Record 19 verified HPC batch manifests

manifests/batches/mathlib/000817.json

@@ -0,0 +1,532 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000817",
+  "batch_fingerprint": "0476eded927ec43114cc7ffe9792907a4344296ab8546e79068148244aba9533",
+  "evidence": {
+    "batch_fingerprint": "0476eded927ec43114cc7ffe9792907a4344296ab8546e79068148244aba9533",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.bipartiteAbove_swap",
+        "id": "Finset.bipartiteAbove_swap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            58,
+            88
+          ],
+          "file_path": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean",
+          "full_name": "Finset.bipartiteAbove_swap",
+          "start": [
+            58,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.bipartiteBelow_swap",
+        "id": "Finset.bipartiteBelow_swap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            55,
+            88
+          ],
+          "file_path": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean",
+          "full_name": "Finset.bipartiteBelow_swap",
+          "start": [
+            55,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rw [\u2190 mul_one s.card, \u2190 mul_one t.card]'",
+        "full_name": "Finset.card_le_card_of_forall_subsingleton",
+        "id": "Finset.card_le_card_of_forall_subsingleton",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            120,
+            23
+          ],
+          "file_path": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean",
+          "full_name": "Finset.card_le_card_of_forall_subsingleton",
+          "start": [
+            110,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"classical\\n    rw [\\u2190 <a>mul_one<\\/a> s.card, \\u2190 <a>mul_one<\\/a> t.card]\\n    exact <a>card_mul_le_card_mul<\\/a> r\\n      (fun a h \\u21a6 <a>card_pos<\\/a>.2 (by\\n        rw [\\u2190 <a>coe_nonempty<\\/a>, <a>coe_bipartiteAbove<\\/a>]\\n        exact hs _ h : (t.bipartiteAbove r a).Nonempty))\\n      (fun b h \\u21a6 <a>card_le_one<\\/a>.2 (by\\n        simp_rw [<a>mem_bipartiteBelow<\\/a>]\\n        exact ht _ h))\"",
+                "[{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"Finset.card_mul_le_card_mul\",\"def_path\":\"Mathlib\\/Combinatorics\\/Enumerative\\/DoubleCounting.lean\",\"def_pos\":[87,9],\"def_end_pos\":[87,29]},{\"full_name\":\"Finset.card_pos\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[74,15],\"def_end_pos\":[74,23]},{\"full_name\":\"Finset.coe_nonempty\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[489,9],\"def_end_pos\":[489,21]},{\"full_name\":\"Finset.coe_bipartiteAbove\",\"def_path\":\"Mathlib\\/Combinatorics\\/Enumerative\\/DoubleCounting.lean\",\"def_pos\":[66,9],\"def_end_pos\":[66,27]},{\"full_name\":\"Finset.card_le_one\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[696,9],\"def_end_pos\":[696,20]},{\"full_name\":\"Finset.mem_bipartiteBelow\",\"def_path\":\"Mathlib\\/Combinatorics\\/Enumerative\\/DoubleCounting.lean\",\"def_pos\":[72,9],\"def_end_pos\":[72,27]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b2 \u2192 Prop\ns : Finset \u03b1\nt : Finset \u03b2\na a' : \u03b1\nb b' : \u03b2\ninst\u271d\u00b9 : DecidablePred (r a)\ninst\u271d : (a : \u03b1) \u2192 Decidable (r a b)\nm n : \u2115\nhs : \u2200 a \u2208 s, \u2203 b \u2208 t, r a b\nht : \u2200 b \u2208 t, {a | a \u2208 s \u2227 r a b}.Subsingleton\n\u22a2 s.card \u2264 t.card",
+              "tactic": "classical\n  rw [\u2190 mul_one s.card, \u2190 mul_one t.card]\n  exact card_mul_le_card_mul r\n    (fun a h \u21a6 card_pos.2 (by\n      rw [\u2190 coe_nonempty, coe_bipartiteAbove]\n      exact hs _ h : (t.bipartiteAbove r a).Nonempty))\n    (fun b h \u21a6 card_le_one.2 (by\n      simp_rw [mem_bipartiteBelow]\n      exact ht _ h))"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>mul_one<\\/a> s.card, \\u2190 <a>mul_one<\\/a> t.card]\"",
+                "[{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]}]"
+              ],
+              "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b2 \u2192 Prop\ns : Finset \u03b1\nt : Finset \u03b2\na a' : \u03b1\nb b' : \u03b2\ninst\u271d\u00b9 : DecidablePred (r a)\ninst\u271d : (a : \u03b1) \u2192 Decidable (r a b)\nm n : \u2115\nhs : \u2200 a \u2208 s, \u2203 b \u2208 t, r a b\nht : \u2200 b \u2208 t, {a | a \u2208 s \u2227 r a b}.Subsingleton\n\u22a2 s.card * 1 \u2264 t.card * 1",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b2 \u2192 Prop\ns : Finset \u03b1\nt : Finset \u03b2\na a' : \u03b1\nb b' : \u03b2\ninst\u271d\u00b9 : DecidablePred (r a)\ninst\u271d : (a : \u03b1) \u2192 Decidable (r a b)\nm n : \u2115\nhs : \u2200 a \u2208 s, \u2203 b \u2208 t, r a b\nht : \u2200 b \u2208 t, {a | a \u2208 s \u2227 r a b}.Subsingleton\n\u22a2 s.card \u2264 t.card",
+              "tactic": "rw [\u2190 mul_one s.card, \u2190 mul_one t.card]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>card_mul_le_card_mul<\\/a> r\\n      (fun a h \\u21a6 <a>card_pos<\\/a>.2 (by\\n        rw [\\u2190 <a>coe_nonempty<\\/a>, <a>coe_bipartiteAbove<\\/a>]\\n        exact hs _ h : (t.bipartiteAbove r a).Nonempty))\\n      (fun b h \\u21a6 <a>card_le_one<\\/a>.2 (by\\n        simp_rw [<a>mem_bipartiteBelow<\\/a>]\\n        exact ht _ h))\"",
+                "[{\"full_name\":\"Finset.card_mul_le_card_mul\",\"def_path\":\"Mathlib\\/Combinatorics\\/Enumerative\\/DoubleCounting.lean\",\"def_pos\":[87,9],\"def_end_pos\":[87,29]},{\"full_name\":\"Finset.card_pos\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[74,15],\"def_end_pos\":[74,23]},{\"full_name\":\"Finset.coe_nonempty\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[489,9],\"def_end_pos\":[489,21]},{\"full_name\":\"Finset.coe_bipartiteAbove\",\"def_path\":\"Mathlib\\/Combinatorics\\/Enumerative\\/DoubleCounting.lean\",\"def_pos\":[66,9],\"def_end_pos\":[66,27]},{\"full_name\":\"Finset.card_le_one\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[696,9],\"def_end_pos\":[696,20]},{\"full_name\":\"Finset.mem_bipartiteBelow\",\"def_path\":\"Mathlib\\/Combinatorics\\/Enumerative\\/DoubleCounting.lean\",\"def_pos\":[72,9],\"def_end_pos\":[72,27]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b2 \u2192 Prop\ns : Finset \u03b1\nt : Finset \u03b2\na a' : \u03b1\nb b' : \u03b2\ninst\u271d\u00b9 : DecidablePred (r a)\ninst\u271d : (a : \u03b1) \u2192 Decidable (r a b)\nm n : \u2115\nhs : \u2200 a \u2208 s, \u2203 b \u2208 t, r a b\nht : \u2200 b \u2208 t, {a | a \u2208 s \u2227 r a b}.Subsingleton\n\u22a2 s.card * 1 \u2264 t.card * 1",
+              "tactic": "exact card_mul_le_card_mul r\n  (fun a h \u21a6 card_pos.2 (by\n    rw [\u2190 coe_nonempty, coe_bipartiteAbove]\n    exact hs _ h : (t.bipartiteAbove r a).Nonempty))\n  (fun b h \u21a6 card_le_one.2 (by\n    simp_rw [mem_bipartiteBelow]\n    exact ht _ h))"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>coe_nonempty<\\/a>, <a>coe_bipartiteAbove<\\/a>]\"",
+                "[{\"full_name\":\"Finset.coe_nonempty\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[489,9],\"def_end_pos\":[489,21]},{\"full_name\":\"Finset.coe_bipartiteAbove\",\"def_path\":\"Mathlib\\/Combinatorics\\/Enumerative\\/DoubleCounting.lean\",\"def_pos\":[66,9],\"def_end_pos\":[66,27]}]"
+              ],
+              "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b2 \u2192 Prop\ns : Finset \u03b1\nt : Finset \u03b2\na\u271d a' : \u03b1\nb b' : \u03b2\ninst\u271d\u00b9 : DecidablePred (r a\u271d)\ninst\u271d : (a : \u03b1) \u2192 Decidable (r a b)\nm n : \u2115\nhs : \u2200 a \u2208 s, \u2203 b \u2208 t, r a b\nht : \u2200 b \u2208 t, {a | a \u2208 s \u2227 r a b}.Subsingleton\na : \u03b1\nh : a \u2208 s\n\u22a2 {b | b \u2208 t \u2227 r a b}.Nonempty",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b2 \u2192 Prop\ns : Finset \u03b1\nt : Finset \u03b2\na\u271d a' : \u03b1\nb b' : \u03b2\ninst\u271d\u00b9 : DecidablePred (r a\u271d)\ninst\u271d : (a : \u03b1) \u2192 Decidable (r a b)\nm n : \u2115\nhs : \u2200 a \u2208 s, \u2203 b \u2208 t, r a b\nht : \u2200 b \u2208 t, {a | a \u2208 s \u2227 r a b}.Subsingleton\na : \u03b1\nh : a \u2208 s\n\u22a2 (bipartiteAbove r t a).Nonempty",
+              "tactic": "rw [\u2190 coe_nonempty, coe_bipartiteAbove]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact hs _ h\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b2 \u2192 Prop\ns : Finset \u03b1\nt : Finset \u03b2\na\u271d a' : \u03b1\nb b' : \u03b2\ninst\u271d\u00b9 : DecidablePred (r a\u271d)\ninst\u271d : (a : \u03b1) \u2192 Decidable (r a b)\nm n : \u2115\nhs : \u2200 a \u2208 s, \u2203 b \u2208 t, r a b\nht : \u2200 b \u2208 t, {a | a \u2208 s \u2227 r a b}.Subsingleton\na : \u03b1\nh : a \u2208 s\n\u22a2 {b | b \u2208 t \u2227 r a b}.Nonempty",
+              "tactic": "exact hs _ h"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp_rw [<a>mem_bipartiteBelow<\\/a>]\"",
+                "[{\"full_name\":\"Finset.mem_bipartiteBelow\",\"def_path\":\"Mathlib\\/Combinatorics\\/Enumerative\\/DoubleCounting.lean\",\"def_pos\":[72,9],\"def_end_pos\":[72,27]}]"
+              ],
+              "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b2 \u2192 Prop\ns : Finset \u03b1\nt : Finset \u03b2\na a' : \u03b1\nb\u271d b' : \u03b2\ninst\u271d\u00b9 : DecidablePred (r a)\ninst\u271d : (a : \u03b1) \u2192 Decidable (r a b\u271d)\nm n : \u2115\nhs : \u2200 a \u2208 s, \u2203 b \u2208 t, r a b\nht : \u2200 b \u2208 t, {a | a \u2208 s \u2227 r a b}.Subsingleton\nb : \u03b2\nh : b \u2208 t\n\u22a2 \u2200 (a : \u03b1), a \u2208 s \u2227 r a b \u2192 \u2200 (b_1 : \u03b1), b_1 \u2208 s \u2227 r b_1 b \u2192 a = b_1",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b2 \u2192 Prop\ns : Finset \u03b1\nt : Finset \u03b2\na a' : \u03b1\nb\u271d b' : \u03b2\ninst\u271d\u00b9 : DecidablePred (r a)\ninst\u271d : (a : \u03b1) \u2192 Decidable (r a b\u271d)\nm n : \u2115\nhs : \u2200 a \u2208 s, \u2203 b \u2208 t, r a b\nht : \u2200 b \u2208 t, {a | a \u2208 s \u2227 r a b}.Subsingleton\nb : \u03b2\nh : b \u2208 t\n\u22a2 \u2200 a \u2208 bipartiteBelow r s b, \u2200 b_1 \u2208 bipartiteBelow r s b, a = b_1",
+              "tactic": "simp_rw [mem_bipartiteBelow]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact ht _ h\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b2 \u2192 Prop\ns : Finset \u03b1\nt : Finset \u03b2\na a' : \u03b1\nb\u271d b' : \u03b2\ninst\u271d\u00b9 : DecidablePred (r a)\ninst\u271d : (a : \u03b1) \u2192 Decidable (r a b\u271d)\nm n : \u2115\nhs : \u2200 a \u2208 s, \u2203 b \u2208 t, r a b\nht : \u2200 b \u2208 t, {a | a \u2208 s \u2227 r a b}.Subsingleton\nb : \u03b2\nh : b \u2208 t\n\u22a2 \u2200 (a : \u03b1), a \u2208 s \u2227 r a b \u2192 \u2200 (b_1 : \u03b1), b_1 \u2208 s \u2227 r b_1 b \u2192 a = b_1",
+              "tactic": "exact ht _ h"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.card_le_card_of_forall_subsingleton'",
+        "id": "Finset.card_le_card_of_forall_subsingleton'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            125,
+            53
+          ],
+          "file_path": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean",
+          "full_name": "Finset.card_le_card_of_forall_subsingleton'",
+          "start": [
+            123,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.card_mul_eq_card_mul",
+        "id": "Finset.card_mul_eq_card_mul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            107,
+            78
+          ],
+          "file_path": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean",
+          "full_name": "Finset.card_mul_eq_card_mul",
+          "start": [
+            103,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.card_mul_le_card_mul",
+        "id": "Finset.card_mul_le_card_mul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            94,
+            40
+          ],
+          "file_path": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean",
+          "full_name": "Finset.card_mul_le_card_mul",
+          "start": [
+            87,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.card_mul_le_card_mul'",
+        "id": "Finset.card_mul_le_card_mul'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            100,
+            38
+          ],
+          "file_path": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean",
+          "full_name": "Finset.card_mul_le_card_mul'",
+          "start": [
+            97,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.coe_bipartiteAbove",
+        "id": "Finset.coe_bipartiteAbove",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            66,
+            98
+          ],
+          "file_path": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean",
+          "full_name": "Finset.coe_bipartiteAbove",
+          "start": [
+            66,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.coe_bipartiteBelow",
+        "id": "Finset.coe_bipartiteBelow",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            62,
+            98
+          ],
+          "file_path": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean",
+          "full_name": "Finset.coe_bipartiteBelow",
+          "start": [
+            62,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.mem_bipartiteAbove",
+        "id": "Finset.mem_bipartiteAbove",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            76,
+            92
+          ],
+          "file_path": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean",
+          "full_name": "Finset.mem_bipartiteAbove",
+          "start": [
+            76,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.mem_bipartiteBelow",
+        "id": "Finset.mem_bipartiteBelow",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            72,
+            92
+          ],
+          "file_path": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean",
+          "full_name": "Finset.mem_bipartiteBelow",
+          "start": [
+            72,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Nat.Partition.count_ofSums_of_ne_zero",
+        "id": "Nat.Partition.count_ofSums_of_ne_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            133,
+            25
+          ],
+          "file_path": "Mathlib/Combinatorics/Enumerative/Partition.lean",
+          "full_name": "Nat.Partition.count_ofSums_of_ne_zero",
+          "start": [
+            131,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Enumerative/Partition.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Nat.Partition.count_ofSums_zero",
+        "id": "Nat.Partition.count_ofSums_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            138,
+            37
+          ],
+          "file_path": "Mathlib/Combinatorics/Enumerative/Partition.lean",
+          "full_name": "Nat.Partition.count_ofSums_zero",
+          "start": [
+            136,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Enumerative/Partition.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'simpa using hb\u2082'",
+        "full_name": "Nat.Partition.ofComposition_surj",
+        "id": "Nat.Partition.ofComposition_surj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            80,
+            62
+          ],
+          "file_path": "Mathlib/Combinatorics/Enumerative/Partition.lean",
+          "full_name": "Nat.Partition.ofComposition_surj",
+          "start": [
+            77,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rintro \\u27e8b, hb\\u2081, hb\\u2082\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "case mk\nn : \u2115\nb : Multiset \u2115\nhb\u2081 : \u2200 {i : \u2115}, i \u2208 b \u2192 0 < i\nhb\u2082 : b.sum = n\n\u22a2 \u2203 a, ofComposition n a = { parts := b, parts_pos := hb\u2081, parts_sum := hb\u2082 }",
+              "state_before": "n : \u2115\n\u22a2 Function.Surjective (ofComposition n)",
+              "tactic": "rintro \u27e8b, hb\u2081, hb\u2082\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"induction b using <a>Quotient.inductionOn<\\/a> with | _ b => ?_\"",
+                "[{\"full_name\":\"Quotient.inductionOn\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1629,19],\"def_end_pos\":[1629,30]}]"
+              ],
+              "state_after": "case mk.h\nn : \u2115\nb : List \u2115\nhb\u2081 : \u2200 {i : \u2115}, i \u2208 \u27e6b\u27e7 \u2192 0 < i\nhb\u2082 : sum \u27e6b\u27e7 = n\n\u22a2 \u2203 a, ofComposition n a = { parts := \u27e6b\u27e7, parts_pos := hb\u2081, parts_sum := hb\u2082 }",
+              "state_before": "case mk\nn : \u2115\nb : Multiset \u2115\nhb\u2081 : \u2200 {i : \u2115}, i \u2208 b \u2192 0 < i\nhb\u2082 : b.sum = n\n\u22a2 \u2203 a, ofComposition n a = { parts := b, parts_pos := hb\u2081, parts_sum := hb\u2082 }",
+              "tactic": "induction b using Quotient.inductionOn with | _ b => ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact \\u27e8\\u27e8b, hb\\u2081, by simpa using hb\\u2082\\u27e9, <a>Partition.ext<\\/a> _ _ <a>rfl<\\/a>\\u27e9\"",
+                "[{\"full_name\":\"Nat.Partition.ext\",\"def_path\":\"Mathlib\\/Combinatorics\\/Enumerative\\/Partition.lean\",\"def_pos\":[51,3],\"def_end_pos\":[51,6]},{\"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 mk.h\nn : \u2115\nb : List \u2115\nhb\u2081 : \u2200 {i : \u2115}, i \u2208 \u27e6b\u27e7 \u2192 0 < i\nhb\u2082 : sum \u27e6b\u27e7 = n\n\u22a2 \u2203 a, ofComposition n a = { parts := \u27e6b\u27e7, parts_pos := hb\u2081, parts_sum := hb\u2082 }",
+              "tactic": "exact \u27e8\u27e8b, hb\u2081, by simpa using hb\u2082\u27e9, Partition.ext _ _ rfl\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"simpa using hb\\u2082\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "n : \u2115\nb : List \u2115\nhb\u2081 : \u2200 {i : \u2115}, i \u2208 \u27e6b\u27e7 \u2192 0 < i\nhb\u2082 : sum \u27e6b\u27e7 = n\n\u22a2 b.sum = n",
+              "tactic": "simpa using hb\u2082"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Enumerative/Partition.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'simpa using (congrArg sum h.symm).trans p.parts_sum'",
+        "full_name": "Nat.Partition.partition_one_parts",
+        "id": "Nat.Partition.partition_one_parts",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            121,
+            28
+          ],
+          "file_path": "Mathlib/Combinatorics/Enumerative/Partition.lean",
+          "full_name": "Nat.Partition.partition_one_parts",
+          "start": [
+            117,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"have h : p.parts = <a>replicate<\\/a> (<a>card<\\/a> p.parts) 1 := <a>eq_replicate_card<\\/a>.2 fun x hx =>\\n    ((<a>le_sum_of_mem<\\/a> hx).<a>trans_eq<\\/a> p.parts_sum).<a>antisymm<\\/a> (p.parts_pos hx)\"",
+                "[{\"full_name\":\"Multiset.replicate\",\"def_path\":\"Mathlib\\/Data\\/Multiset\\/Basic.lean\",\"def_pos\":[929,5],\"def_end_pos\":[929,14]},{\"full_name\":\"Multiset.card\",\"def_path\":\"Mathlib\\/Data\\/Multiset\\/Basic.lean\",\"def_pos\":[758,5],\"def_end_pos\":[758,9]},{\"full_name\":\"Multiset.eq_replicate_card\",\"def_path\":\"Mathlib\\/Data\\/Multiset\\/Basic.lean\",\"def_pos\":[970,9],\"def_end_pos\":[970,26]},{\"full_name\":\"Multiset.le_sum_of_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/BigOperators\\/Group\\/Multiset.lean\",\"def_pos\":[173,3],\"def_end_pos\":[173,14]},{\"full_name\":\"LE.le.trans_eq\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[190,7],\"def_end_pos\":[190,21]},{\"full_name\":\"LE.le.antisymm\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[123,7],\"def_end_pos\":[123,21]}]"
+              ],
+              "state_after": "p : Partition 1\nh : p.parts = replicate (card p.parts) 1\n\u22a2 p.parts = {1}",
+              "state_before": "p : Partition 1\n\u22a2 p.parts = {1}",
+              "tactic": "have h : p.parts = replicate (card p.parts) 1 := eq_replicate_card.2 fun x hx =>\n  ((le_sum_of_mem hx).trans_eq p.parts_sum).antisymm (p.parts_pos hx)"
+            },
+            {
+              "annotated_tactic": [
+                "\"have h' : <a>card<\\/a> p.parts = 1 := by simpa using (<a>congrArg<\\/a> <a>sum<\\/a> h.symm).<a>trans<\\/a> p.parts_sum\"",
+                "[{\"full_name\":\"Multiset.card\",\"def_path\":\"Mathlib\\/Data\\/Multiset\\/Basic.lean\",\"def_pos\":[758,5],\"def_end_pos\":[758,9]},{\"full_name\":\"congrArg\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[362,9],\"def_end_pos\":[362,17]},{\"full_name\":\"Multiset.sum\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Multiset.lean\",\"def_pos\":[37,3],\"def_end_pos\":[37,14]},{\"full_name\":\"Eq.trans\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[335,9],\"def_end_pos\":[335,17]}]"
+              ],
+              "state_after": "p : Partition 1\nh : p.parts = replicate (card p.parts) 1\nh' : card p.parts = 1\n\u22a2 p.parts = {1}",
+              "state_before": "p : Partition 1\nh : p.parts = replicate (card p.parts) 1\n\u22a2 p.parts = {1}",
+              "tactic": "have h' : card p.parts = 1 := by simpa using (congrArg sum h.symm).trans p.parts_sum"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [h, h', <a>replicate_one<\\/a>]\"",
+                "[{\"full_name\":\"Multiset.replicate_one\",\"def_path\":\"Mathlib\\/Data\\/Multiset\\/Basic.lean\",\"def_pos\":[955,9],\"def_end_pos\":[955,22]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : Partition 1\nh : p.parts = replicate (card p.parts) 1\nh' : card p.parts = 1\n\u22a2 p.parts = {1}",
+              "tactic": "rw [h, h', replicate_one]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simpa using (<a>congrArg<\\/a> <a>sum<\\/a> h.symm).<a>trans<\\/a> p.parts_sum\"",
+                "[{\"full_name\":\"congrArg\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[362,9],\"def_end_pos\":[362,17]},{\"full_name\":\"Multiset.sum\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Multiset.lean\",\"def_pos\":[37,3],\"def_end_pos\":[37,14]},{\"full_name\":\"Eq.trans\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[335,9],\"def_end_pos\":[335,17]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : Partition 1\nh : p.parts = replicate (card p.parts) 1\n\u22a2 card p.parts = 1",
+              "tactic": "simpa using (congrArg sum h.symm).trans p.parts_sum"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Enumerative/Partition.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Nat.Partition.partition_zero_parts",
+        "id": "Nat.Partition.partition_zero_parts",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            112,
+            96
+          ],
+          "file_path": "Mathlib/Combinatorics/Enumerative/Partition.lean",
+          "full_name": "Nat.Partition.partition_zero_parts",
+          "start": [
+            111,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Enumerative/Partition.lean"
+      }
+    ],
+    "input_proofs": 20,
+    "input_units": 2,
+    "proofs": 4,
+    "published_proofs": 4,
+    "published_transitions": 5,
+    "replay_failures": [],
+    "transitions": 5,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000817-0000-fa32d26f43c18be1.parquet",
+      "sha256": "fa32d26f43c18be1e8db84c0d68bc1a42793390d42baa1ce2c680cbc59c1f310",
+      "bytes": 49331,
+      "rows": 5,
+      "revision": "1b1732dbac9bd3e39d47d0584914277d2b00812a"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Finset.sum_card_bipartiteAbove_eq_sum_card_bipartiteBelow",
+    "mathlib:Fintype.card_le_card_of_leftTotal_unique",
+    "mathlib:Fintype.card_le_card_of_rightTotal_unique",
+    "mathlib:Nat.Partition.indiscrete_parts"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Enumerative/DoubleCounting.lean\",null,null,\"Finset.sum_card_bipartiteAbove_eq_sum_card_bipartiteBelow\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Enumerative/DoubleCounting.lean\",null,null,\"Fintype.card_le_card_of_leftTotal_unique\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Enumerative/DoubleCounting.lean\",null,null,\"Fintype.card_le_card_of_rightTotal_unique\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Enumerative/Partition.lean\",null,null,\"Nat.Partition.indiscrete_parts\"]"
+  ]
+}

manifests/batches/mathlib/000820.json

@@ -0,0 +1,902 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000820",
+  "batch_fingerprint": "90c4ce8cff03a2ba91f8e1136187c04f6faff4dd9c2da540e7c2532c62685cba",
+  "evidence": {
+    "batch_fingerprint": "90c4ce8cff03a2ba91f8e1136187c04f6faff4dd9c2da540e7c2532c62685cba",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "FractionalOperation.IsValid.contains",
+        "id": "FractionalOperation.IsValid.contains",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            102,
+            39
+          ],
+          "file_path": "Mathlib/Combinatorics/Optimization/ValuedCSP.lean",
+          "full_name": "FractionalOperation.IsValid.contains",
+          "start": [
+            99,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Optimization/ValuedCSP.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rw [two_nsmul, two_nsmul]'",
+        "full_name": "Function.HasMaxCutProperty.forbids_commutativeFractionalPolymorphism",
+        "id": "Function.HasMaxCutProperty.forbids_commutativeFractionalPolymorphism",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            181,
+            27
+          ],
+          "file_path": "Mathlib/Combinatorics/Optimization/ValuedCSP.lean",
+          "full_name": "Function.HasMaxCutProperty.forbids_commutativeFractionalPolymorphism",
+          "start": [
+            151,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"intro contr\"",
+                "[]"
+              ],
+              "state_after": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\nmcf : HasMaxCutProperty f\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\ncontr : AdmitsFractional f \u03c9\n\u22a2 False",
+              "state_before": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\nmcf : HasMaxCutProperty f\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\n\u22a2 \u00acAdmitsFractional f \u03c9",
+              "tactic": "intro contr"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8a, b, hab, mcfab\\u27e9 := mcf\"",
+                "[]"
+              ],
+              "state_after": "case intro.intro.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\ncontr : AdmitsFractional f \u03c9\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\n\u22a2 False",
+              "state_before": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\nmcf : HasMaxCutProperty f\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\ncontr : AdmitsFractional f \u03c9\n\u22a2 False",
+              "tactic": "obtain \u27e8a, b, hab, mcfab\u27e9 := mcf"
+            },
+            {
+              "annotated_tactic": [
+                "\"specialize contr ![![a, b], ![b, a]]\"",
+                "[]"
+              ],
+              "state_after": "case intro.intro.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 \u2211 i : Fin 2, f (![![a, b], ![b, a]] i)\n\u22a2 False",
+              "state_before": "case intro.intro.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\ncontr : AdmitsFractional f \u03c9\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\n\u22a2 False",
+              "tactic": "specialize contr ![![a, b], ![b, a]]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Fin.sum_univ_two'<\\/a>, \\u2190 mcfab.left, \\u2190 <a>two_nsmul<\\/a>] at contr\"",
+                "[{\"full_name\":\"Fin.sum_univ_two'\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Fin.lean\",\"def_pos\":[123,3],\"def_end_pos\":[123,14]},{\"full_name\":\"two_nsmul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[679,15],\"def_end_pos\":[679,24]}]"
+              ],
+              "state_after": "case intro.intro.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\n\u22a2 False",
+              "state_before": "case intro.intro.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 \u2211 i : Fin 2, f (![![a, b], ![b, a]] i)\n\u22a2 False",
+              "tactic": "rw [Fin.sum_univ_two', \u2190 mcfab.left, \u2190 two_nsmul] at contr"
+            },
+            {
+              "annotated_tactic": [
+                "\"have impos : 2 \\u2022 (\\u03c9.map (fun _ => f ![a, b])).<a>sum<\\/a> < \\u03c9.size \\u2022 2 \\u2022 f ![a, b] := by\\n    convert <a>lt_of_lt_of_le<\\/a> sharp contr\\n    simp [<a>FractionalOperation.tt<\\/a>, <a>Multiset.map_map<\\/a>]\"",
+                "[{\"full_name\":\"Multiset.sum\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Multiset.lean\",\"def_pos\":[37,3],\"def_end_pos\":[37,14]},{\"full_name\":\"lt_of_lt_of_le\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[115,9],\"def_end_pos\":[115,23]},{\"full_name\":\"FractionalOperation.tt\",\"def_path\":\"Mathlib\\/Combinatorics\\/Optimization\\/ValuedCSP.lean\",\"def_pos\":[105,5],\"def_end_pos\":[105,27]},{\"full_name\":\"Multiset.map_map\",\"def_path\":\"Mathlib\\/Data\\/Multiset\\/Basic.lean\",\"def_pos\":[1332,9],\"def_end_pos\":[1332,16]}]"
+              ],
+              "state_after": "case intro.intro.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\nsharp :\n  2 \u2022 (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    2 \u2022 (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum\nimpos : 2 \u2022 (Multiset.map (fun x => f ![a, b]) \u03c9).sum < \u03c9.size \u2022 2 \u2022 f ![a, b]\n\u22a2 False",
+              "state_before": "case intro.intro.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\nsharp :\n  2 \u2022 (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    2 \u2022 (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum\n\u22a2 False",
+              "tactic": "have impos : 2 \u2022 (\u03c9.map (fun _ => f ![a, b])).sum < \u03c9.size \u2022 2 \u2022 f ![a, b] := by\n  convert lt_of_lt_of_le sharp contr\n  simp [FractionalOperation.tt, Multiset.map_map]"
+            },
+            {
+              "annotated_tactic": [
+                "\"have rhs_swap : \\u03c9.size \\u2022 2 \\u2022 f ![a, b] = 2 \\u2022 \\u03c9.size \\u2022 f ![a, b] := <a>nsmul_left_comm<\\/a> ..\"",
+                "[{\"full_name\":\"nsmul_left_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[726,15],\"def_end_pos\":[726,30]}]"
+              ],
+              "state_after": "case intro.intro.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\nsharp :\n  2 \u2022 (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    2 \u2022 (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum\nimpos : 2 \u2022 (Multiset.map (fun x => f ![a, b]) \u03c9).sum < \u03c9.size \u2022 2 \u2022 f ![a, b]\nrhs_swap : \u03c9.size \u2022 2 \u2022 f ![a, b] = 2 \u2022 \u03c9.size \u2022 f ![a, b]\n\u22a2 False",
+              "state_before": "case intro.intro.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\nsharp :\n  2 \u2022 (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    2 \u2022 (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum\nimpos : 2 \u2022 (Multiset.map (fun x => f ![a, b]) \u03c9).sum < \u03c9.size \u2022 2 \u2022 f ![a, b]\n\u22a2 False",
+              "tactic": "have rhs_swap : \u03c9.size \u2022 2 \u2022 f ![a, b] = 2 \u2022 \u03c9.size \u2022 f ![a, b] := nsmul_left_comm .."
+            },
+            {
+              "annotated_tactic": [
+                "\"have distrib : (\\u03c9.map (fun _ => f ![a, b])).<a>sum<\\/a> = \\u03c9.size \\u2022 f ![a, b] := by simp\"",
+                "[{\"full_name\":\"Multiset.sum\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Multiset.lean\",\"def_pos\":[37,3],\"def_end_pos\":[37,14]}]"
+              ],
+              "state_after": "case intro.intro.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\nsharp :\n  2 \u2022 (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    2 \u2022 (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum\nimpos : 2 \u2022 (Multiset.map (fun x => f ![a, b]) \u03c9).sum < \u03c9.size \u2022 2 \u2022 f ![a, b]\nrhs_swap : \u03c9.size \u2022 2 \u2022 f ![a, b] = 2 \u2022 \u03c9.size \u2022 f ![a, b]\ndistrib : (Multiset.map (fun x => f ![a, b]) \u03c9).sum = \u03c9.size \u2022 f ![a, b]\n\u22a2 False",
+              "state_before": "case intro.intro.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\nsharp :\n  2 \u2022 (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    2 \u2022 (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum\nimpos : 2 \u2022 (Multiset.map (fun x => f ![a, b]) \u03c9).sum < \u03c9.size \u2022 2 \u2022 f ![a, b]\nrhs_swap : \u03c9.size \u2022 2 \u2022 f ![a, b] = 2 \u2022 \u03c9.size \u2022 f ![a, b]\n\u22a2 False",
+              "tactic": "have distrib : (\u03c9.map (fun _ => f ![a, b])).sum = \u03c9.size \u2022 f ![a, b] := by simp"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [rhs_swap, distrib] at impos\"",
+                "[]"
+              ],
+              "state_after": "case intro.intro.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\nsharp :\n  2 \u2022 (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    2 \u2022 (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum\nimpos : 2 \u2022 \u03c9.size \u2022 f ![a, b] < 2 \u2022 \u03c9.size \u2022 f ![a, b]\nrhs_swap : \u03c9.size \u2022 2 \u2022 f ![a, b] = 2 \u2022 \u03c9.size \u2022 f ![a, b]\ndistrib : (Multiset.map (fun x => f ![a, b]) \u03c9).sum = \u03c9.size \u2022 f ![a, b]\n\u22a2 False",
+              "state_before": "case intro.intro.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\nsharp :\n  2 \u2022 (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    2 \u2022 (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum\nimpos : 2 \u2022 (Multiset.map (fun x => f ![a, b]) \u03c9).sum < \u03c9.size \u2022 2 \u2022 f ![a, b]\nrhs_swap : \u03c9.size \u2022 2 \u2022 f ![a, b] = 2 \u2022 \u03c9.size \u2022 f ![a, b]\ndistrib : (Multiset.map (fun x => f ![a, b]) \u03c9).sum = \u03c9.size \u2022 f ![a, b]\n\u22a2 False",
+              "tactic": "rw [rhs_swap, distrib] at impos"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>ne_of_lt<\\/a> impos <a>rfl<\\/a>\"",
+                "[{\"full_name\":\"ne_of_lt\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[101,9],\"def_end_pos\":[101,17]},{\"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 intro.intro.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\nsharp :\n  2 \u2022 (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    2 \u2022 (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum\nimpos : 2 \u2022 \u03c9.size \u2022 f ![a, b] < 2 \u2022 \u03c9.size \u2022 f ![a, b]\nrhs_swap : \u03c9.size \u2022 2 \u2022 f ![a, b] = 2 \u2022 \u03c9.size \u2022 f ![a, b]\ndistrib : (Multiset.map (fun x => f ![a, b]) \u03c9).sum = \u03c9.size \u2022 f ![a, b]\n\u22a2 False",
+              "tactic": "exact ne_of_lt impos rfl"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>two_nsmul<\\/a>, <a>two_nsmul<\\/a>]\"",
+                "[{\"full_name\":\"two_nsmul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[679,15],\"def_end_pos\":[679,24]},{\"full_name\":\"two_nsmul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[679,15],\"def_end_pos\":[679,24]}]"
+              ],
+              "state_after": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\nhalf_sharp :\n  (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum\n\u22a2 (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum +\n      (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum +\n      (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum",
+              "state_before": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\nhalf_sharp :\n  (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum\n\u22a2 2 \u2022 (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    2 \u2022 (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum",
+              "tactic": "rw [two_nsmul, two_nsmul]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>add_lt_add<\\/a> half_sharp half_sharp\"",
+                "[{\"full_name\":\"add_lt_add\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Unbundled\\/Basic.lean\",\"def_pos\":[167,7],\"def_end_pos\":[167,17]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\nhalf_sharp :\n  (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum\n\u22a2 (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum +\n      (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum +\n      (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum",
+              "tactic": "exact add_lt_add half_sharp half_sharp"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Multiset.sum_lt_sum<\\/a>\"",
+                "[{\"full_name\":\"Multiset.sum_lt_sum\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/BigOperators\\/Group\\/Multiset.lean\",\"def_pos\":[150,15],\"def_end_pos\":[150,25]}]"
+              ],
+              "state_after": "case hle\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\n\u22a2 \u2200 i \u2208 \u03c9.tt ![![a, b], ![b, a]], f ![a, b] \u2264 f i\n\ncase hlt\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\n\u22a2 \u2203 i \u2208 \u03c9.tt ![![a, b], ![b, a]], f ![a, b] < f i",
+              "state_before": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\n\u22a2 (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum",
+              "tactic": "apply Multiset.sum_lt_sum"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro r rin\"",
+                "[]"
+              ],
+              "state_after": "case hle\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\nr : Fin (Nat.succ 0).succ \u2192 D\nrin : r \u2208 \u03c9.tt ![![a, b], ![b, a]]\n\u22a2 f ![a, b] \u2264 f r",
+              "state_before": "case hle\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\n\u22a2 \u2200 i \u2208 \u03c9.tt ![![a, b], ![b, a]], f ![a, b] \u2264 f i",
+              "tactic": "intro r rin"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>le_of_lt<\\/a> (mcfab.rows_lt_aux hab symmega rin)\"",
+                "[{\"full_name\":\"le_of_lt\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[110,9],\"def_end_pos\":[110,17]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case hle\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\nr : Fin (Nat.succ 0).succ \u2192 D\nrin : r \u2208 \u03c9.tt ![![a, b], ![b, a]]\n\u22a2 f ![a, b] \u2264 f r",
+              "tactic": "exact le_of_lt (mcfab.rows_lt_aux hab symmega rin)"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8g, _\\u27e9 := valid.contains\"",
+                "[]"
+              ],
+              "state_after": "case hlt.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\ng : (Fin 2 \u2192 D) \u2192 D\nh\u271d : g \u2208 \u03c9\n\u22a2 \u2203 i \u2208 \u03c9.tt ![![a, b], ![b, a]], f ![a, b] < f i",
+              "state_before": "case hlt\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\n\u22a2 \u2203 i \u2208 \u03c9.tt ![![a, b], ![b, a]], f ![a, b] < f i",
+              "tactic": "obtain \u27e8g, _\u27e9 := valid.contains"
+            },
+            {
+              "annotated_tactic": [
+                "\"have : (fun i => g ((<a>Function.swap<\\/a> ![![a, b], ![b, a]]) i)) \\u2208 \\u03c9.tt ![![a, b], ![b, a]] := by\\n          simp only [<a>FractionalOperation.tt<\\/a>, <a>Multiset.mem_map<\\/a>]\\n          use g\"",
+                "[{\"full_name\":\"Function.swap\",\"def_path\":\"Mathlib\\/Init\\/Function.lean\",\"def_pos\":[78,8],\"def_end_pos\":[78,12]},{\"full_name\":\"FractionalOperation.tt\",\"def_path\":\"Mathlib\\/Combinatorics\\/Optimization\\/ValuedCSP.lean\",\"def_pos\":[105,5],\"def_end_pos\":[105,27]},{\"full_name\":\"Multiset.mem_map\",\"def_path\":\"Mathlib\\/Data\\/Multiset\\/Basic.lean\",\"def_pos\":[1277,9],\"def_end_pos\":[1277,16]}]"
+              ],
+              "state_after": "case hlt.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\ng : (Fin 2 \u2192 D) \u2192 D\nh\u271d : g \u2208 \u03c9\nthis : (fun i => g (swap ![![a, b], ![b, a]] i)) \u2208 \u03c9.tt ![![a, b], ![b, a]]\n\u22a2 \u2203 i \u2208 \u03c9.tt ![![a, b], ![b, a]], f ![a, b] < f i",
+              "state_before": "case hlt.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\ng : (Fin 2 \u2192 D) \u2192 D\nh\u271d : g \u2208 \u03c9\n\u22a2 \u2203 i \u2208 \u03c9.tt ![![a, b], ![b, a]], f ![a, b] < f i",
+              "tactic": "have : (fun i => g ((Function.swap ![![a, b], ![b, a]]) i)) \u2208 \u03c9.tt ![![a, b], ![b, a]] := by\n  simp only [FractionalOperation.tt, Multiset.mem_map]\n  use g"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact \\u27e8_, this, mcfab.rows_lt_aux hab symmega this\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case hlt.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\ng : (Fin 2 \u2192 D) \u2192 D\nh\u271d : g \u2208 \u03c9\nthis : (fun i => g (swap ![![a, b], ![b, a]] i)) \u2208 \u03c9.tt ![![a, b], ![b, a]]\n\u22a2 \u2203 i \u2208 \u03c9.tt ![![a, b], ![b, a]], f ![a, b] < f i",
+              "tactic": "exact \u27e8_, this, mcfab.rows_lt_aux hab symmega this\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>FractionalOperation.tt<\\/a>, <a>Multiset.mem_map<\\/a>]\"",
+                "[{\"full_name\":\"FractionalOperation.tt\",\"def_path\":\"Mathlib\\/Combinatorics\\/Optimization\\/ValuedCSP.lean\",\"def_pos\":[105,5],\"def_end_pos\":[105,27]},{\"full_name\":\"Multiset.mem_map\",\"def_path\":\"Mathlib\\/Data\\/Multiset\\/Basic.lean\",\"def_pos\":[1277,9],\"def_end_pos\":[1277,16]}]"
+              ],
+              "state_after": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\ng : (Fin 2 \u2192 D) \u2192 D\nh\u271d : g \u2208 \u03c9\n\u22a2 \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = fun i => g (swap ![![a, b], ![b, a]] i)",
+              "state_before": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\ng : (Fin 2 \u2192 D) \u2192 D\nh\u271d : g \u2208 \u03c9\n\u22a2 (fun i => g (swap ![![a, b], ![b, a]] i)) \u2208 \u03c9.tt ![![a, b], ![b, a]]",
+              "tactic": "simp only [FractionalOperation.tt, Multiset.mem_map]"
+            },
+            {
+              "annotated_tactic": [
+                "\"use g\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\ng : (Fin 2 \u2192 D) \u2192 D\nh\u271d : g \u2208 \u03c9\n\u22a2 \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = fun i => g (swap ![![a, b], ![b, a]] i)",
+              "tactic": "use g"
+            },
+            {
+              "annotated_tactic": [
+                "\"convert <a>lt_of_lt_of_le<\\/a> sharp contr\"",
+                "[{\"full_name\":\"lt_of_lt_of_le\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[115,9],\"def_end_pos\":[115,23]}]"
+              ],
+              "state_after": "case h.e'_3.h.e'_6.h.e'_3\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\nsharp :\n  2 \u2022 (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    2 \u2022 (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum\n\u22a2 Multiset.map (fun x => f ![a, b]) \u03c9 = Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])",
+              "state_before": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\nsharp :\n  2 \u2022 (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    2 \u2022 (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum\n\u22a2 2 \u2022 (Multiset.map (fun x => f ![a, b]) \u03c9).sum < \u03c9.size \u2022 2 \u2022 f ![a, b]",
+              "tactic": "convert lt_of_lt_of_le sharp contr"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [<a>FractionalOperation.tt<\\/a>, <a>Multiset.map_map<\\/a>]\"",
+                "[{\"full_name\":\"FractionalOperation.tt\",\"def_path\":\"Mathlib\\/Combinatorics\\/Optimization\\/ValuedCSP.lean\",\"def_pos\":[105,5],\"def_end_pos\":[105,27]},{\"full_name\":\"Multiset.map_map\",\"def_path\":\"Mathlib\\/Data\\/Multiset\\/Basic.lean\",\"def_pos\":[1332,9],\"def_end_pos\":[1332,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.e'_3.h.e'_6.h.e'_3\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\nsharp :\n  2 \u2022 (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    2 \u2022 (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum\n\u22a2 Multiset.map (fun x => f ![a, b]) \u03c9 = Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])",
+              "tactic": "simp [FractionalOperation.tt, Multiset.map_map]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\n\u03c9 : FractionalOperation D 2\nvalid : \u03c9.IsValid\nsymmega : \u03c9.IsSymmetric\na b : D\nhab : a \u2260 b\nmcfab : HasMaxCutPropertyAt f a b\ncontr : 2 \u2022 (Multiset.map f (\u03c9.tt ![![a, b], ![b, a]])).sum \u2264 \u03c9.size \u2022 2 \u2022 f ![a, b]\nsharp :\n  2 \u2022 (Multiset.map (fun x => f ![a, b]) (\u03c9.tt ![![a, b], ![b, a]])).sum <\n    2 \u2022 (Multiset.map (fun r => f r) (\u03c9.tt ![![a, b], ![b, a]])).sum\nimpos : 2 \u2022 (Multiset.map (fun x => f ![a, b]) \u03c9).sum < \u03c9.size \u2022 2 \u2022 f ![a, b]\nrhs_swap : \u03c9.size \u2022 2 \u2022 f ![a, b] = 2 \u2022 \u03c9.size \u2022 f ![a, b]\n\u22a2 (Multiset.map (fun x => f ![a, b]) \u03c9).sum = \u03c9.size \u2022 f ![a, b]",
+              "tactic": "simp"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Optimization/ValuedCSP.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rcases (mcf.right (r 0) (r 1)).right equ with \u27e8ha0, hb1\u27e9 | \u27e8ha1, hb0\u27e9'",
+        "full_name": "Function.HasMaxCutPropertyAt.rows_lt_aux",
+        "id": "Function.HasMaxCutPropertyAt.rows_lt_aux",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            149,
+            32
+          ],
+          "file_path": "Mathlib/Combinatorics/Optimization/ValuedCSP.lean",
+          "full_name": "Function.HasMaxCutPropertyAt.rows_lt_aux",
+          "start": [
+            130,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [<a>FractionalOperation.tt<\\/a>, <a>Multiset.mem_map<\\/a>] at rin\"",
+                "[{\"full_name\":\"FractionalOperation.tt\",\"def_path\":\"Mathlib\\/Combinatorics\\/Optimization\\/ValuedCSP.lean\",\"def_pos\":[105,5],\"def_end_pos\":[105,27]},{\"full_name\":\"Multiset.mem_map\",\"def_path\":\"Mathlib\\/Data\\/Multiset\\/Basic.lean\",\"def_pos\":[1277,9],\"def_end_pos\":[1277,16]}]"
+              ],
+              "state_after": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\n\u22a2 f ![a, b] < f r",
+              "state_before": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nrin : r \u2208 \u03c9.tt ![![a, b], ![b, a]]\n\u22a2 f ![a, b] < f r",
+              "tactic": "rw [FractionalOperation.tt, Multiset.mem_map] at rin"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [show r = ![r 0, r 1] from List.ofFn_inj.mp <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": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\n\u22a2 f ![a, b] < f ![r 0, r 1]",
+              "state_before": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\n\u22a2 f ![a, b] < f r",
+              "tactic": "rw [show r = ![r 0, r 1] from List.ofFn_inj.mp rfl]"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>lt_of_le_of_ne<\\/a> (mcf.right (r 0) (r 1)).<a>left<\\/a>\"",
+                "[{\"full_name\":\"lt_of_le_of_ne\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[198,9],\"def_end_pos\":[198,23]},{\"full_name\":\"And.left\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[521,3],\"def_end_pos\":[521,7]}]"
+              ],
+              "state_after": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\n\u22a2 f ![a, b] \u2260 f ![r 0, r 1]",
+              "state_before": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\n\u22a2 f ![a, b] < f ![r 0, r 1]",
+              "tactic": "apply lt_of_le_of_ne (mcf.right (r 0) (r 1)).left"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro equ\"",
+                "[]"
+              ],
+              "state_after": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\nequ : f ![a, b] = f ![r 0, r 1]\n\u22a2 False",
+              "state_before": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\n\u22a2 f ![a, b] \u2260 f ![r 0, r 1]",
+              "tactic": "intro equ"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply asymm\"",
+                "[]"
+              ],
+              "state_after": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\nequ : f ![a, b] = f ![r 0, r 1]\nasymm : r 0 \u2260 r 1\n\u22a2 r 0 = r 1",
+              "state_before": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\nequ : f ![a, b] = f ![r 0, r 1]\nasymm : r 0 \u2260 r 1\n\u22a2 False",
+              "tactic": "apply asymm"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8o, in_omega, rfl\\u27e9 := rin\"",
+                "[]"
+              ],
+              "state_after": "case intro.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\no : (Fin 2 \u2192 D) \u2192 D\nin_omega : o \u2208 \u03c9\nequ : f ![a, b] = f ![(fun i => o (swap ![![a, b], ![b, a]] i)) 0, (fun i => o (swap ![![a, b], ![b, a]] i)) 1]\nasymm : (fun i => o (swap ![![a, b], ![b, a]] i)) 0 \u2260 (fun i => o (swap ![![a, b], ![b, a]] i)) 1\n\u22a2 (fun i => o (swap ![![a, b], ![b, a]] i)) 0 = (fun i => o (swap ![![a, b], ![b, a]] i)) 1",
+              "state_before": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\nequ : f ![a, b] = f ![r 0, r 1]\nasymm : r 0 \u2260 r 1\n\u22a2 r 0 = r 1",
+              "tactic": "obtain \u27e8o, in_omega, rfl\u27e9 := rin"
+            },
+            {
+              "annotated_tactic": [
+                "\"show o (fun j => ![![a, b], ![b, a]] j 0) = o (fun j => ![![a, b], ![b, a]] j 1)\"",
+                "[]"
+              ],
+              "state_after": "case intro.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\no : (Fin 2 \u2192 D) \u2192 D\nin_omega : o \u2208 \u03c9\nequ : f ![a, b] = f ![(fun i => o (swap ![![a, b], ![b, a]] i)) 0, (fun i => o (swap ![![a, b], ![b, a]] i)) 1]\nasymm : (fun i => o (swap ![![a, b], ![b, a]] i)) 0 \u2260 (fun i => o (swap ![![a, b], ![b, a]] i)) 1\n\u22a2 (o fun j => ![![a, b], ![b, a]] j 0) = o fun j => ![![a, b], ![b, a]] j 1",
+              "state_before": "case intro.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\no : (Fin 2 \u2192 D) \u2192 D\nin_omega : o \u2208 \u03c9\nequ : f ![a, b] = f ![(fun i => o (swap ![![a, b], ![b, a]] i)) 0, (fun i => o (swap ![![a, b], ![b, a]] i)) 1]\nasymm : (fun i => o (swap ![![a, b], ![b, a]] i)) 0 \u2260 (fun i => o (swap ![![a, b], ![b, a]] i)) 1\n\u22a2 (fun i => o (swap ![![a, b], ![b, a]] i)) 0 = (fun i => o (swap ![![a, b], ![b, a]] i)) 1",
+              "tactic": "show o (fun j => ![![a, b], ![b, a]] j 0) = o (fun j => ![![a, b], ![b, a]] j 1)"
+            },
+            {
+              "annotated_tactic": [
+                "\"convert symmega ![a, b] ![b, a] (<a>List.Perm.swap<\\/a> b a []) o in_omega using 2 <;>\\n    simp [<a>Matrix.const_fin1_eq<\\/a>]\"",
+                "[{\"full_name\":\"List.Perm.swap\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Data\\/List\\/Basic.lean\",\"def_pos\":[1356,5],\"def_end_pos\":[1356,9]},{\"full_name\":\"Matrix.const_fin1_eq\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/VecNotation.lean\",\"def_pos\":[596,7],\"def_end_pos\":[596,20]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case intro.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\no : (Fin 2 \u2192 D) \u2192 D\nin_omega : o \u2208 \u03c9\nequ : f ![a, b] = f ![(fun i => o (swap ![![a, b], ![b, a]] i)) 0, (fun i => o (swap ![![a, b], ![b, a]] i)) 1]\nasymm : (fun i => o (swap ![![a, b], ![b, a]] i)) 0 \u2260 (fun i => o (swap ![![a, b], ![b, a]] i)) 1\n\u22a2 (o fun j => ![![a, b], ![b, a]] j 0) = o fun j => ![![a, b], ![b, a]] j 1",
+              "tactic": "convert symmega ![a, b] ![b, a] (List.Perm.swap b a []) o in_omega using 2 <;>\n  simp [Matrix.const_fin1_eq]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rcases (mcf.right (r 0) (r 1)).<a>right<\\/a> equ with \\u27e8ha0, hb1\\u27e9 | \\u27e8ha1, hb0\\u27e9\"",
+                "[{\"full_name\":\"And.right\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[524,3],\"def_end_pos\":[524,8]}]"
+              ],
+              "state_after": "case inl.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\nequ : f ![a, b] = f ![r 0, r 1]\nha0 : a = r 0\nhb1 : b = r 1\n\u22a2 r 0 \u2260 r 1\n\ncase inr.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\nequ : f ![a, b] = f ![r 0, r 1]\nha1 : a = r 1\nhb0 : b = r 0\n\u22a2 r 0 \u2260 r 1",
+              "state_before": "D : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\nequ : f ![a, b] = f ![r 0, r 1]\n\u22a2 r 0 \u2260 r 1",
+              "tactic": "rcases (mcf.right (r 0) (r 1)).right equ with \u27e8ha0, hb1\u27e9 | \u27e8ha1, hb0\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [ha0, hb1] at hab\"",
+                "[]"
+              ],
+              "state_after": "case inl.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nhab : r 0 \u2260 r 1\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\nequ : f ![a, b] = f ![r 0, r 1]\nha0 : a = r 0\nhb1 : b = r 1\n\u22a2 r 0 \u2260 r 1",
+              "state_before": "case inl.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\nequ : f ![a, b] = f ![r 0, r 1]\nha0 : a = r 0\nhb1 : b = r 1\n\u22a2 r 0 \u2260 r 1",
+              "tactic": "rw [ha0, hb1] at hab"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact hab\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inl.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nhab : r 0 \u2260 r 1\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\nequ : f ![a, b] = f ![r 0, r 1]\nha0 : a = r 0\nhb1 : b = r 1\n\u22a2 r 0 \u2260 r 1",
+              "tactic": "exact hab"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [ha1, hb0] at hab\"",
+                "[]"
+              ],
+              "state_after": "case inr.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nhab : r 1 \u2260 r 0\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\nequ : f ![a, b] = f ![r 0, r 1]\nha1 : a = r 1\nhb0 : b = r 0\n\u22a2 r 0 \u2260 r 1",
+              "state_before": "case inr.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\nhab : a \u2260 b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\nequ : f ![a, b] = f ![r 0, r 1]\nha1 : a = r 1\nhb0 : b = r 0\n\u22a2 r 0 \u2260 r 1",
+              "tactic": "rw [ha1, hb0] at hab"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact hab.symm\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inr.intro\nD : Type u_1\nC\u271d : Type u_2\ninst\u271d\u00b9 : OrderedAddCommMonoid C\u271d\nm : \u2115\nC : Type u_3\ninst\u271d : OrderedCancelAddCommMonoid C\nf : (Fin 2 \u2192 D) \u2192 C\na b : D\nmcf : HasMaxCutPropertyAt f a b\n\u03c9 : FractionalOperation D 2\nsymmega : \u03c9.IsSymmetric\nr : Fin 2 \u2192 D\nhab : r 1 \u2260 r 0\nrin : \u2203 a_1 \u2208 \u03c9, (fun i => a_1 (swap ![![a, b], ![b, a]] i)) = r\nequ : f ![a, b] = f ![r 0, r 1]\nha1 : a = r 1\nhb0 : b = r 0\n\u22a2 r 0 \u2260 r 1",
+              "tactic": "exact hab.symm"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Optimization/ValuedCSP.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.exists_card_fiber_le_of_card_le_mul",
+        "id": "Finset.exists_card_fiber_le_of_card_le_mul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            305,
+            46
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Finset.exists_card_fiber_le_of_card_le_mul",
+          "start": [
+            303,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.exists_card_fiber_lt_of_card_lt_mul",
+        "id": "Finset.exists_card_fiber_lt_of_card_lt_mul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            265,
+            43
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Finset.exists_card_fiber_lt_of_card_lt_mul",
+          "start": [
+            263,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.exists_le_card_fiber_of_mul_le_card_of_maps_to",
+        "id": "Finset.exists_le_card_fiber_of_mul_le_card_of_maps_to",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            284,
+            60
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Finset.exists_le_card_fiber_of_mul_le_card_of_maps_to",
+          "start": [
+            282,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.exists_lt_card_fiber_of_mul_lt_card_of_maps_to",
+        "id": "Finset.exists_lt_card_fiber_of_mul_lt_card_of_maps_to",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            243,
+            57
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Finset.exists_lt_card_fiber_of_mul_lt_card_of_maps_to",
+          "start": [
+            241,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.exists_sum_fiber_le_of_maps_to_of_sum_le_nsmul",
+        "id": "Finset.exists_sum_fiber_le_of_maps_to_of_sum_le_nsmul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            175,
+            69
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Finset.exists_sum_fiber_le_of_maps_to_of_sum_le_nsmul",
+          "start": [
+            173,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.exists_sum_fiber_le_of_sum_fiber_nonneg_of_sum_le_nsmul",
+        "id": "Finset.exists_sum_fiber_le_of_sum_fiber_nonneg_of_sum_le_nsmul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            201,
+            78
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Finset.exists_sum_fiber_le_of_sum_fiber_nonneg_of_sum_le_nsmul",
+          "start": [
+            198,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.exists_sum_fiber_lt_of_maps_to_of_sum_lt_nsmul",
+        "id": "Finset.exists_sum_fiber_lt_of_maps_to_of_sum_lt_nsmul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            126,
+            66
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Finset.exists_sum_fiber_lt_of_maps_to_of_sum_lt_nsmul",
+          "start": [
+            124,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.exists_sum_fiber_lt_of_sum_fiber_nonneg_of_sum_lt_nsmul",
+        "id": "Finset.exists_sum_fiber_lt_of_sum_fiber_nonneg_of_sum_lt_nsmul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            152,
+            75
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Finset.exists_sum_fiber_lt_of_sum_fiber_nonneg_of_sum_lt_nsmul",
+          "start": [
+            149,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Fintype.exists_card_fiber_le_of_card_le_mul",
+        "id": "Fintype.exists_card_fiber_le_of_card_le_mul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            449,
+            45
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Fintype.exists_card_fiber_le_of_card_le_mul",
+          "start": [
+            447,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Fintype.exists_card_fiber_le_of_card_le_nsmul",
+        "id": "Fintype.exists_card_fiber_le_of_card_le_nsmul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            440,
+            9
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Fintype.exists_card_fiber_le_of_card_le_nsmul",
+          "start": [
+            437,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Fintype.exists_card_fiber_lt_of_card_lt_mul",
+        "id": "Fintype.exists_card_fiber_lt_of_card_lt_mul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            410,
+            45
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Fintype.exists_card_fiber_lt_of_card_lt_mul",
+          "start": [
+            408,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Fintype.exists_card_fiber_lt_of_card_lt_nsmul",
+        "id": "Fintype.exists_card_fiber_lt_of_card_lt_nsmul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            397,
+            9
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Fintype.exists_card_fiber_lt_of_card_lt_nsmul",
+          "start": [
+            394,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Fintype.exists_le_card_fiber_of_mul_le_card",
+        "id": "Fintype.exists_le_card_fiber_of_mul_le_card",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            430,
+            45
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Fintype.exists_le_card_fiber_of_mul_le_card",
+          "start": [
+            428,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Fintype.exists_le_card_fiber_of_nsmul_le_card",
+        "id": "Fintype.exists_le_card_fiber_of_nsmul_le_card",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            421,
+            9
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Fintype.exists_le_card_fiber_of_nsmul_le_card",
+          "start": [
+            417,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Fintype.exists_le_sum_fiber_of_nsmul_le_sum",
+        "id": "Fintype.exists_le_sum_fiber_of_nsmul_le_sum",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            345,
+            10
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Fintype.exists_le_sum_fiber_of_nsmul_le_sum",
+          "start": [
+            341,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Fintype.exists_lt_card_fiber_of_mul_lt_card",
+        "id": "Fintype.exists_lt_card_fiber_of_mul_lt_card",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            388,
+            45
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Fintype.exists_lt_card_fiber_of_mul_lt_card",
+          "start": [
+            386,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Fintype.exists_lt_card_fiber_of_nsmul_lt_card",
+        "id": "Fintype.exists_lt_card_fiber_of_nsmul_lt_card",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            375,
+            9
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Fintype.exists_lt_card_fiber_of_nsmul_lt_card",
+          "start": [
+            372,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Fintype.exists_lt_sum_fiber_of_nsmul_lt_sum",
+        "id": "Fintype.exists_lt_sum_fiber_of_nsmul_lt_sum",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            334,
+            10
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Fintype.exists_lt_sum_fiber_of_nsmul_lt_sum",
+          "start": [
+            331,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Fintype.exists_sum_fiber_le_of_sum_le_nsmul",
+        "id": "Fintype.exists_sum_fiber_le_of_sum_le_nsmul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            362,
+            54
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Fintype.exists_sum_fiber_le_of_sum_le_nsmul",
+          "start": [
+            360,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Fintype.exists_sum_fiber_lt_of_sum_lt_nsmul",
+        "id": "Fintype.exists_sum_fiber_lt_of_sum_lt_nsmul",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            353,
+            54
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Fintype.exists_sum_fiber_lt_of_sum_lt_nsmul",
+          "start": [
+            351,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Nat.exists_lt_modEq_of_infinite",
+        "id": "Nat.exists_lt_modEq_of_infinite",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            463,
+            20
+          ],
+          "file_path": "Mathlib/Combinatorics/Pigeonhole.lean",
+          "full_name": "Nat.exists_lt_modEq_of_infinite",
+          "start": [
+            460,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Pigeonhole.lean"
+      }
+    ],
+    "input_proofs": 32,
+    "input_units": 2,
+    "proofs": 8,
+    "published_proofs": 8,
+    "published_transitions": 12,
+    "replay_failures": [],
+    "transitions": 12,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000820-0000-9cc7ca34cc7a83d3.parquet",
+      "sha256": "9cc7ca34cc7a83d33f7239bf48a05aac9b1ed92edfcda8cbbc10a5c7fec912a1",
+      "bytes": 64638,
+      "rows": 8,
+      "revision": "1b1732dbac9bd3e39d47d0584914277d2b00812a"
+    },
+    {
+      "path": "data/internal_test/mathlib-000820-0000-bf5ffc16d8e85810.parquet",
+      "sha256": "bf5ffc16d8e858108d2edf306ba29994b1cad24e9cfea5323427b235bcafcac8",
+      "bytes": 57563,
+      "rows": 4,
+      "revision": "1b1732dbac9bd3e39d47d0584914277d2b00812a"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Finset.exists_card_fiber_le_of_card_le_nsmul",
+    "mathlib:Finset.exists_card_fiber_lt_of_card_lt_nsmul",
+    "mathlib:Finset.exists_le_card_fiber_of_nsmul_le_card_of_maps_to",
+    "mathlib:Finset.exists_le_sum_fiber_of_maps_to_of_nsmul_le_sum",
+    "mathlib:Finset.exists_le_sum_fiber_of_sum_fiber_nonpos_of_nsmul_le_sum",
+    "mathlib:Finset.exists_lt_card_fiber_of_nsmul_lt_card_of_maps_to",
+    "mathlib:Finset.exists_lt_sum_fiber_of_maps_to_of_nsmul_lt_sum",
+    "mathlib:Finset.exists_lt_sum_fiber_of_sum_fiber_nonpos_of_nsmul_lt_sum"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Pigeonhole.lean\",null,null,\"Finset.exists_card_fiber_le_of_card_le_nsmul\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Pigeonhole.lean\",null,null,\"Finset.exists_card_fiber_lt_of_card_lt_nsmul\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Pigeonhole.lean\",null,null,\"Finset.exists_le_card_fiber_of_nsmul_le_card_of_maps_to\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Pigeonhole.lean\",null,null,\"Finset.exists_le_sum_fiber_of_maps_to_of_nsmul_le_sum\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Pigeonhole.lean\",null,null,\"Finset.exists_le_sum_fiber_of_sum_fiber_nonpos_of_nsmul_le_sum\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Pigeonhole.lean\",null,null,\"Finset.exists_lt_card_fiber_of_nsmul_lt_card_of_maps_to\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Pigeonhole.lean\",null,null,\"Finset.exists_lt_sum_fiber_of_maps_to_of_nsmul_lt_sum\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Pigeonhole.lean\",null,null,\"Finset.exists_lt_sum_fiber_of_sum_fiber_nonpos_of_nsmul_lt_sum\"]"
+  ]
+}

manifests/batches/mathlib/000821.json

@@ -0,0 +1,285 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000821",
+  "batch_fingerprint": "ec5cb9a3c3621fcfd89dab662c380ca6e482e6e5d803c546a7faec0d79fb9fc1",
+  "evidence": {
+    "batch_fingerprint": "ec5cb9a3c3621fcfd89dab662c380ca6e482e6e5d803c546a7faec0d79fb9fc1",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Quiver.shortest_path_spec",
+        "id": "Quiver.shortest_path_spec",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            110,
+            71
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/Arborescence.lean",
+          "full_name": "Quiver.shortest_path_spec",
+          "start": [
+            109,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/Arborescence.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Prefunctor.comp_assoc",
+        "id": "Prefunctor.comp_assoc",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            126,
+            6
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/Basic.lean",
+          "full_name": "Prefunctor.comp_assoc",
+          "start": [
+            123,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Prefunctor.comp_id",
+        "id": "Prefunctor.comp_id",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            114,
+            29
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/Basic.lean",
+          "full_name": "Prefunctor.comp_id",
+          "start": [
+            113,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/Basic.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'ext X'",
+        "full_name": "Prefunctor.ext",
+        "id": "Prefunctor.ext",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            87,
+            26
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/Basic.lean",
+          "full_name": "Prefunctor.ext",
+          "start": [
+            76,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"cases' F with F_obj _\"",
+                "[]"
+              ],
+              "state_after": "case mk\nV : Type u\ninst\u271d\u00b9 : Quiver V\nW : Type u\u2082\ninst\u271d : Quiver W\nG : Prefunctor V W\nF_obj : V \u2192 W\nmap\u271d : {X Y : V} \u2192 (X \u27f6 Y) \u2192 (F_obj X \u27f6 F_obj Y)\nh_obj : \u2200 (X : V), { obj := F_obj, map := map\u271d }.obj X = G.obj X\nh_map : \u2200 (X Y : V) (f : X \u27f6 Y), { obj := F_obj, map := map\u271d }.map f = Eq.recOn \u22ef (Eq.recOn \u22ef (G.map f))\n\u22a2 { obj := F_obj, map := map\u271d } = G",
+              "state_before": "V : Type u\ninst\u271d\u00b9 : Quiver V\nW : Type u\u2082\ninst\u271d : Quiver W\nF G : Prefunctor V W\nh_obj : \u2200 (X : V), F.obj X = G.obj X\nh_map : \u2200 (X Y : V) (f : X \u27f6 Y), F.map f = Eq.recOn \u22ef (Eq.recOn \u22ef (G.map f))\n\u22a2 F = G",
+              "tactic": "cases' F with F_obj _"
+            },
+            {
+              "annotated_tactic": [
+                "\"cases' G with G_obj _\"",
+                "[]"
+              ],
+              "state_after": "case mk.mk\nV : Type u\ninst\u271d\u00b9 : Quiver V\nW : Type u\u2082\ninst\u271d : Quiver W\nF_obj : V \u2192 W\nmap\u271d\u00b9 : {X Y : V} \u2192 (X \u27f6 Y) \u2192 (F_obj X \u27f6 F_obj Y)\nG_obj : V \u2192 W\nmap\u271d : {X Y : V} \u2192 (X \u27f6 Y) \u2192 (G_obj X \u27f6 G_obj Y)\nh_obj : \u2200 (X : V), { obj := F_obj, map := map\u271d\u00b9 }.obj X = { obj := G_obj, map := map\u271d }.obj X\nh_map :\n  \u2200 (X Y : V) (f : X \u27f6 Y),\n    { obj := F_obj, map := map\u271d\u00b9 }.map f = Eq.recOn \u22ef (Eq.recOn \u22ef ({ obj := G_obj, map := map\u271d }.map f))\n\u22a2 { obj := F_obj, map := map\u271d\u00b9 } = { obj := G_obj, map := map\u271d }",
+              "state_before": "case mk\nV : Type u\ninst\u271d\u00b9 : Quiver V\nW : Type u\u2082\ninst\u271d : Quiver W\nG : Prefunctor V W\nF_obj : V \u2192 W\nmap\u271d : {X Y : V} \u2192 (X \u27f6 Y) \u2192 (F_obj X \u27f6 F_obj Y)\nh_obj : \u2200 (X : V), { obj := F_obj, map := map\u271d }.obj X = G.obj X\nh_map : \u2200 (X Y : V) (f : X \u27f6 Y), { obj := F_obj, map := map\u271d }.map f = Eq.recOn \u22ef (Eq.recOn \u22ef (G.map f))\n\u22a2 { obj := F_obj, map := map\u271d } = G",
+              "tactic": "cases' G with G_obj _"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain rfl : F_obj = G_obj := by\\n    ext X\\n    apply h_obj\"",
+                "[]"
+              ],
+              "state_after": "case mk.mk\nV : Type u\ninst\u271d\u00b9 : Quiver V\nW : Type u\u2082\ninst\u271d : Quiver W\nF_obj : V \u2192 W\nmap\u271d\u00b9 map\u271d : {X Y : V} \u2192 (X \u27f6 Y) \u2192 (F_obj X \u27f6 F_obj Y)\nh_obj : \u2200 (X : V), { obj := F_obj, map := map\u271d\u00b9 }.obj X = { obj := F_obj, map := map\u271d }.obj X\nh_map :\n  \u2200 (X Y : V) (f : X \u27f6 Y),\n    { obj := F_obj, map := map\u271d\u00b9 }.map f = Eq.recOn \u22ef (Eq.recOn \u22ef ({ obj := F_obj, map := map\u271d }.map f))\n\u22a2 { obj := F_obj, map := map\u271d\u00b9 } = { obj := F_obj, map := map\u271d }",
+              "state_before": "case mk.mk\nV : Type u\ninst\u271d\u00b9 : Quiver V\nW : Type u\u2082\ninst\u271d : Quiver W\nF_obj : V \u2192 W\nmap\u271d\u00b9 : {X Y : V} \u2192 (X \u27f6 Y) \u2192 (F_obj X \u27f6 F_obj Y)\nG_obj : V \u2192 W\nmap\u271d : {X Y : V} \u2192 (X \u27f6 Y) \u2192 (G_obj X \u27f6 G_obj Y)\nh_obj : \u2200 (X : V), { obj := F_obj, map := map\u271d\u00b9 }.obj X = { obj := G_obj, map := map\u271d }.obj X\nh_map :\n  \u2200 (X Y : V) (f : X \u27f6 Y),\n    { obj := F_obj, map := map\u271d\u00b9 }.map f = Eq.recOn \u22ef (Eq.recOn \u22ef ({ obj := G_obj, map := map\u271d }.map f))\n\u22a2 { obj := F_obj, map := map\u271d\u00b9 } = { obj := G_obj, map := map\u271d }",
+              "tactic": "obtain rfl : F_obj = G_obj := by\n  ext X\n  apply h_obj"
+            },
+            {
+              "annotated_tactic": [
+                "\"congr\"",
+                "[]"
+              ],
+              "state_after": "case mk.mk.e_map\nV : Type u\ninst\u271d\u00b9 : Quiver V\nW : Type u\u2082\ninst\u271d : Quiver W\nF_obj : V \u2192 W\nmap\u271d\u00b9 map\u271d : {X Y : V} \u2192 (X \u27f6 Y) \u2192 (F_obj X \u27f6 F_obj Y)\nh_obj : \u2200 (X : V), { obj := F_obj, map := map\u271d\u00b9 }.obj X = { obj := F_obj, map := map\u271d }.obj X\nh_map :\n  \u2200 (X Y : V) (f : X \u27f6 Y),\n    { obj := F_obj, map := map\u271d\u00b9 }.map f = Eq.recOn \u22ef (Eq.recOn \u22ef ({ obj := F_obj, map := map\u271d }.map f))\n\u22a2 map\u271d\u00b9 = map\u271d",
+              "state_before": "case mk.mk\nV : Type u\ninst\u271d\u00b9 : Quiver V\nW : Type u\u2082\ninst\u271d : Quiver W\nF_obj : V \u2192 W\nmap\u271d\u00b9 map\u271d : {X Y : V} \u2192 (X \u27f6 Y) \u2192 (F_obj X \u27f6 F_obj Y)\nh_obj : \u2200 (X : V), { obj := F_obj, map := map\u271d\u00b9 }.obj X = { obj := F_obj, map := map\u271d }.obj X\nh_map :\n  \u2200 (X Y : V) (f : X \u27f6 Y),\n    { obj := F_obj, map := map\u271d\u00b9 }.map f = Eq.recOn \u22ef (Eq.recOn \u22ef ({ obj := F_obj, map := map\u271d }.map f))\n\u22a2 { obj := F_obj, map := map\u271d\u00b9 } = { obj := F_obj, map := map\u271d }",
+              "tactic": "congr"
+            },
+            {
+              "annotated_tactic": [
+                "\"funext X Y f\"",
+                "[]"
+              ],
+              "state_after": "case mk.mk.e_map.h.h.h\nV : Type u\ninst\u271d\u00b9 : Quiver V\nW : Type u\u2082\ninst\u271d : Quiver W\nF_obj : V \u2192 W\nmap\u271d\u00b9 map\u271d : {X Y : V} \u2192 (X \u27f6 Y) \u2192 (F_obj X \u27f6 F_obj Y)\nh_obj : \u2200 (X : V), { obj := F_obj, map := map\u271d\u00b9 }.obj X = { obj := F_obj, map := map\u271d }.obj X\nh_map :\n  \u2200 (X Y : V) (f : X \u27f6 Y),\n    { obj := F_obj, map := map\u271d\u00b9 }.map f = Eq.recOn \u22ef (Eq.recOn \u22ef ({ obj := F_obj, map := map\u271d }.map f))\nX Y : V\nf : X \u27f6 Y\n\u22a2 map\u271d\u00b9 f = map\u271d f",
+              "state_before": "case mk.mk.e_map\nV : Type u\ninst\u271d\u00b9 : Quiver V\nW : Type u\u2082\ninst\u271d : Quiver W\nF_obj : V \u2192 W\nmap\u271d\u00b9 map\u271d : {X Y : V} \u2192 (X \u27f6 Y) \u2192 (F_obj X \u27f6 F_obj Y)\nh_obj : \u2200 (X : V), { obj := F_obj, map := map\u271d\u00b9 }.obj X = { obj := F_obj, map := map\u271d }.obj X\nh_map :\n  \u2200 (X Y : V) (f : X \u27f6 Y),\n    { obj := F_obj, map := map\u271d\u00b9 }.map f = Eq.recOn \u22ef (Eq.recOn \u22ef ({ obj := F_obj, map := map\u271d }.map f))\n\u22a2 map\u271d\u00b9 = map\u271d",
+              "tactic": "funext X Y f"
+            },
+            {
+              "annotated_tactic": [
+                "\"simpa using h_map X Y f\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case mk.mk.e_map.h.h.h\nV : Type u\ninst\u271d\u00b9 : Quiver V\nW : Type u\u2082\ninst\u271d : Quiver W\nF_obj : V \u2192 W\nmap\u271d\u00b9 map\u271d : {X Y : V} \u2192 (X \u27f6 Y) \u2192 (F_obj X \u27f6 F_obj Y)\nh_obj : \u2200 (X : V), { obj := F_obj, map := map\u271d\u00b9 }.obj X = { obj := F_obj, map := map\u271d }.obj X\nh_map :\n  \u2200 (X Y : V) (f : X \u27f6 Y),\n    { obj := F_obj, map := map\u271d\u00b9 }.map f = Eq.recOn \u22ef (Eq.recOn \u22ef ({ obj := F_obj, map := map\u271d }.map f))\nX Y : V\nf : X \u27f6 Y\n\u22a2 map\u271d\u00b9 f = map\u271d f",
+              "tactic": "simpa using h_map X Y f"
+            },
+            {
+              "annotated_tactic": [
+                "\"ext X\"",
+                "[]"
+              ],
+              "state_after": "case h\nV : Type u\ninst\u271d\u00b9 : Quiver V\nW : Type u\u2082\ninst\u271d : Quiver W\nF_obj : V \u2192 W\nmap\u271d\u00b9 : {X Y : V} \u2192 (X \u27f6 Y) \u2192 (F_obj X \u27f6 F_obj Y)\nG_obj : V \u2192 W\nmap\u271d : {X Y : V} \u2192 (X \u27f6 Y) \u2192 (G_obj X \u27f6 G_obj Y)\nh_obj : \u2200 (X : V), { obj := F_obj, map := map\u271d\u00b9 }.obj X = { obj := G_obj, map := map\u271d }.obj X\nh_map :\n  \u2200 (X Y : V) (f : X \u27f6 Y),\n    { obj := F_obj, map := map\u271d\u00b9 }.map f = Eq.recOn \u22ef (Eq.recOn \u22ef ({ obj := G_obj, map := map\u271d }.map f))\nX : V\n\u22a2 F_obj X = G_obj X",
+              "state_before": "V : Type u\ninst\u271d\u00b9 : Quiver V\nW : Type u\u2082\ninst\u271d : Quiver W\nF_obj : V \u2192 W\nmap\u271d\u00b9 : {X Y : V} \u2192 (X \u27f6 Y) \u2192 (F_obj X \u27f6 F_obj Y)\nG_obj : V \u2192 W\nmap\u271d : {X Y : V} \u2192 (X \u27f6 Y) \u2192 (G_obj X \u27f6 G_obj Y)\nh_obj : \u2200 (X : V), { obj := F_obj, map := map\u271d\u00b9 }.obj X = { obj := G_obj, map := map\u271d }.obj X\nh_map :\n  \u2200 (X Y : V) (f : X \u27f6 Y),\n    { obj := F_obj, map := map\u271d\u00b9 }.map f = Eq.recOn \u22ef (Eq.recOn \u22ef ({ obj := G_obj, map := map\u271d }.map f))\n\u22a2 F_obj = G_obj",
+              "tactic": "ext X"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply h_obj\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h\nV : Type u\ninst\u271d\u00b9 : Quiver V\nW : Type u\u2082\ninst\u271d : Quiver W\nF_obj : V \u2192 W\nmap\u271d\u00b9 : {X Y : V} \u2192 (X \u27f6 Y) \u2192 (F_obj X \u27f6 F_obj Y)\nG_obj : V \u2192 W\nmap\u271d : {X Y : V} \u2192 (X \u27f6 Y) \u2192 (G_obj X \u27f6 G_obj Y)\nh_obj : \u2200 (X : V), { obj := F_obj, map := map\u271d\u00b9 }.obj X = { obj := G_obj, map := map\u271d }.obj X\nh_map :\n  \u2200 (X Y : V) (f : X \u27f6 Y),\n    { obj := F_obj, map := map\u271d\u00b9 }.map f = Eq.recOn \u22ef (Eq.recOn \u22ef ({ obj := G_obj, map := map\u271d }.map f))\nX : V\n\u22a2 F_obj X = G_obj X",
+              "tactic": "apply h_obj"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Prefunctor.id_comp",
+        "id": "Prefunctor.id_comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            119,
+            29
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/Basic.lean",
+          "full_name": "Prefunctor.id_comp",
+          "start": [
+            118,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Prefunctor.mk_map",
+        "id": "Prefunctor.mk_map",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            73,
+            49
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/Basic.lean",
+          "full_name": "Prefunctor.mk_map",
+          "start": [
+            72,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Prefunctor.mk_obj",
+        "id": "Prefunctor.mk_obj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            70,
+            49
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/Basic.lean",
+          "full_name": "Prefunctor.mk_obj",
+          "start": [
+            69,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Quiver.empty_arrow",
+        "id": "Quiver.empty_arrow",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            169,
+            75
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/Basic.lean",
+          "full_name": "Quiver.empty_arrow",
+          "start": [
+            169,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/Basic.lean"
+      }
+    ],
+    "input_proofs": 9,
+    "input_units": 2,
+    "proofs": 1,
+    "published_proofs": 1,
+    "published_transitions": 1,
+    "replay_failures": [],
+    "transitions": 1,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000821-0000-ede680c04089db39.parquet",
+      "sha256": "ede680c04089db3916cd87f11f2eb4a72b0ae8be0da97f43831981635740d606",
+      "bytes": 30235,
+      "rows": 1,
+      "revision": "1b1732dbac9bd3e39d47d0584914277d2b00812a"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Prefunctor.congr_map"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Quiver/Basic.lean\",null,null,\"Prefunctor.congr_map\"]"
+  ]
+}

manifests/batches/mathlib/000822.json

@@ -0,0 +1,312 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000822",
+  "batch_fingerprint": "6e6e4e256a89dd7beecae10759bb9dde2637d6d29cb04bd42f2cdc91a6d000bf",
+  "evidence": {
+    "batch_fingerprint": "6e6e4e256a89dd7beecae10759bb9dde2637d6d29cb04bd42f2cdc91a6d000bf",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Quiver.Hom.cast_rfl_rfl",
+        "id": "Quiver.Hom.cast_rfl_rfl",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            46,
+            6
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/Cast.lean",
+          "full_name": "Quiver.Hom.cast_rfl_rfl",
+          "start": [
+            45,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/Cast.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Quiver.Path.cast_rfl_rfl",
+        "id": "Quiver.Path.cast_rfl_rfl",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            95,
+            6
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/Cast.lean",
+          "full_name": "Quiver.Path.cast_rfl_rfl",
+          "start": [
+            94,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/Cast.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Quiver.Path.eq_cast_iff_heq",
+        "id": "Quiver.Path.eq_cast_iff_heq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            127,
+            50
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/Cast.lean",
+          "full_name": "Quiver.Path.eq_cast_iff_heq",
+          "start": [
+            124,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/Cast.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Quiver.WeaklyConnectedComponent.eq",
+        "id": "Quiver.WeaklyConnectedComponent.eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            59,
+            16
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/ConnectedComponent.lean",
+          "full_name": "Quiver.WeaklyConnectedComponent.eq",
+          "start": [
+            57,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/ConnectedComponent.lean"
+      }
+    ],
+    "input_proofs": 18,
+    "input_units": 2,
+    "proofs": 14,
+    "published_proofs": 11,
+    "published_transitions": 22,
+    "replay_failures": [],
+    "transitions": 31,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Combinatorics/Quiver/Cast.lean",
+        "proof_id": "mathlib:Quiver.Hom.cast_eq_cast",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              41,
+              6
+            ],
+            "file_path": "Mathlib/Combinatorics/Quiver/Cast.lean",
+            "full_name": "Quiver.Hom.cast_eq_cast",
+            "start": [
+              38,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"rw [hu, hv]\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "U : Type u_1\ninst\u271d : Quiver U\nu v u' v' : U\nhu : u = u'\nhv : v = v'\ne : u \u27f6 v\n\u22a2 (u \u27f6 v) = (u' \u27f6 v')",
+                "tactic": "rw [hu, hv]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"subst_vars\"",
+                  "[]"
+                ],
+                "state_after": "U : Type u_1\ninst\u271d : Quiver U\nu' v' : U\ne : u' \u27f6 v'\n\u22a2 cast \u22ef \u22ef e = _root_.cast \u22ef e",
+                "state_before": "U : Type u_1\ninst\u271d : Quiver U\nu v u' v' : U\nhu : u = u'\nhv : v = v'\ne : u \u27f6 v\n\u22a2 cast hu hv e = _root_.cast \u22ef e",
+                "tactic": "subst_vars"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rfl\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "U : Type u_1\ninst\u271d : Quiver U\nu' v' : U\ne : u' \u27f6 v'\n\u22a2 cast \u22ef \u22ef e = _root_.cast \u22ef e",
+                "tactic": "rfl"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Quiver.Hom.cast_eq_cast"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Combinatorics/Quiver/Cast.lean",
+        "proof_id": "mathlib:Quiver.Path.cast_eq_cast",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              90,
+              6
+            ],
+            "file_path": "Mathlib/Combinatorics/Quiver/Cast.lean",
+            "full_name": "Quiver.Path.cast_eq_cast",
+            "start": [
+              87,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"rw [hu, hv]\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "U : Type u_1\ninst\u271d : Quiver U\nu v u' v' : U\nhu : u = u'\nhv : v = v'\np : Path u v\n\u22a2 Path u v = Path u' v'",
+                "tactic": "rw [hu, hv]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"subst_vars\"",
+                  "[]"
+                ],
+                "state_after": "U : Type u_1\ninst\u271d : Quiver U\nu' v' : U\np : Path u' v'\n\u22a2 cast \u22ef \u22ef p = _root_.cast \u22ef p",
+                "state_before": "U : Type u_1\ninst\u271d : Quiver U\nu v u' v' : U\nhu : u = u'\nhv : v = v'\np : Path u v\n\u22a2 cast hu hv p = _root_.cast \u22ef p",
+                "tactic": "subst_vars"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rfl\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "U : Type u_1\ninst\u271d : Quiver U\nu' v' : U\np : Path u' v'\n\u22a2 cast \u22ef \u22ef p = _root_.cast \u22ef p",
+                "tactic": "rfl"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Quiver.Path.cast_eq_cast"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Combinatorics/Quiver/Cast.lean",
+        "proof_id": "mathlib:Quiver.eq_nil_of_length_zero",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              152,
+              55
+            ],
+            "file_path": "Mathlib/Combinatorics/Quiver/Cast.lean",
+            "full_name": "Quiver.eq_nil_of_length_zero",
+            "start": [
+              148,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"cases p\"",
+                  "[]"
+                ],
+                "state_after": "case nil\nU : Type u_1\ninst\u271d : Quiver U\nu : U\nhzero : nil.length = 0\n\u22a2 Path.cast \u22ef \u22ef nil = nil\n\ncase cons\nU : Type u_1\ninst\u271d : Quiver U\nu v b\u271d : U\na\u271d\u00b9 : Path u b\u271d\na\u271d : b\u271d \u27f6 v\nhzero : (a\u271d\u00b9.cons a\u271d).length = 0\n\u22a2 Path.cast \u22ef \u22ef (a\u271d\u00b9.cons a\u271d) = nil",
+                "state_before": "U : Type u_1\ninst\u271d : Quiver U\nu v : U\np : Path u v\nhzero : p.length = 0\n\u22a2 Path.cast \u22ef \u22ef p = nil",
+                "tactic": "cases p"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rfl\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case nil\nU : Type u_1\ninst\u271d : Quiver U\nu : U\nhzero : nil.length = 0\n\u22a2 Path.cast \u22ef \u22ef nil = nil",
+                "tactic": "rfl"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp only [<a>Nat.succ_ne_zero<\\/a>, <a>length_cons<\\/a>] at hzero\"",
+                  "[{\"full_name\":\"Nat.succ_ne_zero\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[708,17],\"def_end_pos\":[708,29]},{\"full_name\":\"Quiver.Path.length_cons\",\"def_path\":\"Mathlib\\/Combinatorics\\/Quiver\\/Path.lean\",\"def_pos\":[77,9],\"def_end_pos\":[77,20]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case cons\nU : Type u_1\ninst\u271d : Quiver U\nu v b\u271d : U\na\u271d\u00b9 : Path u b\u271d\na\u271d : b\u271d \u27f6 v\nhzero : (a\u271d\u00b9.cons a\u271d).length = 0\n\u22a2 Path.cast \u22ef \u22ef (a\u271d\u00b9.cons a\u271d) = nil",
+                "tactic": "simp only [Nat.succ_ne_zero, length_cons] at hzero"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Quiver.eq_nil_of_length_zero"
+      }
+    ],
+    "validation_rejected_proofs": 3,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000822-0000-8d8e9be1a4ac5a58.parquet",
+      "sha256": "8d8e9be1a4ac5a58b53577e3e13a6c112f81607f400e8cad5a3ec3d60ccfbf23",
+      "bytes": 53470,
+      "rows": 18,
+      "revision": "1b1732dbac9bd3e39d47d0584914277d2b00812a"
+    },
+    {
+      "path": "data/internal_test/mathlib-000822-0000-8194129e8b384e20.parquet",
+      "sha256": "8194129e8b384e2014218131b7ea2edf2a433e151b38eecd1539ccc7c22ae8b1",
+      "bytes": 36609,
+      "rows": 4,
+      "revision": "1b1732dbac9bd3e39d47d0584914277d2b00812a"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Quiver.Hom.cast_cast",
+    "mathlib:Quiver.Hom.cast_eq_iff_heq",
+    "mathlib:Quiver.Hom.cast_heq",
+    "mathlib:Quiver.Hom.eq_cast_iff_heq",
+    "mathlib:Quiver.Path.cast_cast",
+    "mathlib:Quiver.Path.cast_cons",
+    "mathlib:Quiver.Path.cast_eq_iff_heq",
+    "mathlib:Quiver.Path.cast_heq",
+    "mathlib:Quiver.Path.cast_nil",
+    "mathlib:Quiver.cast_eq_of_cons_eq_cons",
+    "mathlib:Quiver.hom_cast_eq_of_cons_eq_cons"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Quiver/Cast.lean\",null,null,\"Quiver.Hom.cast_cast\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Quiver/Cast.lean\",null,null,\"Quiver.Hom.cast_eq_iff_heq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Quiver/Cast.lean\",null,null,\"Quiver.Hom.cast_heq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Quiver/Cast.lean\",null,null,\"Quiver.Hom.eq_cast_iff_heq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Quiver/Cast.lean\",null,null,\"Quiver.Path.cast_cast\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Quiver/Cast.lean\",null,null,\"Quiver.Path.cast_cons\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Quiver/Cast.lean\",null,null,\"Quiver.Path.cast_eq_iff_heq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Quiver/Cast.lean\",null,null,\"Quiver.Path.cast_heq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Quiver/Cast.lean\",null,null,\"Quiver.Path.cast_nil\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Quiver/Cast.lean\",null,null,\"Quiver.cast_eq_of_cons_eq_cons\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Quiver/Cast.lean\",null,null,\"Quiver.hom_cast_eq_of_cons_eq_cons\"]"
+  ]
+}

manifests/batches/mathlib/000824.json

@@ -0,0 +1,653 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000824",
+  "batch_fingerprint": "8949cc2cf104647189c47f647634c356ad3c608b49a385aaa1277e2fe3a8265b",
+  "evidence": {
+    "batch_fingerprint": "8949cc2cf104647189c47f647634c356ad3c608b49a385aaa1277e2fe3a8265b",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "no internal trace for tactic 'apply (cast_heq _ _).trans'",
+        "full_name": "Quiver.Push.lift_comp",
+        "id": "Quiver.Push.lift_comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            89,
+            15
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/Push.lean",
+          "full_name": "Quiver.Push.lift_comp",
+          "start": [
+            73,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"fapply <a>Prefunctor.ext<\\/a>\"",
+                "[{\"full_name\":\"Prefunctor.ext\",\"def_path\":\"Mathlib\\/Combinatorics\\/Quiver\\/Basic.lean\",\"def_pos\":[76,9],\"def_end_pos\":[76,12]}]"
+              ],
+              "state_after": "case h_obj\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\n\u22a2 \u2200 (X : V), (of \u03c3 \u22d9q lift \u03c3 \u03c6 \u03c4 h).obj X = \u03c6.obj X\n\ncase h_map\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\n\u22a2 \u2200 (X Y : V) (f : X \u27f6 Y), (of \u03c3 \u22d9q lift \u03c3 \u03c6 \u03c4 h).map f = Eq.recOn \u22ef (Eq.recOn \u22ef (\u03c6.map f))",
+              "state_before": "V : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\n\u22a2 of \u03c3 \u22d9q lift \u03c3 \u03c6 \u03c4 h = \u03c6",
+              "tactic": "fapply Prefunctor.ext"
+            },
+            {
+              "annotated_tactic": [
+                "\"rintro X\"",
+                "[]"
+              ],
+              "state_after": "case h_obj\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX : V\n\u22a2 (of \u03c3 \u22d9q lift \u03c3 \u03c6 \u03c4 h).obj X = \u03c6.obj X",
+              "state_before": "case h_obj\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\n\u22a2 \u2200 (X : V), (of \u03c3 \u22d9q lift \u03c3 \u03c6 \u03c4 h).obj X = \u03c6.obj X",
+              "tactic": "rintro X"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>Prefunctor.comp_obj<\\/a>]\"",
+                "[{\"full_name\":\"Prefunctor.comp_obj\",\"def_path\":\"Mathlib\\/Combinatorics\\/Quiver\\/Basic.lean\",\"def_pos\":[103,3],\"def_end_pos\":[103,8]}]"
+              ],
+              "state_after": "case h_obj\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX : V\n\u22a2 (lift \u03c3 \u03c6 \u03c4 h).obj ((of \u03c3).obj X) = \u03c6.obj X",
+              "state_before": "case h_obj\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX : V\n\u22a2 (of \u03c3 \u22d9q lift \u03c3 \u03c6 \u03c4 h).obj X = \u03c6.obj X",
+              "tactic": "simp only [Prefunctor.comp_obj]"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Eq.symm<\\/a>\"",
+                "[{\"full_name\":\"Eq.symm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[323,9],\"def_end_pos\":[323,16]}]"
+              ],
+              "state_after": "case h_obj.h\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX : V\n\u22a2 \u03c6.obj X = (lift \u03c3 \u03c6 \u03c4 h).obj ((of \u03c3).obj X)",
+              "state_before": "case h_obj\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX : V\n\u22a2 (lift \u03c3 \u03c6 \u03c4 h).obj ((of \u03c3).obj X) = \u03c6.obj X",
+              "tactic": "apply Eq.symm"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact h X\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h_obj.h\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX : V\n\u22a2 \u03c6.obj X = (lift \u03c3 \u03c6 \u03c4 h).obj ((of \u03c3).obj X)",
+              "tactic": "exact h X"
+            },
+            {
+              "annotated_tactic": [
+                "\"rintro X Y f\"",
+                "[]"
+              ],
+              "state_after": "case h_map\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u22a2 (of \u03c3 \u22d9q lift \u03c3 \u03c6 \u03c4 h).map f = Eq.recOn \u22ef (Eq.recOn \u22ef (\u03c6.map f))",
+              "state_before": "case h_map\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\n\u22a2 \u2200 (X Y : V) (f : X \u27f6 Y), (of \u03c3 \u22d9q lift \u03c3 \u03c6 \u03c4 h).map f = Eq.recOn \u22ef (Eq.recOn \u22ef (\u03c6.map f))",
+              "tactic": "rintro X Y f"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>Prefunctor.comp_map<\\/a>]\"",
+                "[{\"full_name\":\"Prefunctor.comp_map\",\"def_path\":\"Mathlib\\/Combinatorics\\/Quiver\\/Basic.lean\",\"def_pos\":[103,3],\"def_end_pos\":[103,8]}]"
+              ],
+              "state_after": "case h_map\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u22a2 (lift \u03c3 \u03c6 \u03c4 h).map ((of \u03c3).map f) = \u22ef \u25b8 \u22ef \u25b8 \u03c6.map f",
+              "state_before": "case h_map\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u22a2 (of \u03c3 \u22d9q lift \u03c3 \u03c6 \u03c4 h).map f = Eq.recOn \u22ef (Eq.recOn \u22ef (\u03c6.map f))",
+              "tactic": "simp only [Prefunctor.comp_map]"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>eq_of_heq<\\/a>\"",
+                "[{\"full_name\":\"eq_of_heq\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[464,9],\"def_end_pos\":[464,18]}]"
+              ],
+              "state_after": "case h_map.h\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u22a2 HEq ((lift \u03c3 \u03c6 \u03c4 h).map ((of \u03c3).map f)) (\u22ef \u25b8 \u22ef \u25b8 \u03c6.map f)",
+              "state_before": "case h_map\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u22a2 (lift \u03c3 \u03c6 \u03c4 h).map ((of \u03c3).map f) = \u22ef \u25b8 \u22ef \u25b8 \u03c6.map f",
+              "tactic": "apply eq_of_heq"
+            },
+            {
+              "annotated_tactic": [
+                "\"iterate 2 apply (<a>cast_heq<\\/a> _ _).<a>trans<\\/a>\"",
+                "[{\"full_name\":\"cast_heq\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[785,9],\"def_end_pos\":[785,17]},{\"full_name\":\"HEq.trans\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[763,9],\"def_end_pos\":[763,18]}]"
+              ],
+              "state_after": "case h_map.h\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u22a2 HEq (\u03c6.map f) (\u22ef \u25b8 \u22ef \u25b8 \u03c6.map f)",
+              "state_before": "case h_map.h\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u22a2 HEq ((lift \u03c3 \u03c6 \u03c4 h).map ((of \u03c3).map f)) (\u22ef \u25b8 \u22ef \u25b8 \u03c6.map f)",
+              "tactic": "iterate 2 apply (cast_heq _ _).trans"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>HEq.symm<\\/a>\"",
+                "[{\"full_name\":\"HEq.symm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[757,9],\"def_end_pos\":[757,17]}]"
+              ],
+              "state_after": "case h_map.h.h\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u22a2 HEq (\u22ef \u25b8 \u22ef \u25b8 \u03c6.map f) (\u03c6.map f)",
+              "state_before": "case h_map.h\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u22a2 HEq (\u03c6.map f) (\u22ef \u25b8 \u22ef \u25b8 \u03c6.map f)",
+              "tactic": "apply HEq.symm"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply (<a>eqRec_heq<\\/a> _ _).<a>trans<\\/a>\"",
+                "[{\"full_name\":\"eqRec_heq\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[777,9],\"def_end_pos\":[777,18]},{\"full_name\":\"HEq.trans\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[763,9],\"def_end_pos\":[763,18]}]"
+              ],
+              "state_after": "case h_map.h.h\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u22a2 HEq (\u22ef \u25b8 \u03c6.map f) (\u03c6.map f)",
+              "state_before": "case h_map.h.h\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u22a2 HEq (\u22ef \u25b8 \u22ef \u25b8 \u03c6.map f) (\u03c6.map f)",
+              "tactic": "apply (eqRec_heq _ _).trans"
+            },
+            {
+              "annotated_tactic": [
+                "\"have : \\u2200 {\\u03b1 \\u03b3} {\\u03b2 : \\u03b1 \\u2192 \\u03b3 \\u2192 Sort _} {a a'} (p : a = a') g (b : \\u03b2 a g), <a>HEq<\\/a> (p \\u25b8 b) b := by\\n      intros\\n      subst_vars\\n      rfl\"",
+                "[{\"full_name\":\"HEq\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[456,11],\"def_end_pos\":[456,14]}]"
+              ],
+              "state_after": "case h_map.h.h\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\nthis :\n  \u2200 {\u03b1 : Sort ?u.2364} {\u03b3 : Sort ?u.2366} {\u03b2 : \u03b1 \u2192 \u03b3 \u2192 Sort ?u.2368} {a a' : \u03b1} (p : a = a') (g : \u03b3) (b : \u03b2 a g),\n    HEq (p \u25b8 b) b\n\u22a2 HEq (\u22ef \u25b8 \u03c6.map f) (\u03c6.map f)",
+              "state_before": "case h_map.h.h\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u22a2 HEq (\u22ef \u25b8 \u03c6.map f) (\u03c6.map f)",
+              "tactic": "have : \u2200 {\u03b1 \u03b3} {\u03b2 : \u03b1 \u2192 \u03b3 \u2192 Sort _} {a a'} (p : a = a') g (b : \u03b2 a g), HEq (p \u25b8 b) b := by\n  intros\n  subst_vars\n  rfl"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply this\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h_map.h.h\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\nthis :\n  \u2200 {\u03b1 : Sort ?u.2364} {\u03b3 : Sort ?u.2366} {\u03b2 : \u03b1 \u2192 \u03b3 \u2192 Sort ?u.2368} {a a' : \u03b1} (p : a = a') (g : \u03b3) (b : \u03b2 a g),\n    HEq (p \u25b8 b) b\n\u22a2 HEq (\u22ef \u25b8 \u03c6.map f) (\u03c6.map f)",
+              "tactic": "apply this"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply (<a>cast_heq<\\/a> _ _).<a>trans<\\/a>\"",
+                "[{\"full_name\":\"cast_heq\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[785,9],\"def_end_pos\":[785,17]},{\"full_name\":\"HEq.trans\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[763,9],\"def_end_pos\":[763,18]}]"
+              ],
+              "state_after": "case h_map.h\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u22a2 HEq (\u03c6.map f) (\u22ef \u25b8 \u22ef \u25b8 \u03c6.map f)",
+              "state_before": "case h_map.h\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u22a2 HEq (\u22ef.mpr (\u03c6.map f)) (\u22ef \u25b8 \u22ef \u25b8 \u03c6.map f)",
+              "tactic": "apply (cast_heq _ _).trans"
+            },
+            {
+              "annotated_tactic": [
+                "\"intros\"",
+                "[]"
+              ],
+              "state_after": "V : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u03b1\u271d : Sort ?u.2364\n\u03b3\u271d : Sort ?u.2366\n\u03b2\u271d : \u03b1\u271d \u2192 \u03b3\u271d \u2192 Sort ?u.2368\na\u271d a'\u271d : \u03b1\u271d\np\u271d : a\u271d = a'\u271d\ng\u271d : \u03b3\u271d\nb\u271d : \u03b2\u271d a\u271d g\u271d\n\u22a2 HEq (p\u271d \u25b8 b\u271d) b\u271d",
+              "state_before": "V : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u22a2 \u2200 {\u03b1 : Sort ?u.2364} {\u03b3 : Sort ?u.2366} {\u03b2 : \u03b1 \u2192 \u03b3 \u2192 Sort ?u.2368} {a a' : \u03b1} (p : a = a') (g : \u03b3) (b : \u03b2 a g),\n    HEq (p \u25b8 b) b",
+              "tactic": "intros"
+            },
+            {
+              "annotated_tactic": [
+                "\"subst_vars\"",
+                "[]"
+              ],
+              "state_after": "V : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u03b1\u271d : Sort ?u.2364\n\u03b3\u271d : Sort ?u.2366\n\u03b2\u271d : \u03b1\u271d \u2192 \u03b3\u271d \u2192 Sort ?u.2368\na'\u271d : \u03b1\u271d\ng\u271d : \u03b3\u271d\nb\u271d : \u03b2\u271d a'\u271d g\u271d\n\u22a2 HEq (\u22ef \u25b8 b\u271d) b\u271d",
+              "state_before": "V : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u03b1\u271d : Sort ?u.2364\n\u03b3\u271d : Sort ?u.2366\n\u03b2\u271d : \u03b1\u271d \u2192 \u03b3\u271d \u2192 Sort ?u.2368\na\u271d a'\u271d : \u03b1\u271d\np\u271d : a\u271d = a'\u271d\ng\u271d : \u03b3\u271d\nb\u271d : \u03b2\u271d a\u271d g\u271d\n\u22a2 HEq (p\u271d \u25b8 b\u271d) b\u271d",
+              "tactic": "subst_vars"
+            },
+            {
+              "annotated_tactic": [
+                "\"rfl\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "V : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\nX Y : V\nf : X \u27f6 Y\n\u03b1\u271d : Sort ?u.2364\n\u03b3\u271d : Sort ?u.2366\n\u03b2\u271d : \u03b1\u271d \u2192 \u03b3\u271d \u2192 Sort ?u.2368\na'\u271d : \u03b1\u271d\ng\u271d : \u03b3\u271d\nb\u271d : \u03b2\u271d a'\u271d g\u271d\n\u22a2 HEq (\u22ef \u25b8 b\u271d) b\u271d",
+              "tactic": "rfl"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/Push.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Quiver.Push.lift_obj",
+        "id": "Quiver.Push.lift_obj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            70,
+            6
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/Push.lean",
+          "full_name": "Quiver.Push.lift_obj",
+          "start": [
+            69,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/Push.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Quiver.Push.of_obj",
+        "id": "Quiver.Push.of_obj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            52,
+            6
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/Push.lean",
+          "full_name": "Quiver.Push.of_obj",
+          "start": [
+            51,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/Push.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Quiver.SingleObj.ext",
+        "id": "Quiver.SingleObj.ext",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            57,
+            54
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/SingleObj.lean",
+          "full_name": "Quiver.SingleObj.ext",
+          "start": [
+            57,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/SingleObj.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Quiver.SingleObj.pathEquivList_cons",
+        "id": "Quiver.SingleObj.pathEquivList_cons",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            158,
+            6
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/SingleObj.lean",
+          "full_name": "Quiver.SingleObj.pathEquivList_cons",
+          "start": [
+            156,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/SingleObj.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Quiver.SingleObj.pathEquivList_nil",
+        "id": "Quiver.SingleObj.pathEquivList_nil",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            152,
+            6
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/SingleObj.lean",
+          "full_name": "Quiver.SingleObj.pathEquivList_nil",
+          "start": [
+            151,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/SingleObj.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Quiver.SingleObj.pathEquivList_symm_cons",
+        "id": "Quiver.SingleObj.pathEquivList_symm_cons",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            169,
+            6
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/SingleObj.lean",
+          "full_name": "Quiver.SingleObj.pathEquivList_symm_cons",
+          "start": [
+            167,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/SingleObj.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Quiver.SingleObj.pathEquivList_symm_nil",
+        "id": "Quiver.SingleObj.pathEquivList_symm_nil",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            163,
+            6
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/SingleObj.lean",
+          "full_name": "Quiver.SingleObj.pathEquivList_symm_nil",
+          "start": [
+            162,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/SingleObj.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Quiver.SingleObj.toPrefunctor_id",
+        "id": "Quiver.SingleObj.toPrefunctor_id",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            96,
+            6
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/SingleObj.lean",
+          "full_name": "Quiver.SingleObj.toPrefunctor_id",
+          "start": [
+            95,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/SingleObj.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Quiver.SingleObj.toPrefunctor_symm_id",
+        "id": "Quiver.SingleObj.toPrefunctor_symm_id",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            101,
+            6
+          ],
+          "file_path": "Mathlib/Combinatorics/Quiver/SingleObj.lean",
+          "full_name": "Quiver.SingleObj.toPrefunctor_symm_id",
+          "start": [
+            100,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Combinatorics/Quiver/SingleObj.lean"
+      }
+    ],
+    "input_proofs": 14,
+    "input_units": 2,
+    "proofs": 4,
+    "published_proofs": 1,
+    "published_transitions": 1,
+    "replay_failures": [],
+    "transitions": 18,
+    "validation_failures": [
+      {
+        "errors": [
+          "goal 0: unresolved fvar _uniq.2982",
+          "goal 0: unresolved fvar _uniq.2715",
+          "goal 0: unresolved fvar _uniq.2982",
+          "goal 0: unresolved fvar _uniq.2715",
+          "goal 0: unresolved fvar _uniq.2982",
+          "goal 0: unresolved fvar _uniq.2715",
+          "goal 0: unresolved fvar _uniq.2982",
+          "goal 0: unresolved fvar _uniq.2715",
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Combinatorics/Quiver/Push.lean",
+        "proof_id": "mathlib:Quiver.Push.lift_unique",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              102,
+              8
+            ],
+            "file_path": "Mathlib/Combinatorics/Quiver/Push.lean",
+            "full_name": "Quiver.Push.lift_unique",
+            "start": [
+              92,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"dsimp only [<a>of<\\/a>, <a>lift<\\/a>]\"",
+                  "[{\"full_name\":\"Quiver.Push.of\",\"def_path\":\"Mathlib\\/Combinatorics\\/Quiver\\/Push.lean\",\"def_pos\":[45,5],\"def_end_pos\":[45,7]},{\"full_name\":\"Quiver.Push.lift\",\"def_path\":\"Mathlib\\/Combinatorics\\/Quiver\\/Push.lean\",\"def_pos\":[60,19],\"def_end_pos\":[60,23]}]"
+                ],
+                "state_after": "V : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\n\u03a6 : Push \u03c3 \u2964q W'\n\u03a6\u2080 : \u03a6.obj = \u03c4\n\u03a6comp : of \u03c3 \u22d9q \u03a6 = \u03c6\n\u22a2 \u03a6 =\n    { obj := \u03c4, map := @PushQuiver.rec V inst\u271d\u00b9 W \u03c3 (fun X Y x => \u03c4 X \u27f6 \u03c4 Y) fun X Y f => id (\u22ef.mpr (\u22ef.mpr (\u03c6.map f))) }",
+                "state_before": "V : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\n\u03a6 : Push \u03c3 \u2964q W'\n\u03a6\u2080 : \u03a6.obj = \u03c4\n\u03a6comp : of \u03c3 \u22d9q \u03a6 = \u03c6\n\u22a2 \u03a6 = lift \u03c3 \u03c6 \u03c4 h",
+                "tactic": "dsimp only [of, lift]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"fapply <a>Prefunctor.ext<\\/a>\"",
+                  "[{\"full_name\":\"Prefunctor.ext\",\"def_path\":\"Mathlib\\/Combinatorics\\/Quiver\\/Basic.lean\",\"def_pos\":[76,9],\"def_end_pos\":[76,12]}]"
+                ],
+                "state_after": "case h_obj\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\n\u03a6 : Push \u03c3 \u2964q W'\n\u03a6\u2080 : \u03a6.obj = \u03c4\n\u03a6comp : of \u03c3 \u22d9q \u03a6 = \u03c6\n\u22a2 \u2200 (X : Push \u03c3),\n    \u03a6.obj X =\n      { obj := \u03c4,\n            map := @PushQuiver.rec V inst\u271d\u00b9 W \u03c3 (fun X Y x => \u03c4 X \u27f6 \u03c4 Y) fun X Y f => id (\u22ef.mpr (\u22ef.mpr (\u03c6.map f))) }.obj\n        X\n\ncase h_map\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\n\u03a6 : Push \u03c3 \u2964q W'\n\u03a6\u2080 : \u03a6.obj = \u03c4\n\u03a6comp : of \u03c3 \u22d9q \u03a6 = \u03c6\n\u22a2 \u2200 (X Y : Push \u03c3) (f : X \u27f6 Y),\n    \u03a6.map f =\n      Eq.recOn \u22ef\n        (Eq.recOn \u22ef\n          ({ obj := \u03c4,\n                map :=\n                  @PushQuiver.rec V inst\u271d\u00b9 W \u03c3 (fun X Y x => \u03c4 X \u27f6 \u03c4 Y) fun X Y f => id (\u22ef.mpr (\u22ef.mpr (\u03c6.map f))) }.map\n            f))",
+                "state_before": "V : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\n\u03a6 : Push \u03c3 \u2964q W'\n\u03a6\u2080 : \u03a6.obj = \u03c4\n\u03a6comp : of \u03c3 \u22d9q \u03a6 = \u03c6\n\u22a2 \u03a6 =\n    { obj := \u03c4, map := @PushQuiver.rec V inst\u271d\u00b9 W \u03c3 (fun X Y x => \u03c4 X \u27f6 \u03c4 Y) fun X Y f => id (\u22ef.mpr (\u22ef.mpr (\u03c6.map f))) }",
+                "tactic": "fapply Prefunctor.ext"
+              },
+              {
+                "annotated_tactic": [
+                  "\"intro X\"",
+                  "[]"
+                ],
+                "state_after": "case h_obj\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\n\u03a6 : Push \u03c3 \u2964q W'\n\u03a6\u2080 : \u03a6.obj = \u03c4\n\u03a6comp : of \u03c3 \u22d9q \u03a6 = \u03c6\nX : Push \u03c3\n\u22a2 \u03a6.obj X =\n    { obj := \u03c4,\n          map := @PushQuiver.rec V inst\u271d\u00b9 W \u03c3 (fun X Y x => \u03c4 X \u27f6 \u03c4 Y) fun X Y f => id (\u22ef.mpr (\u22ef.mpr (\u03c6.map f))) }.obj\n      X",
+                "state_before": "case h_obj\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\n\u03a6 : Push \u03c3 \u2964q W'\n\u03a6\u2080 : \u03a6.obj = \u03c4\n\u03a6comp : of \u03c3 \u22d9q \u03a6 = \u03c6\n\u22a2 \u2200 (X : Push \u03c3),\n    \u03a6.obj X =\n      { obj := \u03c4,\n            map := @PushQuiver.rec V inst\u271d\u00b9 W \u03c3 (fun X Y x => \u03c4 X \u27f6 \u03c4 Y) fun X Y f => id (\u22ef.mpr (\u22ef.mpr (\u03c6.map f))) }.obj\n        X",
+                "tactic": "intro X"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp only\"",
+                  "[]"
+                ],
+                "state_after": "case h_obj\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\n\u03a6 : Push \u03c3 \u2964q W'\n\u03a6\u2080 : \u03a6.obj = \u03c4\n\u03a6comp : of \u03c3 \u22d9q \u03a6 = \u03c6\nX : Push \u03c3\n\u22a2 \u03a6.obj X = \u03c4 X",
+                "state_before": "case h_obj\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\n\u03a6 : Push \u03c3 \u2964q W'\n\u03a6\u2080 : \u03a6.obj = \u03c4\n\u03a6comp : of \u03c3 \u22d9q \u03a6 = \u03c6\nX : Push \u03c3\n\u22a2 \u03a6.obj X =\n    { obj := \u03c4,\n          map := @PushQuiver.rec V inst\u271d\u00b9 W \u03c3 (fun X Y x => \u03c4 X \u27f6 \u03c4 Y) fun X Y f => id (\u22ef.mpr (\u22ef.mpr (\u03c6.map f))) }.obj\n      X",
+                "tactic": "simp only"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [\\u03a6\\u2080]\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case h_obj\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\n\u03a6 : Push \u03c3 \u2964q W'\n\u03a6\u2080 : \u03a6.obj = \u03c4\n\u03a6comp : of \u03c3 \u22d9q \u03a6 = \u03c6\nX : Push \u03c3\n\u22a2 \u03a6.obj X = \u03c4 X",
+                "tactic": "rw [\u03a6\u2080]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rintro _ _ \\u27e8\\u27e9\"",
+                  "[]"
+                ],
+                "state_after": "case h_map.arrow\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\n\u03a6 : Push \u03c3 \u2964q W'\n\u03a6\u2080 : \u03a6.obj = \u03c4\n\u03a6comp : of \u03c3 \u22d9q \u03a6 = \u03c6\nX\u271d Y\u271d : V\nf\u271d : X\u271d \u27f6 Y\u271d\n\u22a2 \u03a6.map (PushQuiver.arrow f\u271d) =\n    Eq.recOn \u22ef\n      (Eq.recOn \u22ef\n        ({ obj := \u03c4,\n              map :=\n                @PushQuiver.rec V inst\u271d\u00b9 W \u03c3 (fun X Y x => \u03c4 X \u27f6 \u03c4 Y) fun X Y f => id (\u22ef.mpr (\u22ef.mpr (\u03c6.map f))) }.map\n          (PushQuiver.arrow f\u271d)))",
+                "state_before": "case h_map\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\n\u03a6 : Push \u03c3 \u2964q W'\n\u03a6\u2080 : \u03a6.obj = \u03c4\n\u03a6comp : of \u03c3 \u22d9q \u03a6 = \u03c6\n\u22a2 \u2200 (X Y : Push \u03c3) (f : X \u27f6 Y),\n    \u03a6.map f =\n      Eq.recOn \u22ef\n        (Eq.recOn \u22ef\n          ({ obj := \u03c4,\n                map :=\n                  @PushQuiver.rec V inst\u271d\u00b9 W \u03c3 (fun X Y x => \u03c4 X \u27f6 \u03c4 Y) fun X Y f => id (\u22ef.mpr (\u22ef.mpr (\u03c6.map f))) }.map\n            f))",
+                "tactic": "rintro _ _ \u27e8\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"subst_vars\"",
+                  "[]"
+                ],
+                "state_after": "case h_map.arrow\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03a6 : Push \u03c3 \u2964q W'\nX\u271d Y\u271d : V\nf\u271d : X\u271d \u27f6 Y\u271d\nh : \u2200 (x : V), (of \u03c3 \u22d9q \u03a6).obj x = \u03a6.obj (\u03c3 x)\n\u22a2 \u03a6.map (PushQuiver.arrow f\u271d) =\n    Eq.recOn \u22ef\n      (Eq.recOn \u22ef\n        ({ obj := \u03a6.obj,\n              map :=\n                @PushQuiver.rec V inst\u271d\u00b9 W \u03c3 (fun X Y x => \u03a6.obj X \u27f6 \u03a6.obj Y) fun X Y f =>\n                  id (\u22ef.mpr (\u22ef.mpr ((of \u03c3 \u22d9q \u03a6).map f))) }.map\n          (PushQuiver.arrow f\u271d)))",
+                "state_before": "case h_map.arrow\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03c6 : V \u2964q W'\n\u03c4 : W \u2192 W'\nh : \u2200 (x : V), \u03c6.obj x = \u03c4 (\u03c3 x)\n\u03a6 : Push \u03c3 \u2964q W'\n\u03a6\u2080 : \u03a6.obj = \u03c4\n\u03a6comp : of \u03c3 \u22d9q \u03a6 = \u03c6\nX\u271d Y\u271d : V\nf\u271d : X\u271d \u27f6 Y\u271d\n\u22a2 \u03a6.map (PushQuiver.arrow f\u271d) =\n    Eq.recOn \u22ef\n      (Eq.recOn \u22ef\n        ({ obj := \u03c4,\n              map :=\n                @PushQuiver.rec V inst\u271d\u00b9 W \u03c3 (fun X Y x => \u03c4 X \u27f6 \u03c4 Y) fun X Y f => id (\u22ef.mpr (\u22ef.mpr (\u03c6.map f))) }.map\n          (PushQuiver.arrow f\u271d)))",
+                "tactic": "subst_vars"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp only [<a>Prefunctor.comp_map<\\/a>, <a>cast_eq<\\/a>]\"",
+                  "[{\"full_name\":\"Prefunctor.comp_map\",\"def_path\":\"Mathlib\\/Combinatorics\\/Quiver\\/Basic.lean\",\"def_pos\":[103,3],\"def_end_pos\":[103,8]},{\"full_name\":\"cast_eq\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[682,17],\"def_end_pos\":[682,24]}]"
+                ],
+                "state_after": "case h_map.arrow\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03a6 : Push \u03c3 \u2964q W'\nX\u271d Y\u271d : V\nf\u271d : X\u271d \u27f6 Y\u271d\nh : \u2200 (x : V), (of \u03c3 \u22d9q \u03a6).obj x = \u03a6.obj (\u03c3 x)\n\u22a2 \u03a6.map (PushQuiver.arrow f\u271d) = id (\u22ef.mpr (\u22ef.mpr (\u03a6.map ((of \u03c3).map f\u271d))))",
+                "state_before": "case h_map.arrow\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03a6 : Push \u03c3 \u2964q W'\nX\u271d Y\u271d : V\nf\u271d : X\u271d \u27f6 Y\u271d\nh : \u2200 (x : V), (of \u03c3 \u22d9q \u03a6).obj x = \u03a6.obj (\u03c3 x)\n\u22a2 \u03a6.map (PushQuiver.arrow f\u271d) =\n    Eq.recOn \u22ef\n      (Eq.recOn \u22ef\n        ({ obj := \u03a6.obj,\n              map :=\n                @PushQuiver.rec V inst\u271d\u00b9 W \u03c3 (fun X Y x => \u03a6.obj X \u27f6 \u03a6.obj Y) fun X Y f =>\n                  id (\u22ef.mpr (\u22ef.mpr ((of \u03c3 \u22d9q \u03a6).map f))) }.map\n          (PushQuiver.arrow f\u271d)))",
+                "tactic": "simp only [Prefunctor.comp_map, cast_eq]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rfl\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case h_map.arrow\nV : Type u_1\ninst\u271d\u00b9 : Quiver V\nW : Type u_2\n\u03c3 : V \u2192 W\nW' : Type u_3\ninst\u271d : Quiver W'\n\u03a6 : Push \u03c3 \u2964q W'\nX\u271d Y\u271d : V\nf\u271d : X\u271d \u27f6 Y\u271d\nh : \u2200 (x : V), (of \u03c3 \u22d9q \u03a6).obj x = \u03a6.obj (\u03c3 x)\n\u22a2 \u03a6.map (PushQuiver.arrow f\u271d) = id (\u22ef.mpr (\u22ef.mpr (\u03a6.map ((of \u03c3).map f\u271d))))",
+                "tactic": "rfl"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Quiver.Push.lift_unique"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Combinatorics/Quiver/SingleObj.lean",
+        "proof_id": "mathlib:Quiver.SingleObj.listToPath_pathToList",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              136,
+              24
+            ],
+            "file_path": "Mathlib/Combinatorics/Quiver/SingleObj.lean",
+            "full_name": "Quiver.SingleObj.listToPath_pathToList",
+            "start": [
+              132,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"induction' p with y z p a ih\"",
+                  "[]"
+                ],
+                "state_after": "case nil\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nx : SingleObj \u03b1\n\u22a2 listToPath (pathToList Path.nil) = Path.cast \u22ef \u22ef Path.nil\n\ncase cons\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nx y z : SingleObj \u03b1\np : Path (star \u03b1) y\na : y \u27f6 z\nih : listToPath (pathToList p) = Path.cast \u22ef \u22ef p\n\u22a2 listToPath (pathToList (p.cons a)) = Path.cast \u22ef \u22ef (p.cons a)",
+                "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nx : SingleObj \u03b1\np : Path (star \u03b1) x\n\u22a2 listToPath (pathToList p) = Path.cast \u22ef \u22ef p",
+                "tactic": "induction' p with y z p a ih"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rfl\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case nil\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nx : SingleObj \u03b1\n\u22a2 listToPath (pathToList Path.nil) = Path.cast \u22ef \u22ef Path.nil",
+                "tactic": "rfl"
+              },
+              {
+                "annotated_tactic": [
+                  "\"dsimp at *\"",
+                  "[]"
+                ],
+                "state_after": "case cons\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nx y z : SingleObj \u03b1\np : Path (star \u03b1) y\na : y \u27f6 z\nih : listToPath (pathToList p) = p\n\u22a2 (listToPath (pathToList p)).cons a = p.cons a",
+                "state_before": "case cons\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nx y z : SingleObj \u03b1\np : Path (star \u03b1) y\na : y \u27f6 z\nih : listToPath (pathToList p) = Path.cast \u22ef \u22ef p\n\u22a2 listToPath (pathToList (p.cons a)) = Path.cast \u22ef \u22ef (p.cons a)",
+                "tactic": "dsimp at *"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [ih]\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case cons\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nx y z : SingleObj \u03b1\np : Path (star \u03b1) y\na : y \u27f6 z\nih : listToPath (pathToList p) = p\n\u22a2 (listToPath (pathToList p)).cons a = p.cons a",
+                "tactic": "rw [ih]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Quiver.SingleObj.listToPath_pathToList"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Combinatorics/Quiver/SingleObj.lean",
+        "proof_id": "mathlib:Quiver.SingleObj.pathToList_listToPath",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              142,
+              60
+            ],
+            "file_path": "Mathlib/Combinatorics/Quiver/SingleObj.lean",
+            "full_name": "Quiver.SingleObj.pathToList_listToPath",
+            "start": [
+              139,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"induction' l with a l ih\"",
+                  "[]"
+                ],
+                "state_after": "case nil\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u22a2 pathToList (listToPath []) = []\n\ncase cons\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\na : \u03b1\nl : List \u03b1\nih : pathToList (listToPath l) = l\n\u22a2 pathToList (listToPath (a :: l)) = a :: l",
+                "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nl : List \u03b1\n\u22a2 pathToList (listToPath l) = l",
+                "tactic": "induction' l with a l ih"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rfl\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case nil\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u22a2 pathToList (listToPath []) = []",
+                "tactic": "rfl"
+              },
+              {
+                "annotated_tactic": [
+                  "\"change a :: <a>pathToList<\\/a> (<a>listToPath<\\/a> l) = a :: l\"",
+                  "[{\"full_name\":\"Quiver.SingleObj.pathToList\",\"def_path\":\"Mathlib\\/Combinatorics\\/Quiver\\/SingleObj.lean\",\"def_pos\":[118,5],\"def_end_pos\":[118,15]},{\"full_name\":\"Quiver.SingleObj.listToPath\",\"def_path\":\"Mathlib\\/Combinatorics\\/Quiver\\/SingleObj.lean\",\"def_pos\":[127,5],\"def_end_pos\":[127,15]}]"
+                ],
+                "state_after": "case cons\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\na : \u03b1\nl : List \u03b1\nih : pathToList (listToPath l) = l\n\u22a2 a :: pathToList (listToPath l) = a :: l",
+                "state_before": "case cons\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\na : \u03b1\nl : List \u03b1\nih : pathToList (listToPath l) = l\n\u22a2 pathToList (listToPath (a :: l)) = a :: l",
+                "tactic": "change a :: pathToList (listToPath l) = a :: l"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [ih]\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case cons\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\na : \u03b1\nl : List \u03b1\nih : pathToList (listToPath l) = l\n\u22a2 a :: pathToList (listToPath l) = a :: l",
+                "tactic": "rw [ih]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Quiver.SingleObj.pathToList_listToPath"
+      }
+    ],
+    "validation_rejected_proofs": 3,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000824-0000-1b42ca1d7073c91d.parquet",
+      "sha256": "1b42ca1d7073c91d527e98867eca58944b127ddc91ba2db4771a080efe326dbd",
+      "bytes": 42821,
+      "rows": 1,
+      "revision": "1b1732dbac9bd3e39d47d0584914277d2b00812a"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Quiver.SingleObj.toPrefunctor_symm_comp"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Combinatorics/Quiver/SingleObj.lean\",null,null,\"Quiver.SingleObj.toPrefunctor_symm_comp\"]"
+  ]
+}

manifests/batches/numina/001577.json

@@ -0,0 +1,51 @@
+{
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+  "batch": "numina/001577",
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+    "failures": [],
+    "input_proofs": 5,
+    "input_units": 5,
+    "proofs": 5,
+    "published_proofs": 5,
+    "published_transitions": 33,
+    "replay_failures": [],
+    "trace_mode": "bundle",
+    "transitions": 33,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/numina-001577-0000-7bb085150b2e37de.parquet",
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+      "rows": 7,
+      "revision": "1b1732dbac9bd3e39d47d0584914277d2b00812a"
+    }
+  ],
+  "proof_ids": [
+    "numina:56562284-be9b-50de-a706-5e16c6e9012a",
+    "numina:6d4a6a7f-46b5-5094-b1bb-58315e8623ae",
+    "numina:807e11c0-dd85-5e4a-9806-4c7ae71e432b",
+    "numina:de04a0ae-7666-5e4c-9ad9-1b35c757c823",
+    "numina:de09857b-4f6a-5022-8170-bbe64512e0a4"
+  ],
+  "proof_keys": [
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_007885.lean\",\"a802612b58356b6ff06da5bca9a6b8f715d8b030795d7a9b296877a9b39cd68b\",0,\"number_theory_261447\"]",
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_007886.lean\",\"b13bc84c4b81370f798402f236372209ae9ca31dc0f35039e26a2edca55ce7ed\",0,\"algebra_10685\"]",
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_007887.lean\",\"6198103cf647ea294838aa211f17fbd26580ac5bd04a3e02710946f6e37c7ce4\",0,\"inequalities_249394\"]",
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_007888.lean\",\"5ff5837a921a22787da3f0d1af324d2a74ddd445959a56bb8abe757081f1c46b\",0,\"algebra_609133\"]",
+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_007889.lean\",\"09b1e9bb3cc60eeb25c3f811c5780d1a334c1d60bc7681a3d50b0e459ba8b168\",0,\"inequalities_299138\"]"
+  ]
+}

manifests/batches/numina/001578.json

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+{
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+    "trace_mode": "bundle",
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+    "validation_failures": [],
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+  },
+  "shards": [
+    {
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+    "numina:4c5644a7-0015-57e6-80cd-d800f8422369",
+    "numina:72c4f9d9-063e-5f6f-b435-942180a823fe",
+    "numina:b0ad8896-40dd-5053-ba9b-8afb4f70cdf2",
+    "numina:e0bf2d65-26df-53e7-8332-fff9581a6387"
+  ],
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+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_007890.lean\",\"7c7e5f3edf7481266f2bc6eff5dfa4b209b8f9ce25fc670cdf2cc4f9d3415862\",0,\"number_theory_87165\"]",
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+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_007894.lean\",\"a0fa10b440ca73a80824dfa5afc425700fc986b7d61e4f63ba12a3078fd26416\",0,\"calculus_16912\"]"
+  ]
+}

manifests/batches/numina/001580.json

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+    "numina:277694b9-644d-58d4-803c-dbb55326c44d",
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+    "numina:f0d3d3dd-577a-5119-a6f8-8db844d7d6f3"
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+    "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_007900.lean\",\"db445f07deed136385830ceae53bea159dfa92a532a8129328f11543615d8d7f\",0,\"algebra_236980\"]",
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+  ]
+}

manifests/batches/numina/001581.json

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+{
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manifests/batches/numina/001582.json

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manifests/batches/numina/001583.json

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manifests/batches/numina/001584.json

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manifests/batches/numina/001585.json

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