),\n    f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) f_1) x) = (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) f_1) (f x) \u2192\n      f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) (r \u2022 f_1)) x) =\n        (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) (r \u2022 f_1)) (f x)",
+              "state_before": "k\u271d G\u271d : Type u\ninst\u271d\u2077 : CommRing k\u271d\ninst\u271d\u2076 : Monoid G\u271d\nk : Type u_1\nG : Type u_2\ninst\u271d\u2075 : CommRing k\ninst\u271d\u2074 : Monoid G\nV : Type u_3\nW : Type u_4\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : AddCommGroup W\ninst\u271d\u00b9 : Module k V\ninst\u271d : Module k W\n\u03c1 : G \u2192* V \u2192\u2097[k] V\n\u03c3 : G \u2192* W \u2192\u2097[k] W\nf : V \u2192\u2097[k] W\nw : \u2200 (g : G), f \u2218\u2097 \u03c1 g = \u03c3 g \u2218\u2097 f\nr : MonoidAlgebra k G\nx : V\n\u22a2 f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) r) x) = (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) r) (f x)",
+              "tactic": "apply MonoidAlgebra.induction_on r"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro g\"",
+                "[]"
+              ],
+              "state_after": "case hM\nk\u271d G\u271d : Type u\ninst\u271d\u2077 : CommRing k\u271d\ninst\u271d\u2076 : Monoid G\u271d\nk : Type u_1\nG : Type u_2\ninst\u271d\u2075 : CommRing k\ninst\u271d\u2074 : Monoid G\nV : Type u_3\nW : Type u_4\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : AddCommGroup W\ninst\u271d\u00b9 : Module k V\ninst\u271d : Module k W\n\u03c1 : G \u2192* V \u2192\u2097[k] V\n\u03c3 : G \u2192* W \u2192\u2097[k] W\nf : V \u2192\u2097[k] W\nw : \u2200 (g : G), f \u2218\u2097 \u03c1 g = \u03c3 g \u2218\u2097 f\nr : MonoidAlgebra k G\nx : V\ng : G\n\u22a2 f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) ((MonoidAlgebra.of k G) g)) x) =\n    (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) ((MonoidAlgebra.of k G) g)) (f x)",
+              "state_before": "case hM\nk\u271d G\u271d : Type u\ninst\u271d\u2077 : CommRing k\u271d\ninst\u271d\u2076 : Monoid G\u271d\nk : Type u_1\nG : Type u_2\ninst\u271d\u2075 : CommRing k\ninst\u271d\u2074 : Monoid G\nV : Type u_3\nW : Type u_4\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : AddCommGroup W\ninst\u271d\u00b9 : Module k V\ninst\u271d : Module k W\n\u03c1 : G \u2192* V \u2192\u2097[k] V\n\u03c3 : G \u2192* W \u2192\u2097[k] W\nf : V \u2192\u2097[k] W\nw : \u2200 (g : G), f \u2218\u2097 \u03c1 g = \u03c3 g \u2218\u2097 f\nr : MonoidAlgebra k G\nx : V\n\u22a2 \u2200 (g : G),\n    f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) ((MonoidAlgebra.of k G) g)) x) =\n      (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) ((MonoidAlgebra.of k G) g)) (f x)",
+              "tactic": "intro g"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>one_smul<\\/a>, <a>MonoidAlgebra.lift_single<\\/a>, <a>MonoidAlgebra.of_apply<\\/a>]\"",
+                "[{\"full_name\":\"one_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[453,7],\"def_end_pos\":[453,15]},{\"full_name\":\"MonoidAlgebra.lift_single\",\"def_path\":\"Mathlib\\/Algebra\\/MonoidAlgebra\\/Basic.lean\",\"def_pos\":[932,9],\"def_end_pos\":[932,20]},{\"full_name\":\"MonoidAlgebra.of_apply\",\"def_path\":\"Mathlib\\/Algebra\\/MonoidAlgebra\\/Basic.lean\",\"def_pos\":[521,3],\"def_end_pos\":[521,8]}]"
+              ],
+              "state_after": "case hM\nk\u271d G\u271d : Type u\ninst\u271d\u2077 : CommRing k\u271d\ninst\u271d\u2076 : Monoid G\u271d\nk : Type u_1\nG : Type u_2\ninst\u271d\u2075 : CommRing k\ninst\u271d\u2074 : Monoid G\nV : Type u_3\nW : Type u_4\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : AddCommGroup W\ninst\u271d\u00b9 : Module k V\ninst\u271d : Module k W\n\u03c1 : G \u2192* V \u2192\u2097[k] V\n\u03c3 : G \u2192* W \u2192\u2097[k] W\nf : V \u2192\u2097[k] W\nw : \u2200 (g : G), f \u2218\u2097 \u03c1 g = \u03c3 g \u2218\u2097 f\nr : MonoidAlgebra k G\nx : V\ng : G\n\u22a2 f ((\u03c1 g) x) = (\u03c3 g) (f x)",
+              "state_before": "case hM\nk\u271d G\u271d : Type u\ninst\u271d\u2077 : CommRing k\u271d\ninst\u271d\u2076 : Monoid G\u271d\nk : Type u_1\nG : Type u_2\ninst\u271d\u2075 : CommRing k\ninst\u271d\u2074 : Monoid G\nV : Type u_3\nW : Type u_4\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : AddCommGroup W\ninst\u271d\u00b9 : Module k V\ninst\u271d : Module k W\n\u03c1 : G \u2192* V \u2192\u2097[k] V\n\u03c3 : G \u2192* W \u2192\u2097[k] W\nf : V \u2192\u2097[k] W\nw : \u2200 (g : G), f \u2218\u2097 \u03c1 g = \u03c3 g \u2218\u2097 f\nr : MonoidAlgebra k G\nx : V\ng : G\n\u22a2 f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) ((MonoidAlgebra.of k G) g)) x) =\n    (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) ((MonoidAlgebra.of k G) g)) (f x)",
+              "tactic": "simp only [one_smul, MonoidAlgebra.lift_single, MonoidAlgebra.of_apply]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>LinearMap.congr_fun<\\/a> (w g) x\"",
+                "[{\"full_name\":\"LinearMap.congr_fun\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/LinearMap\\/Defs.lean\",\"def_pos\":[344,19],\"def_end_pos\":[344,28]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case hM\nk\u271d G\u271d : Type u\ninst\u271d\u2077 : CommRing k\u271d\ninst\u271d\u2076 : Monoid G\u271d\nk : Type u_1\nG : Type u_2\ninst\u271d\u2075 : CommRing k\ninst\u271d\u2074 : Monoid G\nV : Type u_3\nW : Type u_4\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : AddCommGroup W\ninst\u271d\u00b9 : Module k V\ninst\u271d : Module k W\n\u03c1 : G \u2192* V \u2192\u2097[k] V\n\u03c3 : G \u2192* W \u2192\u2097[k] W\nf : V \u2192\u2097[k] W\nw : \u2200 (g : G), f \u2218\u2097 \u03c1 g = \u03c3 g \u2218\u2097 f\nr : MonoidAlgebra k G\nx : V\ng : G\n\u22a2 f ((\u03c1 g) x) = (\u03c3 g) (f x)",
+              "tactic": "exact LinearMap.congr_fun (w g) x"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro g h gw hw\"",
+                "[]"
+              ],
+              "state_after": "case hadd\nk\u271d G\u271d : Type u\ninst\u271d\u2077 : CommRing k\u271d\ninst\u271d\u2076 : Monoid G\u271d\nk : Type u_1\nG : Type u_2\ninst\u271d\u2075 : CommRing k\ninst\u271d\u2074 : Monoid G\nV : Type u_3\nW : Type u_4\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : AddCommGroup W\ninst\u271d\u00b9 : Module k V\ninst\u271d : Module k W\n\u03c1 : G \u2192* V \u2192\u2097[k] V\n\u03c3 : G \u2192* W \u2192\u2097[k] W\nf : V \u2192\u2097[k] W\nw : \u2200 (g : G), f \u2218\u2097 \u03c1 g = \u03c3 g \u2218\u2097 f\nr : MonoidAlgebra k G\nx : V\ng h : MonoidAlgebra k G\ngw : f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) g) x) = (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) g) (f x)\nhw : f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) h) x) = (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) h) (f x)\n\u22a2 f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) (g + h)) x) = (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) (g + h)) (f x)",
+              "state_before": "case hadd\nk\u271d G\u271d : Type u\ninst\u271d\u2077 : CommRing k\u271d\ninst\u271d\u2076 : Monoid G\u271d\nk : Type u_1\nG : Type u_2\ninst\u271d\u2075 : CommRing k\ninst\u271d\u2074 : Monoid G\nV : Type u_3\nW : Type u_4\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : AddCommGroup W\ninst\u271d\u00b9 : Module k V\ninst\u271d : Module k W\n\u03c1 : G \u2192* V \u2192\u2097[k] V\n\u03c3 : G \u2192* W \u2192\u2097[k] W\nf : V \u2192\u2097[k] W\nw : \u2200 (g : G), f \u2218\u2097 \u03c1 g = \u03c3 g \u2218\u2097 f\nr : MonoidAlgebra k G\nx : V\n\u22a2 \u2200 (f_1 g : MonoidAlgebra k G),\n    f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) f_1) x) = (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) f_1) (f x) \u2192\n      f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) g) x) = (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) g) (f x) \u2192\n        f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) (f_1 + g)) x) =\n          (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) (f_1 + g)) (f x)",
+              "tactic": "intro g h gw hw"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>map_add<\\/a>, <a>add_left_inj<\\/a>, <a>LinearMap.add_apply<\\/a>, hw, gw]\"",
+                "[{\"full_name\":\"map_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[308,3],\"def_end_pos\":[308,14]},{\"full_name\":\"add_left_inj\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[90,3],\"def_end_pos\":[90,14]},{\"full_name\":\"LinearMap.add_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/LinearMap\\/Defs.lean\",\"def_pos\":[910,9],\"def_end_pos\":[910,18]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case hadd\nk\u271d G\u271d : Type u\ninst\u271d\u2077 : CommRing k\u271d\ninst\u271d\u2076 : Monoid G\u271d\nk : Type u_1\nG : Type u_2\ninst\u271d\u2075 : CommRing k\ninst\u271d\u2074 : Monoid G\nV : Type u_3\nW : Type u_4\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : AddCommGroup W\ninst\u271d\u00b9 : Module k V\ninst\u271d : Module k W\n\u03c1 : G \u2192* V \u2192\u2097[k] V\n\u03c3 : G \u2192* W \u2192\u2097[k] W\nf : V \u2192\u2097[k] W\nw : \u2200 (g : G), f \u2218\u2097 \u03c1 g = \u03c3 g \u2218\u2097 f\nr : MonoidAlgebra k G\nx : V\ng h : MonoidAlgebra k G\ngw : f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) g) x) = (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) g) (f x)\nhw : f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) h) x) = (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) h) (f x)\n\u22a2 f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) (g + h)) x) = (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) (g + h)) (f x)",
+              "tactic": "simp only [map_add, add_left_inj, LinearMap.add_apply, hw, gw]"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro r g w\"",
+                "[]"
+              ],
+              "state_after": "case hsmul\nk\u271d G\u271d : Type u\ninst\u271d\u2077 : CommRing k\u271d\ninst\u271d\u2076 : Monoid G\u271d\nk : Type u_1\nG : Type u_2\ninst\u271d\u2075 : CommRing k\ninst\u271d\u2074 : Monoid G\nV : Type u_3\nW : Type u_4\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : AddCommGroup W\ninst\u271d\u00b9 : Module k V\ninst\u271d : Module k W\n\u03c1 : G \u2192* V \u2192\u2097[k] V\n\u03c3 : G \u2192* W \u2192\u2097[k] W\nf : V \u2192\u2097[k] W\nw\u271d : \u2200 (g : G), f \u2218\u2097 \u03c1 g = \u03c3 g \u2218\u2097 f\nr\u271d : MonoidAlgebra k G\nx : V\nr : k\ng : MonoidAlgebra k G\nw : f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) g) x) = (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) g) (f x)\n\u22a2 f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) (r \u2022 g)) x) = (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) (r \u2022 g)) (f x)",
+              "state_before": "case hsmul\nk\u271d G\u271d : Type u\ninst\u271d\u2077 : CommRing k\u271d\ninst\u271d\u2076 : Monoid G\u271d\nk : Type u_1\nG : Type u_2\ninst\u271d\u2075 : CommRing k\ninst\u271d\u2074 : Monoid G\nV : Type u_3\nW : Type u_4\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : AddCommGroup W\ninst\u271d\u00b9 : Module k V\ninst\u271d : Module k W\n\u03c1 : G \u2192* V \u2192\u2097[k] V\n\u03c3 : G \u2192* W \u2192\u2097[k] W\nf : V \u2192\u2097[k] W\nw : \u2200 (g : G), f \u2218\u2097 \u03c1 g = \u03c3 g \u2218\u2097 f\nr : MonoidAlgebra k G\nx : V\n\u22a2 \u2200 (r : k) (f_1 : MonoidAlgebra k G),\n    f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) f_1) x) = (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) f_1) (f x) \u2192\n      f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) (r \u2022 f_1)) x) =\n        (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) (r \u2022 f_1)) (f x)",
+              "tactic": "intro r g w"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>AlgHom.map_smul<\\/a>, w, <a>RingHom.id_apply<\\/a>, <a>LinearMap.smul_apply<\\/a>, <a>LinearMap.map_smul\\u209b\\u2097<\\/a>]\"",
+                "[{\"full_name\":\"AlgHom.map_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Algebra\\/Hom.lean\",\"def_pos\":[259,19],\"def_end_pos\":[259,27]},{\"full_name\":\"RingHom.id_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Hom\\/Defs.lean\",\"def_pos\":[638,9],\"def_end_pos\":[638,17]},{\"full_name\":\"LinearMap.smul_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/LinearMap\\/Defs.lean\",\"def_pos\":[831,9],\"def_end_pos\":[831,19]},{\"full_name\":\"LinearMap.map_smul\\u209b\\u2097\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/LinearMap\\/Defs.lean\",\"def_pos\":[372,19],\"def_end_pos\":[372,29]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case hsmul\nk\u271d G\u271d : Type u\ninst\u271d\u2077 : CommRing k\u271d\ninst\u271d\u2076 : Monoid G\u271d\nk : Type u_1\nG : Type u_2\ninst\u271d\u2075 : CommRing k\ninst\u271d\u2074 : Monoid G\nV : Type u_3\nW : Type u_4\ninst\u271d\u00b3 : AddCommGroup V\ninst\u271d\u00b2 : AddCommGroup W\ninst\u271d\u00b9 : Module k V\ninst\u271d : Module k W\n\u03c1 : G \u2192* V \u2192\u2097[k] V\n\u03c3 : G \u2192* W \u2192\u2097[k] W\nf : V \u2192\u2097[k] W\nw\u271d : \u2200 (g : G), f \u2218\u2097 \u03c1 g = \u03c3 g \u2218\u2097 f\nr\u271d : MonoidAlgebra k G\nx : V\nr : k\ng : MonoidAlgebra k G\nw : f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) g) x) = (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) g) (f x)\n\u22a2 f ((((MonoidAlgebra.lift k G (V \u2192\u2097[k] V)) \u03c1) (r \u2022 g)) x) = (((MonoidAlgebra.lift k G (W \u2192\u2097[k] W)) \u03c3) (r \u2022 g)) (f x)",
+              "tactic": "simp only [AlgHom.map_smul, w, RingHom.id_apply, LinearMap.smul_apply, LinearMap.map_smul\u209b\u2097]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.trivial_def",
+        "id": "Rep.trivial_def",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            136,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.trivial_def",
+          "start": [
+            134,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.unit_iso_comm",
+        "id": "Rep.unit_iso_comm",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            691,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.unit_iso_comm",
+          "start": [
+            683,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"dsimp [<a>unitIsoAddEquiv<\\/a>, <a>ofModuleMonoidAlgebra<\\/a>, <a>toModuleMonoidAlgebra<\\/a>]\"",
+                "[{\"full_name\":\"Rep.unitIsoAddEquiv\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Rep.lean\",\"def_pos\":[660,5],\"def_end_pos\":[660,20]},{\"full_name\":\"Rep.ofModuleMonoidAlgebra\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Rep.lean\",\"def_pos\":[630,5],\"def_end_pos\":[630,26]},{\"full_name\":\"Rep.toModuleMonoidAlgebra\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Rep.lean\",\"def_pos\":[623,5],\"def_end_pos\":[623,26]}]"
+              ],
+              "state_after": "k G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Monoid G\nV : Rep k G\ng : G\nx : CoeSort.coe V\n\u22a2 (RestrictScalars.addEquiv k (MonoidAlgebra k G) V.\u03c1.asModule).symm (V.\u03c1.asModuleEquiv.symm ((V.\u03c1 g) x)) =\n    ((Representation.ofModule \u2191(ModuleCat.of (MonoidAlgebra k G) V.\u03c1.asModule)) g)\n      ((RestrictScalars.addEquiv k (MonoidAlgebra k G) V.\u03c1.asModule).symm (V.\u03c1.asModuleEquiv.symm x))",
+              "state_before": "k G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Monoid G\nV : Rep k G\ng : G\nx : CoeSort.coe V\n\u22a2 unitIsoAddEquiv ((V.\u03c1 g).toFun x) =\n    ((ofModuleMonoidAlgebra.obj (toModuleMonoidAlgebra.obj V)).\u03c1 g).toFun (unitIsoAddEquiv x)",
+              "tactic": "dsimp [unitIsoAddEquiv, ofModuleMonoidAlgebra, toModuleMonoidAlgebra]"
+            },
+            {
+              "annotated_tactic": [
+                "\"erw [<a>Representation.asModuleEquiv_symm_map_rho<\\/a>]\"",
+                "[{\"full_name\":\"Representation.asModuleEquiv_symm_map_rho\",\"def_path\":\"Mathlib\\/RepresentationTheory\\/Basic.lean\",\"def_pos\":[165,9],\"def_end_pos\":[165,35]}]"
+              ],
+              "state_after": "k G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Monoid G\nV : Rep k G\ng : G\nx : CoeSort.coe V\n\u22a2 (MonoidAlgebra.of k G) g \u2022 V.\u03c1.asModuleEquiv.symm x =\n    ((Representation.ofModule \u2191(ModuleCat.of (MonoidAlgebra k G) V.\u03c1.asModule)) g)\n      ((RestrictScalars.addEquiv k (MonoidAlgebra k G) V.\u03c1.asModule).symm (V.\u03c1.asModuleEquiv.symm x))",
+              "state_before": "k G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Monoid G\nV : Rep k G\ng : G\nx : CoeSort.coe V\n\u22a2 (RestrictScalars.addEquiv k (MonoidAlgebra k G) V.\u03c1.asModule).symm (V.\u03c1.asModuleEquiv.symm ((V.\u03c1 g) x)) =\n    ((Representation.ofModule \u2191(ModuleCat.of (MonoidAlgebra k G) V.\u03c1.asModule)) g)\n      ((RestrictScalars.addEquiv k (MonoidAlgebra k G) V.\u03c1.asModule).symm (V.\u03c1.asModuleEquiv.symm x))",
+              "tactic": "erw [Representation.asModuleEquiv_symm_map_rho]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rfl\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "k G : Type u\ninst\u271d\u00b9 : CommRing k\ninst\u271d : Monoid G\nV : Rep k G\ng : G\nx : CoeSort.coe V\n\u22a2 (MonoidAlgebra.of k G) g \u2022 V.\u03c1.asModuleEquiv.symm x =\n    ((Representation.ofModule \u2191(ModuleCat.of (MonoidAlgebra k G) V.\u03c1.asModule)) g)\n      ((RestrictScalars.addEquiv k (MonoidAlgebra k G) V.\u03c1.asModule).symm (V.\u03c1.asModuleEquiv.symm x))",
+              "tactic": "rfl"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.\u03c1_inv_self_apply",
+        "id": "Rep.\u03c1_inv_self_apply",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            107,
+            93
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.\u03c1_inv_self_apply",
+          "start": [
+            105,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>map_mul<\\/a>, <a>inv_mul_self<\\/a>, <a>map_one<\\/a>, <a>LinearMap.one_apply<\\/a>]\"",
+                "[{\"full_name\":\"map_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[309,9],\"def_end_pos\":[309,16]},{\"full_name\":\"inv_mul_self\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1228,9],\"def_end_pos\":[1228,21]},{\"full_name\":\"map_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[204,9],\"def_end_pos\":[204,16]},{\"full_name\":\"LinearMap.one_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/LinearMap\\/End.lean\",\"def_pos\":[58,9],\"def_end_pos\":[58,18]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "k G\u271d : Type u\ninst\u271d\u00b2 : CommRing k\ninst\u271d\u00b9 : Monoid G\u271d\nG : Type u\ninst\u271d : Group G\nA : Rep k G\ng : G\nx : CoeSort.coe A\n\u22a2 (A.\u03c1 g\u207b\u00b9 * A.\u03c1 g) x = x",
+              "tactic": "rw [\u2190 map_mul, inv_mul_self, map_one, LinearMap.one_apply]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Rep.\u03c1_self_inv_apply",
+        "id": "Rep.\u03c1_self_inv_apply",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            114,
+            93
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Rep.\u03c1_self_inv_apply",
+          "start": [
+            112,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>map_mul<\\/a>, <a>mul_inv_self<\\/a>, <a>map_one<\\/a>, <a>LinearMap.one_apply<\\/a>]\"",
+                "[{\"full_name\":\"map_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[309,9],\"def_end_pos\":[309,16]},{\"full_name\":\"mul_inv_self\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1244,9],\"def_end_pos\":[1244,21]},{\"full_name\":\"map_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[204,9],\"def_end_pos\":[204,16]},{\"full_name\":\"LinearMap.one_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/LinearMap\\/End.lean\",\"def_pos\":[58,9],\"def_end_pos\":[58,18]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "k G\u271d : Type u\ninst\u271d\u00b2 : CommRing k\ninst\u271d\u00b9 : Monoid G\u271d\nG : Type u\ninst\u271d : Group G\nA : Rep k G\ng : G\nx : CoeSort.coe A\n\u22a2 (A.\u03c1 g * A.\u03c1 g\u207b\u00b9) x = x",
+              "tactic": "rw [\u2190 map_mul, mul_inv_self, map_one, LinearMap.one_apply]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Representation.repOfTprodIso_apply",
+        "id": "Representation.repOfTprodIso_apply",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            568,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Representation.repOfTprodIso_apply",
+          "start": [
+            567,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      },
+      {
+        "full_name": "Representation.repOfTprodIso_inv_apply",
+        "id": "Representation.repOfTprodIso_inv_apply",
+        "reason": "missing_trace",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            573,
+            6
+          ],
+          "file_path": "Mathlib/RepresentationTheory/Rep.lean",
+          "full_name": "Representation.repOfTprodIso_inv_apply",
+          "start": [
+            572,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RepresentationTheory/Rep.lean"
+      }
+    ],
+    "input_proofs": 47,
+    "input_units": 2,
+    "proofs": 4,
+    "published_proofs": 4,
+    "published_transitions": 7,
+    "replay_failures": [],
+    "transitions": 7,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001640-0000-ae26d1527588ec8b.parquet",
+      "sha256": "ae26d1527588ec8b39f95b425a91a24f618cade67cc9bc6c96d93dd650a56321",
+      "bytes": 81293,
+      "rows": 6,
+      "revision": "df8c9c479578582ca5384c5c62608ea4677707ca"
+    },
+    {
+      "path": "data/dev/mathlib-001640-0000-3c488b5f7caeb4cd.parquet",
+      "sha256": "3c488b5f7caeb4cd173c964f7b4bc11ecf340eefe6ded37ef70e21ee39ccefc5",
+      "bytes": 60425,
+      "rows": 1,
+      "revision": "df8c9c479578582ca5384c5c62608ea4677707ca"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:LinearMap.conjugate_i",
+    "mathlib:LinearMap.equivariantProjection_apply",
+    "mathlib:LinearMap.equivariantProjection_condition",
+    "mathlib:MonoidAlgebra.Submodule.exists_isCompl"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Maschke.lean\",null,null,\"LinearMap.conjugate_i\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Maschke.lean\",null,null,\"LinearMap.equivariantProjection_apply\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Maschke.lean\",null,null,\"LinearMap.equivariantProjection_condition\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RepresentationTheory/Maschke.lean\",null,null,\"MonoidAlgebra.Submodule.exists_isCompl\"]"
+  ]
+}

manifests/batches/mathlib/001648.json

@@ -0,0 +1,643 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001648",
+  "batch_fingerprint": "9b146fc657fdef4587ac9d95d3d626040ee4b17857d426eda083ef459776260e",
+  "evidence": {
+    "batch_fingerprint": "9b146fc657fdef4587ac9d95d3d626040ee4b17857d426eda083ef459776260e",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "no internal trace for tactic 'intro H'",
+        "full_name": "IsBezout.TFAE",
+        "id": "IsBezout.TFAE",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            78,
+            16
+          ],
+          "file_path": "Mathlib/RingTheory/Bezout.lean",
+          "full_name": "IsBezout.TFAE",
+          "start": [
+            53,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"tfae_have 1 \\u2192 2\"",
+                "[]"
+              ],
+              "state_after": "case tfae_1_to_2\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\n\u22a2 IsNoetherianRing R \u2192 IsPrincipalIdealRing R\n\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\n\u22a2 [IsNoetherianRing R, IsPrincipalIdealRing R, UniqueFactorizationMonoid R, WfDvdMonoid R].TFAE",
+              "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\n\u22a2 [IsNoetherianRing R, IsPrincipalIdealRing R, UniqueFactorizationMonoid R, WfDvdMonoid R].TFAE",
+              "tactic": "tfae_have 1 \u2192 2"
+            },
+            {
+              "annotated_tactic": [
+                "\"tfae_have 2 \\u2192 3\"",
+                "[]"
+              ],
+              "state_after": "case tfae_2_to_3\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\n\u22a2 IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\n\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\n\u22a2 [IsNoetherianRing R, IsPrincipalIdealRing R, UniqueFactorizationMonoid R, WfDvdMonoid R].TFAE",
+              "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\n\u22a2 [IsNoetherianRing R, IsPrincipalIdealRing R, UniqueFactorizationMonoid R, WfDvdMonoid R].TFAE",
+              "tactic": "tfae_have 2 \u2192 3"
+            },
+            {
+              "annotated_tactic": [
+                "\"tfae_have 3 \\u2192 4\"",
+                "[]"
+              ],
+              "state_after": "case tfae_3_to_4\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\n\u22a2 UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\n\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\n\u22a2 [IsNoetherianRing R, IsPrincipalIdealRing R, UniqueFactorizationMonoid R, WfDvdMonoid R].TFAE",
+              "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\n\u22a2 [IsNoetherianRing R, IsPrincipalIdealRing R, UniqueFactorizationMonoid R, WfDvdMonoid R].TFAE",
+              "tactic": "tfae_have 3 \u2192 4"
+            },
+            {
+              "annotated_tactic": [
+                "\"tfae_have 4 \\u2192 1\"",
+                "[]"
+              ],
+              "state_after": "case tfae_4_to_1\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\n\u22a2 WfDvdMonoid R \u2192 IsNoetherianRing R\n\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\ntfae_4_to_1 : WfDvdMonoid R \u2192 IsNoetherianRing R\n\u22a2 [IsNoetherianRing R, IsPrincipalIdealRing R, UniqueFactorizationMonoid R, WfDvdMonoid R].TFAE",
+              "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\n\u22a2 [IsNoetherianRing R, IsPrincipalIdealRing R, UniqueFactorizationMonoid R, WfDvdMonoid R].TFAE",
+              "tactic": "tfae_have 4 \u2192 1"
+            },
+            {
+              "annotated_tactic": [
+                "\"tfae_finish\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\ntfae_4_to_1 : WfDvdMonoid R \u2192 IsNoetherianRing R\n\u22a2 [IsNoetherianRing R, IsPrincipalIdealRing R, UniqueFactorizationMonoid R, WfDvdMonoid R].TFAE",
+              "tactic": "tfae_finish"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro H\"",
+                "[]"
+              ],
+              "state_after": "case tfae_1_to_2\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\nH : IsNoetherianRing R\n\u22a2 IsPrincipalIdealRing R",
+              "state_before": "case tfae_1_to_2\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\n\u22a2 IsNoetherianRing R \u2192 IsPrincipalIdealRing R",
+              "tactic": "intro H"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact \\u27e8fun I => <a>isPrincipal_of_FG<\\/a> _ (<a>IsNoetherian.noetherian<\\/a> _)\\u27e9\"",
+                "[{\"full_name\":\"IsBezout.isPrincipal_of_FG\",\"def_path\":\"Mathlib\\/RingTheory\\/PrincipalIdealDomain.lean\",\"def_pos\":[63,3],\"def_end_pos\":[63,20]},{\"full_name\":\"IsNoetherian.noetherian\",\"def_path\":\"Mathlib\\/RingTheory\\/Noetherian.lean\",\"def_pos\":[63,3],\"def_end_pos\":[63,13]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case tfae_1_to_2\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\nH : IsNoetherianRing R\n\u22a2 IsPrincipalIdealRing R",
+              "tactic": "exact \u27e8fun I => isPrincipal_of_FG _ (IsNoetherian.noetherian _)\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro\"",
+                "[]"
+              ],
+              "state_after": "case tfae_2_to_3\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\na\u271d : IsPrincipalIdealRing R\n\u22a2 UniqueFactorizationMonoid R",
+              "state_before": "case tfae_2_to_3\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\n\u22a2 IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R",
+              "tactic": "intro"
+            },
+            {
+              "annotated_tactic": [
+                "\"infer_instance\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case tfae_2_to_3\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\na\u271d : IsPrincipalIdealRing R\n\u22a2 UniqueFactorizationMonoid R",
+              "tactic": "infer_instance"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro\"",
+                "[]"
+              ],
+              "state_after": "case tfae_3_to_4\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\na\u271d : UniqueFactorizationMonoid R\n\u22a2 WfDvdMonoid R",
+              "state_before": "case tfae_3_to_4\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\n\u22a2 UniqueFactorizationMonoid R \u2192 WfDvdMonoid R",
+              "tactic": "intro"
+            },
+            {
+              "annotated_tactic": [
+                "\"infer_instance\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case tfae_3_to_4\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\na\u271d : UniqueFactorizationMonoid R\n\u22a2 WfDvdMonoid R",
+              "tactic": "infer_instance"
+            },
+            {
+              "annotated_tactic": [
+                "\"rintro \\u27e8h\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "case tfae_4_to_1.mk\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\n\u22a2 IsNoetherianRing R",
+              "state_before": "case tfae_4_to_1\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\n\u22a2 WfDvdMonoid R \u2192 IsNoetherianRing R",
+              "tactic": "rintro \u27e8h\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>isNoetherianRing_iff<\\/a>, <a>isNoetherian_iff_fg_wellFounded<\\/a>]\"",
+                "[{\"full_name\":\"isNoetherianRing_iff\",\"def_path\":\"Mathlib\\/RingTheory\\/Noetherian.lean\",\"def_pos\":[538,9],\"def_end_pos\":[538,29]},{\"full_name\":\"isNoetherian_iff_fg_wellFounded\",\"def_path\":\"Mathlib\\/RingTheory\\/Noetherian.lean\",\"def_pos\":[323,9],\"def_end_pos\":[323,40]}]"
+              ],
+              "state_after": "case tfae_4_to_1.mk\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\n\u22a2 WellFounded fun x x_1 => x > x_1",
+              "state_before": "case tfae_4_to_1.mk\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\n\u22a2 IsNoetherianRing R",
+              "tactic": "rw [isNoetherianRing_iff, isNoetherian_iff_fg_wellFounded]"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>RelEmbedding.wellFounded<\\/a> _ h\"",
+                "[{\"full_name\":\"RelEmbedding.wellFounded\",\"def_path\":\"Mathlib\\/Order\\/RelIso\\/Basic.lean\",\"def_pos\":[385,19],\"def_end_pos\":[385,30]}]"
+              ],
+              "state_after": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\n\u22a2 (fun x x_1 => x > x_1) \u21aar DvdNotUnit",
+              "state_before": "case tfae_4_to_1.mk\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\n\u22a2 WellFounded fun x x_1 => x > x_1",
+              "tactic": "apply RelEmbedding.wellFounded _ h"
+            },
+            {
+              "annotated_tactic": [
+                "\"have : \\u2200 I : { J : <a>Ideal<\\/a> R \\/\\/ J.FG }, \\u2203 x : R, (I : <a>Ideal<\\/a> R) = <a>Ideal.span<\\/a> {x} :=\\n        fun \\u27e8I, hI\\u27e9 => (<a>IsBezout.isPrincipal_of_FG<\\/a> I hI).1\"",
+                "[{\"full_name\":\"Ideal\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Basic.lean\",\"def_pos\":[41,8],\"def_end_pos\":[41,13]},{\"full_name\":\"Ideal\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Basic.lean\",\"def_pos\":[41,8],\"def_end_pos\":[41,13]},{\"full_name\":\"Ideal.span\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Basic.lean\",\"def_pos\":[115,5],\"def_end_pos\":[115,9]},{\"full_name\":\"IsBezout.isPrincipal_of_FG\",\"def_path\":\"Mathlib\\/RingTheory\\/PrincipalIdealDomain.lean\",\"def_pos\":[63,3],\"def_end_pos\":[63,20]}]"
+              ],
+              "state_after": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\nthis : \u2200 (I : { J // J.FG }), \u2203 x, \u2191I = Ideal.span {x}\n\u22a2 (fun x x_1 => x > x_1) \u21aar DvdNotUnit",
+              "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\n\u22a2 (fun x x_1 => x > x_1) \u21aar DvdNotUnit",
+              "tactic": "have : \u2200 I : { J : Ideal R // J.FG }, \u2203 x : R, (I : Ideal R) = Ideal.span {x} :=\n  fun \u27e8I, hI\u27e9 => (IsBezout.isPrincipal_of_FG I hI).1"
+            },
+            {
+              "annotated_tactic": [
+                "\"choose f hf using this\"",
+                "[]"
+              ],
+              "state_after": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\nf : { J // J.FG } \u2192 R\nhf : \u2200 (I : { J // J.FG }), \u2191I = Ideal.span {f I}\n\u22a2 (fun x x_1 => x > x_1) \u21aar DvdNotUnit",
+              "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\nthis : \u2200 (I : { J // J.FG }), \u2203 x, \u2191I = Ideal.span {x}\n\u22a2 (fun x x_1 => x > x_1) \u21aar DvdNotUnit",
+              "tactic": "choose f hf using this"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact\\n        { toFun := f\\n          inj' := fun x y e => by ext1; rw [hf, hf, e]\\n          map_rel_iff' := by\\n            dsimp\\n            intro a b\\n            rw [\\u2190 <a>Ideal.span_singleton_lt_span_singleton<\\/a>, \\u2190 hf, \\u2190 hf]\\n            rfl }\"",
+                "[{\"full_name\":\"Ideal.span_singleton_lt_span_singleton\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Basic.lean\",\"def_pos\":[555,9],\"def_end_pos\":[555,41]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\nf : { J // J.FG } \u2192 R\nhf : \u2200 (I : { J // J.FG }), \u2191I = Ideal.span {f I}\n\u22a2 (fun x x_1 => x > x_1) \u21aar DvdNotUnit",
+              "tactic": "exact\n  { toFun := f\n    inj' := fun x y e => by ext1; rw [hf, hf, e]\n    map_rel_iff' := by\n      dsimp\n      intro a b\n      rw [\u2190 Ideal.span_singleton_lt_span_singleton, \u2190 hf, \u2190 hf]\n      rfl }"
+            },
+            {
+              "annotated_tactic": [
+                "\"ext1\"",
+                "[]"
+              ],
+              "state_after": "case a\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\nf : { J // J.FG } \u2192 R\nhf : \u2200 (I : { J // J.FG }), \u2191I = Ideal.span {f I}\nx y : { N // N.FG }\ne : f x = f y\n\u22a2 \u2191x = \u2191y",
+              "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\nf : { J // J.FG } \u2192 R\nhf : \u2200 (I : { J // J.FG }), \u2191I = Ideal.span {f I}\nx y : { N // N.FG }\ne : f x = f y\n\u22a2 x = y",
+              "tactic": "ext1"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [hf, hf, e]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case a\nR : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\nf : { J // J.FG } \u2192 R\nhf : \u2200 (I : { J // J.FG }), \u2191I = Ideal.span {f I}\nx y : { N // N.FG }\ne : f x = f y\n\u22a2 \u2191x = \u2191y",
+              "tactic": "rw [hf, hf, e]"
+            },
+            {
+              "annotated_tactic": [
+                "\"dsimp\"",
+                "[]"
+              ],
+              "state_after": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\nf : { J // J.FG } \u2192 R\nhf : \u2200 (I : { J // J.FG }), \u2191I = Ideal.span {f I}\n\u22a2 \u2200 {a b : { N // N.FG }}, DvdNotUnit (f a) (f b) \u2194 a > b",
+              "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\nf : { J // J.FG } \u2192 R\nhf : \u2200 (I : { J // J.FG }), \u2191I = Ideal.span {f I}\n\u22a2 \u2200 {a b : { N // N.FG }}, DvdNotUnit ({ toFun := f, inj' := \u22ef } a) ({ toFun := f, inj' := \u22ef } b) \u2194 a > b",
+              "tactic": "dsimp"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro a b\"",
+                "[]"
+              ],
+              "state_after": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\nf : { J // J.FG } \u2192 R\nhf : \u2200 (I : { J // J.FG }), \u2191I = Ideal.span {f I}\na b : { N // N.FG }\n\u22a2 DvdNotUnit (f a) (f b) \u2194 a > b",
+              "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\nf : { J // J.FG } \u2192 R\nhf : \u2200 (I : { J // J.FG }), \u2191I = Ideal.span {f I}\n\u22a2 \u2200 {a b : { N // N.FG }}, DvdNotUnit (f a) (f b) \u2194 a > b",
+              "tactic": "intro a b"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>Ideal.span_singleton_lt_span_singleton<\\/a>, \\u2190 hf, \\u2190 hf]\"",
+                "[{\"full_name\":\"Ideal.span_singleton_lt_span_singleton\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Basic.lean\",\"def_pos\":[555,9],\"def_end_pos\":[555,41]}]"
+              ],
+              "state_after": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\nf : { J // J.FG } \u2192 R\nhf : \u2200 (I : { J // J.FG }), \u2191I = Ideal.span {f I}\na b : { N // N.FG }\n\u22a2 \u2191b < \u2191a \u2194 a > b",
+              "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\nf : { J // J.FG } \u2192 R\nhf : \u2200 (I : { J // J.FG }), \u2191I = Ideal.span {f I}\na b : { N // N.FG }\n\u22a2 DvdNotUnit (f a) (f b) \u2194 a > b",
+              "tactic": "rw [\u2190 Ideal.span_singleton_lt_span_singleton, \u2190 hf, \u2190 hf]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rfl\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\ninst\u271d\u00b9 : IsBezout R\ninst\u271d : IsDomain R\ntfae_1_to_2 : IsNoetherianRing R \u2192 IsPrincipalIdealRing R\ntfae_2_to_3 : IsPrincipalIdealRing R \u2192 UniqueFactorizationMonoid R\ntfae_3_to_4 : UniqueFactorizationMonoid R \u2192 WfDvdMonoid R\nh : WellFounded DvdNotUnit\nf : { J // J.FG } \u2192 R\nhf : \u2200 (I : { J // J.FG }), \u2191I = Ideal.span {f I}\na b : { N // N.FG }\n\u22a2 \u2191b < \u2191a \u2194 a > b",
+              "tactic": "rfl"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bezout.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'intro H x y'",
+        "full_name": "IsBezout.iff_span_pair_isPrincipal",
+        "id": "IsBezout.iff_span_pair_isPrincipal",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            39,
+            84
+          ],
+          "file_path": "Mathlib/RingTheory/Bezout.lean",
+          "full_name": "IsBezout.iff_span_pair_isPrincipal",
+          "start": [
+            30,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"constructor\"",
+                "[]"
+              ],
+              "state_after": "case mp\nR : Type u\ninst\u271d : CommRing R\n\u22a2 IsBezout R \u2192 \u2200 (x y : R), Submodule.IsPrincipal (Ideal.span {x, y})\n\ncase mpr\nR : Type u\ninst\u271d : CommRing R\n\u22a2 (\u2200 (x y : R), Submodule.IsPrincipal (Ideal.span {x, y})) \u2192 IsBezout R",
+              "state_before": "R : Type u\ninst\u271d : CommRing R\n\u22a2 IsBezout R \u2194 \u2200 (x y : R), Submodule.IsPrincipal (Ideal.span {x, y})",
+              "tactic": "constructor"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro H x y\"",
+                "[]"
+              ],
+              "state_after": "case mp\nR : Type u\ninst\u271d : CommRing R\nH : IsBezout R\nx y : R\n\u22a2 Submodule.IsPrincipal (Ideal.span {x, y})",
+              "state_before": "case mp\nR : Type u\ninst\u271d : CommRing R\n\u22a2 IsBezout R \u2192 \u2200 (x y : R), Submodule.IsPrincipal (Ideal.span {x, y})",
+              "tactic": "intro H x y"
+            },
+            {
+              "annotated_tactic": [
+                "\"infer_instance\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case mp\nR : Type u\ninst\u271d : CommRing R\nH : IsBezout R\nx y : R\n\u22a2 Submodule.IsPrincipal (Ideal.span {x, y})",
+              "tactic": "infer_instance"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro H\"",
+                "[]"
+              ],
+              "state_after": "case mpr\nR : Type u\ninst\u271d : CommRing R\nH : \u2200 (x y : R), Submodule.IsPrincipal (Ideal.span {x, y})\n\u22a2 IsBezout R",
+              "state_before": "case mpr\nR : Type u\ninst\u271d : CommRing R\n\u22a2 (\u2200 (x y : R), Submodule.IsPrincipal (Ideal.span {x, y})) \u2192 IsBezout R",
+              "tactic": "intro H"
+            },
+            {
+              "annotated_tactic": [
+                "\"constructor\"",
+                "[]"
+              ],
+              "state_after": "case mpr.isPrincipal_of_FG\nR : Type u\ninst\u271d : CommRing R\nH : \u2200 (x y : R), Submodule.IsPrincipal (Ideal.span {x, y})\n\u22a2 \u2200 (I : Ideal R), I.FG \u2192 Submodule.IsPrincipal I",
+              "state_before": "case mpr\nR : Type u\ninst\u271d : CommRing R\nH : \u2200 (x y : R), Submodule.IsPrincipal (Ideal.span {x, y})\n\u22a2 IsBezout R",
+              "tactic": "constructor"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Submodule.fg_induction<\\/a>\"",
+                "[{\"full_name\":\"Submodule.fg_induction\",\"def_path\":\"Mathlib\\/RingTheory\\/Finiteness.lean\",\"def_pos\":[335,9],\"def_end_pos\":[335,21]}]"
+              ],
+              "state_after": "case mpr.isPrincipal_of_FG.h\u2081\nR : Type u\ninst\u271d : CommRing R\nH : \u2200 (x y : R), Submodule.IsPrincipal (Ideal.span {x, y})\n\u22a2 \u2200 (x : R), (Submodule.span R {x}).IsPrincipal\n\ncase mpr.isPrincipal_of_FG.h\u2082\nR : Type u\ninst\u271d : CommRing R\nH : \u2200 (x y : R), Submodule.IsPrincipal (Ideal.span {x, y})\n\u22a2 \u2200 (M\u2081 M\u2082 : Submodule R R), M\u2081.IsPrincipal \u2192 M\u2082.IsPrincipal \u2192 (M\u2081 \u2294 M\u2082).IsPrincipal",
+              "state_before": "case mpr.isPrincipal_of_FG\nR : Type u\ninst\u271d : CommRing R\nH : \u2200 (x y : R), Submodule.IsPrincipal (Ideal.span {x, y})\n\u22a2 \u2200 (I : Ideal R), I.FG \u2192 Submodule.IsPrincipal I",
+              "tactic": "apply Submodule.fg_induction"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact fun _ => \\u27e8\\u27e8_, <a>rfl<\\/a>\\u27e9\\u27e9\"",
+                "[{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case mpr.isPrincipal_of_FG.h\u2081\nR : Type u\ninst\u271d : CommRing R\nH : \u2200 (x y : R), Submodule.IsPrincipal (Ideal.span {x, y})\n\u22a2 \u2200 (x : R), (Submodule.span R {x}).IsPrincipal",
+              "tactic": "exact fun _ => \u27e8\u27e8_, rfl\u27e9\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rintro _ _ \\u27e8\\u27e8x, rfl\\u27e9\\u27e9 \\u27e8\\u27e8y, rfl\\u27e9\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "case mpr.isPrincipal_of_FG.h\u2082.mk.intro.mk.intro\nR : Type u\ninst\u271d : CommRing R\nH : \u2200 (x y : R), Submodule.IsPrincipal (Ideal.span {x, y})\nx y : R\n\u22a2 (Submodule.span R {x} \u2294 Submodule.span R {y}).IsPrincipal",
+              "state_before": "case mpr.isPrincipal_of_FG.h\u2082\nR : Type u\ninst\u271d : CommRing R\nH : \u2200 (x y : R), Submodule.IsPrincipal (Ideal.span {x, y})\n\u22a2 \u2200 (M\u2081 M\u2082 : Submodule R R), M\u2081.IsPrincipal \u2192 M\u2082.IsPrincipal \u2192 (M\u2081 \u2294 M\u2082).IsPrincipal",
+              "tactic": "rintro _ _ \u27e8\u27e8x, rfl\u27e9\u27e9 \u27e8\u27e8y, rfl\u27e9\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>Submodule.span_insert<\\/a>]\"",
+                "[{\"full_name\":\"Submodule.span_insert\",\"def_path\":\"Mathlib\\/LinearAlgebra\\/Span.lean\",\"def_pos\":[562,9],\"def_end_pos\":[562,20]}]"
+              ],
+              "state_after": "case mpr.isPrincipal_of_FG.h\u2082.mk.intro.mk.intro\nR : Type u\ninst\u271d : CommRing R\nH : \u2200 (x y : R), Submodule.IsPrincipal (Ideal.span {x, y})\nx y : R\n\u22a2 (Submodule.span R {x, y}).IsPrincipal",
+              "state_before": "case mpr.isPrincipal_of_FG.h\u2082.mk.intro.mk.intro\nR : Type u\ninst\u271d : CommRing R\nH : \u2200 (x y : R), Submodule.IsPrincipal (Ideal.span {x, y})\nx y : R\n\u22a2 (Submodule.span R {x} \u2294 Submodule.span R {y}).IsPrincipal",
+              "tactic": "rw [\u2190 Submodule.span_insert]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact H _ _\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case mpr.isPrincipal_of_FG.h\u2082.mk.intro.mk.intro\nR : Type u\ninst\u271d : CommRing R\nH : \u2200 (x y : R), Submodule.IsPrincipal (Ideal.span {x, y})\nx y : R\n\u22a2 (Submodule.span R {x, y}).IsPrincipal",
+              "tactic": "exact H _ _"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bezout.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Bialgebra.comul_algebraMap",
+        "id": "Bialgebra.comul_algebraMap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            129,
+            31
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Basic.lean",
+          "full_name": "Bialgebra.comul_algebraMap",
+          "start": [
+            127,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Bialgebra.comul_mul",
+        "id": "Bialgebra.comul_mul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            90,
+            63
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Basic.lean",
+          "full_name": "Bialgebra.comul_mul",
+          "start": [
+            89,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Bialgebra.comul_natCast",
+        "id": "Bialgebra.comul_natCast",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            135,
+            34
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Basic.lean",
+          "full_name": "Bialgebra.comul_natCast",
+          "start": [
+            134,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Bialgebra.comul_pow",
+        "id": "Bialgebra.comul_pow",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            141,
+            32
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Basic.lean",
+          "full_name": "Bialgebra.comul_pow",
+          "start": [
+            140,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Bialgebra.counit_algebraMap",
+        "id": "Bialgebra.counit_algebraMap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            125,
+            32
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Basic.lean",
+          "full_name": "Bialgebra.counit_algebraMap",
+          "start": [
+            124,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Bialgebra.counit_mul",
+        "id": "Bialgebra.counit_mul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            87,
+            64
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Basic.lean",
+          "full_name": "Bialgebra.counit_mul",
+          "start": [
+            86,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Bialgebra.counit_natCast",
+        "id": "Bialgebra.counit_natCast",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            132,
+            35
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Basic.lean",
+          "full_name": "Bialgebra.counit_natCast",
+          "start": [
+            131,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Bialgebra.counit_pow",
+        "id": "Bialgebra.counit_pow",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            138,
+            33
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Basic.lean",
+          "full_name": "Bialgebra.counit_pow",
+          "start": [
+            137,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Basic.lean"
+      }
+    ],
+    "input_proofs": 11,
+    "input_units": 2,
+    "proofs": 1,
+    "published_proofs": 0,
+    "published_transitions": 0,
+    "replay_failures": [],
+    "transitions": 8,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/RingTheory/Bezout.lean",
+        "proof_id": "mathlib:Function.Surjective.isBezout",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              50,
+              50
+            ],
+            "file_path": "Mathlib/RingTheory/Bezout.lean",
+            "full_name": "Function.Surjective.isBezout",
+            "start": [
+              42,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>iff_span_pair_isPrincipal<\\/a>]\"",
+                  "[{\"full_name\":\"IsBezout.iff_span_pair_isPrincipal\",\"def_path\":\"Mathlib\\/RingTheory\\/Bezout.lean\",\"def_pos\":[30,9],\"def_end_pos\":[30,34]}]"
+                ],
+                "state_after": "R : Type u\ninst\u271d\u00b2 : CommRing R\nS : Type v\ninst\u271d\u00b9 : CommRing S\nf : R \u2192+* S\nhf : Function.Surjective \u21d1f\ninst\u271d : IsBezout R\n\u22a2 \u2200 (x y : S), Submodule.IsPrincipal (Ideal.span {x, y})",
+                "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\nS : Type v\ninst\u271d\u00b9 : CommRing S\nf : R \u2192+* S\nhf : Function.Surjective \u21d1f\ninst\u271d : IsBezout R\n\u22a2 IsBezout S",
+                "tactic": "rw [iff_span_pair_isPrincipal]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"intro x y\"",
+                  "[]"
+                ],
+                "state_after": "R : Type u\ninst\u271d\u00b2 : CommRing R\nS : Type v\ninst\u271d\u00b9 : CommRing S\nf : R \u2192+* S\nhf : Function.Surjective \u21d1f\ninst\u271d : IsBezout R\nx y : S\n\u22a2 Submodule.IsPrincipal (Ideal.span {x, y})",
+                "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\nS : Type v\ninst\u271d\u00b9 : CommRing S\nf : R \u2192+* S\nhf : Function.Surjective \u21d1f\ninst\u271d : IsBezout R\n\u22a2 \u2200 (x y : S), Submodule.IsPrincipal (Ideal.span {x, y})",
+                "tactic": "intro x y"
+              },
+              {
+                "annotated_tactic": [
+                  "\"obtain \\u27e8\\u27e8x, rfl\\u27e9, \\u27e8y, rfl\\u27e9\\u27e9 := hf x, hf y\"",
+                  "[]"
+                ],
+                "state_after": "case intro.intro\nR : Type u\ninst\u271d\u00b2 : CommRing R\nS : Type v\ninst\u271d\u00b9 : CommRing S\nf : R \u2192+* S\nhf : Function.Surjective \u21d1f\ninst\u271d : IsBezout R\nx y : R\n\u22a2 Submodule.IsPrincipal (Ideal.span {f x, f y})",
+                "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\nS : Type v\ninst\u271d\u00b9 : CommRing S\nf : R \u2192+* S\nhf : Function.Surjective \u21d1f\ninst\u271d : IsBezout R\nx y : S\n\u22a2 Submodule.IsPrincipal (Ideal.span {x, y})",
+                "tactic": "obtain \u27e8\u27e8x, rfl\u27e9, \u27e8y, rfl\u27e9\u27e9 := hf x, hf y"
+              },
+              {
+                "annotated_tactic": [
+                  "\"use f (<a>gcd<\\/a> x y)\"",
+                  "[{\"full_name\":\"IsBezout.gcd\",\"def_path\":\"Mathlib\\/RingTheory\\/PrincipalIdealDomain.lean\",\"def_pos\":[174,19],\"def_end_pos\":[174,22]}]"
+                ],
+                "state_after": "case h\nR : Type u\ninst\u271d\u00b2 : CommRing R\nS : Type v\ninst\u271d\u00b9 : CommRing S\nf : R \u2192+* S\nhf : Function.Surjective \u21d1f\ninst\u271d : IsBezout R\nx y : R\n\u22a2 Ideal.span {f x, f y} = Submodule.span S {f (gcd x y)}",
+                "state_before": "case intro.intro\nR : Type u\ninst\u271d\u00b2 : CommRing R\nS : Type v\ninst\u271d\u00b9 : CommRing S\nf : R \u2192+* S\nhf : Function.Surjective \u21d1f\ninst\u271d : IsBezout R\nx y : R\n\u22a2 Submodule.IsPrincipal (Ideal.span {f x, f y})",
+                "tactic": "use f (gcd x y)"
+              },
+              {
+                "annotated_tactic": [
+                  "\"trans <a>Ideal.map<\\/a> f (<a>Ideal.span<\\/a> {<a>gcd<\\/a> x y})\"",
+                  "[{\"full_name\":\"Ideal.map\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Maps.lean\",\"def_pos\":[36,5],\"def_end_pos\":[36,8]},{\"full_name\":\"Ideal.span\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Basic.lean\",\"def_pos\":[115,5],\"def_end_pos\":[115,9]},{\"full_name\":\"IsBezout.gcd\",\"def_path\":\"Mathlib\\/RingTheory\\/PrincipalIdealDomain.lean\",\"def_pos\":[174,19],\"def_end_pos\":[174,22]}]"
+                ],
+                "state_after": "R : Type u\ninst\u271d\u00b2 : CommRing R\nS : Type v\ninst\u271d\u00b9 : CommRing S\nf : R \u2192+* S\nhf : Function.Surjective \u21d1f\ninst\u271d : IsBezout R\nx y : R\n\u22a2 Ideal.span {f x, f y} = Ideal.map f (Ideal.span {gcd x y})\n\nR : Type u\ninst\u271d\u00b2 : CommRing R\nS : Type v\ninst\u271d\u00b9 : CommRing S\nf : R \u2192+* S\nhf : Function.Surjective \u21d1f\ninst\u271d : IsBezout R\nx y : R\n\u22a2 Ideal.map f (Ideal.span {gcd x y}) = Submodule.span S {f (gcd x y)}",
+                "state_before": "case h\nR : Type u\ninst\u271d\u00b2 : CommRing R\nS : Type v\ninst\u271d\u00b9 : CommRing S\nf : R \u2192+* S\nhf : Function.Surjective \u21d1f\ninst\u271d : IsBezout R\nx y : R\n\u22a2 Ideal.span {f x, f y} = Submodule.span S {f (gcd x y)}",
+                "tactic": "trans Ideal.map f (Ideal.span {gcd x y})"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>span_gcd<\\/a>, <a>Ideal.map_span<\\/a>, <a>Set.image_insert_eq<\\/a>, <a>Set.image_singleton<\\/a>]\"",
+                  "[{\"full_name\":\"IsBezout.span_gcd\",\"def_path\":\"Mathlib\\/RingTheory\\/PrincipalIdealDomain.lean\",\"def_pos\":[177,9],\"def_end_pos\":[177,17]},{\"full_name\":\"Ideal.map_span\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Maps.lean\",\"def_pos\":[149,9],\"def_end_pos\":[149,17]},{\"full_name\":\"Set.image_insert_eq\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Image.lean\",\"def_pos\":[389,9],\"def_end_pos\":[389,24]},{\"full_name\":\"Set.image_singleton\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Image.lean\",\"def_pos\":[335,9],\"def_end_pos\":[335,24]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\nS : Type v\ninst\u271d\u00b9 : CommRing S\nf : R \u2192+* S\nhf : Function.Surjective \u21d1f\ninst\u271d : IsBezout R\nx y : R\n\u22a2 Ideal.span {f x, f y} = Ideal.map f (Ideal.span {gcd x y})",
+                "tactic": "rw [span_gcd, Ideal.map_span, Set.image_insert_eq, Set.image_singleton]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>Ideal.map_span<\\/a>, <a>Set.image_singleton<\\/a>]\"",
+                  "[{\"full_name\":\"Ideal.map_span\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Maps.lean\",\"def_pos\":[149,9],\"def_end_pos\":[149,17]},{\"full_name\":\"Set.image_singleton\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Image.lean\",\"def_pos\":[335,9],\"def_end_pos\":[335,24]}]"
+                ],
+                "state_after": "R : Type u\ninst\u271d\u00b2 : CommRing R\nS : Type v\ninst\u271d\u00b9 : CommRing S\nf : R \u2192+* S\nhf : Function.Surjective \u21d1f\ninst\u271d : IsBezout R\nx y : R\n\u22a2 Ideal.span {f (gcd x y)} = Submodule.span S {f (gcd x y)}",
+                "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\nS : Type v\ninst\u271d\u00b9 : CommRing S\nf : R \u2192+* S\nhf : Function.Surjective \u21d1f\ninst\u271d : IsBezout R\nx y : R\n\u22a2 Ideal.map f (Ideal.span {gcd x y}) = Submodule.span S {f (gcd x y)}",
+                "tactic": "rw [Ideal.map_span, Set.image_singleton]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rfl\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "R : Type u\ninst\u271d\u00b2 : CommRing R\nS : Type v\ninst\u271d\u00b9 : CommRing S\nf : R \u2192+* S\nhf : Function.Surjective \u21d1f\ninst\u271d : IsBezout R\nx y : R\n\u22a2 Ideal.span {f (gcd x y)} = Submodule.span S {f (gcd x y)}",
+                "tactic": "rfl"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Function.Surjective.isBezout"
+      }
+    ],
+    "validation_rejected_proofs": 1,
+    "zero_transition_proofs": 0
+  },
+  "shards": [],
+  "proof_ids": [],
+  "proof_keys": []
+}

manifests/batches/mathlib/001649.json

@@ -0,0 +1,1367 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001649",
+  "batch_fingerprint": "8e0c87a8945ecd492918de6627a5f9b411d3fff18e78461503d2cdfdc3ace3b5",
+  "evidence": {
+    "batch_fingerprint": "8e0c87a8945ecd492918de6627a5f9b411d3fff18e78461503d2cdfdc3ace3b5",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.coe_coe",
+        "id": "BialgEquiv.coe_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            158,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.coe_coe",
+          "start": [
+            157,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.coe_mk",
+        "id": "BialgEquiv.coe_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            137,
+            73
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.coe_mk",
+          "start": [
+            136,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.coe_toAlgEquiv",
+        "id": "BialgEquiv.coe_toAlgEquiv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            182,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.coe_toAlgEquiv",
+          "start": [
+            181,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.coe_toBialgHom",
+        "id": "BialgEquiv.coe_toBialgHom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            178,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.coe_toBialgHom",
+          "start": [
+            177,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.coe_toCoalgEquiv",
+        "id": "BialgEquiv.coe_toCoalgEquiv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            174,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.coe_toCoalgEquiv",
+          "start": [
+            173,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.coe_toEquiv_symm",
+        "id": "BialgEquiv.coe_toEquiv_symm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            249,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.coe_toEquiv_symm",
+          "start": [
+            248,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.coe_toEquiv_trans",
+        "id": "BialgEquiv.coe_toEquiv_trans",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            268,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.coe_toEquiv_trans",
+          "start": [
+            267,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.congr_arg",
+        "id": "BialgEquiv.congr_arg",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            201,
+            23
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.congr_arg",
+          "start": [
+            200,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.congr_fun",
+        "id": "BialgEquiv.congr_fun",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            204,
+            25
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.congr_fun",
+          "start": [
+            203,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.ext",
+        "id": "BialgEquiv.ext",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            195,
+            21
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.ext",
+          "start": [
+            194,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.ext_iff",
+        "id": "BialgEquiv.ext_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            198,
+            19
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.ext_iff",
+          "start": [
+            197,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.invFun_eq_symm",
+        "id": "BialgEquiv.invFun_eq_symm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            245,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.invFun_eq_symm",
+          "start": [
+            244,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.refl_toBialgHom",
+        "id": "BialgEquiv.refl_toBialgHom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            224,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.refl_toBialgHom",
+          "start": [
+            223,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.refl_toCoalgEquiv",
+        "id": "BialgEquiv.refl_toCoalgEquiv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            220,
+            66
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.refl_toCoalgEquiv",
+          "start": [
+            220,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.symm_toCoalgEquiv",
+        "id": "BialgEquiv.symm_toCoalgEquiv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            233,
+            42
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.symm_toCoalgEquiv",
+          "start": [
+            232,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.toAlgEquiv_eq_coe",
+        "id": "BialgEquiv.toAlgEquiv_eq_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            170,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.toAlgEquiv_eq_coe",
+          "start": [
+            169,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.toBialgHom_eq_coe",
+        "id": "BialgEquiv.toBialgHom_eq_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            166,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.toBialgHom_eq_coe",
+          "start": [
+            165,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.toBialgHom_inj",
+        "id": "BialgEquiv.toBialgHom_inj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            133,
+            30
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.toBialgHom_inj",
+          "start": [
+            132,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.toBialgHom_injective",
+        "id": "BialgEquiv.toBialgHom_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            112,
+            70
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.toBialgHom_injective",
+          "start": [
+            111,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.toBialgHom_toAlgHom",
+        "id": "BialgEquiv.toBialgHom_toAlgHom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            187,
+            72
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.toBialgHom_toAlgHom",
+          "start": [
+            187,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.toCoalgEquiv_eq_coe",
+        "id": "BialgEquiv.toCoalgEquiv_eq_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            162,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.toCoalgEquiv_eq_coe",
+          "start": [
+            161,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.toCoalgEquiv_toCoalgHom",
+        "id": "BialgEquiv.toCoalgEquiv_toCoalgHom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            185,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.toCoalgEquiv_toCoalgHom",
+          "start": [
+            184,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.toEquiv_inj",
+        "id": "BialgEquiv.toEquiv_inj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            109,
+            27
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.toEquiv_inj",
+          "start": [
+            108,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.toEquiv_injective",
+        "id": "BialgEquiv.toEquiv_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            105,
+            71
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.toEquiv_injective",
+          "start": [
+            103,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.trans_toBialgHom",
+        "id": "BialgEquiv.trans_toBialgHom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            264,
+            70
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.trans_toBialgHom",
+          "start": [
+            263,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgEquiv.trans_toCoalgEquiv",
+        "id": "BialgEquiv.trans_toCoalgEquiv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            260,
+            86
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Equiv.lean",
+          "full_name": "BialgEquiv.trans_toCoalgEquiv",
+          "start": [
+            259,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.coe_algHom_injective",
+        "id": "BialgHom.coe_algHom_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            179,
+            84
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.coe_algHom_injective",
+          "start": [
+            177,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.coe_coalgHom_injective",
+        "id": "BialgHom.coe_coalgHom_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            175,
+            86
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.coe_coalgHom_injective",
+          "start": [
+            173,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.coe_coe",
+        "id": "BialgHom.coe_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            133,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.coe_coe",
+          "start": [
+            131,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.coe_comp",
+        "id": "BialgHom.coe_comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            250,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.coe_comp",
+          "start": [
+            249,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.coe_copy",
+        "id": "BialgHom.coe_copy",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            215,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.coe_copy",
+          "start": [
+            214,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.coe_fn_inj",
+        "id": "BialgHom.coe_fn_inj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            171,
+            21
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.coe_fn_inj",
+          "start": [
+            170,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.coe_fn_injective",
+        "id": "BialgHom.coe_fn_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            168,
+            25
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.coe_fn_injective",
+          "start": [
+            167,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.coe_id",
+        "id": "BialgHom.coe_id",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            232,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.coe_id",
+          "start": [
+            231,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.coe_linearMap_injective",
+        "id": "BialgHom.coe_linearMap_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            182,
+            63
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.coe_linearMap_injective",
+          "start": [
+            181,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.coe_mk",
+        "id": "BialgHom.coe_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            137,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.coe_mk",
+          "start": [
+            136,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.coe_mks",
+        "id": "BialgHom.coe_mks",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            142,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.coe_mks",
+          "start": [
+            140,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.coe_toAlgHom",
+        "id": "BialgHom.coe_toAlgHom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            159,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.coe_toAlgHom",
+          "start": [
+            158,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.coe_toCoalgHom",
+        "id": "BialgHom.coe_toCoalgHom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            151,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.coe_toCoalgHom",
+          "start": [
+            150,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.coe_toLinearMap",
+        "id": "BialgHom.coe_toLinearMap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            155,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.coe_toLinearMap",
+          "start": [
+            154,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.comp_assoc",
+        "id": "BialgHom.comp_assoc",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            272,
+            20
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.comp_assoc",
+          "start": [
+            270,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.comp_id",
+        "id": "BialgHom.comp_id",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            264,
+            20
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.comp_id",
+          "start": [
+            263,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.comp_toAlgHom",
+        "id": "BialgHom.comp_toAlgHom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            260,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.comp_toAlgHom",
+          "start": [
+            258,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.comp_toCoalgHom",
+        "id": "BialgHom.comp_toCoalgHom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            255,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.comp_toCoalgHom",
+          "start": [
+            253,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.congr_arg",
+        "id": "BialgHom.congr_arg",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            188,
+            25
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.congr_arg",
+          "start": [
+            187,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.congr_fun",
+        "id": "BialgHom.congr_fun",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            185,
+            25
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.congr_fun",
+          "start": [
+            184,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.copy_eq",
+        "id": "BialgHom.copy_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            218,
+            18
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.copy_eq",
+          "start": [
+            217,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.ext",
+        "id": "BialgHom.ext",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            192,
+            21
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.ext",
+          "start": [
+            191,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.ext_iff",
+        "id": "BialgHom.ext_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            195,
+            19
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.ext_iff",
+          "start": [
+            194,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.id_comp",
+        "id": "BialgHom.id_comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            268,
+            20
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.id_comp",
+          "start": [
+            267,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.id_toCoalgHom",
+        "id": "BialgHom.id_toCoalgHom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            236,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.id_toCoalgHom",
+          "start": [
+            235,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.map_smul_of_tower",
+        "id": "BialgHom.map_smul_of_tower",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            276,
+            38
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.map_smul_of_tower",
+          "start": [
+            274,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.mk_coe",
+        "id": "BialgHom.mk_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            204,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.mk_coe",
+          "start": [
+            202,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.mul_apply",
+        "id": "BialgHom.mul_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            292,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.mul_apply",
+          "start": [
+            291,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHom.one_apply",
+        "id": "BialgHom.one_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            288,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHom.one_apply",
+          "start": [
+            287,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHomClass.counitAlgHom_comp",
+        "id": "BialgHomClass.counitAlgHom_comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            91,
+            61
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHomClass.counitAlgHom_comp",
+          "start": [
+            89,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BialgHomClass.map_comp_comulAlgHom",
+        "id": "BialgHomClass.map_comp_comulAlgHom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            96,
+            64
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "BialgHomClass.map_comp_comulAlgHom",
+          "start": [
+            94,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Bialgebra.counitBialgHom_apply",
+        "id": "Bialgebra.counitBialgHom_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            308,
+            53
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "Bialgebra.counitBialgHom_apply",
+          "start": [
+            307,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Bialgebra.counitBialgHom_toCoalgHom",
+        "id": "Bialgebra.counitBialgHom_toCoalgHom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            312,
+            61
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "Bialgebra.counitBialgHom_toCoalgHom",
+          "start": [
+            311,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Bialgebra.ext_to_ring",
+        "id": "Bialgebra.ext_to_ring",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            320,
+            72
+          ],
+          "file_path": "Mathlib/RingTheory/Bialgebra/Hom.lean",
+          "full_name": "Bialgebra.ext_to_ring",
+          "start": [
+            320,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Bialgebra/Hom.lean"
+      }
+    ],
+    "input_proofs": 63,
+    "input_units": 2,
+    "proofs": 3,
+    "published_proofs": 3,
+    "published_transitions": 4,
+    "replay_failures": [],
+    "transitions": 4,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001649-0000-516cfe32f03ba9ee.parquet",
+      "sha256": "516cfe32f03ba9ee69b6c51f4a817f32d9492c0774dee36fefbcf964cba9f2fc",
+      "bytes": 59614,
+      "rows": 3,
+      "revision": "df8c9c479578582ca5384c5c62608ea4677707ca"
+    },
+    {
+      "path": "data/internal_test/mathlib-001649-0000-eacbf2684f501409.parquet",
+      "sha256": "eacbf2684f501409297b736026808c67c63abe8945c1b762305a24022db58b62",
+      "bytes": 43440,
+      "rows": 1,
+      "revision": "df8c9c479578582ca5384c5c62608ea4677707ca"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:BialgHom.coe_coalgHom_mk",
+    "mathlib:BialgHom.ext_of_ring",
+    "mathlib:BialgHom.toAlgHom_toLinearMap"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Bialgebra/Hom.lean\",null,null,\"BialgHom.coe_coalgHom_mk\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Bialgebra/Hom.lean\",null,null,\"BialgHom.ext_of_ring\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Bialgebra/Hom.lean\",null,null,\"BialgHom.toAlgHom_toLinearMap\"]"
+  ]
+}

manifests/batches/mathlib/001652.json

@@ -0,0 +1,1290 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001652",
+  "batch_fingerprint": "05ff929542bf4fc7ab360526dbcc7fec381bc5631aa3dbc77a3dadc20014faf0",
+  "evidence": {
+    "batch_fingerprint": "05ff929542bf4fc7ab360526dbcc7fec381bc5631aa3dbc77a3dadc20014faf0",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.coe_coe",
+        "id": "CoalgEquiv.coe_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            131,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.coe_coe",
+          "start": [
+            130,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.coe_mk",
+        "id": "CoalgEquiv.coe_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            110,
+            67
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.coe_mk",
+          "start": [
+            109,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.coe_toCoalgHom",
+        "id": "CoalgEquiv.coe_toCoalgHom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            147,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.coe_toCoalgHom",
+          "start": [
+            146,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.coe_toEquiv_symm",
+        "id": "CoalgEquiv.coe_toEquiv_symm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            225,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.coe_toEquiv_symm",
+          "start": [
+            224,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.coe_toEquiv_trans",
+        "id": "CoalgEquiv.coe_toEquiv_trans",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            243,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.coe_toEquiv_trans",
+          "start": [
+            242,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.coe_toLinearEquiv",
+        "id": "CoalgEquiv.coe_toLinearEquiv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            143,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.coe_toLinearEquiv",
+          "start": [
+            142,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.congr_arg",
+        "id": "CoalgEquiv.congr_arg",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            164,
+            23
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.congr_arg",
+          "start": [
+            163,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.congr_fun",
+        "id": "CoalgEquiv.congr_fun",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            167,
+            25
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.congr_fun",
+          "start": [
+            166,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.ext",
+        "id": "CoalgEquiv.ext",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            158,
+            21
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.ext",
+          "start": [
+            157,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.ext_iff",
+        "id": "CoalgEquiv.ext_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            161,
+            19
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.ext_iff",
+          "start": [
+            160,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.invFun_eq_symm",
+        "id": "CoalgEquiv.invFun_eq_symm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            221,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.invFun_eq_symm",
+          "start": [
+            220,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.refl_toCoalgHom",
+        "id": "CoalgEquiv.refl_toCoalgHom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            187,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.refl_toCoalgHom",
+          "start": [
+            186,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.refl_toLinearEquiv",
+        "id": "CoalgEquiv.refl_toLinearEquiv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            183,
+            68
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.refl_toLinearEquiv",
+          "start": [
+            183,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.symm_toCoalgHom",
+        "id": "CoalgEquiv.symm_toCoalgHom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            208,
+            70
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.symm_toCoalgHom",
+          "start": [
+            207,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.symm_toLinearEquiv",
+        "id": "CoalgEquiv.symm_toLinearEquiv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            204,
+            41
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.symm_toLinearEquiv",
+          "start": [
+            203,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.toCoalgHom_eq_coe",
+        "id": "CoalgEquiv.toCoalgHom_eq_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            139,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.toCoalgHom_eq_coe",
+          "start": [
+            138,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.toCoalgHom_inj",
+        "id": "CoalgEquiv.toCoalgHom_inj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            106,
+            30
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.toCoalgHom_inj",
+          "start": [
+            105,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.toCoalgHom_injective",
+        "id": "CoalgEquiv.toCoalgHom_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            86,
+            70
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.toCoalgHom_injective",
+          "start": [
+            85,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.toEquiv_inj",
+        "id": "CoalgEquiv.toEquiv_inj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            83,
+            27
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.toEquiv_inj",
+          "start": [
+            82,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.toEquiv_injective",
+        "id": "CoalgEquiv.toEquiv_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            79,
+            72
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.toEquiv_injective",
+          "start": [
+            76,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.toLinearEquiv_eq_coe",
+        "id": "CoalgEquiv.toLinearEquiv_eq_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            135,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.toLinearEquiv_eq_coe",
+          "start": [
+            134,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.toLinearEquiv_toLinearMap",
+        "id": "CoalgEquiv.toLinearEquiv_toLinearMap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            150,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.toLinearEquiv_toLinearMap",
+          "start": [
+            149,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.trans_toCoalgHom",
+        "id": "CoalgEquiv.trans_toCoalgHom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            239,
+            55
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.trans_toCoalgHom",
+          "start": [
+            238,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgEquiv.trans_toLinearEquiv",
+        "id": "CoalgEquiv.trans_toLinearEquiv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            235,
+            67
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Equiv.lean",
+          "full_name": "CoalgEquiv.trans_toLinearEquiv",
+          "start": [
+            234,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Equiv.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.coe_addMonoidHom_injective",
+        "id": "CoalgHom.coe_addMonoidHom_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            158,
+            66
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.coe_addMonoidHom_injective",
+          "start": [
+            157,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.coe_coe",
+        "id": "CoalgHom.coe_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            121,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.coe_coe",
+          "start": [
+            119,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.coe_comp",
+        "id": "CoalgHom.coe_comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            220,
+            86
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.coe_comp",
+          "start": [
+            220,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.coe_copy",
+        "id": "CoalgHom.coe_copy",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            191,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.coe_copy",
+          "start": [
+            190,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.coe_fn_inj",
+        "id": "CoalgHom.coe_fn_inj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            151,
+            21
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.coe_fn_inj",
+          "start": [
+            150,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.coe_fn_injective",
+        "id": "CoalgHom.coe_fn_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            148,
+            25
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.coe_fn_injective",
+          "start": [
+            147,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.coe_id",
+        "id": "CoalgHom.coe_id",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            208,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.coe_id",
+          "start": [
+            207,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.coe_linearMap_injective",
+        "id": "CoalgHom.coe_linearMap_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            155,
+            84
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.coe_linearMap_injective",
+          "start": [
+            153,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.coe_linearMap_mk",
+        "id": "CoalgHom.coe_linearMap_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            133,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.coe_linearMap_mk",
+          "start": [
+            132,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.coe_mk",
+        "id": "CoalgHom.coe_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            125,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.coe_mk",
+          "start": [
+            124,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.coe_mks",
+        "id": "CoalgHom.coe_mks",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            129,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.coe_mks",
+          "start": [
+            128,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.coe_toAddMonoidHom",
+        "id": "CoalgHom.coe_toAddMonoidHom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            145,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.coe_toAddMonoidHom",
+          "start": [
+            144,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.coe_toLinearMap",
+        "id": "CoalgHom.coe_toLinearMap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            141,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.coe_toLinearMap",
+          "start": [
+            140,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.comp_assoc",
+        "id": "CoalgHom.comp_assoc",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            238,
+            20
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.comp_assoc",
+          "start": [
+            236,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.comp_id",
+        "id": "CoalgHom.comp_id",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            230,
+            20
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.comp_id",
+          "start": [
+            229,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.comp_toLinearMap",
+        "id": "CoalgHom.comp_toLinearMap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            224,
+            61
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.comp_toLinearMap",
+          "start": [
+            223,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.congr_arg",
+        "id": "CoalgHom.congr_arg",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            164,
+            25
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.congr_arg",
+          "start": [
+            163,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.congr_fun",
+        "id": "CoalgHom.congr_fun",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            161,
+            25
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.congr_fun",
+          "start": [
+            160,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.copy_eq",
+        "id": "CoalgHom.copy_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            194,
+            18
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.copy_eq",
+          "start": [
+            193,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.ext",
+        "id": "CoalgHom.ext",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            168,
+            21
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.ext",
+          "start": [
+            167,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.ext_iff",
+        "id": "CoalgHom.ext_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            171,
+            19
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.ext_iff",
+          "start": [
+            170,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.id_comp",
+        "id": "CoalgHom.id_comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            234,
+            20
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.id_comp",
+          "start": [
+            233,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.id_toLinearMap",
+        "id": "CoalgHom.id_toLinearMap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            211,
+            77
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.id_toLinearMap",
+          "start": [
+            211,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.map_smul_of_tower",
+        "id": "CoalgHom.map_smul_of_tower",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            242,
+            38
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.map_smul_of_tower",
+          "start": [
+            240,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.mk_coe",
+        "id": "CoalgHom.mk_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            179,
+            19
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.mk_coe",
+          "start": [
+            178,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.mul_apply",
+        "id": "CoalgHom.mul_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            258,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.mul_apply",
+          "start": [
+            257,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.one_apply",
+        "id": "CoalgHom.one_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            254,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.one_apply",
+          "start": [
+            253,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHom.toLinearMap_eq_coe",
+        "id": "CoalgHom.toLinearMap_eq_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            137,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHom.toLinearMap_eq_coe",
+          "start": [
+            136,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHomClass.counit_comp_apply",
+        "id": "CoalgHomClass.counit_comp_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            78,
+            40
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHomClass.counit_comp_apply",
+          "start": [
+            77,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CoalgHomClass.map_comp_comul_apply",
+        "id": "CoalgHomClass.map_comp_comul_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            83,
+            43
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "CoalgHomClass.map_comp_comul_apply",
+          "start": [
+            81,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Coalgebra.counitCoalgHom_apply",
+        "id": "Coalgebra.counitCoalgHom_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            281,
+            43
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "Coalgebra.counitCoalgHom_apply",
+          "start": [
+            280,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Coalgebra.counitCoalgHom_toLinearMap",
+        "id": "Coalgebra.counitCoalgHom_toLinearMap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            285,
+            57
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "Coalgebra.counitCoalgHom_toLinearMap",
+          "start": [
+            284,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Coalgebra.ext_to_ring",
+        "id": "Coalgebra.ext_to_ring",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            297,
+            72
+          ],
+          "file_path": "Mathlib/RingTheory/Coalgebra/Hom.lean",
+          "full_name": "Coalgebra.ext_to_ring",
+          "start": [
+            297,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Coalgebra/Hom.lean"
+      }
+    ],
+    "input_proofs": 58,
+    "input_units": 2,
+    "proofs": 1,
+    "published_proofs": 1,
+    "published_transitions": 2,
+    "replay_failures": [],
+    "transitions": 2,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001652-0000-bdde609d05e24214.parquet",
+      "sha256": "bdde609d05e24214395b7ab25d323576219324f449752864668e7baab9ccdc1e",
+      "bytes": 58695,
+      "rows": 2,
+      "revision": "df8c9c479578582ca5384c5c62608ea4677707ca"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:CoalgHom.ext_of_ring"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Coalgebra/Hom.lean\",null,null,\"CoalgHom.ext_of_ring\"]"
+  ]
+}

manifests/batches/mathlib/001653.json

@@ -0,0 +1,934 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001653",
+  "batch_fingerprint": "59be9b1d01ef579f29c321d8385f4884ee4301170ec0223a93aa29fe27afc269",
+  "evidence": {
+    "batch_fingerprint": "59be9b1d01ef579f29c321d8385f4884ee4301170ec0223a93aa29fe27afc269",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "no internal trace for tactic 'simp only [Fin.mk_one, Matrix.cons_val_one, Matrix.head_cons, I_re, mul_zero, I_im, mul_one,\\n  zero_sub, add_zero]'",
+        "full_name": "Algebra.leftMulMatrix_complex",
+        "id": "Algebra.leftMulMatrix_complex",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            28,
+            24
+          ],
+          "file_path": "Mathlib/RingTheory/Complex.lean",
+          "full_name": "Algebra.leftMulMatrix_complex",
+          "start": [
+            17,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"ext i j\"",
+                "[]"
+              ],
+              "state_after": "case a\nz : \u2102\ni j : Fin 2\n\u22a2 (leftMulMatrix basisOneI) z i j = Matrix.of ![![z.re, -z.im], ![z.im, z.re]] i j",
+              "state_before": "z : \u2102\n\u22a2 (leftMulMatrix basisOneI) z = Matrix.of ![![z.re, -z.im], ![z.im, z.re]]",
+              "tactic": "ext i j"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Algebra.leftMulMatrix_eq_repr_mul<\\/a>, <a>Complex.coe_basisOneI_repr<\\/a>, <a>Complex.coe_basisOneI<\\/a>, <a>mul_re<\\/a>,\\n    <a>mul_im<\\/a>, <a>Matrix.of_apply<\\/a>]\"",
+                "[{\"full_name\":\"Algebra.leftMulMatrix_eq_repr_mul\",\"def_path\":\"Mathlib\\/LinearAlgebra\\/Matrix\\/ToLin.lean\",\"def_pos\":[927,9],\"def_end_pos\":[927,34]},{\"full_name\":\"Complex.coe_basisOneI_repr\",\"def_path\":\"Mathlib\\/Data\\/Complex\\/Module.lean\",\"def_pos\":[150,9],\"def_end_pos\":[150,27]},{\"full_name\":\"Complex.coe_basisOneI\",\"def_path\":\"Mathlib\\/Data\\/Complex\\/Module.lean\",\"def_pos\":[156,9],\"def_end_pos\":[156,22]},{\"full_name\":\"Complex.mul_re\",\"def_path\":\"Mathlib\\/Data\\/Complex\\/Basic.lean\",\"def_pos\":[247,9],\"def_end_pos\":[247,15]},{\"full_name\":\"Complex.mul_im\",\"def_path\":\"Mathlib\\/Data\\/Complex\\/Basic.lean\",\"def_pos\":[252,9],\"def_end_pos\":[252,15]},{\"full_name\":\"Matrix.of_apply\",\"def_path\":\"Mathlib\\/Data\\/Matrix\\/Basic.lean\",\"def_pos\":[100,9],\"def_end_pos\":[100,17]}]"
+              ],
+              "state_after": "case a\nz : \u2102\ni j : Fin 2\n\u22a2 ![z.re * (![1, I] j).re - z.im * (![1, I] j).im, z.re * (![1, I] j).im + z.im * (![1, I] j).re] i =\n    ![![z.re, -z.im], ![z.im, z.re]] i j",
+              "state_before": "case a\nz : \u2102\ni j : Fin 2\n\u22a2 (leftMulMatrix basisOneI) z i j = Matrix.of ![![z.re, -z.im], ![z.im, z.re]] i j",
+              "tactic": "rw [Algebra.leftMulMatrix_eq_repr_mul, Complex.coe_basisOneI_repr, Complex.coe_basisOneI, mul_re,\n  mul_im, Matrix.of_apply]"
+            },
+            {
+              "annotated_tactic": [
+                "\"fin_cases j\"",
+                "[]"
+              ],
+              "state_after": "case a.head\nz : \u2102\ni : Fin 2\n\u22a2 ![z.re * (![1, I] \u27e80, \u22ef\u27e9).re - z.im * (![1, I] \u27e80, \u22ef\u27e9).im, z.re * (![1, I] \u27e80, \u22ef\u27e9).im + z.im * (![1, I] \u27e80, \u22ef\u27e9).re]\n      i =\n    ![![z.re, -z.im], ![z.im, z.re]] i \u27e80, \u22ef\u27e9\n\ncase a.tail.head\nz : \u2102\ni : Fin 2\n\u22a2 ![z.re * (![1, I] \u27e81, \u22ef\u27e9).re - z.im * (![1, I] \u27e81, \u22ef\u27e9).im, z.re * (![1, I] \u27e81, \u22ef\u27e9).im + z.im * (![1, I] \u27e81, \u22ef\u27e9).re]\n      i =\n    ![![z.re, -z.im], ![z.im, z.re]] i \u27e81, \u22ef\u27e9",
+              "state_before": "case a\nz : \u2102\ni j : Fin 2\n\u22a2 ![z.re * (![1, I] j).re - z.im * (![1, I] j).im, z.re * (![1, I] j).im + z.im * (![1, I] j).re] i =\n    ![![z.re, -z.im], ![z.im, z.re]] i j",
+              "tactic": "fin_cases j"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>Fin.mk_zero<\\/a>, <a>Matrix.cons_val_zero<\\/a>, <a>one_re<\\/a>, <a>mul_one<\\/a>, <a>one_im<\\/a>, <a>mul_zero<\\/a>, <a>sub_zero<\\/a>,\\n      <a>zero_add<\\/a>]\"",
+                "[{\"full_name\":\"Fin.mk_zero\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[128,17],\"def_end_pos\":[128,24]},{\"full_name\":\"Matrix.cons_val_zero\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/VecNotation.lean\",\"def_pos\":[132,9],\"def_end_pos\":[132,22]},{\"full_name\":\"Complex.one_re\",\"def_path\":\"Mathlib\\/Data\\/Complex\\/Basic.lean\",\"def_pos\":[170,9],\"def_end_pos\":[170,15]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"Complex.one_im\",\"def_path\":\"Mathlib\\/Data\\/Complex\\/Basic.lean\",\"def_pos\":[175,9],\"def_end_pos\":[175,15]},{\"full_name\":\"MulZeroClass.mul_zero\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Defs.lean\",\"def_pos\":[39,3],\"def_end_pos\":[39,11]},{\"full_name\":\"sub_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[489,3],\"def_end_pos\":[489,14]},{\"full_name\":\"zero_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[476,3],\"def_end_pos\":[476,14]}]"
+              ],
+              "state_after": "case a.head\nz : \u2102\ni : Fin 2\n\u22a2 ![z.re, z.im] i = ![![z.re, -z.im], ![z.im, z.re]] i 0",
+              "state_before": "case a.head\nz : \u2102\ni : Fin 2\n\u22a2 ![z.re * (![1, I] \u27e80, \u22ef\u27e9).re - z.im * (![1, I] \u27e80, \u22ef\u27e9).im, z.re * (![1, I] \u27e80, \u22ef\u27e9).im + z.im * (![1, I] \u27e80, \u22ef\u27e9).re]\n      i =\n    ![![z.re, -z.im], ![z.im, z.re]] i \u27e80, \u22ef\u27e9",
+              "tactic": "simp only [Fin.mk_zero, Matrix.cons_val_zero, one_re, mul_one, one_im, mul_zero, sub_zero,\n  zero_add]"
+            },
+            {
+              "annotated_tactic": [
+                "\"fin_cases i <;> rfl\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case a.head\nz : \u2102\ni : Fin 2\n\u22a2 ![z.re, z.im] i = ![![z.re, -z.im], ![z.im, z.re]] i 0",
+              "tactic": "fin_cases i <;> rfl"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>Fin.mk_one<\\/a>, <a>Matrix.cons_val_one<\\/a>, <a>Matrix.head_cons<\\/a>, <a>I_re<\\/a>, <a>mul_zero<\\/a>, <a>I_im<\\/a>, <a>mul_one<\\/a>,\\n      <a>zero_sub<\\/a>, <a>add_zero<\\/a>]\"",
+                "[{\"full_name\":\"Fin.mk_one\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[188,17],\"def_end_pos\":[188,23]},{\"full_name\":\"Matrix.cons_val_one\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/VecNotation.lean\",\"def_pos\":[209,9],\"def_end_pos\":[209,21]},{\"full_name\":\"Matrix.head_cons\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/VecNotation.lean\",\"def_pos\":[152,9],\"def_end_pos\":[152,18]},{\"full_name\":\"Complex.I_re\",\"def_path\":\"Mathlib\\/Data\\/Complex\\/Basic.lean\",\"def_pos\":[284,9],\"def_end_pos\":[284,13]},{\"full_name\":\"MulZeroClass.mul_zero\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Defs.lean\",\"def_pos\":[39,3],\"def_end_pos\":[39,11]},{\"full_name\":\"Complex.I_im\",\"def_path\":\"Mathlib\\/Data\\/Complex\\/Basic.lean\",\"def_pos\":[290,9],\"def_end_pos\":[290,13]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"zero_sub\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[467,3],\"def_end_pos\":[467,14]},{\"full_name\":\"add_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[482,3],\"def_end_pos\":[482,14]}]"
+              ],
+              "state_after": "case a.tail.head\nz : \u2102\ni : Fin 2\n\u22a2 ![-z.im, z.re] i = ![![z.re, -z.im], ![z.im, z.re]] i 1",
+              "state_before": "case a.tail.head\nz : \u2102\ni : Fin 2\n\u22a2 ![z.re * (![1, I] \u27e81, \u22ef\u27e9).re - z.im * (![1, I] \u27e81, \u22ef\u27e9).im, z.re * (![1, I] \u27e81, \u22ef\u27e9).im + z.im * (![1, I] \u27e81, \u22ef\u27e9).re]\n      i =\n    ![![z.re, -z.im], ![z.im, z.re]] i \u27e81, \u22ef\u27e9",
+              "tactic": "simp only [Fin.mk_one, Matrix.cons_val_one, Matrix.head_cons, I_re, mul_zero, I_im, mul_one,\n  zero_sub, add_zero]"
+            },
+            {
+              "annotated_tactic": [
+                "\"fin_cases i <;> rfl\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case a.tail.head\nz : \u2102\ni : Fin 2\n\u22a2 ![-z.im, z.re] i = ![![z.re, -z.im], ![z.im, z.re]] i 1",
+              "tactic": "fin_cases i <;> rfl"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Complex.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Algebra.norm_complex_eq",
+        "id": "Algebra.norm_complex_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            44,
+            43
+          ],
+          "file_path": "Mathlib/RingTheory/Complex.lean",
+          "full_name": "Algebra.norm_complex_eq",
+          "start": [
+            43,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Complex.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.add",
+        "id": "RingCon.add",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            107,
+            9
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.add",
+          "start": [
+            106,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.coe_add",
+        "id": "RingCon.coe_add",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            202,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.coe_add",
+          "start": [
+            201,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.coe_bot",
+        "id": "RingCon.coe_bot",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            518,
+            47
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.coe_bot",
+          "start": [
+            518,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.coe_inf",
+        "id": "RingCon.coe_inf",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            523,
+            62
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.coe_inf",
+          "start": [
+            523,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.coe_intCast",
+        "id": "RingCon.coe_intCast",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            334,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.coe_intCast",
+          "start": [
+            333,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.coe_mul",
+        "id": "RingCon.coe_mul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            209,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.coe_mul",
+          "start": [
+            208,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.coe_natCast",
+        "id": "RingCon.coe_natCast",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            317,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.coe_natCast",
+          "start": [
+            316,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.coe_neg",
+        "id": "RingCon.coe_neg",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            261,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.coe_neg",
+          "start": [
+            260,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.coe_nsmul",
+        "id": "RingCon.coe_nsmul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            290,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.coe_nsmul",
+          "start": [
+            289,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.coe_one",
+        "id": "RingCon.coe_one",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            235,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.coe_one",
+          "start": [
+            234,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.coe_pow",
+        "id": "RingCon.coe_pow",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            303,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.coe_pow",
+          "start": [
+            302,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.coe_smul",
+        "id": "RingCon.coe_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            248,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.coe_smul",
+          "start": [
+            247,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.coe_sub",
+        "id": "RingCon.coe_sub",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            268,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.coe_sub",
+          "start": [
+            267,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.coe_top",
+        "id": "RingCon.coe_top",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            515,
+            46
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.coe_top",
+          "start": [
+            515,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.coe_zero",
+        "id": "RingCon.coe_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            222,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.coe_zero",
+          "start": [
+            221,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.coe_zsmul",
+        "id": "RingCon.coe_zsmul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            276,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.coe_zsmul",
+          "start": [
+            275,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.eq",
+        "id": "RingCon.eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            181,
+            16
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.eq",
+          "start": [
+            180,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.ext'",
+        "id": "RingCon.ext'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            134,
+            81
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.ext'",
+          "start": [
+            134,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.inf_iff_and",
+        "id": "RingCon.inf_iff_and",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            527,
+            10
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.inf_iff_and",
+          "start": [
+            526,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.le_def",
+        "id": "RingCon.le_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            456,
+            10
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.le_def",
+          "start": [
+            455,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.mul",
+        "id": "RingCon.mul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            111,
+            9
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.mul",
+          "start": [
+            110,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.neg",
+        "id": "RingCon.neg",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            118,
+            56
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.neg",
+          "start": [
+            117,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.nsmul",
+        "id": "RingCon.nsmul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            121,
+            80
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.nsmul",
+          "start": [
+            120,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.quot_mk_eq_coe",
+        "id": "RingCon.quot_mk_eq_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            174,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.quot_mk_eq_coe",
+          "start": [
+            173,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.refl",
+        "id": "RingCon.refl",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            95,
+            12
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.refl",
+          "start": [
+            94,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.rel_eq_coe",
+        "id": "RingCon.rel_eq_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            87,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.rel_eq_coe",
+          "start": [
+            86,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.rel_mk",
+        "id": "RingCon.rel_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            131,
+            10
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.rel_mk",
+          "start": [
+            130,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.ringConGen_eq",
+        "id": "RingCon.ringConGen_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            544,
+            47
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.ringConGen_eq",
+          "start": [
+            536,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.ringConGen_idem",
+        "id": "RingCon.ringConGen_idem",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            565,
+            26
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.ringConGen_idem",
+          "start": [
+            564,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.ringConGen_mono",
+        "id": "RingCon.ringConGen_mono",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            556,
+            64
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.ringConGen_mono",
+          "start": [
+            554,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.sub",
+        "id": "RingCon.sub",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            115,
+            86
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.sub",
+          "start": [
+            114,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.symm",
+        "id": "RingCon.symm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            99,
+            10
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.symm",
+          "start": [
+            98,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.toCon_coe_eq_coe",
+        "id": "RingCon.toCon_coe_eq_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            92,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.toCon_coe_eq_coe",
+          "start": [
+            91,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.trans",
+        "id": "RingCon.trans",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            103,
+            11
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.trans",
+          "start": [
+            102,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.zsmul",
+        "id": "RingCon.zsmul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            124,
+            80
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Basic.lean",
+          "full_name": "RingCon.zsmul",
+          "start": [
+            123,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Basic.lean"
+      }
+    ],
+    "input_proofs": 48,
+    "input_units": 2,
+    "proofs": 11,
+    "published_proofs": 11,
+    "published_transitions": 26,
+    "replay_failures": [],
+    "transitions": 26,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001653-0000-e184d5bb98024187.parquet",
+      "sha256": "e184d5bb9802418722aa59ff617b15ed0827c675e9ce019cbdb5ca1272dc165e",
+      "bytes": 80193,
+      "rows": 26,
+      "revision": "df8c9c479578582ca5384c5c62608ea4677707ca"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Algebra.norm_complex_apply",
+    "mathlib:Algebra.trace_complex_apply",
+    "mathlib:RingCon.coe_iInf",
+    "mathlib:RingCon.coe_sInf",
+    "mathlib:RingCon.ringConGen_le",
+    "mathlib:RingCon.ringConGen_of_ringCon",
+    "mathlib:RingCon.sInf_toSetoid",
+    "mathlib:RingCon.sSup_def",
+    "mathlib:RingCon.sSup_eq_ringConGen",
+    "mathlib:RingCon.sup_def",
+    "mathlib:RingCon.sup_eq_ringConGen"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Complex.lean\",null,null,\"Algebra.norm_complex_apply\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Complex.lean\",null,null,\"Algebra.trace_complex_apply\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Congruence/Basic.lean\",null,null,\"RingCon.coe_iInf\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Congruence/Basic.lean\",null,null,\"RingCon.coe_sInf\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Congruence/Basic.lean\",null,null,\"RingCon.ringConGen_le\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Congruence/Basic.lean\",null,null,\"RingCon.ringConGen_of_ringCon\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Congruence/Basic.lean\",null,null,\"RingCon.sInf_toSetoid\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Congruence/Basic.lean\",null,null,\"RingCon.sSup_def\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Congruence/Basic.lean\",null,null,\"RingCon.sSup_eq_ringConGen\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Congruence/Basic.lean\",null,null,\"RingCon.sup_def\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Congruence/Basic.lean\",null,null,\"RingCon.sup_eq_ringConGen\"]"
+  ]
+}

manifests/batches/mathlib/001654.json

@@ -0,0 +1,135 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001654",
+  "batch_fingerprint": "bc21851655bc2d90121ffa19c40705daaf95ecffdf357acb41e631e036fc543c",
+  "evidence": {
+    "batch_fingerprint": "bc21851655bc2d90121ffa19c40705daaf95ecffdf357acb41e631e036fc543c",
+    "batch_outcome": "all_inputs_failed_with_evidence",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.finsetSum",
+        "id": "RingCon.finsetSum",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            34,
+            28
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/BigOperators.lean",
+          "full_name": "RingCon.finsetSum",
+          "start": [
+            30,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/BigOperators.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.listSum",
+        "id": "RingCon.listSum",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            22,
+            24
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/BigOperators.lean",
+          "full_name": "RingCon.listSum",
+          "start": [
+            18,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/BigOperators.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.multisetSum",
+        "id": "RingCon.multisetSum",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            28,
+            28
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/BigOperators.lean",
+          "full_name": "RingCon.multisetSum",
+          "start": [
+            24,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/BigOperators.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.op_iff",
+        "id": "RingCon.op_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            30,
+            82
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Opposite.lean",
+          "full_name": "RingCon.op_iff",
+          "start": [
+            30,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Opposite.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "RingCon.unop_iff",
+        "id": "RingCon.unop_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            40,
+            88
+          ],
+          "file_path": "Mathlib/RingTheory/Congruence/Opposite.lean",
+          "full_name": "RingCon.unop_iff",
+          "start": [
+            40,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Congruence/Opposite.lean"
+      }
+    ],
+    "input_proofs": 5,
+    "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/001662.json

@@ -0,0 +1,1187 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001662",
+  "batch_fingerprint": "fc0bef2c39bbc4e8c62556e0831f4bd0d9b1041c146fe80997081aeef2e3c746",
+  "evidence": {
+    "batch_fingerprint": "fc0bef2c39bbc4e8c62556e0831f4bd0d9b1041c146fe80997081aeef2e3c746",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.add_apply",
+        "id": "Derivation.add_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            226,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.add_apply",
+          "start": [
+            225,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.coeFn_coe",
+        "id": "Derivation.coeFn_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            99,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.coeFn_coe",
+          "start": [
+            98,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.coe_add",
+        "id": "Derivation.coe_add",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            217,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.coe_add",
+          "start": [
+            216,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.coe_add_linearMap",
+        "id": "Derivation.coe_add_linearMap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            222,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.coe_add_linearMap",
+          "start": [
+            221,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.coe_comp",
+        "id": "Derivation.coe_comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            315,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.coe_comp",
+          "start": [
+            314,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.coe_injective",
+        "id": "Derivation.coe_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            103,
+            25
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.coe_injective",
+          "start": [
+            102,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.coe_mk'",
+        "id": "Derivation.coe_mk'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            380,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.coe_mk'",
+          "start": [
+            379,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.coe_mk'_linearMap",
+        "id": "Derivation.coe_mk'_linearMap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            385,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.coe_mk'_linearMap",
+          "start": [
+            384,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.coe_neg",
+        "id": "Derivation.coe_neg",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            444,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.coe_neg",
+          "start": [
+            443,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.coe_neg_linearMap",
+        "id": "Derivation.coe_neg_linearMap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            449,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.coe_neg_linearMap",
+          "start": [
+            448,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.coe_smul",
+        "id": "Derivation.coe_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            247,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.coe_smul",
+          "start": [
+            246,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.coe_smul_linearMap",
+        "id": "Derivation.coe_smul_linearMap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            252,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.coe_smul_linearMap",
+          "start": [
+            251,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.coe_sub",
+        "id": "Derivation.coe_sub",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            463,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.coe_sub",
+          "start": [
+            462,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.coe_sub_linearMap",
+        "id": "Derivation.coe_sub_linearMap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            468,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.coe_sub_linearMap",
+          "start": [
+            467,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.coe_to_linearMap_comp",
+        "id": "Derivation.coe_to_linearMap_comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            310,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.coe_to_linearMap_comp",
+          "start": [
+            309,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.coe_zero",
+        "id": "Derivation.coe_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            196,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.coe_zero",
+          "start": [
+            195,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.coe_zero_linearMap",
+        "id": "Derivation.coe_zero_linearMap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            201,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.coe_zero_linearMap",
+          "start": [
+            200,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.congr_fun",
+        "id": "Derivation.congr_fun",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            112,
+            25
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.congr_fun",
+          "start": [
+            111,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.ext",
+        "id": "Derivation.ext",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            108,
+            21
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.ext",
+          "start": [
+            107,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.ext_of_adjoin_eq_top",
+        "id": "Derivation.ext_of_adjoin_eq_top",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            185,
+            50
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.ext_of_adjoin_eq_top",
+          "start": [
+            184,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.leibniz",
+        "id": "Derivation.leibniz",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            130,
+            17
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.leibniz",
+          "start": [
+            129,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.leibniz_invOf",
+        "id": "Derivation.leibniz_invOf",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            427,
+            46
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.leibniz_invOf",
+          "start": [
+            426,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'simp only [smul_smul, h, one_smul, sq]'",
+        "full_name": "Derivation.leibniz_of_mul_eq_one",
+        "id": "Derivation.leibniz_of_mul_eq_one",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            422,
+            51
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.leibniz_of_mul_eq_one",
+          "start": [
+            416,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [<a>neg_smul<\\/a>]\"",
+                "[{\"full_name\":\"neg_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Defs.lean\",\"def_pos\":[253,9],\"def_end_pos\":[253,17]}]"
+              ],
+              "state_after": "R : Type u_1\ninst\u271d\u2075 : CommRing R\nA : Type u_2\ninst\u271d\u2074 : CommRing A\ninst\u271d\u00b3 : Algebra R A\nM : Type u_3\ninst\u271d\u00b2 : AddCommGroup M\ninst\u271d\u00b9 : Module A M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na\u271d b\u271d a b : A\nh : a * b = 1\n\u22a2 D a = -(a ^ 2 \u2022 D b)",
+              "state_before": "R : Type u_1\ninst\u271d\u2075 : CommRing R\nA : Type u_2\ninst\u271d\u2074 : CommRing A\ninst\u271d\u00b3 : Algebra R A\nM : Type u_3\ninst\u271d\u00b2 : AddCommGroup M\ninst\u271d\u00b9 : Module A M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na\u271d b\u271d a b : A\nh : a * b = 1\n\u22a2 D a = -a ^ 2 \u2022 D b",
+              "tactic": "rw [neg_smul]"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine <a>eq_neg_of_add_eq_zero_left<\\/a> ?_\"",
+                "[{\"full_name\":\"eq_neg_of_add_eq_zero_left\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1170,3],\"def_end_pos\":[1170,14]}]"
+              ],
+              "state_after": "R : Type u_1\ninst\u271d\u2075 : CommRing R\nA : Type u_2\ninst\u271d\u2074 : CommRing A\ninst\u271d\u00b3 : Algebra R A\nM : Type u_3\ninst\u271d\u00b2 : AddCommGroup M\ninst\u271d\u00b9 : Module A M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na\u271d b\u271d a b : A\nh : a * b = 1\n\u22a2 D a + a ^ 2 \u2022 D b = 0",
+              "state_before": "R : Type u_1\ninst\u271d\u2075 : CommRing R\nA : Type u_2\ninst\u271d\u2074 : CommRing A\ninst\u271d\u00b3 : Algebra R A\nM : Type u_3\ninst\u271d\u00b2 : AddCommGroup M\ninst\u271d\u00b9 : Module A M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na\u271d b\u271d a b : A\nh : a * b = 1\n\u22a2 D a = -(a ^ 2 \u2022 D b)",
+              "tactic": "refine eq_neg_of_add_eq_zero_left ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"calc\\n    D a + a ^ 2 \\u2022 D b = a \\u2022 b \\u2022 D a + a \\u2022 a \\u2022 D b := by simp only [<a>smul_smul<\\/a>, h, <a>one_smul<\\/a>, <a>sq<\\/a>]\\n    _ = a \\u2022 D (a * b) := by rw [<a>leibniz<\\/a>, <a>smul_add<\\/a>, <a>add_comm<\\/a>]\\n    _ = 0 := by rw [h, <a>map_one_eq_zero<\\/a>, <a>smul_zero<\\/a>]\"",
+                "[{\"full_name\":\"smul_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[446,7],\"def_end_pos\":[446,16]},{\"full_name\":\"one_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[453,7],\"def_end_pos\":[453,15]},{\"full_name\":\"sq\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[684,41],\"def_end_pos\":[684,43]},{\"full_name\":\"Derivation.leibniz\",\"def_path\":\"Mathlib\\/RingTheory\\/Derivation\\/Basic.lean\",\"def_pos\":[129,9],\"def_end_pos\":[129,16]},{\"full_name\":\"smul_add\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Defs.lean\",\"def_pos\":[145,9],\"def_end_pos\":[145,17]},{\"full_name\":\"add_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[331,3],\"def_end_pos\":[331,14]},{\"full_name\":\"Derivation.map_one_eq_zero\",\"def_path\":\"Mathlib\\/RingTheory\\/Derivation\\/Basic.lean\",\"def_pos\":[142,9],\"def_end_pos\":[142,24]},{\"full_name\":\"smul_zero\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Defs.lean\",\"def_pos\":[66,9],\"def_end_pos\":[66,18]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\ninst\u271d\u2075 : CommRing R\nA : Type u_2\ninst\u271d\u2074 : CommRing A\ninst\u271d\u00b3 : Algebra R A\nM : Type u_3\ninst\u271d\u00b2 : AddCommGroup M\ninst\u271d\u00b9 : Module A M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na\u271d b\u271d a b : A\nh : a * b = 1\n\u22a2 D a + a ^ 2 \u2022 D b = 0",
+              "tactic": "calc\n  D a + a ^ 2 \u2022 D b = a \u2022 b \u2022 D a + a \u2022 a \u2022 D b := by simp only [smul_smul, h, one_smul, sq]\n  _ = a \u2022 D (a * b) := by rw [leibniz, smul_add, add_comm]\n  _ = 0 := by rw [h, map_one_eq_zero, smul_zero]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>smul_smul<\\/a>, h, <a>one_smul<\\/a>, <a>sq<\\/a>]\"",
+                "[{\"full_name\":\"smul_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[446,7],\"def_end_pos\":[446,16]},{\"full_name\":\"one_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[453,7],\"def_end_pos\":[453,15]},{\"full_name\":\"sq\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[684,41],\"def_end_pos\":[684,43]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\ninst\u271d\u2075 : CommRing R\nA : Type u_2\ninst\u271d\u2074 : CommRing A\ninst\u271d\u00b3 : Algebra R A\nM : Type u_3\ninst\u271d\u00b2 : AddCommGroup M\ninst\u271d\u00b9 : Module A M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na\u271d b\u271d a b : A\nh : a * b = 1\n\u22a2 D a + a ^ 2 \u2022 D b = a \u2022 b \u2022 D a + a \u2022 a \u2022 D b",
+              "tactic": "simp only [smul_smul, h, one_smul, sq]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>leibniz<\\/a>, <a>smul_add<\\/a>, <a>add_comm<\\/a>]\"",
+                "[{\"full_name\":\"Derivation.leibniz\",\"def_path\":\"Mathlib\\/RingTheory\\/Derivation\\/Basic.lean\",\"def_pos\":[129,9],\"def_end_pos\":[129,16]},{\"full_name\":\"smul_add\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Defs.lean\",\"def_pos\":[145,9],\"def_end_pos\":[145,17]},{\"full_name\":\"add_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[331,3],\"def_end_pos\":[331,14]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\ninst\u271d\u2075 : CommRing R\nA : Type u_2\ninst\u271d\u2074 : CommRing A\ninst\u271d\u00b3 : Algebra R A\nM : Type u_3\ninst\u271d\u00b2 : AddCommGroup M\ninst\u271d\u00b9 : Module A M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na\u271d b\u271d a b : A\nh : a * b = 1\n\u22a2 a \u2022 b \u2022 D a + a \u2022 a \u2022 D b = a \u2022 D (a * b)",
+              "tactic": "rw [leibniz, smul_add, add_comm]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [h, <a>map_one_eq_zero<\\/a>, <a>smul_zero<\\/a>]\"",
+                "[{\"full_name\":\"Derivation.map_one_eq_zero\",\"def_path\":\"Mathlib\\/RingTheory\\/Derivation\\/Basic.lean\",\"def_pos\":[142,9],\"def_end_pos\":[142,24]},{\"full_name\":\"smul_zero\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Defs.lean\",\"def_pos\":[66,9],\"def_end_pos\":[66,18]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\ninst\u271d\u2075 : CommRing R\nA : Type u_2\ninst\u271d\u2074 : CommRing A\ninst\u271d\u00b3 : Algebra R A\nM : Type u_3\ninst\u271d\u00b2 : AddCommGroup M\ninst\u271d\u00b9 : Module A M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na\u271d b\u271d a b : A\nh : a * b = 1\n\u22a2 a \u2022 D (a * b) = 0",
+              "tactic": "rw [h, map_one_eq_zero, smul_zero]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "no internal trace for tactic \"rw [\u2190 pow_succ', Nat.sub_add_cancel hpos]\"",
+        "full_name": "Derivation.leibniz_pow",
+        "id": "Derivation.leibniz_pow",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            165,
+            72
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.leibniz_pow",
+          "start": [
+            158,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"induction' n with n ihn\"",
+                "[]"
+              ],
+              "state_after": "case zero\nR : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\n\u22a2 D (a ^ 0) = 0 \u2022 a ^ (0 - 1) \u2022 D a\n\ncase succ\nR : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\nn : \u2115\nihn : D (a ^ n) = n \u2022 a ^ (n - 1) \u2022 D a\n\u22a2 D (a ^ (n + 1)) = (n + 1) \u2022 a ^ (n + 1 - 1) \u2022 D a",
+              "state_before": "R : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\nn : \u2115\n\u22a2 D (a ^ n) = n \u2022 a ^ (n - 1) \u2022 D a",
+              "tactic": "induction' n with n ihn"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>pow_zero<\\/a>, <a>map_one_eq_zero<\\/a>, <a>zero_smul<\\/a>]\"",
+                "[{\"full_name\":\"pow_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[651,9],\"def_end_pos\":[651,17]},{\"full_name\":\"Derivation.map_one_eq_zero\",\"def_path\":\"Mathlib\\/RingTheory\\/Derivation\\/Basic.lean\",\"def_pos\":[142,9],\"def_end_pos\":[142,24]},{\"full_name\":\"zero_smul\",\"def_path\":\"Mathlib\\/Algebra\\/SMulWithZero.lean\",\"def_pos\":[70,9],\"def_end_pos\":[70,18]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case zero\nR : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\n\u22a2 D (a ^ 0) = 0 \u2022 a ^ (0 - 1) \u2022 D a",
+              "tactic": "rw [pow_zero, map_one_eq_zero, zero_smul]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rcases (<a>zero_le<\\/a> n).<a>eq_or_lt<\\/a> with (rfl | hpos)\"",
+                "[{\"full_name\":\"zero_le\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Canonical\\/Defs.lean\",\"def_pos\":[204,30],\"def_end_pos\":[204,37]},{\"full_name\":\"LE.le.eq_or_lt\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[395,7],\"def_end_pos\":[395,21]}]"
+              ],
+              "state_after": "case succ.inl\nR : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\nihn : D (a ^ 0) = 0 \u2022 a ^ (0 - 1) \u2022 D a\n\u22a2 D (a ^ (0 + 1)) = (0 + 1) \u2022 a ^ (0 + 1 - 1) \u2022 D a\n\ncase succ.inr\nR : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\nn : \u2115\nihn : D (a ^ n) = n \u2022 a ^ (n - 1) \u2022 D a\nhpos : 0 < n\n\u22a2 D (a ^ (n + 1)) = (n + 1) \u2022 a ^ (n + 1 - 1) \u2022 D a",
+              "state_before": "case succ\nR : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\nn : \u2115\nihn : D (a ^ n) = n \u2022 a ^ (n - 1) \u2022 D a\n\u22a2 D (a ^ (n + 1)) = (n + 1) \u2022 a ^ (n + 1 - 1) \u2022 D a",
+              "tactic": "rcases (zero_le n).eq_or_lt with (rfl | hpos)"
+            },
+            {
+              "annotated_tactic": [
+                "\"erw [<a>pow_one<\\/a>, <a>one_smul<\\/a>, <a>pow_zero<\\/a>, <a>one_smul<\\/a>]\"",
+                "[{\"full_name\":\"pow_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[663,7],\"def_end_pos\":[663,14]},{\"full_name\":\"one_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[453,7],\"def_end_pos\":[453,15]},{\"full_name\":\"pow_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[651,9],\"def_end_pos\":[651,17]},{\"full_name\":\"one_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[453,7],\"def_end_pos\":[453,15]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case succ.inl\nR : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\nihn : D (a ^ 0) = 0 \u2022 a ^ (0 - 1) \u2022 D a\n\u22a2 D (a ^ (0 + 1)) = (0 + 1) \u2022 a ^ (0 + 1 - 1) \u2022 D a",
+              "tactic": "erw [pow_one, one_smul, pow_zero, one_smul]"
+            },
+            {
+              "annotated_tactic": [
+                "\"have : a * a ^ (n - 1) = a ^ n := by rw [\\u2190 <a>pow_succ'<\\/a>, <a>Nat.sub_add_cancel<\\/a> hpos]\"",
+                "[{\"full_name\":\"pow_succ'\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[667,34],\"def_end_pos\":[667,43]},{\"full_name\":\"Nat.sub_add_cancel\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[893,27],\"def_end_pos\":[893,41]}]"
+              ],
+              "state_after": "case succ.inr\nR : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\nn : \u2115\nihn : D (a ^ n) = n \u2022 a ^ (n - 1) \u2022 D a\nhpos : 0 < n\nthis : a * a ^ (n - 1) = a ^ n\n\u22a2 D (a ^ (n + 1)) = (n + 1) \u2022 a ^ (n + 1 - 1) \u2022 D a",
+              "state_before": "case succ.inr\nR : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\nn : \u2115\nihn : D (a ^ n) = n \u2022 a ^ (n - 1) \u2022 D a\nhpos : 0 < n\n\u22a2 D (a ^ (n + 1)) = (n + 1) \u2022 a ^ (n + 1 - 1) \u2022 D a",
+              "tactic": "have : a * a ^ (n - 1) = a ^ n := by rw [\u2190 pow_succ', Nat.sub_add_cancel hpos]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>pow_succ'<\\/a>, <a>leibniz<\\/a>, ihn, <a>smul_comm<\\/a> a n (_ : M), <a>smul_smul<\\/a> a, <a>add_smul<\\/a>, this,\\n        <a>Nat.succ_eq_add_one<\\/a>, <a>Nat.add_succ_sub_one<\\/a>, <a>add_zero<\\/a>, <a>one_nsmul<\\/a>]\"",
+                "[{\"full_name\":\"pow_succ'\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[667,34],\"def_end_pos\":[667,43]},{\"full_name\":\"Derivation.leibniz\",\"def_path\":\"Mathlib\\/RingTheory\\/Derivation\\/Basic.lean\",\"def_pos\":[129,9],\"def_end_pos\":[129,16]},{\"full_name\":\"SMulCommClass.smul_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[183,3],\"def_end_pos\":[183,12]},{\"full_name\":\"smul_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[446,7],\"def_end_pos\":[446,16]},{\"full_name\":\"add_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Defs.lean\",\"def_pos\":[93,9],\"def_end_pos\":[93,17]},{\"full_name\":\"Nat.succ_eq_add_one\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[154,17],\"def_end_pos\":[154,32]},{\"full_name\":\"Nat.add_succ_sub_one\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Defs.lean\",\"def_pos\":[240,15],\"def_end_pos\":[240,31]},{\"full_name\":\"add_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[482,3],\"def_end_pos\":[482,14]},{\"full_name\":\"one_nsmul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[662,30],\"def_end_pos\":[662,39]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case succ.inr\nR : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\nn : \u2115\nihn : D (a ^ n) = n \u2022 a ^ (n - 1) \u2022 D a\nhpos : 0 < n\nthis : a * a ^ (n - 1) = a ^ n\n\u22a2 D (a ^ (n + 1)) = (n + 1) \u2022 a ^ (n + 1 - 1) \u2022 D a",
+              "tactic": "simp only [pow_succ', leibniz, ihn, smul_comm a n (_ : M), smul_smul a, add_smul, this,\n  Nat.succ_eq_add_one, Nat.add_succ_sub_one, add_zero, one_nsmul]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>pow_succ'<\\/a>, <a>Nat.sub_add_cancel<\\/a> hpos]\"",
+                "[{\"full_name\":\"pow_succ'\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[667,34],\"def_end_pos\":[667,43]},{\"full_name\":\"Nat.sub_add_cancel\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[893,27],\"def_end_pos\":[893,41]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\nn : \u2115\nihn : D (a ^ n) = n \u2022 a ^ (n - 1) \u2022 D a\nhpos : 0 < n\n\u22a2 a * a ^ (n - 1) = a ^ n",
+              "tactic": "rw [\u2190 pow_succ', Nat.sub_add_cancel hpos]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.map_add",
+        "id": "Derivation.map_add",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            116,
+            16
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.map_add",
+          "start": [
+            115,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.map_neg",
+        "id": "Derivation.map_neg",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            401,
+            14
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.map_neg",
+          "start": [
+            400,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.map_one_eq_zero",
+        "id": "Derivation.map_one_eq_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            143,
+            21
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.map_one_eq_zero",
+          "start": [
+            142,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.map_smul",
+        "id": "Derivation.map_smul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            125,
+            29
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.map_smul",
+          "start": [
+            124,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.map_smul_of_tower",
+        "id": "Derivation.map_smul_of_tower",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            138,
+            38
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.map_smul_of_tower",
+          "start": [
+            136,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.map_sub",
+        "id": "Derivation.map_sub",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            405,
+            16
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.map_sub",
+          "start": [
+            404,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.map_zero",
+        "id": "Derivation.map_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            120,
+            13
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.map_zero",
+          "start": [
+            119,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.mk_coe",
+        "id": "Derivation.mk_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            94,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.mk_coe",
+          "start": [
+            93,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.neg_apply",
+        "id": "Derivation.neg_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            453,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.neg_apply",
+          "start": [
+            452,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.smul_apply",
+        "id": "Derivation.smul_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            256,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.smul_apply",
+          "start": [
+            255,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.sub_apply",
+        "id": "Derivation.sub_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            472,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.sub_apply",
+          "start": [
+            471,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.toFun_eq_coe",
+        "id": "Derivation.toFun_eq_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            76,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.toFun_eq_coe",
+          "start": [
+            75,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.zero_apply",
+        "id": "Derivation.zero_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            205,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+          "full_name": "Derivation.zero_apply",
+          "start": [
+            204,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.commutator_apply",
+        "id": "Derivation.commutator_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            44,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Lie.lean",
+          "full_name": "Derivation.commutator_apply",
+          "start": [
+            43,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Lie.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Derivation.commutator_coe_linear_map",
+        "id": "Derivation.commutator_coe_linear_map",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            40,
+            6
+          ],
+          "file_path": "Mathlib/RingTheory/Derivation/Lie.lean",
+          "full_name": "Derivation.commutator_coe_linear_map",
+          "start": [
+            39,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Derivation/Lie.lean"
+      }
+    ],
+    "input_proofs": 45,
+    "input_units": 2,
+    "proofs": 6,
+    "published_proofs": 3,
+    "published_transitions": 3,
+    "replay_failures": [],
+    "transitions": 12,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+        "proof_id": "mathlib:Derivation.eqOn_adjoin",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              179,
+              92
+            ],
+            "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+            "full_name": "Derivation.eqOn_adjoin",
+            "start": [
+              177,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"simp only [<a>map_add<\\/a>, *]\"",
+                  "[{\"full_name\":\"map_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[308,3],\"def_end_pos\":[308,14]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "R : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\ns : Set A\nh : Set.EqOn (\u21d1D1) (\u21d1D2) s\nx\u271d : A\nhx\u271d : x\u271d \u2208 \u2191(adjoin R s)\nx y : A\nhx : D1 x = D2 x\nhy : D1 y = D2 y\n\u22a2 D1 (x + y) = D2 (x + y)",
+                "tactic": "simp only [map_add, *]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp only [<a>leibniz<\\/a>, *]\"",
+                  "[{\"full_name\":\"Derivation.leibniz\",\"def_path\":\"Mathlib\\/RingTheory\\/Derivation\\/Basic.lean\",\"def_pos\":[129,9],\"def_end_pos\":[129,16]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "R : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\ns : Set A\nh : Set.EqOn (\u21d1D1) (\u21d1D2) s\nx\u271d : A\nhx\u271d : x\u271d \u2208 \u2191(adjoin R s)\nx y : A\nhx : D1 x = D2 x\nhy : D1 y = D2 y\n\u22a2 D1 (x * y) = D2 (x * y)",
+                "tactic": "simp only [leibniz, *]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Derivation.eqOn_adjoin"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+        "proof_id": "mathlib:Derivation.leibniz_inv",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              434,
+              54
+            ],
+            "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+            "full_name": "Derivation.leibniz_inv",
+            "start": [
+              430,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"rcases <a>eq_or_ne<\\/a> a 0 with (rfl | ha)\"",
+                  "[{\"full_name\":\"eq_or_ne\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[212,9],\"def_end_pos\":[212,17]}]"
+                ],
+                "state_after": "case inl\nR : Type u_1\ninst\u271d\u2078 : CommRing R\nA : Type u_2\ninst\u271d\u2077 : CommRing A\ninst\u271d\u2076 : Algebra R A\nM : Type u_3\ninst\u271d\u2075 : AddCommGroup M\ninst\u271d\u2074 : Module A M\ninst\u271d\u00b3 : Module R M\nD\u271d D1 D2 : Derivation R A M\nr : R\na b : A\nK : Type u_4\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Module K M\ninst\u271d : Algebra R K\nD : Derivation R K M\n\u22a2 D 0\u207b\u00b9 = -0\u207b\u00b9 ^ 2 \u2022 D 0\n\ncase inr\nR : Type u_1\ninst\u271d\u2078 : CommRing R\nA : Type u_2\ninst\u271d\u2077 : CommRing A\ninst\u271d\u2076 : Algebra R A\nM : Type u_3\ninst\u271d\u2075 : AddCommGroup M\ninst\u271d\u2074 : Module A M\ninst\u271d\u00b3 : Module R M\nD\u271d D1 D2 : Derivation R A M\nr : R\na\u271d b : A\nK : Type u_4\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Module K M\ninst\u271d : Algebra R K\nD : Derivation R K M\na : K\nha : a \u2260 0\n\u22a2 D a\u207b\u00b9 = -a\u207b\u00b9 ^ 2 \u2022 D a",
+                "state_before": "R : Type u_1\ninst\u271d\u2078 : CommRing R\nA : Type u_2\ninst\u271d\u2077 : CommRing A\ninst\u271d\u2076 : Algebra R A\nM : Type u_3\ninst\u271d\u2075 : AddCommGroup M\ninst\u271d\u2074 : Module A M\ninst\u271d\u00b3 : Module R M\nD\u271d D1 D2 : Derivation R A M\nr : R\na\u271d b : A\nK : Type u_4\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Module K M\ninst\u271d : Algebra R K\nD : Derivation R K M\na : K\n\u22a2 D a\u207b\u00b9 = -a\u207b\u00b9 ^ 2 \u2022 D a",
+                "tactic": "rcases eq_or_ne a 0 with (rfl | ha)"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case inl\nR : Type u_1\ninst\u271d\u2078 : CommRing R\nA : Type u_2\ninst\u271d\u2077 : CommRing A\ninst\u271d\u2076 : Algebra R A\nM : Type u_3\ninst\u271d\u2075 : AddCommGroup M\ninst\u271d\u2074 : Module A M\ninst\u271d\u00b3 : Module R M\nD\u271d D1 D2 : Derivation R A M\nr : R\na b : A\nK : Type u_4\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Module K M\ninst\u271d : Algebra R K\nD : Derivation R K M\n\u22a2 D 0\u207b\u00b9 = -0\u207b\u00b9 ^ 2 \u2022 D 0",
+                "tactic": "simp"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact D.leibniz_of_mul_eq_one (<a>inv_mul_cancel<\\/a> ha)\"",
+                  "[{\"full_name\":\"inv_mul_cancel\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/NeZero.lean\",\"def_pos\":[55,9],\"def_end_pos\":[55,23]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case inr\nR : Type u_1\ninst\u271d\u2078 : CommRing R\nA : Type u_2\ninst\u271d\u2077 : CommRing A\ninst\u271d\u2076 : Algebra R A\nM : Type u_3\ninst\u271d\u2075 : AddCommGroup M\ninst\u271d\u2074 : Module A M\ninst\u271d\u00b3 : Module R M\nD\u271d D1 D2 : Derivation R A M\nr : R\na\u271d b : A\nK : Type u_4\ninst\u271d\u00b2 : Field K\ninst\u271d\u00b9 : Module K M\ninst\u271d : Algebra R K\nD : Derivation R K M\na : K\nha : a \u2260 0\n\u22a2 D a\u207b\u00b9 = -a\u207b\u00b9 ^ 2 \u2022 D a",
+                "tactic": "exact D.leibniz_of_mul_eq_one (inv_mul_cancel ha)"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Derivation.leibniz_inv"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+        "proof_id": "mathlib:Derivation.map_aeval",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              175,
+              42
+            ],
+            "file_path": "Mathlib/RingTheory/Derivation/Basic.lean",
+            "full_name": "Derivation.map_aeval",
+            "start": [
+              170,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"induction P using <a>Polynomial.induction_on<\\/a>\"",
+                  "[{\"full_name\":\"Polynomial.induction_on\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Induction.lean\",\"def_pos\":[39,19],\"def_end_pos\":[39,31]}]"
+                ],
+                "state_after": "case h_C\nR : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b x : A\na\u271d : R\n\u22a2 D ((aeval x) (C a\u271d)) = (aeval x) (derivative (C a\u271d)) \u2022 D x\n\ncase h_add\nR : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b x : A\np\u271d q\u271d : R[X]\na\u271d\u00b9 : D ((aeval x) p\u271d) = (aeval x) (derivative p\u271d) \u2022 D x\na\u271d : D ((aeval x) q\u271d) = (aeval x) (derivative q\u271d) \u2022 D x\n\u22a2 D ((aeval x) (p\u271d + q\u271d)) = (aeval x) (derivative (p\u271d + q\u271d)) \u2022 D x\n\ncase h_monomial\nR : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b x : A\nn\u271d : \u2115\na\u271d\u00b9 : R\na\u271d : D ((aeval x) (C a\u271d\u00b9 * X ^ n\u271d)) = (aeval x) (derivative (C a\u271d\u00b9 * X ^ n\u271d)) \u2022 D x\n\u22a2 D ((aeval x) (C a\u271d\u00b9 * X ^ (n\u271d + 1))) = (aeval x) (derivative (C a\u271d\u00b9 * X ^ (n\u271d + 1))) \u2022 D x",
+                "state_before": "R : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\nP : R[X]\nx : A\n\u22a2 D ((aeval x) P) = (aeval x) (derivative P) \u2022 D x",
+                "tactic": "induction P using Polynomial.induction_on"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case h_C\nR : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b x : A\na\u271d : R\n\u22a2 D ((aeval x) (C a\u271d)) = (aeval x) (derivative (C a\u271d)) \u2022 D x",
+                "tactic": "simp"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp [<a>add_smul<\\/a>, *]\"",
+                  "[{\"full_name\":\"add_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Defs.lean\",\"def_pos\":[93,9],\"def_end_pos\":[93,17]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case h_add\nR : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b x : A\np\u271d q\u271d : R[X]\na\u271d\u00b9 : D ((aeval x) p\u271d) = (aeval x) (derivative p\u271d) \u2022 D x\na\u271d : D ((aeval x) q\u271d) = (aeval x) (derivative q\u271d) \u2022 D x\n\u22a2 D ((aeval x) (p\u271d + q\u271d)) = (aeval x) (derivative (p\u271d + q\u271d)) \u2022 D x",
+                "tactic": "simp [add_smul, *]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp [<a>mul_smul<\\/a>, <a>nsmul_eq_smul_cast<\\/a> A]\"",
+                  "[{\"full_name\":\"MulAction.mul_smul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Action\\/Defs.lean\",\"def_pos\":[114,3],\"def_end_pos\":[114,11]},{\"full_name\":\"nsmul_eq_smul_cast\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Defs.lean\",\"def_pos\":[365,9],\"def_end_pos\":[365,27]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case h_monomial\nR : Type u_1\nA : Type u_2\nB : Type u_3\nM : Type u_4\ninst\u271d\u2078 : CommSemiring R\ninst\u271d\u2077 : CommSemiring A\ninst\u271d\u2076 : CommSemiring B\ninst\u271d\u2075 : AddCommMonoid M\ninst\u271d\u2074 : Algebra R A\ninst\u271d\u00b3 : Algebra R B\ninst\u271d\u00b2 : Module A M\ninst\u271d\u00b9 : Module B M\ninst\u271d : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b x : A\nn\u271d : \u2115\na\u271d\u00b9 : R\na\u271d : D ((aeval x) (C a\u271d\u00b9 * X ^ n\u271d)) = (aeval x) (derivative (C a\u271d\u00b9 * X ^ n\u271d)) \u2022 D x\n\u22a2 D ((aeval x) (C a\u271d\u00b9 * X ^ (n\u271d + 1))) = (aeval x) (derivative (C a\u271d\u00b9 * X ^ (n\u271d + 1))) \u2022 D x",
+                "tactic": "simp [mul_smul, nsmul_eq_smul_cast A]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Derivation.map_aeval"
+      }
+    ],
+    "validation_rejected_proofs": 3,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001662-0000-7d3f1fd2c2e415b9.parquet",
+      "sha256": "7d3f1fd2c2e415b9c0322200502307a566e6bc2a1cec4a7bff870e5d18f20da0",
+      "bytes": 46711,
+      "rows": 2,
+      "revision": "df8c9c479578582ca5384c5c62608ea4677707ca"
+    },
+    {
+      "path": "data/internal_test/mathlib-001662-0000-644846d9dbb9a031.parquet",
+      "sha256": "644846d9dbb9a031aaf56aa2ef33ab75cf5c75833afe289f318372225c99914e",
+      "bytes": 49972,
+      "rows": 1,
+      "revision": "df8c9c479578582ca5384c5c62608ea4677707ca"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Derivation.map_algebraMap",
+    "mathlib:Derivation.map_intCast",
+    "mathlib:Derivation.map_natCast"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Derivation/Basic.lean\",null,null,\"Derivation.map_algebraMap\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Derivation/Basic.lean\",null,null,\"Derivation.map_intCast\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Derivation/Basic.lean\",null,null,\"Derivation.map_natCast\"]"
+  ]
+}

manifests/batches/mathlib/001665.json

@@ -0,0 +1,656 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001665",
+  "batch_fingerprint": "84d8efcd63fef1c78309f612afc5f4665e5f28b0358688aa7c83d8888432cee9",
+  "evidence": {
+    "batch_fingerprint": "84d8efcd63fef1c78309f612afc5f4665e5f28b0358688aa7c83d8888432cee9",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "no internal trace for tactic 'simp [hf0]'",
+        "full_name": "Polynomial.EisensteinCriterionAux.map_eq_C_mul_X_pow_of_forall_coeff_mem",
+        "id": "Polynomial.EisensteinCriterionAux.map_eq_C_mul_X_pow_of_forall_coeff_mem",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            48,
+            51
+          ],
+          "file_path": "Mathlib/RingTheory/EisensteinCriterion.lean",
+          "full_name": "Polynomial.EisensteinCriterionAux.map_eq_C_mul_X_pow_of_forall_coeff_mem",
+          "start": [
+            32,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"by_cases hf0 : f = 0\"",
+                "[]"
+              ],
+              "state_after": "case pos\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : f = 0\n\u22a2 (map (mk P) f).coeff n = (C ((mk P) f.leadingCoeff) * X ^ f.natDegree).coeff n\n\ncase neg\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : \u00acf = 0\n\u22a2 (map (mk P) f).coeff n = (C ((mk P) f.leadingCoeff) * X ^ f.natDegree).coeff n",
+              "state_before": "R : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\n\u22a2 (map (mk P) f).coeff n = (C ((mk P) f.leadingCoeff) * X ^ f.natDegree).coeff n",
+              "tactic": "by_cases hf0 : f = 0"
+            },
+            {
+              "annotated_tactic": [
+                "\"rcases <a>lt_trichotomy<\\/a> (n : <a>WithBot<\\/a> \\u2115) (<a>degree<\\/a> f) with (h | h | h)\"",
+                "[{\"full_name\":\"lt_trichotomy\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[313,9],\"def_end_pos\":[313,22]},{\"full_name\":\"WithBot\",\"def_path\":\"Mathlib\\/Order\\/WithBot.lean\",\"def_pos\":[29,5],\"def_end_pos\":[29,12]},{\"full_name\":\"Polynomial.degree\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[52,5],\"def_end_pos\":[52,11]}]"
+              ],
+              "state_after": "case neg.inl\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : \u00acf = 0\nh : \u2191n < f.degree\n\u22a2 (map (mk P) f).coeff n = (C ((mk P) f.leadingCoeff) * X ^ f.natDegree).coeff n\n\ncase neg.inr.inl\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : \u00acf = 0\nh : \u2191n = f.degree\n\u22a2 (map (mk P) f).coeff n = (C ((mk P) f.leadingCoeff) * X ^ f.natDegree).coeff n\n\ncase neg.inr.inr\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : \u00acf = 0\nh : f.degree < \u2191n\n\u22a2 (map (mk P) f).coeff n = (C ((mk P) f.leadingCoeff) * X ^ f.natDegree).coeff n",
+              "state_before": "case neg\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : \u00acf = 0\n\u22a2 (map (mk P) f).coeff n = (C ((mk P) f.leadingCoeff) * X ^ f.natDegree).coeff n",
+              "tactic": "rcases lt_trichotomy (n : WithBot \u2115) (degree f) with (h | h | h)"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [hf0]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case pos\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : f = 0\n\u22a2 (map (mk P) f).coeff n = (C ((mk P) f.leadingCoeff) * X ^ f.natDegree).coeff n",
+              "tactic": "simp [hf0]"
+            },
+            {
+              "annotated_tactic": [
+                "\"erw [<a>coeff_map<\\/a>, <a>eq_zero_iff_mem<\\/a>.2 (hfP n h), <a>coeff_C_mul<\\/a>, <a>coeff_X_pow<\\/a>, <a>if_neg<\\/a>,\\n        <a>mul_zero<\\/a>]\"",
+                "[{\"full_name\":\"Polynomial.coeff_map\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[803,9],\"def_end_pos\":[803,18]},{\"full_name\":\"Ideal.Quotient.eq_zero_iff_mem\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Quotient.lean\",\"def_pos\":[125,9],\"def_end_pos\":[125,24]},{\"full_name\":\"Polynomial.coeff_C_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Coeff.lean\",\"def_pos\":[172,9],\"def_end_pos\":[172,20]},{\"full_name\":\"Polynomial.coeff_X_pow\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Coeff.lean\",\"def_pos\":[211,9],\"def_end_pos\":[211,20]},{\"full_name\":\"if_neg\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[937,9],\"def_end_pos\":[937,15]},{\"full_name\":\"MulZeroClass.mul_zero\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Defs.lean\",\"def_pos\":[39,3],\"def_end_pos\":[39,11]}]"
+              ],
+              "state_after": "case neg.inl.hnc\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : \u00acf = 0\nh : \u2191n < f.degree\n\u22a2 \u00acn = f.natDegree",
+              "state_before": "case neg.inl\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : \u00acf = 0\nh : \u2191n < f.degree\n\u22a2 (map (mk P) f).coeff n = (C ((mk P) f.leadingCoeff) * X ^ f.natDegree).coeff n",
+              "tactic": "erw [coeff_map, eq_zero_iff_mem.2 (hfP n h), coeff_C_mul, coeff_X_pow, if_neg,\n  mul_zero]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rintro rfl\"",
+                "[]"
+              ],
+              "state_after": "case neg.inl.hnc\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nhf0 : \u00acf = 0\nh : \u2191f.natDegree < f.degree\n\u22a2 False",
+              "state_before": "case neg.inl.hnc\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : \u00acf = 0\nh : \u2191n < f.degree\n\u22a2 \u00acn = f.natDegree",
+              "tactic": "rintro rfl"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>not_lt_of_ge<\\/a> <a>degree_le_natDegree<\\/a> h\"",
+                "[{\"full_name\":\"not_lt_of_ge\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[152,9],\"def_end_pos\":[152,21]},{\"full_name\":\"Polynomial.degree_le_natDegree\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[167,9],\"def_end_pos\":[167,28]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case neg.inl.hnc\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nhf0 : \u00acf = 0\nh : \u2191f.natDegree < f.degree\n\u22a2 False",
+              "tactic": "exact not_lt_of_ge degree_le_natDegree h"
+            },
+            {
+              "annotated_tactic": [
+                "\"have : <a>natDegree<\\/a> f = n := <a>natDegree_eq_of_degree_eq_some<\\/a> h.symm\"",
+                "[{\"full_name\":\"Polynomial.natDegree\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[67,5],\"def_end_pos\":[67,14]},{\"full_name\":\"Polynomial.natDegree_eq_of_degree_eq_some\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[157,9],\"def_end_pos\":[157,39]}]"
+              ],
+              "state_after": "case neg.inr.inl\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : \u00acf = 0\nh : \u2191n = f.degree\nthis : f.natDegree = n\n\u22a2 (map (mk P) f).coeff n = (C ((mk P) f.leadingCoeff) * X ^ f.natDegree).coeff n",
+              "state_before": "case neg.inr.inl\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : \u00acf = 0\nh : \u2191n = f.degree\n\u22a2 (map (mk P) f).coeff n = (C ((mk P) f.leadingCoeff) * X ^ f.natDegree).coeff n",
+              "tactic": "have : natDegree f = n := natDegree_eq_of_degree_eq_some h.symm"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>coeff_C_mul<\\/a>, <a>coeff_X_pow<\\/a>, <a>if_pos<\\/a> this.symm, <a>mul_one<\\/a>, <a>leadingCoeff<\\/a>, this, <a>coeff_map<\\/a>]\"",
+                "[{\"full_name\":\"Polynomial.coeff_C_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Coeff.lean\",\"def_pos\":[172,9],\"def_end_pos\":[172,20]},{\"full_name\":\"Polynomial.coeff_X_pow\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Coeff.lean\",\"def_pos\":[211,9],\"def_end_pos\":[211,20]},{\"full_name\":\"if_pos\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[932,9],\"def_end_pos\":[932,15]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"Polynomial.leadingCoeff\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[72,5],\"def_end_pos\":[72,17]},{\"full_name\":\"Polynomial.coeff_map\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[803,9],\"def_end_pos\":[803,18]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case neg.inr.inl\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : \u00acf = 0\nh : \u2191n = f.degree\nthis : f.natDegree = n\n\u22a2 (map (mk P) f).coeff n = (C ((mk P) f.leadingCoeff) * X ^ f.natDegree).coeff n",
+              "tactic": "rw [coeff_C_mul, coeff_X_pow, if_pos this.symm, mul_one, leadingCoeff, this, coeff_map]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>coeff_eq_zero_of_degree_lt<\\/a>, <a>coeff_eq_zero_of_degree_lt<\\/a>]\"",
+                "[{\"full_name\":\"Polynomial.coeff_eq_zero_of_degree_lt\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[350,9],\"def_end_pos\":[350,35]},{\"full_name\":\"Polynomial.coeff_eq_zero_of_degree_lt\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[350,9],\"def_end_pos\":[350,35]}]"
+              ],
+              "state_after": "case neg.inr.inr\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : \u00acf = 0\nh : f.degree < \u2191n\n\u22a2 (C ((mk P) f.leadingCoeff) * X ^ f.natDegree).degree < \u2191n\n\ncase neg.inr.inr\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : \u00acf = 0\nh : f.degree < \u2191n\n\u22a2 (map (mk P) f).degree < \u2191n",
+              "state_before": "case neg.inr.inr\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : \u00acf = 0\nh : f.degree < \u2191n\n\u22a2 (map (mk P) f).coeff n = (C ((mk P) f.leadingCoeff) * X ^ f.natDegree).coeff n",
+              "tactic": "rw [coeff_eq_zero_of_degree_lt, coeff_eq_zero_of_degree_lt]"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine <a>lt_of_le_of_lt<\\/a> (<a>degree_C_mul_X_pow_le<\\/a> _ _) ?_\"",
+                "[{\"full_name\":\"lt_of_le_of_lt\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[122,9],\"def_end_pos\":[122,23]},{\"full_name\":\"Polynomial.degree_C_mul_X_pow_le\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[311,9],\"def_end_pos\":[311,30]}]"
+              ],
+              "state_after": "case neg.inr.inr\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : \u00acf = 0\nh : f.degree < \u2191n\n\u22a2 \u2191f.natDegree < \u2191n",
+              "state_before": "case neg.inr.inr\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : \u00acf = 0\nh : f.degree < \u2191n\n\u22a2 (C ((mk P) f.leadingCoeff) * X ^ f.natDegree).degree < \u2191n",
+              "tactic": "refine lt_of_le_of_lt (degree_C_mul_X_pow_le _ _) ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"rwa [\\u2190 <a>degree_eq_natDegree<\\/a> hf0]\"",
+                "[{\"full_name\":\"Polynomial.degree_eq_natDegree\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[132,9],\"def_end_pos\":[132,28]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case neg.inr.inr\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : \u00acf = 0\nh : f.degree < \u2191n\n\u22a2 \u2191f.natDegree < \u2191n",
+              "tactic": "rwa [\u2190 degree_eq_natDegree hf0]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>lt_of_le_of_lt<\\/a> (<a>degree_map_le<\\/a> _ _) h\"",
+                "[{\"full_name\":\"lt_of_le_of_lt\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[122,9],\"def_end_pos\":[122,23]},{\"full_name\":\"Polynomial.degree_map_le\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[862,9],\"def_end_pos\":[862,22]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case neg.inr.inr\nR : Type u_1\ninst\u271d : CommRing R\nf : R[X]\nP : Ideal R\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nn : \u2115\nhf0 : \u00acf = 0\nh : f.degree < \u2191n\n\u22a2 (map (mk P) f).degree < \u2191n",
+              "tactic": "exact lt_of_le_of_lt (degree_map_le _ _) h"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/EisensteinCriterion.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'intro hm0 hn0'",
+        "full_name": "Polynomial.irreducible_of_eisenstein_criterion",
+        "id": "Polynomial.irreducible_of_eisenstein_criterion",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            136,
+            22
+          ],
+          "file_path": "Mathlib/RingTheory/EisensteinCriterion.lean",
+          "full_name": "Polynomial.irreducible_of_eisenstein_criterion",
+          "start": [
+            91,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"simp_all only [<a>not_true<\\/a>, <a>Submodule.zero_mem<\\/a>, <a>coeff_zero<\\/a>]\"",
+                "[{\"full_name\":\"not_true\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1369,9],\"def_end_pos\":[1369,17]},{\"full_name\":\"Submodule.zero_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/Submodule\\/Basic.lean\",\"def_pos\":[216,19],\"def_end_pos\":[216,27]},{\"full_name\":\"Polynomial.coeff_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Basic.lean\",\"def_pos\":[689,9],\"def_end_pos\":[689,19]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nf : R[X]\nP : Ideal R\nhP : P.IsPrime\nhfl : f.leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nhfd0 : 0 < f.degree\nh0 : f.coeff 0 \u2209 P ^ 2\nhu : f.IsPrimitive\nx\u271d : f = 0\n\u22a2 False",
+              "tactic": "simp_all only [not_true, Submodule.zero_mem, coeff_zero]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp_all only [<a>lt_irrefl<\\/a>]\"",
+                "[{\"full_name\":\"lt_irrefl\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[79,9],\"def_end_pos\":[79,18]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nf : R[X]\nP : Ideal R\nhP : P.IsPrime\nhfl : f.leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nhfd0\u271d : 0 < f.degree\nh0 : f.coeff 0 \u2209 P ^ 2\nhu : f.IsPrimitive\nhf0 : f \u2260 0\nhf : map (mk P) f = C ((mk P) f.leadingCoeff) * X ^ f.natDegree\nhfd0 : 0 < f.natDegree\nh : f.degree = 0\n\u22a2 False",
+              "tactic": "simp_all only [lt_irrefl]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rintro p q rfl\"",
+                "[]"
+              ],
+              "state_after": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) (p * q) = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nf : R[X]\nP : Ideal R\nhP : P.IsPrime\nhfl : f.leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < f.degree \u2192 f.coeff n \u2208 P\nhfd0\u271d : 0 < f.degree\nh0 : f.coeff 0 \u2209 P ^ 2\nhu : f.IsPrimitive\nhf0 : f \u2260 0\nhf : map (mk P) f = C ((mk P) f.leadingCoeff) * X ^ f.natDegree\nhfd0 : 0 < f.natDegree\n\u22a2 \u2200 (a b : R[X]), f = a * b \u2192 IsUnit a \u2228 IsUnit b",
+              "tactic": "rintro p q rfl"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Polynomial.map_mul<\\/a>] at hf\"",
+                "[{\"full_name\":\"Polynomial.map_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[749,19],\"def_end_pos\":[749,26]}]"
+              ],
+              "state_after": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) (p * q) = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "tactic": "rw [Polynomial.map_mul] at hf"
+            },
+            {
+              "annotated_tactic": [
+                "\"rcases <a>mul_eq_mul_prime_pow<\\/a>\\n        (show <a>Prime<\\/a> (<a>X<\\/a> : <a>Polynomial<\\/a> (R \\u29f8 P)) from monic_X.prime_of_degree_eq_one <a>degree_X<\\/a>) hf with\\n      \\u27e8m, n, b, c, hmnd, hbc, hp, hq\\u27e9\"",
+                "[{\"full_name\":\"mul_eq_mul_prime_pow\",\"def_path\":\"Mathlib\\/RingTheory\\/Prime.lean\",\"def_pos\":[51,9],\"def_end_pos\":[51,29]},{\"full_name\":\"Prime\",\"def_path\":\"Mathlib\\/Algebra\\/Associated.lean\",\"def_pos\":[41,5],\"def_end_pos\":[41,10]},{\"full_name\":\"Polynomial.X\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Basic.lean\",\"def_pos\":[564,5],\"def_end_pos\":[564,6]},{\"full_name\":\"Polynomial\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Basic.lean\",\"def_pos\":[63,11],\"def_end_pos\":[63,21]},{\"full_name\":\"Polynomial.degree_X\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[522,9],\"def_end_pos\":[522,17]}]"
+              ],
+              "state_after": "case intro.intro.intro.intro.intro.intro.intro\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "tactic": "rcases mul_eq_mul_prime_pow\n    (show Prime (X : Polynomial (R \u29f8 P)) from monic_X.prime_of_degree_eq_one degree_X) hf with\n  \u27e8m, n, b, c, hmnd, hbc, hp, hq\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hmn : 0 < m \\u2192 0 < n \\u2192 <a>False<\\/a> := by\\n      intro hm0 hn0\\n      refine h0 ?_\\n      rw [<a>coeff_zero_eq_eval_zero<\\/a>, <a>eval_mul<\\/a>, <a>sq<\\/a>]\\n      exact\\n        <a>Ideal.mul_mem_mul<\\/a> (<a>eval_zero_mem_ideal_of_eq_mul_X_pow<\\/a> hp hm0.ne')\\n          (<a>eval_zero_mem_ideal_of_eq_mul_X_pow<\\/a> hq hn0.ne')\"",
+                "[{\"full_name\":\"False\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[202,11],\"def_end_pos\":[202,16]},{\"full_name\":\"Polynomial.coeff_zero_eq_eval_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[505,9],\"def_end_pos\":[505,32]},{\"full_name\":\"Polynomial.eval_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[1106,9],\"def_end_pos\":[1106,17]},{\"full_name\":\"sq\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[684,41],\"def_end_pos\":[684,43]},{\"full_name\":\"Ideal.mul_mem_mul\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Operations.lean\",\"def_pos\":[434,9],\"def_end_pos\":[434,20]},{\"full_name\":\"Polynomial.EisensteinCriterionAux.eval_zero_mem_ideal_of_eq_mul_X_pow\",\"def_path\":\"Mathlib\\/RingTheory\\/EisensteinCriterion.lean\",\"def_pos\":[65,9],\"def_end_pos\":[65,44]},{\"full_name\":\"Polynomial.EisensteinCriterionAux.eval_zero_mem_ideal_of_eq_mul_X_pow\",\"def_path\":\"Mathlib\\/RingTheory\\/EisensteinCriterion.lean\",\"def_pos\":[65,9],\"def_end_pos\":[65,44]}]"
+              ],
+              "state_after": "case intro.intro.intro.intro.intro.intro.intro\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "state_before": "case intro.intro.intro.intro.intro.intro.intro\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "tactic": "have hmn : 0 < m \u2192 0 < n \u2192 False := by\n  intro hm0 hn0\n  refine h0 ?_\n  rw [coeff_zero_eq_eval_zero, eval_mul, sq]\n  exact\n    Ideal.mul_mem_mul (eval_zero_mem_ideal_of_eq_mul_X_pow hp hm0.ne')\n      (eval_zero_mem_ideal_of_eq_mul_X_pow hq hn0.ne')"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hpql0 : (<a>mk<\\/a> P) (p * q).<a>leadingCoeff<\\/a> \\u2260 0 := by rwa [<a>Ne<\\/a>, <a>eq_zero_iff_mem<\\/a>]\"",
+                "[{\"full_name\":\"Ideal.Quotient.mk\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Quotient.lean\",\"def_pos\":[92,5],\"def_end_pos\":[92,7]},{\"full_name\":\"Polynomial.leadingCoeff\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[72,5],\"def_end_pos\":[72,17]},{\"full_name\":\"Ne\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[689,18],\"def_end_pos\":[689,20]},{\"full_name\":\"Ideal.Quotient.eq_zero_iff_mem\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Quotient.lean\",\"def_pos\":[125,9],\"def_end_pos\":[125,24]}]"
+              ],
+              "state_after": "case intro.intro.intro.intro.intro.intro.intro\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "state_before": "case intro.intro.intro.intro.intro.intro.intro\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "tactic": "have hpql0 : (mk P) (p * q).leadingCoeff \u2260 0 := by rwa [Ne, eq_zero_iff_mem]"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hp0 : p \\u2260 0 := fun h => by\\n      simp_all only [<a>zero_mul<\\/a>, <a>eq_self_iff_true<\\/a>, <a>not_true<\\/a>, <a>Ne<\\/a>]\"",
+                "[{\"full_name\":\"MulZeroClass.zero_mul\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Defs.lean\",\"def_pos\":[37,3],\"def_end_pos\":[37,11]},{\"full_name\":\"eq_self_iff_true\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1380,9],\"def_end_pos\":[1380,25]},{\"full_name\":\"not_true\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1369,9],\"def_end_pos\":[1369,17]},{\"full_name\":\"Ne\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[689,18],\"def_end_pos\":[689,20]}]"
+              ],
+              "state_after": "case intro.intro.intro.intro.intro.intro.intro\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "state_before": "case intro.intro.intro.intro.intro.intro.intro\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "tactic": "have hp0 : p \u2260 0 := fun h => by\n  simp_all only [zero_mul, eq_self_iff_true, not_true, Ne]"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hq0 : q \\u2260 0 := fun h => by\\n      simp_all only [<a>eq_self_iff_true<\\/a>, <a>not_true<\\/a>, <a>Ne<\\/a>, <a>mul_zero<\\/a>]\"",
+                "[{\"full_name\":\"eq_self_iff_true\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1380,9],\"def_end_pos\":[1380,25]},{\"full_name\":\"not_true\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1369,9],\"def_end_pos\":[1369,17]},{\"full_name\":\"Ne\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[689,18],\"def_end_pos\":[689,20]},{\"full_name\":\"MulZeroClass.mul_zero\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Defs.lean\",\"def_pos\":[39,3],\"def_end_pos\":[39,11]}]"
+              ],
+              "state_after": "case intro.intro.intro.intro.intro.intro.intro\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "state_before": "case intro.intro.intro.intro.intro.intro.intro\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "tactic": "have hq0 : q \u2260 0 := fun h => by\n  simp_all only [eq_self_iff_true, not_true, Ne, mul_zero]"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hbc0 : <a>degree<\\/a> b = 0 \\u2227 <a>degree<\\/a> c = 0 := by\\n      apply_fun <a>degree<\\/a> at hbc\\n      rwa [<a>degree_C<\\/a> hpql0, <a>degree_mul<\\/a>, <a>eq_comm<\\/a>, <a>Nat.WithBot.add_eq_zero_iff<\\/a>] at hbc\"",
+                "[{\"full_name\":\"Polynomial.degree\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[52,5],\"def_end_pos\":[52,11]},{\"full_name\":\"Polynomial.degree\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[52,5],\"def_end_pos\":[52,11]},{\"full_name\":\"Polynomial.degree\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[52,5],\"def_end_pos\":[52,11]},{\"full_name\":\"Polynomial.degree_C\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[246,9],\"def_end_pos\":[246,17]},{\"full_name\":\"Polynomial.degree_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[1651,9],\"def_end_pos\":[1651,19]},{\"full_name\":\"eq_comm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[811,9],\"def_end_pos\":[811,16]},{\"full_name\":\"Nat.WithBot.add_eq_zero_iff\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/WithBot.lean\",\"def_pos\":[28,9],\"def_end_pos\":[28,24]}]"
+              ],
+              "state_after": "case intro.intro.intro.intro.intro.intro.intro\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "state_before": "case intro.intro.intro.intro.intro.intro.intro\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "tactic": "have hbc0 : degree b = 0 \u2227 degree c = 0 := by\n  apply_fun degree at hbc\n  rwa [degree_C hpql0, degree_mul, eq_comm, Nat.WithBot.add_eq_zero_iff] at hbc"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hmp : m \\u2264 <a>natDegree<\\/a> p := <a>le_natDegree_of_map_eq_mul_X_pow<\\/a> hP hp hbc0.1\"",
+                "[{\"full_name\":\"Polynomial.natDegree\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[67,5],\"def_end_pos\":[67,14]},{\"full_name\":\"Polynomial.EisensteinCriterionAux.le_natDegree_of_map_eq_mul_X_pow\",\"def_path\":\"Mathlib\\/RingTheory\\/EisensteinCriterion.lean\",\"def_pos\":[52,9],\"def_end_pos\":[52,41]}]"
+              ],
+              "state_after": "case intro.intro.intro.intro.intro.intro.intro\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "state_before": "case intro.intro.intro.intro.intro.intro.intro\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "tactic": "have hmp : m \u2264 natDegree p := le_natDegree_of_map_eq_mul_X_pow hP hp hbc0.1"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hnq : n \\u2264 <a>natDegree<\\/a> q := <a>le_natDegree_of_map_eq_mul_X_pow<\\/a> hP hq hbc0.2\"",
+                "[{\"full_name\":\"Polynomial.natDegree\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[67,5],\"def_end_pos\":[67,14]},{\"full_name\":\"Polynomial.EisensteinCriterionAux.le_natDegree_of_map_eq_mul_X_pow\",\"def_path\":\"Mathlib\\/RingTheory\\/EisensteinCriterion.lean\",\"def_pos\":[52,9],\"def_end_pos\":[52,41]}]"
+              ],
+              "state_after": "case intro.intro.intro.intro.intro.intro.intro\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhnq : n \u2264 q.natDegree\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "state_before": "case intro.intro.intro.intro.intro.intro.intro\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "tactic": "have hnq : n \u2264 natDegree q := le_natDegree_of_map_eq_mul_X_pow hP hq hbc0.2"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain rfl | rfl : m = 0 \\u2228 n = 0 := by\\n      rwa [<a>pos_iff_ne_zero<\\/a>, <a>pos_iff_ne_zero<\\/a>, <a>imp_false<\\/a>, <a>Classical.not_not<\\/a>, \\u2190 <a>or_iff_not_imp_left<\\/a>]\\n        at hmn\"",
+                "[{\"full_name\":\"pos_iff_ne_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Canonical\\/Defs.lean\",\"def_pos\":[230,3],\"def_end_pos\":[230,14]},{\"full_name\":\"pos_iff_ne_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Canonical\\/Defs.lean\",\"def_pos\":[230,3],\"def_end_pos\":[230,14]},{\"full_name\":\"imp_false\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1420,17],\"def_end_pos\":[1420,26]},{\"full_name\":\"Classical.not_not\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Classical.lean\",\"def_pos\":[135,17],\"def_end_pos\":[135,24]},{\"full_name\":\"Classical.or_iff_not_imp_left\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Classical.lean\",\"def_pos\":[147,9],\"def_end_pos\":[147,28]}]"
+              ],
+              "state_after": "case intro.intro.intro.intro.intro.intro.intro.inl\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nn : \u2115\nb c : (R \u29f8 P)[X]\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhq : map (mk P) q = c * X ^ n\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhnq : n \u2264 q.natDegree\nhmnd : 0 + n = (p * q).natDegree\nhp : map (mk P) p = b * X ^ 0\nhmn : 0 < 0 \u2192 0 < n \u2192 False\nhmp : 0 \u2264 p.natDegree\nhpmqn : p.natDegree = 0 \u2227 q.natDegree = n\n\u22a2 IsUnit p \u2228 IsUnit q\n\ncase intro.intro.intro.intro.intro.intro.intro.inr\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm : \u2115\nb c : (R \u29f8 P)[X]\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhmnd : m + 0 = (p * q).natDegree\nhq : map (mk P) q = c * X ^ 0\nhmn : 0 < m \u2192 0 < 0 \u2192 False\nhnq : 0 \u2264 q.natDegree\nhpmqn : p.natDegree = m \u2227 q.natDegree = 0\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "state_before": "case intro.intro.intro.intro.intro.intro.intro\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhnq : n \u2264 q.natDegree\nhpmqn : p.natDegree = m \u2227 q.natDegree = n\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "tactic": "obtain rfl | rfl : m = 0 \u2228 n = 0 := by\n  rwa [pos_iff_ne_zero, pos_iff_ne_zero, imp_false, Classical.not_not, \u2190 or_iff_not_imp_left]\n    at hmn"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro hm0 hn0\"",
+                "[]"
+              ],
+              "state_after": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhm0 : 0 < m\nhn0 : 0 < n\n\u22a2 False",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\n\u22a2 0 < m \u2192 0 < n \u2192 False",
+              "tactic": "intro hm0 hn0"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine h0 ?_\"",
+                "[]"
+              ],
+              "state_after": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhm0 : 0 < m\nhn0 : 0 < n\n\u22a2 (p * q).coeff 0 \u2208 P ^ 2",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhm0 : 0 < m\nhn0 : 0 < n\n\u22a2 False",
+              "tactic": "refine h0 ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>coeff_zero_eq_eval_zero<\\/a>, <a>eval_mul<\\/a>, <a>sq<\\/a>]\"",
+                "[{\"full_name\":\"Polynomial.coeff_zero_eq_eval_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[505,9],\"def_end_pos\":[505,32]},{\"full_name\":\"Polynomial.eval_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[1106,9],\"def_end_pos\":[1106,17]},{\"full_name\":\"sq\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[684,41],\"def_end_pos\":[684,43]}]"
+              ],
+              "state_after": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhm0 : 0 < m\nhn0 : 0 < n\n\u22a2 eval 0 p * eval 0 q \u2208 P * P",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhm0 : 0 < m\nhn0 : 0 < n\n\u22a2 (p * q).coeff 0 \u2208 P ^ 2",
+              "tactic": "rw [coeff_zero_eq_eval_zero, eval_mul, sq]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact\\n        <a>Ideal.mul_mem_mul<\\/a> (<a>eval_zero_mem_ideal_of_eq_mul_X_pow<\\/a> hp hm0.ne')\\n          (<a>eval_zero_mem_ideal_of_eq_mul_X_pow<\\/a> hq hn0.ne')\"",
+                "[{\"full_name\":\"Ideal.mul_mem_mul\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Operations.lean\",\"def_pos\":[434,9],\"def_end_pos\":[434,20]},{\"full_name\":\"Polynomial.EisensteinCriterionAux.eval_zero_mem_ideal_of_eq_mul_X_pow\",\"def_path\":\"Mathlib\\/RingTheory\\/EisensteinCriterion.lean\",\"def_pos\":[65,9],\"def_end_pos\":[65,44]},{\"full_name\":\"Polynomial.EisensteinCriterionAux.eval_zero_mem_ideal_of_eq_mul_X_pow\",\"def_path\":\"Mathlib\\/RingTheory\\/EisensteinCriterion.lean\",\"def_pos\":[65,9],\"def_end_pos\":[65,44]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhm0 : 0 < m\nhn0 : 0 < n\n\u22a2 eval 0 p * eval 0 q \u2208 P * P",
+              "tactic": "exact\n  Ideal.mul_mem_mul (eval_zero_mem_ideal_of_eq_mul_X_pow hp hm0.ne')\n    (eval_zero_mem_ideal_of_eq_mul_X_pow hq hn0.ne')"
+            },
+            {
+              "annotated_tactic": [
+                "\"rwa [<a>Ne<\\/a>, <a>eq_zero_iff_mem<\\/a>]\"",
+                "[{\"full_name\":\"Ne\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[689,18],\"def_end_pos\":[689,20]},{\"full_name\":\"Ideal.Quotient.eq_zero_iff_mem\",\"def_path\":\"Mathlib\\/RingTheory\\/Ideal\\/Quotient.lean\",\"def_pos\":[125,9],\"def_end_pos\":[125,24]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\n\u22a2 (mk P) (p * q).leadingCoeff \u2260 0",
+              "tactic": "rwa [Ne, eq_zero_iff_mem]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp_all only [<a>zero_mul<\\/a>, <a>eq_self_iff_true<\\/a>, <a>not_true<\\/a>, <a>Ne<\\/a>]\"",
+                "[{\"full_name\":\"MulZeroClass.zero_mul\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Defs.lean\",\"def_pos\":[37,3],\"def_end_pos\":[37,11]},{\"full_name\":\"eq_self_iff_true\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1380,9],\"def_end_pos\":[1380,25]},{\"full_name\":\"not_true\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1369,9],\"def_end_pos\":[1369,17]},{\"full_name\":\"Ne\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[689,18],\"def_end_pos\":[689,20]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nh : p = 0\n\u22a2 False",
+              "tactic": "simp_all only [zero_mul, eq_self_iff_true, not_true, Ne]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp_all only [<a>eq_self_iff_true<\\/a>, <a>not_true<\\/a>, <a>Ne<\\/a>, <a>mul_zero<\\/a>]\"",
+                "[{\"full_name\":\"eq_self_iff_true\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1380,9],\"def_end_pos\":[1380,25]},{\"full_name\":\"not_true\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1369,9],\"def_end_pos\":[1369,17]},{\"full_name\":\"Ne\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[689,18],\"def_end_pos\":[689,20]},{\"full_name\":\"MulZeroClass.mul_zero\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Defs.lean\",\"def_pos\":[39,3],\"def_end_pos\":[39,11]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nh : q = 0\n\u22a2 False",
+              "tactic": "simp_all only [eq_self_iff_true, not_true, Ne, mul_zero]"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply_fun <a>degree<\\/a> at hbc\"",
+                "[{\"full_name\":\"Polynomial.degree\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[52,5],\"def_end_pos\":[52,11]}]"
+              ],
+              "state_after": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc : (C ((mk P) (p * q).leadingCoeff)).degree = (b * c).degree\n\u22a2 b.degree = 0 \u2227 c.degree = 0",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\n\u22a2 b.degree = 0 \u2227 c.degree = 0",
+              "tactic": "apply_fun degree at hbc"
+            },
+            {
+              "annotated_tactic": [
+                "\"rwa [<a>degree_C<\\/a> hpql0, <a>degree_mul<\\/a>, <a>eq_comm<\\/a>, <a>Nat.WithBot.add_eq_zero_iff<\\/a>] at hbc\"",
+                "[{\"full_name\":\"Polynomial.degree_C\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[246,9],\"def_end_pos\":[246,17]},{\"full_name\":\"Polynomial.degree_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Degree\\/Definitions.lean\",\"def_pos\":[1651,9],\"def_end_pos\":[1651,19]},{\"full_name\":\"eq_comm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[811,9],\"def_end_pos\":[811,16]},{\"full_name\":\"Nat.WithBot.add_eq_zero_iff\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/WithBot.lean\",\"def_pos\":[28,9],\"def_end_pos\":[28,24]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc : (C ((mk P) (p * q).leadingCoeff)).degree = (b * c).degree\n\u22a2 b.degree = 0 \u2227 c.degree = 0",
+              "tactic": "rwa [degree_C hpql0, degree_mul, eq_comm, Nat.WithBot.add_eq_zero_iff] at hbc"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>natDegree_mul<\\/a> hp0 hq0] at hmnd\"",
+                "[{\"full_name\":\"Polynomial.natDegree_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/RingDivision.lean\",\"def_pos\":[124,9],\"def_end_pos\":[124,22]}]"
+              ],
+              "state_after": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = p.natDegree + q.natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhnq : n \u2264 q.natDegree\n\u22a2 p.natDegree = m \u2227 q.natDegree = n",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhnq : n \u2264 q.natDegree\n\u22a2 p.natDegree = m \u2227 q.natDegree = n",
+              "tactic": "rw [natDegree_mul hp0 hq0] at hmnd"
+            },
+            {
+              "annotated_tactic": [
+                "\"contrapose hmnd\"",
+                "[]"
+              ],
+              "state_after": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhnq : n \u2264 q.natDegree\nhmnd : \u00ac(p.natDegree = m \u2227 q.natDegree = n)\n\u22a2 \u00acm + n = p.natDegree + q.natDegree",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = p.natDegree + q.natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhnq : n \u2264 q.natDegree\n\u22a2 p.natDegree = m \u2227 q.natDegree = n",
+              "tactic": "contrapose hmnd"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>ne_of_lt<\\/a>\"",
+                "[{\"full_name\":\"ne_of_lt\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[101,9],\"def_end_pos\":[101,17]}]"
+              ],
+              "state_after": "case h\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhnq : n \u2264 q.natDegree\nhmnd : \u00ac(p.natDegree = m \u2227 q.natDegree = n)\n\u22a2 m + n < p.natDegree + q.natDegree",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhnq : n \u2264 q.natDegree\nhmnd : \u00ac(p.natDegree = m \u2227 q.natDegree = n)\n\u22a2 \u00acm + n = p.natDegree + q.natDegree",
+              "tactic": "apply ne_of_lt"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>not_and_or<\\/a>] at hmnd\"",
+                "[{\"full_name\":\"not_and_or\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[481,9],\"def_end_pos\":[481,19]}]"
+              ],
+              "state_after": "case h\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhnq : n \u2264 q.natDegree\nhmnd : \u00acp.natDegree = m \u2228 \u00acq.natDegree = n\n\u22a2 m + n < p.natDegree + q.natDegree",
+              "state_before": "case h\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhnq : n \u2264 q.natDegree\nhmnd : \u00ac(p.natDegree = m \u2227 q.natDegree = n)\n\u22a2 m + n < p.natDegree + q.natDegree",
+              "tactic": "rw [not_and_or] at hmnd"
+            },
+            {
+              "annotated_tactic": [
+                "\"cases' hmnd with hmnd hmnd\"",
+                "[]"
+              ],
+              "state_after": "case h.inl\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhnq : n \u2264 q.natDegree\nhmnd : \u00acp.natDegree = m\n\u22a2 m + n < p.natDegree + q.natDegree\n\ncase h.inr\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhnq : n \u2264 q.natDegree\nhmnd : \u00acq.natDegree = n\n\u22a2 m + n < p.natDegree + q.natDegree",
+              "state_before": "case h\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhnq : n \u2264 q.natDegree\nhmnd : \u00acp.natDegree = m \u2228 \u00acq.natDegree = n\n\u22a2 m + n < p.natDegree + q.natDegree",
+              "tactic": "cases' hmnd with hmnd hmnd"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>add_lt_add_of_lt_of_le<\\/a> (<a>lt_of_le_of_ne<\\/a> hmp (<a>Ne.symm<\\/a> hmnd)) hnq\"",
+                "[{\"full_name\":\"add_lt_add_of_lt_of_le\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Unbundled\\/Basic.lean\",\"def_pos\":[178,3],\"def_end_pos\":[178,14]},{\"full_name\":\"lt_of_le_of_ne\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[198,9],\"def_end_pos\":[198,23]},{\"full_name\":\"Ne.symm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[704,9],\"def_end_pos\":[704,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.inl\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhnq : n \u2264 q.natDegree\nhmnd : \u00acp.natDegree = m\n\u22a2 m + n < p.natDegree + q.natDegree",
+              "tactic": "exact add_lt_add_of_lt_of_le (lt_of_le_of_ne hmp (Ne.symm hmnd)) hnq"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>add_lt_add_of_le_of_lt<\\/a> hmp (<a>lt_of_le_of_ne<\\/a> hnq (<a>Ne.symm<\\/a> hmnd))\"",
+                "[{\"full_name\":\"add_lt_add_of_le_of_lt\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Unbundled\\/Basic.lean\",\"def_pos\":[170,3],\"def_end_pos\":[170,14]},{\"full_name\":\"lt_of_le_of_ne\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[198,9],\"def_end_pos\":[198,23]},{\"full_name\":\"Ne.symm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[704,9],\"def_end_pos\":[704,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.inr\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhnq : n \u2264 q.natDegree\nhmnd : \u00acq.natDegree = n\n\u22a2 m + n < p.natDegree + q.natDegree",
+              "tactic": "exact add_lt_add_of_le_of_lt hmp (lt_of_le_of_ne hnq (Ne.symm hmnd))"
+            },
+            {
+              "annotated_tactic": [
+                "\"rwa [<a>pos_iff_ne_zero<\\/a>, <a>pos_iff_ne_zero<\\/a>, <a>imp_false<\\/a>, <a>Classical.not_not<\\/a>, \\u2190 <a>or_iff_not_imp_left<\\/a>]\\n        at hmn\"",
+                "[{\"full_name\":\"pos_iff_ne_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Canonical\\/Defs.lean\",\"def_pos\":[230,3],\"def_end_pos\":[230,14]},{\"full_name\":\"pos_iff_ne_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Canonical\\/Defs.lean\",\"def_pos\":[230,3],\"def_end_pos\":[230,14]},{\"full_name\":\"imp_false\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1420,17],\"def_end_pos\":[1420,26]},{\"full_name\":\"Classical.not_not\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Classical.lean\",\"def_pos\":[135,17],\"def_end_pos\":[135,24]},{\"full_name\":\"Classical.or_iff_not_imp_left\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Classical.lean\",\"def_pos\":[147,9],\"def_end_pos\":[147,28]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm n : \u2115\nb c : (R \u29f8 P)[X]\nhmnd : m + n = (p * q).natDegree\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhq : map (mk P) q = c * X ^ n\nhmn : 0 < m \u2192 0 < n \u2192 False\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhnq : n \u2264 q.natDegree\nhpmqn : p.natDegree = m \u2227 q.natDegree = n\n\u22a2 m = 0 \u2228 n = 0",
+              "tactic": "rwa [pos_iff_ne_zero, pos_iff_ne_zero, imp_false, Classical.not_not, \u2190 or_iff_not_imp_left]\n  at hmn"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>Or.inl<\\/a> (<a>isUnit_of_natDegree_eq_zero_of_isPrimitive<\\/a> hu hpmqn.1)\"",
+                "[{\"full_name\":\"Or.inl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[534,5],\"def_end_pos\":[534,8]},{\"full_name\":\"Polynomial.EisensteinCriterionAux.isUnit_of_natDegree_eq_zero_of_isPrimitive\",\"def_path\":\"Mathlib\\/RingTheory\\/EisensteinCriterion.lean\",\"def_pos\":[72,9],\"def_end_pos\":[72,51]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case intro.intro.intro.intro.intro.intro.intro.inl\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nn : \u2115\nb c : (R \u29f8 P)[X]\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhq : map (mk P) q = c * X ^ n\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhnq : n \u2264 q.natDegree\nhmnd : 0 + n = (p * q).natDegree\nhp : map (mk P) p = b * X ^ 0\nhmn : 0 < 0 \u2192 0 < n \u2192 False\nhmp : 0 \u2264 p.natDegree\nhpmqn : p.natDegree = 0 \u2227 q.natDegree = n\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "tactic": "exact Or.inl (isUnit_of_natDegree_eq_zero_of_isPrimitive hu hpmqn.1)"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>Or.inr<\\/a>\\n          (<a>isUnit_of_natDegree_eq_zero_of_isPrimitive<\\/a>\\n            (show <a>IsPrimitive<\\/a> (q * p) by simpa [<a>mul_comm<\\/a>] using hu)\\n            hpmqn.2)\"",
+                "[{\"full_name\":\"Or.inr\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[536,5],\"def_end_pos\":[536,8]},{\"full_name\":\"Polynomial.EisensteinCriterionAux.isUnit_of_natDegree_eq_zero_of_isPrimitive\",\"def_path\":\"Mathlib\\/RingTheory\\/EisensteinCriterion.lean\",\"def_pos\":[72,9],\"def_end_pos\":[72,51]},{\"full_name\":\"Polynomial.IsPrimitive\",\"def_path\":\"Mathlib\\/RingTheory\\/Polynomial\\/Content.lean\",\"def_pos\":[42,5],\"def_end_pos\":[42,16]},{\"full_name\":\"mul_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[332,9],\"def_end_pos\":[332,17]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case intro.intro.intro.intro.intro.intro.intro.inr\nR : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm : \u2115\nb c : (R \u29f8 P)[X]\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhmnd : m + 0 = (p * q).natDegree\nhq : map (mk P) q = c * X ^ 0\nhmn : 0 < m \u2192 0 < 0 \u2192 False\nhnq : 0 \u2264 q.natDegree\nhpmqn : p.natDegree = m \u2227 q.natDegree = 0\n\u22a2 IsUnit p \u2228 IsUnit q",
+              "tactic": "exact Or.inr\n    (isUnit_of_natDegree_eq_zero_of_isPrimitive\n      (show IsPrimitive (q * p) by simpa [mul_comm] using hu)\n      hpmqn.2)"
+            },
+            {
+              "annotated_tactic": [
+                "\"simpa [<a>mul_comm<\\/a>] using hu\"",
+                "[{\"full_name\":\"mul_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[332,9],\"def_end_pos\":[332,17]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\ninst\u271d\u00b9 : CommRing R\ninst\u271d : IsDomain R\nP : Ideal R\nhP : P.IsPrime\np q : R[X]\nhfl : (p * q).leadingCoeff \u2209 P\nhfP : \u2200 (n : \u2115), \u2191n < (p * q).degree \u2192 (p * q).coeff n \u2208 P\nhfd0\u271d : 0 < (p * q).degree\nh0 : (p * q).coeff 0 \u2209 P ^ 2\nhu : (p * q).IsPrimitive\nhf0 : p * q \u2260 0\nhf : map (mk P) p * map (mk P) q = C ((mk P) (p * q).leadingCoeff) * X ^ (p * q).natDegree\nhfd0 : 0 < (p * q).natDegree\nm : \u2115\nb c : (R \u29f8 P)[X]\nhbc : C ((mk P) (p * q).leadingCoeff) = b * c\nhp : map (mk P) p = b * X ^ m\nhpql0 : (mk P) (p * q).leadingCoeff \u2260 0\nhp0 : p \u2260 0\nhq0 : q \u2260 0\nhbc0 : b.degree = 0 \u2227 c.degree = 0\nhmp : m \u2264 p.natDegree\nhmnd : m + 0 = (p * q).natDegree\nhq : map (mk P) q = c * X ^ 0\nhmn : 0 < m \u2192 0 < 0 \u2192 False\nhnq : 0 \u2264 q.natDegree\nhpmqn : p.natDegree = m \u2227 q.natDegree = 0\n\u22a2 (q * p).IsPrimitive",
+              "tactic": "simpa [mul_comm] using hu"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/EisensteinCriterion.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Algebra.Etale.comp",
+        "id": "Algebra.Etale.comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            210,
+            55
+          ],
+          "file_path": "Mathlib/RingTheory/Etale/Basic.lean",
+          "full_name": "Algebra.Etale.comp",
+          "start": [
+            208,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Etale/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Algebra.Etale.of_isLocalization_Away",
+        "id": "Algebra.Etale.of_isLocalization_Away",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            220,
+            65
+          ],
+          "file_path": "Mathlib/RingTheory/Etale/Basic.lean",
+          "full_name": "Algebra.Etale.of_isLocalization_Away",
+          "start": [
+            218,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Etale/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Algebra.FormallyEtale.comp",
+        "id": "Algebra.FormallyEtale.comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            106,
+            63
+          ],
+          "file_path": "Mathlib/RingTheory/Etale/Basic.lean",
+          "full_name": "Algebra.FormallyEtale.comp",
+          "start": [
+            104,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Etale/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Algebra.FormallyEtale.localization_base",
+        "id": "Algebra.FormallyEtale.localization_base",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            161,
+            81
+          ],
+          "file_path": "Mathlib/RingTheory/Etale/Basic.lean",
+          "full_name": "Algebra.FormallyEtale.localization_base",
+          "start": [
+            159,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Etale/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Algebra.FormallyEtale.of_equiv",
+        "id": "Algebra.FormallyEtale.of_equiv",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            93,
+            63
+          ],
+          "file_path": "Mathlib/RingTheory/Etale/Basic.lean",
+          "full_name": "Algebra.FormallyEtale.of_equiv",
+          "start": [
+            91,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Etale/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Algebra.FormallyEtale.of_isLocalization",
+        "id": "Algebra.FormallyEtale.of_isLocalization",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            156,
+            81
+          ],
+          "file_path": "Mathlib/RingTheory/Etale/Basic.lean",
+          "full_name": "Algebra.FormallyEtale.of_isLocalization",
+          "start": [
+            154,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Etale/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Algebra.FormallyEtale.of_unramified_and_smooth",
+        "id": "Algebra.FormallyEtale.of_unramified_and_smooth",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            81,
+            55
+          ],
+          "file_path": "Mathlib/RingTheory/Etale/Basic.lean",
+          "full_name": "Algebra.FormallyEtale.of_unramified_and_smooth",
+          "start": [
+            79,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/RingTheory/Etale/Basic.lean"
+      }
+    ],
+    "input_proofs": 14,
+    "input_units": 2,
+    "proofs": 5,
+    "published_proofs": 5,
+    "published_transitions": 11,
+    "replay_failures": [],
+    "transitions": 11,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001665-0000-21020ea7c50d19f7.parquet",
+      "sha256": "21020ea7c50d19f7faae5b24c94ec3fc33e013ba0ece8cb51e9ff267a957345b",
+      "bytes": 71610,
+      "rows": 7,
+      "revision": "df8c9c479578582ca5384c5c62608ea4677707ca"
+    },
+    {
+      "path": "data/internal_test/mathlib-001665-0000-1b1d2d2570dd972c.parquet",
+      "sha256": "1b1d2d2570dd972ce5bf4e89044bc23914b43ebd6928e86f0d6a13209c919eb2",
+      "bytes": 53008,
+      "rows": 4,
+      "revision": "df8c9c479578582ca5384c5c62608ea4677707ca"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Algebra.FormallyEtale.iff_unramified_and_smooth",
+    "mathlib:Algebra.FormallyEtale.localization_map",
+    "mathlib:Polynomial.EisensteinCriterionAux.eval_zero_mem_ideal_of_eq_mul_X_pow",
+    "mathlib:Polynomial.EisensteinCriterionAux.isUnit_of_natDegree_eq_zero_of_isPrimitive",
+    "mathlib:Polynomial.EisensteinCriterionAux.le_natDegree_of_map_eq_mul_X_pow"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/EisensteinCriterion.lean\",null,null,\"Polynomial.EisensteinCriterionAux.eval_zero_mem_ideal_of_eq_mul_X_pow\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/EisensteinCriterion.lean\",null,null,\"Polynomial.EisensteinCriterionAux.isUnit_of_natDegree_eq_zero_of_isPrimitive\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/EisensteinCriterion.lean\",null,null,\"Polynomial.EisensteinCriterionAux.le_natDegree_of_map_eq_mul_X_pow\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Etale/Basic.lean\",null,null,\"Algebra.FormallyEtale.iff_unramified_and_smooth\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/RingTheory/Etale/Basic.lean\",null,null,\"Algebra.FormallyEtale.localization_map\"]"
+  ]
+}