Record 20 verified HPC batch manifests

manifests/batches/mathlib/000891.json

@@ -0,0 +1,278 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000891",
+  "batch_fingerprint": "356c9c8cbf266fc1cd204de07e931534030b8b690171c5da1cc7449c13c9da9e",
+  "evidence": {
+    "batch_fingerprint": "356c9c8cbf266fc1cd204de07e931534030b8b690171c5da1cc7449c13c9da9e",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ENat.coe_iInf",
+        "id": "ENat.coe_iInf",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            46,
+            41
+          ],
+          "file_path": "Mathlib/Data/ENat/Lattice.lean",
+          "full_name": "ENat.coe_iInf",
+          "start": [
+            45,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/ENat/Lattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ENat.coe_iSup",
+        "id": "ENat.coe_iSup",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            43,
+            90
+          ],
+          "file_path": "Mathlib/Data/ENat/Lattice.lean",
+          "full_name": "ENat.coe_iSup",
+          "start": [
+            43,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/ENat/Lattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ENat.coe_sInf",
+        "id": "ENat.coe_sInf",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            41,
+            44
+          ],
+          "file_path": "Mathlib/Data/ENat/Lattice.lean",
+          "full_name": "ENat.coe_sInf",
+          "start": [
+            40,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/ENat/Lattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ENat.coe_sSup",
+        "id": "ENat.coe_sSup",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            38,
+            80
+          ],
+          "file_path": "Mathlib/Data/ENat/Lattice.lean",
+          "full_name": "ENat.coe_sSup",
+          "start": [
+            38,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/ENat/Lattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ENat.iInf_coe_eq_top",
+        "id": "ENat.iInf_coe_eq_top",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            33,
+            83
+          ],
+          "file_path": "Mathlib/Data/ENat/Lattice.lean",
+          "full_name": "ENat.iInf_coe_eq_top",
+          "start": [
+            33,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/ENat/Lattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ENat.iInf_coe_lt_top",
+        "id": "ENat.iInf_coe_lt_top",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            36,
+            84
+          ],
+          "file_path": "Mathlib/Data/ENat/Lattice.lean",
+          "full_name": "ENat.iInf_coe_lt_top",
+          "start": [
+            36,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/ENat/Lattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ENat.iSup_coe_eq_top",
+        "id": "ENat.iSup_coe_eq_top",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            30,
+            94
+          ],
+          "file_path": "Mathlib/Data/ENat/Lattice.lean",
+          "full_name": "ENat.iSup_coe_eq_top",
+          "start": [
+            30,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/ENat/Lattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ENat.iSup_coe_lt_top",
+        "id": "ENat.iSup_coe_lt_top",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            32,
+            92
+          ],
+          "file_path": "Mathlib/Data/ENat/Lattice.lean",
+          "full_name": "ENat.iSup_coe_lt_top",
+          "start": [
+            32,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/ENat/Lattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ENat.iSup_coe_ne_top",
+        "id": "ENat.iSup_coe_ne_top",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            31,
+            93
+          ],
+          "file_path": "Mathlib/Data/ENat/Lattice.lean",
+          "full_name": "ENat.iSup_coe_ne_top",
+          "start": [
+            31,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/ENat/Lattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Functor.map_equiv_apply",
+        "id": "Functor.map_equiv_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            38,
+            93
+          ],
+          "file_path": "Mathlib/Data/Equiv/Functor.lean",
+          "full_name": "Functor.map_equiv_apply",
+          "start": [
+            37,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Equiv/Functor.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Functor.map_equiv_symm_apply",
+        "id": "Functor.map_equiv_symm_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            42,
+            61
+          ],
+          "file_path": "Mathlib/Data/Equiv/Functor.lean",
+          "full_name": "Functor.map_equiv_symm_apply",
+          "start": [
+            40,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Equiv/Functor.lean"
+      }
+    ],
+    "input_proofs": 12,
+    "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-000891-0000-57c18906addee3cf.parquet",
+      "sha256": "57c18906addee3cf9cc3a6f780dcabfb3f31ec5b9a6807bd9130eed3a8cb81ff",
+      "bytes": 33894,
+      "rows": 1,
+      "revision": "9931f7e263b644970d94314c5ccd8bc8f7920aee"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:ENat.iInf_coe_ne_top"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/ENat/Lattice.lean\",null,null,\"ENat.iInf_coe_ne_top\"]"
+  ]
+}

manifests/batches/mathlib/000892.json

@@ -0,0 +1,350 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000892",
+  "batch_fingerprint": "456d4b077a4a56b4ebbbfb784ffa18956516c1d76eeb46470e2ddfb2ccbc495c",
+  "evidence": {
+    "batch_fingerprint": "456d4b077a4a56b4ebbbfb784ffa18956516c1d76eeb46470e2ddfb2ccbc495c",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Erased.bind_def",
+        "id": "Erased.bind_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            147,
+            6
+          ],
+          "file_path": "Mathlib/Data/Erased.lean",
+          "full_name": "Erased.bind_def",
+          "start": [
+            146,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Erased.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Erased.bind_eq_out",
+        "id": "Erased.bind_eq_out",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            107,
+            65
+          ],
+          "file_path": "Mathlib/Data/Erased.lean",
+          "full_name": "Erased.bind_eq_out",
+          "start": [
+            107,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Erased.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Erased.join_eq_out",
+        "id": "Erased.join_eq_out",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            118,
+            18
+          ],
+          "file_path": "Mathlib/Data/Erased.lean",
+          "full_name": "Erased.join_eq_out",
+          "start": [
+            117,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Erased.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Erased.map_def",
+        "id": "Erased.map_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            152,
+            6
+          ],
+          "file_path": "Mathlib/Data/Erased.lean",
+          "full_name": "Erased.map_def",
+          "start": [
+            151,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Erased.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Erased.nonempty_iff",
+        "id": "Erased.nonempty_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            91,
+            42
+          ],
+          "file_path": "Mathlib/Data/Erased.lean",
+          "full_name": "Erased.nonempty_iff",
+          "start": [
+            90,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Erased.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Erased.out_proof",
+        "id": "Erased.out_proof",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            52,
+            8
+          ],
+          "file_path": "Mathlib/Data/Erased.lean",
+          "full_name": "Erased.out_proof",
+          "start": [
+            51,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Erased.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Erased.pure_def",
+        "id": "Erased.pure_def",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            142,
+            6
+          ],
+          "file_path": "Mathlib/Data/Erased.lean",
+          "full_name": "Erased.pure_def",
+          "start": [
+            141,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Erased.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rw [max_eq_right]'",
+        "full_name": "FP.Float.Zero.valid",
+        "id": "FP.Float.Zero.valid",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            102,
+            51
+          ],
+          "file_path": "Mathlib/Data/FP/Basic.lean",
+          "full_name": "FP.Float.Zero.valid",
+          "start": [
+            87,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [<a>add_sub_assoc<\\/a>]\"",
+                "[{\"full_name\":\"add_sub_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[455,3],\"def_end_pos\":[455,14]}]"
+              ],
+              "state_after": "C : FloatCfg\n\u22a2 emin \u2264 emin + (\u2191prec - 1)",
+              "state_before": "C : FloatCfg\n\u22a2 emin \u2264 emin + \u2191prec - 1",
+              "tactic": "rw [add_sub_assoc]"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>le_add_of_nonneg_right<\\/a>\"",
+                "[{\"full_name\":\"le_add_of_nonneg_right\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Unbundled\\/Basic.lean\",\"def_pos\":[391,15],\"def_end_pos\":[391,37]}]"
+              ],
+              "state_after": "case h\nC : FloatCfg\n\u22a2 0 \u2264 \u2191prec - 1",
+              "state_before": "C : FloatCfg\n\u22a2 emin \u2264 emin + (\u2191prec - 1)",
+              "tactic": "apply le_add_of_nonneg_right"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>sub_nonneg_of_le<\\/a>\"",
+                "[{\"full_name\":\"sub_nonneg_of_le\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Defs.lean\",\"def_pos\":[726,26],\"def_end_pos\":[726,42]}]"
+              ],
+              "state_after": "case h.a\nC : FloatCfg\n\u22a2 1 \u2264 \u2191prec",
+              "state_before": "case h\nC : FloatCfg\n\u22a2 0 \u2264 \u2191prec - 1",
+              "tactic": "apply sub_nonneg_of_le"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Int.ofNat_le_ofNat_of_le<\\/a>\"",
+                "[{\"full_name\":\"Int.ofNat_le_ofNat_of_le\",\"def_path\":\"Mathlib\\/Init\\/Data\\/Int\\/Order.lean\",\"def_pos\":[29,30],\"def_end_pos\":[29,50]}]"
+              ],
+              "state_after": "case h.a.a\nC : FloatCfg\n\u22a2 1 \u2264 prec",
+              "state_before": "case h.a\nC : FloatCfg\n\u22a2 1 \u2264 \u2191prec",
+              "tactic": "apply Int.ofNat_le_ofNat_of_le"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact C.precPos\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.a.a\nC : FloatCfg\n\u22a2 1 \u2264 prec",
+              "tactic": "exact C.precPos"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>Int.ofNat_le<\\/a>] at this\"",
+                "[{\"full_name\":\"Int.ofNat_le\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Order.lean\",\"def_pos\":[51,28],\"def_end_pos\":[51,36]}]"
+              ],
+              "state_after": "C : FloatCfg\nthis : \u2191prec \u2264 \u2191(2 * emax)\n\u22a2 emin + \u2191prec - 1 \u2264 \u2191emax",
+              "state_before": "C : FloatCfg\nthis : prec \u2264 2 * emax\n\u22a2 emin + \u2191prec - 1 \u2264 \u2191emax",
+              "tactic": "rw [\u2190 Int.ofNat_le] at this"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>sub_nonneg<\\/a>] at *\"",
+                "[{\"full_name\":\"sub_nonneg\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Defs.lean\",\"def_pos\":[720,30],\"def_end_pos\":[720,40]}]"
+              ],
+              "state_after": "C : FloatCfg\nthis : 0 \u2264 \u2191(2 * emax) - \u2191prec\n\u22a2 0 \u2264 \u2191emax - (emin + \u2191prec - 1)",
+              "state_before": "C : FloatCfg\nthis : \u2191prec \u2264 \u2191(2 * emax)\n\u22a2 emin + \u2191prec - 1 \u2264 \u2191emax",
+              "tactic": "rw [\u2190 sub_nonneg] at *"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>emin<\\/a>, <a>emax<\\/a>] at *\"",
+                "[{\"full_name\":\"FP.emin\",\"def_path\":\"Mathlib\\/Data\\/FP\\/Basic.lean\",\"def_pos\":[53,5],\"def_end_pos\":[53,9]},{\"full_name\":\"FP.emax\",\"def_path\":\"Mathlib\\/Data\\/FP\\/Basic.lean\",\"def_pos\":[48,5],\"def_end_pos\":[48,9]}]"
+              ],
+              "state_after": "C : FloatCfg\nthis : 0 \u2264 \u2191(2 * FloatCfg.emax) - \u2191prec\n\u22a2 0 \u2264 \u2191FloatCfg.emax - (1 - \u2191FloatCfg.emax + \u2191prec - 1)",
+              "state_before": "C : FloatCfg\nthis : 0 \u2264 \u2191(2 * emax) - \u2191prec\n\u22a2 0 \u2264 \u2191emax - (emin + \u2191prec - 1)",
+              "tactic": "simp only [emin, emax] at *"
+            },
+            {
+              "annotated_tactic": [
+                "\"ring_nf\"",
+                "[]"
+              ],
+              "state_after": "C : FloatCfg\nthis : 0 \u2264 \u2191(2 * FloatCfg.emax) - \u2191prec\n\u22a2 0 \u2264 \u2191FloatCfg.emax * 2 - \u2191prec",
+              "state_before": "C : FloatCfg\nthis : 0 \u2264 \u2191(2 * FloatCfg.emax) - \u2191prec\n\u22a2 0 \u2264 \u2191FloatCfg.emax - (1 - \u2191FloatCfg.emax + \u2191prec - 1)",
+              "tactic": "ring_nf"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>mul_comm<\\/a>]\"",
+                "[{\"full_name\":\"mul_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[332,9],\"def_end_pos\":[332,17]}]"
+              ],
+              "state_after": "C : FloatCfg\nthis : 0 \u2264 \u2191(2 * FloatCfg.emax) - \u2191prec\n\u22a2 0 \u2264 2 * \u2191FloatCfg.emax - \u2191prec",
+              "state_before": "C : FloatCfg\nthis : 0 \u2264 \u2191(2 * FloatCfg.emax) - \u2191prec\n\u22a2 0 \u2264 \u2191FloatCfg.emax * 2 - \u2191prec",
+              "tactic": "rw [mul_comm]"
+            },
+            {
+              "annotated_tactic": [
+                "\"assumption\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C : FloatCfg\nthis : 0 \u2264 \u2191(2 * FloatCfg.emax) - \u2191prec\n\u22a2 0 \u2264 2 * \u2191FloatCfg.emax - \u2191prec",
+              "tactic": "assumption"
+            },
+            {
+              "annotated_tactic": [
+                "\"(rw [<a>max_eq_right<\\/a>]; simp [<a>sub_eq_add_neg<\\/a>])\"",
+                "[{\"full_name\":\"max_eq_right\",\"def_path\":\"Mathlib\\/Init\\/Order\\/LinearOrder.lean\",\"def_pos\":[137,9],\"def_end_pos\":[137,21]},{\"full_name\":\"sub_eq_add_neg\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1057,3],\"def_end_pos\":[1057,14]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C : FloatCfg\n\u22a2 emin = max (emin + \u2191(Nat.size 0) - \u2191prec) emin",
+              "tactic": "(rw [max_eq_right]; simp [sub_eq_add_neg])"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>max_eq_right<\\/a>]\"",
+                "[{\"full_name\":\"max_eq_right\",\"def_path\":\"Mathlib\\/Init\\/Order\\/LinearOrder.lean\",\"def_pos\":[137,9],\"def_end_pos\":[137,21]}]"
+              ],
+              "state_after": "C : FloatCfg\n\u22a2 emin + \u2191(Nat.size 0) - \u2191prec \u2264 emin",
+              "state_before": "C : FloatCfg\n\u22a2 emin = max (emin + \u2191(Nat.size 0) - \u2191prec) emin",
+              "tactic": "rw [max_eq_right]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [<a>sub_eq_add_neg<\\/a>]\"",
+                "[{\"full_name\":\"sub_eq_add_neg\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1057,3],\"def_end_pos\":[1057,14]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "C : FloatCfg\n\u22a2 emin + \u2191(Nat.size 0) - \u2191prec \u2264 emin",
+              "tactic": "simp [sub_eq_add_neg]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/FP/Basic.lean"
+      }
+    ],
+    "input_proofs": 11,
+    "input_units": 2,
+    "proofs": 3,
+    "published_proofs": 3,
+    "published_transitions": 5,
+    "replay_failures": [],
+    "transitions": 5,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000892-0000-04ddbe2d96fe8362.parquet",
+      "sha256": "04ddbe2d96fe83620455a978daa137c269a733bd372e704be9e2bbcb0761f2d7",
+      "bytes": 34627,
+      "rows": 4,
+      "revision": "9931f7e263b644970d94314c5ccd8bc8f7920aee"
+    },
+    {
+      "path": "data/internal_test/mathlib-000892-0000-be388b9fb6ac3f2d.parquet",
+      "sha256": "be388b9fb6ac3f2d12af7218da8e2f2762547404d5cd6e8124852dfd4a964b2a",
+      "bytes": 29971,
+      "rows": 1,
+      "revision": "9931f7e263b644970d94314c5ccd8bc8f7920aee"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Erased.map_out",
+    "mathlib:Erased.mk_out",
+    "mathlib:Erased.out_inj"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Erased.lean\",null,null,\"Erased.map_out\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Erased.lean\",null,null,\"Erased.mk_out\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Erased.lean\",null,null,\"Erased.out_inj\"]"
+  ]
+}

manifests/batches/mathlib/000894.json

@@ -0,0 +1,257 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000894",
+  "batch_fingerprint": "d2302d2e8753d43a658ee48f1a64747cbdb6f198ae0650776e9fd1d84bbc50b6",
+  "evidence": {
+    "batch_fingerprint": "d2302d2e8753d43a658ee48f1a64747cbdb6f198ae0650776e9fd1d84bbc50b6",
+    "batch_outcome": "all_inputs_failed_with_evidence",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Flag.mem_rangeFin",
+        "id": "Flag.mem_rangeFin",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            60,
+            10
+          ],
+          "file_path": "Mathlib/Data/Fin/FlagRange.lean",
+          "full_name": "Flag.mem_rangeFin",
+          "start": [
+            58,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/FlagRange.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'simpa [hlast] using this (.last _)'",
+        "full_name": "IsMaxChain.range_fin_of_covBy",
+        "id": "IsMaxChain.range_fin_of_covBy",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            44,
+            80
+          ],
+          "file_path": "Mathlib/Data/Fin/FlagRange.lean",
+          "full_name": "IsMaxChain.range_fin_of_covBy",
+          "start": [
+            32,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"have hmono : <a>Monotone<\\/a> f := <a>Fin.monotone_iff_le_succ<\\/a>.2 fun k \\u21a6 (hcovBy k).1\"",
+                "[{\"full_name\":\"Monotone\",\"def_path\":\"Mathlib\\/Order\\/Monotone\\/Basic.lean\",\"def_pos\":[77,5],\"def_end_pos\":[77,13]},{\"full_name\":\"Fin.monotone_iff_le_succ\",\"def_path\":\"Mathlib\\/Order\\/Fin.lean\",\"def_pos\":[113,7],\"def_end_pos\":[113,27]}]"
+              ],
+              "state_after": "\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : BoundedOrder \u03b1\nn : \u2115\nf : Fin (n + 1) \u2192 \u03b1\nh0 : f 0 = \u22a5\nhlast : f (Fin.last n) = \u22a4\nhcovBy : \u2200 (k : Fin n), f k.castSucc \u2a7f f k.succ\nhmono : Monotone f\n\u22a2 IsMaxChain (fun x x_1 => x \u2264 x_1) (range f)",
+              "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : BoundedOrder \u03b1\nn : \u2115\nf : Fin (n + 1) \u2192 \u03b1\nh0 : f 0 = \u22a5\nhlast : f (Fin.last n) = \u22a4\nhcovBy : \u2200 (k : Fin n), f k.castSucc \u2a7f f k.succ\n\u22a2 IsMaxChain (fun x x_1 => x \u2264 x_1) (range f)",
+              "tactic": "have hmono : Monotone f := Fin.monotone_iff_le_succ.2 fun k \u21a6 (hcovBy k).1"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine \\u27e8hmono.isChain_range, fun t htc hbt \\u21a6 hbt.antisymm fun x hx \\u21a6 ?_\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : BoundedOrder \u03b1\nn : \u2115\nf : Fin (n + 1) \u2192 \u03b1\nh0 : f 0 = \u22a5\nhlast : f (Fin.last n) = \u22a4\nhcovBy : \u2200 (k : Fin n), f k.castSucc \u2a7f f k.succ\nhmono : Monotone f\nt : Set \u03b1\nhtc : IsChain (fun x x_1 => x \u2264 x_1) t\nhbt : range f \u2286 t\nx : \u03b1\nhx : x \u2208 t\n\u22a2 x \u2208 range f",
+              "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : BoundedOrder \u03b1\nn : \u2115\nf : Fin (n + 1) \u2192 \u03b1\nh0 : f 0 = \u22a5\nhlast : f (Fin.last n) = \u22a4\nhcovBy : \u2200 (k : Fin n), f k.castSucc \u2a7f f k.succ\nhmono : Monotone f\n\u22a2 IsMaxChain (fun x x_1 => x \u2264 x_1) (range f)",
+              "tactic": "refine \u27e8hmono.isChain_range, fun t htc hbt \u21a6 hbt.antisymm fun x hx \u21a6 ?_\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>mem_range<\\/a>]\"",
+                "[{\"full_name\":\"Set.mem_range\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Defs.lean\",\"def_pos\":[160,17],\"def_end_pos\":[160,26]}]"
+              ],
+              "state_after": "\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : BoundedOrder \u03b1\nn : \u2115\nf : Fin (n + 1) \u2192 \u03b1\nh0 : f 0 = \u22a5\nhlast : f (Fin.last n) = \u22a4\nhcovBy : \u2200 (k : Fin n), f k.castSucc \u2a7f f k.succ\nhmono : Monotone f\nt : Set \u03b1\nhtc : IsChain (fun x x_1 => x \u2264 x_1) t\nhbt : range f \u2286 t\nx : \u03b1\nhx : x \u2208 t\n\u22a2 \u2203 y, f y = x",
+              "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : BoundedOrder \u03b1\nn : \u2115\nf : Fin (n + 1) \u2192 \u03b1\nh0 : f 0 = \u22a5\nhlast : f (Fin.last n) = \u22a4\nhcovBy : \u2200 (k : Fin n), f k.castSucc \u2a7f f k.succ\nhmono : Monotone f\nt : Set \u03b1\nhtc : IsChain (fun x x_1 => x \u2264 x_1) t\nhbt : range f \u2286 t\nx : \u03b1\nhx : x \u2208 t\n\u22a2 x \u2208 range f",
+              "tactic": "rw [mem_range]"
+            },
+            {
+              "annotated_tactic": [
+                "\"by_contra! h\"",
+                "[]"
+              ],
+              "state_after": "\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : BoundedOrder \u03b1\nn : \u2115\nf : Fin (n + 1) \u2192 \u03b1\nh0 : f 0 = \u22a5\nhlast : f (Fin.last n) = \u22a4\nhcovBy : \u2200 (k : Fin n), f k.castSucc \u2a7f f k.succ\nhmono : Monotone f\nt : Set \u03b1\nhtc : IsChain (fun x x_1 => x \u2264 x_1) t\nhbt : range f \u2286 t\nx : \u03b1\nhx : x \u2208 t\nh : \u2200 (y : Fin (n + 1)), f y \u2260 x\n\u22a2 False",
+              "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : BoundedOrder \u03b1\nn : \u2115\nf : Fin (n + 1) \u2192 \u03b1\nh0 : f 0 = \u22a5\nhlast : f (Fin.last n) = \u22a4\nhcovBy : \u2200 (k : Fin n), f k.castSucc \u2a7f f k.succ\nhmono : Monotone f\nt : Set \u03b1\nhtc : IsChain (fun x x_1 => x \u2264 x_1) t\nhbt : range f \u2286 t\nx : \u03b1\nhx : x \u2208 t\n\u22a2 \u2203 y, f y = x",
+              "tactic": "by_contra! h"
+            },
+            {
+              "annotated_tactic": [
+                "\"suffices \\u2200 k, f k < x by simpa [hlast] using this (.last _)\"",
+                "[]"
+              ],
+              "state_after": "\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : BoundedOrder \u03b1\nn : \u2115\nf : Fin (n + 1) \u2192 \u03b1\nh0 : f 0 = \u22a5\nhlast : f (Fin.last n) = \u22a4\nhcovBy : \u2200 (k : Fin n), f k.castSucc \u2a7f f k.succ\nhmono : Monotone f\nt : Set \u03b1\nhtc : IsChain (fun x x_1 => x \u2264 x_1) t\nhbt : range f \u2286 t\nx : \u03b1\nhx : x \u2208 t\nh : \u2200 (y : Fin (n + 1)), f y \u2260 x\n\u22a2 \u2200 (k : Fin (n + 1)), f k < x",
+              "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : BoundedOrder \u03b1\nn : \u2115\nf : Fin (n + 1) \u2192 \u03b1\nh0 : f 0 = \u22a5\nhlast : f (Fin.last n) = \u22a4\nhcovBy : \u2200 (k : Fin n), f k.castSucc \u2a7f f k.succ\nhmono : Monotone f\nt : Set \u03b1\nhtc : IsChain (fun x x_1 => x \u2264 x_1) t\nhbt : range f \u2286 t\nx : \u03b1\nhx : x \u2208 t\nh : \u2200 (y : Fin (n + 1)), f y \u2260 x\n\u22a2 False",
+              "tactic": "suffices \u2200 k, f k < x by simpa [hlast] using this (.last _)"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro k\"",
+                "[]"
+              ],
+              "state_after": "\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : BoundedOrder \u03b1\nn : \u2115\nf : Fin (n + 1) \u2192 \u03b1\nh0 : f 0 = \u22a5\nhlast : f (Fin.last n) = \u22a4\nhcovBy : \u2200 (k : Fin n), f k.castSucc \u2a7f f k.succ\nhmono : Monotone f\nt : Set \u03b1\nhtc : IsChain (fun x x_1 => x \u2264 x_1) t\nhbt : range f \u2286 t\nx : \u03b1\nhx : x \u2208 t\nh : \u2200 (y : Fin (n + 1)), f y \u2260 x\nk : Fin (n + 1)\n\u22a2 f k < x",
+              "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : BoundedOrder \u03b1\nn : \u2115\nf : Fin (n + 1) \u2192 \u03b1\nh0 : f 0 = \u22a5\nhlast : f (Fin.last n) = \u22a4\nhcovBy : \u2200 (k : Fin n), f k.castSucc \u2a7f f k.succ\nhmono : Monotone f\nt : Set \u03b1\nhtc : IsChain (fun x x_1 => x \u2264 x_1) t\nhbt : range f \u2286 t\nx : \u03b1\nhx : x \u2208 t\nh : \u2200 (y : Fin (n + 1)), f y \u2260 x\n\u22a2 \u2200 (k : Fin (n + 1)), f k < x",
+              "tactic": "intro k"
+            },
+            {
+              "annotated_tactic": [
+                "\"induction k using <a>Fin.induction<\\/a> with\\n  | zero => simpa [h0, <a>bot_lt_iff_ne_bot<\\/a>] using (h 0).<a>symm<\\/a>\\n  | <a>succ<\\/a> k ihk =>\\n    rw [<a>range_subset_iff<\\/a>] at hbt\\n    exact (htc.lt_of_le (hbt k.succ) hx (h _)).<a>resolve_right<\\/a> ((hcovBy k).2 ihk)\"",
+                "[{\"full_name\":\"Fin.induction\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[624,21],\"def_end_pos\":[624,30]},{\"full_name\":\"bot_lt_iff_ne_bot\",\"def_path\":\"Mathlib\\/Order\\/BoundedOrder.lean\",\"def_pos\":[339,9],\"def_end_pos\":[339,26]},{\"full_name\":\"Ne.symm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[704,9],\"def_end_pos\":[704,16]},{\"full_name\":\"Fin.succ\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Basic.lean\",\"def_pos\":[34,5],\"def_end_pos\":[34,9]},{\"full_name\":\"Set.range_subset_iff\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Image.lean\",\"def_pos\":[734,9],\"def_end_pos\":[734,25]},{\"full_name\":\"Or.resolve_right\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[556,9],\"def_end_pos\":[556,25]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : BoundedOrder \u03b1\nn : \u2115\nf : Fin (n + 1) \u2192 \u03b1\nh0 : f 0 = \u22a5\nhlast : f (Fin.last n) = \u22a4\nhcovBy : \u2200 (k : Fin n), f k.castSucc \u2a7f f k.succ\nhmono : Monotone f\nt : Set \u03b1\nhtc : IsChain (fun x x_1 => x \u2264 x_1) t\nhbt : range f \u2286 t\nx : \u03b1\nhx : x \u2208 t\nh : \u2200 (y : Fin (n + 1)), f y \u2260 x\nk : Fin (n + 1)\n\u22a2 f k < x",
+              "tactic": "induction k using Fin.induction with\n| zero => simpa [h0, bot_lt_iff_ne_bot] using (h 0).symm\n| succ k ihk =>\n  rw [range_subset_iff] at hbt\n  exact (htc.lt_of_le (hbt k.succ) hx (h _)).resolve_right ((hcovBy k).2 ihk)"
+            },
+            {
+              "annotated_tactic": [
+                "\"simpa [hlast] using this (.last _)\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : BoundedOrder \u03b1\nn : \u2115\nf : Fin (n + 1) \u2192 \u03b1\nh0 : f 0 = \u22a5\nhlast : f (Fin.last n) = \u22a4\nhcovBy : \u2200 (k : Fin n), f k.castSucc \u2a7f f k.succ\nhmono : Monotone f\nt : Set \u03b1\nhtc : IsChain (fun x x_1 => x \u2264 x_1) t\nhbt : range f \u2286 t\nx : \u03b1\nhx : x \u2208 t\nh : \u2200 (y : Fin (n + 1)), f y \u2260 x\nthis : \u2200 (k : Fin (n + 1)), f k < x\n\u22a2 False",
+              "tactic": "simpa [hlast] using this (.last _)"
+            },
+            {
+              "annotated_tactic": [
+                "\"simpa [h0, <a>bot_lt_iff_ne_bot<\\/a>] using (h 0).<a>symm<\\/a>\"",
+                "[{\"full_name\":\"bot_lt_iff_ne_bot\",\"def_path\":\"Mathlib\\/Order\\/BoundedOrder.lean\",\"def_pos\":[339,9],\"def_end_pos\":[339,26]},{\"full_name\":\"Ne.symm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[704,9],\"def_end_pos\":[704,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case zero\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : BoundedOrder \u03b1\nn : \u2115\nf : Fin (n + 1) \u2192 \u03b1\nh0 : f 0 = \u22a5\nhlast : f (Fin.last n) = \u22a4\nhcovBy : \u2200 (k : Fin n), f k.castSucc \u2a7f f k.succ\nhmono : Monotone f\nt : Set \u03b1\nhtc : IsChain (fun x x_1 => x \u2264 x_1) t\nhbt : range f \u2286 t\nx : \u03b1\nhx : x \u2208 t\nh : \u2200 (y : Fin (n + 1)), f y \u2260 x\n\u22a2 f 0 < x",
+              "tactic": "simpa [h0, bot_lt_iff_ne_bot] using (h 0).symm"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>range_subset_iff<\\/a>] at hbt\"",
+                "[{\"full_name\":\"Set.range_subset_iff\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Image.lean\",\"def_pos\":[734,9],\"def_end_pos\":[734,25]}]"
+              ],
+              "state_after": "case succ\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : BoundedOrder \u03b1\nn : \u2115\nf : Fin (n + 1) \u2192 \u03b1\nh0 : f 0 = \u22a5\nhlast : f (Fin.last n) = \u22a4\nhcovBy : \u2200 (k : Fin n), f k.castSucc \u2a7f f k.succ\nhmono : Monotone f\nt : Set \u03b1\nhtc : IsChain (fun x x_1 => x \u2264 x_1) t\nhbt : \u2200 (y : Fin (n + 1)), f y \u2208 t\nx : \u03b1\nhx : x \u2208 t\nh : \u2200 (y : Fin (n + 1)), f y \u2260 x\nk : Fin n\nihk : f k.castSucc < x\n\u22a2 f k.succ < x",
+              "state_before": "case succ\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : BoundedOrder \u03b1\nn : \u2115\nf : Fin (n + 1) \u2192 \u03b1\nh0 : f 0 = \u22a5\nhlast : f (Fin.last n) = \u22a4\nhcovBy : \u2200 (k : Fin n), f k.castSucc \u2a7f f k.succ\nhmono : Monotone f\nt : Set \u03b1\nhtc : IsChain (fun x x_1 => x \u2264 x_1) t\nhbt : range f \u2286 t\nx : \u03b1\nhx : x \u2208 t\nh : \u2200 (y : Fin (n + 1)), f y \u2260 x\nk : Fin n\nihk : f k.castSucc < x\n\u22a2 f k.succ < x",
+              "tactic": "rw [range_subset_iff] at hbt"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact (htc.lt_of_le (hbt k.succ) hx (h _)).<a>resolve_right<\\/a> ((hcovBy k).2 ihk)\"",
+                "[{\"full_name\":\"Or.resolve_right\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[556,9],\"def_end_pos\":[556,25]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case succ\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : BoundedOrder \u03b1\nn : \u2115\nf : Fin (n + 1) \u2192 \u03b1\nh0 : f 0 = \u22a5\nhlast : f (Fin.last n) = \u22a4\nhcovBy : \u2200 (k : Fin n), f k.castSucc \u2a7f f k.succ\nhmono : Monotone f\nt : Set \u03b1\nhtc : IsChain (fun x x_1 => x \u2264 x_1) t\nhbt : \u2200 (y : Fin (n + 1)), f y \u2208 t\nx : \u03b1\nhx : x \u2208 t\nh : \u2200 (y : Fin (n + 1)), f y \u2260 x\nk : Fin n\nihk : f k.castSucc < x\n\u22a2 f k.succ < x",
+              "tactic": "exact (htc.lt_of_le (hbt k.succ) hx (h _)).resolve_right ((hcovBy k).2 ihk)"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/FlagRange.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Fin.pred_apply",
+        "id": "Fin.pred_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            74,
+            6
+          ],
+          "file_path": "Mathlib/Data/Fin/SuccPred.lean",
+          "full_name": "Fin.pred_apply",
+          "start": [
+            73,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/SuccPred.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Fin.pred_eq",
+        "id": "Fin.pred_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            69,
+            6
+          ],
+          "file_path": "Mathlib/Data/Fin/SuccPred.lean",
+          "full_name": "Fin.pred_eq",
+          "start": [
+            68,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/SuccPred.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Fin.succ_apply",
+        "id": "Fin.succ_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            47,
+            6
+          ],
+          "file_path": "Mathlib/Data/Fin/SuccPred.lean",
+          "full_name": "Fin.succ_apply",
+          "start": [
+            46,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/SuccPred.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Fin.succ_eq",
+        "id": "Fin.succ_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            42,
+            6
+          ],
+          "file_path": "Mathlib/Data/Fin/SuccPred.lean",
+          "full_name": "Fin.succ_eq",
+          "start": [
+            41,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/SuccPred.lean"
+      }
+    ],
+    "input_proofs": 6,
+    "input_units": 2,
+    "proofs": 0,
+    "published_proofs": 0,
+    "published_transitions": 0,
+    "replay_failures": [],
+    "transitions": 0,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [],
+  "proof_ids": [],
+  "proof_keys": []
+}

manifests/batches/mathlib/000896.json

@@ -0,0 +1,323 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000896",
+  "batch_fingerprint": "214d26d9f448b3620fa3550805afdafc4e7d8f2b62cb9d9edfce6cf19f38260e",
+  "evidence": {
+    "batch_fingerprint": "214d26d9f448b3620fa3550805afdafc4e7d8f2b62cb9d9edfce6cf19f38260e",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.FromTypes.curry_apply_cons",
+        "id": "Function.FromTypes.curry_apply_cons",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            63,
+            54
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Curry.lean",
+          "full_name": "Function.FromTypes.curry_apply_cons",
+          "start": [
+            61,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Curry.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.FromTypes.curry_apply_succ",
+        "id": "Function.FromTypes.curry_apply_succ",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            68,
+            46
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Curry.lean",
+          "full_name": "Function.FromTypes.curry_apply_succ",
+          "start": [
+            66,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Curry.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.FromTypes.curry_two_eq_curry",
+        "id": "Function.FromTypes.curry_two_eq_curry",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            96,
+            65
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Curry.lean",
+          "full_name": "Function.FromTypes.curry_two_eq_curry",
+          "start": [
+            94,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Curry.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.FromTypes.uncurry_apply_cons",
+        "id": "Function.FromTypes.uncurry_apply_cons",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            52,
+            67
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Curry.lean",
+          "full_name": "Function.FromTypes.uncurry_apply_cons",
+          "start": [
+            50,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Curry.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.FromTypes.uncurry_apply_succ",
+        "id": "Function.FromTypes.uncurry_apply_succ",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            58,
+            71
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Curry.lean",
+          "full_name": "Function.FromTypes.uncurry_apply_succ",
+          "start": [
+            55,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Curry.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'exact congrArg f (Subsingleton.allEq _ _)'",
+        "full_name": "Function.FromTypes.uncurry_curry",
+        "id": "Function.FromTypes.uncurry_curry",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            84,
+            80
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Curry.lean",
+          "full_name": "Function.FromTypes.uncurry_curry",
+          "start": [
+            79,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"ext args\"",
+                "[]"
+              ],
+              "state_after": "case h\nn : \u2115\np : Fin n \u2192 Type u\n\u03c4 : Type u\nf : ((i : Fin n) \u2192 p i) \u2192 \u03c4\nargs : (i : Fin n) \u2192 p i\n\u22a2 (curry f).uncurry args = f args",
+              "state_before": "n : \u2115\np : Fin n \u2192 Type u\n\u03c4 : Type u\nf : ((i : Fin n) \u2192 p i) \u2192 \u03c4\n\u22a2 (curry f).uncurry = f",
+              "tactic": "ext args"
+            },
+            {
+              "annotated_tactic": [
+                "\"induction n with\\n  | zero => exact <a>congrArg<\\/a> f (<a>Subsingleton.allEq<\\/a> _ _)\\n  | succ n ih => exact <a>Eq.trans<\\/a> (ih _ _) (<a>congrArg<\\/a> f (<a>Fin.cons_self_tail<\\/a> args))\"",
+                "[{\"full_name\":\"congrArg\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[362,9],\"def_end_pos\":[362,17]},{\"full_name\":\"Subsingleton.allEq\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1013,3],\"def_end_pos\":[1013,8]},{\"full_name\":\"Eq.trans\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[335,9],\"def_end_pos\":[335,17]},{\"full_name\":\"congrArg\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[362,9],\"def_end_pos\":[362,17]},{\"full_name\":\"Fin.cons_self_tail\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Basic.lean\",\"def_pos\":[185,9],\"def_end_pos\":[185,23]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h\nn : \u2115\np : Fin n \u2192 Type u\n\u03c4 : Type u\nf : ((i : Fin n) \u2192 p i) \u2192 \u03c4\nargs : (i : Fin n) \u2192 p i\n\u22a2 (curry f).uncurry args = f args",
+              "tactic": "induction n with\n| zero => exact congrArg f (Subsingleton.allEq _ _)\n| succ n ih => exact Eq.trans (ih _ _) (congrArg f (Fin.cons_self_tail args))"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>congrArg<\\/a> f (<a>Subsingleton.allEq<\\/a> _ _)\"",
+                "[{\"full_name\":\"congrArg\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[362,9],\"def_end_pos\":[362,17]},{\"full_name\":\"Subsingleton.allEq\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1013,3],\"def_end_pos\":[1013,8]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.zero\n\u03c4 : Type u\np : Fin 0 \u2192 Type u\nf : ((i : Fin 0) \u2192 p i) \u2192 \u03c4\nargs : (i : Fin 0) \u2192 p i\n\u22a2 (curry f).uncurry args = f args",
+              "tactic": "exact congrArg f (Subsingleton.allEq _ _)"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>Eq.trans<\\/a> (ih _ _) (<a>congrArg<\\/a> f (<a>Fin.cons_self_tail<\\/a> args))\"",
+                "[{\"full_name\":\"Eq.trans\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[335,9],\"def_end_pos\":[335,17]},{\"full_name\":\"congrArg\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[362,9],\"def_end_pos\":[362,17]},{\"full_name\":\"Fin.cons_self_tail\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Basic.lean\",\"def_pos\":[185,9],\"def_end_pos\":[185,23]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.succ\n\u03c4 : Type u\nn : \u2115\nih : \u2200 {p : Fin n \u2192 Type u} (f : ((i : Fin n) \u2192 p i) \u2192 \u03c4) (args : (i : Fin n) \u2192 p i), (curry f).uncurry args = f args\np : Fin (n + 1) \u2192 Type u\nf : ((i : Fin (n + 1)) \u2192 p i) \u2192 \u03c4\nargs : (i : Fin (n + 1)) \u2192 p i\n\u22a2 (curry f).uncurry args = f args",
+              "tactic": "exact Eq.trans (ih _ _) (congrArg f (Fin.cons_self_tail args))"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Curry.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.FromTypes.uncurry_two_eq_uncurry",
+        "id": "Function.FromTypes.uncurry_two_eq_uncurry",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            100,
+            60
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Curry.lean",
+          "full_name": "Function.FromTypes.uncurry_two_eq_uncurry",
+          "start": [
+            98,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Curry.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.OfArity.curry_two_eq_curry",
+        "id": "Function.OfArity.curry_two_eq_curry",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            131,
+            33
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Curry.lean",
+          "full_name": "Function.OfArity.curry_two_eq_curry",
+          "start": [
+            129,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Curry.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.OfArity.curry_uncurry",
+        "id": "Function.OfArity.curry_uncurry",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            118,
+            55
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Curry.lean",
+          "full_name": "Function.OfArity.curry_uncurry",
+          "start": [
+            117,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Curry.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.OfArity.uncurry_curry",
+        "id": "Function.OfArity.uncurry_curry",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            122,
+            55
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Curry.lean",
+          "full_name": "Function.OfArity.uncurry_curry",
+          "start": [
+            121,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Curry.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Function.OfArity.uncurry_two_eq_uncurry",
+        "id": "Function.OfArity.uncurry_two_eq_uncurry",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            135,
+            41
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Curry.lean",
+          "full_name": "Function.OfArity.uncurry_two_eq_uncurry",
+          "start": [
+            133,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Curry.lean"
+      }
+    ],
+    "input_proofs": 16,
+    "input_units": 2,
+    "proofs": 5,
+    "published_proofs": 5,
+    "published_transitions": 5,
+    "replay_failures": [],
+    "transitions": 5,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000896-0000-f2884fa8ddf6db2d.parquet",
+      "sha256": "f2884fa8ddf6db2d0dc792e778c6f72ddfc7460c20645ec8fe5a228d542c756c",
+      "bytes": 40781,
+      "rows": 5,
+      "revision": "9931f7e263b644970d94314c5ccd8bc8f7920aee"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Fin.cons_mem_piFinset_cons",
+    "mathlib:Fin.mem_piFinset_succ",
+    "mathlib:Fin.mem_piFinset_succ'",
+    "mathlib:Fin.snoc_mem_piFinset_snoc",
+    "mathlib:Function.FromTypes.curry_uncurry"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Fin/Tuple/Curry.lean\",null,null,\"Function.FromTypes.curry_uncurry\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Fin/Tuple/Finset.lean\",null,null,\"Fin.cons_mem_piFinset_cons\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Fin/Tuple/Finset.lean\",null,null,\"Fin.mem_piFinset_succ\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Fin/Tuple/Finset.lean\",null,null,\"Fin.mem_piFinset_succ'\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Fin/Tuple/Finset.lean\",null,null,\"Fin.snoc_mem_piFinset_snoc\"]"
+  ]
+}

manifests/batches/mathlib/000897.json

@@ -0,0 +1,1024 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000897",
+  "batch_fingerprint": "b1b45e6f3ba7c08c6c7cb8ddde94e0e127b6d4af4d138965cc97567f03435b3a",
+  "evidence": {
+    "batch_fingerprint": "b1b45e6f3ba7c08c6c7cb8ddde94e0e127b6d4af4d138965cc97567f03435b3a",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Antitone.vecCons",
+        "id": "Antitone.vecCons",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            78,
+            30
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Monotone.lean",
+          "full_name": "Antitone.vecCons",
+          "start": [
+            77,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Monotone.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Monotone.vecCons",
+        "id": "Monotone.vecCons",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            74,
+            30
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Monotone.lean",
+          "full_name": "Monotone.vecCons",
+          "start": [
+            73,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Monotone.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "StrictAnti.vecCons",
+        "id": "StrictAnti.vecCons",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            70,
+            32
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Monotone.lean",
+          "full_name": "StrictAnti.vecCons",
+          "start": [
+            69,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Monotone.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "StrictMono.vecCons",
+        "id": "StrictMono.vecCons",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            66,
+            32
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Monotone.lean",
+          "full_name": "StrictMono.vecCons",
+          "start": [
+            65,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Monotone.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "antitone_vecCons",
+        "id": "antitone_vecCons",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            54,
+            32
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Monotone.lean",
+          "full_name": "antitone_vecCons",
+          "start": [
+            53,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Monotone.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "antitone_vecEmpty",
+        "id": "antitone_vecEmpty",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            59,
+            35
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Monotone.lean",
+          "full_name": "antitone_vecEmpty",
+          "start": [
+            58,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Monotone.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "monotone_vecCons",
+        "id": "monotone_vecCons",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            36,
+            79
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Monotone.lean",
+          "full_name": "monotone_vecCons",
+          "start": [
+            35,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Monotone.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "monotone_vecEmpty",
+        "id": "monotone_vecEmpty",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            41,
+            35
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Monotone.lean",
+          "full_name": "monotone_vecEmpty",
+          "start": [
+            40,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Monotone.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "strictAnti_vecCons",
+        "id": "strictAnti_vecCons",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            49,
+            26
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Monotone.lean",
+          "full_name": "strictAnti_vecCons",
+          "start": [
+            48,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Monotone.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "strictAnti_vecEmpty",
+        "id": "strictAnti_vecEmpty",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            63,
+            43
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Monotone.lean",
+          "full_name": "strictAnti_vecEmpty",
+          "start": [
+            62,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Monotone.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "strictMono_vecCons",
+        "id": "strictMono_vecCons",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            31,
+            26
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Monotone.lean",
+          "full_name": "strictMono_vecCons",
+          "start": [
+            30,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Monotone.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "strictMono_vecEmpty",
+        "id": "strictMono_vecEmpty",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            45,
+            43
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Monotone.lean",
+          "full_name": "strictMono_vecEmpty",
+          "start": [
+            44,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Monotone.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.Nat.antidiagonalTuple_one",
+        "id": "Finset.Nat.antidiagonalTuple_one",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            250,
+            58
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean",
+          "full_name": "Finset.Nat.antidiagonalTuple_one",
+          "start": [
+            249,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.Nat.antidiagonalTuple_two",
+        "id": "Finset.Nat.antidiagonalTuple_two",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            255,
+            58
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean",
+          "full_name": "Finset.Nat.antidiagonalTuple_two",
+          "start": [
+            253,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.Nat.antidiagonalTuple_zero_right",
+        "id": "Finset.Nat.antidiagonalTuple_zero_right",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            245,
+            65
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean",
+          "full_name": "Finset.Nat.antidiagonalTuple_zero_right",
+          "start": [
+            244,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.Nat.antidiagonalTuple_zero_succ",
+        "id": "Finset.Nat.antidiagonalTuple_zero_succ",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            236,
+            6
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean",
+          "full_name": "Finset.Nat.antidiagonalTuple_zero_succ",
+          "start": [
+            235,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.Nat.antidiagonalTuple_zero_zero",
+        "id": "Finset.Nat.antidiagonalTuple_zero_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            231,
+            6
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean",
+          "full_name": "Finset.Nat.antidiagonalTuple_zero_zero",
+          "start": [
+            230,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finset.Nat.mem_antidiagonalTuple",
+        "id": "Finset.Nat.mem_antidiagonalTuple",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            241,
+            33
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean",
+          "full_name": "Finset.Nat.mem_antidiagonalTuple",
+          "start": [
+            239,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rw [List.mem_map, Prod.exists] at hp'",
+        "full_name": "List.Nat.antidiagonalTuple_pairwise_pi_lex",
+        "id": "List.Nat.antidiagonalTuple_pairwise_pi_lex",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            169,
+            17
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean",
+          "full_name": "List.Nat.antidiagonalTuple_pairwise_pi_lex",
+          "start": [
+            148,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"simp_rw [<a>antidiagonalTuple<\\/a>, <a>List.pairwise_bind<\\/a>, <a>List.pairwise_map<\\/a>, <a>List.mem_map<\\/a>,\\n      <a>forall_exists_index<\\/a>, <a>and_imp<\\/a>, <a>forall_apply_eq_imp_iff\\u2082<\\/a>]\"",
+                "[{\"full_name\":\"List.Nat.antidiagonalTuple\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/NatAntidiagonal.lean\",\"def_pos\":[61,5],\"def_end_pos\":[61,22]},{\"full_name\":\"List.pairwise_bind\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Data\\/List\\/Pairwise.lean\",\"def_pos\":[168,9],\"def_end_pos\":[168,22]},{\"full_name\":\"List.pairwise_map\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Data\\/List\\/Lemmas.lean\",\"def_pos\":[773,9],\"def_end_pos\":[773,21]},{\"full_name\":\"List.mem_map\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/List\\/Lemmas.lean\",\"def_pos\":[750,17],\"def_end_pos\":[750,24]},{\"full_name\":\"forall_exists_index\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/PropLemmas.lean\",\"def_pos\":[189,17],\"def_end_pos\":[189,36]},{\"full_name\":\"and_imp\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[115,17],\"def_end_pos\":[115,24]},{\"full_name\":\"forall_apply_eq_imp_iff\\u2082\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/PropLemmas.lean\",\"def_pos\":[327,17],\"def_end_pos\":[327,41]}]"
+              ],
+              "state_after": "k n : \u2115\n\u22a2 (\u2200 a \u2208 antidiagonal n,\n      Pairwise (fun a_2 b => Pi.Lex (fun x x_1 => x < x_1) (fun x x x_1 => x < x_1) (Fin.cons a.1 a_2) (Fin.cons a.1 b))\n        (antidiagonalTuple k a.2)) \u2227\n    Pairwise\n      (fun a\u2081 a\u2082 =>\n        \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n          \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n            Pi.Lex (fun x x_1 => x < x_1) (fun x x x_1 => x < x_1) (Fin.cons a\u2081.1 a) (Fin.cons a\u2082.1 a_2))\n      (antidiagonal n)",
+              "state_before": "k n : \u2115\n\u22a2 Pairwise (Pi.Lex (fun x x_1 => x < x_1) fun x x x_1 => x < x_1) (antidiagonalTuple (k + 1) n)",
+              "tactic": "simp_rw [antidiagonalTuple, List.pairwise_bind, List.pairwise_map, List.mem_map,\n  forall_exists_index, and_imp, forall_apply_eq_imp_iff\u2082]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>mem_antidiagonal<\\/a>, <a>Prod.forall<\\/a>, <a>and_imp<\\/a>, <a>forall_apply_eq_imp_iff\\u2082<\\/a>]\"",
+                "[{\"full_name\":\"List.Nat.mem_antidiagonal\",\"def_path\":\"Mathlib\\/Data\\/List\\/NatAntidiagonal.lean\",\"def_pos\":[38,9],\"def_end_pos\":[38,25]},{\"full_name\":\"Prod.forall\",\"def_path\":\"Mathlib\\/Data\\/Prod\\/Basic.lean\",\"def_pos\":[32,9],\"def_end_pos\":[32,17]},{\"full_name\":\"and_imp\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[115,17],\"def_end_pos\":[115,24]},{\"full_name\":\"forall_apply_eq_imp_iff\\u2082\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/PropLemmas.lean\",\"def_pos\":[327,17],\"def_end_pos\":[327,41]}]"
+              ],
+              "state_after": "k n : \u2115\n\u22a2 (\u2200 (a b : \u2115),\n      a + b = n \u2192\n        Pairwise (fun a_2 b => Pi.Lex (fun x x_1 => x < x_1) (fun x x x_1 => x < x_1) (Fin.cons a a_2) (Fin.cons a b))\n          (antidiagonalTuple k b)) \u2227\n    Pairwise\n      (fun a\u2081 a\u2082 =>\n        \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n          \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n            Pi.Lex (fun x x_1 => x < x_1) (fun x x x_1 => x < x_1) (Fin.cons a\u2081.1 a) (Fin.cons a\u2082.1 a_2))\n      (antidiagonal n)",
+              "state_before": "k n : \u2115\n\u22a2 (\u2200 a \u2208 antidiagonal n,\n      Pairwise (fun a_2 b => Pi.Lex (fun x x_1 => x < x_1) (fun x x x_1 => x < x_1) (Fin.cons a.1 a_2) (Fin.cons a.1 b))\n        (antidiagonalTuple k a.2)) \u2227\n    Pairwise\n      (fun a\u2081 a\u2082 =>\n        \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n          \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n            Pi.Lex (fun x x_1 => x < x_1) (fun x x x_1 => x < x_1) (Fin.cons a\u2081.1 a) (Fin.cons a\u2082.1 a_2))\n      (antidiagonal n)",
+              "tactic": "simp only [mem_antidiagonal, Prod.forall, and_imp, forall_apply_eq_imp_iff\u2082]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>Fin.pi_lex_lt_cons_cons<\\/a>, <a>eq_self_iff_true<\\/a>, <a>true_and_iff<\\/a>, <a>lt_self_iff_false<\\/a>,\\n      <a>false_or_iff<\\/a>]\"",
+                "[{\"full_name\":\"Fin.pi_lex_lt_cons_cons\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Basic.lean\",\"def_pos\":[317,9],\"def_end_pos\":[317,28]},{\"full_name\":\"eq_self_iff_true\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1380,9],\"def_end_pos\":[1380,25]},{\"full_name\":\"true_and_iff\",\"def_path\":\"Mathlib\\/Init\\/Logic.lean\",\"def_pos\":[118,9],\"def_end_pos\":[118,21]},{\"full_name\":\"lt_self_iff_false\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[165,9],\"def_end_pos\":[165,26]},{\"full_name\":\"false_or_iff\",\"def_path\":\"Mathlib\\/Init\\/Logic.lean\",\"def_pos\":[154,9],\"def_end_pos\":[154,21]}]"
+              ],
+              "state_after": "k n : \u2115\n\u22a2 (\u2200 (a b : \u2115),\n      a + b = n \u2192\n        Pairwise (fun a b => Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a b) (antidiagonalTuple k b)) \u2227\n    Pairwise\n      (fun a\u2081 a\u2082 =>\n        \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n          \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n            a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n      (antidiagonal n)",
+              "state_before": "k n : \u2115\n\u22a2 (\u2200 (a b : \u2115),\n      a + b = n \u2192\n        Pairwise (fun a_2 b => Pi.Lex (fun x x_1 => x < x_1) (fun x x x_1 => x < x_1) (Fin.cons a a_2) (Fin.cons a b))\n          (antidiagonalTuple k b)) \u2227\n    Pairwise\n      (fun a\u2081 a\u2082 =>\n        \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n          \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n            Pi.Lex (fun x x_1 => x < x_1) (fun x x x_1 => x < x_1) (Fin.cons a\u2081.1 a) (Fin.cons a\u2082.1 a_2))\n      (antidiagonal n)",
+              "tactic": "simp only [Fin.pi_lex_lt_cons_cons, eq_self_iff_true, true_and_iff, lt_self_iff_false,\n  false_or_iff]"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine \\u27e8fun _ _ _ => antidiagonalTuple_pairwise_pi_lex k _, ?_\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "k n : \u2115\n\u22a2 Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal n)",
+              "state_before": "k n : \u2115\n\u22a2 (\u2200 (a b : \u2115),\n      a + b = n \u2192\n        Pairwise (fun a b => Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a b) (antidiagonalTuple k b)) \u2227\n    Pairwise\n      (fun a\u2081 a\u2082 =>\n        \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n          \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n            a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n      (antidiagonal n)",
+              "tactic": "refine \u27e8fun _ _ _ => antidiagonalTuple_pairwise_pi_lex k _, ?_\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"induction' n with n n_ih\"",
+                "[]"
+              ],
+              "state_after": "case zero\nk : \u2115\n\u22a2 Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal 0)\n\ncase succ\nk n : \u2115\nn_ih :\n  Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal n)\n\u22a2 Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal (n + 1))",
+              "state_before": "k n : \u2115\n\u22a2 Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal n)",
+              "tactic": "induction' n with n n_ih"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>antidiagonal_zero<\\/a>]\"",
+                "[{\"full_name\":\"List.Nat.antidiagonal_zero\",\"def_path\":\"Mathlib\\/Data\\/List\\/NatAntidiagonal.lean\",\"def_pos\":[58,9],\"def_end_pos\":[58,26]}]"
+              ],
+              "state_after": "case zero\nk : \u2115\n\u22a2 Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    [(0, 0)]",
+              "state_before": "case zero\nk : \u2115\n\u22a2 Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal 0)",
+              "tactic": "rw [antidiagonal_zero]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>List.pairwise_singleton<\\/a> _ _\"",
+                "[{\"full_name\":\"List.pairwise_singleton\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Data\\/List\\/Pairwise.lean\",\"def_pos\":[104,9],\"def_end_pos\":[104,27]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case zero\nk : \u2115\n\u22a2 Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    [(0, 0)]",
+              "tactic": "exact List.pairwise_singleton _ _"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>antidiagonal_succ<\\/a>, <a>List.pairwise_cons<\\/a>, <a>List.pairwise_map<\\/a>]\"",
+                "[{\"full_name\":\"List.Nat.antidiagonal_succ\",\"def_path\":\"Mathlib\\/Data\\/List\\/NatAntidiagonal.lean\",\"def_pos\":[68,9],\"def_end_pos\":[68,26]},{\"full_name\":\"List.pairwise_cons\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Data\\/List\\/Basic.lean\",\"def_pos\":[833,17],\"def_end_pos\":[833,30]},{\"full_name\":\"List.pairwise_map\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Data\\/List\\/Lemmas.lean\",\"def_pos\":[773,9],\"def_end_pos\":[773,21]}]"
+              ],
+              "state_after": "case succ\nk n : \u2115\nn_ih :\n  Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal n)\n\u22a2 (\u2200 a' \u2208 map (Prod.map Nat.succ id) (antidiagonal n),\n      \u2200 a \u2208 antidiagonalTuple k (0, n + 1).2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a'.2,\n          (0, n + 1).1 < a'.1 \u2228 (0, n + 1).1 = a'.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2) \u2227\n    Pairwise\n      (fun a b =>\n        \u2200 a_1 \u2208 antidiagonalTuple k (Prod.map Nat.succ id a).2,\n          \u2200 a_3 \u2208 antidiagonalTuple k (Prod.map Nat.succ id b).2,\n            (Prod.map Nat.succ id a).1 < (Prod.map Nat.succ id b).1 \u2228\n              (Prod.map Nat.succ id a).1 = (Prod.map Nat.succ id b).1 \u2227\n                Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a_1 a_3)\n      (antidiagonal n)",
+              "state_before": "case succ\nk n : \u2115\nn_ih :\n  Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal n)\n\u22a2 Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal (n + 1))",
+              "tactic": "rw [antidiagonal_succ, List.pairwise_cons, List.pairwise_map]"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine \\u27e8fun p hp x hx y hy => ?_, ?_\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "case succ.refine_1\nk n : \u2115\nn_ih :\n  Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal n)\np : \u2115 \u00d7 \u2115\nhp : p \u2208 map (Prod.map Nat.succ id) (antidiagonal n)\nx : Fin k \u2192 \u2115\nhx : x \u2208 antidiagonalTuple k (0, n + 1).2\ny : Fin k \u2192 \u2115\nhy : y \u2208 antidiagonalTuple k p.2\n\u22a2 (0, n + 1).1 < p.1 \u2228 (0, n + 1).1 = p.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) x y\n\ncase succ.refine_2\nk n : \u2115\nn_ih :\n  Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal n)\n\u22a2 Pairwise\n    (fun a b =>\n      \u2200 a_1 \u2208 antidiagonalTuple k (Prod.map Nat.succ id a).2,\n        \u2200 a_3 \u2208 antidiagonalTuple k (Prod.map Nat.succ id b).2,\n          (Prod.map Nat.succ id a).1 < (Prod.map Nat.succ id b).1 \u2228\n            (Prod.map Nat.succ id a).1 = (Prod.map Nat.succ id b).1 \u2227\n              Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a_1 a_3)\n    (antidiagonal n)",
+              "state_before": "case succ\nk n : \u2115\nn_ih :\n  Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal n)\n\u22a2 (\u2200 a' \u2208 map (Prod.map Nat.succ id) (antidiagonal n),\n      \u2200 a \u2208 antidiagonalTuple k (0, n + 1).2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a'.2,\n          (0, n + 1).1 < a'.1 \u2228 (0, n + 1).1 = a'.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2) \u2227\n    Pairwise\n      (fun a b =>\n        \u2200 a_1 \u2208 antidiagonalTuple k (Prod.map Nat.succ id a).2,\n          \u2200 a_3 \u2208 antidiagonalTuple k (Prod.map Nat.succ id b).2,\n            (Prod.map Nat.succ id a).1 < (Prod.map Nat.succ id b).1 \u2228\n              (Prod.map Nat.succ id a).1 = (Prod.map Nat.succ id b).1 \u2227\n                Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a_1 a_3)\n      (antidiagonal n)",
+              "tactic": "refine \u27e8fun p hp x hx y hy => ?_, ?_\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"dsimp\"",
+                "[]"
+              ],
+              "state_after": "case succ.refine_2\nk n : \u2115\nn_ih :\n  Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal n)\n\u22a2 Pairwise\n    (fun a b =>\n      \u2200 a_1 \u2208 antidiagonalTuple k a.2,\n        \u2200 a_3 \u2208 antidiagonalTuple k b.2,\n          a.1 + 1 < b.1 + 1 \u2228 a.1 + 1 = b.1 + 1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a_1 a_3)\n    (antidiagonal n)",
+              "state_before": "case succ.refine_2\nk n : \u2115\nn_ih :\n  Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal n)\n\u22a2 Pairwise\n    (fun a b =>\n      \u2200 a_1 \u2208 antidiagonalTuple k (Prod.map Nat.succ id a).2,\n        \u2200 a_3 \u2208 antidiagonalTuple k (Prod.map Nat.succ id b).2,\n          (Prod.map Nat.succ id a).1 < (Prod.map Nat.succ id b).1 \u2228\n            (Prod.map Nat.succ id a).1 = (Prod.map Nat.succ id b).1 \u2227\n              Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a_1 a_3)\n    (antidiagonal n)",
+              "tactic": "dsimp"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp_rw [<a>Nat.succ_inj'<\\/a>, <a>Nat.succ_lt_succ_iff<\\/a>]\"",
+                "[{\"full_name\":\"Nat.succ_inj'\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[633,9],\"def_end_pos\":[633,18]},{\"full_name\":\"Nat.succ_lt_succ_iff\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[637,9],\"def_end_pos\":[637,25]}]"
+              ],
+              "state_after": "case succ.refine_2\nk n : \u2115\nn_ih :\n  Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal n)\n\u22a2 Pairwise\n    (fun a b =>\n      \u2200 a_1 \u2208 antidiagonalTuple k a.2,\n        \u2200 a_3 \u2208 antidiagonalTuple k b.2,\n          a.1 < b.1 \u2228 a.1 = b.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a_1 a_3)\n    (antidiagonal n)",
+              "state_before": "case succ.refine_2\nk n : \u2115\nn_ih :\n  Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal n)\n\u22a2 Pairwise\n    (fun a b =>\n      \u2200 a_1 \u2208 antidiagonalTuple k a.2,\n        \u2200 a_3 \u2208 antidiagonalTuple k b.2,\n          a.1 + 1 < b.1 + 1 \u2228 a.1 + 1 = b.1 + 1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a_1 a_3)\n    (antidiagonal n)",
+              "tactic": "simp_rw [Nat.succ_inj', Nat.succ_lt_succ_iff]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact n_ih\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case succ.refine_2\nk n : \u2115\nn_ih :\n  Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal n)\n\u22a2 Pairwise\n    (fun a b =>\n      \u2200 a_1 \u2208 antidiagonalTuple k a.2,\n        \u2200 a_3 \u2208 antidiagonalTuple k b.2,\n          a.1 < b.1 \u2228 a.1 = b.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a_1 a_3)\n    (antidiagonal n)",
+              "tactic": "exact n_ih"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>List.mem_map<\\/a>, <a>Prod.exists<\\/a>] at hp\"",
+                "[{\"full_name\":\"List.mem_map\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/List\\/Lemmas.lean\",\"def_pos\":[750,17],\"def_end_pos\":[750,24]},{\"full_name\":\"Prod.exists\",\"def_path\":\"Mathlib\\/Data\\/Prod\\/Basic.lean\",\"def_pos\":[37,9],\"def_end_pos\":[37,17]}]"
+              ],
+              "state_after": "case succ.refine_1\nk n : \u2115\nn_ih :\n  Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal n)\np : \u2115 \u00d7 \u2115\nhp : \u2203 a b, (a, b) \u2208 antidiagonal n \u2227 Prod.map Nat.succ id (a, b) = p\nx : Fin k \u2192 \u2115\nhx : x \u2208 antidiagonalTuple k (0, n + 1).2\ny : Fin k \u2192 \u2115\nhy : y \u2208 antidiagonalTuple k p.2\n\u22a2 (0, n + 1).1 < p.1 \u2228 (0, n + 1).1 = p.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) x y",
+              "state_before": "case succ.refine_1\nk n : \u2115\nn_ih :\n  Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal n)\np : \u2115 \u00d7 \u2115\nhp : p \u2208 map (Prod.map Nat.succ id) (antidiagonal n)\nx : Fin k \u2192 \u2115\nhx : x \u2208 antidiagonalTuple k (0, n + 1).2\ny : Fin k \u2192 \u2115\nhy : y \u2208 antidiagonalTuple k p.2\n\u22a2 (0, n + 1).1 < p.1 \u2228 (0, n + 1).1 = p.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) x y",
+              "tactic": "rw [List.mem_map, Prod.exists] at hp"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8a, b, _, rfl : (<a>Nat.succ<\\/a> a, b) = p\\u27e9 := hp\"",
+                "[{\"full_name\":\"Nat.succ\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1083,5],\"def_end_pos\":[1083,9]}]"
+              ],
+              "state_after": "case succ.refine_1.intro.intro.intro\nk n : \u2115\nn_ih :\n  Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal n)\nx : Fin k \u2192 \u2115\nhx : x \u2208 antidiagonalTuple k (0, n + 1).2\ny : Fin k \u2192 \u2115\na b : \u2115\nleft\u271d : (a, b) \u2208 antidiagonal n\nhy : y \u2208 antidiagonalTuple k (a.succ, b).2\n\u22a2 (0, n + 1).1 < (a.succ, b).1 \u2228\n    (0, n + 1).1 = (a.succ, b).1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) x y",
+              "state_before": "case succ.refine_1\nk n : \u2115\nn_ih :\n  Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal n)\np : \u2115 \u00d7 \u2115\nhp : \u2203 a b, (a, b) \u2208 antidiagonal n \u2227 Prod.map Nat.succ id (a, b) = p\nx : Fin k \u2192 \u2115\nhx : x \u2208 antidiagonalTuple k (0, n + 1).2\ny : Fin k \u2192 \u2115\nhy : y \u2208 antidiagonalTuple k p.2\n\u22a2 (0, n + 1).1 < p.1 \u2228 (0, n + 1).1 = p.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) x y",
+              "tactic": "obtain \u27e8a, b, _, rfl : (Nat.succ a, b) = p\u27e9 := hp"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>Or.inl<\\/a> (<a>Nat.zero_lt_succ<\\/a> _)\"",
+                "[{\"full_name\":\"Or.inl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[534,5],\"def_end_pos\":[534,8]},{\"full_name\":\"Nat.zero_lt_succ\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1671,9],\"def_end_pos\":[1671,25]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case succ.refine_1.intro.intro.intro\nk n : \u2115\nn_ih :\n  Pairwise\n    (fun a\u2081 a\u2082 =>\n      \u2200 a \u2208 antidiagonalTuple k a\u2081.2,\n        \u2200 a_2 \u2208 antidiagonalTuple k a\u2082.2,\n          a\u2081.1 < a\u2082.1 \u2228 a\u2081.1 = a\u2082.1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) a a_2)\n    (antidiagonal n)\nx : Fin k \u2192 \u2115\nhx : x \u2208 antidiagonalTuple k (0, n + 1).2\ny : Fin k \u2192 \u2115\na b : \u2115\nleft\u271d : (a, b) \u2208 antidiagonal n\nhy : y \u2208 antidiagonalTuple k (a.succ, b).2\n\u22a2 (0, n + 1).1 < (a.succ, b).1 \u2228\n    (0, n + 1).1 = (a.succ, b).1 \u2227 Pi.Lex (fun x x_1 => x < x_1) (fun i x x_1 => x < x_1) x y",
+              "tactic": "exact Or.inl (Nat.zero_lt_succ _)"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "List.Nat.antidiagonalTuple_zero_succ",
+        "id": "List.Nat.antidiagonalTuple_zero_succ",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            76,
+            6
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean",
+          "full_name": "List.Nat.antidiagonalTuple_zero_succ",
+          "start": [
+            75,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "List.Nat.antidiagonalTuple_zero_zero",
+        "id": "List.Nat.antidiagonalTuple_zero_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            71,
+            6
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean",
+          "full_name": "List.Nat.antidiagonalTuple_zero_zero",
+          "start": [
+            70,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'cases n'",
+        "full_name": "List.Nat.nodup_antidiagonalTuple",
+        "id": "List.Nat.nodup_antidiagonalTuple",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            117,
+            70
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean",
+          "full_name": "List.Nat.nodup_antidiagonalTuple",
+          "start": [
+            94,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"induction' k with k ih generalizing n\"",
+                "[]"
+              ],
+              "state_after": "case zero\nn : \u2115\n\u22a2 (antidiagonalTuple 0 n).Nodup\n\ncase succ\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\n\u22a2 (antidiagonalTuple (k + 1) n).Nodup",
+              "state_before": "k n : \u2115\n\u22a2 (antidiagonalTuple k n).Nodup",
+              "tactic": "induction' k with k ih generalizing n"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp_rw [<a>antidiagonalTuple<\\/a>, <a>List.nodup_bind<\\/a>]\"",
+                "[{\"full_name\":\"List.Nat.antidiagonalTuple\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/NatAntidiagonal.lean\",\"def_pos\":[61,5],\"def_end_pos\":[61,22]},{\"full_name\":\"List.nodup_bind\",\"def_path\":\"Mathlib\\/Data\\/List\\/Nodup.lean\",\"def_pos\":[367,9],\"def_end_pos\":[367,19]}]"
+              ],
+              "state_after": "case succ\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\n\u22a2 (\u2200 x \u2208 antidiagonal n, (map (fun x_1 => Fin.cons x.1 x_1) (antidiagonalTuple k x.2)).Nodup) \u2227\n    Pairwise\n      (fun a b =>\n        (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n          (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n      (antidiagonal n)",
+              "state_before": "case succ\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\n\u22a2 (antidiagonalTuple (k + 1) n).Nodup",
+              "tactic": "simp_rw [antidiagonalTuple, List.nodup_bind]"
+            },
+            {
+              "annotated_tactic": [
+                "\"constructor\"",
+                "[]"
+              ],
+              "state_after": "case succ.left\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\n\u22a2 \u2200 x \u2208 antidiagonal n, (map (fun x_1 => Fin.cons x.1 x_1) (antidiagonalTuple k x.2)).Nodup\n\ncase succ.right\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\n\u22a2 Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)",
+              "state_before": "case succ\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\n\u22a2 (\u2200 x \u2208 antidiagonal n, (map (fun x_1 => Fin.cons x.1 x_1) (antidiagonalTuple k x.2)).Nodup) \u2227\n    Pairwise\n      (fun a b =>\n        (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n          (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n      (antidiagonal n)",
+              "tactic": "constructor"
+            },
+            {
+              "annotated_tactic": [
+                "\"induction' n with n n_ih\"",
+                "[]"
+              ],
+              "state_after": "case succ.right.zero\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\n\u22a2 Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal 0)\n\ncase succ.right.succ\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\n\u22a2 Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal (n + 1))",
+              "state_before": "case succ.right\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\n\u22a2 Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)",
+              "tactic": "induction' n with n n_ih"
+            },
+            {
+              "annotated_tactic": [
+                "\"cases n\"",
+                "[]"
+              ],
+              "state_after": "case zero.zero\n\n\u22a2 (antidiagonalTuple 0 0).Nodup\n\ncase zero.succ\nn\u271d : \u2115\n\u22a2 (antidiagonalTuple 0 (n\u271d + 1)).Nodup",
+              "state_before": "case zero\nn : \u2115\n\u22a2 (antidiagonalTuple 0 n).Nodup",
+              "tactic": "cases n"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case zero.zero\n\n\u22a2 (antidiagonalTuple 0 0).Nodup",
+              "tactic": "simp"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [<a>eq_comm<\\/a>]\"",
+                "[{\"full_name\":\"eq_comm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[811,9],\"def_end_pos\":[811,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case zero.succ\nn\u271d : \u2115\n\u22a2 (antidiagonalTuple 0 (n\u271d + 1)).Nodup",
+              "tactic": "simp [eq_comm]"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro i _\"",
+                "[]"
+              ],
+              "state_after": "case succ.left\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\ni : \u2115 \u00d7 \u2115\na\u271d : i \u2208 antidiagonal n\n\u22a2 (map (fun x => Fin.cons i.1 x) (antidiagonalTuple k i.2)).Nodup",
+              "state_before": "case succ.left\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\n\u22a2 \u2200 x \u2208 antidiagonal n, (map (fun x_1 => Fin.cons x.1 x_1) (antidiagonalTuple k x.2)).Nodup",
+              "tactic": "intro i _"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact (ih i.snd).<a>map<\\/a> (<a>Fin.cons_right_injective<\\/a> (\\u03b1 := fun _ => \\u2115) i.fst)\"",
+                "[{\"full_name\":\"List.Nodup.map\",\"def_path\":\"Mathlib\\/Data\\/List\\/Nodup.lean\",\"def_pos\":[277,19],\"def_end_pos\":[277,28]},{\"full_name\":\"Fin.cons_right_injective\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Basic.lean\",\"def_pos\":[166,9],\"def_end_pos\":[166,29]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case succ.left\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\ni : \u2115 \u00d7 \u2115\na\u271d : i \u2208 antidiagonal n\n\u22a2 (map (fun x => Fin.cons i.1 x) (antidiagonalTuple k i.2)).Nodup",
+              "tactic": "exact (ih i.snd).map (Fin.cons_right_injective (\u03b1 := fun _ => \u2115) i.fst)"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>List.pairwise_singleton<\\/a> _ _\"",
+                "[{\"full_name\":\"List.pairwise_singleton\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Data\\/List\\/Pairwise.lean\",\"def_pos\":[104,9],\"def_end_pos\":[104,27]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case succ.right.zero\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\n\u22a2 Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal 0)",
+              "tactic": "exact List.pairwise_singleton _ _"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>List.Nat.antidiagonal_succ<\\/a>]\"",
+                "[{\"full_name\":\"List.Nat.antidiagonal_succ\",\"def_path\":\"Mathlib\\/Data\\/List\\/NatAntidiagonal.lean\",\"def_pos\":[68,9],\"def_end_pos\":[68,26]}]"
+              ],
+              "state_after": "case succ.right.succ\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\n\u22a2 Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    ((0, n + 1) :: map (Prod.map Nat.succ id) (antidiagonal n))",
+              "state_before": "case succ.right.succ\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\n\u22a2 Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal (n + 1))",
+              "tactic": "rw [List.Nat.antidiagonal_succ]"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine <a>List.Pairwise.cons<\\/a> (fun a ha x hx\\u2081 hx\\u2082 => ?_) (n_ih.map _ fun a b h x hx\\u2081 hx\\u2082 => ?_)\"",
+                "[{\"full_name\":\"List.Pairwise.cons\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Data\\/List\\/Basic.lean\",\"def_pos\":[827,5],\"def_end_pos\":[827,9]}]"
+              ],
+              "state_after": "case succ.right.succ.refine_1\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na : \u2115 \u00d7 \u2115\nha : a \u2208 map (Prod.map Nat.succ id) (antidiagonal n)\nx : Fin (k + 1) \u2192 \u2115\nhx\u2081 : x \u2208 map (fun x => Fin.cons (0, n + 1).1 x) (antidiagonalTuple k (0, n + 1).2)\nhx\u2082 : x \u2208 map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)\n\u22a2 False\n\ncase succ.right.succ.refine_2\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na b : \u2115 \u00d7 \u2115\nh :\n  (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n    (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2))\nx : Fin (k + 1) \u2192 \u2115\nhx\u2081 : x \u2208 map (fun x => Fin.cons (Prod.map Nat.succ id a).1 x) (antidiagonalTuple k (Prod.map Nat.succ id a).2)\nhx\u2082 : x \u2208 map (fun x => Fin.cons (Prod.map Nat.succ id b).1 x) (antidiagonalTuple k (Prod.map Nat.succ id b).2)\n\u22a2 False",
+              "state_before": "case succ.right.succ\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\n\u22a2 Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    ((0, n + 1) :: map (Prod.map Nat.succ id) (antidiagonal n))",
+              "tactic": "refine List.Pairwise.cons (fun a ha x hx\u2081 hx\u2082 => ?_) (n_ih.map _ fun a b h x hx\u2081 hx\u2082 => ?_)"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>List.mem_map<\\/a>] at hx\\u2081 hx\\u2082 ha\"",
+                "[{\"full_name\":\"List.mem_map\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/List\\/Lemmas.lean\",\"def_pos\":[750,17],\"def_end_pos\":[750,24]}]"
+              ],
+              "state_after": "case succ.right.succ.refine_1\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na : \u2115 \u00d7 \u2115\nha : \u2203 a_1 \u2208 antidiagonal n, Prod.map Nat.succ id a_1 = a\nx : Fin (k + 1) \u2192 \u2115\nhx\u2081 : \u2203 a \u2208 antidiagonalTuple k (0, n + 1).2, Fin.cons (0, n + 1).1 a = x\nhx\u2082 : \u2203 a_1 \u2208 antidiagonalTuple k a.2, Fin.cons a.1 a_1 = x\n\u22a2 False",
+              "state_before": "case succ.right.succ.refine_1\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na : \u2115 \u00d7 \u2115\nha : a \u2208 map (Prod.map Nat.succ id) (antidiagonal n)\nx : Fin (k + 1) \u2192 \u2115\nhx\u2081 : x \u2208 map (fun x => Fin.cons (0, n + 1).1 x) (antidiagonalTuple k (0, n + 1).2)\nhx\u2082 : x \u2208 map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)\n\u22a2 False",
+              "tactic": "rw [List.mem_map] at hx\u2081 hx\u2082 ha"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8\\u27e8a, -, rfl\\u27e9, \\u27e8x\\u2081, -, rfl\\u27e9, \\u27e8x\\u2082, -, h\\u27e9\\u27e9 := ha, hx\\u2081, hx\\u2082\"",
+                "[]"
+              ],
+              "state_after": "case succ.right.succ.refine_1.intro.intro.intro.intro.intro.intro\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na : \u2115 \u00d7 \u2115\nx\u2081 x\u2082 : Fin k \u2192 \u2115\nh : Fin.cons (Prod.map Nat.succ id a).1 x\u2082 = Fin.cons (0, n + 1).1 x\u2081\n\u22a2 False",
+              "state_before": "case succ.right.succ.refine_1\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na : \u2115 \u00d7 \u2115\nha : \u2203 a_1 \u2208 antidiagonal n, Prod.map Nat.succ id a_1 = a\nx : Fin (k + 1) \u2192 \u2115\nhx\u2081 : \u2203 a \u2208 antidiagonalTuple k (0, n + 1).2, Fin.cons (0, n + 1).1 a = x\nhx\u2082 : \u2203 a_1 \u2208 antidiagonalTuple k a.2, Fin.cons a.1 a_1 = x\n\u22a2 False",
+              "tactic": "obtain \u27e8\u27e8a, -, rfl\u27e9, \u27e8x\u2081, -, rfl\u27e9, \u27e8x\u2082, -, h\u27e9\u27e9 := ha, hx\u2081, hx\u2082"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Fin.cons_eq_cons<\\/a>] at h\"",
+                "[{\"full_name\":\"Fin.cons_eq_cons\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Basic.lean\",\"def_pos\":[157,9],\"def_end_pos\":[157,21]}]"
+              ],
+              "state_after": "case succ.right.succ.refine_1.intro.intro.intro.intro.intro.intro\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na : \u2115 \u00d7 \u2115\nx\u2081 x\u2082 : Fin k \u2192 \u2115\nh : (Prod.map Nat.succ id a).1 = (0, n + 1).1 \u2227 x\u2082 = x\u2081\n\u22a2 False",
+              "state_before": "case succ.right.succ.refine_1.intro.intro.intro.intro.intro.intro\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na : \u2115 \u00d7 \u2115\nx\u2081 x\u2082 : Fin k \u2192 \u2115\nh : Fin.cons (Prod.map Nat.succ id a).1 x\u2082 = Fin.cons (0, n + 1).1 x\u2081\n\u22a2 False",
+              "tactic": "rw [Fin.cons_eq_cons] at h"
+            },
+            {
+              "annotated_tactic": [
+                "\"injection h.1\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case succ.right.succ.refine_1.intro.intro.intro.intro.intro.intro\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na : \u2115 \u00d7 \u2115\nx\u2081 x\u2082 : Fin k \u2192 \u2115\nh : (Prod.map Nat.succ id a).1 = (0, n + 1).1 \u2227 x\u2082 = x\u2081\n\u22a2 False",
+              "tactic": "injection h.1"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>List.mem_map<\\/a>] at hx\\u2081 hx\\u2082\"",
+                "[{\"full_name\":\"List.mem_map\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/List\\/Lemmas.lean\",\"def_pos\":[750,17],\"def_end_pos\":[750,24]}]"
+              ],
+              "state_after": "case succ.right.succ.refine_2\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na b : \u2115 \u00d7 \u2115\nh :\n  (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n    (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2))\nx : Fin (k + 1) \u2192 \u2115\nhx\u2081 : \u2203 a_1 \u2208 antidiagonalTuple k (Prod.map Nat.succ id a).2, Fin.cons (Prod.map Nat.succ id a).1 a_1 = x\nhx\u2082 : \u2203 a \u2208 antidiagonalTuple k (Prod.map Nat.succ id b).2, Fin.cons (Prod.map Nat.succ id b).1 a = x\n\u22a2 False",
+              "state_before": "case succ.right.succ.refine_2\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na b : \u2115 \u00d7 \u2115\nh :\n  (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n    (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2))\nx : Fin (k + 1) \u2192 \u2115\nhx\u2081 : x \u2208 map (fun x => Fin.cons (Prod.map Nat.succ id a).1 x) (antidiagonalTuple k (Prod.map Nat.succ id a).2)\nhx\u2082 : x \u2208 map (fun x => Fin.cons (Prod.map Nat.succ id b).1 x) (antidiagonalTuple k (Prod.map Nat.succ id b).2)\n\u22a2 False",
+              "tactic": "rw [List.mem_map] at hx\u2081 hx\u2082"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8\\u27e8x\\u2081, hx\\u2081, rfl\\u27e9, \\u27e8x\\u2082, hx\\u2082, h\\u2081\\u2082\\u27e9\\u27e9 := hx\\u2081, hx\\u2082\"",
+                "[]"
+              ],
+              "state_after": "case succ.right.succ.refine_2.intro.intro.intro.intro\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na b : \u2115 \u00d7 \u2115\nh :\n  (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n    (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2))\nx\u2081 : Fin k \u2192 \u2115\nhx\u2081 : x\u2081 \u2208 antidiagonalTuple k (Prod.map Nat.succ id a).2\nx\u2082 : Fin k \u2192 \u2115\nhx\u2082 : x\u2082 \u2208 antidiagonalTuple k (Prod.map Nat.succ id b).2\nh\u2081\u2082 : Fin.cons (Prod.map Nat.succ id b).1 x\u2082 = Fin.cons (Prod.map Nat.succ id a).1 x\u2081\n\u22a2 False",
+              "state_before": "case succ.right.succ.refine_2\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na b : \u2115 \u00d7 \u2115\nh :\n  (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n    (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2))\nx : Fin (k + 1) \u2192 \u2115\nhx\u2081 : \u2203 a_1 \u2208 antidiagonalTuple k (Prod.map Nat.succ id a).2, Fin.cons (Prod.map Nat.succ id a).1 a_1 = x\nhx\u2082 : \u2203 a \u2208 antidiagonalTuple k (Prod.map Nat.succ id b).2, Fin.cons (Prod.map Nat.succ id b).1 a = x\n\u22a2 False",
+              "tactic": "obtain \u27e8\u27e8x\u2081, hx\u2081, rfl\u27e9, \u27e8x\u2082, hx\u2082, h\u2081\u2082\u27e9\u27e9 := hx\u2081, hx\u2082"
+            },
+            {
+              "annotated_tactic": [
+                "\"dsimp at h\\u2081\\u2082\"",
+                "[]"
+              ],
+              "state_after": "case succ.right.succ.refine_2.intro.intro.intro.intro\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na b : \u2115 \u00d7 \u2115\nh :\n  (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n    (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2))\nx\u2081 : Fin k \u2192 \u2115\nhx\u2081 : x\u2081 \u2208 antidiagonalTuple k (Prod.map Nat.succ id a).2\nx\u2082 : Fin k \u2192 \u2115\nhx\u2082 : x\u2082 \u2208 antidiagonalTuple k (Prod.map Nat.succ id b).2\nh\u2081\u2082 : Fin.cons (b.1 + 1) x\u2082 = Fin.cons (a.1 + 1) x\u2081\n\u22a2 False",
+              "state_before": "case succ.right.succ.refine_2.intro.intro.intro.intro\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na b : \u2115 \u00d7 \u2115\nh :\n  (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n    (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2))\nx\u2081 : Fin k \u2192 \u2115\nhx\u2081 : x\u2081 \u2208 antidiagonalTuple k (Prod.map Nat.succ id a).2\nx\u2082 : Fin k \u2192 \u2115\nhx\u2082 : x\u2082 \u2208 antidiagonalTuple k (Prod.map Nat.succ id b).2\nh\u2081\u2082 : Fin.cons (Prod.map Nat.succ id b).1 x\u2082 = Fin.cons (Prod.map Nat.succ id a).1 x\u2081\n\u22a2 False",
+              "tactic": "dsimp at h\u2081\u2082"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Fin.cons_eq_cons<\\/a>, <a>Nat.succ_inj'<\\/a>] at h\\u2081\\u2082\"",
+                "[{\"full_name\":\"Fin.cons_eq_cons\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Basic.lean\",\"def_pos\":[157,9],\"def_end_pos\":[157,21]},{\"full_name\":\"Nat.succ_inj'\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[633,9],\"def_end_pos\":[633,18]}]"
+              ],
+              "state_after": "case succ.right.succ.refine_2.intro.intro.intro.intro\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na b : \u2115 \u00d7 \u2115\nh :\n  (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n    (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2))\nx\u2081 : Fin k \u2192 \u2115\nhx\u2081 : x\u2081 \u2208 antidiagonalTuple k (Prod.map Nat.succ id a).2\nx\u2082 : Fin k \u2192 \u2115\nhx\u2082 : x\u2082 \u2208 antidiagonalTuple k (Prod.map Nat.succ id b).2\nh\u2081\u2082 : b.1 = a.1 \u2227 x\u2082 = x\u2081\n\u22a2 False",
+              "state_before": "case succ.right.succ.refine_2.intro.intro.intro.intro\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na b : \u2115 \u00d7 \u2115\nh :\n  (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n    (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2))\nx\u2081 : Fin k \u2192 \u2115\nhx\u2081 : x\u2081 \u2208 antidiagonalTuple k (Prod.map Nat.succ id a).2\nx\u2082 : Fin k \u2192 \u2115\nhx\u2082 : x\u2082 \u2208 antidiagonalTuple k (Prod.map Nat.succ id b).2\nh\u2081\u2082 : Fin.cons (b.1 + 1) x\u2082 = Fin.cons (a.1 + 1) x\u2081\n\u22a2 False",
+              "tactic": "rw [Fin.cons_eq_cons, Nat.succ_inj'] at h\u2081\u2082"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8h\\u2081\\u2082, rfl\\u27e9 := h\\u2081\\u2082\"",
+                "[]"
+              ],
+              "state_after": "case succ.right.succ.refine_2.intro.intro.intro.intro.intro\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na b : \u2115 \u00d7 \u2115\nh :\n  (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n    (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2))\nx\u2082 : Fin k \u2192 \u2115\nhx\u2082 : x\u2082 \u2208 antidiagonalTuple k (Prod.map Nat.succ id b).2\nh\u2081\u2082 : b.1 = a.1\nhx\u2081 : x\u2082 \u2208 antidiagonalTuple k (Prod.map Nat.succ id a).2\n\u22a2 False",
+              "state_before": "case succ.right.succ.refine_2.intro.intro.intro.intro\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na b : \u2115 \u00d7 \u2115\nh :\n  (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n    (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2))\nx\u2081 : Fin k \u2192 \u2115\nhx\u2081 : x\u2081 \u2208 antidiagonalTuple k (Prod.map Nat.succ id a).2\nx\u2082 : Fin k \u2192 \u2115\nhx\u2082 : x\u2082 \u2208 antidiagonalTuple k (Prod.map Nat.succ id b).2\nh\u2081\u2082 : b.1 = a.1 \u2227 x\u2082 = x\u2081\n\u22a2 False",
+              "tactic": "obtain \u27e8h\u2081\u2082, rfl\u27e9 := h\u2081\u2082"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [h\\u2081\\u2082] at h\"",
+                "[]"
+              ],
+              "state_after": "case succ.right.succ.refine_2.intro.intro.intro.intro.intro\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na b : \u2115 \u00d7 \u2115\nh :\n  (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n    (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k b.2))\nx\u2082 : Fin k \u2192 \u2115\nhx\u2082 : x\u2082 \u2208 antidiagonalTuple k (Prod.map Nat.succ id b).2\nh\u2081\u2082 : b.1 = a.1\nhx\u2081 : x\u2082 \u2208 antidiagonalTuple k (Prod.map Nat.succ id a).2\n\u22a2 False",
+              "state_before": "case succ.right.succ.refine_2.intro.intro.intro.intro.intro\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na b : \u2115 \u00d7 \u2115\nh :\n  (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n    (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2))\nx\u2082 : Fin k \u2192 \u2115\nhx\u2082 : x\u2082 \u2208 antidiagonalTuple k (Prod.map Nat.succ id b).2\nh\u2081\u2082 : b.1 = a.1\nhx\u2081 : x\u2082 \u2208 antidiagonalTuple k (Prod.map Nat.succ id a).2\n\u22a2 False",
+              "tactic": "rw [h\u2081\u2082] at h"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact h (<a>List.mem_map_of_mem<\\/a> _ hx\\u2081) (<a>List.mem_map_of_mem<\\/a> _ hx\\u2082)\"",
+                "[{\"full_name\":\"List.mem_map_of_mem\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/List\\/Lemmas.lean\",\"def_pos\":[756,9],\"def_end_pos\":[756,23]},{\"full_name\":\"List.mem_map_of_mem\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/List\\/Lemmas.lean\",\"def_pos\":[756,9],\"def_end_pos\":[756,23]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case succ.right.succ.refine_2.intro.intro.intro.intro.intro\nk : \u2115\nih : \u2200 (n : \u2115), (antidiagonalTuple k n).Nodup\nn : \u2115\nn_ih :\n  Pairwise\n    (fun a b =>\n      (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n        (map (fun x => Fin.cons b.1 x) (antidiagonalTuple k b.2)))\n    (antidiagonal n)\na b : \u2115 \u00d7 \u2115\nh :\n  (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k a.2)).Disjoint\n    (map (fun x => Fin.cons a.1 x) (antidiagonalTuple k b.2))\nx\u2082 : Fin k \u2192 \u2115\nhx\u2082 : x\u2082 \u2208 antidiagonalTuple k (Prod.map Nat.succ id b).2\nh\u2081\u2082 : b.1 = a.1\nhx\u2081 : x\u2082 \u2208 antidiagonalTuple k (Prod.map Nat.succ id a).2\n\u22a2 False",
+              "tactic": "exact h (List.mem_map_of_mem _ hx\u2081) (List.mem_map_of_mem _ hx\u2082)"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Multiset.Nat.antidiagonalTuple_one",
+        "id": "Multiset.Nat.antidiagonalTuple_one",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            209,
+            49
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean",
+          "full_name": "Multiset.Nat.antidiagonalTuple_one",
+          "start": [
+            208,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Multiset.Nat.antidiagonalTuple_two",
+        "id": "Multiset.Nat.antidiagonalTuple_two",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            214,
+            49
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean",
+          "full_name": "Multiset.Nat.antidiagonalTuple_two",
+          "start": [
+            212,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Multiset.Nat.antidiagonalTuple_zero_right",
+        "id": "Multiset.Nat.antidiagonalTuple_zero_right",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            204,
+            56
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean",
+          "full_name": "Multiset.Nat.antidiagonalTuple_zero_right",
+          "start": [
+            203,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Multiset.Nat.antidiagonalTuple_zero_succ",
+        "id": "Multiset.Nat.antidiagonalTuple_zero_succ",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            191,
+            6
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean",
+          "full_name": "Multiset.Nat.antidiagonalTuple_zero_succ",
+          "start": [
+            190,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Multiset.Nat.antidiagonalTuple_zero_zero",
+        "id": "Multiset.Nat.antidiagonalTuple_zero_zero",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            186,
+            6
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean",
+          "full_name": "Multiset.Nat.antidiagonalTuple_zero_zero",
+          "start": [
+            185,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Multiset.Nat.mem_antidiagonalTuple",
+        "id": "Multiset.Nat.mem_antidiagonalTuple",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            196,
+            33
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean",
+          "full_name": "Multiset.Nat.mem_antidiagonalTuple",
+          "start": [
+            194,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Multiset.Nat.nodup_antidiagonalTuple",
+        "id": "Multiset.Nat.nodup_antidiagonalTuple",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            200,
+            39
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean",
+          "full_name": "Multiset.Nat.nodup_antidiagonalTuple",
+          "start": [
+            199,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean"
+      }
+    ],
+    "input_proofs": 33,
+    "input_units": 2,
+    "proofs": 4,
+    "published_proofs": 4,
+    "published_transitions": 14,
+    "replay_failures": [],
+    "transitions": 14,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000897-0000-d6895874413203e3.parquet",
+      "sha256": "d6895874413203e37eca1b67d8969fda53fa2ab900e77d0bb36ffe99337dd384",
+      "bytes": 59387,
+      "rows": 14,
+      "revision": "9931f7e263b644970d94314c5ccd8bc8f7920aee"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:List.Nat.antidiagonalTuple_one",
+    "mathlib:List.Nat.antidiagonalTuple_two",
+    "mathlib:List.Nat.antidiagonalTuple_zero_right",
+    "mathlib:liftFun_vecCons"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Fin/Tuple/Monotone.lean\",null,null,\"liftFun_vecCons\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean\",null,null,\"List.Nat.antidiagonalTuple_one\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean\",null,null,\"List.Nat.antidiagonalTuple_two\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean\",null,null,\"List.Nat.antidiagonalTuple_zero_right\"]"
+  ]
+}

manifests/batches/mathlib/000898.json

@@ -0,0 +1,838 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000898",
+  "batch_fingerprint": "ce59cda6a8b259a59c37dc34e9a1d985d7f005a79e5eadcbbdfd70afa416e554",
+  "evidence": {
+    "batch_fingerprint": "ce59cda6a8b259a59c37dc34e9a1d985d7f005a79e5eadcbbdfd70afa416e554",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "FinVec.etaExpand_eq",
+        "id": "FinVec.etaExpand_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            89,
+            14
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Reflection.lean",
+          "full_name": "FinVec.etaExpand_eq",
+          "start": [
+            88,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Reflection.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "FinVec.map_eq",
+        "id": "FinVec.map_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            70,
+            13
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Reflection.lean",
+          "full_name": "FinVec.map_eq",
+          "start": [
+            69,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Reflection.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Tuple.antitone_pair_of_not_sorted",
+        "id": "Tuple.antitone_pair_of_not_sorted",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            214,
+            61
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Sort.lean",
+          "full_name": "Tuple.antitone_pair_of_not_sorted",
+          "start": [
+            213,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Sort.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Tuple.comp_sort_eq_comp_iff_monotone",
+        "id": "Tuple.comp_sort_eq_comp_iff_monotone",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            194,
+            84
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Sort.lean",
+          "full_name": "Tuple.comp_sort_eq_comp_iff_monotone",
+          "start": [
+            193,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Sort.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Tuple.graphEquiv\u2082_apply",
+        "id": "Tuple.graphEquiv\u2082_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            92,
+            44
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Sort.lean",
+          "full_name": "Tuple.graphEquiv\u2082_apply",
+          "start": [
+            90,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Sort.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Tuple.lt_card_ge_iff_apply_ge_of_antitone",
+        "id": "Tuple.lt_card_ge_iff_apply_ge_of_antitone",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            150,
+            83
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Sort.lean",
+          "full_name": "Tuple.lt_card_ge_iff_apply_ge_of_antitone",
+          "start": [
+            147,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Sort.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'refine \u27e8h1 j, fun h \u21a6 ?_\u27e9'",
+        "full_name": "Tuple.lt_card_le_iff_apply_le_of_monotone",
+        "id": "Tuple.lt_card_le_iff_apply_le_of_monotone",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            145,
+            48
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Sort.lean",
+          "full_name": "Tuple.lt_card_le_iff_apply_le_of_monotone",
+          "start": [
+            120,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"suffices h1 : \\u2200 k : <a>Fin<\\/a> m, (k < <a>Fintype.card<\\/a> {i \\/\\/ f i \\u2264 a}) \\u2192 f k \\u2264 a by\\n    refine \\u27e8h1 j, fun h \\u21a6 ?_\\u27e9\\n    by_contra! hc\\n    let p : <a>Fin<\\/a> m \\u2192 Prop := fun x \\u21a6 f x \\u2264 a\\n    let q : <a>Fin<\\/a> m \\u2192 Prop := fun x \\u21a6 x < <a>Fintype.card<\\/a> {i \\/\\/ f i \\u2264 a}\\n    let q' : {i \\/\\/ f i \\u2264 a} \\u2192 Prop := fun x \\u21a6 q x\\n    have hw : 0 < <a>Fintype.card<\\/a> {j : {x : <a>Fin<\\/a> m \\/\\/ f x \\u2264 a} \\/\\/ \\u00ac q' j} :=\\n      <a>Fintype.card_pos_iff<\\/a>.2 \\u27e8\\u27e8\\u27e8j, h\\u27e9, <a>not_lt<\\/a>.2 hc\\u27e9\\u27e9\\n    apply hw.ne'\\n    have he := <a>Fintype.card_congr<\\/a> <| <a>Equiv.sumCompl<\\/a> <| q'\\n    have h4 := (<a>Fintype.card_congr<\\/a> (@<a>Equiv.subtypeSubtypeEquivSubtype<\\/a> _ p q (h1 _)))\\n    have h_le : <a>Fintype.card<\\/a> { i \\/\\/ f i \\u2264 a } \\u2264 m := by\\n      conv_rhs => rw [\\u2190 <a>Fintype.card_fin<\\/a> m]\\n      exact <a>Fintype.card_subtype_le<\\/a> _\\n    rwa [<a>Fintype.card_sum<\\/a>, h4, <a>Fintype.card_fin_lt_of_le<\\/a> h_le, <a>add_right_eq_self<\\/a>] at he\"",
+                "[{\"full_name\":\"Fin\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1831,11],\"def_end_pos\":[1831,14]},{\"full_name\":\"Fintype.card\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[63,5],\"def_end_pos\":[63,9]},{\"full_name\":\"Fin\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1831,11],\"def_end_pos\":[1831,14]},{\"full_name\":\"Fin\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1831,11],\"def_end_pos\":[1831,14]},{\"full_name\":\"Fintype.card\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[63,5],\"def_end_pos\":[63,9]},{\"full_name\":\"Fintype.card\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[63,5],\"def_end_pos\":[63,9]},{\"full_name\":\"Fin\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1831,11],\"def_end_pos\":[1831,14]},{\"full_name\":\"Fintype.card_pos_iff\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[560,9],\"def_end_pos\":[560,21]},{\"full_name\":\"not_lt\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[370,9],\"def_end_pos\":[370,15]},{\"full_name\":\"Fintype.card_congr\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[151,9],\"def_end_pos\":[151,19]},{\"full_name\":\"Equiv.sumCompl\",\"def_path\":\"Mathlib\\/Logic\\/Equiv\\/Basic.lean\",\"def_pos\":[574,5],\"def_end_pos\":[574,13]},{\"full_name\":\"Fintype.card_congr\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[151,9],\"def_end_pos\":[151,19]},{\"full_name\":\"Equiv.subtypeSubtypeEquivSubtype\",\"def_path\":\"Mathlib\\/Logic\\/Equiv\\/Basic.lean\",\"def_pos\":[1275,5],\"def_end_pos\":[1275,31]},{\"full_name\":\"Fintype.card\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[63,5],\"def_end_pos\":[63,9]},{\"full_name\":\"Fintype.card_fin\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[311,9],\"def_end_pos\":[311,25]},{\"full_name\":\"Fintype.card_subtype_le\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[872,9],\"def_end_pos\":[872,32]},{\"full_name\":\"Fintype.card_sum\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Sum.lean\",\"def_pos\":[36,9],\"def_end_pos\":[36,25]},{\"full_name\":\"Fintype.card_fin_lt_of_le\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[315,9],\"def_end_pos\":[315,34]},{\"full_name\":\"add_right_eq_self\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[322,3],\"def_end_pos\":[322,14]}]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\n\u22a2 \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\n\u22a2 \u2191j < Fintype.card { i // f i \u2264 a } \u2194 f j \u2264 a",
+              "tactic": "suffices h1 : \u2200 k : Fin m, (k < Fintype.card {i // f i \u2264 a}) \u2192 f k \u2264 a by\n  refine \u27e8h1 j, fun h \u21a6 ?_\u27e9\n  by_contra! hc\n  let p : Fin m \u2192 Prop := fun x \u21a6 f x \u2264 a\n  let q : Fin m \u2192 Prop := fun x \u21a6 x < Fintype.card {i // f i \u2264 a}\n  let q' : {i // f i \u2264 a} \u2192 Prop := fun x \u21a6 q x\n  have hw : 0 < Fintype.card {j : {x : Fin m // f x \u2264 a} // \u00ac q' j} :=\n    Fintype.card_pos_iff.2 \u27e8\u27e8\u27e8j, h\u27e9, not_lt.2 hc\u27e9\u27e9\n  apply hw.ne'\n  have he := Fintype.card_congr <| Equiv.sumCompl <| q'\n  have h4 := (Fintype.card_congr (@Equiv.subtypeSubtypeEquivSubtype _ p q (h1 _)))\n  have h_le : Fintype.card { i // f i \u2264 a } \u2264 m := by\n    conv_rhs => rw [\u2190 Fintype.card_fin m]\n    exact Fintype.card_subtype_le _\n  rwa [Fintype.card_sum, h4, Fintype.card_fin_lt_of_le h_le, add_right_eq_self] at he"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro _ h\"",
+                "[]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj k\u271d : Fin m\nh : \u2191k\u271d < Fintype.card { i // f i \u2264 a }\n\u22a2 f k\u271d \u2264 a",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\n\u22a2 \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a",
+              "tactic": "intro _ h"
+            },
+            {
+              "annotated_tactic": [
+                "\"contrapose! h\"",
+                "[]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj k\u271d : Fin m\nh : \u00acf k\u271d \u2264 a\n\u22a2 Fintype.card { i // f i \u2264 a } \u2264 \u2191k\u271d",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj k\u271d : Fin m\nh : \u2191k\u271d < Fintype.card { i // f i \u2264 a }\n\u22a2 f k\u271d \u2264 a",
+              "tactic": "contrapose! h"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>Fin.card_Iio<\\/a>, <a>Fintype.card_subtype<\\/a>]\"",
+                "[{\"full_name\":\"Fin.card_Iio\",\"def_path\":\"Mathlib\\/Order\\/Interval\\/Finset\\/Fin.lean\",\"def_pos\":[235,9],\"def_end_pos\":[235,17]},{\"full_name\":\"Fintype.card_subtype\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[883,9],\"def_end_pos\":[883,29]}]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj k\u271d : Fin m\nh : \u00acf k\u271d \u2264 a\n\u22a2 (Finset.filter (fun i => f i \u2264 a) Finset.univ).card \u2264 (Finset.Iio k\u271d).card",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj k\u271d : Fin m\nh : \u00acf k\u271d \u2264 a\n\u22a2 Fintype.card { i // f i \u2264 a } \u2264 \u2191k\u271d",
+              "tactic": "rw [\u2190 Fin.card_Iio, Fintype.card_subtype]"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine <a>Finset.card_mono<\\/a> (fun i => <a>Function.mtr<\\/a> ?_)\"",
+                "[{\"full_name\":\"Finset.card_mono\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,18]},{\"full_name\":\"Function.mtr\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[398,19],\"def_end_pos\":[398,31]}]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj k\u271d : Fin m\nh : \u00acf k\u271d \u2264 a\ni : Fin m\n\u22a2 i \u2209 Finset.Iio k\u271d \u2192 i \u2209 Finset.filter (fun i => f i \u2264 a) Finset.univ",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj k\u271d : Fin m\nh : \u00acf k\u271d \u2264 a\n\u22a2 (Finset.filter (fun i => f i \u2264 a) Finset.univ).card \u2264 (Finset.Iio k\u271d).card",
+              "tactic": "refine Finset.card_mono (fun i => Function.mtr ?_)"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp_rw [<a>Finset.mem_filter<\\/a>, <a>Finset.mem_univ<\\/a>, <a>true_and<\\/a>, <a>Finset.mem_Iio<\\/a>]\"",
+                "[{\"full_name\":\"Finset.mem_filter\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[2593,9],\"def_end_pos\":[2593,19]},{\"full_name\":\"Finset.mem_univ\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Basic.lean\",\"def_pos\":[75,9],\"def_end_pos\":[75,17]},{\"full_name\":\"true_and\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[105,17],\"def_end_pos\":[105,25]},{\"full_name\":\"Finset.mem_Iio\",\"def_path\":\"Mathlib\\/Order\\/Interval\\/Finset\\/Defs.lean\",\"def_pos\":[410,9],\"def_end_pos\":[410,16]}]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj k\u271d : Fin m\nh : \u00acf k\u271d \u2264 a\ni : Fin m\n\u22a2 \u00aci < k\u271d \u2192 \u00acf i \u2264 a",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj k\u271d : Fin m\nh : \u00acf k\u271d \u2264 a\ni : Fin m\n\u22a2 i \u2209 Finset.Iio k\u271d \u2192 i \u2209 Finset.filter (fun i => f i \u2264 a) Finset.univ",
+              "tactic": "simp_rw [Finset.mem_filter, Finset.mem_univ, true_and, Finset.mem_Iio]"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro hij hia\"",
+                "[]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj k\u271d : Fin m\nh : \u00acf k\u271d \u2264 a\ni : Fin m\nhij : \u00aci < k\u271d\nhia : f i \u2264 a\n\u22a2 False",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj k\u271d : Fin m\nh : \u00acf k\u271d \u2264 a\ni : Fin m\n\u22a2 \u00aci < k\u271d \u2192 \u00acf i \u2264 a",
+              "tactic": "intro hij hia"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply h\"",
+                "[]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj k\u271d : Fin m\nh : \u00acf k\u271d \u2264 a\ni : Fin m\nhij : \u00aci < k\u271d\nhia : f i \u2264 a\n\u22a2 f k\u271d \u2264 a",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj k\u271d : Fin m\nh : \u00acf k\u271d \u2264 a\ni : Fin m\nhij : \u00aci < k\u271d\nhia : f i \u2264 a\n\u22a2 False",
+              "tactic": "apply h"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact (h_sorted (<a>le_of_not_lt<\\/a> hij)).<a>trans<\\/a> hia\"",
+                "[{\"full_name\":\"le_of_not_lt\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[323,9],\"def_end_pos\":[323,21]},{\"full_name\":\"LE.le.trans\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[115,7],\"def_end_pos\":[115,18]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj k\u271d : Fin m\nh : \u00acf k\u271d \u2264 a\ni : Fin m\nhij : \u00aci < k\u271d\nhia : f i \u2264 a\n\u22a2 f k\u271d \u2264 a",
+              "tactic": "exact (h_sorted (le_of_not_lt hij)).trans hia"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine \\u27e8h1 j, fun h \\u21a6 ?_\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\n\u22a2 \u2191j < Fintype.card { i // f i \u2264 a }",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\n\u22a2 \u2191j < Fintype.card { i // f i \u2264 a } \u2194 f j \u2264 a",
+              "tactic": "refine \u27e8h1 j, fun h \u21a6 ?_\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"by_contra! hc\"",
+                "[]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\n\u22a2 False",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\n\u22a2 \u2191j < Fintype.card { i // f i \u2264 a }",
+              "tactic": "by_contra! hc"
+            },
+            {
+              "annotated_tactic": [
+                "\"let p : <a>Fin<\\/a> m \\u2192 Prop := fun x \\u21a6 f x \\u2264 a\"",
+                "[{\"full_name\":\"Fin\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1831,11],\"def_end_pos\":[1831,14]}]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\n\u22a2 False",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\n\u22a2 False",
+              "tactic": "let p : Fin m \u2192 Prop := fun x \u21a6 f x \u2264 a"
+            },
+            {
+              "annotated_tactic": [
+                "\"let q : <a>Fin<\\/a> m \\u2192 Prop := fun x \\u21a6 x < <a>Fintype.card<\\/a> {i \\/\\/ f i \\u2264 a}\"",
+                "[{\"full_name\":\"Fin\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1831,11],\"def_end_pos\":[1831,14]},{\"full_name\":\"Fintype.card\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[63,5],\"def_end_pos\":[63,9]}]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\nq : Fin m \u2192 Prop := fun x => \u2191x < Fintype.card { i // f i \u2264 a }\n\u22a2 False",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\n\u22a2 False",
+              "tactic": "let q : Fin m \u2192 Prop := fun x \u21a6 x < Fintype.card {i // f i \u2264 a}"
+            },
+            {
+              "annotated_tactic": [
+                "\"let q' : {i \\/\\/ f i \\u2264 a} \\u2192 Prop := fun x \\u21a6 q x\"",
+                "[]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\nq : Fin m \u2192 Prop := fun x => \u2191x < Fintype.card { i // f i \u2264 a }\nq' : { i // f i \u2264 a } \u2192 Prop := fun x => q \u2191x\n\u22a2 False",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\nq : Fin m \u2192 Prop := fun x => \u2191x < Fintype.card { i // f i \u2264 a }\n\u22a2 False",
+              "tactic": "let q' : {i // f i \u2264 a} \u2192 Prop := fun x \u21a6 q x"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hw : 0 < <a>Fintype.card<\\/a> {j : {x : <a>Fin<\\/a> m \\/\\/ f x \\u2264 a} \\/\\/ \\u00ac q' j} :=\\n      <a>Fintype.card_pos_iff<\\/a>.2 \\u27e8\\u27e8\\u27e8j, h\\u27e9, <a>not_lt<\\/a>.2 hc\\u27e9\\u27e9\"",
+                "[{\"full_name\":\"Fintype.card\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[63,5],\"def_end_pos\":[63,9]},{\"full_name\":\"Fin\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1831,11],\"def_end_pos\":[1831,14]},{\"full_name\":\"Fintype.card_pos_iff\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[560,9],\"def_end_pos\":[560,21]},{\"full_name\":\"not_lt\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[370,9],\"def_end_pos\":[370,15]}]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\nq : Fin m \u2192 Prop := fun x => \u2191x < Fintype.card { i // f i \u2264 a }\nq' : { i // f i \u2264 a } \u2192 Prop := fun x => q \u2191x\nhw : 0 < Fintype.card { j // \u00acq' j }\n\u22a2 False",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\nq : Fin m \u2192 Prop := fun x => \u2191x < Fintype.card { i // f i \u2264 a }\nq' : { i // f i \u2264 a } \u2192 Prop := fun x => q \u2191x\n\u22a2 False",
+              "tactic": "have hw : 0 < Fintype.card {j : {x : Fin m // f x \u2264 a} // \u00ac q' j} :=\n  Fintype.card_pos_iff.2 \u27e8\u27e8\u27e8j, h\u27e9, not_lt.2 hc\u27e9\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply hw.ne'\"",
+                "[]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\nq : Fin m \u2192 Prop := fun x => \u2191x < Fintype.card { i // f i \u2264 a }\nq' : { i // f i \u2264 a } \u2192 Prop := fun x => q \u2191x\nhw : 0 < Fintype.card { j // \u00acq' j }\n\u22a2 Fintype.card { j // \u00acq' j } = 0",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\nq : Fin m \u2192 Prop := fun x => \u2191x < Fintype.card { i // f i \u2264 a }\nq' : { i // f i \u2264 a } \u2192 Prop := fun x => q \u2191x\nhw : 0 < Fintype.card { j // \u00acq' j }\n\u22a2 False",
+              "tactic": "apply hw.ne'"
+            },
+            {
+              "annotated_tactic": [
+                "\"have he := <a>Fintype.card_congr<\\/a> <| <a>Equiv.sumCompl<\\/a> <| q'\"",
+                "[{\"full_name\":\"Fintype.card_congr\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[151,9],\"def_end_pos\":[151,19]},{\"full_name\":\"Equiv.sumCompl\",\"def_path\":\"Mathlib\\/Logic\\/Equiv\\/Basic.lean\",\"def_pos\":[574,5],\"def_end_pos\":[574,13]}]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\nq : Fin m \u2192 Prop := fun x => \u2191x < Fintype.card { i // f i \u2264 a }\nq' : { i // f i \u2264 a } \u2192 Prop := fun x => q \u2191x\nhw : 0 < Fintype.card { j // \u00acq' j }\nhe : Fintype.card ({ a // q' a } \u2295 { a // \u00acq' a }) = Fintype.card { i // f i \u2264 a }\n\u22a2 Fintype.card { j // \u00acq' j } = 0",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\nq : Fin m \u2192 Prop := fun x => \u2191x < Fintype.card { i // f i \u2264 a }\nq' : { i // f i \u2264 a } \u2192 Prop := fun x => q \u2191x\nhw : 0 < Fintype.card { j // \u00acq' j }\n\u22a2 Fintype.card { j // \u00acq' j } = 0",
+              "tactic": "have he := Fintype.card_congr <| Equiv.sumCompl <| q'"
+            },
+            {
+              "annotated_tactic": [
+                "\"have h4 := (<a>Fintype.card_congr<\\/a> (@<a>Equiv.subtypeSubtypeEquivSubtype<\\/a> _ p q (h1 _)))\"",
+                "[{\"full_name\":\"Fintype.card_congr\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[151,9],\"def_end_pos\":[151,19]},{\"full_name\":\"Equiv.subtypeSubtypeEquivSubtype\",\"def_path\":\"Mathlib\\/Logic\\/Equiv\\/Basic.lean\",\"def_pos\":[1275,5],\"def_end_pos\":[1275,31]}]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\nq : Fin m \u2192 Prop := fun x => \u2191x < Fintype.card { i // f i \u2264 a }\nq' : { i // f i \u2264 a } \u2192 Prop := fun x => q \u2191x\nhw : 0 < Fintype.card { j // \u00acq' j }\nhe : Fintype.card ({ a // q' a } \u2295 { a // \u00acq' a }) = Fintype.card { i // f i \u2264 a }\nh4 : Fintype.card { x // q \u2191x } = Fintype.card (Subtype q)\n\u22a2 Fintype.card { j // \u00acq' j } = 0",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\nq : Fin m \u2192 Prop := fun x => \u2191x < Fintype.card { i // f i \u2264 a }\nq' : { i // f i \u2264 a } \u2192 Prop := fun x => q \u2191x\nhw : 0 < Fintype.card { j // \u00acq' j }\nhe : Fintype.card ({ a // q' a } \u2295 { a // \u00acq' a }) = Fintype.card { i // f i \u2264 a }\n\u22a2 Fintype.card { j // \u00acq' j } = 0",
+              "tactic": "have h4 := (Fintype.card_congr (@Equiv.subtypeSubtypeEquivSubtype _ p q (h1 _)))"
+            },
+            {
+              "annotated_tactic": [
+                "\"have h_le : <a>Fintype.card<\\/a> { i \\/\\/ f i \\u2264 a } \\u2264 m := by\\n      conv_rhs => rw [\\u2190 <a>Fintype.card_fin<\\/a> m]\\n      exact <a>Fintype.card_subtype_le<\\/a> _\"",
+                "[{\"full_name\":\"Fintype.card\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[63,5],\"def_end_pos\":[63,9]},{\"full_name\":\"Fintype.card_fin\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[311,9],\"def_end_pos\":[311,25]},{\"full_name\":\"Fintype.card_subtype_le\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[872,9],\"def_end_pos\":[872,32]}]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\nq : Fin m \u2192 Prop := fun x => \u2191x < Fintype.card { i // f i \u2264 a }\nq' : { i // f i \u2264 a } \u2192 Prop := fun x => q \u2191x\nhw : 0 < Fintype.card { j // \u00acq' j }\nhe : Fintype.card ({ a // q' a } \u2295 { a // \u00acq' a }) = Fintype.card { i // f i \u2264 a }\nh4 : Fintype.card { x // q \u2191x } = Fintype.card (Subtype q)\nh_le : Fintype.card { i // f i \u2264 a } \u2264 m\n\u22a2 Fintype.card { j // \u00acq' j } = 0",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\nq : Fin m \u2192 Prop := fun x => \u2191x < Fintype.card { i // f i \u2264 a }\nq' : { i // f i \u2264 a } \u2192 Prop := fun x => q \u2191x\nhw : 0 < Fintype.card { j // \u00acq' j }\nhe : Fintype.card ({ a // q' a } \u2295 { a // \u00acq' a }) = Fintype.card { i // f i \u2264 a }\nh4 : Fintype.card { x // q \u2191x } = Fintype.card (Subtype q)\n\u22a2 Fintype.card { j // \u00acq' j } = 0",
+              "tactic": "have h_le : Fintype.card { i // f i \u2264 a } \u2264 m := by\n  conv_rhs => rw [\u2190 Fintype.card_fin m]\n  exact Fintype.card_subtype_le _"
+            },
+            {
+              "annotated_tactic": [
+                "\"rwa [<a>Fintype.card_sum<\\/a>, h4, <a>Fintype.card_fin_lt_of_le<\\/a> h_le, <a>add_right_eq_self<\\/a>] at he\"",
+                "[{\"full_name\":\"Fintype.card_sum\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Sum.lean\",\"def_pos\":[36,9],\"def_end_pos\":[36,25]},{\"full_name\":\"Fintype.card_fin_lt_of_le\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[315,9],\"def_end_pos\":[315,34]},{\"full_name\":\"add_right_eq_self\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[322,3],\"def_end_pos\":[322,14]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\nq : Fin m \u2192 Prop := fun x => \u2191x < Fintype.card { i // f i \u2264 a }\nq' : { i // f i \u2264 a } \u2192 Prop := fun x => q \u2191x\nhw : 0 < Fintype.card { j // \u00acq' j }\nhe : Fintype.card ({ a // q' a } \u2295 { a // \u00acq' a }) = Fintype.card { i // f i \u2264 a }\nh4 : Fintype.card { x // q \u2191x } = Fintype.card (Subtype q)\nh_le : Fintype.card { i // f i \u2264 a } \u2264 m\n\u22a2 Fintype.card { j // \u00acq' j } = 0",
+              "tactic": "rwa [Fintype.card_sum, h4, Fintype.card_fin_lt_of_le h_le, add_right_eq_self] at he"
+            },
+            {
+              "annotated_tactic": [
+                "\"conv_rhs => rw [\\u2190 <a>Fintype.card_fin<\\/a> m]\"",
+                "[{\"full_name\":\"Fintype.card_fin\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[311,9],\"def_end_pos\":[311,25]}]"
+              ],
+              "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\nq : Fin m \u2192 Prop := fun x => \u2191x < Fintype.card { i // f i \u2264 a }\nq' : { i // f i \u2264 a } \u2192 Prop := fun x => q \u2191x\nhw : 0 < Fintype.card { j // \u00acq' j }\nhe : Fintype.card ({ a // q' a } \u2295 { a // \u00acq' a }) = Fintype.card { i // f i \u2264 a }\nh4 : Fintype.card { x // q \u2191x } = Fintype.card (Subtype q)\n\u22a2 Fintype.card { i // f i \u2264 a } \u2264 Fintype.card (Fin m)",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\nq : Fin m \u2192 Prop := fun x => \u2191x < Fintype.card { i // f i \u2264 a }\nq' : { i // f i \u2264 a } \u2192 Prop := fun x => q \u2191x\nhw : 0 < Fintype.card { j // \u00acq' j }\nhe : Fintype.card ({ a // q' a } \u2295 { a // \u00acq' a }) = Fintype.card { i // f i \u2264 a }\nh4 : Fintype.card { x // q \u2191x } = Fintype.card (Subtype q)\n\u22a2 Fintype.card { i // f i \u2264 a } \u2264 m",
+              "tactic": "conv_rhs => rw [\u2190 Fintype.card_fin m]"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>Fintype.card_subtype_le<\\/a> _\"",
+                "[{\"full_name\":\"Fintype.card_subtype_le\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[872,9],\"def_end_pos\":[872,32]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d\u00b9 : PartialOrder \u03b1\ninst\u271d : DecidableRel LE.le\nm : \u2115\nf : Fin m \u2192 \u03b1\na : \u03b1\nh_sorted : Monotone f\nj : Fin m\nh1 : \u2200 (k : Fin m), \u2191k < Fintype.card { i // f i \u2264 a } \u2192 f k \u2264 a\nh : f j \u2264 a\nhc : Fintype.card { i // f i \u2264 a } \u2264 \u2191j\np : Fin m \u2192 Prop := fun x => f x \u2264 a\nq : Fin m \u2192 Prop := fun x => \u2191x < Fintype.card { i // f i \u2264 a }\nq' : { i // f i \u2264 a } \u2192 Prop := fun x => q \u2191x\nhw : 0 < Fintype.card { j // \u00acq' j }\nhe : Fintype.card ({ a // q' a } \u2295 { a // \u00acq' a }) = Fintype.card { i // f i \u2264 a }\nh4 : Fintype.card { x // q \u2191x } = Fintype.card (Subtype q)\n\u22a2 Fintype.card { i // f i \u2264 a } \u2264 Fintype.card (Fin m)",
+              "tactic": "exact Fintype.card_subtype_le _"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Sort.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Tuple.proj_equiv\u2081'",
+        "id": "Tuple.proj_equiv\u2081'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            76,
+            6
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Sort.lean",
+          "full_name": "Tuple.proj_equiv\u2081'",
+          "start": [
+            75,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Sort.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Tuple.unique_monotone",
+        "id": "Tuple.unique_monotone",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            157,
+            38
+          ],
+          "file_path": "Mathlib/Data/Fin/Tuple/Sort.lean",
+          "full_name": "Tuple.unique_monotone",
+          "start": [
+            153,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Fin/Tuple/Sort.lean"
+      }
+    ],
+    "input_proofs": 21,
+    "input_units": 2,
+    "proofs": 12,
+    "published_proofs": 6,
+    "published_transitions": 11,
+    "replay_failures": [],
+    "transitions": 37,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Data/Fin/Tuple/Reflection.lean",
+        "proof_id": "mathlib:FinVec.exists_iff",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              134,
+              92
+            ],
+            "file_path": "Mathlib/Data/Fin/Tuple/Reflection.lean",
+            "full_name": "FinVec.exists_iff",
+            "start": [
+              130,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"simp only [<a>Exists<\\/a>, <a>Fin.exists_fin_zero_pi<\\/a>, <a>Matrix.vecEmpty<\\/a>]\"",
+                  "[{\"full_name\":\"FinVec.Exists\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Reflection.lean\",\"def_pos\":[119,5],\"def_end_pos\":[119,11]},{\"full_name\":\"Fin.exists_fin_zero_pi\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Basic.lean\",\"def_pos\":[255,9],\"def_end_pos\":[255,27]},{\"full_name\":\"Matrix.vecEmpty\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/VecNotation.lean\",\"def_pos\":[50,5],\"def_end_pos\":[50,13]}]"
+                ],
+                "state_after": "m n : \u2115\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nP : (Fin 0 \u2192 \u03b1) \u2192 Prop\n\u22a2 P Fin.elim0 \u2194 P finZeroElim",
+                "state_before": "m n : \u2115\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nP : (Fin 0 \u2192 \u03b1) \u2192 Prop\n\u22a2 Exists P \u2194 \u2203 x, P x",
+                "tactic": "simp only [Exists, Fin.exists_fin_zero_pi, Matrix.vecEmpty]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rfl\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "m n : \u2115\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nP : (Fin 0 \u2192 \u03b1) \u2192 Prop\n\u22a2 P Fin.elim0 \u2194 P finZeroElim",
+                "tactic": "rfl"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp only [<a>Exists<\\/a>, exists_iff, <a>Fin.exists_fin_succ_pi<\\/a>, <a>Matrix.vecCons<\\/a>]\"",
+                  "[{\"full_name\":\"FinVec.Exists\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Reflection.lean\",\"def_pos\":[119,5],\"def_end_pos\":[119,11]},{\"full_name\":\"Fin.exists_fin_succ_pi\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Basic.lean\",\"def_pos\":[264,9],\"def_end_pos\":[264,27]},{\"full_name\":\"Matrix.vecCons\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/VecNotation.lean\",\"def_pos\":[59,5],\"def_end_pos\":[59,12]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "m n\u271d : \u2115\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nn : \u2115\nP : (Fin n.succ \u2192 \u03b1) \u2192 Prop\n\u22a2 Exists P \u2194 \u2203 x, P x",
+                "tactic": "simp only [Exists, exists_iff, Fin.exists_fin_succ_pi, Matrix.vecCons]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "FinVec.exists_iff"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Data/Fin/Tuple/Reflection.lean",
+        "proof_id": "mathlib:FinVec.forall_iff",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              112,
+              92
+            ],
+            "file_path": "Mathlib/Data/Fin/Tuple/Reflection.lean",
+            "full_name": "FinVec.forall_iff",
+            "start": [
+              108,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"simp only [<a>Forall<\\/a>, <a>Fin.forall_fin_zero_pi<\\/a>]\"",
+                  "[{\"full_name\":\"FinVec.Forall\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Reflection.lean\",\"def_pos\":[96,5],\"def_end_pos\":[96,11]},{\"full_name\":\"Fin.forall_fin_zero_pi\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Basic.lean\",\"def_pos\":[249,9],\"def_end_pos\":[249,27]}]"
+                ],
+                "state_after": "m n : \u2115\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nP : (Fin 0 \u2192 \u03b1) \u2192 Prop\n\u22a2 P ![] \u2194 P finZeroElim",
+                "state_before": "m n : \u2115\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nP : (Fin 0 \u2192 \u03b1) \u2192 Prop\n\u22a2 Forall P \u2194 \u2200 (x : Fin 0 \u2192 \u03b1), P x",
+                "tactic": "simp only [Forall, Fin.forall_fin_zero_pi]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rfl\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "m n : \u2115\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nP : (Fin 0 \u2192 \u03b1) \u2192 Prop\n\u22a2 P ![] \u2194 P finZeroElim",
+                "tactic": "rfl"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp only [<a>Forall<\\/a>, forall_iff, <a>Fin.forall_fin_succ_pi<\\/a>, <a>Matrix.vecCons<\\/a>]\"",
+                  "[{\"full_name\":\"FinVec.Forall\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Reflection.lean\",\"def_pos\":[96,5],\"def_end_pos\":[96,11]},{\"full_name\":\"Fin.forall_fin_succ_pi\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Basic.lean\",\"def_pos\":[260,9],\"def_end_pos\":[260,27]},{\"full_name\":\"Matrix.vecCons\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/VecNotation.lean\",\"def_pos\":[59,5],\"def_end_pos\":[59,12]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "m n\u271d : \u2115\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nn : \u2115\nP : (Fin n.succ \u2192 \u03b1) \u2192 Prop\n\u22a2 Forall P \u2194 \u2200 (x : Fin n.succ \u2192 \u03b1), P x",
+                "tactic": "simp only [Forall, forall_iff, Fin.forall_fin_succ_pi, Matrix.vecCons]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "FinVec.forall_iff"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Data/Fin/Tuple/Sort.lean",
+        "proof_id": "mathlib:Tuple.eq_sort_iff",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              182,
+              52
+            ],
+            "file_path": "Mathlib/Data/Fin/Tuple/Sort.lean",
+            "full_name": "Tuple.eq_sort_iff",
+            "start": [
+              176,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>eq_sort_iff'<\\/a>]\"",
+                  "[{\"full_name\":\"Tuple.eq_sort_iff'\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Sort.lean\",\"def_pos\":[164,9],\"def_end_pos\":[164,21]}]"
+                ],
+                "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\n\u22a2 StrictMono \u21d1(Equiv.trans \u03c3 (graphEquiv\u2081 f)) \u2194\n    Monotone (f \u2218 \u21d1\u03c3) \u2227 \u2200 (i j : Fin n), i < j \u2192 f (\u03c3 i) = f (\u03c3 j) \u2192 \u03c3 i < \u03c3 j",
+                "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\n\u22a2 \u03c3 = sort f \u2194 Monotone (f \u2218 \u21d1\u03c3) \u2227 \u2200 (i j : Fin n), i < j \u2192 f (\u03c3 i) = f (\u03c3 j) \u2192 \u03c3 i < \u03c3 j",
+                "tactic": "rw [eq_sort_iff']"
+              },
+              {
+                "annotated_tactic": [
+                  "\"refine \\u27e8fun h => \\u27e8(<a>monotone_proj<\\/a> f).<a>comp<\\/a> h.monotone, fun i j hij hfij => ?_\\u27e9, fun h i j hij => ?_\\u27e9\"",
+                  "[{\"full_name\":\"Tuple.monotone_proj\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Sort.lean\",\"def_pos\":[99,9],\"def_end_pos\":[99,22]},{\"full_name\":\"Monotone.comp\",\"def_path\":\"Mathlib\\/Order\\/Monotone\\/Basic.lean\",\"def_pos\":[690,19],\"def_end_pos\":[690,32]}]"
+                ],
+                "state_after": "case refine_1\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\nh : StrictMono \u21d1(Equiv.trans \u03c3 (graphEquiv\u2081 f))\ni j : Fin n\nhij : i < j\nhfij : f (\u03c3 i) = f (\u03c3 j)\n\u22a2 \u03c3 i < \u03c3 j\n\ncase refine_2\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\nh : Monotone (f \u2218 \u21d1\u03c3) \u2227 \u2200 (i j : Fin n), i < j \u2192 f (\u03c3 i) = f (\u03c3 j) \u2192 \u03c3 i < \u03c3 j\ni j : Fin n\nhij : i < j\n\u22a2 (Equiv.trans \u03c3 (graphEquiv\u2081 f)) i < (Equiv.trans \u03c3 (graphEquiv\u2081 f)) j",
+                "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\n\u22a2 StrictMono \u21d1(Equiv.trans \u03c3 (graphEquiv\u2081 f)) \u2194\n    Monotone (f \u2218 \u21d1\u03c3) \u2227 \u2200 (i j : Fin n), i < j \u2192 f (\u03c3 i) = f (\u03c3 j) \u2192 \u03c3 i < \u03c3 j",
+                "tactic": "refine \u27e8fun h => \u27e8(monotone_proj f).comp h.monotone, fun i j hij hfij => ?_\u27e9, fun h i j hij => ?_\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact (((<a>Prod.Lex.lt_iff<\\/a> _ _).1 <| h hij).<a>resolve_left<\\/a> hfij.not_lt).2\"",
+                  "[{\"full_name\":\"Prod.Lex.lt_iff\",\"def_path\":\"Mathlib\\/Data\\/Prod\\/Lex.lean\",\"def_pos\":[60,9],\"def_end_pos\":[60,15]},{\"full_name\":\"Or.resolve_left\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[555,9],\"def_end_pos\":[555,24]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case refine_1\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\nh : StrictMono \u21d1(Equiv.trans \u03c3 (graphEquiv\u2081 f))\ni j : Fin n\nhij : i < j\nhfij : f (\u03c3 i) = f (\u03c3 j)\n\u22a2 \u03c3 i < \u03c3 j",
+                "tactic": "exact (((Prod.Lex.lt_iff _ _).1 <| h hij).resolve_left hfij.not_lt).2"
+              },
+              {
+                "annotated_tactic": [
+                  "\"obtain he | hl := (h.1 hij.le).<a>eq_or_lt<\\/a> <;> apply (<a>Prod.Lex.lt_iff<\\/a> _ _).2\"",
+                  "[{\"full_name\":\"LE.le.eq_or_lt\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[395,7],\"def_end_pos\":[395,21]},{\"full_name\":\"Prod.Lex.lt_iff\",\"def_path\":\"Mathlib\\/Data\\/Prod\\/Lex.lean\",\"def_pos\":[60,9],\"def_end_pos\":[60,15]}]"
+                ],
+                "state_after": "case refine_2.inl\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\nh : Monotone (f \u2218 \u21d1\u03c3) \u2227 \u2200 (i j : Fin n), i < j \u2192 f (\u03c3 i) = f (\u03c3 j) \u2192 \u03c3 i < \u03c3 j\ni j : Fin n\nhij : i < j\nhe : (f \u2218 \u21d1\u03c3) i = (f \u2218 \u21d1\u03c3) j\n\u22a2 (f (\u03c3 i), \u03c3 i).1 < (f (\u03c3 j), \u03c3 j).1 \u2228 (f (\u03c3 i), \u03c3 i).1 = (f (\u03c3 j), \u03c3 j).1 \u2227 (f (\u03c3 i), \u03c3 i).2 < (f (\u03c3 j), \u03c3 j).2\n\ncase refine_2.inr\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\nh : Monotone (f \u2218 \u21d1\u03c3) \u2227 \u2200 (i j : Fin n), i < j \u2192 f (\u03c3 i) = f (\u03c3 j) \u2192 \u03c3 i < \u03c3 j\ni j : Fin n\nhij : i < j\nhl : (f \u2218 \u21d1\u03c3) i < (f \u2218 \u21d1\u03c3) j\n\u22a2 (f (\u03c3 i), \u03c3 i).1 < (f (\u03c3 j), \u03c3 j).1 \u2228 (f (\u03c3 i), \u03c3 i).1 = (f (\u03c3 j), \u03c3 j).1 \u2227 (f (\u03c3 i), \u03c3 i).2 < (f (\u03c3 j), \u03c3 j).2",
+                "state_before": "case refine_2\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\nh : Monotone (f \u2218 \u21d1\u03c3) \u2227 \u2200 (i j : Fin n), i < j \u2192 f (\u03c3 i) = f (\u03c3 j) \u2192 \u03c3 i < \u03c3 j\ni j : Fin n\nhij : i < j\n\u22a2 (Equiv.trans \u03c3 (graphEquiv\u2081 f)) i < (Equiv.trans \u03c3 (graphEquiv\u2081 f)) j",
+                "tactic": "obtain he | hl := (h.1 hij.le).eq_or_lt <;> apply (Prod.Lex.lt_iff _ _).2"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exacts [<a>Or.inr<\\/a> \\u27e8he, h.2 i j hij he\\u27e9, <a>Or.inl<\\/a> hl]\"",
+                  "[{\"full_name\":\"Or.inr\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[536,5],\"def_end_pos\":[536,8]},{\"full_name\":\"Or.inl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[534,5],\"def_end_pos\":[534,8]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case refine_2.inl\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\nh : Monotone (f \u2218 \u21d1\u03c3) \u2227 \u2200 (i j : Fin n), i < j \u2192 f (\u03c3 i) = f (\u03c3 j) \u2192 \u03c3 i < \u03c3 j\ni j : Fin n\nhij : i < j\nhe : (f \u2218 \u21d1\u03c3) i = (f \u2218 \u21d1\u03c3) j\n\u22a2 (f (\u03c3 i), \u03c3 i).1 < (f (\u03c3 j), \u03c3 j).1 \u2228 (f (\u03c3 i), \u03c3 i).1 = (f (\u03c3 j), \u03c3 j).1 \u2227 (f (\u03c3 i), \u03c3 i).2 < (f (\u03c3 j), \u03c3 j).2\n\ncase refine_2.inr\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\nh : Monotone (f \u2218 \u21d1\u03c3) \u2227 \u2200 (i j : Fin n), i < j \u2192 f (\u03c3 i) = f (\u03c3 j) \u2192 \u03c3 i < \u03c3 j\ni j : Fin n\nhij : i < j\nhl : (f \u2218 \u21d1\u03c3) i < (f \u2218 \u21d1\u03c3) j\n\u22a2 (f (\u03c3 i), \u03c3 i).1 < (f (\u03c3 j), \u03c3 j).1 \u2228 (f (\u03c3 i), \u03c3 i).1 = (f (\u03c3 j), \u03c3 j).1 \u2227 (f (\u03c3 i), \u03c3 i).2 < (f (\u03c3 j), \u03c3 j).2",
+                "tactic": "exacts [Or.inr \u27e8he, h.2 i j hij he\u27e9, Or.inl hl]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Tuple.eq_sort_iff"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Data/Fin/Tuple/Sort.lean",
+        "proof_id": "mathlib:Tuple.eq_sort_iff'",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              170,
+              88
+            ],
+            "file_path": "Mathlib/Data/Fin/Tuple/Sort.lean",
+            "full_name": "Tuple.eq_sort_iff'",
+            "start": [
+              164,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"constructor <;> intro h\"",
+                  "[]"
+                ],
+                "state_after": "case mp\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\nh : \u03c3 = sort f\n\u22a2 StrictMono \u21d1(Equiv.trans \u03c3 (graphEquiv\u2081 f))\n\ncase mpr\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\nh : StrictMono \u21d1(Equiv.trans \u03c3 (graphEquiv\u2081 f))\n\u22a2 \u03c3 = sort f",
+                "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\n\u22a2 \u03c3 = sort f \u2194 StrictMono \u21d1(Equiv.trans \u03c3 (graphEquiv\u2081 f))",
+                "tactic": "constructor <;> intro h"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [h, <a>sort<\\/a>, <a>Equiv.trans_assoc<\\/a>, <a>Equiv.symm_trans_self<\\/a>]\"",
+                  "[{\"full_name\":\"Tuple.sort\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Sort.lean\",\"def_pos\":[86,5],\"def_end_pos\":[86,9]},{\"full_name\":\"Equiv.trans_assoc\",\"def_path\":\"Mathlib\\/Logic\\/Equiv\\/Defs.lean\",\"def_pos\":[371,9],\"def_end_pos\":[371,20]},{\"full_name\":\"Equiv.symm_trans_self\",\"def_path\":\"Mathlib\\/Logic\\/Equiv\\/Defs.lean\",\"def_pos\":[365,17],\"def_end_pos\":[365,32]}]"
+                ],
+                "state_after": "case mp\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\nh : \u03c3 = sort f\n\u22a2 StrictMono \u21d1((graphEquiv\u2082 f).trans (Equiv.refl { x // x \u2208 graph f }))",
+                "state_before": "case mp\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\nh : \u03c3 = sort f\n\u22a2 StrictMono \u21d1(Equiv.trans \u03c3 (graphEquiv\u2081 f))",
+                "tactic": "rw [h, sort, Equiv.trans_assoc, Equiv.symm_trans_self]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact (<a>graphEquiv\\u2082<\\/a> f).<a>strictMono<\\/a>\"",
+                  "[{\"full_name\":\"Tuple.graphEquiv\\u2082\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Sort.lean\",\"def_pos\":[81,5],\"def_end_pos\":[81,16]},{\"full_name\":\"OrderIso.strictMono\",\"def_path\":\"Mathlib\\/Order\\/Hom\\/Basic.lean\",\"def_pos\":[1074,19],\"def_end_pos\":[1074,29]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case mp\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\nh : \u03c3 = sort f\n\u22a2 StrictMono \u21d1((graphEquiv\u2082 f).trans (Equiv.refl { x // x \u2208 graph f }))",
+                "tactic": "exact (graphEquiv\u2082 f).strictMono"
+              },
+              {
+                "annotated_tactic": [
+                  "\"have := <a>Subsingleton.elim<\\/a> (<a>graphEquiv\\u2082<\\/a> f) (h.orderIsoOfSurjective _ <| <a>Equiv.surjective<\\/a> _)\"",
+                  "[{\"full_name\":\"Subsingleton.elim\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1015,19],\"def_end_pos\":[1015,36]},{\"full_name\":\"Tuple.graphEquiv\\u2082\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Sort.lean\",\"def_pos\":[81,5],\"def_end_pos\":[81,16]},{\"full_name\":\"Equiv.surjective\",\"def_path\":\"Mathlib\\/Logic\\/Equiv\\/Defs.lean\",\"def_pos\":[199,19],\"def_end_pos\":[199,29]}]"
+                ],
+                "state_after": "case mpr\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\nh : StrictMono \u21d1(Equiv.trans \u03c3 (graphEquiv\u2081 f))\nthis : graphEquiv\u2082 f = StrictMono.orderIsoOfSurjective (\u21d1(Equiv.trans \u03c3 (graphEquiv\u2081 f))) h \u22ef\n\u22a2 \u03c3 = sort f",
+                "state_before": "case mpr\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\nh : StrictMono \u21d1(Equiv.trans \u03c3 (graphEquiv\u2081 f))\n\u22a2 \u03c3 = sort f",
+                "tactic": "have := Subsingleton.elim (graphEquiv\u2082 f) (h.orderIsoOfSurjective _ <| Equiv.surjective _)"
+              },
+              {
+                "annotated_tactic": [
+                  "\"ext1 x\"",
+                  "[]"
+                ],
+                "state_after": "case mpr.H\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\nh : StrictMono \u21d1(Equiv.trans \u03c3 (graphEquiv\u2081 f))\nthis : graphEquiv\u2082 f = StrictMono.orderIsoOfSurjective (\u21d1(Equiv.trans \u03c3 (graphEquiv\u2081 f))) h \u22ef\nx : Fin n\n\u22a2 \u03c3 x = (sort f) x",
+                "state_before": "case mpr\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\nh : StrictMono \u21d1(Equiv.trans \u03c3 (graphEquiv\u2081 f))\nthis : graphEquiv\u2082 f = StrictMono.orderIsoOfSurjective (\u21d1(Equiv.trans \u03c3 (graphEquiv\u2081 f))) h \u22ef\n\u22a2 \u03c3 = sort f",
+                "tactic": "ext1 x"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact (<a>graphEquiv\\u2081<\\/a> f).<a>apply_eq_iff_eq_symm_apply<\\/a>.1 (<a>DFunLike.congr_fun<\\/a> this x).<a>symm<\\/a>\"",
+                  "[{\"full_name\":\"Tuple.graphEquiv\\u2081\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Sort.lean\",\"def_pos\":[62,5],\"def_end_pos\":[62,16]},{\"full_name\":\"Equiv.apply_eq_iff_eq_symm_apply\",\"def_path\":\"Mathlib\\/Logic\\/Equiv\\/Defs.lean\",\"def_pos\":[319,9],\"def_end_pos\":[319,35]},{\"full_name\":\"DFunLike.congr_fun\",\"def_path\":\"Mathlib\\/Data\\/FunLike\\/Basic.lean\",\"def_pos\":[209,19],\"def_end_pos\":[209,28]},{\"full_name\":\"Eq.symm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[323,9],\"def_end_pos\":[323,16]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case mpr.H\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u03c3 : Equiv.Perm (Fin n)\nh : StrictMono \u21d1(Equiv.trans \u03c3 (graphEquiv\u2081 f))\nthis : graphEquiv\u2082 f = StrictMono.orderIsoOfSurjective (\u21d1(Equiv.trans \u03c3 (graphEquiv\u2081 f))) h \u22ef\nx : Fin n\n\u22a2 \u03c3 x = (sort f) x",
+                "tactic": "exact (graphEquiv\u2081 f).apply_eq_iff_eq_symm_apply.1 (DFunLike.congr_fun this x).symm"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Tuple.eq_sort_iff'"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Data/Fin/Tuple/Sort.lean",
+        "proof_id": "mathlib:Tuple.graph.card",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              57,
+              9
+            ],
+            "file_path": "Mathlib/Data/Fin/Tuple/Sort.lean",
+            "full_name": "Tuple.graph.card",
+            "start": [
+              50,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>graph<\\/a>, <a>Finset.card_image_of_injective<\\/a>]\"",
+                  "[{\"full_name\":\"Tuple.graph\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Sort.lean\",\"def_pos\":[39,5],\"def_end_pos\":[39,10]},{\"full_name\":\"Finset.card_image_of_injective\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Card.lean\",\"def_pos\":[286,9],\"def_end_pos\":[286,32]}]"
+                ],
+                "state_after": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u22a2 Finset.univ.card = n\n\ncase H\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u22a2 Function.Injective fun i => (f i, i)",
+                "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u22a2 (graph f).card = n",
+                "tactic": "rw [graph, Finset.card_image_of_injective]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact <a>Finset.card_fin<\\/a> _\"",
+                  "[{\"full_name\":\"Finset.card_fin\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[324,9],\"def_end_pos\":[324,24]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u22a2 Finset.univ.card = n",
+                "tactic": "exact Finset.card_fin _"
+              },
+              {
+                "annotated_tactic": [
+                  "\"intro _ _\"",
+                  "[]"
+                ],
+                "state_after": "case H\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\na\u2081\u271d a\u2082\u271d : Fin n\n\u22a2 (fun i => (f i, i)) a\u2081\u271d = (fun i => (f i, i)) a\u2082\u271d \u2192 a\u2081\u271d = a\u2082\u271d",
+                "state_before": "case H\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u22a2 Function.Injective fun i => (f i, i)",
+                "tactic": "intro _ _"
+              },
+              {
+                "annotated_tactic": [
+                  "\"dsimp only\"",
+                  "[]"
+                ],
+                "state_after": "case H\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\na\u2081\u271d a\u2082\u271d : Fin n\n\u22a2 (f a\u2081\u271d, a\u2081\u271d) = (f a\u2082\u271d, a\u2082\u271d) \u2192 a\u2081\u271d = a\u2082\u271d",
+                "state_before": "case H\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\na\u2081\u271d a\u2082\u271d : Fin n\n\u22a2 (fun i => (f i, i)) a\u2081\u271d = (fun i => (f i, i)) a\u2082\u271d \u2192 a\u2081\u271d = a\u2082\u271d",
+                "tactic": "dsimp only"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>Prod.ext_iff<\\/a>]\"",
+                  "[{\"full_name\":\"Prod.ext_iff\",\"def_path\":\"Mathlib\\/Data\\/Prod\\/Basic.lean\",\"def_pos\":[124,9],\"def_end_pos\":[124,16]}]"
+                ],
+                "state_after": "case H\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\na\u2081\u271d a\u2082\u271d : Fin n\n\u22a2 (f a\u2081\u271d, a\u2081\u271d).1 = (f a\u2082\u271d, a\u2082\u271d).1 \u2227 (f a\u2081\u271d, a\u2081\u271d).2 = (f a\u2082\u271d, a\u2082\u271d).2 \u2192 a\u2081\u271d = a\u2082\u271d",
+                "state_before": "case H\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\na\u2081\u271d a\u2082\u271d : Fin n\n\u22a2 (f a\u2081\u271d, a\u2081\u271d) = (f a\u2082\u271d, a\u2082\u271d) \u2192 a\u2081\u271d = a\u2082\u271d",
+                "tactic": "rw [Prod.ext_iff]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case H\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\na\u2081\u271d a\u2082\u271d : Fin n\n\u22a2 (f a\u2081\u271d, a\u2081\u271d).1 = (f a\u2082\u271d, a\u2082\u271d).1 \u2227 (f a\u2081\u271d, a\u2081\u271d).2 = (f a\u2082\u271d, a\u2082\u271d).2 \u2192 a\u2081\u271d = a\u2082\u271d",
+                "tactic": "simp"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Tuple.graph.card"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Data/Fin/Tuple/Sort.lean",
+        "proof_id": "mathlib:Tuple.monotone_proj",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              102,
+              22
+            ],
+            "file_path": "Mathlib/Data/Fin/Tuple/Sort.lean",
+            "full_name": "Tuple.monotone_proj",
+            "start": [
+              99,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"rintro \\u27e8\\u27e8x, i\\u27e9, hx\\u27e9 \\u27e8\\u27e8y, j\\u27e9, hy\\u27e9 (_ | h)\"",
+                  "[]"
+                ],
+                "state_after": "case mk.mk.mk.mk.left\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\nx : \u03b1\ni : Fin n\nhx : (x, i) \u2208 graph f\ny : \u03b1\nj : Fin n\nhy : (y, j) \u2208 graph f\nh\u271d : x < y\n\u22a2 graph.proj \u27e8(x, i), hx\u27e9 \u2264 graph.proj \u27e8(y, j), hy\u27e9\n\ncase mk.mk.mk.mk.right\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\nx : \u03b1\ni : Fin n\nhx : (x, i) \u2208 graph f\nj : Fin n\nhy : (x, j) \u2208 graph f\nh\u271d : i \u2264 j\n\u22a2 graph.proj \u27e8(x, i), hx\u27e9 \u2264 graph.proj \u27e8(x, j), hy\u27e9",
+                "state_before": "n : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\n\u22a2 Monotone graph.proj",
+                "tactic": "rintro \u27e8\u27e8x, i\u27e9, hx\u27e9 \u27e8\u27e8y, j\u27e9, hy\u27e9 (_ | h)"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact <a>le_of_lt<\\/a> \\u2039_\\u203a\"",
+                  "[{\"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 mk.mk.mk.mk.left\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\nx : \u03b1\ni : Fin n\nhx : (x, i) \u2208 graph f\ny : \u03b1\nj : Fin n\nhy : (y, j) \u2208 graph f\nh\u271d : x < y\n\u22a2 graph.proj \u27e8(x, i), hx\u27e9 \u2264 graph.proj \u27e8(y, j), hy\u27e9",
+                "tactic": "exact le_of_lt \u2039_\u203a"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp [<a>graph.proj<\\/a>]\"",
+                  "[{\"full_name\":\"Tuple.graph.proj\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Tuple\\/Sort.lean\",\"def_pos\":[46,5],\"def_end_pos\":[46,15]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case mk.mk.mk.mk.right\nn : \u2115\n\u03b1 : Type u_1\ninst\u271d : LinearOrder \u03b1\nf : Fin n \u2192 \u03b1\nx : \u03b1\ni : Fin n\nhx : (x, i) \u2208 graph f\nj : Fin n\nhy : (x, j) \u2208 graph f\nh\u271d : i \u2264 j\n\u22a2 graph.proj \u27e8(x, i), hx\u27e9 \u2264 graph.proj \u27e8(x, j), hy\u27e9",
+                "tactic": "simp [graph.proj]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Tuple.monotone_proj"
+      }
+    ],
+    "validation_rejected_proofs": 6,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000898-0000-6d89db7fcca1453b.parquet",
+      "sha256": "6d89db7fcca1453b829f46247f31a040077fd06adeffe556231fdefdedf78796",
+      "bytes": 54081,
+      "rows": 11,
+      "revision": "9931f7e263b644970d94314c5ccd8bc8f7920aee"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:FinVec.sum_eq",
+    "mathlib:Tuple.antitone_pair_of_not_sorted'",
+    "mathlib:Tuple.comp_perm_comp_sort_eq_comp_sort",
+    "mathlib:Tuple.monotone_sort",
+    "mathlib:Tuple.self_comp_sort",
+    "mathlib:Tuple.sort_eq_refl_iff_monotone"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Fin/Tuple/Reflection.lean\",null,null,\"FinVec.sum_eq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Fin/Tuple/Sort.lean\",null,null,\"Tuple.antitone_pair_of_not_sorted'\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Fin/Tuple/Sort.lean\",null,null,\"Tuple.comp_perm_comp_sort_eq_comp_sort\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Fin/Tuple/Sort.lean\",null,null,\"Tuple.monotone_sort\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Fin/Tuple/Sort.lean\",null,null,\"Tuple.self_comp_sort\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Fin/Tuple/Sort.lean\",null,null,\"Tuple.sort_eq_refl_iff_monotone\"]"
+  ]
+}

manifests/batches/mathlib/000900.json

@@ -0,0 +1,557 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/000900",
+  "batch_fingerprint": "26d6b02d507c0b095e6a51f006f3b79870bcca0d3c398feb67ce78342ec26fc4",
+  "evidence": {
+    "batch_fingerprint": "26d6b02d507c0b095e6a51f006f3b79870bcca0d3c398feb67ce78342ec26fc4",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finite.prod_left",
+        "id": "Finite.prod_left",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            74,
+            59
+          ],
+          "file_path": "Mathlib/Data/Finite/Basic.lean",
+          "full_name": "Finite.prod_left",
+          "start": [
+            73,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Finite/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finite.prod_right",
+        "id": "Finite.prod_right",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            78,
+            59
+          ],
+          "file_path": "Mathlib/Data/Finite/Basic.lean",
+          "full_name": "Finite.prod_right",
+          "start": [
+            77,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Finite/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finite.sum_left",
+        "id": "Finite.sum_left",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            87,
+            57
+          ],
+          "file_path": "Mathlib/Data/Finite/Basic.lean",
+          "full_name": "Finite.sum_left",
+          "start": [
+            86,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Finite/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finite.sum_right",
+        "id": "Finite.sum_right",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            91,
+            57
+          ],
+          "file_path": "Mathlib/Data/Finite/Basic.lean",
+          "full_name": "Finite.sum_right",
+          "start": [
+            90,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Finite/Basic.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finite.card_eq_zero_of_embedding",
+        "id": "Finite.card_eq_zero_of_embedding",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            163,
+            34
+          ],
+          "file_path": "Mathlib/Data/Finite/Card.lean",
+          "full_name": "Finite.card_eq_zero_of_embedding",
+          "start": [
+            162,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Finite/Card.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finite.card_eq_zero_of_injective",
+        "id": "Finite.card_eq_zero_of_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            158,
+            63
+          ],
+          "file_path": "Mathlib/Data/Finite/Card.lean",
+          "full_name": "Finite.card_eq_zero_of_injective",
+          "start": [
+            156,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Finite/Card.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finite.card_image_le",
+        "id": "Finite.card_image_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            173,
+            52
+          ],
+          "file_path": "Mathlib/Data/Finite/Card.lean",
+          "full_name": "Finite.card_image_le",
+          "start": [
+            172,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Finite/Card.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finite.card_le_of_embedding",
+        "id": "Finite.card_le_of_embedding",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            106,
+            37
+          ],
+          "file_path": "Mathlib/Data/Finite/Card.lean",
+          "full_name": "Finite.card_le_of_embedding",
+          "start": [
+            105,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Finite/Card.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finite.card_le_of_embedding'",
+        "id": "Finite.card_le_of_embedding'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            133,
+            30
+          ],
+          "file_path": "Mathlib/Data/Finite/Card.lean",
+          "full_name": "Finite.card_le_of_embedding'",
+          "start": [
+            131,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Finite/Card.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finite.card_le_of_injective'",
+        "id": "Finite.card_le_of_injective'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            126,
+            66
+          ],
+          "file_path": "Mathlib/Data/Finite/Card.lean",
+          "full_name": "Finite.card_le_of_injective'",
+          "start": [
+            123,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Finite/Card.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finite.card_le_of_surjective'",
+        "id": "Finite.card_le_of_surjective'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            141,
+            67
+          ],
+          "file_path": "Mathlib/Data/Finite/Card.lean",
+          "full_name": "Finite.card_le_of_surjective'",
+          "start": [
+            138,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Finite/Card.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finite.card_pos",
+        "id": "Finite.card_pos",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            63,
+            28
+          ],
+          "file_path": "Mathlib/Data/Finite/Card.lean",
+          "full_name": "Finite.card_pos",
+          "start": [
+            62,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Finite/Card.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finite.card_range_le",
+        "id": "Finite.card_range_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            177,
+            52
+          ],
+          "file_path": "Mathlib/Data/Finite/Card.lean",
+          "full_name": "Finite.card_range_le",
+          "start": [
+            176,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Finite/Card.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finite.cast_card_eq_mk",
+        "id": "Finite.cast_card_eq_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            69,
+            68
+          ],
+          "file_path": "Mathlib/Data/Finite/Card.lean",
+          "full_name": "Finite.cast_card_eq_mk",
+          "start": [
+            68,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Finite/Card.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Finite.one_lt_card",
+        "id": "Finite.one_lt_card",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            89,
+            35
+          ],
+          "file_path": "Mathlib/Data/Finite/Card.lean",
+          "full_name": "Finite.one_lt_card",
+          "start": [
+            88,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Finite/Card.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.Finite.eq_of_subset_of_card_le",
+        "id": "Set.Finite.eq_of_subset_of_card_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            230,
+            99
+          ],
+          "file_path": "Mathlib/Data/Finite/Card.lean",
+          "full_name": "Set.Finite.eq_of_subset_of_card_le",
+          "start": [
+            229,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Data/Finite/Card.lean"
+      }
+    ],
+    "input_proofs": 31,
+    "input_units": 2,
+    "proofs": 15,
+    "published_proofs": 13,
+    "published_transitions": 32,
+    "replay_failures": [],
+    "transitions": 42,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Data/Finite/Card.lean",
+        "proof_id": "mathlib:Nat.card_eq",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              54,
+              85
+            ],
+            "file_path": "Mathlib/Data/Finite/Card.lean",
+            "full_name": "Nat.card_eq",
+            "start": [
+              49,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"cases <a>finite_or_infinite<\\/a> \\u03b1\"",
+                  "[{\"full_name\":\"finite_or_infinite\",\"def_path\":\"Mathlib\\/Data\\/Finite\\/Defs.lean\",\"def_pos\":[142,9],\"def_end_pos\":[142,27]}]"
+                ],
+                "state_after": "case inl\n\u03b1\u271d : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b1 : Type u_4\nh\u271d : Finite \u03b1\n\u22a2 Nat.card \u03b1 = if h : Finite \u03b1 then Fintype.card \u03b1 else 0\n\ncase inr\n\u03b1\u271d : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b1 : Type u_4\nh\u271d : Infinite \u03b1\n\u22a2 Nat.card \u03b1 = if h : Finite \u03b1 then Fintype.card \u03b1 else 0",
+                "state_before": "\u03b1\u271d : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b1 : Type u_4\n\u22a2 Nat.card \u03b1 = if h : Finite \u03b1 then Fintype.card \u03b1 else 0",
+                "tactic": "cases finite_or_infinite \u03b1"
+              },
+              {
+                "annotated_tactic": [
+                  "\"letI := <a>Fintype.ofFinite<\\/a> \\u03b1\"",
+                  "[{\"full_name\":\"Fintype.ofFinite\",\"def_path\":\"Mathlib\\/Data\\/Fintype\\/Card.lean\",\"def_pos\":[449,19],\"def_end_pos\":[449,35]}]"
+                ],
+                "state_after": "case inl\n\u03b1\u271d : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b1 : Type u_4\nh\u271d : Finite \u03b1\nthis : Fintype \u03b1 := Fintype.ofFinite \u03b1\n\u22a2 Nat.card \u03b1 = if h : Finite \u03b1 then Fintype.card \u03b1 else 0",
+                "state_before": "case inl\n\u03b1\u271d : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b1 : Type u_4\nh\u271d : Finite \u03b1\n\u22a2 Nat.card \u03b1 = if h : Finite \u03b1 then Fintype.card \u03b1 else 0",
+                "tactic": "letI := Fintype.ofFinite \u03b1"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp only [*, <a>Nat.card_eq_fintype_card<\\/a>, <a>dif_pos<\\/a>]\"",
+                  "[{\"full_name\":\"Nat.card_eq_fintype_card\",\"def_path\":\"Mathlib\\/SetTheory\\/Cardinal\\/Finite.lean\",\"def_pos\":[40,9],\"def_end_pos\":[40,29]},{\"full_name\":\"dif_pos\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[949,9],\"def_end_pos\":[949,16]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case inl\n\u03b1\u271d : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b1 : Type u_4\nh\u271d : Finite \u03b1\nthis : Fintype \u03b1 := Fintype.ofFinite \u03b1\n\u22a2 Nat.card \u03b1 = if h : Finite \u03b1 then Fintype.card \u03b1 else 0",
+                "tactic": "simp only [*, Nat.card_eq_fintype_card, dif_pos]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp only [*, <a>card_eq_zero_of_infinite<\\/a>, not_finite_iff_infinite.mpr, <a>dite_false<\\/a>]\"",
+                  "[{\"full_name\":\"Nat.card_eq_zero_of_infinite\",\"def_path\":\"Mathlib\\/SetTheory\\/Cardinal\\/Finite.lean\",\"def_pos\":[61,15],\"def_end_pos\":[61,39]},{\"full_name\":\"dite_false\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[94,17],\"def_end_pos\":[94,27]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case inr\n\u03b1\u271d : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b1 : Type u_4\nh\u271d : Infinite \u03b1\n\u22a2 Nat.card \u03b1 = if h : Finite \u03b1 then Fintype.card \u03b1 else 0",
+                "tactic": "simp only [*, card_eq_zero_of_infinite, not_finite_iff_infinite.mpr, dite_false]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Nat.card_eq"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Data/Finite/Card.lean",
+        "proof_id": "mathlib:Set.card_union_le",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              216,
+              60
+            ],
+            "file_path": "Mathlib/Data/Finite/Card.lean",
+            "full_name": "Set.card_union_le",
+            "start": [
+              209,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"cases' <a>_root_.finite_or_infinite<\\/a> (\\u21a5(s \\u222a t)) with h h\"",
+                  "[{\"full_name\":\"finite_or_infinite\",\"def_path\":\"Mathlib\\/Data\\/Finite\\/Defs.lean\",\"def_pos\":[142,9],\"def_end_pos\":[142,27]}]"
+                ],
+                "state_after": "case inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ns t : Set \u03b1\nh : Finite \u2191(s \u222a t)\n\u22a2 Nat.card \u2191(s \u222a t) \u2264 Nat.card \u2191s + Nat.card \u2191t\n\ncase inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ns t : Set \u03b1\nh : Infinite \u2191(s \u222a t)\n\u22a2 Nat.card \u2191(s \u222a t) \u2264 Nat.card \u2191s + Nat.card \u2191t",
+                "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ns t : Set \u03b1\n\u22a2 Nat.card \u2191(s \u222a t) \u2264 Nat.card \u2191s + Nat.card \u2191t",
+                "tactic": "cases' _root_.finite_or_infinite (\u21a5(s \u222a t)) with h h"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>finite_coe_iff<\\/a>, <a>finite_union<\\/a>, \\u2190 <a>finite_coe_iff<\\/a>, \\u2190 <a>finite_coe_iff<\\/a>] at h\"",
+                  "[{\"full_name\":\"Set.finite_coe_iff\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Finite.lean\",\"def_pos\":[73,9],\"def_end_pos\":[73,23]},{\"full_name\":\"Set.finite_union\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Finite.lean\",\"def_pos\":[1085,9],\"def_end_pos\":[1085,21]},{\"full_name\":\"Set.finite_coe_iff\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Finite.lean\",\"def_pos\":[73,9],\"def_end_pos\":[73,23]},{\"full_name\":\"Set.finite_coe_iff\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Finite.lean\",\"def_pos\":[73,9],\"def_end_pos\":[73,23]}]"
+                ],
+                "state_after": "case inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ns t : Set \u03b1\nh : Finite \u2191s \u2227 Finite \u2191t\n\u22a2 Nat.card \u2191(s \u222a t) \u2264 Nat.card \u2191s + Nat.card \u2191t",
+                "state_before": "case inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ns t : Set \u03b1\nh : Finite \u2191(s \u222a t)\n\u22a2 Nat.card \u2191(s \u222a t) \u2264 Nat.card \u2191s + Nat.card \u2191t",
+                "tactic": "rw [finite_coe_iff, finite_union, \u2190 finite_coe_iff, \u2190 finite_coe_iff] at h"
+              },
+              {
+                "annotated_tactic": [
+                  "\"cases h\"",
+                  "[]"
+                ],
+                "state_after": "case inl.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ns t : Set \u03b1\nleft\u271d : Finite \u2191s\nright\u271d : Finite \u2191t\n\u22a2 Nat.card \u2191(s \u222a t) \u2264 Nat.card \u2191s + Nat.card \u2191t",
+                "state_before": "case inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ns t : Set \u03b1\nh : Finite \u2191s \u2227 Finite \u2191t\n\u22a2 Nat.card \u2191(s \u222a t) \u2264 Nat.card \u2191s + Nat.card \u2191t",
+                "tactic": "cases h"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [\\u2190 <a>Cardinal.natCast_le<\\/a>, <a>Nat.cast_add<\\/a>, <a>Finite.cast_card_eq_mk<\\/a>, <a>Finite.cast_card_eq_mk<\\/a>,\\n      <a>Finite.cast_card_eq_mk<\\/a>]\"",
+                  "[{\"full_name\":\"Cardinal.natCast_le\",\"def_path\":\"Mathlib\\/SetTheory\\/Cardinal\\/Basic.lean\",\"def_pos\":[1447,9],\"def_end_pos\":[1447,19]},{\"full_name\":\"Nat.cast_add\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Defs.lean\",\"def_pos\":[159,9],\"def_end_pos\":[159,17]},{\"full_name\":\"Finite.cast_card_eq_mk\",\"def_path\":\"Mathlib\\/Data\\/Finite\\/Card.lean\",\"def_pos\":[68,9],\"def_end_pos\":[68,24]},{\"full_name\":\"Finite.cast_card_eq_mk\",\"def_path\":\"Mathlib\\/Data\\/Finite\\/Card.lean\",\"def_pos\":[68,9],\"def_end_pos\":[68,24]},{\"full_name\":\"Finite.cast_card_eq_mk\",\"def_path\":\"Mathlib\\/Data\\/Finite\\/Card.lean\",\"def_pos\":[68,9],\"def_end_pos\":[68,24]}]"
+                ],
+                "state_after": "case inl.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ns t : Set \u03b1\nleft\u271d : Finite \u2191s\nright\u271d : Finite \u2191t\n\u22a2 Cardinal.mk \u2191(s \u222a t) \u2264 Cardinal.mk \u2191s + Cardinal.mk \u2191t",
+                "state_before": "case inl.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ns t : Set \u03b1\nleft\u271d : Finite \u2191s\nright\u271d : Finite \u2191t\n\u22a2 Nat.card \u2191(s \u222a t) \u2264 Nat.card \u2191s + Nat.card \u2191t",
+                "tactic": "rw [\u2190 Cardinal.natCast_le, Nat.cast_add, Finite.cast_card_eq_mk, Finite.cast_card_eq_mk,\n  Finite.cast_card_eq_mk]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact <a>Cardinal.mk_union_le<\\/a> s t\"",
+                  "[{\"full_name\":\"Cardinal.mk_union_le\",\"def_path\":\"Mathlib\\/SetTheory\\/Cardinal\\/Basic.lean\",\"def_pos\":[2093,9],\"def_end_pos\":[2093,20]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case inl.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ns t : Set \u03b1\nleft\u271d : Finite \u2191s\nright\u271d : Finite \u2191t\n\u22a2 Cardinal.mk \u2191(s \u222a t) \u2264 Cardinal.mk \u2191s + Cardinal.mk \u2191t",
+                "tactic": "exact Cardinal.mk_union_le s t"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact Nat.card_eq_zero_of_infinite.trans_le (<a>zero_le<\\/a> _)\"",
+                  "[{\"full_name\":\"zero_le\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Canonical\\/Defs.lean\",\"def_pos\":[204,30],\"def_end_pos\":[204,37]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\ns t : Set \u03b1\nh : Infinite \u2191(s \u222a t)\n\u22a2 Nat.card \u2191(s \u222a t) \u2264 Nat.card \u2191s + Nat.card \u2191t",
+                "tactic": "exact Nat.card_eq_zero_of_infinite.trans_le (zero_le _)"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "Set.card_union_le"
+      }
+    ],
+    "validation_rejected_proofs": 2,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-000900-0000-cab5405d8cce6589.parquet",
+      "sha256": "cab5405d8cce65896d74f6c9b8c9c975f0d9e215645cc42005a0755a362d4d1a",
+      "bytes": 68316,
+      "rows": 32,
+      "revision": "9931f7e263b644970d94314c5ccd8bc8f7920aee"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Finite.card_eq",
+    "mathlib:Finite.card_eq_zero_iff",
+    "mathlib:Finite.card_le_of_surjective",
+    "mathlib:Finite.card_le_one_iff_subsingleton",
+    "mathlib:Finite.card_option",
+    "mathlib:Finite.card_pos_iff",
+    "mathlib:Finite.card_subtype_le",
+    "mathlib:Finite.card_subtype_lt",
+    "mathlib:Finite.card_sum",
+    "mathlib:Finite.one_lt_card_iff_nontrivial",
+    "mathlib:PartENat.card_eq_coe_natCard",
+    "mathlib:Set.Finite.card_lt_card",
+    "mathlib:Set.Finite.equiv_image_eq_iff_subset"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Finite/Card.lean\",null,null,\"Finite.card_eq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Finite/Card.lean\",null,null,\"Finite.card_eq_zero_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Finite/Card.lean\",null,null,\"Finite.card_le_of_surjective\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Finite/Card.lean\",null,null,\"Finite.card_le_one_iff_subsingleton\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Finite/Card.lean\",null,null,\"Finite.card_option\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Finite/Card.lean\",null,null,\"Finite.card_pos_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Finite/Card.lean\",null,null,\"Finite.card_subtype_le\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Finite/Card.lean\",null,null,\"Finite.card_subtype_lt\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Finite/Card.lean\",null,null,\"Finite.card_sum\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Finite/Card.lean\",null,null,\"Finite.one_lt_card_iff_nontrivial\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Finite/Card.lean\",null,null,\"PartENat.card_eq_coe_natCard\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Data/Finite/Card.lean\",null,null,\"Set.Finite.card_lt_card\"]",
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manifests/batches/numina/001650.json

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manifests/batches/numina/001651.json

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manifests/batches/numina/001652.json

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manifests/batches/numina/001653.json

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manifests/batches/numina/001654.json

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manifests/batches/numina/001655.json

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manifests/batches/numina/001656.json

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manifests/batches/numina/001657.json

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manifests/batches/numina/001659.json

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manifests/batches/numina/001660.json

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