Record 20 verified HPC batch manifests

manifests/batches/mathlib/000837.json

@@ -0,0 +1,651 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000837",
+  "batch_fingerprint": "610e40d22d6ab33c08945cfbbe03b09b0a67eb0183dc894ea5750e1b1d254e06",
+  "evidence": {
+    "batch_fingerprint": "610e40d22d6ab33c08945cfbbe03b09b0a67eb0183dc894ea5750e1b1d254e06",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.ComponentCompl.coe_inj",
+        "id": "SimpleGraph.ComponentCompl.coe_inj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            112,
+            21
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean",
+          "full_name": "SimpleGraph.ComponentCompl.coe_inj",
+          "start": [
+            111,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'exact dis \u27e8hK.choose_spec, this \u25b8 Set.mem_univ hK.some\u27e9'",
+        "full_name": "SimpleGraph.ComponentCompl.exists_adj_boundary_pair",
+        "id": "SimpleGraph.ComponentCompl.exists_adj_boundary_pair",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            168,
+            73
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean",
+          "full_name": "SimpleGraph.ComponentCompl.exists_adj_boundary_pair",
+          "start": [
+            154,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"refine <a>ComponentCompl.ind<\\/a> fun v vnK => ?_\"",
+                "[{\"full_name\":\"SimpleGraph.ComponentCompl.ind\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Ends\\/Defs.lean\",\"def_pos\":[100,19],\"def_end_pos\":[100,22]}]"
+              ],
+              "state_after": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\n\u22a2 \u2203 ck, ck.1 \u2208 G.componentComplMk vnK \u2227 ck.2 \u2208 K \u2227 G.Adj ck.1 ck.2",
+              "state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\n\u22a2 \u2200 (C : G.ComponentCompl K), \u2203 ck, ck.1 \u2208 C \u2227 ck.2 \u2208 K \u2227 G.Adj ck.1 ck.2",
+              "tactic": "refine ComponentCompl.ind fun v vnK => ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"let C : G.ComponentCompl K := G.componentComplMk vnK\"",
+                "[]"
+              ],
+              "state_after": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\n\u22a2 \u2203 ck, ck.1 \u2208 G.componentComplMk vnK \u2227 ck.2 \u2208 K \u2227 G.Adj ck.1 ck.2",
+              "state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\n\u22a2 \u2203 ck, ck.1 \u2208 G.componentComplMk vnK \u2227 ck.2 \u2208 K \u2227 G.Adj ck.1 ck.2",
+              "tactic": "let C : G.ComponentCompl K := G.componentComplMk vnK"
+            },
+            {
+              "annotated_tactic": [
+                "\"let dis := Set.disjoint_iff.mp C.disjoint_right\"",
+                "[]"
+              ],
+              "state_after": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\n\u22a2 \u2203 ck, ck.1 \u2208 G.componentComplMk vnK \u2227 ck.2 \u2208 K \u2227 G.Adj ck.1 ck.2",
+              "state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\n\u22a2 \u2203 ck, ck.1 \u2208 G.componentComplMk vnK \u2227 ck.2 \u2208 K \u2227 G.Adj ck.1 ck.2",
+              "tactic": "let dis := Set.disjoint_iff.mp C.disjoint_right"
+            },
+            {
+              "annotated_tactic": [
+                "\"by_contra! h\"",
+                "[]"
+              ],
+              "state_after": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\nh : \u2200 (ck : V \u00d7 V), ck.1 \u2208 G.componentComplMk vnK \u2192 ck.2 \u2208 K \u2192 \u00acG.Adj ck.1 ck.2\n\u22a2 False",
+              "state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\n\u22a2 \u2203 ck, ck.1 \u2208 G.componentComplMk vnK \u2227 ck.2 \u2208 K \u2227 G.Adj ck.1 ck.2",
+              "tactic": "by_contra! h"
+            },
+            {
+              "annotated_tactic": [
+                "\"suffices <a>Set.univ<\\/a> = (C : <a>Set<\\/a> V) by exact dis \\u27e8hK.choose_spec, this \\u25b8 <a>Set.mem_univ<\\/a> hK.some\\u27e9\"",
+                "[{\"full_name\":\"Set.univ\",\"def_path\":\"Mathlib\\/Init\\/Set.lean\",\"def_pos\":[153,5],\"def_end_pos\":[153,9]},{\"full_name\":\"Set\",\"def_path\":\"Mathlib\\/Init\\/Set.lean\",\"def_pos\":[47,5],\"def_end_pos\":[47,8]},{\"full_name\":\"Set.mem_univ\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Defs.lean\",\"def_pos\":[82,29],\"def_end_pos\":[82,37]}]"
+              ],
+              "state_after": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\nh : \u2200 (ck : V \u00d7 V), ck.1 \u2208 G.componentComplMk vnK \u2192 ck.2 \u2208 K \u2192 \u00acG.Adj ck.1 ck.2\n\u22a2 Set.univ = \u2191C",
+              "state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\nh : \u2200 (ck : V \u00d7 V), ck.1 \u2208 G.componentComplMk vnK \u2192 ck.2 \u2208 K \u2192 \u00acG.Adj ck.1 ck.2\n\u22a2 False",
+              "tactic": "suffices Set.univ = (C : Set V) by exact dis \u27e8hK.choose_spec, this \u25b8 Set.mem_univ hK.some\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"symm\"",
+                "[]"
+              ],
+              "state_after": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\nh : \u2200 (ck : V \u00d7 V), ck.1 \u2208 G.componentComplMk vnK \u2192 ck.2 \u2208 K \u2192 \u00acG.Adj ck.1 ck.2\n\u22a2 \u2191C = Set.univ",
+              "state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\nh : \u2200 (ck : V \u00d7 V), ck.1 \u2208 G.componentComplMk vnK \u2192 ck.2 \u2208 K \u2192 \u00acG.Adj ck.1 ck.2\n\u22a2 Set.univ = \u2191C",
+              "tactic": "symm"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Set.eq_univ_iff_forall<\\/a>]\"",
+                "[{\"full_name\":\"Set.eq_univ_iff_forall\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[668,9],\"def_end_pos\":[668,27]}]"
+              ],
+              "state_after": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\nh : \u2200 (ck : V \u00d7 V), ck.1 \u2208 G.componentComplMk vnK \u2192 ck.2 \u2208 K \u2192 \u00acG.Adj ck.1 ck.2\n\u22a2 \u2200 (x : V), x \u2208 \u2191C",
+              "state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\nh : \u2200 (ck : V \u00d7 V), ck.1 \u2208 G.componentComplMk vnK \u2192 ck.2 \u2208 K \u2192 \u00acG.Adj ck.1 ck.2\n\u22a2 \u2191C = Set.univ",
+              "tactic": "rw [Set.eq_univ_iff_forall]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rintro u\"",
+                "[]"
+              ],
+              "state_after": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\nh : \u2200 (ck : V \u00d7 V), ck.1 \u2208 G.componentComplMk vnK \u2192 ck.2 \u2208 K \u2192 \u00acG.Adj ck.1 ck.2\nu : V\n\u22a2 u \u2208 \u2191C",
+              "state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\nh : \u2200 (ck : V \u00d7 V), ck.1 \u2208 G.componentComplMk vnK \u2192 ck.2 \u2208 K \u2192 \u00acG.Adj ck.1 ck.2\n\u22a2 \u2200 (x : V), x \u2208 \u2191C",
+              "tactic": "rintro u"
+            },
+            {
+              "annotated_tactic": [
+                "\"by_contra unC\"",
+                "[]"
+              ],
+              "state_after": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\nh : \u2200 (ck : V \u00d7 V), ck.1 \u2208 G.componentComplMk vnK \u2192 ck.2 \u2208 K \u2192 \u00acG.Adj ck.1 ck.2\nu : V\nunC : u \u2209 \u2191C\n\u22a2 False",
+              "state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\nh : \u2200 (ck : V \u00d7 V), ck.1 \u2208 G.componentComplMk vnK \u2192 ck.2 \u2208 K \u2192 \u00acG.Adj ck.1 ck.2\nu : V\n\u22a2 u \u2208 \u2191C",
+              "tactic": "by_contra unC"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8p\\u27e9 := Gc v u\"",
+                "[]"
+              ],
+              "state_after": "case intro\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\nh : \u2200 (ck : V \u00d7 V), ck.1 \u2208 G.componentComplMk vnK \u2192 ck.2 \u2208 K \u2192 \u00acG.Adj ck.1 ck.2\nu : V\nunC : u \u2209 \u2191C\np : G.Walk v u\n\u22a2 False",
+              "state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\nh : \u2200 (ck : V \u00d7 V), ck.1 \u2208 G.componentComplMk vnK \u2192 ck.2 \u2208 K \u2192 \u00acG.Adj ck.1 ck.2\nu : V\nunC : u \u2209 \u2191C\n\u22a2 False",
+              "tactic": "obtain \u27e8p\u27e9 := Gc v u"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8\\u27e8\\u27e8x, y\\u27e9, xy\\u27e9, -, xC, ynC\\u27e9 :=\\n    p.exists_boundary_dart (C : <a>Set<\\/a> V) (G.componentComplMk_mem vnK) unC\"",
+                "[{\"full_name\":\"Set\",\"def_path\":\"Mathlib\\/Init\\/Set.lean\",\"def_pos\":[47,5],\"def_end_pos\":[47,8]}]"
+              ],
+              "state_after": "case intro.intro.mk.mk.intro.intro\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\nh : \u2200 (ck : V \u00d7 V), ck.1 \u2208 G.componentComplMk vnK \u2192 ck.2 \u2208 K \u2192 \u00acG.Adj ck.1 ck.2\nu : V\nunC : u \u2209 \u2191C\np : G.Walk v u\nx y : V\nxy : G.Adj (x, y).1 (x, y).2\nxC : { toProd := (x, y), adj := xy }.toProd.1 \u2208 \u2191C\nynC : { toProd := (x, y), adj := xy }.toProd.2 \u2209 \u2191C\n\u22a2 False",
+              "state_before": "case intro\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\nh : \u2200 (ck : V \u00d7 V), ck.1 \u2208 G.componentComplMk vnK \u2192 ck.2 \u2208 K \u2192 \u00acG.Adj ck.1 ck.2\nu : V\nunC : u \u2209 \u2191C\np : G.Walk v u\n\u22a2 False",
+              "tactic": "obtain \u27e8\u27e8\u27e8x, y\u27e9, xy\u27e9, -, xC, ynC\u27e9 :=\n  p.exists_boundary_dart (C : Set V) (G.componentComplMk_mem vnK) unC"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact ynC (<a>mem_of_adj<\\/a> x y xC (fun yK : y \\u2208 K => h \\u27e8x, y\\u27e9 xC yK xy) xy)\"",
+                "[{\"full_name\":\"SimpleGraph.ComponentCompl.mem_of_adj\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Ends\\/Defs.lean\",\"def_pos\":[143,9],\"def_end_pos\":[143,19]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case intro.intro.mk.mk.intro.intro\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\nh : \u2200 (ck : V \u00d7 V), ck.1 \u2208 G.componentComplMk vnK \u2192 ck.2 \u2208 K \u2192 \u00acG.Adj ck.1 ck.2\nu : V\nunC : u \u2209 \u2191C\np : G.Walk v u\nx y : V\nxy : G.Adj (x, y).1 (x, y).2\nxC : { toProd := (x, y), adj := xy }.toProd.1 \u2208 \u2191C\nynC : { toProd := (x, y), adj := xy }.toProd.2 \u2209 \u2191C\n\u22a2 False",
+              "tactic": "exact ynC (mem_of_adj x y xC (fun yK : y \u2208 K => h \u27e8x, y\u27e9 xC yK xy) xy)"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact dis \\u27e8hK.choose_spec, this \\u25b8 <a>Set.mem_univ<\\/a> hK.some\\u27e9\"",
+                "[{\"full_name\":\"Set.mem_univ\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Defs.lean\",\"def_pos\":[82,29],\"def_end_pos\":[82,37]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nGc : G.Preconnected\nhK : K.Nonempty\nv : V\nvnK : v \u2209 K\nC : G.ComponentCompl K := G.componentComplMk vnK\ndis : K \u2229 \u2191C \u2286 \u2205 := Set.disjoint_iff.mp (ComponentCompl.disjoint_right C)\nh : \u2200 (ck : V \u00d7 V), ck.1 \u2208 G.componentComplMk vnK \u2192 ck.2 \u2208 K \u2192 \u00acG.Adj ck.1 ck.2\nthis : Set.univ = \u2191C\n\u22a2 False",
+              "tactic": "exact dis \u27e8hK.choose_spec, this \u25b8 Set.mem_univ hK.some\u27e9"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.ComponentCompl.hom_eq_iff_le",
+        "id": "SimpleGraph.ComponentCompl.hom_eq_iff_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            191,
+            85
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean",
+          "full_name": "SimpleGraph.ComponentCompl.hom_eq_iff_le",
+          "start": [
+            189,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'exact \u27e8x, \u27e8xnL, rfl\u27e9, \u27e8fun xK => xnL (h xK), rfl\u27e9\u27e9'",
+        "full_name": "SimpleGraph.ComponentCompl.hom_eq_iff_not_disjoint",
+        "id": "SimpleGraph.ComponentCompl.hom_eq_iff_not_disjoint",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            204,
+            8
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean",
+          "full_name": "SimpleGraph.ComponentCompl.hom_eq_iff_not_disjoint",
+          "start": [
+            194,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Set.not_disjoint_iff<\\/a>]\"",
+                "[{\"full_name\":\"Set.not_disjoint_iff\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[1502,7],\"def_end_pos\":[1502,23]}]"
+              ],
+              "state_after": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : G.ComponentCompl L\nh : K \u2286 L\nD : G.ComponentCompl K\n\u22a2 hom h C = D \u2194 \u2203 x \u2208 \u2191C, x \u2208 \u2191D",
+              "state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : G.ComponentCompl L\nh : K \u2286 L\nD : G.ComponentCompl K\n\u22a2 hom h C = D \u2194 \u00acDisjoint \u2191C \u2191D",
+              "tactic": "rw [Set.not_disjoint_iff]"
+            },
+            {
+              "annotated_tactic": [
+                "\"constructor\"",
+                "[]"
+              ],
+              "state_after": "case mp\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : G.ComponentCompl L\nh : K \u2286 L\nD : G.ComponentCompl K\n\u22a2 hom h C = D \u2192 \u2203 x \u2208 \u2191C, x \u2208 \u2191D\n\ncase mpr\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : G.ComponentCompl L\nh : K \u2286 L\nD : G.ComponentCompl K\n\u22a2 (\u2203 x \u2208 \u2191C, x \u2208 \u2191D) \u2192 hom h C = D",
+              "state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : G.ComponentCompl L\nh : K \u2286 L\nD : G.ComponentCompl K\n\u22a2 hom h C = D \u2194 \u2203 x \u2208 \u2191C, x \u2208 \u2191D",
+              "tactic": "constructor"
+            },
+            {
+              "annotated_tactic": [
+                "\"rintro rfl\"",
+                "[]"
+              ],
+              "state_after": "case mp\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : G.ComponentCompl L\nh : K \u2286 L\n\u22a2 \u2203 x \u2208 \u2191C, x \u2208 \u2191(hom h C)",
+              "state_before": "case mp\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : G.ComponentCompl L\nh : K \u2286 L\nD : G.ComponentCompl K\n\u22a2 hom h C = D \u2192 \u2203 x \u2208 \u2191C, x \u2208 \u2191D",
+              "tactic": "rintro rfl"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine C.ind fun x xnL => ?_\"",
+                "[]"
+              ],
+              "state_after": "case mp\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : G.ComponentCompl L\nh : K \u2286 L\nx : V\nxnL : x \u2209 L\n\u22a2 \u2203 x_1 \u2208 \u2191(G.componentComplMk xnL), x_1 \u2208 \u2191(hom h (G.componentComplMk xnL))",
+              "state_before": "case mp\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : G.ComponentCompl L\nh : K \u2286 L\n\u22a2 \u2203 x \u2208 \u2191C, x \u2208 \u2191(hom h C)",
+              "tactic": "refine C.ind fun x xnL => ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact \\u27e8x, \\u27e8xnL, <a>rfl<\\/a>\\u27e9, \\u27e8fun xK => xnL (h xK), <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]},{\"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 mp\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : G.ComponentCompl L\nh : K \u2286 L\nx : V\nxnL : x \u2209 L\n\u22a2 \u2203 x_1 \u2208 \u2191(G.componentComplMk xnL), x_1 \u2208 \u2191(hom h (G.componentComplMk xnL))",
+              "tactic": "exact \u27e8x, \u27e8xnL, rfl\u27e9, \u27e8fun xK => xnL (h xK), rfl\u27e9\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine C.ind fun x xnL => ?_\"",
+                "[]"
+              ],
+              "state_after": "case mpr\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : G.ComponentCompl L\nh : K \u2286 L\nD : G.ComponentCompl K\nx : V\nxnL : x \u2209 L\n\u22a2 (\u2203 x_1 \u2208 \u2191(G.componentComplMk xnL), x_1 \u2208 \u2191D) \u2192 hom h (G.componentComplMk xnL) = D",
+              "state_before": "case mpr\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : G.ComponentCompl L\nh : K \u2286 L\nD : G.ComponentCompl K\n\u22a2 (\u2203 x \u2208 \u2191C, x \u2208 \u2191D) \u2192 hom h C = D",
+              "tactic": "refine C.ind fun x xnL => ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"rintro \\u27e8x, \\u27e8_, e\\u2081\\u27e9, _, rfl\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "case mpr.intro.intro.intro.intro\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : G.ComponentCompl L\nh : K \u2286 L\nx\u271d : V\nxnL : x\u271d \u2209 L\nx : V\nw\u271d\u00b9 : x \u2209 L\ne\u2081 : G.componentComplMk w\u271d\u00b9 = G.componentComplMk xnL\nw\u271d : x \u2209 K\n\u22a2 hom h (G.componentComplMk xnL) = G.componentComplMk w\u271d",
+              "state_before": "case mpr\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : G.ComponentCompl L\nh : K \u2286 L\nD : G.ComponentCompl K\nx : V\nxnL : x \u2209 L\n\u22a2 (\u2203 x_1 \u2208 \u2191(G.componentComplMk xnL), x_1 \u2208 \u2191D) \u2192 hom h (G.componentComplMk xnL) = D",
+              "tactic": "rintro \u27e8x, \u27e8_, e\u2081\u27e9, _, rfl\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 e\\u2081]\"",
+                "[]"
+              ],
+              "state_after": "case mpr.intro.intro.intro.intro\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : G.ComponentCompl L\nh : K \u2286 L\nx\u271d : V\nxnL : x\u271d \u2209 L\nx : V\nw\u271d\u00b9 : x \u2209 L\ne\u2081 : G.componentComplMk w\u271d\u00b9 = G.componentComplMk xnL\nw\u271d : x \u2209 K\n\u22a2 hom h (G.componentComplMk w\u271d\u00b9) = G.componentComplMk w\u271d",
+              "state_before": "case mpr.intro.intro.intro.intro\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : G.ComponentCompl L\nh : K \u2286 L\nx\u271d : V\nxnL : x\u271d \u2209 L\nx : V\nw\u271d\u00b9 : x \u2209 L\ne\u2081 : G.componentComplMk w\u271d\u00b9 = G.componentComplMk xnL\nw\u271d : x \u2209 K\n\u22a2 hom h (G.componentComplMk xnL) = G.componentComplMk w\u271d",
+              "tactic": "rw [\u2190 e\u2081]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rfl\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case mpr.intro.intro.intro.intro\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : G.ComponentCompl L\nh : K \u2286 L\nx\u271d : V\nxnL : x\u271d \u2209 L\nx : V\nw\u271d\u00b9 : x \u2209 L\ne\u2081 : G.componentComplMk w\u271d\u00b9 = G.componentComplMk xnL\nw\u271d : x \u2209 K\n\u22a2 hom h (G.componentComplMk w\u271d\u00b9) = G.componentComplMk w\u271d",
+              "tactic": "rfl"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.ComponentCompl.hom_infinite",
+        "id": "SimpleGraph.ComponentCompl.hom_infinite",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            226,
+            42
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean",
+          "full_name": "SimpleGraph.ComponentCompl.hom_infinite",
+          "start": [
+            224,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.ComponentCompl.hom_mk",
+        "id": "SimpleGraph.ComponentCompl.hom_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            221,
+            6
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean",
+          "full_name": "SimpleGraph.ComponentCompl.hom_mk",
+          "start": [
+            219,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.ComponentCompl.mem_supp_iff",
+        "id": "SimpleGraph.ComponentCompl.mem_supp_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            64,
+            10
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean",
+          "full_name": "SimpleGraph.ComponentCompl.mem_supp_iff",
+          "start": [
+            62,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.ComponentCompl.not_mem_of_mem",
+        "id": "SimpleGraph.ComponentCompl.not_mem_of_mem",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            131,
+            48
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean",
+          "full_name": "SimpleGraph.ComponentCompl.not_mem_of_mem",
+          "start": [
+            130,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.ComponentCompl.supp_inj",
+        "id": "SimpleGraph.ComponentCompl.supp_inj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            53,
+            39
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean",
+          "full_name": "SimpleGraph.ComponentCompl.supp_inj",
+          "start": [
+            52,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.componentComplMk_mem_hom",
+        "id": "SimpleGraph.componentComplMk_mem_hom",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            186,
+            67
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean",
+          "full_name": "SimpleGraph.componentComplMk_mem_hom",
+          "start": [
+            183,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'apply nonempty_sections_of_finite_inverse_system G.componentComplFunctor'",
+        "full_name": "SimpleGraph.nonempty_ends_of_infinite",
+        "id": "SimpleGraph.nonempty_ends_of_infinite",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            48,
+            75
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Ends/Properties.lean",
+          "full_name": "SimpleGraph.nonempty_ends_of_infinite",
+          "start": [
+            44,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"classical\\n  apply <a>nonempty_sections_of_finite_inverse_system<\\/a> G.componentComplFunctor\"",
+                "[{\"full_name\":\"nonempty_sections_of_finite_inverse_system\",\"def_path\":\"Mathlib\\/CategoryTheory\\/CofilteredSystem.lean\",\"def_pos\":[114,9],\"def_end_pos\":[114,51]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type\nG : SimpleGraph V\ninst\u271d\u00b2 : G.LocallyFinite\ninst\u271d\u00b9 : Fact G.Preconnected\ninst\u271d : Infinite V\n\u22a2 G.end.Nonempty",
+              "tactic": "classical\napply nonempty_sections_of_finite_inverse_system G.componentComplFunctor"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>nonempty_sections_of_finite_inverse_system<\\/a> G.componentComplFunctor\"",
+                "[{\"full_name\":\"nonempty_sections_of_finite_inverse_system\",\"def_path\":\"Mathlib\\/CategoryTheory\\/CofilteredSystem.lean\",\"def_pos\":[114,9],\"def_end_pos\":[114,51]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type\nG : SimpleGraph V\ninst\u271d\u00b2 : G.LocallyFinite\ninst\u271d\u00b9 : Fact G.Preconnected\ninst\u271d : Infinite V\n\u22a2 G.end.Nonempty",
+              "tactic": "apply nonempty_sections_of_finite_inverse_system G.componentComplFunctor"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Ends/Properties.lean"
+      }
+    ],
+    "input_proofs": 24,
+    "input_units": 2,
+    "proofs": 13,
+    "published_proofs": 12,
+    "published_transitions": 30,
+    "replay_failures": [],
+    "transitions": 40,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean",
+        "proof_id": "mathlib:SimpleGraph.ComponentCompl.infinite_iff_in_all_ranges",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              242,
+              74
+            ],
+            "file_path": "Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean",
+            "full_name": "SimpleGraph.ComponentCompl.infinite_iff_in_all_ranges",
+            "start": [
+              229,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"constructor\"",
+                  "[]"
+                ],
+                "state_after": "case mp\nV : Type u\nG : SimpleGraph V\nK\u271d L L' M : Set V\nK : Finset V\nC : G.ComponentCompl \u2191K\n\u22a2 C.supp.Infinite \u2192 \u2200 (L : Finset V) (h : K \u2286 L), \u2203 D, hom h D = C\n\ncase mpr\nV : Type u\nG : SimpleGraph V\nK\u271d L L' M : Set V\nK : Finset V\nC : G.ComponentCompl \u2191K\n\u22a2 (\u2200 (L : Finset V) (h : K \u2286 L), \u2203 D, hom h D = C) \u2192 C.supp.Infinite",
+                "state_before": "V : Type u\nG : SimpleGraph V\nK\u271d L L' M : Set V\nK : Finset V\nC : G.ComponentCompl \u2191K\n\u22a2 C.supp.Infinite \u2194 \u2200 (L : Finset V) (h : K \u2286 L), \u2203 D, hom h D = C",
+                "tactic": "constructor"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rintro Cinf L h\"",
+                  "[]"
+                ],
+                "state_after": "case mp\nV : Type u\nG : SimpleGraph V\nK\u271d L\u271d L' M : Set V\nK : Finset V\nC : G.ComponentCompl \u2191K\nCinf : C.supp.Infinite\nL : Finset V\nh : K \u2286 L\n\u22a2 \u2203 D, hom h D = C",
+                "state_before": "case mp\nV : Type u\nG : SimpleGraph V\nK\u271d L L' M : Set V\nK : Finset V\nC : G.ComponentCompl \u2191K\n\u22a2 C.supp.Infinite \u2192 \u2200 (L : Finset V) (h : K \u2286 L), \u2203 D, hom h D = C",
+                "tactic": "rintro Cinf L h"
+              },
+              {
+                "annotated_tactic": [
+                  "\"obtain \\u27e8v, \\u27e8vK, rfl\\u27e9, vL\\u27e9 := <a>Set.Infinite.nonempty<\\/a> (<a>Set.Infinite.diff<\\/a> Cinf L.finite_toSet)\"",
+                  "[{\"full_name\":\"Set.Infinite.nonempty\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Finite.lean\",\"def_pos\":[843,19],\"def_end_pos\":[843,36]},{\"full_name\":\"Set.Infinite.diff\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Finite.lean\",\"def_pos\":[1381,9],\"def_end_pos\":[1381,22]}]"
+                ],
+                "state_after": "case mp.intro.intro.intro\nV : Type u\nG : SimpleGraph V\nK\u271d L\u271d L' M : Set V\nK L : Finset V\nh : K \u2286 L\nv : V\nvL : v \u2209 \u2191L\nvK : v \u2209 \u2191K\nCinf : (G.componentComplMk vK).supp.Infinite\n\u22a2 \u2203 D, hom h D = G.componentComplMk vK",
+                "state_before": "case mp\nV : Type u\nG : SimpleGraph V\nK\u271d L\u271d L' M : Set V\nK : Finset V\nC : G.ComponentCompl \u2191K\nCinf : C.supp.Infinite\nL : Finset V\nh : K \u2286 L\n\u22a2 \u2203 D, hom h D = C",
+                "tactic": "obtain \u27e8v, \u27e8vK, rfl\u27e9, vL\u27e9 := Set.Infinite.nonempty (Set.Infinite.diff Cinf L.finite_toSet)"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact \\u27e8<a>componentComplMk<\\/a> _ vL, <a>rfl<\\/a>\\u27e9\"",
+                  "[{\"full_name\":\"SimpleGraph.componentComplMk\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Ends\\/Defs.lean\",\"def_pos\":[34,8],\"def_end_pos\":[34,24]},{\"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 mp.intro.intro.intro\nV : Type u\nG : SimpleGraph V\nK\u271d L\u271d L' M : Set V\nK L : Finset V\nh : K \u2286 L\nv : V\nvL : v \u2209 \u2191L\nvK : v \u2209 \u2191K\nCinf : (G.componentComplMk vK).supp.Infinite\n\u22a2 \u2203 D, hom h D = G.componentComplMk vK",
+                "tactic": "exact \u27e8componentComplMk _ vL, rfl\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rintro h Cfin\"",
+                  "[]"
+                ],
+                "state_after": "case mpr\nV : Type u\nG : SimpleGraph V\nK\u271d L L' M : Set V\nK : Finset V\nC : G.ComponentCompl \u2191K\nh : \u2200 (L : Finset V) (h : K \u2286 L), \u2203 D, hom h D = C\nCfin : C.supp.Finite\n\u22a2 False",
+                "state_before": "case mpr\nV : Type u\nG : SimpleGraph V\nK\u271d L L' M : Set V\nK : Finset V\nC : G.ComponentCompl \u2191K\n\u22a2 (\u2200 (L : Finset V) (h : K \u2286 L), \u2203 D, hom h D = C) \u2192 C.supp.Infinite",
+                "tactic": "rintro h Cfin"
+              },
+              {
+                "annotated_tactic": [
+                  "\"obtain \\u27e8D, e\\u27e9 := h (K \\u222a Cfin.toFinset) <a>Finset.subset_union_left<\\/a>\"",
+                  "[{\"full_name\":\"Finset.subset_union_left\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[1438,9],\"def_end_pos\":[1438,26]}]"
+                ],
+                "state_after": "case mpr.intro\nV : Type u\nG : SimpleGraph V\nK\u271d L L' M : Set V\nK : Finset V\nC : G.ComponentCompl \u2191K\nh : \u2200 (L : Finset V) (h : K \u2286 L), \u2203 D, hom h D = C\nCfin : C.supp.Finite\nD : G.ComponentCompl \u2191(K \u222a Cfin.toFinset)\ne : hom \u22ef D = C\n\u22a2 False",
+                "state_before": "case mpr\nV : Type u\nG : SimpleGraph V\nK\u271d L L' M : Set V\nK : Finset V\nC : G.ComponentCompl \u2191K\nh : \u2200 (L : Finset V) (h : K \u2286 L), \u2203 D, hom h D = C\nCfin : C.supp.Finite\n\u22a2 False",
+                "tactic": "obtain \u27e8D, e\u27e9 := h (K \u222a Cfin.toFinset) Finset.subset_union_left"
+              },
+              {
+                "annotated_tactic": [
+                  "\"obtain \\u27e8v, vD\\u27e9 := D.nonempty\"",
+                  "[]"
+                ],
+                "state_after": "case mpr.intro.intro\nV : Type u\nG : SimpleGraph V\nK\u271d L L' M : Set V\nK : Finset V\nC : G.ComponentCompl \u2191K\nh : \u2200 (L : Finset V) (h : K \u2286 L), \u2203 D, hom h D = C\nCfin : C.supp.Finite\nD : G.ComponentCompl \u2191(K \u222a Cfin.toFinset)\ne : hom \u22ef D = C\nv : V\nvD : v \u2208 \u2191D\n\u22a2 False",
+                "state_before": "case mpr.intro\nV : Type u\nG : SimpleGraph V\nK\u271d L L' M : Set V\nK : Finset V\nC : G.ComponentCompl \u2191K\nh : \u2200 (L : Finset V) (h : K \u2286 L), \u2203 D, hom h D = C\nCfin : C.supp.Finite\nD : G.ComponentCompl \u2191(K \u222a Cfin.toFinset)\ne : hom \u22ef D = C\n\u22a2 False",
+                "tactic": "obtain \u27e8v, vD\u27e9 := D.nonempty"
+              },
+              {
+                "annotated_tactic": [
+                  "\"let Ddis := D.disjoint_right\"",
+                  "[]"
+                ],
+                "state_after": "case mpr.intro.intro\nV : Type u\nG : SimpleGraph V\nK\u271d L L' M : Set V\nK : Finset V\nC : G.ComponentCompl \u2191K\nh : \u2200 (L : Finset V) (h : K \u2286 L), \u2203 D, hom h D = C\nCfin : C.supp.Finite\nD : G.ComponentCompl \u2191(K \u222a Cfin.toFinset)\ne : hom \u22ef D = C\nv : V\nvD : v \u2208 \u2191D\nDdis : Disjoint \u2191(K \u222a Cfin.toFinset) \u2191D := ComponentCompl.disjoint_right D\n\u22a2 False",
+                "state_before": "case mpr.intro.intro\nV : Type u\nG : SimpleGraph V\nK\u271d L L' M : Set V\nK : Finset V\nC : G.ComponentCompl \u2191K\nh : \u2200 (L : Finset V) (h : K \u2286 L), \u2203 D, hom h D = C\nCfin : C.supp.Finite\nD : G.ComponentCompl \u2191(K \u222a Cfin.toFinset)\ne : hom \u22ef D = C\nv : V\nvD : v \u2208 \u2191D\n\u22a2 False",
+                "tactic": "let Ddis := D.disjoint_right"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp_rw [<a>Finset.coe_union<\\/a>, <a>Set.Finite.coe_toFinset<\\/a>, <a>Set.disjoint_union_left<\\/a>,\\n        <a>Set.disjoint_iff<\\/a>] at Ddis\"",
+                  "[{\"full_name\":\"Finset.coe_union\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[1430,9],\"def_end_pos\":[1430,18]},{\"full_name\":\"Set.Finite.coe_toFinset\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Finite.lean\",\"def_pos\":[171,19],\"def_end_pos\":[171,31]},{\"full_name\":\"Set.disjoint_union_left\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[1533,7],\"def_end_pos\":[1533,26]},{\"full_name\":\"Set.disjoint_iff\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[1483,19],\"def_end_pos\":[1483,31]}]"
+                ],
+                "state_after": "case mpr.intro.intro\nV : Type u\nG : SimpleGraph V\nK\u271d L L' M : Set V\nK : Finset V\nC : G.ComponentCompl \u2191K\nh : \u2200 (L : Finset V) (h : K \u2286 L), \u2203 D, hom h D = C\nCfin : C.supp.Finite\nD : G.ComponentCompl \u2191(K \u222a Cfin.toFinset)\ne : hom \u22ef D = C\nv : V\nvD : v \u2208 \u2191D\nDdis : \u2191K \u2229 \u2191D \u2286 \u2205 \u2227 C.supp \u2229 \u2191D \u2286 \u2205\n\u22a2 False",
+                "state_before": "case mpr.intro.intro\nV : Type u\nG : SimpleGraph V\nK\u271d L L' M : Set V\nK : Finset V\nC : G.ComponentCompl \u2191K\nh : \u2200 (L : Finset V) (h : K \u2286 L), \u2203 D, hom h D = C\nCfin : C.supp.Finite\nD : G.ComponentCompl \u2191(K \u222a Cfin.toFinset)\ne : hom \u22ef D = C\nv : V\nvD : v \u2208 \u2191D\nDdis : Disjoint \u2191(K \u222a Cfin.toFinset) \u2191D := ComponentCompl.disjoint_right D\n\u22a2 False",
+                "tactic": "simp_rw [Finset.coe_union, Set.Finite.coe_toFinset, Set.disjoint_union_left,\n  Set.disjoint_iff] at Ddis"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact Ddis.right \\u27e8(<a>ComponentCompl.hom_eq_iff_le<\\/a> _ _ _).<a>mp<\\/a> e vD, vD\\u27e9\"",
+                  "[{\"full_name\":\"SimpleGraph.ComponentCompl.hom_eq_iff_le\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Ends\\/Defs.lean\",\"def_pos\":[189,9],\"def_end_pos\":[189,22]},{\"full_name\":\"Iff.mp\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[118,3],\"def_end_pos\":[118,5]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case mpr.intro.intro\nV : Type u\nG : SimpleGraph V\nK\u271d L L' M : Set V\nK : Finset V\nC : G.ComponentCompl \u2191K\nh : \u2200 (L : Finset V) (h : K \u2286 L), \u2203 D, hom h D = C\nCfin : C.supp.Finite\nD : G.ComponentCompl \u2191(K \u222a Cfin.toFinset)\ne : hom \u22ef D = C\nv : V\nvD : v \u2208 \u2191D\nDdis : \u2191K \u2229 \u2191D \u2286 \u2205 \u2227 C.supp \u2229 \u2191D \u2286 \u2205\n\u22a2 False",
+                "tactic": "exact Ddis.right \u27e8(ComponentCompl.hom_eq_iff_le _ _ _).mp e vD, vD\u27e9"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "SimpleGraph.ComponentCompl.infinite_iff_in_all_ranges"
+      }
+    ],
+    "validation_rejected_proofs": 1,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000837-0000-7d253771160a14b4.parquet",
+      "sha256": "7d253771160a14b40c46b68e49d00c21c732315b47a2d86e1f538fd745f68c7f",
+      "bytes": 90793,
+      "rows": 25,
+      "revision": "70b6b795247ac9d70fb829e06dbcf94288c16b02"
+    },
+    {
+      "path": "data/dev/mathlib-000837-0000-73190a18bb727f31.parquet",
+      "sha256": "73190a18bb727f31b2621b4a5636622fb9cbe8cba1ef88c54d2898d776499f58",
+      "bytes": 39848,
+      "rows": 2,
+      "revision": "70b6b795247ac9d70fb829e06dbcf94288c16b02"
+    },
+    {
+      "path": "data/internal_test/mathlib-000837-0000-66ccec5885ce052b.parquet",
+      "sha256": "66ccec5885ce052b1cc4cf15e2018356e6f4fd09013a3204a6d8506682f861c9",
+      "bytes": 48204,
+      "rows": 3,
+      "revision": "70b6b795247ac9d70fb829e06dbcf94288c16b02"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:SimpleGraph.ComponentCompl.disjoint_right",
+    "mathlib:SimpleGraph.ComponentCompl.hom_refl",
+    "mathlib:SimpleGraph.ComponentCompl.hom_trans",
+    "mathlib:SimpleGraph.ComponentCompl.ind",
+    "mathlib:SimpleGraph.ComponentCompl.mem_of_adj",
+    "mathlib:SimpleGraph.ComponentCompl.pairwise_disjoint",
+    "mathlib:SimpleGraph.ComponentCompl.subset_hom",
+    "mathlib:SimpleGraph.ComponentCompl.supp_injective",
+    "mathlib:SimpleGraph.componentComplMk_eq_of_adj",
+    "mathlib:SimpleGraph.end_componentCompl_infinite",
+    "mathlib:SimpleGraph.end_hom_mk_of_mk",
+    "mathlib:SimpleGraph.infinite_iff_in_eventualRange"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean\",null,null,\"SimpleGraph.ComponentCompl.disjoint_right\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean\",null,null,\"SimpleGraph.ComponentCompl.hom_refl\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean\",null,null,\"SimpleGraph.ComponentCompl.hom_trans\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean\",null,null,\"SimpleGraph.ComponentCompl.ind\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean\",null,null,\"SimpleGraph.ComponentCompl.mem_of_adj\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean\",null,null,\"SimpleGraph.ComponentCompl.pairwise_disjoint\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean\",null,null,\"SimpleGraph.ComponentCompl.subset_hom\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean\",null,null,\"SimpleGraph.ComponentCompl.supp_injective\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean\",null,null,\"SimpleGraph.componentComplMk_eq_of_adj\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean\",null,null,\"SimpleGraph.end_hom_mk_of_mk\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean\",null,null,\"SimpleGraph.infinite_iff_in_eventualRange\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Ends/Properties.lean\",null,null,\"SimpleGraph.end_componentCompl_infinite\"]"
+  ]
+}

manifests/batches/mathlib/000839.json

@@ -0,0 +1,563 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000839",
+  "batch_fingerprint": "cdd6fc14cf8629dc67b4c567f7bfbab549e1e85dfcce04dc530ca3fdb3ef68d6",
+  "evidence": {
+    "batch_fingerprint": "cdd6fc14cf8629dc67b4c567f7bfbab549e1e85dfcce04dc530ca3fdb3ef68d6",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "no internal trace for tactic 'rfl'",
+        "full_name": "SimpleGraph.IsHamiltonian.connected",
+        "id": "SimpleGraph.IsHamiltonian.connected",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            136,
+            92
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean",
+          "full_name": "SimpleGraph.IsHamiltonian.connected",
+          "start": [
+            127,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"obtain rfl | hab := <a>eq_or_ne<\\/a> a b\"",
+                "[{\"full_name\":\"eq_or_ne\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[212,9],\"def_end_pos\":[212,17]}]"
+              ],
+              "state_after": "case inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na\u271d b : \u03b1\np : G.Walk a\u271d b\nhG : G.IsHamiltonian\na : \u03b1\n\u22a2 G.Reachable a a\n\ncase inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na\u271d b\u271d : \u03b1\np : G.Walk a\u271d b\u271d\nhG : G.IsHamiltonian\na b : \u03b1\nhab : a \u2260 b\n\u22a2 G.Reachable a b",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na\u271d b\u271d : \u03b1\np : G.Walk a\u271d b\u271d\nhG : G.IsHamiltonian\na b : \u03b1\n\u22a2 G.Reachable a b",
+              "tactic": "obtain rfl | hab := eq_or_ne a b"
+            },
+            {
+              "annotated_tactic": [
+                "\"have : <a>Nontrivial<\\/a> \\u03b1 := \\u27e8a, b, hab\\u27e9\"",
+                "[{\"full_name\":\"Nontrivial\",\"def_path\":\"Mathlib\\/Logic\\/Nontrivial\\/Defs.lean\",\"def_pos\":[31,7],\"def_end_pos\":[31,17]}]"
+              ],
+              "state_after": "case inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na\u271d b\u271d : \u03b1\np : G.Walk a\u271d b\u271d\nhG : G.IsHamiltonian\na b : \u03b1\nhab : a \u2260 b\nthis : Nontrivial \u03b1\n\u22a2 G.Reachable a b",
+              "state_before": "case inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na\u271d b\u271d : \u03b1\np : G.Walk a\u271d b\u271d\nhG : G.IsHamiltonian\na b : \u03b1\nhab : a \u2260 b\n\u22a2 G.Reachable a b",
+              "tactic": "have : Nontrivial \u03b1 := \u27e8a, b, hab\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8_, p, hp\\u27e9 := hG Fintype.one_lt_card.ne'\"",
+                "[]"
+              ],
+              "state_after": "case inr.intro.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na\u271d b\u271d : \u03b1\np\u271d : G.Walk a\u271d b\u271d\nhG : G.IsHamiltonian\na b : \u03b1\nhab : a \u2260 b\nthis : Nontrivial \u03b1\nw\u271d : \u03b1\np : G.Walk w\u271d w\u271d\nhp : p.IsHamiltonianCycle\n\u22a2 G.Reachable a b",
+              "state_before": "case inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na\u271d b\u271d : \u03b1\np : G.Walk a\u271d b\u271d\nhG : G.IsHamiltonian\na b : \u03b1\nhab : a \u2260 b\nthis : Nontrivial \u03b1\n\u22a2 G.Reachable a b",
+              "tactic": "obtain \u27e8_, p, hp\u27e9 := hG Fintype.one_lt_card.ne'"
+            },
+            {
+              "annotated_tactic": [
+                "\"have a_mem := hp.mem_support a\"",
+                "[]"
+              ],
+              "state_after": "case inr.intro.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na\u271d b\u271d : \u03b1\np\u271d : G.Walk a\u271d b\u271d\nhG : G.IsHamiltonian\na b : \u03b1\nhab : a \u2260 b\nthis : Nontrivial \u03b1\nw\u271d : \u03b1\np : G.Walk w\u271d w\u271d\nhp : p.IsHamiltonianCycle\na_mem : a \u2208 p.support\n\u22a2 G.Reachable a b",
+              "state_before": "case inr.intro.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na\u271d b\u271d : \u03b1\np\u271d : G.Walk a\u271d b\u271d\nhG : G.IsHamiltonian\na b : \u03b1\nhab : a \u2260 b\nthis : Nontrivial \u03b1\nw\u271d : \u03b1\np : G.Walk w\u271d w\u271d\nhp : p.IsHamiltonianCycle\n\u22a2 G.Reachable a b",
+              "tactic": "have a_mem := hp.mem_support a"
+            },
+            {
+              "annotated_tactic": [
+                "\"have b_mem := hp.mem_support b\"",
+                "[]"
+              ],
+              "state_after": "case inr.intro.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na\u271d b\u271d : \u03b1\np\u271d : G.Walk a\u271d b\u271d\nhG : G.IsHamiltonian\na b : \u03b1\nhab : a \u2260 b\nthis : Nontrivial \u03b1\nw\u271d : \u03b1\np : G.Walk w\u271d w\u271d\nhp : p.IsHamiltonianCycle\na_mem : a \u2208 p.support\nb_mem : b \u2208 p.support\n\u22a2 G.Reachable a b",
+              "state_before": "case inr.intro.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na\u271d b\u271d : \u03b1\np\u271d : G.Walk a\u271d b\u271d\nhG : G.IsHamiltonian\na b : \u03b1\nhab : a \u2260 b\nthis : Nontrivial \u03b1\nw\u271d : \u03b1\np : G.Walk w\u271d w\u271d\nhp : p.IsHamiltonianCycle\na_mem : a \u2208 p.support\n\u22a2 G.Reachable a b",
+              "tactic": "have b_mem := hp.mem_support b"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact ((p.takeUntil a a_mem).reverse.append $ p.takeUntil b b_mem).<a>reachable<\\/a>\"",
+                "[{\"full_name\":\"SimpleGraph.Walk.reachable\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Connectivity.lean\",\"def_pos\":[2013,19],\"def_end_pos\":[2013,33]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inr.intro.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na\u271d b\u271d : \u03b1\np\u271d : G.Walk a\u271d b\u271d\nhG : G.IsHamiltonian\na b : \u03b1\nhab : a \u2260 b\nthis : Nontrivial \u03b1\nw\u271d : \u03b1\np : G.Walk w\u271d w\u271d\nhp : p.IsHamiltonianCycle\na_mem : a \u2208 p.support\nb_mem : b \u2208 p.support\n\u22a2 G.Reachable a b",
+              "tactic": "exact ((p.takeUntil a a_mem).reverse.append $ p.takeUntil b b_mem).reachable"
+            },
+            {
+              "annotated_tactic": [
+                "\"rfl\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na\u271d b : \u03b1\np : G.Walk a\u271d b\nhG : G.IsHamiltonian\na : \u03b1\n\u22a2 G.Reachable a a",
+              "tactic": "rfl"
+            },
+            {
+              "annotated_tactic": [
+                "\"simpa using hG $ by simp [@<a>Fintype.card_eq_zero<\\/a>]\"",
+                "[{\"full_name\":\"Fintype.card_eq_zero\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[541,17],\"def_end_pos\":[541,29]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na b : \u03b1\np : G.Walk a b\nhG : G.IsHamiltonian\nx\u271d : IsEmpty \u03b1\n\u22a2 False",
+              "tactic": "simpa using hG $ by simp [@Fintype.card_eq_zero]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [@<a>Fintype.card_eq_zero<\\/a>]\"",
+                "[{\"full_name\":\"Fintype.card_eq_zero\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[541,17],\"def_end_pos\":[541,29]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na b : \u03b1\np : G.Walk a b\nhG : G.IsHamiltonian\nx\u271d : IsEmpty \u03b1\n\u22a2 Fintype.card \u03b1 \u2260 1",
+              "tactic": "simp [@Fintype.card_eq_zero]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.IsHamiltonian.mono",
+        "id": "SimpleGraph.IsHamiltonian.mono",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            125,
+            82
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean",
+          "full_name": "SimpleGraph.IsHamiltonian.mono",
+          "start": [
+            123,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.Walk.IsHamiltonian.isPath",
+        "id": "SimpleGraph.Walk.IsHamiltonian.isPath",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            54,
+            68
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean",
+          "full_name": "SimpleGraph.Walk.IsHamiltonian.isPath",
+          "start": [
+            52,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.Walk.IsHamiltonianCycle.isCycle",
+        "id": "SimpleGraph.Walk.IsHamiltonianCycle.isCycle",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            71,
+            15
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean",
+          "full_name": "SimpleGraph.Walk.IsHamiltonianCycle.isCycle",
+          "start": [
+            70,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'cases hp.ne_nil rfl'",
+        "full_name": "SimpleGraph.Walk.IsHamiltonianCycle.map",
+        "id": "SimpleGraph.Walk.IsHamiltonianCycle.map",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            85,
+            34
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean",
+          "full_name": "SimpleGraph.Walk.IsHamiltonianCycle.map",
+          "start": [
+            73,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>IsHamiltonian<\\/a>, <a>support_tail<\\/a>, <a>support_map<\\/a>, <a>ne_eq<\\/a>, <a>List.map_eq_nil<\\/a>, <a>support_ne_nil<\\/a>,\\n      <a>not_false_eq_true<\\/a>, <a>List.count_tail<\\/a>, hf.surjective.forall, hf.injective,\\n      <a>List.count_map_of_injective<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.Walk.IsHamiltonian\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Hamiltonian.lean\",\"def_pos\":[32,5],\"def_end_pos\":[32,18]},{\"full_name\":\"SimpleGraph.Walk.support_tail\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Connectivity.lean\",\"def_pos\":[934,15],\"def_end_pos\":[934,27]},{\"full_name\":\"SimpleGraph.Walk.support_map\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Connectivity.lean\",\"def_pos\":[1661,9],\"def_end_pos\":[1661,20]},{\"full_name\":\"ne_eq\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[89,17],\"def_end_pos\":[89,22]},{\"full_name\":\"List.map_eq_nil\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/List\\/Lemmas.lean\",\"def_pos\":[769,17],\"def_end_pos\":[769,27]},{\"full_name\":\"SimpleGraph.Walk.support_ne_nil\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Connectivity.lean\",\"def_pos\":[579,9],\"def_end_pos\":[579,23]},{\"full_name\":\"not_false_eq_true\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[134,17],\"def_end_pos\":[134,34]},{\"full_name\":\"List.count_tail\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Data\\/List\\/Count.lean\",\"def_pos\":[146,9],\"def_end_pos\":[146,19]},{\"full_name\":\"List.count_map_of_injective\",\"def_path\":\"Mathlib\\/Data\\/List\\/Count.lean\",\"def_pos\":[150,9],\"def_end_pos\":[150,31]}]"
+              ],
+              "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na b : \u03b1\np\u271d : G.Walk a b\np : G.Walk a a\nH : SimpleGraph \u03b2\nf : G \u2192g H\nhf : Bijective \u21d1f\nhp : p.IsHamiltonianCycle\n\u22a2 \u2200 (x : \u03b1), (List.count x p.support - if f x = (List.map (\u21d1f) p.support).head \u22ef then 1 else 0) = 1",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na b : \u03b1\np\u271d : G.Walk a b\np : G.Walk a a\nH : SimpleGraph \u03b2\nf : G \u2192g H\nhf : Bijective \u21d1f\nhp : p.IsHamiltonianCycle\n\u22a2 ((Walk.map f p).tail \u22ef).IsHamiltonian",
+              "tactic": "simp only [IsHamiltonian, support_tail, support_map, ne_eq, List.map_eq_nil, support_ne_nil,\n  not_false_eq_true, List.count_tail, hf.surjective.forall, hf.injective,\n  List.count_map_of_injective]"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro x\"",
+                "[]"
+              ],
+              "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na b : \u03b1\np\u271d : G.Walk a b\np : G.Walk a a\nH : SimpleGraph \u03b2\nf : G \u2192g H\nhf : Bijective \u21d1f\nhp : p.IsHamiltonianCycle\nx : \u03b1\n\u22a2 (List.count x p.support - if f x = (List.map (\u21d1f) p.support).head \u22ef then 1 else 0) = 1",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na b : \u03b1\np\u271d : G.Walk a b\np : G.Walk a a\nH : SimpleGraph \u03b2\nf : G \u2192g H\nhf : Bijective \u21d1f\nhp : p.IsHamiltonianCycle\n\u22a2 \u2200 (x : \u03b1), (List.count x p.support - if f x = (List.map (\u21d1f) p.support).head \u22ef then 1 else 0) = 1",
+              "tactic": "intro x"
+            },
+            {
+              "annotated_tactic": [
+                "\"rcases p with (_ | \\u27e8y, p\\u27e9)\"",
+                "[]"
+              ],
+              "state_after": "case nil\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na b : \u03b1\np : G.Walk a b\nH : SimpleGraph \u03b2\nf : G \u2192g H\nhf : Bijective \u21d1f\nx : \u03b1\nhp : nil.IsHamiltonianCycle\n\u22a2 (List.count x nil.support - if f x = (List.map (\u21d1f) nil.support).head \u22ef then 1 else 0) = 1\n\ncase cons\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na b : \u03b1\np\u271d : G.Walk a b\nH : SimpleGraph \u03b2\nf : G \u2192g H\nhf : Bijective \u21d1f\nx v\u271d : \u03b1\ny : G.Adj a v\u271d\np : G.Walk v\u271d a\nhp : (cons y p).IsHamiltonianCycle\n\u22a2 (List.count x (cons y p).support - if f x = (List.map (\u21d1f) (cons y p).support).head \u22ef then 1 else 0) = 1",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na b : \u03b1\np\u271d : G.Walk a b\np : G.Walk a a\nH : SimpleGraph \u03b2\nf : G \u2192g H\nhf : Bijective \u21d1f\nhp : p.IsHamiltonianCycle\nx : \u03b1\n\u22a2 (List.count x p.support - if f x = (List.map (\u21d1f) p.support).head \u22ef then 1 else 0) = 1",
+              "tactic": "rcases p with (_ | \u27e8y, p\u27e9)"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>support_cons<\\/a>, <a>List.count_cons<\\/a>, <a>List.map_cons<\\/a>, <a>List.head_cons<\\/a>, hf.injective.eq_iff,\\n      <a>add_tsub_cancel_right<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.Walk.support_cons\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Connectivity.lean\",\"def_pos\":[551,9],\"def_end_pos\":[551,21]},{\"full_name\":\"List.count_cons\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Data\\/List\\/Count.lean\",\"def_pos\":[136,9],\"def_end_pos\":[136,19]},{\"full_name\":\"List.map_cons\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/List\\/Basic.lean\",\"def_pos\":[366,17],\"def_end_pos\":[366,25]},{\"full_name\":\"List.head_cons\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/List\\/Basic.lean\",\"def_pos\":[286,17],\"def_end_pos\":[286,26]},{\"full_name\":\"add_tsub_cancel_right\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Sub\\/Defs.lean\",\"def_pos\":[356,9],\"def_end_pos\":[356,30]}]"
+              ],
+              "state_after": "case cons\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na b : \u03b1\np\u271d : G.Walk a b\nH : SimpleGraph \u03b2\nf : G \u2192g H\nhf : Bijective \u21d1f\nx v\u271d : \u03b1\ny : G.Adj a v\u271d\np : G.Walk v\u271d a\nhp : (cons y p).IsHamiltonianCycle\n\u22a2 List.count x p.support = 1",
+              "state_before": "case cons\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na b : \u03b1\np\u271d : G.Walk a b\nH : SimpleGraph \u03b2\nf : G \u2192g H\nhf : Bijective \u21d1f\nx v\u271d : \u03b1\ny : G.Adj a v\u271d\np : G.Walk v\u271d a\nhp : (cons y p).IsHamiltonianCycle\n\u22a2 (List.count x (cons y p).support - if f x = (List.map (\u21d1f) (cons y p).support).head \u22ef then 1 else 0) = 1",
+              "tactic": "simp only [support_cons, List.count_cons, List.map_cons, List.head_cons, hf.injective.eq_iff,\n  add_tsub_cancel_right]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact hp.isHamiltonian_tail _\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case cons\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na b : \u03b1\np\u271d : G.Walk a b\nH : SimpleGraph \u03b2\nf : G \u2192g H\nhf : Bijective \u21d1f\nx v\u271d : \u03b1\ny : G.Adj a v\u271d\np : G.Walk v\u271d a\nhp : (cons y p).IsHamiltonianCycle\n\u22a2 List.count x p.support = 1",
+              "tactic": "exact hp.isHamiltonian_tail _"
+            },
+            {
+              "annotated_tactic": [
+                "\"cases hp.ne_nil <a>rfl<\\/a>\"",
+                "[{\"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 nil\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b3 : Fintype \u03b1\ninst\u271d\u00b2 : Fintype \u03b2\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableEq \u03b2\nG : SimpleGraph \u03b1\na b : \u03b1\np : G.Walk a b\nH : SimpleGraph \u03b2\nf : G \u2192g H\nhf : Bijective \u21d1f\nx : \u03b1\nhp : nil.IsHamiltonianCycle\n\u22a2 (List.count x nil.support - if f x = (List.map (\u21d1f) nil.support).head \u22ef then 1 else 0) = 1",
+              "tactic": "cases hp.ne_nil rfl"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.Walk.IsHamiltonianCycle.mem_support",
+        "id": "SimpleGraph.Walk.IsHamiltonianCycle.mem_support",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            98,
+            100
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean",
+          "full_name": "SimpleGraph.Walk.IsHamiltonianCycle.mem_support",
+          "start": [
+            96,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.Walk.IsPath.isHamiltonian_iff",
+        "id": "SimpleGraph.Walk.IsPath.isHamiltonian_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            62,
+            45
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean",
+          "full_name": "SimpleGraph.Walk.IsPath.isHamiltonian_iff",
+          "start": [
+            61,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.Walk.IsPath.isHamiltonian_of_mem",
+        "id": "SimpleGraph.Walk.IsPath.isHamiltonian_of_mem",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            59,
+            100
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean",
+          "full_name": "SimpleGraph.Walk.IsPath.isHamiltonian_of_mem",
+          "start": [
+            56,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.Walk.isHamiltonianCycle_isCycle_and_isHamiltonian_tail",
+        "id": "SimpleGraph.Walk.isHamiltonianCycle_isCycle_and_isHamiltonian_tail",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            89,
+            49
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean",
+          "full_name": "SimpleGraph.Walk.isHamiltonianCycle_isCycle_and_isHamiltonian_tail",
+          "start": [
+            87,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean"
+      }
+    ],
+    "input_proofs": 23,
+    "input_units": 2,
+    "proofs": 14,
+    "published_proofs": 12,
+    "published_transitions": 14,
+    "replay_failures": [],
+    "transitions": 26,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Combinatorics/SimpleGraph/Girth.lean",
+        "proof_id": "mathlib:SimpleGraph.exists_girth_eq_length",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              41,
+              22
+            ],
+            "file_path": "Mathlib/Combinatorics/SimpleGraph/Girth.lean",
+            "full_name": "SimpleGraph.exists_girth_eq_length",
+            "start": [
+              34,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"refine \\u27e8?_, fun h \\u21a6 ?_\\u27e9\"",
+                  "[]"
+                ],
+                "state_after": "case refine_1\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\n\u22a2 (\u2203 a w, w.IsCycle \u2227 G.girth = \u2191w.length) \u2192 \u00acG.IsAcyclic\n\ncase refine_2\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\nh : \u00acG.IsAcyclic\n\u22a2 \u2203 a w, w.IsCycle \u2227 G.girth = \u2191w.length",
+                "state_before": "\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\n\u22a2 (\u2203 a w, w.IsCycle \u2227 G.girth = \u2191w.length) \u2194 \u00acG.IsAcyclic",
+                "tactic": "refine \u27e8?_, fun h \u21a6 ?_\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rintro \\u27e8a, w, hw, _\\u27e9 hG\"",
+                  "[]"
+                ],
+                "state_after": "case refine_1.intro.intro.intro\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\na : \u03b1\nw : G.Walk a a\nhw : w.IsCycle\nright\u271d : G.girth = \u2191w.length\nhG : G.IsAcyclic\n\u22a2 False",
+                "state_before": "case refine_1\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\n\u22a2 (\u2203 a w, w.IsCycle \u2227 G.girth = \u2191w.length) \u2192 \u00acG.IsAcyclic",
+                "tactic": "rintro \u27e8a, w, hw, _\u27e9 hG"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact hG _ hw\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case refine_1.intro.intro.intro\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\na : \u03b1\nw : G.Walk a a\nhw : w.IsCycle\nright\u271d : G.girth = \u2191w.length\nhG : G.IsAcyclic\n\u22a2 False",
+                "tactic": "exact hG _ hw"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp_rw [\\u2190 <a>girth_eq_top<\\/a>, \\u2190 Ne.eq_def, <a>girth<\\/a>, <a>iInf_subtype'<\\/a>, <a>iInf_sigma'<\\/a>, <a>ENat.iInf_coe_ne_top<\\/a>,\\n      \\u2190 <a>exists_prop<\\/a>, <a>Subtype.exists'<\\/a>, <a>Sigma.exists'<\\/a>, <a>eq_comm<\\/a>] at h \\u22a2\"",
+                  "[{\"full_name\":\"SimpleGraph.girth_eq_top\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Girth.lean\",\"def_pos\":[27,15],\"def_end_pos\":[27,27]},{\"full_name\":\"SimpleGraph.girth\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Girth.lean\",\"def_pos\":[21,19],\"def_end_pos\":[21,24]},{\"full_name\":\"iInf_subtype'\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[1154,9],\"def_end_pos\":[1154,22]},{\"full_name\":\"iInf_sigma'\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[1519,7],\"def_end_pos\":[1519,18]},{\"full_name\":\"ENat.iInf_coe_ne_top\",\"def_path\":\"Mathlib\\/Data\\/ENat\\/Lattice.lean\",\"def_pos\":[34,7],\"def_end_pos\":[34,22]},{\"full_name\":\"exists_prop\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/PropLemmas.lean\",\"def_pos\":[307,17],\"def_end_pos\":[307,28]},{\"full_name\":\"Subtype.exists'\",\"def_path\":\"Mathlib\\/Data\\/Subtype.lean\",\"def_pos\":[69,19],\"def_end_pos\":[69,26]},{\"full_name\":\"Sigma.exists'\",\"def_path\":\"Mathlib\\/Data\\/Sigma\\/Basic.lean\",\"def_pos\":[104,7],\"def_end_pos\":[104,14]},{\"full_name\":\"eq_comm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[811,9],\"def_end_pos\":[811,16]}]"
+                ],
+                "state_after": "case refine_2\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\nh : Nonempty ((i : \u03b1) \u00d7 Subtype Walk.IsCycle)\n\u22a2 \u2203 x, \u2191(\u2191x.snd).length = \u2a05 x, \u2191(\u2191x.snd).length",
+                "state_before": "case refine_2\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\nh : \u00acG.IsAcyclic\n\u22a2 \u2203 a w, w.IsCycle \u2227 G.girth = \u2191w.length",
+                "tactic": "simp_rw [\u2190 girth_eq_top, \u2190 Ne.eq_def, girth, iInf_subtype', iInf_sigma', ENat.iInf_coe_ne_top,\n  \u2190 exists_prop, Subtype.exists', Sigma.exists', eq_comm] at h \u22a2"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact <a>ciInf_mem<\\/a> _\"",
+                  "[{\"full_name\":\"ciInf_mem\",\"def_path\":\"Mathlib\\/Order\\/ConditionallyCompleteLattice\\/Basic.lean\",\"def_pos\":[1161,9],\"def_end_pos\":[1161,18]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case refine_2\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\nh : Nonempty ((i : \u03b1) \u00d7 Subtype Walk.IsCycle)\n\u22a2 \u2203 x, \u2191(\u2191x.snd).length = \u2a05 x, \u2191(\u2191x.snd).length",
+                "tactic": "exact ciInf_mem _"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "SimpleGraph.exists_girth_eq_length"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Combinatorics/SimpleGraph/Girth.lean",
+        "proof_id": "mathlib:SimpleGraph.three_le_girth",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              50,
+              82
+            ],
+            "file_path": "Mathlib/Combinatorics/SimpleGraph/Girth.lean",
+            "full_name": "SimpleGraph.three_le_girth",
+            "start": [
+              43,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"by_cases h : G.IsAcyclic\"",
+                  "[]"
+                ],
+                "state_after": "case pos\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\nh : G.IsAcyclic\n\u22a2 3 \u2264 G.girth\n\ncase neg\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\nh : \u00acG.IsAcyclic\n\u22a2 3 \u2264 G.girth",
+                "state_before": "\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\n\u22a2 3 \u2264 G.girth",
+                "tactic": "by_cases h : G.IsAcyclic"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [\\u2190 <a>girth_eq_top<\\/a>] at h\"",
+                  "[{\"full_name\":\"SimpleGraph.girth_eq_top\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Girth.lean\",\"def_pos\":[27,15],\"def_end_pos\":[27,27]}]"
+                ],
+                "state_after": "case pos\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\nh : G.girth = \u22a4\n\u22a2 3 \u2264 G.girth",
+                "state_before": "case pos\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\nh : G.IsAcyclic\n\u22a2 3 \u2264 G.girth",
+                "tactic": "rw [\u2190 girth_eq_top] at h"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [h]\"",
+                  "[]"
+                ],
+                "state_after": "case pos\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\nh : G.girth = \u22a4\n\u22a2 3 \u2264 \u22a4",
+                "state_before": "case pos\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\nh : G.girth = \u22a4\n\u22a2 3 \u2264 G.girth",
+                "tactic": "rw [h]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"apply <a>le_top<\\/a>\"",
+                  "[{\"full_name\":\"le_top\",\"def_path\":\"Mathlib\\/Order\\/BoundedOrder.lean\",\"def_pos\":[66,9],\"def_end_pos\":[66,15]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case pos\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\nh : G.girth = \u22a4\n\u22a2 3 \u2264 \u22a4",
+                "tactic": "apply le_top"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [\\u2190 <a>exists_girth_eq_length<\\/a>] at h\"",
+                  "[{\"full_name\":\"SimpleGraph.exists_girth_eq_length\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Girth.lean\",\"def_pos\":[34,7],\"def_end_pos\":[34,29]}]"
+                ],
+                "state_after": "case neg\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\nh : \u2203 a w, w.IsCycle \u2227 G.girth = \u2191w.length\n\u22a2 3 \u2264 G.girth",
+                "state_before": "case neg\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\nh : \u00acG.IsAcyclic\n\u22a2 3 \u2264 G.girth",
+                "tactic": "rw [\u2190 exists_girth_eq_length] at h"
+              },
+              {
+                "annotated_tactic": [
+                  "\"have \\u27e8_, _, _\\u27e9 := h\"",
+                  "[]"
+                ],
+                "state_after": "case neg\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\nh : \u2203 a w, w.IsCycle \u2227 G.girth = \u2191w.length\nw\u271d\u00b9 : \u03b1\nw\u271d : G.Walk w\u271d\u00b9 w\u271d\u00b9\nh\u271d : w\u271d.IsCycle \u2227 G.girth = \u2191w\u271d.length\n\u22a2 3 \u2264 G.girth",
+                "state_before": "case neg\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\nh : \u2203 a w, w.IsCycle \u2227 G.girth = \u2191w.length\n\u22a2 3 \u2264 G.girth",
+                "tactic": "have \u27e8_, _, _\u27e9 := h"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp_all only [<a>Nat.cast_inj<\\/a>, <a>Nat.ofNat_le_cast<\\/a>, <a>Walk.IsCycle.three_le_length<\\/a>]\"",
+                  "[{\"full_name\":\"Nat.cast_inj\",\"def_path\":\"Mathlib\\/Algebra\\/CharZero\\/Defs.lean\",\"def_pos\":[74,9],\"def_end_pos\":[74,17]},{\"full_name\":\"Nat.ofNat_le_cast\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Order.lean\",\"def_pos\":[173,9],\"def_end_pos\":[173,22]},{\"full_name\":\"SimpleGraph.Walk.IsCycle.three_le_length\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Connectivity.lean\",\"def_pos\":[1123,7],\"def_end_pos\":[1123,30]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case neg\n\u03b1 : Type u_1\nG : SimpleGraph \u03b1\nn : \u2115\u221e\nh : \u2203 a w, w.IsCycle \u2227 G.girth = \u2191w.length\nw\u271d\u00b9 : \u03b1\nw\u271d : G.Walk w\u271d\u00b9 w\u271d\u00b9\nh\u271d : w\u271d.IsCycle \u2227 G.girth = \u2191w\u271d.length\n\u22a2 3 \u2264 G.girth",
+                "tactic": "simp_all only [Nat.cast_inj, Nat.ofNat_le_cast, Walk.IsCycle.three_le_length]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "SimpleGraph.three_le_girth"
+      }
+    ],
+    "validation_rejected_proofs": 2,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000839-0000-05c331ed2df9a1e8.parquet",
+      "sha256": "05c331ed2df9a1e80fd1b2fea3aed96735b7376776c8203c2c18db86ec3180bc",
+      "bytes": 59719,
+      "rows": 9,
+      "revision": "70b6b795247ac9d70fb829e06dbcf94288c16b02"
+    },
+    {
+      "path": "data/internal_test/mathlib-000839-0000-9c6fa3e4d8cb80a8.parquet",
+      "sha256": "9c6fa3e4d8cb80a8a7230873b7762fabb916e6e8fa46c4a7d6bea91ecf027e11",
+      "bytes": 46199,
+      "rows": 5,
+      "revision": "70b6b795247ac9d70fb829e06dbcf94288c16b02"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:SimpleGraph.Walk.IsHamiltonian.length_eq",
+    "mathlib:SimpleGraph.Walk.IsHamiltonian.map",
+    "mathlib:SimpleGraph.Walk.IsHamiltonian.mem_support",
+    "mathlib:SimpleGraph.Walk.IsHamiltonian.support_toFinset",
+    "mathlib:SimpleGraph.Walk.IsHamiltonianCycle.count_support_self",
+    "mathlib:SimpleGraph.Walk.IsHamiltonianCycle.length_eq",
+    "mathlib:SimpleGraph.Walk.IsHamiltonianCycle.support_count_of_ne",
+    "mathlib:SimpleGraph.Walk.isHamiltonianCycle_iff_isCycle_and_support_count_tail_eq_one",
+    "mathlib:SimpleGraph.girth_anti",
+    "mathlib:SimpleGraph.girth_bot",
+    "mathlib:SimpleGraph.girth_eq_top",
+    "mathlib:SimpleGraph.le_girth"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Girth.lean\",null,null,\"SimpleGraph.girth_anti\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Girth.lean\",null,null,\"SimpleGraph.girth_bot\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Girth.lean\",null,null,\"SimpleGraph.girth_eq_top\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Girth.lean\",null,null,\"SimpleGraph.le_girth\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean\",null,null,\"SimpleGraph.Walk.IsHamiltonian.length_eq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean\",null,null,\"SimpleGraph.Walk.IsHamiltonian.map\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean\",null,null,\"SimpleGraph.Walk.IsHamiltonian.mem_support\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean\",null,null,\"SimpleGraph.Walk.IsHamiltonian.support_toFinset\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean\",null,null,\"SimpleGraph.Walk.IsHamiltonianCycle.count_support_self\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean\",null,null,\"SimpleGraph.Walk.IsHamiltonianCycle.length_eq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean\",null,null,\"SimpleGraph.Walk.IsHamiltonianCycle.support_count_of_ne\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Hamiltonian.lean\",null,null,\"SimpleGraph.Walk.isHamiltonianCycle_iff_isCycle_and_support_count_tail_eq_one\"]"
+  ]
+}

manifests/batches/mathlib/000840.json

@@ -0,0 +1,848 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000840",
+  "batch_fingerprint": "feb5b71a2a5d9cac7b45bb15615b329b71517d67bcf517886c7fbe4729c345f0",
+  "evidence": {
+    "batch_fingerprint": "feb5b71a2a5d9cac7b45bb15615b329b71517d67bcf517886c7fbe4729c345f0",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.hasseDualIso_apply",
+        "id": "SimpleGraph.hasseDualIso_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            58,
+            6
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Hasse.lean",
+          "full_name": "SimpleGraph.hasseDualIso_apply",
+          "start": [
+            57,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Hasse.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.hasseDualIso_symm_apply",
+        "id": "SimpleGraph.hasseDualIso_symm_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            63,
+            6
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Hasse.lean",
+          "full_name": "SimpleGraph.hasseDualIso_symm_apply",
+          "start": [
+            62,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Hasse.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.hasse_adj",
+        "id": "SimpleGraph.hasse_adj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            48,
+            10
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Hasse.lean",
+          "full_name": "SimpleGraph.hasse_adj",
+          "start": [
+            47,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Hasse.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.pathGraph_connected",
+        "id": "SimpleGraph.pathGraph_connected",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            118,
+            29
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Hasse.lean",
+          "full_name": "SimpleGraph.pathGraph_connected",
+          "start": [
+            117,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Hasse.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.pathGraph_preconnected",
+        "id": "SimpleGraph.pathGraph_preconnected",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            114,
+            31
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Hasse.lean",
+          "full_name": "SimpleGraph.pathGraph_preconnected",
+          "start": [
+            113,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Hasse.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.incMatrix_apply",
+        "id": "SimpleGraph.incMatrix_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            65,
+            6
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean",
+          "full_name": "SimpleGraph.incMatrix_apply",
+          "start": [
+            63,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'simp only [incMatrix, Set.indicator_apply, ite_zero_mul_ite_zero, Pi.one_apply, mul_one,\\nSet.mem_inter_iff]'",
+        "full_name": "SimpleGraph.incMatrix_apply_mul_incMatrix_apply",
+        "id": "SimpleGraph.incMatrix_apply_mul_incMatrix_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            82,
+            23
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean",
+          "full_name": "SimpleGraph.incMatrix_apply_mul_incMatrix_apply",
+          "start": [
+            79,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"classical simp only [<a>incMatrix<\\/a>, <a>Set.indicator_apply<\\/a>, <a>ite_zero_mul_ite_zero<\\/a>, <a>Pi.one_apply<\\/a>, <a>mul_one<\\/a>,\\n    <a>Set.mem_inter_iff<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.incMatrix\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/IncMatrix.lean\",\"def_pos\":[57,19],\"def_end_pos\":[57,28]},{\"full_name\":\"Set.indicator_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[60,3],\"def_end_pos\":[60,14]},{\"full_name\":\"ite_zero_mul_ite_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[237,7],\"def_end_pos\":[237,28]},{\"full_name\":\"Pi.one_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[63,9],\"def_end_pos\":[63,18]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"Set.mem_inter_iff\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[874,9],\"def_end_pos\":[874,22]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d : MulZeroOneClass R\na b : \u03b1\ne : Sym2 \u03b1\n\u22a2 incMatrix R G a e * incMatrix R G b e = (G.incidenceSet a \u2229 G.incidenceSet b).indicator 1 e",
+              "tactic": "classical simp only [incMatrix, Set.indicator_apply, ite_zero_mul_ite_zero, Pi.one_apply, mul_one,\n  Set.mem_inter_iff]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>incMatrix<\\/a>, <a>Set.indicator_apply<\\/a>, <a>ite_zero_mul_ite_zero<\\/a>, <a>Pi.one_apply<\\/a>, <a>mul_one<\\/a>,\\n    <a>Set.mem_inter_iff<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.incMatrix\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/IncMatrix.lean\",\"def_pos\":[57,19],\"def_end_pos\":[57,28]},{\"full_name\":\"Set.indicator_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[60,3],\"def_end_pos\":[60,14]},{\"full_name\":\"ite_zero_mul_ite_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[237,7],\"def_end_pos\":[237,28]},{\"full_name\":\"Pi.one_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[63,9],\"def_end_pos\":[63,18]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"Set.mem_inter_iff\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[874,9],\"def_end_pos\":[874,22]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d : MulZeroOneClass R\na b : \u03b1\ne : Sym2 \u03b1\n\u22a2 incMatrix R G a e * incMatrix R G b e = (G.incidenceSet a \u2229 G.incidenceSet b).indicator 1 e",
+              "tactic": "simp only [incMatrix, Set.indicator_apply, ite_zero_mul_ite_zero, Pi.one_apply, mul_one,\nSet.mem_inter_iff]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'simp_rw [Matrix.mul_apply, Matrix.transpose_apply, incMatrix_apply_mul_incMatrix_apply,\\n  Set.indicator_apply, Pi.one_apply, sum_boole]'",
+        "full_name": "SimpleGraph.incMatrix_mul_transpose_apply_of_adj",
+        "id": "SimpleGraph.incMatrix_mul_transpose_apply_of_adj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            187,
+            53
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean",
+          "full_name": "SimpleGraph.incMatrix_mul_transpose_apply_of_adj",
+          "start": [
+            179,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"classical\\n    simp_rw [<a>Matrix.mul_apply<\\/a>, <a>Matrix.transpose_apply<\\/a>, <a>incMatrix_apply_mul_incMatrix_apply<\\/a>,\\n      <a>Set.indicator_apply<\\/a>, <a>Pi.one_apply<\\/a>, <a>sum_boole<\\/a>]\\n    convert @<a>Nat.cast_one<\\/a> R _\\n    convert <a>card_singleton<\\/a> s(a, b)\\n    rw [\\u2190 <a>coe_eq_singleton<\\/a>, <a>coe_filter_univ<\\/a>]\\n    exact G.incidenceSet_inter_incidenceSet_of_adj h\"",
+                "[{\"full_name\":\"Matrix.mul_apply\",\"def_path\":\"Mathlib\\/Data\\/Matrix\\/Basic.lean\",\"def_pos\":[984,9],\"def_end_pos\":[984,18]},{\"full_name\":\"Matrix.transpose_apply\",\"def_path\":\"Mathlib\\/Data\\/Matrix\\/Basic.lean\",\"def_pos\":[159,9],\"def_end_pos\":[159,24]},{\"full_name\":\"SimpleGraph.incMatrix_apply_mul_incMatrix_apply\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/IncMatrix.lean\",\"def_pos\":[79,9],\"def_end_pos\":[79,44]},{\"full_name\":\"Set.indicator_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[60,3],\"def_end_pos\":[60,14]},{\"full_name\":\"Pi.one_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[63,9],\"def_end_pos\":[63,18]},{\"full_name\":\"Finset.sum_boole\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Ring.lean\",\"def_pos\":[47,15],\"def_end_pos\":[47,24]},{\"full_name\":\"Nat.cast_one\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Defs.lean\",\"def_pos\":[154,9],\"def_end_pos\":[154,17]},{\"full_name\":\"Finset.card_singleton\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[88,9],\"def_end_pos\":[88,23]},{\"full_name\":\"Finset.coe_eq_singleton\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[733,9],\"def_end_pos\":[733,25]},{\"full_name\":\"Finset.coe_filter_univ\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Basic.lean\",\"def_pos\":[325,9],\"def_end_pos\":[325,24]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : Fintype (Sym2 \u03b1)\ninst\u271d : Semiring R\na b : \u03b1\ne : Sym2 \u03b1\nh : G.Adj a b\n\u22a2 (incMatrix R G * (incMatrix R G)\u1d40) a b = 1",
+              "tactic": "classical\n  simp_rw [Matrix.mul_apply, Matrix.transpose_apply, incMatrix_apply_mul_incMatrix_apply,\n    Set.indicator_apply, Pi.one_apply, sum_boole]\n  convert @Nat.cast_one R _\n  convert card_singleton s(a, b)\n  rw [\u2190 coe_eq_singleton, coe_filter_univ]\n  exact G.incidenceSet_inter_incidenceSet_of_adj h"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp_rw [<a>Matrix.mul_apply<\\/a>, <a>Matrix.transpose_apply<\\/a>, <a>incMatrix_apply_mul_incMatrix_apply<\\/a>,\\n      <a>Set.indicator_apply<\\/a>, <a>Pi.one_apply<\\/a>, <a>sum_boole<\\/a>]\"",
+                "[{\"full_name\":\"Matrix.mul_apply\",\"def_path\":\"Mathlib\\/Data\\/Matrix\\/Basic.lean\",\"def_pos\":[984,9],\"def_end_pos\":[984,18]},{\"full_name\":\"Matrix.transpose_apply\",\"def_path\":\"Mathlib\\/Data\\/Matrix\\/Basic.lean\",\"def_pos\":[159,9],\"def_end_pos\":[159,24]},{\"full_name\":\"SimpleGraph.incMatrix_apply_mul_incMatrix_apply\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/IncMatrix.lean\",\"def_pos\":[79,9],\"def_end_pos\":[79,44]},{\"full_name\":\"Set.indicator_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[60,3],\"def_end_pos\":[60,14]},{\"full_name\":\"Pi.one_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[63,9],\"def_end_pos\":[63,18]},{\"full_name\":\"Finset.sum_boole\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Ring.lean\",\"def_pos\":[47,15],\"def_end_pos\":[47,24]}]"
+              ],
+              "state_after": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : Fintype (Sym2 \u03b1)\ninst\u271d : Semiring R\na b : \u03b1\ne : Sym2 \u03b1\nh : G.Adj a b\n\u22a2 \u2191(filter (fun x => x \u2208 G.incidenceSet a \u2229 G.incidenceSet b) univ).card = 1",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : Fintype (Sym2 \u03b1)\ninst\u271d : Semiring R\na b : \u03b1\ne : Sym2 \u03b1\nh : G.Adj a b\n\u22a2 (incMatrix R G * (incMatrix R G)\u1d40) a b = 1",
+              "tactic": "simp_rw [Matrix.mul_apply, Matrix.transpose_apply, incMatrix_apply_mul_incMatrix_apply,\n  Set.indicator_apply, Pi.one_apply, sum_boole]"
+            },
+            {
+              "annotated_tactic": [
+                "\"convert @<a>Nat.cast_one<\\/a> R _\"",
+                "[{\"full_name\":\"Nat.cast_one\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Defs.lean\",\"def_pos\":[154,9],\"def_end_pos\":[154,17]}]"
+              ],
+              "state_after": "case h.e'_2.h.e'_3\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : Fintype (Sym2 \u03b1)\ninst\u271d : Semiring R\na b : \u03b1\ne : Sym2 \u03b1\nh : G.Adj a b\n\u22a2 (filter (fun x => x \u2208 G.incidenceSet a \u2229 G.incidenceSet b) univ).card = 1",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : Fintype (Sym2 \u03b1)\ninst\u271d : Semiring R\na b : \u03b1\ne : Sym2 \u03b1\nh : G.Adj a b\n\u22a2 \u2191(filter (fun x => x \u2208 G.incidenceSet a \u2229 G.incidenceSet b) univ).card = 1",
+              "tactic": "convert @Nat.cast_one R _"
+            },
+            {
+              "annotated_tactic": [
+                "\"convert <a>card_singleton<\\/a> s(a, b)\"",
+                "[{\"full_name\":\"Finset.card_singleton\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[88,9],\"def_end_pos\":[88,23]}]"
+              ],
+              "state_after": "case h.e'_2.h.e'_2\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : Fintype (Sym2 \u03b1)\ninst\u271d : Semiring R\na b : \u03b1\ne : Sym2 \u03b1\nh : G.Adj a b\n\u22a2 filter (fun x => x \u2208 G.incidenceSet a \u2229 G.incidenceSet b) univ = {s(a, b)}",
+              "state_before": "case h.e'_2.h.e'_3\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : Fintype (Sym2 \u03b1)\ninst\u271d : Semiring R\na b : \u03b1\ne : Sym2 \u03b1\nh : G.Adj a b\n\u22a2 (filter (fun x => x \u2208 G.incidenceSet a \u2229 G.incidenceSet b) univ).card = 1",
+              "tactic": "convert card_singleton s(a, b)"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>coe_eq_singleton<\\/a>, <a>coe_filter_univ<\\/a>]\"",
+                "[{\"full_name\":\"Finset.coe_eq_singleton\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[733,9],\"def_end_pos\":[733,25]},{\"full_name\":\"Finset.coe_filter_univ\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Basic.lean\",\"def_pos\":[325,9],\"def_end_pos\":[325,24]}]"
+              ],
+              "state_after": "case h.e'_2.h.e'_2\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : Fintype (Sym2 \u03b1)\ninst\u271d : Semiring R\na b : \u03b1\ne : Sym2 \u03b1\nh : G.Adj a b\n\u22a2 {x | x \u2208 G.incidenceSet a \u2229 G.incidenceSet b} = {s(a, b)}",
+              "state_before": "case h.e'_2.h.e'_2\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : Fintype (Sym2 \u03b1)\ninst\u271d : Semiring R\na b : \u03b1\ne : Sym2 \u03b1\nh : G.Adj a b\n\u22a2 filter (fun x => x \u2208 G.incidenceSet a \u2229 G.incidenceSet b) univ = {s(a, b)}",
+              "tactic": "rw [\u2190 coe_eq_singleton, coe_filter_univ]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact G.incidenceSet_inter_incidenceSet_of_adj h\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.e'_2.h.e'_2\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : Fintype (Sym2 \u03b1)\ninst\u271d : Semiring R\na b : \u03b1\ne : Sym2 \u03b1\nh : G.Adj a b\n\u22a2 {x | x \u2208 G.incidenceSet a \u2229 G.incidenceSet b} = {s(a, b)}",
+              "tactic": "exact G.incidenceSet_inter_incidenceSet_of_adj h"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rw [\u2190 sum_incMatrix_apply]'",
+        "full_name": "SimpleGraph.incMatrix_mul_transpose_diag",
+        "id": "SimpleGraph.incMatrix_mul_transpose_diag",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            131,
+            38
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean",
+          "full_name": "SimpleGraph.incMatrix_mul_transpose_diag",
+          "start": [
+            126,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"classical\\n  rw [\\u2190 <a>sum_incMatrix_apply<\\/a>]\\n  simp only [<a>mul_apply<\\/a>, <a>incMatrix_apply'<\\/a>, <a>transpose_apply<\\/a>, <a>mul_ite<\\/a>, <a>mul_one<\\/a>, <a>mul_zero<\\/a>]\\n  simp_all only [<a>ite_true<\\/a>, <a>sum_boole<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.sum_incMatrix_apply\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/IncMatrix.lean\",\"def_pos\":[121,9],\"def_end_pos\":[121,28]},{\"full_name\":\"Matrix.mul_apply\",\"def_path\":\"Mathlib\\/Data\\/Matrix\\/Basic.lean\",\"def_pos\":[984,9],\"def_end_pos\":[984,18]},{\"full_name\":\"SimpleGraph.incMatrix_apply'\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/IncMatrix.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,25]},{\"full_name\":\"Matrix.transpose_apply\",\"def_path\":\"Mathlib\\/Data\\/Matrix\\/Basic.lean\",\"def_pos\":[159,9],\"def_end_pos\":[159,24]},{\"full_name\":\"mul_ite\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[197,9],\"def_end_pos\":[197,16]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"MulZeroClass.mul_zero\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Defs.lean\",\"def_pos\":[39,3],\"def_end_pos\":[39,11]},{\"full_name\":\"ite_true\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[91,17],\"def_end_pos\":[91,25]},{\"full_name\":\"Finset.sum_boole\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Ring.lean\",\"def_pos\":[47,15],\"def_end_pos\":[47,24]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u2191(G.neighborSet a)\n\u22a2 (incMatrix R G * (incMatrix R G)\u1d40) a a = \u2191(G.degree a)",
+              "tactic": "classical\nrw [\u2190 sum_incMatrix_apply]\nsimp only [mul_apply, incMatrix_apply', transpose_apply, mul_ite, mul_one, mul_zero]\nsimp_all only [ite_true, sum_boole]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>sum_incMatrix_apply<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.sum_incMatrix_apply\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/IncMatrix.lean\",\"def_pos\":[121,9],\"def_end_pos\":[121,28]}]"
+              ],
+              "state_after": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u2191(G.neighborSet a)\n\u22a2 (incMatrix R G * (incMatrix R G)\u1d40) a a = \u2211 e : Sym2 \u03b1, incMatrix R G a e",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u2191(G.neighborSet a)\n\u22a2 (incMatrix R G * (incMatrix R G)\u1d40) a a = \u2191(G.degree a)",
+              "tactic": "rw [\u2190 sum_incMatrix_apply]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>mul_apply<\\/a>, <a>incMatrix_apply'<\\/a>, <a>transpose_apply<\\/a>, <a>mul_ite<\\/a>, <a>mul_one<\\/a>, <a>mul_zero<\\/a>]\"",
+                "[{\"full_name\":\"Matrix.mul_apply\",\"def_path\":\"Mathlib\\/Data\\/Matrix\\/Basic.lean\",\"def_pos\":[984,9],\"def_end_pos\":[984,18]},{\"full_name\":\"SimpleGraph.incMatrix_apply'\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/IncMatrix.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,25]},{\"full_name\":\"Matrix.transpose_apply\",\"def_path\":\"Mathlib\\/Data\\/Matrix\\/Basic.lean\",\"def_pos\":[159,9],\"def_end_pos\":[159,24]},{\"full_name\":\"mul_ite\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[197,9],\"def_end_pos\":[197,16]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"MulZeroClass.mul_zero\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Defs.lean\",\"def_pos\":[39,3],\"def_end_pos\":[39,11]}]"
+              ],
+              "state_after": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u2191(G.neighborSet a)\n\u22a2 (\u2211 x : Sym2 \u03b1, if x \u2208 G.incidenceSet a then if x \u2208 G.incidenceSet a then 1 else 0 else 0) =\n    \u2211 x : Sym2 \u03b1, if x \u2208 G.incidenceSet a then 1 else 0",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u2191(G.neighborSet a)\n\u22a2 (incMatrix R G * (incMatrix R G)\u1d40) a a = \u2211 e : Sym2 \u03b1, incMatrix R G a e",
+              "tactic": "simp only [mul_apply, incMatrix_apply', transpose_apply, mul_ite, mul_one, mul_zero]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp_all only [<a>ite_true<\\/a>, <a>sum_boole<\\/a>]\"",
+                "[{\"full_name\":\"ite_true\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[91,17],\"def_end_pos\":[91,25]},{\"full_name\":\"Finset.sum_boole\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Ring.lean\",\"def_pos\":[47,15],\"def_end_pos\":[47,24]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u2191(G.neighborSet a)\n\u22a2 (\u2211 x : Sym2 \u03b1, if x \u2208 G.incidenceSet a then if x \u2208 G.incidenceSet a then 1 else 0 else 0) =\n    \u2211 x : Sym2 \u03b1, if x \u2208 G.incidenceSet a then 1 else 0",
+              "tactic": "simp_all only [ite_true, sum_boole]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rw [\u2190 Nat.cast_two, \u2190 card_pair (G.ne_of_adj h)]'",
+        "full_name": "SimpleGraph.incMatrix_transpose_mul_diag",
+        "id": "SimpleGraph.incMatrix_transpose_mul_diag",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            170,
+            62
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean",
+          "full_name": "SimpleGraph.incMatrix_transpose_mul_diag",
+          "start": [
+            152,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>Matrix.mul_apply<\\/a>, <a>incMatrix_apply'<\\/a>, <a>transpose_apply<\\/a>, <a>ite_zero_mul_ite_zero<\\/a>, <a>one_mul<\\/a>,\\n      <a>sum_boole<\\/a>, <a>and_self_iff<\\/a>]\"",
+                "[{\"full_name\":\"Matrix.mul_apply\",\"def_path\":\"Mathlib\\/Data\\/Matrix\\/Basic.lean\",\"def_pos\":[984,9],\"def_end_pos\":[984,18]},{\"full_name\":\"SimpleGraph.incMatrix_apply'\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/IncMatrix.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,25]},{\"full_name\":\"Matrix.transpose_apply\",\"def_path\":\"Mathlib\\/Data\\/Matrix\\/Basic.lean\",\"def_pos\":[159,9],\"def_end_pos\":[159,24]},{\"full_name\":\"ite_zero_mul_ite_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[237,7],\"def_end_pos\":[237,28]},{\"full_name\":\"one_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[477,9],\"def_end_pos\":[477,16]},{\"full_name\":\"Finset.sum_boole\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Ring.lean\",\"def_pos\":[47,15],\"def_end_pos\":[47,24]},{\"full_name\":\"and_self_iff\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/PropLemmas.lean\",\"def_pos\":[35,9],\"def_end_pos\":[35,21]}]"
+              ],
+              "state_after": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\n\u22a2 \u2191(filter (fun x => e \u2208 G.incidenceSet x) univ).card = if e \u2208 G.edgeSet then 2 else 0",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\n\u22a2 ((incMatrix R G)\u1d40 * incMatrix R G) e e = if e \u2208 G.edgeSet then 2 else 0",
+              "tactic": "simp only [Matrix.mul_apply, incMatrix_apply', transpose_apply, ite_zero_mul_ite_zero, one_mul,\n  sum_boole, and_self_iff]"
+            },
+            {
+              "annotated_tactic": [
+                "\"split_ifs with h\"",
+                "[]"
+              ],
+              "state_after": "case pos\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\nh : e \u2208 G.edgeSet\n\u22a2 \u2191(filter (fun x => e \u2208 G.incidenceSet x) univ).card = 2\n\ncase neg\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\nh : e \u2209 G.edgeSet\n\u22a2 \u2191(filter (fun x => e \u2208 G.incidenceSet x) univ).card = 0",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\n\u22a2 \u2191(filter (fun x => e \u2208 G.incidenceSet x) univ).card = if e \u2208 G.edgeSet then 2 else 0",
+              "tactic": "split_ifs with h"
+            },
+            {
+              "annotated_tactic": [
+                "\"revert h\"",
+                "[]"
+              ],
+              "state_after": "case pos\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\n\u22a2 e \u2208 G.edgeSet \u2192 \u2191(filter (fun x => e \u2208 G.incidenceSet x) univ).card = 2",
+              "state_before": "case pos\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\nh : e \u2208 G.edgeSet\n\u22a2 \u2191(filter (fun x => e \u2208 G.incidenceSet x) univ).card = 2",
+              "tactic": "revert h"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine e.ind ?_\"",
+                "[]"
+              ],
+              "state_after": "case pos\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\n\u22a2 \u2200 (x y : \u03b1), s(x, y) \u2208 G.edgeSet \u2192 \u2191(filter (fun x_1 => s(x, y) \u2208 G.incidenceSet x_1) univ).card = 2",
+              "state_before": "case pos\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\n\u22a2 e \u2208 G.edgeSet \u2192 \u2191(filter (fun x => e \u2208 G.incidenceSet x) univ).card = 2",
+              "tactic": "refine e.ind ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro v w h\"",
+                "[]"
+              ],
+              "state_after": "case pos\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\nv w : \u03b1\nh : s(v, w) \u2208 G.edgeSet\n\u22a2 \u2191(filter (fun x => s(v, w) \u2208 G.incidenceSet x) univ).card = 2",
+              "state_before": "case pos\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\n\u22a2 \u2200 (x y : \u03b1), s(x, y) \u2208 G.edgeSet \u2192 \u2191(filter (fun x_1 => s(x, y) \u2208 G.incidenceSet x_1) univ).card = 2",
+              "tactic": "intro v w h"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>Nat.cast_two<\\/a>, \\u2190 <a>card_pair<\\/a> (G.ne_of_adj h)]\"",
+                "[{\"full_name\":\"Nat.cast_two\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Defs.lean\",\"def_pos\":[208,9],\"def_end_pos\":[208,17]},{\"full_name\":\"Finset.card_pair\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[156,9],\"def_end_pos\":[156,18]}]"
+              ],
+              "state_after": "case pos\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\nv w : \u03b1\nh : s(v, w) \u2208 G.edgeSet\n\u22a2 \u2191(filter (fun x => s(v, w) \u2208 G.incidenceSet x) univ).card = \u2191{(v, w).1, (v, w).2}.card",
+              "state_before": "case pos\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\nv w : \u03b1\nh : s(v, w) \u2208 G.edgeSet\n\u22a2 \u2191(filter (fun x => s(v, w) \u2208 G.incidenceSet x) univ).card = 2",
+              "tactic": "rw [\u2190 Nat.cast_two, \u2190 card_pair (G.ne_of_adj h)]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>mk'_mem_incidenceSet_iff<\\/a>, G.mem_edgeSet.mp h, <a>true_and<\\/a>, <a>mem_univ<\\/a>, <a>forall_true_left<\\/a>,\\n        <a>forall_eq_or_imp<\\/a>, <a>forall_eq<\\/a>, <a>and_self<\\/a>, <a>mem_singleton<\\/a>, <a>ne_eq<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.mk'_mem_incidenceSet_iff\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[718,9],\"def_end_pos\":[718,33]},{\"full_name\":\"true_and\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[105,17],\"def_end_pos\":[105,25]},{\"full_name\":\"Finset.mem_univ\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Basic.lean\",\"def_pos\":[75,9],\"def_end_pos\":[75,17]},{\"full_name\":\"forall_true_left\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[967,17],\"def_end_pos\":[967,33]},{\"full_name\":\"forall_eq_or_imp\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/PropLemmas.lean\",\"def_pos\":[295,17],\"def_end_pos\":[295,33]},{\"full_name\":\"forall_eq\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/PropLemmas.lean\",\"def_pos\":[273,17],\"def_end_pos\":[273,26]},{\"full_name\":\"and_self\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[111,17],\"def_end_pos\":[111,25]},{\"full_name\":\"Finset.mem_singleton\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[680,9],\"def_end_pos\":[680,22]},{\"full_name\":\"ne_eq\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[89,17],\"def_end_pos\":[89,22]}]"
+              ],
+              "state_after": "case pos\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\nv w : \u03b1\nh : s(v, w) \u2208 G.edgeSet\n\u22a2 \u2191(filter (fun x => x = v \u2228 x = w) univ).card = \u2191{v, w}.card",
+              "state_before": "case pos\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\nv w : \u03b1\nh : s(v, w) \u2208 G.edgeSet\n\u22a2 \u2191(filter (fun x => s(v, w) \u2208 G.incidenceSet x) univ).card = \u2191{(v, w).1, (v, w).2}.card",
+              "tactic": "simp only [mk'_mem_incidenceSet_iff, G.mem_edgeSet.mp h, true_and, mem_univ, forall_true_left,\n  forall_eq_or_imp, forall_eq, and_self, mem_singleton, ne_eq]"
+            },
+            {
+              "annotated_tactic": [
+                "\"congr 2\"",
+                "[]"
+              ],
+              "state_after": "case pos.e_a.e_s\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\nv w : \u03b1\nh : s(v, w) \u2208 G.edgeSet\n\u22a2 filter (fun x => x = v \u2228 x = w) univ = {v, w}",
+              "state_before": "case pos\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\nv w : \u03b1\nh : s(v, w) \u2208 G.edgeSet\n\u22a2 \u2191(filter (fun x => x = v \u2228 x = w) univ).card = \u2191{v, w}.card",
+              "tactic": "congr 2"
+            },
+            {
+              "annotated_tactic": [
+                "\"ext u\"",
+                "[]"
+              ],
+              "state_after": "case pos.e_a.e_s.a\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\nv w : \u03b1\nh : s(v, w) \u2208 G.edgeSet\nu : \u03b1\n\u22a2 u \u2208 filter (fun x => x = v \u2228 x = w) univ \u2194 u \u2208 {v, w}",
+              "state_before": "case pos.e_a.e_s\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\nv w : \u03b1\nh : s(v, w) \u2208 G.edgeSet\n\u22a2 filter (fun x => x = v \u2228 x = w) univ = {v, w}",
+              "tactic": "ext u"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case pos.e_a.e_s.a\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\nv w : \u03b1\nh : s(v, w) \u2208 G.edgeSet\nu : \u03b1\n\u22a2 u \u2208 filter (fun x => x = v \u2228 x = w) univ \u2194 u \u2208 {v, w}",
+              "tactic": "simp"
+            },
+            {
+              "annotated_tactic": [
+                "\"revert h\"",
+                "[]"
+              ],
+              "state_after": "case neg\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\n\u22a2 e \u2209 G.edgeSet \u2192 \u2191(filter (fun x => e \u2208 G.incidenceSet x) univ).card = 0",
+              "state_before": "case neg\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\nh : e \u2209 G.edgeSet\n\u22a2 \u2191(filter (fun x => e \u2208 G.incidenceSet x) univ).card = 0",
+              "tactic": "revert h"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine e.ind ?_\"",
+                "[]"
+              ],
+              "state_after": "case neg\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\n\u22a2 \u2200 (x y : \u03b1), s(x, y) \u2209 G.edgeSet \u2192 \u2191(filter (fun x_1 => s(x, y) \u2208 G.incidenceSet x_1) univ).card = 0",
+              "state_before": "case neg\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\n\u22a2 e \u2209 G.edgeSet \u2192 \u2191(filter (fun x => e \u2208 G.incidenceSet x) univ).card = 0",
+              "tactic": "refine e.ind ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro v w h\"",
+                "[]"
+              ],
+              "state_after": "case neg\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\nv w : \u03b1\nh : s(v, w) \u2209 G.edgeSet\n\u22a2 \u2191(filter (fun x => s(v, w) \u2208 G.incidenceSet x) univ).card = 0",
+              "state_before": "case neg\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\n\u22a2 \u2200 (x y : \u03b1), s(x, y) \u2209 G.edgeSet \u2192 \u2191(filter (fun x_1 => s(x, y) \u2208 G.incidenceSet x_1) univ).card = 0",
+              "tactic": "intro v w h"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [<a>mk'_mem_incidenceSet_iff<\\/a>, G.mem_edgeSet.not.mp h]\"",
+                "[{\"full_name\":\"SimpleGraph.mk'_mem_incidenceSet_iff\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[718,9],\"def_end_pos\":[718,33]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case neg\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b3 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b2 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b9 : Fintype \u03b1\ninst\u271d : Decidable (e \u2208 G.edgeSet)\nv w : \u03b1\nh : s(v, w) \u2209 G.edgeSet\n\u22a2 \u2191(filter (fun x => s(v, w) \u2208 G.incidenceSet x) univ).card = 0",
+              "tactic": "simp [mk'_mem_incidenceSet_iff, G.mem_edgeSet.not.mp h]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean"
+      },
+      {
+        "error": "no internal trace for tactic \"simp [incMatrix_apply', sum_boole, Set.filter_mem_univ_eq_toFinset]\"",
+        "full_name": "SimpleGraph.sum_incMatrix_apply",
+        "id": "SimpleGraph.sum_incMatrix_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            123,
+            80
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean",
+          "full_name": "SimpleGraph.sum_incMatrix_apply",
+          "start": [
+            121,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"classical simp [<a>incMatrix_apply'<\\/a>, <a>sum_boole<\\/a>, <a>Set.filter_mem_univ_eq_toFinset<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.incMatrix_apply'\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/IncMatrix.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,25]},{\"full_name\":\"Finset.sum_boole\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Ring.lean\",\"def_pos\":[47,15],\"def_end_pos\":[47,24]},{\"full_name\":\"Set.filter_mem_univ_eq_toFinset\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Basic.lean\",\"def_pos\":[800,9],\"def_end_pos\":[800,36]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u2191(G.neighborSet a)\n\u22a2 \u2211 e : Sym2 \u03b1, incMatrix R G a e = \u2191(G.degree a)",
+              "tactic": "classical simp [incMatrix_apply', sum_boole, Set.filter_mem_univ_eq_toFinset]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [<a>incMatrix_apply'<\\/a>, <a>sum_boole<\\/a>, <a>Set.filter_mem_univ_eq_toFinset<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.incMatrix_apply'\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/IncMatrix.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,25]},{\"full_name\":\"Finset.sum_boole\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Ring.lean\",\"def_pos\":[47,15],\"def_end_pos\":[47,24]},{\"full_name\":\"Set.filter_mem_univ_eq_toFinset\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Basic.lean\",\"def_pos\":[800,9],\"def_end_pos\":[800,36]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u2191(G.neighborSet a)\n\u22a2 \u2211 e : Sym2 \u03b1, incMatrix R G a e = \u2191(G.degree a)",
+              "tactic": "simp [incMatrix_apply', sum_boole, Set.filter_mem_univ_eq_toFinset]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'refine e.ind ?_'",
+        "full_name": "SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet",
+        "id": "SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            144,
+            78
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean",
+          "full_name": "SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet",
+          "start": [
+            134,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"classical\\n    refine e.ind ?_\\n    intro a b h\\n    rw [<a>mem_edgeSet<\\/a>] at h\\n    rw [\\u2190 <a>Nat.cast_two<\\/a>, \\u2190 <a>card_pair<\\/a> h.ne]\\n    simp only [<a>incMatrix_apply'<\\/a>, <a>sum_boole<\\/a>, <a>mk'_mem_incidenceSet_iff<\\/a>, h, <a>true_and_iff<\\/a>]\\n    congr 2\\n    ext e\\n    simp only [<a>mem_filter<\\/a>, <a>mem_univ<\\/a>, <a>true_and_iff<\\/a>, <a>mem_insert<\\/a>, <a>mem_singleton<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.mem_edgeSet\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[471,9],\"def_end_pos\":[471,20]},{\"full_name\":\"Nat.cast_two\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Defs.lean\",\"def_pos\":[208,9],\"def_end_pos\":[208,17]},{\"full_name\":\"Finset.card_pair\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[156,9],\"def_end_pos\":[156,18]},{\"full_name\":\"SimpleGraph.incMatrix_apply'\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/IncMatrix.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,25]},{\"full_name\":\"Finset.sum_boole\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Ring.lean\",\"def_pos\":[47,15],\"def_end_pos\":[47,24]},{\"full_name\":\"SimpleGraph.mk'_mem_incidenceSet_iff\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[718,9],\"def_end_pos\":[718,33]},{\"full_name\":\"true_and_iff\",\"def_path\":\"Mathlib\\/Init\\/Logic.lean\",\"def_pos\":[118,9],\"def_end_pos\":[118,21]},{\"full_name\":\"Finset.mem_filter\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[2593,9],\"def_end_pos\":[2593,19]},{\"full_name\":\"Finset.mem_univ\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Basic.lean\",\"def_pos\":[75,9],\"def_end_pos\":[75,17]},{\"full_name\":\"true_and_iff\",\"def_path\":\"Mathlib\\/Init\\/Logic.lean\",\"def_pos\":[118,9],\"def_end_pos\":[118,21]},{\"full_name\":\"Finset.mem_insert\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[1113,9],\"def_end_pos\":[1113,19]},{\"full_name\":\"Finset.mem_singleton\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[680,9],\"def_end_pos\":[680,22]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u03b1\n\u22a2 e \u2208 G.edgeSet \u2192 \u2211 a : \u03b1, incMatrix R G a e = 2",
+              "tactic": "classical\n  refine e.ind ?_\n  intro a b h\n  rw [mem_edgeSet] at h\n  rw [\u2190 Nat.cast_two, \u2190 card_pair h.ne]\n  simp only [incMatrix_apply', sum_boole, mk'_mem_incidenceSet_iff, h, true_and_iff]\n  congr 2\n  ext e\n  simp only [mem_filter, mem_univ, true_and_iff, mem_insert, mem_singleton]"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine e.ind ?_\"",
+                "[]"
+              ],
+              "state_after": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u03b1\n\u22a2 \u2200 (x y : \u03b1), s(x, y) \u2208 G.edgeSet \u2192 \u2211 a : \u03b1, incMatrix R G a s(x, y) = 2",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u03b1\n\u22a2 e \u2208 G.edgeSet \u2192 \u2211 a : \u03b1, incMatrix R G a e = 2",
+              "tactic": "refine e.ind ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro a b h\"",
+                "[]"
+              ],
+              "state_after": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na\u271d b\u271d : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u03b1\na b : \u03b1\nh : s(a, b) \u2208 G.edgeSet\n\u22a2 \u2211 a_1 : \u03b1, incMatrix R G a_1 s(a, b) = 2",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u03b1\n\u22a2 \u2200 (x y : \u03b1), s(x, y) \u2208 G.edgeSet \u2192 \u2211 a : \u03b1, incMatrix R G a s(x, y) = 2",
+              "tactic": "intro a b h"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>mem_edgeSet<\\/a>] at h\"",
+                "[{\"full_name\":\"SimpleGraph.mem_edgeSet\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[471,9],\"def_end_pos\":[471,20]}]"
+              ],
+              "state_after": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na\u271d b\u271d : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u03b1\na b : \u03b1\nh : G.Adj a b\n\u22a2 \u2211 a_1 : \u03b1, incMatrix R G a_1 s(a, b) = 2",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na\u271d b\u271d : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u03b1\na b : \u03b1\nh : s(a, b) \u2208 G.edgeSet\n\u22a2 \u2211 a_1 : \u03b1, incMatrix R G a_1 s(a, b) = 2",
+              "tactic": "rw [mem_edgeSet] at h"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>Nat.cast_two<\\/a>, \\u2190 <a>card_pair<\\/a> h.ne]\"",
+                "[{\"full_name\":\"Nat.cast_two\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Defs.lean\",\"def_pos\":[208,9],\"def_end_pos\":[208,17]},{\"full_name\":\"Finset.card_pair\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[156,9],\"def_end_pos\":[156,18]}]"
+              ],
+              "state_after": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na\u271d b\u271d : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u03b1\na b : \u03b1\nh : G.Adj a b\n\u22a2 \u2211 a_1 : \u03b1, incMatrix R G a_1 s(a, b) = \u2191{a, b}.card",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na\u271d b\u271d : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u03b1\na b : \u03b1\nh : G.Adj a b\n\u22a2 \u2211 a_1 : \u03b1, incMatrix R G a_1 s(a, b) = 2",
+              "tactic": "rw [\u2190 Nat.cast_two, \u2190 card_pair h.ne]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>incMatrix_apply'<\\/a>, <a>sum_boole<\\/a>, <a>mk'_mem_incidenceSet_iff<\\/a>, h, <a>true_and_iff<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.incMatrix_apply'\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/IncMatrix.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,25]},{\"full_name\":\"Finset.sum_boole\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Ring.lean\",\"def_pos\":[47,15],\"def_end_pos\":[47,24]},{\"full_name\":\"SimpleGraph.mk'_mem_incidenceSet_iff\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[718,9],\"def_end_pos\":[718,33]},{\"full_name\":\"true_and_iff\",\"def_path\":\"Mathlib\\/Init\\/Logic.lean\",\"def_pos\":[118,9],\"def_end_pos\":[118,21]}]"
+              ],
+              "state_after": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na\u271d b\u271d : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u03b1\na b : \u03b1\nh : G.Adj a b\n\u22a2 \u2191(filter (fun x => x = a \u2228 x = b) univ).card = \u2191{a, b}.card",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na\u271d b\u271d : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u03b1\na b : \u03b1\nh : G.Adj a b\n\u22a2 \u2211 a_1 : \u03b1, incMatrix R G a_1 s(a, b) = \u2191{a, b}.card",
+              "tactic": "simp only [incMatrix_apply', sum_boole, mk'_mem_incidenceSet_iff, h, true_and_iff]"
+            },
+            {
+              "annotated_tactic": [
+                "\"congr 2\"",
+                "[]"
+              ],
+              "state_after": "case e_a.e_s\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na\u271d b\u271d : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u03b1\na b : \u03b1\nh : G.Adj a b\n\u22a2 filter (fun x => x = a \u2228 x = b) univ = {a, b}",
+              "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na\u271d b\u271d : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u03b1\na b : \u03b1\nh : G.Adj a b\n\u22a2 \u2191(filter (fun x => x = a \u2228 x = b) univ).card = \u2191{a, b}.card",
+              "tactic": "congr 2"
+            },
+            {
+              "annotated_tactic": [
+                "\"ext e\"",
+                "[]"
+              ],
+              "state_after": "case e_a.e_s.a\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na\u271d b\u271d : \u03b1\ne\u271d : Sym2 \u03b1\ninst\u271d : Fintype \u03b1\na b : \u03b1\nh : G.Adj a b\ne : \u03b1\n\u22a2 e \u2208 filter (fun x => x = a \u2228 x = b) univ \u2194 e \u2208 {a, b}",
+              "state_before": "case e_a.e_s\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na\u271d b\u271d : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Fintype \u03b1\na b : \u03b1\nh : G.Adj a b\n\u22a2 filter (fun x => x = a \u2228 x = b) univ = {a, b}",
+              "tactic": "ext e"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>mem_filter<\\/a>, <a>mem_univ<\\/a>, <a>true_and_iff<\\/a>, <a>mem_insert<\\/a>, <a>mem_singleton<\\/a>]\"",
+                "[{\"full_name\":\"Finset.mem_filter\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[2593,9],\"def_end_pos\":[2593,19]},{\"full_name\":\"Finset.mem_univ\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Basic.lean\",\"def_pos\":[75,9],\"def_end_pos\":[75,17]},{\"full_name\":\"true_and_iff\",\"def_path\":\"Mathlib\\/Init\\/Logic.lean\",\"def_pos\":[118,9],\"def_end_pos\":[118,21]},{\"full_name\":\"Finset.mem_insert\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[1113,9],\"def_end_pos\":[1113,19]},{\"full_name\":\"Finset.mem_singleton\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[680,9],\"def_end_pos\":[680,22]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case e_a.e_s.a\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b2 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b9 : NonAssocSemiring R\na\u271d b\u271d : \u03b1\ne\u271d : Sym2 \u03b1\ninst\u271d : Fintype \u03b1\na b : \u03b1\nh : G.Adj a b\ne : \u03b1\n\u22a2 e \u2208 filter (fun x => x = a \u2228 x = b) univ \u2194 e \u2208 {a, b}",
+              "tactic": "simp only [mem_filter, mem_univ, true_and_iff, mem_insert, mem_singleton]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.sum_incMatrix_apply_of_not_mem_edgeSet",
+        "id": "SimpleGraph.sum_incMatrix_apply_of_not_mem_edgeSet",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            149,
+            78
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean",
+          "full_name": "SimpleGraph.sum_incMatrix_apply_of_not_mem_edgeSet",
+          "start": [
+            147,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean"
+      }
+    ],
+    "input_proofs": 25,
+    "input_units": 2,
+    "proofs": 12,
+    "published_proofs": 10,
+    "published_transitions": 18,
+    "replay_failures": [],
+    "transitions": 29,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean",
+        "proof_id": "mathlib:SimpleGraph.incMatrix_apply_eq_one_iff",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              112,
+              29
+            ],
+            "file_path": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean",
+            "full_name": "SimpleGraph.incMatrix_apply_eq_one_iff",
+            "start": [
+              106,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"unfold <a>incMatrix<\\/a> <a>Set.indicator<\\/a>\"",
+                  "[{\"full_name\":\"SimpleGraph.incMatrix\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/IncMatrix.lean\",\"def_pos\":[57,19],\"def_end_pos\":[57,28]},{\"full_name\":\"Set.indicator\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[47,3],\"def_end_pos\":[47,14]}]"
+                ],
+                "state_after": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : MulZeroOneClass R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Nontrivial R\n\u22a2 (if e \u2208 G.incidenceSet a then 1 e else 0) = 1 \u2194 e \u2208 G.incidenceSet a",
+                "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : MulZeroOneClass R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Nontrivial R\n\u22a2 incMatrix R G a e = 1 \u2194 e \u2208 G.incidenceSet a",
+                "tactic": "unfold incMatrix Set.indicator"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp only [<a>Pi.one_apply<\\/a>]\"",
+                  "[{\"full_name\":\"Pi.one_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[63,9],\"def_end_pos\":[63,18]}]"
+                ],
+                "state_after": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : MulZeroOneClass R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Nontrivial R\n\u22a2 (if e \u2208 G.incidenceSet a then 1 else 0) = 1 \u2194 e \u2208 G.incidenceSet a",
+                "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : MulZeroOneClass R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Nontrivial R\n\u22a2 (if e \u2208 G.incidenceSet a then 1 e else 0) = 1 \u2194 e \u2208 G.incidenceSet a",
+                "tactic": "simp only [Pi.one_apply]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"apply <a>Iff.intro<\\/a> <;> intro h\"",
+                  "[{\"full_name\":\"Iff.intro\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[116,3],\"def_end_pos\":[116,8]}]"
+                ],
+                "state_after": "case mp\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : MulZeroOneClass R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Nontrivial R\nh : (if e \u2208 G.incidenceSet a then 1 else 0) = 1\n\u22a2 e \u2208 G.incidenceSet a\n\ncase mpr\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : MulZeroOneClass R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Nontrivial R\nh : e \u2208 G.incidenceSet a\n\u22a2 (if e \u2208 G.incidenceSet a then 1 else 0) = 1",
+                "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : MulZeroOneClass R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Nontrivial R\n\u22a2 (if e \u2208 G.incidenceSet a then 1 else 0) = 1 \u2194 e \u2208 G.incidenceSet a",
+                "tactic": "apply Iff.intro <;> intro h"
+              },
+              {
+                "annotated_tactic": [
+                  "\"split at h <;> simp_all only [<a>zero_ne_one<\\/a>]\"",
+                  "[{\"full_name\":\"zero_ne_one\",\"def_path\":\"Mathlib\\/Algebra\\/NeZero.lean\",\"def_pos\":[55,15],\"def_end_pos\":[55,26]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case mp\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : MulZeroOneClass R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Nontrivial R\nh : (if e \u2208 G.incidenceSet a then 1 else 0) = 1\n\u22a2 e \u2208 G.incidenceSet a",
+                "tactic": "split at h <;> simp_all only [zero_ne_one]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp_all only [<a>ite_true<\\/a>]\"",
+                  "[{\"full_name\":\"ite_true\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[91,17],\"def_end_pos\":[91,25]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case mpr\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u00b9 : MulZeroOneClass R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d : Nontrivial R\nh : e \u2208 G.incidenceSet a\n\u22a2 (if e \u2208 G.incidenceSet a then 1 else 0) = 1",
+                "tactic": "simp_all only [ite_true]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "SimpleGraph.incMatrix_apply_eq_one_iff"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean",
+        "proof_id": "mathlib:SimpleGraph.incMatrix_mul_transpose",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              200,
+              77
+            ],
+            "file_path": "Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean",
+            "full_name": "SimpleGraph.incMatrix_mul_transpose",
+            "start": [
+              190,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"ext a b\"",
+                  "[]"
+                ],
+                "state_after": "case a\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u2074 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b3 : Semiring R\na\u271d b\u271d : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b2 : (a : \u03b1) \u2192 Fintype \u2191(G.neighborSet a)\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableRel G.Adj\na b : \u03b1\n\u22a2 (incMatrix R G * (incMatrix R G)\u1d40) a b = if a = b then \u2191(G.degree a) else if G.Adj a b then 1 else 0",
+                "state_before": "R : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u2074 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b3 : Semiring R\na b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b2 : (a : \u03b1) \u2192 Fintype \u2191(G.neighborSet a)\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableRel G.Adj\n\u22a2 incMatrix R G * (incMatrix R G)\u1d40 = fun a b => if a = b then \u2191(G.degree a) else if G.Adj a b then 1 else 0",
+                "tactic": "ext a b"
+              },
+              {
+                "annotated_tactic": [
+                  "\"split_ifs with h h'\"",
+                  "[]"
+                ],
+                "state_after": "case pos\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u2074 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b3 : Semiring R\na\u271d b\u271d : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b2 : (a : \u03b1) \u2192 Fintype \u2191(G.neighborSet a)\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableRel G.Adj\na b : \u03b1\nh : a = b\n\u22a2 (incMatrix R G * (incMatrix R G)\u1d40) a b = \u2191(G.degree a)\n\ncase pos\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u2074 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b3 : Semiring R\na\u271d b\u271d : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b2 : (a : \u03b1) \u2192 Fintype \u2191(G.neighborSet a)\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableRel G.Adj\na b : \u03b1\nh : \u00aca = b\nh' : G.Adj a b\n\u22a2 (incMatrix R G * (incMatrix R G)\u1d40) a b = 1\n\ncase neg\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u2074 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b3 : Semiring R\na\u271d b\u271d : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b2 : (a : \u03b1) \u2192 Fintype \u2191(G.neighborSet a)\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableRel G.Adj\na b : \u03b1\nh : \u00aca = b\nh' : \u00acG.Adj a b\n\u22a2 (incMatrix R G * (incMatrix R G)\u1d40) a b = 0",
+                "state_before": "case a\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u2074 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b3 : Semiring R\na\u271d b\u271d : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b2 : (a : \u03b1) \u2192 Fintype \u2191(G.neighborSet a)\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableRel G.Adj\na b : \u03b1\n\u22a2 (incMatrix R G * (incMatrix R G)\u1d40) a b = if a = b then \u2191(G.degree a) else if G.Adj a b then 1 else 0",
+                "tactic": "split_ifs with h h'"
+              },
+              {
+                "annotated_tactic": [
+                  "\"subst b\"",
+                  "[]"
+                ],
+                "state_after": "case pos\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u2074 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b3 : Semiring R\na\u271d b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b2 : (a : \u03b1) \u2192 Fintype \u2191(G.neighborSet a)\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableRel G.Adj\na : \u03b1\n\u22a2 (incMatrix R G * (incMatrix R G)\u1d40) a a = \u2191(G.degree a)",
+                "state_before": "case pos\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u2074 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b3 : Semiring R\na\u271d b\u271d : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b2 : (a : \u03b1) \u2192 Fintype \u2191(G.neighborSet a)\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableRel G.Adj\na b : \u03b1\nh : a = b\n\u22a2 (incMatrix R G * (incMatrix R G)\u1d40) a b = \u2191(G.degree a)",
+                "tactic": "subst b"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact <a>incMatrix_mul_transpose_diag<\\/a> (R := R) G\"",
+                  "[{\"full_name\":\"SimpleGraph.incMatrix_mul_transpose_diag\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/IncMatrix.lean\",\"def_pos\":[126,9],\"def_end_pos\":[126,37]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case pos\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u2074 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b3 : Semiring R\na\u271d b : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b2 : (a : \u03b1) \u2192 Fintype \u2191(G.neighborSet a)\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableRel G.Adj\na : \u03b1\n\u22a2 (incMatrix R G * (incMatrix R G)\u1d40) a a = \u2191(G.degree a)",
+                "tactic": "exact incMatrix_mul_transpose_diag (R := R) G"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact G.incMatrix_mul_transpose_apply_of_adj h'\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case pos\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u2074 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b3 : Semiring R\na\u271d b\u271d : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b2 : (a : \u03b1) \u2192 Fintype \u2191(G.neighborSet a)\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableRel G.Adj\na b : \u03b1\nh : \u00aca = b\nh' : G.Adj a b\n\u22a2 (incMatrix R G * (incMatrix R G)\u1d40) a b = 1",
+                "tactic": "exact G.incMatrix_mul_transpose_apply_of_adj h'"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp only [<a>Matrix.mul_apply<\\/a>, <a>Matrix.transpose_apply<\\/a>,\\n      G.incMatrix_apply_mul_incMatrix_apply_of_not_adj h h', <a>sum_const_zero<\\/a>]\"",
+                  "[{\"full_name\":\"Matrix.mul_apply\",\"def_path\":\"Mathlib\\/Data\\/Matrix\\/Basic.lean\",\"def_pos\":[984,9],\"def_end_pos\":[984,18]},{\"full_name\":\"Matrix.transpose_apply\",\"def_path\":\"Mathlib\\/Data\\/Matrix\\/Basic.lean\",\"def_pos\":[159,9],\"def_end_pos\":[159,24]},{\"full_name\":\"Finset.sum_const_zero\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Finset.lean\",\"def_pos\":[394,3],\"def_end_pos\":[394,14]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case neg\nR : Type u_1\n\u03b1 : Type u_2\nG : SimpleGraph \u03b1\ninst\u271d\u2074 : Fintype (Sym2 \u03b1)\ninst\u271d\u00b3 : Semiring R\na\u271d b\u271d : \u03b1\ne : Sym2 \u03b1\ninst\u271d\u00b2 : (a : \u03b1) \u2192 Fintype \u2191(G.neighborSet a)\ninst\u271d\u00b9 : DecidableEq \u03b1\ninst\u271d : DecidableRel G.Adj\na b : \u03b1\nh : \u00aca = b\nh' : \u00acG.Adj a b\n\u22a2 (incMatrix R G * (incMatrix R G)\u1d40) a b = 0",
+                "tactic": "simp only [Matrix.mul_apply, Matrix.transpose_apply,\n  G.incMatrix_apply_mul_incMatrix_apply_of_not_adj h h', sum_const_zero]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "SimpleGraph.incMatrix_mul_transpose"
+      }
+    ],
+    "validation_rejected_proofs": 2,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000840-0000-47ce30029cb45d46.parquet",
+      "sha256": "47ce30029cb45d46f017993f7edf24993b113e8224d505e3e29c5aff28546c11",
+      "bytes": 55585,
+      "rows": 12,
+      "revision": "70b6b795247ac9d70fb829e06dbcf94288c16b02"
+    },
+    {
+      "path": "data/dev/mathlib-000840-0000-0a2d290156908d70.parquet",
+      "sha256": "0a2d290156908d70c3b23a13517e353a871eb15ac07df86bf02da05f109800e7",
+      "bytes": 48046,
+      "rows": 2,
+      "revision": "70b6b795247ac9d70fb829e06dbcf94288c16b02"
+    },
+    {
+      "path": "data/internal_test/mathlib-000840-0000-e4705cbe860586c1.parquet",
+      "sha256": "e4705cbe860586c1d5f5358fe89ec0ae4c6c7c3e96cee9b6a84f3e5b590badb1",
+      "bytes": 46205,
+      "rows": 4,
+      "revision": "70b6b795247ac9d70fb829e06dbcf94288c16b02"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:SimpleGraph.hasse_preconnected_of_pred",
+    "mathlib:SimpleGraph.hasse_preconnected_of_succ",
+    "mathlib:SimpleGraph.hasse_prod",
+    "mathlib:SimpleGraph.incMatrix_apply'",
+    "mathlib:SimpleGraph.incMatrix_apply_eq_zero_iff",
+    "mathlib:SimpleGraph.incMatrix_apply_mul_incMatrix_apply_of_not_adj",
+    "mathlib:SimpleGraph.incMatrix_of_mem_incidenceSet",
+    "mathlib:SimpleGraph.incMatrix_of_not_mem_incidenceSet",
+    "mathlib:SimpleGraph.pathGraph_adj",
+    "mathlib:SimpleGraph.pathGraph_two_eq_top"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Hasse.lean\",null,null,\"SimpleGraph.hasse_preconnected_of_pred\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Hasse.lean\",null,null,\"SimpleGraph.hasse_preconnected_of_succ\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Hasse.lean\",null,null,\"SimpleGraph.hasse_prod\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Hasse.lean\",null,null,\"SimpleGraph.pathGraph_adj\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Hasse.lean\",null,null,\"SimpleGraph.pathGraph_two_eq_top\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean\",null,null,\"SimpleGraph.incMatrix_apply'\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean\",null,null,\"SimpleGraph.incMatrix_apply_eq_zero_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean\",null,null,\"SimpleGraph.incMatrix_apply_mul_incMatrix_apply_of_not_adj\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean\",null,null,\"SimpleGraph.incMatrix_of_mem_incidenceSet\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean\",null,null,\"SimpleGraph.incMatrix_of_not_mem_incidenceSet\"]"
+  ]
+}

manifests/batches/mathlib/000842.json

@@ -0,0 +1,599 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000842",
+  "batch_fingerprint": "45d2d3b5be26486dd05625418558353894101ebdd6bcd88c598fab943738f969",
+  "evidence": {
+    "batch_fingerprint": "45d2d3b5be26486dd05625418558353894101ebdd6bcd88c598fab943738f969",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "no internal trace for tactic 'classical\\nrw [isMatching_iff_forall_degree] at h\\nuse M.coe.edgeFinset.card\\nrw [\u2190 two_mul, \u2190 M.coe.sum_degrees_eq_twice_card_edges]\\nconvert_to _ = Finset.sum Finset.univ fun v => SimpleGraph.degree (Subgraph.coe M) v using 3\\nsimp [h, Finset.card_univ]'",
+        "full_name": "SimpleGraph.Subgraph.IsMatching.even_card",
+        "id": "SimpleGraph.Subgraph.IsMatching.even_card",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            111,
+            29
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Matching.lean",
+          "full_name": "SimpleGraph.Subgraph.IsMatching.even_card",
+          "start": [
+            101,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"classical\\n  rw [<a>isMatching_iff_forall_degree<\\/a>] at h\\n  use M.coe.edgeFinset.card\\n  rw [\\u2190 <a>two_mul<\\/a>, \\u2190 M.coe.sum_degrees_eq_twice_card_edges]\\n  -- Porting note: `SimpleGraph.Subgraph.coe_degree` does not trigger because it uses\\n  -- instance arguments instead of implicit arguments for the first `Fintype` argument.\\n  -- Using a `convert_to` to swap out the `Fintype` instance to the \\\"right\\\" one.\\n  convert_to _ = <a>Finset.sum<\\/a> <a>Finset.univ<\\/a> fun v => <a>SimpleGraph.degree<\\/a> (<a>Subgraph.coe<\\/a> M) v using 3\\n  simp [h, <a>Finset.card_univ<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.Subgraph.isMatching_iff_forall_degree\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Matching.lean\",\"def_pos\":[96,9],\"def_end_pos\":[96,37]},{\"full_name\":\"two_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[179,9],\"def_end_pos\":[179,16]},{\"full_name\":\"Finset.sum\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Finset.lean\",\"def_pos\":[52,3],\"def_end_pos\":[52,14]},{\"full_name\":\"Finset.univ\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Basic.lean\",\"def_pos\":[70,5],\"def_end_pos\":[70,9]},{\"full_name\":\"SimpleGraph.degree\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Finite.lean\",\"def_pos\":[223,5],\"def_end_pos\":[223,11]},{\"full_name\":\"SimpleGraph.Subgraph.coe\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Subgraph.lean\",\"def_pos\":[136,15],\"def_end_pos\":[136,18]},{\"full_name\":\"Finset.card_univ\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[250,9],\"def_end_pos\":[250,25]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u\nG : SimpleGraph V\nM\u271d M : G.Subgraph\ninst\u271d : Fintype \u2191M.verts\nh : M.IsMatching\n\u22a2 Even M.verts.toFinset.card",
+              "tactic": "classical\nrw [isMatching_iff_forall_degree] at h\nuse M.coe.edgeFinset.card\nrw [\u2190 two_mul, \u2190 M.coe.sum_degrees_eq_twice_card_edges]\nconvert_to _ = Finset.sum Finset.univ fun v => SimpleGraph.degree (Subgraph.coe M) v using 3\nsimp [h, Finset.card_univ]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>isMatching_iff_forall_degree<\\/a>] at h\"",
+                "[{\"full_name\":\"SimpleGraph.Subgraph.isMatching_iff_forall_degree\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Matching.lean\",\"def_pos\":[96,9],\"def_end_pos\":[96,37]}]"
+              ],
+              "state_after": "V : Type u\nG : SimpleGraph V\nM\u271d M : G.Subgraph\ninst\u271d : Fintype \u2191M.verts\nh : \u2200 v \u2208 M.verts, M.degree v = 1\n\u22a2 Even M.verts.toFinset.card",
+              "state_before": "V : Type u\nG : SimpleGraph V\nM\u271d M : G.Subgraph\ninst\u271d : Fintype \u2191M.verts\nh : M.IsMatching\n\u22a2 Even M.verts.toFinset.card",
+              "tactic": "rw [isMatching_iff_forall_degree] at h"
+            },
+            {
+              "annotated_tactic": [
+                "\"use M.coe.edgeFinset.card\"",
+                "[]"
+              ],
+              "state_after": "case h\nV : Type u\nG : SimpleGraph V\nM\u271d M : G.Subgraph\ninst\u271d : Fintype \u2191M.verts\nh : \u2200 v \u2208 M.verts, M.degree v = 1\n\u22a2 M.verts.toFinset.card = M.coe.edgeFinset.card + M.coe.edgeFinset.card",
+              "state_before": "V : Type u\nG : SimpleGraph V\nM\u271d M : G.Subgraph\ninst\u271d : Fintype \u2191M.verts\nh : \u2200 v \u2208 M.verts, M.degree v = 1\n\u22a2 Even M.verts.toFinset.card",
+              "tactic": "use M.coe.edgeFinset.card"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>two_mul<\\/a>, \\u2190 M.coe.sum_degrees_eq_twice_card_edges]\"",
+                "[{\"full_name\":\"two_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[179,9],\"def_end_pos\":[179,16]}]"
+              ],
+              "state_after": "case h\nV : Type u\nG : SimpleGraph V\nM\u271d M : G.Subgraph\ninst\u271d : Fintype \u2191M.verts\nh : \u2200 v \u2208 M.verts, M.degree v = 1\n\u22a2 M.verts.toFinset.card = \u2211 v : \u2191M.verts, M.coe.degree v",
+              "state_before": "case h\nV : Type u\nG : SimpleGraph V\nM\u271d M : G.Subgraph\ninst\u271d : Fintype \u2191M.verts\nh : \u2200 v \u2208 M.verts, M.degree v = 1\n\u22a2 M.verts.toFinset.card = M.coe.edgeFinset.card + M.coe.edgeFinset.card",
+              "tactic": "rw [\u2190 two_mul, \u2190 M.coe.sum_degrees_eq_twice_card_edges]"
+            },
+            {
+              "annotated_tactic": [
+                "\"convert_to _ = <a>Finset.sum<\\/a> <a>Finset.univ<\\/a> fun v => <a>SimpleGraph.degree<\\/a> (<a>Subgraph.coe<\\/a> M) v using 3\"",
+                "[{\"full_name\":\"Finset.sum\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Finset.lean\",\"def_pos\":[52,3],\"def_end_pos\":[52,14]},{\"full_name\":\"Finset.univ\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Basic.lean\",\"def_pos\":[70,5],\"def_end_pos\":[70,9]},{\"full_name\":\"SimpleGraph.degree\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Finite.lean\",\"def_pos\":[223,5],\"def_end_pos\":[223,11]},{\"full_name\":\"SimpleGraph.Subgraph.coe\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Subgraph.lean\",\"def_pos\":[136,15],\"def_end_pos\":[136,18]}]"
+              ],
+              "state_after": "case h.convert_2\nV : Type u\nG : SimpleGraph V\nM\u271d M : G.Subgraph\ninst\u271d : Fintype \u2191M.verts\nh : \u2200 v \u2208 M.verts, M.degree v = 1\n\u22a2 M.verts.toFinset.card = \u2211 v : \u2191M.verts, M.coe.degree v",
+              "state_before": "case h\nV : Type u\nG : SimpleGraph V\nM\u271d M : G.Subgraph\ninst\u271d : Fintype \u2191M.verts\nh : \u2200 v \u2208 M.verts, M.degree v = 1\n\u22a2 M.verts.toFinset.card = \u2211 v : \u2191M.verts, M.coe.degree v",
+              "tactic": "convert_to _ = Finset.sum Finset.univ fun v => SimpleGraph.degree (Subgraph.coe M) v using 3"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [h, <a>Finset.card_univ<\\/a>]\"",
+                "[{\"full_name\":\"Finset.card_univ\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[250,9],\"def_end_pos\":[250,25]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.convert_2\nV : Type u\nG : SimpleGraph V\nM\u271d M : G.Subgraph\ninst\u271d : Fintype \u2191M.verts\nh : \u2200 v \u2208 M.verts, M.degree v = 1\n\u22a2 M.verts.toFinset.card = \u2211 v : \u2191M.verts, M.coe.degree v",
+              "tactic": "simp [h, Finset.card_univ]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Matching.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'simpa only [h.2.card_verts] using IsMatching.even_card h.1'",
+        "full_name": "SimpleGraph.Subgraph.IsPerfectMatching.even_card",
+        "id": "SimpleGraph.Subgraph.IsPerfectMatching.even_card",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            130,
+            61
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Matching.lean",
+          "full_name": "SimpleGraph.Subgraph.IsPerfectMatching.even_card",
+          "start": [
+            127,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"classical\\n  simpa only [h.2.<a>card_verts<\\/a>] using <a>IsMatching.even_card<\\/a> h.1\"",
+                "[{\"full_name\":\"SimpleGraph.Subgraph.IsSpanning.card_verts\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Subgraph.lean\",\"def_pos\":[784,9],\"def_end_pos\":[784,30]},{\"full_name\":\"SimpleGraph.Subgraph.IsMatching.even_card\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Matching.lean\",\"def_pos\":[101,9],\"def_end_pos\":[101,29]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u\nG : SimpleGraph V\nM\u271d M : G.Subgraph\ninst\u271d : Fintype V\nh : M.IsPerfectMatching\n\u22a2 Even (Fintype.card V)",
+              "tactic": "classical\nsimpa only [h.2.card_verts] using IsMatching.even_card h.1"
+            },
+            {
+              "annotated_tactic": [
+                "\"simpa only [h.2.<a>card_verts<\\/a>] using <a>IsMatching.even_card<\\/a> h.1\"",
+                "[{\"full_name\":\"SimpleGraph.Subgraph.IsSpanning.card_verts\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Subgraph.lean\",\"def_pos\":[784,9],\"def_end_pos\":[784,30]},{\"full_name\":\"SimpleGraph.Subgraph.IsMatching.even_card\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Matching.lean\",\"def_pos\":[101,9],\"def_end_pos\":[101,29]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u\nG : SimpleGraph V\nM\u271d M : G.Subgraph\ninst\u271d : Fintype V\nh : M.IsPerfectMatching\n\u22a2 Even (Fintype.card V)",
+              "tactic": "simpa only [h.2.card_verts] using IsMatching.even_card h.1"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Matching.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.Connected.exists_walk_of_dist",
+        "id": "SimpleGraph.Connected.exists_walk_of_dist",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            62,
+            34
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Metric.lean",
+          "full_name": "SimpleGraph.Connected.exists_walk_of_dist",
+          "start": [
+            60,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.Reachable.exists_walk_of_dist",
+        "id": "SimpleGraph.Reachable.exists_walk_of_dist",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            57,
+            56
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Metric.lean",
+          "full_name": "SimpleGraph.Reachable.exists_walk_of_dist",
+          "start": [
+            55,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.Reachable.of_dist_ne_zero",
+        "id": "SimpleGraph.Reachable.of_dist_ne_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            130,
+            45
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Metric.lean",
+          "full_name": "SimpleGraph.Reachable.of_dist_ne_zero",
+          "start": [
+            129,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Metric.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'have : p.bypass = p := by\\n  apply Walk.bypass_eq_self_of_length_le\\n  calc p.length\\n    _ = G.dist u v := hp\\n    _ \u2264 p.bypass.length := dist_le p.bypass'",
+        "full_name": "SimpleGraph.Walk.isPath_of_length_eq_dist",
+        "id": "SimpleGraph.Walk.isPath_of_length_eq_dist",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            153,
+            27
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Metric.lean",
+          "full_name": "SimpleGraph.Walk.isPath_of_length_eq_dist",
+          "start": [
+            144,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"classical\\n  have : p.bypass = p := by\\n    apply <a>Walk.bypass_eq_self_of_length_le<\\/a>\\n    calc <a>p.length<\\/a>\\n      _ = G.dist u v := hp\\n      _ \\u2264 p.bypass.length := <a>dist_le<\\/a> p.bypass\\n  rw [\\u2190 this]\\n  apply <a>Walk.bypass_isPath<\\/a>\"",
+                "[{\"full_name\":\"SimpleGraph.Walk.bypass_eq_self_of_length_le\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Connectivity.lean\",\"def_pos\":[1524,7],\"def_end_pos\":[1524,34]},{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]},{\"full_name\":\"SimpleGraph.dist_le\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Metric.lean\",\"def_pos\":[65,9],\"def_end_pos\":[65,16]},{\"full_name\":\"SimpleGraph.Walk.bypass_isPath\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Connectivity.lean\",\"def_pos\":[1500,9],\"def_end_pos\":[1500,22]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u_1\nG : SimpleGraph V\nu v : V\np : G.Walk u v\nhp : p.length = G.dist u v\n\u22a2 p.IsPath",
+              "tactic": "classical\nhave : p.bypass = p := by\n  apply Walk.bypass_eq_self_of_length_le\n  calc p.length\n    _ = G.dist u v := hp\n    _ \u2264 p.bypass.length := dist_le p.bypass\nrw [\u2190 this]\napply Walk.bypass_isPath"
+            },
+            {
+              "annotated_tactic": [
+                "\"have : p.bypass = p := by\\n    apply <a>Walk.bypass_eq_self_of_length_le<\\/a>\\n    calc <a>p.length<\\/a>\\n      _ = G.dist u v := hp\\n      _ \\u2264 p.bypass.length := <a>dist_le<\\/a> p.bypass\"",
+                "[{\"full_name\":\"SimpleGraph.Walk.bypass_eq_self_of_length_le\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Connectivity.lean\",\"def_pos\":[1524,7],\"def_end_pos\":[1524,34]},{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]},{\"full_name\":\"SimpleGraph.dist_le\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Metric.lean\",\"def_pos\":[65,9],\"def_end_pos\":[65,16]}]"
+              ],
+              "state_after": "V : Type u_1\nG : SimpleGraph V\nu v : V\np : G.Walk u v\nhp : p.length = G.dist u v\nthis : p.bypass = p\n\u22a2 p.IsPath",
+              "state_before": "V : Type u_1\nG : SimpleGraph V\nu v : V\np : G.Walk u v\nhp : p.length = G.dist u v\n\u22a2 p.IsPath",
+              "tactic": "have : p.bypass = p := by\n  apply Walk.bypass_eq_self_of_length_le\n  calc p.length\n    _ = G.dist u v := hp\n    _ \u2264 p.bypass.length := dist_le p.bypass"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 this]\"",
+                "[]"
+              ],
+              "state_after": "V : Type u_1\nG : SimpleGraph V\nu v : V\np : G.Walk u v\nhp : p.length = G.dist u v\nthis : p.bypass = p\n\u22a2 p.bypass.IsPath",
+              "state_before": "V : Type u_1\nG : SimpleGraph V\nu v : V\np : G.Walk u v\nhp : p.length = G.dist u v\nthis : p.bypass = p\n\u22a2 p.IsPath",
+              "tactic": "rw [\u2190 this]"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Walk.bypass_isPath<\\/a>\"",
+                "[{\"full_name\":\"SimpleGraph.Walk.bypass_isPath\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Connectivity.lean\",\"def_pos\":[1500,9],\"def_end_pos\":[1500,22]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u_1\nG : SimpleGraph V\nu v : V\np : G.Walk u v\nhp : p.length = G.dist u v\nthis : p.bypass = p\n\u22a2 p.bypass.IsPath",
+              "tactic": "apply Walk.bypass_isPath"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Walk.bypass_eq_self_of_length_le<\\/a>\"",
+                "[{\"full_name\":\"SimpleGraph.Walk.bypass_eq_self_of_length_le\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Connectivity.lean\",\"def_pos\":[1524,7],\"def_end_pos\":[1524,34]}]"
+              ],
+              "state_after": "case h\nV : Type u_1\nG : SimpleGraph V\nu v : V\np : G.Walk u v\nhp : p.length = G.dist u v\n\u22a2 p.length \u2264 p.bypass.length",
+              "state_before": "V : Type u_1\nG : SimpleGraph V\nu v : V\np : G.Walk u v\nhp : p.length = G.dist u v\n\u22a2 p.bypass = p",
+              "tactic": "apply Walk.bypass_eq_self_of_length_le"
+            },
+            {
+              "annotated_tactic": [
+                "\"calc <a>p.length<\\/a>\\n      _ = G.dist u v := hp\\n      _ \\u2264 p.bypass.length := <a>dist_le<\\/a> p.bypass\"",
+                "[{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]},{\"full_name\":\"SimpleGraph.dist_le\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Metric.lean\",\"def_pos\":[65,9],\"def_end_pos\":[65,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h\nV : Type u_1\nG : SimpleGraph V\nu v : V\np : G.Walk u v\nhp : p.length = G.dist u v\n\u22a2 p.length \u2264 p.bypass.length",
+              "tactic": "calc p.length\n  _ = G.dist u v := hp\n  _ \u2264 p.bypass.length := dist_le p.bypass"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.dist_le",
+        "id": "SimpleGraph.dist_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            66,
+            23
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Metric.lean",
+          "full_name": "SimpleGraph.dist_le",
+          "start": [
+            65,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Metric.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.exists_walk_of_dist_ne_zero",
+        "id": "SimpleGraph.exists_walk_of_dist_ne_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            134,
+            52
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Metric.lean",
+          "full_name": "SimpleGraph.exists_walk_of_dist_ne_zero",
+          "start": [
+            132,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Metric.lean"
+      }
+    ],
+    "input_proofs": 30,
+    "input_units": 2,
+    "proofs": 22,
+    "published_proofs": 19,
+    "published_transitions": 35,
+    "replay_failures": [],
+    "transitions": 49,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Combinatorics/SimpleGraph/Matching.lean",
+        "proof_id": "mathlib:SimpleGraph.Subgraph.isPerfectMatching_iff",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              119,
+              25
+            ],
+            "file_path": "Mathlib/Combinatorics/SimpleGraph/Matching.lean",
+            "full_name": "SimpleGraph.Subgraph.isPerfectMatching_iff",
+            "start": [
+              114,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"refine \\u27e8?_, fun hm => \\u27e8fun v _ => hm v, fun v => ?_\\u27e9\\u27e9\"",
+                  "[]"
+                ],
+                "state_after": "case refine_1\nV : Type u\nG : SimpleGraph V\nM : G.Subgraph\n\u22a2 M.IsPerfectMatching \u2192 \u2200 (v : V), \u2203! w, M.Adj v w\n\ncase refine_2\nV : Type u\nG : SimpleGraph V\nM : G.Subgraph\nhm : \u2200 (v : V), \u2203! w, M.Adj v w\nv : V\n\u22a2 v \u2208 M.verts",
+                "state_before": "V : Type u\nG : SimpleGraph V\nM : G.Subgraph\n\u22a2 M.IsPerfectMatching \u2194 \u2200 (v : V), \u2203! w, M.Adj v w",
+                "tactic": "refine \u27e8?_, fun hm => \u27e8fun v _ => hm v, fun v => ?_\u27e9\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rintro \\u27e8hm, hs\\u27e9 v\"",
+                  "[]"
+                ],
+                "state_after": "case refine_1.intro\nV : Type u\nG : SimpleGraph V\nM : G.Subgraph\nhm : M.IsMatching\nhs : M.IsSpanning\nv : V\n\u22a2 \u2203! w, M.Adj v w",
+                "state_before": "case refine_1\nV : Type u\nG : SimpleGraph V\nM : G.Subgraph\n\u22a2 M.IsPerfectMatching \u2192 \u2200 (v : V), \u2203! w, M.Adj v w",
+                "tactic": "rintro \u27e8hm, hs\u27e9 v"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact hm (hs v)\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case refine_1.intro\nV : Type u\nG : SimpleGraph V\nM : G.Subgraph\nhm : M.IsMatching\nhs : M.IsSpanning\nv : V\n\u22a2 \u2203! w, M.Adj v w",
+                "tactic": "exact hm (hs v)"
+              },
+              {
+                "annotated_tactic": [
+                  "\"obtain \\u27e8w, hw, -\\u27e9 := hm v\"",
+                  "[]"
+                ],
+                "state_after": "case refine_2.intro.intro\nV : Type u\nG : SimpleGraph V\nM : G.Subgraph\nhm : \u2200 (v : V), \u2203! w, M.Adj v w\nv w : V\nhw : M.Adj v w\n\u22a2 v \u2208 M.verts",
+                "state_before": "case refine_2\nV : Type u\nG : SimpleGraph V\nM : G.Subgraph\nhm : \u2200 (v : V), \u2203! w, M.Adj v w\nv : V\n\u22a2 v \u2208 M.verts",
+                "tactic": "obtain \u27e8w, hw, -\u27e9 := hm v"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact M.edge_vert hw\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case refine_2.intro.intro\nV : Type u\nG : SimpleGraph V\nM : G.Subgraph\nhm : \u2200 (v : V), \u2203! w, M.Adj v w\nv w : V\nhw : M.Adj v w\n\u22a2 v \u2208 M.verts",
+                "tactic": "exact M.edge_vert hw"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "SimpleGraph.Subgraph.isPerfectMatching_iff"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Combinatorics/SimpleGraph/Metric.lean",
+        "proof_id": "mathlib:SimpleGraph.dist_comm",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              122,
+              48
+            ],
+            "file_path": "Mathlib/Combinatorics/SimpleGraph/Metric.lean",
+            "full_name": "SimpleGraph.dist_comm",
+            "start": [
+              118,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"by_cases h : G.Reachable u v\"",
+                  "[]"
+                ],
+                "state_after": "case pos\nV : Type u_1\nG : SimpleGraph V\nu v : V\nh : G.Reachable u v\n\u22a2 G.dist u v = G.dist v u\n\ncase neg\nV : Type u_1\nG : SimpleGraph V\nu v : V\nh : \u00acG.Reachable u v\n\u22a2 G.dist u v = G.dist v u",
+                "state_before": "V : Type u_1\nG : SimpleGraph V\nu v : V\n\u22a2 G.dist u v = G.dist v u",
+                "tactic": "by_cases h : G.Reachable u v"
+              },
+              {
+                "annotated_tactic": [
+                  "\"apply <a>le_antisymm<\\/a> (<a>dist_comm_aux<\\/a> h) (<a>dist_comm_aux<\\/a> h.symm)\"",
+                  "[{\"full_name\":\"le_antisymm\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[188,9],\"def_end_pos\":[188,20]},{\"full_name\":\"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.dist_comm_aux\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Metric.lean\",\"def_pos\":[113,17],\"def_end_pos\":[113,30]},{\"full_name\":\"_private.Mathlib.Combinatorics.SimpleGraph.Metric.0.SimpleGraph.dist_comm_aux\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Metric.lean\",\"def_pos\":[113,17],\"def_end_pos\":[113,30]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case pos\nV : Type u_1\nG : SimpleGraph V\nu v : V\nh : G.Reachable u v\n\u22a2 G.dist u v = G.dist v u",
+                "tactic": "apply le_antisymm (dist_comm_aux h) (dist_comm_aux h.symm)"
+              },
+              {
+                "annotated_tactic": [
+                  "\"have h' : \\u00acG.Reachable v u := fun h' => <a>absurd<\\/a> h'.symm h\"",
+                  "[{\"full_name\":\"absurd\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[246,21],\"def_end_pos\":[246,27]}]"
+                ],
+                "state_after": "case neg\nV : Type u_1\nG : SimpleGraph V\nu v : V\nh : \u00acG.Reachable u v\nh' : \u00acG.Reachable v u\n\u22a2 G.dist u v = G.dist v u",
+                "state_before": "case neg\nV : Type u_1\nG : SimpleGraph V\nu v : V\nh : \u00acG.Reachable u v\n\u22a2 G.dist u v = G.dist v u",
+                "tactic": "have h' : \u00acG.Reachable v u := fun h' => absurd h'.symm h"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp [h, h', <a>dist_eq_zero_of_not_reachable<\\/a>]\"",
+                  "[{\"full_name\":\"SimpleGraph.dist_eq_zero_of_not_reachable\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Metric.lean\",\"def_pos\":[95,9],\"def_end_pos\":[95,38]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case neg\nV : Type u_1\nG : SimpleGraph V\nu v : V\nh : \u00acG.Reachable u v\nh' : \u00acG.Reachable v u\n\u22a2 G.dist u v = G.dist v u",
+                "tactic": "simp [h, h', dist_eq_zero_of_not_reachable]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "SimpleGraph.dist_comm"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Combinatorics/SimpleGraph/Metric.lean",
+        "proof_id": "mathlib:SimpleGraph.dist_eq_one_iff_adj",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              142,
+              75
+            ],
+            "file_path": "Mathlib/Combinatorics/SimpleGraph/Metric.lean",
+            "full_name": "SimpleGraph.dist_eq_one_iff_adj",
+            "start": [
+              137,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"refine \\u27e8fun h \\u21a6 ?_, fun h \\u21a6 ?_\\u27e9\"",
+                  "[]"
+                ],
+                "state_after": "case refine_1\nV : Type u_1\nG : SimpleGraph V\nu v : V\nh : G.dist u v = 1\n\u22a2 G.Adj u v\n\ncase refine_2\nV : Type u_1\nG : SimpleGraph V\nu v : V\nh : G.Adj u v\n\u22a2 G.dist u v = 1",
+                "state_before": "V : Type u_1\nG : SimpleGraph V\nu v : V\n\u22a2 G.dist u v = 1 \u2194 G.Adj u v",
+                "tactic": "refine \u27e8fun h \u21a6 ?_, fun h \u21a6 ?_\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"let \\u27e8w, hw\\u27e9 := <a>exists_walk_of_dist_ne_zero<\\/a> <| <a>ne_zero_of_eq_one<\\/a> h\"",
+                  "[{\"full_name\":\"SimpleGraph.exists_walk_of_dist_ne_zero\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Metric.lean\",\"def_pos\":[132,7],\"def_end_pos\":[132,34]},{\"full_name\":\"ne_zero_of_eq_one\",\"def_path\":\"Mathlib\\/Algebra\\/NeZero.lean\",\"def_pos\":[61,7],\"def_end_pos\":[61,24]}]"
+                ],
+                "state_after": "case refine_1\nV : Type u_1\nG : SimpleGraph V\nu v : V\nh : G.dist u v = 1\nw : G.Walk u v\nhw : w.length = G.dist u v\n\u22a2 G.Adj u v",
+                "state_before": "case refine_1\nV : Type u_1\nG : SimpleGraph V\nu v : V\nh : G.dist u v = 1\n\u22a2 G.Adj u v",
+                "tactic": "let \u27e8w, hw\u27e9 := exists_walk_of_dist_ne_zero <| ne_zero_of_eq_one h"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact w.adj_of_length_eq_one <| h \\u25b8 hw\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case refine_1\nV : Type u_1\nG : SimpleGraph V\nu v : V\nh : G.dist u v = 1\nw : G.Walk u v\nhw : w.length = G.dist u v\n\u22a2 G.Adj u v",
+                "tactic": "exact w.adj_of_length_eq_one <| h \u25b8 hw"
+              },
+              {
+                "annotated_tactic": [
+                  "\"have : h.toWalk.length = 1 := <a>Walk.length_cons<\\/a> _ _\"",
+                  "[{\"full_name\":\"SimpleGraph.Walk.length_cons\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Connectivity.lean\",\"def_pos\":[380,9],\"def_end_pos\":[380,20]}]"
+                ],
+                "state_after": "case refine_2\nV : Type u_1\nG : SimpleGraph V\nu v : V\nh : G.Adj u v\nthis : h.toWalk.length = 1\n\u22a2 G.dist u v = 1",
+                "state_before": "case refine_2\nV : Type u_1\nG : SimpleGraph V\nu v : V\nh : G.Adj u v\n\u22a2 G.dist u v = 1",
+                "tactic": "have : h.toWalk.length = 1 := Walk.length_cons _ _"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact <a>ge_antisymm<\\/a> (h.reachable.pos_dist_of_ne h.ne) (this \\u25b8 <a>dist_le<\\/a> _)\"",
+                  "[{\"full_name\":\"ge_antisymm\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[94,9],\"def_end_pos\":[94,20]},{\"full_name\":\"SimpleGraph.dist_le\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Metric.lean\",\"def_pos\":[65,9],\"def_end_pos\":[65,16]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case refine_2\nV : Type u_1\nG : SimpleGraph V\nu v : V\nh : G.Adj u v\nthis : h.toWalk.length = 1\n\u22a2 G.dist u v = 1",
+                "tactic": "exact ge_antisymm (h.reachable.pos_dist_of_ne h.ne) (this \u25b8 dist_le _)"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "SimpleGraph.dist_eq_one_iff_adj"
+      }
+    ],
+    "validation_rejected_proofs": 3,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000842-0000-b6bf4fb79b538bfe.parquet",
+      "sha256": "b6bf4fb79b538bfe83f6db5cbd4e14ca52f1ebd0b5296e514a848b5b6045b2ed",
+      "bytes": 68489,
+      "rows": 23,
+      "revision": "70b6b795247ac9d70fb829e06dbcf94288c16b02"
+    },
+    {
+      "path": "data/dev/mathlib-000842-0000-53859af47b96dd5c.parquet",
+      "sha256": "53859af47b96dd5c03c289a1d948e5e98d7906f0fcdf8004dfb46170eb705dd8",
+      "bytes": 30906,
+      "rows": 4,
+      "revision": "70b6b795247ac9d70fb829e06dbcf94288c16b02"
+    },
+    {
+      "path": "data/internal_test/mathlib-000842-0000-b89c470872cb17ef.parquet",
+      "sha256": "b89c470872cb17ef514eb373c983cd4053b3f0feeaf09cf49a5a23df5b3bc16b",
+      "bytes": 48676,
+      "rows": 8,
+      "revision": "70b6b795247ac9d70fb829e06dbcf94288c16b02"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:SimpleGraph.Connected.dist_eq_zero_iff",
+    "mathlib:SimpleGraph.Connected.dist_triangle",
+    "mathlib:SimpleGraph.Connected.exists_path_of_dist",
+    "mathlib:SimpleGraph.Connected.pos_dist_of_ne",
+    "mathlib:SimpleGraph.Reachable.dist_eq_zero_iff",
+    "mathlib:SimpleGraph.Reachable.exists_path_of_dist",
+    "mathlib:SimpleGraph.Reachable.pos_dist_of_ne",
+    "mathlib:SimpleGraph.Subgraph.IsMatching.support_eq_verts",
+    "mathlib:SimpleGraph.Subgraph.IsMatching.toEdge.surjective",
+    "mathlib:SimpleGraph.Subgraph.IsMatching.toEdge_eq_of_adj",
+    "mathlib:SimpleGraph.Subgraph.IsMatching.toEdge_eq_toEdge_of_adj",
+    "mathlib:SimpleGraph.Subgraph.isMatching_iff_forall_degree",
+    "mathlib:SimpleGraph.Subgraph.isPerfectMatching_iff_forall_degree",
+    "mathlib:SimpleGraph.dist_comm_aux",
+    "mathlib:SimpleGraph.dist_eq_zero_iff_eq_or_not_reachable",
+    "mathlib:SimpleGraph.dist_eq_zero_of_not_reachable",
+    "mathlib:SimpleGraph.dist_ne_zero_iff_ne_and_reachable",
+    "mathlib:SimpleGraph.dist_self",
+    "mathlib:SimpleGraph.nonempty_of_pos_dist"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Matching.lean\",null,null,\"SimpleGraph.Subgraph.IsMatching.support_eq_verts\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Matching.lean\",null,null,\"SimpleGraph.Subgraph.IsMatching.toEdge.surjective\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Matching.lean\",null,null,\"SimpleGraph.Subgraph.IsMatching.toEdge_eq_of_adj\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Matching.lean\",null,null,\"SimpleGraph.Subgraph.IsMatching.toEdge_eq_toEdge_of_adj\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Matching.lean\",null,null,\"SimpleGraph.Subgraph.isMatching_iff_forall_degree\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Matching.lean\",null,null,\"SimpleGraph.Subgraph.isPerfectMatching_iff_forall_degree\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Metric.lean\",null,null,\"SimpleGraph.Connected.dist_eq_zero_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Metric.lean\",null,null,\"SimpleGraph.Connected.dist_triangle\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Metric.lean\",null,null,\"SimpleGraph.Connected.exists_path_of_dist\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Metric.lean\",null,null,\"SimpleGraph.Connected.pos_dist_of_ne\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Metric.lean\",null,null,\"SimpleGraph.Reachable.dist_eq_zero_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Metric.lean\",null,null,\"SimpleGraph.Reachable.exists_path_of_dist\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Metric.lean\",null,null,\"SimpleGraph.Reachable.pos_dist_of_ne\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Metric.lean\",null,null,\"SimpleGraph.dist_comm_aux\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Metric.lean\",null,null,\"SimpleGraph.dist_eq_zero_iff_eq_or_not_reachable\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Metric.lean\",null,null,\"SimpleGraph.dist_eq_zero_of_not_reachable\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Metric.lean\",null,null,\"SimpleGraph.dist_ne_zero_iff_ne_and_reachable\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Metric.lean\",null,null,\"SimpleGraph.dist_self\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/SimpleGraph/Metric.lean\",null,null,\"SimpleGraph.nonempty_of_pos_dist\"]"
+  ]
+}

manifests/batches/mathlib/000843.json

@@ -0,0 +1,822 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000843",
+  "batch_fingerprint": "c58bf8dc3439a377dd5d2a157b4f55f66c1a6f5771337f35e4c2180b7bb1802b",
+  "evidence": {
+    "batch_fingerprint": "c58bf8dc3439a377dd5d2a157b4f55f66c1a6f5771337f35e4c2180b7bb1802b",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "no internal trace for tactic 'simp [incidenceFinset, incidenceSet_subset]'",
+        "full_name": "SimpleGraph.card_edgeFinset_replaceVertex_of_adj",
+        "id": "SimpleGraph.card_edgeFinset_replaceVertex_of_adj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            135,
+            8
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Operations.lean",
+          "full_name": "SimpleGraph.card_edgeFinset_replaceVertex_of_adj",
+          "start": [
+            126,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"have inc : G.incidenceFinset t \\u2286 G.edgeFinset := by simp [<a>incidenceFinset<\\/a>, <a>incidenceSet_subset<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.incidenceFinset\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Finite.lean\",\"def_pos\":[255,5],\"def_end_pos\":[255,20]},{\"full_name\":\"SimpleGraph.incidenceSet_subset\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[715,9],\"def_end_pos\":[715,28]}]"
+              ],
+              "state_after": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nha : G.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 (G.replaceVertex s t).edgeFinset.card = G.edgeFinset.card + G.degree s - G.degree t - 1",
+              "state_before": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nha : G.Adj s t\n\u22a2 (G.replaceVertex s t).edgeFinset.card = G.edgeFinset.card + G.degree s - G.degree t - 1",
+              "tactic": "have inc : G.incidenceFinset t \u2286 G.edgeFinset := by simp [incidenceFinset, incidenceSet_subset]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [G.edgeFinset_replaceVertex_of_adj ha, <a>card_sdiff<\\/a> (by simp [ha]),\\n    <a>card_union_of_disjoint<\\/a> G.disjoint_sdiff_neighborFinset_image, <a>card_sdiff<\\/a> inc,\\n    \\u2190 <a>Nat.sub_add_comm<\\/a> <| <a>card_le_card<\\/a> inc, <a>card_incidenceFinset_eq_degree<\\/a>]\"",
+                "[{\"full_name\":\"Finset.card_sdiff\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[562,9],\"def_end_pos\":[562,19]},{\"full_name\":\"Finset.card_union_of_disjoint\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[547,19],\"def_end_pos\":[547,41]},{\"full_name\":\"Finset.card_sdiff\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[562,9],\"def_end_pos\":[562,19]},{\"full_name\":\"Nat.sub_add_comm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Lemmas.lean\",\"def_pos\":[125,19],\"def_end_pos\":[125,31]},{\"full_name\":\"Finset.card_le_card\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[64,9],\"def_end_pos\":[64,21]},{\"full_name\":\"SimpleGraph.card_incidenceFinset_eq_degree\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Finite.lean\",\"def_pos\":[267,9],\"def_end_pos\":[267,39]}]"
+              ],
+              "state_after": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nha : G.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 G.edgeFinset.card + (image (fun x => s(x, t)) (G.neighborFinset s)).card - G.degree t - {s(t, t)}.card =\n    G.edgeFinset.card + G.degree s - G.degree t - 1",
+              "state_before": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nha : G.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 (G.replaceVertex s t).edgeFinset.card = G.edgeFinset.card + G.degree s - G.degree t - 1",
+              "tactic": "rw [G.edgeFinset_replaceVertex_of_adj ha, card_sdiff (by simp [ha]),\n  card_union_of_disjoint G.disjoint_sdiff_neighborFinset_image, card_sdiff inc,\n  \u2190 Nat.sub_add_comm <| card_le_card inc, card_incidenceFinset_eq_degree]"
+            },
+            {
+              "annotated_tactic": [
+                "\"congr 2\"",
+                "[]"
+              ],
+              "state_after": "case e_a.e_a\nV : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nha : G.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 G.edgeFinset.card + (image (fun x => s(x, t)) (G.neighborFinset s)).card = G.edgeFinset.card + G.degree s",
+              "state_before": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nha : G.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 G.edgeFinset.card + (image (fun x => s(x, t)) (G.neighborFinset s)).card - G.degree t - {s(t, t)}.card =\n    G.edgeFinset.card + G.degree s - G.degree t - 1",
+              "tactic": "congr 2"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>card_image_of_injective<\\/a>, <a>card_neighborFinset_eq_degree<\\/a>]\"",
+                "[{\"full_name\":\"Finset.card_image_of_injective\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[286,9],\"def_end_pos\":[286,32]},{\"full_name\":\"SimpleGraph.card_neighborFinset_eq_degree\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Finite.lean\",\"def_pos\":[232,9],\"def_end_pos\":[232,38]}]"
+              ],
+              "state_after": "case e_a.e_a.H\nV : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nha : G.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 Function.Injective fun x => s(x, t)",
+              "state_before": "case e_a.e_a\nV : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nha : G.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 G.edgeFinset.card + (image (fun x => s(x, t)) (G.neighborFinset s)).card = G.edgeFinset.card + G.degree s",
+              "tactic": "rw [card_image_of_injective, card_neighborFinset_eq_degree]"
+            },
+            {
+              "annotated_tactic": [
+                "\"unfold <a>Function.Injective<\\/a>\"",
+                "[{\"full_name\":\"Function.Injective\",\"def_path\":\"Mathlib\\/Init\\/Function.lean\",\"def_pos\":[123,5],\"def_end_pos\":[123,14]}]"
+              ],
+              "state_after": "case e_a.e_a.H\nV : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nha : G.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 \u2200 \u2983a\u2081 a\u2082 : V\u2984, (fun x => s(x, t)) a\u2081 = (fun x => s(x, t)) a\u2082 \u2192 a\u2081 = a\u2082",
+              "state_before": "case e_a.e_a.H\nV : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nha : G.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 Function.Injective fun x => s(x, t)",
+              "tactic": "unfold Function.Injective"
+            },
+            {
+              "annotated_tactic": [
+                "\"aesop\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case e_a.e_a.H\nV : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nha : G.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 \u2200 \u2983a\u2081 a\u2082 : V\u2984, (fun x => s(x, t)) a\u2081 = (fun x => s(x, t)) a\u2082 \u2192 a\u2081 = a\u2082",
+              "tactic": "aesop"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [<a>incidenceFinset<\\/a>, <a>incidenceSet_subset<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.incidenceFinset\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Finite.lean\",\"def_pos\":[255,5],\"def_end_pos\":[255,20]},{\"full_name\":\"SimpleGraph.incidenceSet_subset\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[715,9],\"def_end_pos\":[715,28]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nha : G.Adj s t\n\u22a2 G.incidenceFinset t \u2286 G.edgeFinset",
+              "tactic": "simp [incidenceFinset, incidenceSet_subset]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [ha]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nha : G.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 {s(t, t)} \u2286 G.edgeFinset \\ G.incidenceFinset t \u222a image (fun x => s(x, t)) (G.neighborFinset s)",
+              "tactic": "simp [ha]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Operations.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'simp [incidenceFinset, incidenceSet_subset]'",
+        "full_name": "SimpleGraph.card_edgeFinset_replaceVertex_of_not_adj",
+        "id": "SimpleGraph.card_edgeFinset_replaceVertex_of_not_adj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            124,
+            8
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Operations.lean",
+          "full_name": "SimpleGraph.card_edgeFinset_replaceVertex_of_not_adj",
+          "start": [
+            115,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"have inc : G.incidenceFinset t \\u2286 G.edgeFinset := by simp [<a>incidenceFinset<\\/a>, <a>incidenceSet_subset<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.incidenceFinset\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Finite.lean\",\"def_pos\":[255,5],\"def_end_pos\":[255,20]},{\"full_name\":\"SimpleGraph.incidenceSet_subset\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[715,9],\"def_end_pos\":[715,28]}]"
+              ],
+              "state_after": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nhn : \u00acG.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 (G.replaceVertex s t).edgeFinset.card = G.edgeFinset.card + G.degree s - G.degree t",
+              "state_before": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nhn : \u00acG.Adj s t\n\u22a2 (G.replaceVertex s t).edgeFinset.card = G.edgeFinset.card + G.degree s - G.degree t",
+              "tactic": "have inc : G.incidenceFinset t \u2286 G.edgeFinset := by simp [incidenceFinset, incidenceSet_subset]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [G.edgeFinset_replaceVertex_of_not_adj hn,\\n    <a>card_union_of_disjoint<\\/a> G.disjoint_sdiff_neighborFinset_image, <a>card_sdiff<\\/a> inc,\\n    \\u2190 <a>Nat.sub_add_comm<\\/a> <| <a>card_le_card<\\/a> inc, <a>card_incidenceFinset_eq_degree<\\/a>]\"",
+                "[{\"full_name\":\"Finset.card_union_of_disjoint\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[547,19],\"def_end_pos\":[547,41]},{\"full_name\":\"Finset.card_sdiff\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[562,9],\"def_end_pos\":[562,19]},{\"full_name\":\"Nat.sub_add_comm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Lemmas.lean\",\"def_pos\":[125,19],\"def_end_pos\":[125,31]},{\"full_name\":\"Finset.card_le_card\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[64,9],\"def_end_pos\":[64,21]},{\"full_name\":\"SimpleGraph.card_incidenceFinset_eq_degree\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Finite.lean\",\"def_pos\":[267,9],\"def_end_pos\":[267,39]}]"
+              ],
+              "state_after": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nhn : \u00acG.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 G.edgeFinset.card + (image (fun x => s(x, t)) (G.neighborFinset s)).card - G.degree t =\n    G.edgeFinset.card + G.degree s - G.degree t",
+              "state_before": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nhn : \u00acG.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 (G.replaceVertex s t).edgeFinset.card = G.edgeFinset.card + G.degree s - G.degree t",
+              "tactic": "rw [G.edgeFinset_replaceVertex_of_not_adj hn,\n  card_union_of_disjoint G.disjoint_sdiff_neighborFinset_image, card_sdiff inc,\n  \u2190 Nat.sub_add_comm <| card_le_card inc, card_incidenceFinset_eq_degree]"
+            },
+            {
+              "annotated_tactic": [
+                "\"congr 2\"",
+                "[]"
+              ],
+              "state_after": "case e_a.e_a\nV : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nhn : \u00acG.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 (image (fun x => s(x, t)) (G.neighborFinset s)).card = G.degree s",
+              "state_before": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nhn : \u00acG.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 G.edgeFinset.card + (image (fun x => s(x, t)) (G.neighborFinset s)).card - G.degree t =\n    G.edgeFinset.card + G.degree s - G.degree t",
+              "tactic": "congr 2"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>card_image_of_injective<\\/a>, <a>card_neighborFinset_eq_degree<\\/a>]\"",
+                "[{\"full_name\":\"Finset.card_image_of_injective\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[286,9],\"def_end_pos\":[286,32]},{\"full_name\":\"SimpleGraph.card_neighborFinset_eq_degree\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Finite.lean\",\"def_pos\":[232,9],\"def_end_pos\":[232,38]}]"
+              ],
+              "state_after": "case e_a.e_a.H\nV : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nhn : \u00acG.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 Function.Injective fun x => s(x, t)",
+              "state_before": "case e_a.e_a\nV : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nhn : \u00acG.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 (image (fun x => s(x, t)) (G.neighborFinset s)).card = G.degree s",
+              "tactic": "rw [card_image_of_injective, card_neighborFinset_eq_degree]"
+            },
+            {
+              "annotated_tactic": [
+                "\"unfold <a>Function.Injective<\\/a>\"",
+                "[{\"full_name\":\"Function.Injective\",\"def_path\":\"Mathlib\\/Init\\/Function.lean\",\"def_pos\":[123,5],\"def_end_pos\":[123,14]}]"
+              ],
+              "state_after": "case e_a.e_a.H\nV : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nhn : \u00acG.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 \u2200 \u2983a\u2081 a\u2082 : V\u2984, (fun x => s(x, t)) a\u2081 = (fun x => s(x, t)) a\u2082 \u2192 a\u2081 = a\u2082",
+              "state_before": "case e_a.e_a.H\nV : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nhn : \u00acG.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 Function.Injective fun x => s(x, t)",
+              "tactic": "unfold Function.Injective"
+            },
+            {
+              "annotated_tactic": [
+                "\"aesop\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case e_a.e_a.H\nV : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nhn : \u00acG.Adj s t\ninc : G.incidenceFinset t \u2286 G.edgeFinset\n\u22a2 \u2200 \u2983a\u2081 a\u2082 : V\u2984, (fun x => s(x, t)) a\u2081 = (fun x => s(x, t)) a\u2082 \u2192 a\u2081 = a\u2082",
+              "tactic": "aesop"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [<a>incidenceFinset<\\/a>, <a>incidenceSet_subset<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.incidenceFinset\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Finite.lean\",\"def_pos\":[255,5],\"def_end_pos\":[255,20]},{\"full_name\":\"SimpleGraph.incidenceSet_subset\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[715,9],\"def_end_pos\":[715,28]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\nhn : \u00acG.Adj s t\n\u22a2 G.incidenceFinset t \u2286 G.edgeFinset",
+              "tactic": "simp [incidenceFinset, incidenceSet_subset]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Operations.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rw [mem_sdiff, mem_incidenceFinset] at he'",
+        "full_name": "SimpleGraph.disjoint_sdiff_neighborFinset_image",
+        "id": "SimpleGraph.disjoint_sdiff_neighborFinset_image",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            113,
+            8
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Operations.lean",
+          "full_name": "SimpleGraph.disjoint_sdiff_neighborFinset_image",
+          "start": [
+            104,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [<a>disjoint_iff_ne<\\/a>]\"",
+                "[{\"full_name\":\"Finset.disjoint_iff_ne\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[969,9],\"def_end_pos\":[969,24]}]"
+              ],
+              "state_after": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\n\u22a2 \u2200 a \u2208 G.edgeFinset \\ G.incidenceFinset t, \u2200 b \u2208 image (fun x => s(x, t)) (G.neighborFinset s), a \u2260 b",
+              "state_before": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\n\u22a2 Disjoint (G.edgeFinset \\ G.incidenceFinset t) (image (fun x => s(x, t)) (G.neighborFinset s))",
+              "tactic": "rw [disjoint_iff_ne]"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro e he\"",
+                "[]"
+              ],
+              "state_after": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\ne : Sym2 V\nhe : e \u2208 G.edgeFinset \\ G.incidenceFinset t\n\u22a2 \u2200 b \u2208 image (fun x => s(x, t)) (G.neighborFinset s), e \u2260 b",
+              "state_before": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\n\u22a2 \u2200 a \u2208 G.edgeFinset \\ G.incidenceFinset t, \u2200 b \u2208 image (fun x => s(x, t)) (G.neighborFinset s), a \u2260 b",
+              "tactic": "intro e he"
+            },
+            {
+              "annotated_tactic": [
+                "\"have : t \\u2209 e := by\\n    rw [<a>mem_sdiff<\\/a>, <a>mem_incidenceFinset<\\/a>] at he\\n    obtain \\u27e8_, h\\u27e9 := he\\n    contrapose! h\\n    simp_all [<a>incidenceSet<\\/a>]\"",
+                "[{\"full_name\":\"Finset.mem_sdiff\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[2102,9],\"def_end_pos\":[2102,18]},{\"full_name\":\"SimpleGraph.mem_incidenceFinset\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Finite.lean\",\"def_pos\":[274,9],\"def_end_pos\":[274,28]},{\"full_name\":\"SimpleGraph.incidenceSet\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[711,5],\"def_end_pos\":[711,17]}]"
+              ],
+              "state_after": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\ne : Sym2 V\nhe : e \u2208 G.edgeFinset \\ G.incidenceFinset t\nthis : t \u2209 e\n\u22a2 \u2200 b \u2208 image (fun x => s(x, t)) (G.neighborFinset s), e \u2260 b",
+              "state_before": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\ne : Sym2 V\nhe : e \u2208 G.edgeFinset \\ G.incidenceFinset t\n\u22a2 \u2200 b \u2208 image (fun x => s(x, t)) (G.neighborFinset s), e \u2260 b",
+              "tactic": "have : t \u2209 e := by\n  rw [mem_sdiff, mem_incidenceFinset] at he\n  obtain \u27e8_, h\u27e9 := he\n  contrapose! h\n  simp_all [incidenceSet]"
+            },
+            {
+              "annotated_tactic": [
+                "\"aesop\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\ne : Sym2 V\nhe : e \u2208 G.edgeFinset \\ G.incidenceFinset t\nthis : t \u2209 e\n\u22a2 \u2200 b \u2208 image (fun x => s(x, t)) (G.neighborFinset s), e \u2260 b",
+              "tactic": "aesop"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>mem_sdiff<\\/a>, <a>mem_incidenceFinset<\\/a>] at he\"",
+                "[{\"full_name\":\"Finset.mem_sdiff\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[2102,9],\"def_end_pos\":[2102,18]},{\"full_name\":\"SimpleGraph.mem_incidenceFinset\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Finite.lean\",\"def_pos\":[274,9],\"def_end_pos\":[274,28]}]"
+              ],
+              "state_after": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\ne : Sym2 V\nhe : e \u2208 G.edgeFinset \u2227 e \u2209 G.incidenceSet t\n\u22a2 t \u2209 e",
+              "state_before": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\ne : Sym2 V\nhe : e \u2208 G.edgeFinset \\ G.incidenceFinset t\n\u22a2 t \u2209 e",
+              "tactic": "rw [mem_sdiff, mem_incidenceFinset] at he"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8_, h\\u27e9 := he\"",
+                "[]"
+              ],
+              "state_after": "case intro\nV : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\ne : Sym2 V\nleft\u271d : e \u2208 G.edgeFinset\nh : e \u2209 G.incidenceSet t\n\u22a2 t \u2209 e",
+              "state_before": "V : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\ne : Sym2 V\nhe : e \u2208 G.edgeFinset \u2227 e \u2209 G.incidenceSet t\n\u22a2 t \u2209 e",
+              "tactic": "obtain \u27e8_, h\u27e9 := he"
+            },
+            {
+              "annotated_tactic": [
+                "\"contrapose! h\"",
+                "[]"
+              ],
+              "state_after": "case intro\nV : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\ne : Sym2 V\nleft\u271d : e \u2208 G.edgeFinset\nh : t \u2208 e\n\u22a2 e \u2208 G.incidenceSet t",
+              "state_before": "case intro\nV : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\ne : Sym2 V\nleft\u271d : e \u2208 G.edgeFinset\nh : e \u2209 G.incidenceSet t\n\u22a2 t \u2209 e",
+              "tactic": "contrapose! h"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp_all [<a>incidenceSet<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.incidenceSet\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[711,5],\"def_end_pos\":[711,17]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case intro\nV : Type u_1\ninst\u271d\u00b2 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b9 : Fintype V\ninst\u271d : DecidableRel G.Adj\ne : Sym2 V\nleft\u271d : e \u2208 G.edgeFinset\nh : t \u2208 e\n\u22a2 e \u2208 G.incidenceSet t",
+              "tactic": "simp_all [incidenceSet]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Operations.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'simp_all'",
+        "full_name": "SimpleGraph.edgeSet_replaceVertex_of_adj",
+        "id": "SimpleGraph.edgeSet_replaceVertex_of_adj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            86,
+            87
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Operations.lean",
+          "full_name": "SimpleGraph.edgeSet_replaceVertex_of_adj",
+          "start": [
+            82,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"ext e\"",
+                "[]"
+              ],
+              "state_after": "case h\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\n\u22a2 e \u2208 (G.replaceVertex s t).edgeSet \u2194\n    e \u2208 (G.edgeSet \\ G.incidenceSet t \u222a (fun x => s(x, t)) '' G.neighborSet s) \\ {s(t, t)}",
+              "state_before": "V : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\n\u22a2 (G.replaceVertex s t).edgeSet = (G.edgeSet \\ G.incidenceSet t \u222a (fun x => s(x, t)) '' G.neighborSet s) \\ {s(t, t)}",
+              "tactic": "ext e"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine e.inductionOn ?_\"",
+                "[]"
+              ],
+              "state_after": "case h\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\n\u22a2 \u2200 (x y : V),\n    s(x, y) \u2208 (G.replaceVertex s t).edgeSet \u2194\n      s(x, y) \u2208 (G.edgeSet \\ G.incidenceSet t \u222a (fun x => s(x, t)) '' G.neighborSet s) \\ {s(t, t)}",
+              "state_before": "case h\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\n\u22a2 e \u2208 (G.replaceVertex s t).edgeSet \u2194\n    e \u2208 (G.edgeSet \\ G.incidenceSet t \u222a (fun x => s(x, t)) '' G.neighborSet s) \\ {s(t, t)}",
+              "tactic": "refine e.inductionOn ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>replaceVertex<\\/a>, <a>mem_edgeSet<\\/a>, <a>Set.mem_union<\\/a>, <a>Set.mem_diff<\\/a>, <a>mk'_mem_incidenceSet_iff<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.replaceVertex\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Operations.lean\",\"def_pos\":[47,5],\"def_end_pos\":[47,18]},{\"full_name\":\"SimpleGraph.mem_edgeSet\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[471,9],\"def_end_pos\":[471,20]},{\"full_name\":\"Set.mem_union\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[734,9],\"def_end_pos\":[734,18]},{\"full_name\":\"Set.mem_diff\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Defs.lean\",\"def_pos\":[93,17],\"def_end_pos\":[93,25]},{\"full_name\":\"SimpleGraph.mk'_mem_incidenceSet_iff\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[718,9],\"def_end_pos\":[718,33]}]"
+              ],
+              "state_after": "case h\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\n\u22a2 \u2200 (x y : V),\n    (if x = t then if y = t then False else G.Adj s y else if y = t then G.Adj x s else G.Adj x y) \u2194\n      (G.Adj x y \u2227 \u00ac(G.Adj x y \u2227 (t = x \u2228 t = y)) \u2228 s(x, y) \u2208 (fun x => s(x, t)) '' G.neighborSet s) \u2227\n        s(x, y) \u2209 {s(t, t)}",
+              "state_before": "case h\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\n\u22a2 \u2200 (x y : V),\n    s(x, y) \u2208 (G.replaceVertex s t).edgeSet \u2194\n      s(x, y) \u2208 (G.edgeSet \\ G.incidenceSet t \u222a (fun x => s(x, t)) '' G.neighborSet s) \\ {s(t, t)}",
+              "tactic": "simp only [replaceVertex, mem_edgeSet, Set.mem_union, Set.mem_diff, mk'_mem_incidenceSet_iff]"
+            },
+            {
+              "annotated_tactic": [
+                "\"intros\"",
+                "[]"
+              ],
+              "state_after": "case h\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\n\u22a2 (if x\u271d = t then if y\u271d = t then False else G.Adj s y\u271d else if y\u271d = t then G.Adj x\u271d s else G.Adj x\u271d y\u271d) \u2194\n    (G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s) \u2227\n      s(x\u271d, y\u271d) \u2209 {s(t, t)}",
+              "state_before": "case h\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\n\u22a2 \u2200 (x y : V),\n    (if x = t then if y = t then False else G.Adj s y else if y = t then G.Adj x s else G.Adj x y) \u2194\n      (G.Adj x y \u2227 \u00ac(G.Adj x y \u2227 (t = x \u2228 t = y)) \u2228 s(x, y) \u2208 (fun x => s(x, t)) '' G.neighborSet s) \u2227\n        s(x, y) \u2209 {s(t, t)}",
+              "tactic": "intros"
+            },
+            {
+              "annotated_tactic": [
+                "\"split_ifs\"",
+                "[]"
+              ],
+              "state_after": "case pos\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : x\u271d = t\nh\u271d : y\u271d = t\n\u22a2 False \u2194\n    (G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s) \u2227\n      s(x\u271d, y\u271d) \u2209 {s(t, t)}\n\ncase neg\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : x\u271d = t\nh\u271d : \u00acy\u271d = t\n\u22a2 G.Adj s y\u271d \u2194\n    (G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s) \u2227\n      s(x\u271d, y\u271d) \u2209 {s(t, t)}\n\ncase pos\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : \u00acx\u271d = t\nh\u271d : y\u271d = t\n\u22a2 G.Adj x\u271d s \u2194\n    (G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s) \u2227\n      s(x\u271d, y\u271d) \u2209 {s(t, t)}\n\ncase neg\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : \u00acx\u271d = t\nh\u271d : \u00acy\u271d = t\n\u22a2 G.Adj x\u271d y\u271d \u2194\n    (G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s) \u2227\n      s(x\u271d, y\u271d) \u2209 {s(t, t)}",
+              "state_before": "case h\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\n\u22a2 (if x\u271d = t then if y\u271d = t then False else G.Adj s y\u271d else if y\u271d = t then G.Adj x\u271d s else G.Adj x\u271d y\u271d) \u2194\n    (G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s) \u2227\n      s(x\u271d, y\u271d) \u2209 {s(t, t)}",
+              "tactic": "split_ifs"
+            },
+            {
+              "annotated_tactic": [
+                "\"exacts [by simp_all, by aesop, by rw [<a>adj_comm<\\/a>]; aesop, by aesop]\"",
+                "[{\"full_name\":\"SimpleGraph.adj_comm\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[175,9],\"def_end_pos\":[175,17]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case pos\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : x\u271d = t\nh\u271d : y\u271d = t\n\u22a2 False \u2194\n    (G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s) \u2227\n      s(x\u271d, y\u271d) \u2209 {s(t, t)}\n\ncase neg\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : x\u271d = t\nh\u271d : \u00acy\u271d = t\n\u22a2 G.Adj s y\u271d \u2194\n    (G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s) \u2227\n      s(x\u271d, y\u271d) \u2209 {s(t, t)}\n\ncase pos\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : \u00acx\u271d = t\nh\u271d : y\u271d = t\n\u22a2 G.Adj x\u271d s \u2194\n    (G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s) \u2227\n      s(x\u271d, y\u271d) \u2209 {s(t, t)}\n\ncase neg\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : \u00acx\u271d = t\nh\u271d : \u00acy\u271d = t\n\u22a2 G.Adj x\u271d y\u271d \u2194\n    (G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s) \u2227\n      s(x\u271d, y\u271d) \u2209 {s(t, t)}",
+              "tactic": "exacts [by simp_all, by aesop, by rw [adj_comm]; aesop, by aesop]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp_all\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : x\u271d = t\nh\u271d : y\u271d = t\n\u22a2 False \u2194\n    (G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s) \u2227\n      s(x\u271d, y\u271d) \u2209 {s(t, t)}",
+              "tactic": "simp_all"
+            },
+            {
+              "annotated_tactic": [
+                "\"aesop\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : x\u271d = t\nh\u271d : \u00acy\u271d = t\n\u22a2 G.Adj s y\u271d \u2194\n    (G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s) \u2227\n      s(x\u271d, y\u271d) \u2209 {s(t, t)}",
+              "tactic": "aesop"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>adj_comm<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.adj_comm\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[175,9],\"def_end_pos\":[175,17]}]"
+              ],
+              "state_after": "V : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : \u00acx\u271d = t\nh\u271d : y\u271d = t\n\u22a2 G.Adj s x\u271d \u2194\n    (G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s) \u2227\n      s(x\u271d, y\u271d) \u2209 {s(t, t)}",
+              "state_before": "V : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : \u00acx\u271d = t\nh\u271d : y\u271d = t\n\u22a2 G.Adj x\u271d s \u2194\n    (G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s) \u2227\n      s(x\u271d, y\u271d) \u2209 {s(t, t)}",
+              "tactic": "rw [adj_comm]"
+            },
+            {
+              "annotated_tactic": [
+                "\"aesop\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : \u00acx\u271d = t\nh\u271d : y\u271d = t\n\u22a2 G.Adj s x\u271d \u2194\n    (G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s) \u2227\n      s(x\u271d, y\u271d) \u2209 {s(t, t)}",
+              "tactic": "aesop"
+            },
+            {
+              "annotated_tactic": [
+                "\"aesop\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nha : G.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : \u00acx\u271d = t\nh\u271d : \u00acy\u271d = t\n\u22a2 G.Adj x\u271d y\u271d \u2194\n    (G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s) \u2227\n      s(x\u271d, y\u271d) \u2209 {s(t, t)}",
+              "tactic": "aesop"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Operations.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'simp_all'",
+        "full_name": "SimpleGraph.edgeSet_replaceVertex_of_not_adj",
+        "id": "SimpleGraph.edgeSet_replaceVertex_of_not_adj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            80,
+            87
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Operations.lean",
+          "full_name": "SimpleGraph.edgeSet_replaceVertex_of_not_adj",
+          "start": [
+            76,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"ext e\"",
+                "[]"
+              ],
+              "state_after": "case h\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\n\u22a2 e \u2208 (G.replaceVertex s t).edgeSet \u2194 e \u2208 G.edgeSet \\ G.incidenceSet t \u222a (fun x => s(x, t)) '' G.neighborSet s",
+              "state_before": "V : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\n\u22a2 (G.replaceVertex s t).edgeSet = G.edgeSet \\ G.incidenceSet t \u222a (fun x => s(x, t)) '' G.neighborSet s",
+              "tactic": "ext e"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine e.inductionOn ?_\"",
+                "[]"
+              ],
+              "state_after": "case h\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\n\u22a2 \u2200 (x y : V),\n    s(x, y) \u2208 (G.replaceVertex s t).edgeSet \u2194\n      s(x, y) \u2208 G.edgeSet \\ G.incidenceSet t \u222a (fun x => s(x, t)) '' G.neighborSet s",
+              "state_before": "case h\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\n\u22a2 e \u2208 (G.replaceVertex s t).edgeSet \u2194 e \u2208 G.edgeSet \\ G.incidenceSet t \u222a (fun x => s(x, t)) '' G.neighborSet s",
+              "tactic": "refine e.inductionOn ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>replaceVertex<\\/a>, <a>mem_edgeSet<\\/a>, <a>Set.mem_union<\\/a>, <a>Set.mem_diff<\\/a>, <a>mk'_mem_incidenceSet_iff<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.replaceVertex\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Operations.lean\",\"def_pos\":[47,5],\"def_end_pos\":[47,18]},{\"full_name\":\"SimpleGraph.mem_edgeSet\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[471,9],\"def_end_pos\":[471,20]},{\"full_name\":\"Set.mem_union\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[734,9],\"def_end_pos\":[734,18]},{\"full_name\":\"Set.mem_diff\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Defs.lean\",\"def_pos\":[93,17],\"def_end_pos\":[93,25]},{\"full_name\":\"SimpleGraph.mk'_mem_incidenceSet_iff\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[718,9],\"def_end_pos\":[718,33]}]"
+              ],
+              "state_after": "case h\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\n\u22a2 \u2200 (x y : V),\n    (if x = t then if y = t then False else G.Adj s y else if y = t then G.Adj x s else G.Adj x y) \u2194\n      G.Adj x y \u2227 \u00ac(G.Adj x y \u2227 (t = x \u2228 t = y)) \u2228 s(x, y) \u2208 (fun x => s(x, t)) '' G.neighborSet s",
+              "state_before": "case h\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\n\u22a2 \u2200 (x y : V),\n    s(x, y) \u2208 (G.replaceVertex s t).edgeSet \u2194\n      s(x, y) \u2208 G.edgeSet \\ G.incidenceSet t \u222a (fun x => s(x, t)) '' G.neighborSet s",
+              "tactic": "simp only [replaceVertex, mem_edgeSet, Set.mem_union, Set.mem_diff, mk'_mem_incidenceSet_iff]"
+            },
+            {
+              "annotated_tactic": [
+                "\"intros\"",
+                "[]"
+              ],
+              "state_after": "case h\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\n\u22a2 (if x\u271d = t then if y\u271d = t then False else G.Adj s y\u271d else if y\u271d = t then G.Adj x\u271d s else G.Adj x\u271d y\u271d) \u2194\n    G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s",
+              "state_before": "case h\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\n\u22a2 \u2200 (x y : V),\n    (if x = t then if y = t then False else G.Adj s y else if y = t then G.Adj x s else G.Adj x y) \u2194\n      G.Adj x y \u2227 \u00ac(G.Adj x y \u2227 (t = x \u2228 t = y)) \u2228 s(x, y) \u2208 (fun x => s(x, t)) '' G.neighborSet s",
+              "tactic": "intros"
+            },
+            {
+              "annotated_tactic": [
+                "\"split_ifs\"",
+                "[]"
+              ],
+              "state_after": "case pos\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : x\u271d = t\nh\u271d : y\u271d = t\n\u22a2 False \u2194 G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s\n\ncase neg\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : x\u271d = t\nh\u271d : \u00acy\u271d = t\n\u22a2 G.Adj s y\u271d \u2194 G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s\n\ncase pos\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : \u00acx\u271d = t\nh\u271d : y\u271d = t\n\u22a2 G.Adj x\u271d s \u2194 G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s\n\ncase neg\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : \u00acx\u271d = t\nh\u271d : \u00acy\u271d = t\n\u22a2 G.Adj x\u271d y\u271d \u2194 G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s",
+              "state_before": "case h\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\n\u22a2 (if x\u271d = t then if y\u271d = t then False else G.Adj s y\u271d else if y\u271d = t then G.Adj x\u271d s else G.Adj x\u271d y\u271d) \u2194\n    G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s",
+              "tactic": "split_ifs"
+            },
+            {
+              "annotated_tactic": [
+                "\"exacts [by simp_all, by aesop, by rw [<a>adj_comm<\\/a>]; aesop, by aesop]\"",
+                "[{\"full_name\":\"SimpleGraph.adj_comm\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[175,9],\"def_end_pos\":[175,17]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case pos\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : x\u271d = t\nh\u271d : y\u271d = t\n\u22a2 False \u2194 G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s\n\ncase neg\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : x\u271d = t\nh\u271d : \u00acy\u271d = t\n\u22a2 G.Adj s y\u271d \u2194 G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s\n\ncase pos\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : \u00acx\u271d = t\nh\u271d : y\u271d = t\n\u22a2 G.Adj x\u271d s \u2194 G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s\n\ncase neg\nV : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : \u00acx\u271d = t\nh\u271d : \u00acy\u271d = t\n\u22a2 G.Adj x\u271d y\u271d \u2194 G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s",
+              "tactic": "exacts [by simp_all, by aesop, by rw [adj_comm]; aesop, by aesop]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp_all\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : x\u271d = t\nh\u271d : y\u271d = t\n\u22a2 False \u2194 G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s",
+              "tactic": "simp_all"
+            },
+            {
+              "annotated_tactic": [
+                "\"aesop\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : x\u271d = t\nh\u271d : \u00acy\u271d = t\n\u22a2 G.Adj s y\u271d \u2194 G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s",
+              "tactic": "aesop"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>adj_comm<\\/a>]\"",
+                "[{\"full_name\":\"SimpleGraph.adj_comm\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Basic.lean\",\"def_pos\":[175,9],\"def_end_pos\":[175,17]}]"
+              ],
+              "state_after": "V : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : \u00acx\u271d = t\nh\u271d : y\u271d = t\n\u22a2 G.Adj s x\u271d \u2194 G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s",
+              "state_before": "V : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : \u00acx\u271d = t\nh\u271d : y\u271d = t\n\u22a2 G.Adj x\u271d s \u2194 G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s",
+              "tactic": "rw [adj_comm]"
+            },
+            {
+              "annotated_tactic": [
+                "\"aesop\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : \u00acx\u271d = t\nh\u271d : y\u271d = t\n\u22a2 G.Adj s x\u271d \u2194 G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s",
+              "tactic": "aesop"
+            },
+            {
+              "annotated_tactic": [
+                "\"aesop\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u_1\ninst\u271d : DecidableEq V\nG : SimpleGraph V\ns t : V\nhn : \u00acG.Adj s t\ne : Sym2 V\nx\u271d y\u271d : V\nh\u271d\u00b9 : \u00acx\u271d = t\nh\u271d : \u00acy\u271d = t\n\u22a2 G.Adj x\u271d y\u271d \u2194 G.Adj x\u271d y\u271d \u2227 \u00ac(G.Adj x\u271d y\u271d \u2227 (t = x\u271d \u2228 t = y\u271d)) \u2228 s(x\u271d, y\u271d) \u2208 (fun x => s(x, t)) '' G.neighborSet s",
+              "tactic": "aesop"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Operations.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SimpleGraph.Partition.colorable",
+        "id": "SimpleGraph.Partition.colorable",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            120,
+            25
+          ],
+          "file_path": "Mathlib/Combinatorics/SimpleGraph/Partition.lean",
+          "full_name": "SimpleGraph.Partition.colorable",
+          "start": [
+            119,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/SimpleGraph/Partition.lean"
+      }
+    ],
+    "input_proofs": 24,
+    "input_units": 2,
+    "proofs": 18,
+    "published_proofs": 16,
+    "published_transitions": 29,
+    "replay_failures": [],
+    "transitions": 46,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Combinatorics/SimpleGraph/Operations.lean",
+        "proof_id": "mathlib:SimpleGraph.edgeFinset_sup_edge",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              175,
+              50
+            ],
+            "file_path": "Mathlib/Combinatorics/SimpleGraph/Operations.lean",
+            "full_name": "SimpleGraph.edgeFinset_sup_edge",
+            "start": [
+              171,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"simp_all\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "V : Type u_1\ninst\u271d\u00b3 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b2 : Fintype V\ninst\u271d\u00b9 : DecidableRel G.Adj\ninst\u271d : Fintype \u2191(G \u2294 edge s t).edgeSet\nhn : \u00acG.Adj s t\nh : s \u2260 t\n\u22a2 s(s, t) \u2209 G.edgeFinset",
+                "tactic": "simp_all"
+              },
+              {
+                "annotated_tactic": [
+                  "\"letI := <a>Classical.decEq<\\/a> V\"",
+                  "[{\"full_name\":\"Classical.decEq\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[1020,19],\"def_end_pos\":[1020,24]}]"
+                ],
+                "state_after": "V : Type u_1\ninst\u271d\u00b3 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b2 : Fintype V\ninst\u271d\u00b9 : DecidableRel G.Adj\ninst\u271d : Fintype \u2191(G \u2294 edge s t).edgeSet\nhn : \u00acG.Adj s t\nh : s \u2260 t\nthis : DecidableEq V := Classical.decEq V\n\u22a2 (G \u2294 edge s t).edgeFinset = cons s(s, t) G.edgeFinset \u22ef",
+                "state_before": "V : Type u_1\ninst\u271d\u00b3 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b2 : Fintype V\ninst\u271d\u00b9 : DecidableRel G.Adj\ninst\u271d : Fintype \u2191(G \u2294 edge s t).edgeSet\nhn : \u00acG.Adj s t\nh : s \u2260 t\n\u22a2 (G \u2294 edge s t).edgeFinset = cons s(s, t) G.edgeFinset \u22ef",
+                "tactic": "letI := Classical.decEq V"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>edgeFinset_sup<\\/a>, <a>cons_eq_insert<\\/a>, <a>insert_eq<\\/a>, <a>union_comm<\\/a>]\"",
+                  "[{\"full_name\":\"SimpleGraph.edgeFinset_sup\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Finite.lean\",\"def_pos\":[94,9],\"def_end_pos\":[94,23]},{\"full_name\":\"Finset.cons_eq_insert\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[1137,9],\"def_end_pos\":[1137,23]},{\"full_name\":\"Finset.insert_eq\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[1517,9],\"def_end_pos\":[1517,18]},{\"full_name\":\"Finset.union_comm\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[1459,9],\"def_end_pos\":[1459,19]}]"
+                ],
+                "state_after": "V : Type u_1\ninst\u271d\u00b3 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b2 : Fintype V\ninst\u271d\u00b9 : DecidableRel G.Adj\ninst\u271d : Fintype \u2191(G \u2294 edge s t).edgeSet\nhn : \u00acG.Adj s t\nh : s \u2260 t\nthis : DecidableEq V := Classical.decEq V\n\u22a2 (edge s t).edgeFinset \u222a G.edgeFinset = {s(s, t)} \u222a G.edgeFinset",
+                "state_before": "V : Type u_1\ninst\u271d\u00b3 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b2 : Fintype V\ninst\u271d\u00b9 : DecidableRel G.Adj\ninst\u271d : Fintype \u2191(G \u2294 edge s t).edgeSet\nhn : \u00acG.Adj s t\nh : s \u2260 t\nthis : DecidableEq V := Classical.decEq V\n\u22a2 (G \u2294 edge s t).edgeFinset = cons s(s, t) G.edgeFinset \u22ef",
+                "tactic": "rw [edgeFinset_sup, cons_eq_insert, insert_eq, union_comm]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp_rw [<a>edgeFinset<\\/a>, <a>edge_edgeSet_of_ne<\\/a> h]\"",
+                  "[{\"full_name\":\"SimpleGraph.edgeFinset\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Finite.lean\",\"def_pos\":[53,8],\"def_end_pos\":[53,18]},{\"full_name\":\"SimpleGraph.edge_edgeSet_of_ne\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Operations.lean\",\"def_pos\":[159,7],\"def_end_pos\":[159,25]}]"
+                ],
+                "state_after": "V : Type u_1\ninst\u271d\u00b3 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b2 : Fintype V\ninst\u271d\u00b9 : DecidableRel G.Adj\ninst\u271d : Fintype \u2191(G \u2294 edge s t).edgeSet\nhn : \u00acG.Adj s t\nh : s \u2260 t\nthis : DecidableEq V := Classical.decEq V\n\u22a2 {s(s, t)}.toFinset \u222a G.edgeSet.toFinset = {s(s, t)} \u222a G.edgeSet.toFinset",
+                "state_before": "V : Type u_1\ninst\u271d\u00b3 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b2 : Fintype V\ninst\u271d\u00b9 : DecidableRel G.Adj\ninst\u271d : Fintype \u2191(G \u2294 edge s t).edgeSet\nhn : \u00acG.Adj s t\nh : s \u2260 t\nthis : DecidableEq V := Classical.decEq V\n\u22a2 (edge s t).edgeFinset \u222a G.edgeFinset = {s(s, t)} \u222a G.edgeFinset",
+                "tactic": "simp_rw [edgeFinset, edge_edgeSet_of_ne h]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rfl\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "V : Type u_1\ninst\u271d\u00b3 : DecidableEq V\nG : SimpleGraph V\ns t : V\ninst\u271d\u00b2 : Fintype V\ninst\u271d\u00b9 : DecidableRel G.Adj\ninst\u271d : Fintype \u2191(G \u2294 edge s t).edgeSet\nhn : \u00acG.Adj s t\nh : s \u2260 t\nthis : DecidableEq V := Classical.decEq V\n\u22a2 {s(s, t)}.toFinset \u222a G.edgeSet.toFinset = {s(s, t)} \u222a G.edgeSet.toFinset",
+                "tactic": "rfl"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "SimpleGraph.edgeFinset_sup_edge"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Combinatorics/SimpleGraph/Partition.lean",
+        "proof_id": "mathlib:SimpleGraph.partitionable_iff_colorable",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              153,
+              33
+            ],
+            "file_path": "Mathlib/Combinatorics/SimpleGraph/Partition.lean",
+            "full_name": "SimpleGraph.partitionable_iff_colorable",
+            "start": [
+              141,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"constructor\"",
+                  "[]"
+                ],
+                "state_after": "case mp\nV : Type u\nG : SimpleGraph V\nn : \u2115\n\u22a2 G.Partitionable n \u2192 G.Colorable n\n\ncase mpr\nV : Type u\nG : SimpleGraph V\nn : \u2115\n\u22a2 G.Colorable n \u2192 G.Partitionable n",
+                "state_before": "V : Type u\nG : SimpleGraph V\nn : \u2115\n\u22a2 G.Partitionable n \u2194 G.Colorable n",
+                "tactic": "constructor"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rintro \\u27e8P, hf, hc\\u27e9\"",
+                  "[]"
+                ],
+                "state_after": "case mp.intro.intro\nV : Type u\nG : SimpleGraph V\nn : \u2115\nP : G.Partition\nhf : P.parts.Finite\nhc : hf.toFinset.card \u2264 n\n\u22a2 G.Colorable n",
+                "state_before": "case mp\nV : Type u\nG : SimpleGraph V\nn : \u2115\n\u22a2 G.Partitionable n \u2192 G.Colorable n",
+                "tactic": "rintro \u27e8P, hf, hc\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"have : <a>Fintype<\\/a> P.parts := hf.fintype\"",
+                  "[{\"full_name\":\"Fintype\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Basic.lean\",\"def_pos\":[57,7],\"def_end_pos\":[57,14]}]"
+                ],
+                "state_after": "case mp.intro.intro\nV : Type u\nG : SimpleGraph V\nn : \u2115\nP : G.Partition\nhf : P.parts.Finite\nhc : hf.toFinset.card \u2264 n\nthis : Fintype \u2191P.parts\n\u22a2 G.Colorable n",
+                "state_before": "case mp.intro.intro\nV : Type u\nG : SimpleGraph V\nn : \u2115\nP : G.Partition\nhf : P.parts.Finite\nhc : hf.toFinset.card \u2264 n\n\u22a2 G.Colorable n",
+                "tactic": "have : Fintype P.parts := hf.fintype"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>Set.Finite.card_toFinset<\\/a> hf] at hc\"",
+                  "[{\"full_name\":\"Set.Finite.card_toFinset\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Finite.lean\",\"def_pos\":[1314,9],\"def_end_pos\":[1314,29]}]"
+                ],
+                "state_after": "case mp.intro.intro\nV : Type u\nG : SimpleGraph V\nn : \u2115\nP : G.Partition\nhf : P.parts.Finite\nthis : Fintype \u2191P.parts\nhc : Fintype.card \u2191P.parts \u2264 n\n\u22a2 G.Colorable n",
+                "state_before": "case mp.intro.intro\nV : Type u\nG : SimpleGraph V\nn : \u2115\nP : G.Partition\nhf : P.parts.Finite\nhc : hf.toFinset.card \u2264 n\nthis : Fintype \u2191P.parts\n\u22a2 G.Colorable n",
+                "tactic": "rw [Set.Finite.card_toFinset hf] at hc"
+              },
+              {
+                "annotated_tactic": [
+                  "\"apply P.colorable.mono hc\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case mp.intro.intro\nV : Type u\nG : SimpleGraph V\nn : \u2115\nP : G.Partition\nhf : P.parts.Finite\nthis : Fintype \u2191P.parts\nhc : Fintype.card \u2191P.parts \u2264 n\n\u22a2 G.Colorable n",
+                "tactic": "apply P.colorable.mono hc"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rintro \\u27e8C\\u27e9\"",
+                  "[]"
+                ],
+                "state_after": "case mpr.intro\nV : Type u\nG : SimpleGraph V\nn : \u2115\nC : G.Coloring (Fin n)\n\u22a2 G.Partitionable n",
+                "state_before": "case mpr\nV : Type u\nG : SimpleGraph V\nn : \u2115\n\u22a2 G.Colorable n \u2192 G.Partitionable n",
+                "tactic": "rintro \u27e8C\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"refine \\u27e8C.toPartition, C.colorClasses_finite, <a>le_trans<\\/a> ?_ (<a>Fintype.card_fin<\\/a> n).<a>le<\\/a>\\u27e9\"",
+                  "[{\"full_name\":\"le_trans\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[56,9],\"def_end_pos\":[56,17]},{\"full_name\":\"Fintype.card_fin\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[311,9],\"def_end_pos\":[311,25]},{\"full_name\":\"Eq.le\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[154,7],\"def_end_pos\":[154,12]}]"
+                ],
+                "state_after": "case mpr.intro\nV : Type u\nG : SimpleGraph V\nn : \u2115\nC : G.Coloring (Fin n)\n\u22a2 \u22ef.toFinset.card \u2264 Fintype.card (Fin n)",
+                "state_before": "case mpr.intro\nV : Type u\nG : SimpleGraph V\nn : \u2115\nC : G.Coloring (Fin n)\n\u22a2 G.Partitionable n",
+                "tactic": "refine \u27e8C.toPartition, C.colorClasses_finite, le_trans ?_ (Fintype.card_fin n).le\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"generalize_proofs h\"",
+                  "[]"
+                ],
+                "state_after": "case mpr.intro\nV : Type u\nG : SimpleGraph V\nn : \u2115\nC : G.Coloring (Fin n)\nh : C.toPartition.parts.Finite\n\u22a2 h.toFinset.card \u2264 Fintype.card (Fin n)",
+                "state_before": "case mpr.intro\nV : Type u\nG : SimpleGraph V\nn : \u2115\nC : G.Coloring (Fin n)\n\u22a2 \u22ef.toFinset.card \u2264 Fintype.card (Fin n)",
+                "tactic": "generalize_proofs h"
+              },
+              {
+                "annotated_tactic": [
+                  "\"change <a>Set.Finite<\\/a> (<a>Coloring.colorClasses<\\/a> C) at h\"",
+                  "[{\"full_name\":\"Set.Finite\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Finite.lean\",\"def_pos\":[58,15],\"def_end_pos\":[58,21]},{\"full_name\":\"SimpleGraph.Coloring.colorClasses\",\"def_path\":\"Mathlib\\/Combinatorics\\/SimpleGraph\\/Coloring.lean\",\"def_pos\":[97,5],\"def_end_pos\":[97,26]}]"
+                ],
+                "state_after": "case mpr.intro\nV : Type u\nG : SimpleGraph V\nn : \u2115\nC : G.Coloring (Fin n)\nh : C.colorClasses.Finite\n\u22a2 h.toFinset.card \u2264 Fintype.card (Fin n)",
+                "state_before": "case mpr.intro\nV : Type u\nG : SimpleGraph V\nn : \u2115\nC : G.Coloring (Fin n)\nh : C.toPartition.parts.Finite\n\u22a2 h.toFinset.card \u2264 Fintype.card (Fin n)",
+                "tactic": "change Set.Finite (Coloring.colorClasses C) at h"
+              },
+              {
+                "annotated_tactic": [
+                  "\"have : <a>Fintype<\\/a> C.colorClasses := C.colorClasses_finite.fintype\"",
+                  "[{\"full_name\":\"Fintype\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Basic.lean\",\"def_pos\":[57,7],\"def_end_pos\":[57,14]}]"
+                ],
+                "state_after": "case mpr.intro\nV : Type u\nG : SimpleGraph V\nn : \u2115\nC : G.Coloring (Fin n)\nh : C.colorClasses.Finite\nthis : Fintype \u2191C.colorClasses\n\u22a2 h.toFinset.card \u2264 Fintype.card (Fin n)",
+                "state_before": "case mpr.intro\nV : Type u\nG : SimpleGraph V\nn : \u2115\nC : G.Coloring (Fin n)\nh : C.colorClasses.Finite\n\u22a2 h.toFinset.card \u2264 Fintype.card (Fin n)",
+                "tactic": "have : Fintype C.colorClasses := C.colorClasses_finite.fintype"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [h.card_toFinset]\"",
+                  "[]"
+                ],
+                "state_after": "case mpr.intro\nV : Type u\nG : SimpleGraph V\nn : \u2115\nC : G.Coloring (Fin n)\nh : C.colorClasses.Finite\nthis : Fintype \u2191C.colorClasses\n\u22a2 Fintype.card \u2191C.colorClasses \u2264 Fintype.card (Fin n)",
+                "state_before": "case mpr.intro\nV : Type u\nG : SimpleGraph V\nn : \u2115\nC : G.Coloring (Fin n)\nh : C.colorClasses.Finite\nthis : Fintype \u2191C.colorClasses\n\u22a2 h.toFinset.card \u2264 Fintype.card (Fin n)",
+                "tactic": "rw [h.card_toFinset]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact C.card_colorClasses_le\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case mpr.intro\nV : Type u\nG : SimpleGraph V\nn : \u2115\nC : G.Coloring (Fin n)\nh : C.colorClasses.Finite\nthis : Fintype \u2191C.colorClasses\n\u22a2 Fintype.card \u2191C.colorClasses \u2264 Fintype.card (Fin n)",
+                "tactic": "exact C.card_colorClasses_le"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "SimpleGraph.partitionable_iff_colorable"
+      }
+    ],
+    "validation_rejected_proofs": 2,
+    "zero_transition_proofs": 0
+  },
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manifests/batches/numina/001597.json

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manifests/batches/numina/001598.json

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manifests/batches/numina/001599.json

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manifests/batches/numina/001600.json

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manifests/batches/numina/001601.json

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manifests/batches/numina/001602.json

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+}

manifests/batches/numina/001603.json

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manifests/batches/numina/001604.json

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manifests/batches/numina/001606.json

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