Record 31 verified HPC batch manifests

manifests/batches/mathlib/001507.json

@@ -0,0 +1,487 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001507",
+  "batch_fingerprint": "253d11cdc02139adec75538b43c514bde5c09c17ed80d54b0759e53697f09d42",
+  "evidence": {
+    "batch_fingerprint": "253d11cdc02139adec75538b43c514bde5c09c17ed80d54b0759e53697f09d42",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "no internal trace for tactic 'rcases exists_infinite_primes (n + 1) with \u27e8p, hnp, hp\u27e9'",
+        "full_name": "Nat.exists_prime_gt_modEq_one",
+        "id": "Nat.exists_prime_gt_modEq_one",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            57,
+            54
+          ],
+          "file_path": "Mathlib/NumberTheory/PrimesCongruentOne.lean",
+          "full_name": "Nat.exists_prime_gt_modEq_one",
+          "start": [
+            26,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rcases (<a>one_le_iff_ne_zero<\\/a>.2 hk0).<a>eq_or_lt<\\/a> with (rfl | hk1)\"",
+                "[{\"full_name\":\"Nat.one_le_iff_ne_zero\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Defs.lean\",\"def_pos\":[166,7],\"def_end_pos\":[166,25]},{\"full_name\":\"LE.le.eq_or_lt\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[395,7],\"def_end_pos\":[395,21]}]"
+              ],
+              "state_after": "case inl\nn : \u2115\nhk0 : 1 \u2260 0\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD 1]\n\ncase inr\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD k]",
+              "state_before": "k n : \u2115\nhk0 : k \u2260 0\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD k]",
+              "tactic": "rcases (one_le_iff_ne_zero.2 hk0).eq_or_lt with (rfl | hk1)"
+            },
+            {
+              "annotated_tactic": [
+                "\"let b := k * (n !)\"",
+                "[]"
+              ],
+              "state_after": "case inr\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD k]",
+              "state_before": "case inr\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD k]",
+              "tactic": "let b := k * (n !)"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hgt : 1 < (<a>eval<\\/a> (\\u2191b) (<a>cyclotomic<\\/a> k \\u2124)).<a>natAbs<\\/a> := by\\n    rcases <a>le_iff_exists_add'<\\/a>.1 hk1.le with \\u27e8k, rfl\\u27e9\\n    have hb : 2 \\u2264 b := <a>le_mul_of_le_of_one_le<\\/a> hk1 n.factorial_pos\\n    calc\\n      1 \\u2264 b - 1 := <a>le_tsub_of_add_le_left<\\/a> hb\\n      _ < (<a>eval<\\/a> (b : \\u2124) (<a>cyclotomic<\\/a> (k + 1) \\u2124)).<a>natAbs<\\/a> :=\\n        <a>sub_one_lt_natAbs_cyclotomic_eval<\\/a> hk1 (<a>succ_le_iff<\\/a>.1 hb).<a>ne'<\\/a>\"",
+                "[{\"full_name\":\"Polynomial.eval\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[310,5],\"def_end_pos\":[310,9]},{\"full_name\":\"Polynomial.cyclotomic\",\"def_path\":\"Mathlib\\/RingTheory\\/Polynomial\\/Cyclotomic\\/Basic.lean\",\"def_pos\":[253,5],\"def_end_pos\":[253,15]},{\"full_name\":\"Int.natAbs\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Basic.lean\",\"def_pos\":[262,5],\"def_end_pos\":[262,11]},{\"full_name\":\"le_iff_exists_add'\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Canonical\\/Defs.lean\",\"def_pos\":[198,3],\"def_end_pos\":[198,14]},{\"full_name\":\"le_mul_of_le_of_one_le\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Unbundled\\/Basic.lean\",\"def_pos\":[714,9],\"def_end_pos\":[714,31]},{\"full_name\":\"le_tsub_of_add_le_left\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Sub\\/Defs.lean\",\"def_pos\":[234,9],\"def_end_pos\":[234,31]},{\"full_name\":\"Polynomial.eval\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[310,5],\"def_end_pos\":[310,9]},{\"full_name\":\"Polynomial.cyclotomic\",\"def_path\":\"Mathlib\\/RingTheory\\/Polynomial\\/Cyclotomic\\/Basic.lean\",\"def_pos\":[253,5],\"def_end_pos\":[253,15]},{\"full_name\":\"Int.natAbs\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Basic.lean\",\"def_pos\":[262,5],\"def_end_pos\":[262,11]},{\"full_name\":\"Polynomial.sub_one_lt_natAbs_cyclotomic_eval\",\"def_path\":\"Mathlib\\/RingTheory\\/Polynomial\\/Cyclotomic\\/Eval.lean\",\"def_pos\":[317,9],\"def_end_pos\":[317,42]},{\"full_name\":\"Nat.succ_le_iff\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Defs.lean\",\"def_pos\":[128,7],\"def_end_pos\":[128,18]},{\"full_name\":\"LT.lt.ne'\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[306,9],\"def_end_pos\":[306,12]}]"
+              ],
+              "state_after": "case inr\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD k]",
+              "state_before": "case inr\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD k]",
+              "tactic": "have hgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs := by\n  rcases le_iff_exists_add'.1 hk1.le with \u27e8k, rfl\u27e9\n  have hb : 2 \u2264 b := le_mul_of_le_of_one_le hk1 n.factorial_pos\n  calc\n    1 \u2264 b - 1 := le_tsub_of_add_le_left hb\n    _ < (eval (b : \u2124) (cyclotomic (k + 1) \u2124)).natAbs :=\n      sub_one_lt_natAbs_cyclotomic_eval hk1 (succ_le_iff.1 hb).ne'"
+            },
+            {
+              "annotated_tactic": [
+                "\"let p := <a>minFac<\\/a> (<a>eval<\\/a> (\\u2191b) (<a>cyclotomic<\\/a> k \\u2124)).<a>natAbs<\\/a>\"",
+                "[{\"full_name\":\"Nat.minFac\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Prime.lean\",\"def_pos\":[269,5],\"def_end_pos\":[269,11]},{\"full_name\":\"Polynomial.eval\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[310,5],\"def_end_pos\":[310,9]},{\"full_name\":\"Polynomial.cyclotomic\",\"def_path\":\"Mathlib\\/RingTheory\\/Polynomial\\/Cyclotomic\\/Basic.lean\",\"def_pos\":[253,5],\"def_end_pos\":[253,15]},{\"full_name\":\"Int.natAbs\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Basic.lean\",\"def_pos\":[262,5],\"def_end_pos\":[262,11]}]"
+              ],
+              "state_after": "case inr\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD k]",
+              "state_before": "case inr\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD k]",
+              "tactic": "let p := minFac (eval (\u2191b) (cyclotomic k \u2124)).natAbs"
+            },
+            {
+              "annotated_tactic": [
+                "\"haveI hprime : <a>Fact<\\/a> p.Prime := \\u27e8<a>minFac_prime<\\/a> (<a>ne_of_lt<\\/a> hgt).<a>symm<\\/a>\\u27e9\"",
+                "[{\"full_name\":\"Fact\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[114,7],\"def_end_pos\":[114,11]},{\"full_name\":\"Nat.minFac_prime\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Prime.lean\",\"def_pos\":[342,9],\"def_end_pos\":[342,21]},{\"full_name\":\"Nat.ne_of_lt\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[382,9],\"def_end_pos\":[382,17]},{\"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": "case inr\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD k]",
+              "state_before": "case inr\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD k]",
+              "tactic": "haveI hprime : Fact p.Prime := \u27e8minFac_prime (ne_of_lt hgt).symm\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hroot : <a>IsRoot<\\/a> (<a>cyclotomic<\\/a> k (<a>ZMod<\\/a> p)) (<a>castRingHom<\\/a> (<a>ZMod<\\/a> p) b) := by\\n    have : ((b : \\u2124) : <a>ZMod<\\/a> p) = \\u2191(<a>Int.castRingHom<\\/a> (<a>ZMod<\\/a> p) b) := by simp\\n    rw [<a>IsRoot.def<\\/a>, \\u2190 <a>map_cyclotomic_int<\\/a> k (<a>ZMod<\\/a> p), <a>eval_map<\\/a>, <a>coe_castRingHom<\\/a>,\\n      \\u2190 <a>Int.cast_natCast<\\/a>, this, <a>eval\\u2082_hom<\\/a>, <a>Int.coe_castRingHom<\\/a>, <a>ZMod.intCast_zmod_eq_zero_iff_dvd<\\/a>]\\n    apply <a>Int.dvd_natAbs<\\/a>.1\\n    exact mod_cast <a>minFac_dvd<\\/a> (<a>eval<\\/a> (\\u2191b) (<a>cyclotomic<\\/a> k \\u2124)).<a>natAbs<\\/a>\"",
+                "[{\"full_name\":\"Polynomial.IsRoot\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[488,5],\"def_end_pos\":[488,11]},{\"full_name\":\"Polynomial.cyclotomic\",\"def_path\":\"Mathlib\\/RingTheory\\/Polynomial\\/Cyclotomic\\/Basic.lean\",\"def_pos\":[253,5],\"def_end_pos\":[253,15]},{\"full_name\":\"ZMod\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Defs.lean\",\"def_pos\":[95,5],\"def_end_pos\":[95,9]},{\"full_name\":\"Nat.castRingHom\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Basic.lean\",\"def_pos\":[68,5],\"def_end_pos\":[68,16]},{\"full_name\":\"ZMod\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Defs.lean\",\"def_pos\":[95,5],\"def_end_pos\":[95,9]},{\"full_name\":\"ZMod\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Defs.lean\",\"def_pos\":[95,5],\"def_end_pos\":[95,9]},{\"full_name\":\"Int.castRingHom\",\"def_path\":\"Mathlib\\/Data\\/Int\\/Cast\\/Lemmas.lean\",\"def_pos\":[98,5],\"def_end_pos\":[98,16]},{\"full_name\":\"ZMod\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Defs.lean\",\"def_pos\":[95,5],\"def_end_pos\":[95,9]},{\"full_name\":\"Polynomial.IsRoot.def\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[497,9],\"def_end_pos\":[497,19]},{\"full_name\":\"Polynomial.map_cyclotomic_int\",\"def_path\":\"Mathlib\\/RingTheory\\/Polynomial\\/Cyclotomic\\/Basic.lean\",\"def_pos\":[266,9],\"def_end_pos\":[266,27]},{\"full_name\":\"ZMod\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Defs.lean\",\"def_pos\":[95,5],\"def_end_pos\":[95,9]},{\"full_name\":\"Polynomial.eval_map\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[964,9],\"def_end_pos\":[964,17]},{\"full_name\":\"Nat.coe_castRingHom\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Basic.lean\",\"def_pos\":[72,26],\"def_end_pos\":[72,41]},{\"full_name\":\"Int.cast_natCast\",\"def_path\":\"Mathlib\\/Data\\/Int\\/Cast\\/Basic.lean\",\"def_pos\":[66,9],\"def_end_pos\":[66,21]},{\"full_name\":\"Polynomial.eval\\u2082_hom\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[1052,9],\"def_end_pos\":[1052,18]},{\"full_name\":\"Int.coe_castRingHom\",\"def_path\":\"Mathlib\\/Data\\/Int\\/Cast\\/Lemmas.lean\",\"def_pos\":[106,15],\"def_end_pos\":[106,30]},{\"full_name\":\"ZMod.intCast_zmod_eq_zero_iff_dvd\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Basic.lean\",\"def_pos\":[595,9],\"def_end_pos\":[595,37]},{\"full_name\":\"Int.dvd_natAbs\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/DivModLemmas.lean\",\"def_pos\":[107,9],\"def_end_pos\":[107,19]},{\"full_name\":\"Nat.minFac_dvd\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Prime.lean\",\"def_pos\":[338,9],\"def_end_pos\":[338,19]},{\"full_name\":\"Polynomial.eval\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[310,5],\"def_end_pos\":[310,9]},{\"full_name\":\"Polynomial.cyclotomic\",\"def_path\":\"Mathlib\\/RingTheory\\/Polynomial\\/Cyclotomic\\/Basic.lean\",\"def_pos\":[253,5],\"def_end_pos\":[253,15]},{\"full_name\":\"Int.natAbs\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Basic.lean\",\"def_pos\":[262,5],\"def_end_pos\":[262,11]}]"
+              ],
+              "state_after": "case inr\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nhroot : (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD k]",
+              "state_before": "case inr\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD k]",
+              "tactic": "have hroot : IsRoot (cyclotomic k (ZMod p)) (castRingHom (ZMod p) b) := by\n  have : ((b : \u2124) : ZMod p) = \u2191(Int.castRingHom (ZMod p) b) := by simp\n  rw [IsRoot.def, \u2190 map_cyclotomic_int k (ZMod p), eval_map, coe_castRingHom,\n    \u2190 Int.cast_natCast, this, eval\u2082_hom, Int.coe_castRingHom, ZMod.intCast_zmod_eq_zero_iff_dvd]\n  apply Int.dvd_natAbs.1\n  exact mod_cast minFac_dvd (eval (\u2191b) (cyclotomic k \u2124)).natAbs"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hpb : \\u00acp \\u2223 b :=\\n    hprime.1.<a>coprime_iff_not_dvd<\\/a>.1 (<a>coprime_of_root_cyclotomic<\\/a> hk0.bot_lt hroot).<a>symm<\\/a>\"",
+                "[{\"full_name\":\"Nat.Prime.coprime_iff_not_dvd\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Prime.lean\",\"def_pos\":[565,9],\"def_end_pos\":[565,34]},{\"full_name\":\"Polynomial.coprime_of_root_cyclotomic\",\"def_path\":\"Mathlib\\/RingTheory\\/Polynomial\\/Cyclotomic\\/Basic.lean\",\"def_pos\":[619,9],\"def_end_pos\":[619,35]},{\"full_name\":\"Nat.Coprime.symm\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Data\\/Nat\\/Gcd.lean\",\"def_pos\":[28,9],\"def_end_pos\":[28,21]}]"
+              ],
+              "state_after": "case inr\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nhroot : (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)\nhpb : \u00acp \u2223 b\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD k]",
+              "state_before": "case inr\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nhroot : (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD k]",
+              "tactic": "have hpb : \u00acp \u2223 b :=\n  hprime.1.coprime_iff_not_dvd.1 (coprime_of_root_cyclotomic hk0.bot_lt hroot).symm"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine \\u27e8p, hprime.1, <a>not_le<\\/a>.1 fun habs => ?_, ?_\\u27e9\"",
+                "[{\"full_name\":\"not_le\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[375,9],\"def_end_pos\":[375,15]}]"
+              ],
+              "state_after": "case inr.refine_1\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nhroot : (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)\nhpb : \u00acp \u2223 b\nhabs : p \u2264 n\n\u22a2 False\n\ncase inr.refine_2\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nhroot : (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)\nhpb : \u00acp \u2223 b\n\u22a2 p \u2261 1 [MOD k]",
+              "state_before": "case inr\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nhroot : (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)\nhpb : \u00acp \u2223 b\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD k]",
+              "tactic": "refine \u27e8p, hprime.1, not_le.1 fun habs => ?_, ?_\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rcases <a>exists_infinite_primes<\\/a> (n + 1) with \\u27e8p, hnp, hp\\u27e9\"",
+                "[{\"full_name\":\"Nat.exists_infinite_primes\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Prime.lean\",\"def_pos\":[496,9],\"def_end_pos\":[496,31]}]"
+              ],
+              "state_after": "case inl.intro.intro\nn : \u2115\nhk0 : 1 \u2260 0\np : \u2115\nhnp : n + 1 \u2264 p\nhp : Prime p\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD 1]",
+              "state_before": "case inl\nn : \u2115\nhk0 : 1 \u2260 0\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD 1]",
+              "tactic": "rcases exists_infinite_primes (n + 1) with \u27e8p, hnp, hp\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact \\u27e8p, hp, hnp, <a>modEq_one<\\/a>\\u27e9\"",
+                "[{\"full_name\":\"Nat.modEq_one\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/ModEq.lean\",\"def_pos\":[232,7],\"def_end_pos\":[232,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inl.intro.intro\nn : \u2115\nhk0 : 1 \u2260 0\np : \u2115\nhnp : n + 1 \u2264 p\nhp : Prime p\n\u22a2 \u2203 p, Prime p \u2227 n < p \u2227 p \u2261 1 [MOD 1]",
+              "tactic": "exact \u27e8p, hp, hnp, modEq_one\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rcases <a>le_iff_exists_add'<\\/a>.1 hk1.le with \\u27e8k, rfl\\u27e9\"",
+                "[{\"full_name\":\"le_iff_exists_add'\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Canonical\\/Defs.lean\",\"def_pos\":[198,3],\"def_end_pos\":[198,14]}]"
+              ],
+              "state_after": "case intro\nn k : \u2115\nhk0 : k + 1 \u2260 0\nhk1 : 1 < k + 1\nb : \u2115 := (k + 1) * n !\n\u22a2 1 < (eval (\u2191b) (cyclotomic (k + 1) \u2124)).natAbs",
+              "state_before": "k n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\n\u22a2 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs",
+              "tactic": "rcases le_iff_exists_add'.1 hk1.le with \u27e8k, rfl\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hb : 2 \\u2264 b := <a>le_mul_of_le_of_one_le<\\/a> hk1 n.factorial_pos\"",
+                "[{\"full_name\":\"le_mul_of_le_of_one_le\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Unbundled\\/Basic.lean\",\"def_pos\":[714,9],\"def_end_pos\":[714,31]}]"
+              ],
+              "state_after": "case intro\nn k : \u2115\nhk0 : k + 1 \u2260 0\nhk1 : 1 < k + 1\nb : \u2115 := (k + 1) * n !\nhb : 2 \u2264 b\n\u22a2 1 < (eval (\u2191b) (cyclotomic (k + 1) \u2124)).natAbs",
+              "state_before": "case intro\nn k : \u2115\nhk0 : k + 1 \u2260 0\nhk1 : 1 < k + 1\nb : \u2115 := (k + 1) * n !\n\u22a2 1 < (eval (\u2191b) (cyclotomic (k + 1) \u2124)).natAbs",
+              "tactic": "have hb : 2 \u2264 b := le_mul_of_le_of_one_le hk1 n.factorial_pos"
+            },
+            {
+              "annotated_tactic": [
+                "\"calc\\n      1 \\u2264 b - 1 := <a>le_tsub_of_add_le_left<\\/a> hb\\n      _ < (<a>eval<\\/a> (b : \\u2124) (<a>cyclotomic<\\/a> (k + 1) \\u2124)).<a>natAbs<\\/a> :=\\n        <a>sub_one_lt_natAbs_cyclotomic_eval<\\/a> hk1 (<a>succ_le_iff<\\/a>.1 hb).<a>ne'<\\/a>\"",
+                "[{\"full_name\":\"le_tsub_of_add_le_left\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Sub\\/Defs.lean\",\"def_pos\":[234,9],\"def_end_pos\":[234,31]},{\"full_name\":\"Polynomial.eval\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[310,5],\"def_end_pos\":[310,9]},{\"full_name\":\"Polynomial.cyclotomic\",\"def_path\":\"Mathlib\\/RingTheory\\/Polynomial\\/Cyclotomic\\/Basic.lean\",\"def_pos\":[253,5],\"def_end_pos\":[253,15]},{\"full_name\":\"Int.natAbs\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Basic.lean\",\"def_pos\":[262,5],\"def_end_pos\":[262,11]},{\"full_name\":\"Polynomial.sub_one_lt_natAbs_cyclotomic_eval\",\"def_path\":\"Mathlib\\/RingTheory\\/Polynomial\\/Cyclotomic\\/Eval.lean\",\"def_pos\":[317,9],\"def_end_pos\":[317,42]},{\"full_name\":\"Nat.succ_le_iff\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Defs.lean\",\"def_pos\":[128,7],\"def_end_pos\":[128,18]},{\"full_name\":\"LT.lt.ne'\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[306,9],\"def_end_pos\":[306,12]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case intro\nn k : \u2115\nhk0 : k + 1 \u2260 0\nhk1 : 1 < k + 1\nb : \u2115 := (k + 1) * n !\nhb : 2 \u2264 b\n\u22a2 1 < (eval (\u2191b) (cyclotomic (k + 1) \u2124)).natAbs",
+              "tactic": "calc\n  1 \u2264 b - 1 := le_tsub_of_add_le_left hb\n  _ < (eval (b : \u2124) (cyclotomic (k + 1) \u2124)).natAbs :=\n    sub_one_lt_natAbs_cyclotomic_eval hk1 (succ_le_iff.1 hb).ne'"
+            },
+            {
+              "annotated_tactic": [
+                "\"have : ((b : \\u2124) : <a>ZMod<\\/a> p) = \\u2191(<a>Int.castRingHom<\\/a> (<a>ZMod<\\/a> p) b) := by simp\"",
+                "[{\"full_name\":\"ZMod\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Defs.lean\",\"def_pos\":[95,5],\"def_end_pos\":[95,9]},{\"full_name\":\"Int.castRingHom\",\"def_path\":\"Mathlib\\/Data\\/Int\\/Cast\\/Lemmas.lean\",\"def_pos\":[98,5],\"def_end_pos\":[98,16]},{\"full_name\":\"ZMod\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Defs.lean\",\"def_pos\":[95,5],\"def_end_pos\":[95,9]}]"
+              ],
+              "state_after": "k n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nthis : \u2191\u2191b = (Int.castRingHom (ZMod p)) \u2191b\n\u22a2 (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)",
+              "state_before": "k n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\n\u22a2 (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)",
+              "tactic": "have : ((b : \u2124) : ZMod p) = \u2191(Int.castRingHom (ZMod p) b) := by simp"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>IsRoot.def<\\/a>, \\u2190 <a>map_cyclotomic_int<\\/a> k (<a>ZMod<\\/a> p), <a>eval_map<\\/a>, <a>coe_castRingHom<\\/a>,\\n      \\u2190 <a>Int.cast_natCast<\\/a>, this, <a>eval\\u2082_hom<\\/a>, <a>Int.coe_castRingHom<\\/a>, <a>ZMod.intCast_zmod_eq_zero_iff_dvd<\\/a>]\"",
+                "[{\"full_name\":\"Polynomial.IsRoot.def\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[497,9],\"def_end_pos\":[497,19]},{\"full_name\":\"Polynomial.map_cyclotomic_int\",\"def_path\":\"Mathlib\\/RingTheory\\/Polynomial\\/Cyclotomic\\/Basic.lean\",\"def_pos\":[266,9],\"def_end_pos\":[266,27]},{\"full_name\":\"ZMod\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Defs.lean\",\"def_pos\":[95,5],\"def_end_pos\":[95,9]},{\"full_name\":\"Polynomial.eval_map\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[964,9],\"def_end_pos\":[964,17]},{\"full_name\":\"Nat.coe_castRingHom\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Basic.lean\",\"def_pos\":[72,26],\"def_end_pos\":[72,41]},{\"full_name\":\"Int.cast_natCast\",\"def_path\":\"Mathlib\\/Data\\/Int\\/Cast\\/Basic.lean\",\"def_pos\":[66,9],\"def_end_pos\":[66,21]},{\"full_name\":\"Polynomial.eval\\u2082_hom\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[1052,9],\"def_end_pos\":[1052,18]},{\"full_name\":\"Int.coe_castRingHom\",\"def_path\":\"Mathlib\\/Data\\/Int\\/Cast\\/Lemmas.lean\",\"def_pos\":[106,15],\"def_end_pos\":[106,30]},{\"full_name\":\"ZMod.intCast_zmod_eq_zero_iff_dvd\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Basic.lean\",\"def_pos\":[595,9],\"def_end_pos\":[595,37]}]"
+              ],
+              "state_after": "k n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nthis : \u2191\u2191b = (Int.castRingHom (ZMod p)) \u2191b\n\u22a2 \u2191p \u2223 eval (\u2191b) (cyclotomic k \u2124)",
+              "state_before": "k n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nthis : \u2191\u2191b = (Int.castRingHom (ZMod p)) \u2191b\n\u22a2 (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)",
+              "tactic": "rw [IsRoot.def, \u2190 map_cyclotomic_int k (ZMod p), eval_map, coe_castRingHom,\n  \u2190 Int.cast_natCast, this, eval\u2082_hom, Int.coe_castRingHom, ZMod.intCast_zmod_eq_zero_iff_dvd]"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Int.dvd_natAbs<\\/a>.1\"",
+                "[{\"full_name\":\"Int.dvd_natAbs\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/DivModLemmas.lean\",\"def_pos\":[107,9],\"def_end_pos\":[107,19]}]"
+              ],
+              "state_after": "k n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nthis : \u2191\u2191b = (Int.castRingHom (ZMod p)) \u2191b\n\u22a2 \u2191p \u2223 \u2191(eval (\u2191b) (cyclotomic k \u2124)).natAbs",
+              "state_before": "k n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nthis : \u2191\u2191b = (Int.castRingHom (ZMod p)) \u2191b\n\u22a2 \u2191p \u2223 eval (\u2191b) (cyclotomic k \u2124)",
+              "tactic": "apply Int.dvd_natAbs.1"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact mod_cast <a>minFac_dvd<\\/a> (<a>eval<\\/a> (\\u2191b) (<a>cyclotomic<\\/a> k \\u2124)).<a>natAbs<\\/a>\"",
+                "[{\"full_name\":\"Nat.minFac_dvd\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Prime.lean\",\"def_pos\":[338,9],\"def_end_pos\":[338,19]},{\"full_name\":\"Polynomial.eval\",\"def_path\":\"Mathlib\\/Algebra\\/Polynomial\\/Eval.lean\",\"def_pos\":[310,5],\"def_end_pos\":[310,9]},{\"full_name\":\"Polynomial.cyclotomic\",\"def_path\":\"Mathlib\\/RingTheory\\/Polynomial\\/Cyclotomic\\/Basic.lean\",\"def_pos\":[253,5],\"def_end_pos\":[253,15]},{\"full_name\":\"Int.natAbs\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Basic.lean\",\"def_pos\":[262,5],\"def_end_pos\":[262,11]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "k n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nthis : \u2191\u2191b = (Int.castRingHom (ZMod p)) \u2191b\n\u22a2 \u2191p \u2223 \u2191(eval (\u2191b) (cyclotomic k \u2124)).natAbs",
+              "tactic": "exact mod_cast minFac_dvd (eval (\u2191b) (cyclotomic k \u2124)).natAbs"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "k n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\n\u22a2 \u2191\u2191b = (Int.castRingHom (ZMod p)) \u2191b",
+              "tactic": "simp"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact hpb (<a>dvd_mul_of_dvd_right<\\/a> (<a>dvd_factorial<\\/a> (<a>minFac_pos<\\/a> _) habs) _)\"",
+                "[{\"full_name\":\"dvd_mul_of_dvd_right\",\"def_path\":\"Mathlib\\/Algebra\\/Divisibility\\/Basic.lean\",\"def_pos\":[209,9],\"def_end_pos\":[209,29]},{\"full_name\":\"Nat.dvd_factorial\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Factorial\\/Basic.lean\",\"def_pos\":[79,9],\"def_end_pos\":[79,22]},{\"full_name\":\"Nat.minFac_pos\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Prime.lean\",\"def_pos\":[352,9],\"def_end_pos\":[352,19]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inr.refine_1\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nhroot : (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)\nhpb : \u00acp \u2223 b\nhabs : p \u2264 n\n\u22a2 False",
+              "tactic": "exact hpb (dvd_mul_of_dvd_right (dvd_factorial (minFac_pos _) habs) _)"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hdiv : <a>orderOf<\\/a> (b : <a>ZMod<\\/a> p) \\u2223 p - 1 :=\\n      <a>ZMod.orderOf_dvd_card_sub_one<\\/a> (<a>mt<\\/a> (<a>CharP.cast_eq_zero_iff<\\/a> _ _ _).1 hpb)\"",
+                "[{\"full_name\":\"orderOf\",\"def_path\":\"Mathlib\\/GroupTheory\\/OrderOfElement.lean\",\"def_pos\":[155,19],\"def_end_pos\":[155,26]},{\"full_name\":\"ZMod\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Defs.lean\",\"def_pos\":[95,5],\"def_end_pos\":[95,9]},{\"full_name\":\"ZMod.orderOf_dvd_card_sub_one\",\"def_path\":\"Mathlib\\/FieldTheory\\/Finite\\/Basic.lean\",\"def_pos\":[545,9],\"def_end_pos\":[545,33]},{\"full_name\":\"mt\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[647,9],\"def_end_pos\":[647,11]},{\"full_name\":\"CharP.cast_eq_zero_iff\",\"def_path\":\"Mathlib\\/Algebra\\/CharP\\/Defs.lean\",\"def_pos\":[48,7],\"def_end_pos\":[48,23]}]"
+              ],
+              "state_after": "case inr.refine_2\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nhroot : (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)\nhpb : \u00acp \u2223 b\nhdiv : orderOf \u2191b \u2223 p - 1\n\u22a2 p \u2261 1 [MOD k]",
+              "state_before": "case inr.refine_2\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nhroot : (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)\nhpb : \u00acp \u2223 b\n\u22a2 p \u2261 1 [MOD k]",
+              "tactic": "have hdiv : orderOf (b : ZMod p) \u2223 p - 1 :=\n  ZMod.orderOf_dvd_card_sub_one (mt (CharP.cast_eq_zero_iff _ _ _).1 hpb)"
+            },
+            {
+              "annotated_tactic": [
+                "\"haveI : <a>NeZero<\\/a> (k : <a>ZMod<\\/a> p) :=\\n      <a>NeZero.of_not_dvd<\\/a> (<a>ZMod<\\/a> p) fun hpk => hpb (<a>dvd_mul_of_dvd_left<\\/a> hpk _)\"",
+                "[{\"full_name\":\"NeZero\",\"def_path\":\"Mathlib\\/Algebra\\/NeZero.lean\",\"def_pos\":[25,7],\"def_end_pos\":[25,13]},{\"full_name\":\"ZMod\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Defs.lean\",\"def_pos\":[95,5],\"def_end_pos\":[95,9]},{\"full_name\":\"NeZero.of_not_dvd\",\"def_path\":\"Mathlib\\/Algebra\\/CharP\\/Defs.lean\",\"def_pos\":[432,7],\"def_end_pos\":[432,17]},{\"full_name\":\"ZMod\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Defs.lean\",\"def_pos\":[95,5],\"def_end_pos\":[95,9]},{\"full_name\":\"dvd_mul_of_dvd_left\",\"def_path\":\"Mathlib\\/Algebra\\/Divisibility\\/Basic.lean\",\"def_pos\":[87,9],\"def_end_pos\":[87,28]}]"
+              ],
+              "state_after": "case inr.refine_2\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nhroot : (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)\nhpb : \u00acp \u2223 b\nhdiv : orderOf \u2191b \u2223 p - 1\nthis : NeZero \u2191k\n\u22a2 p \u2261 1 [MOD k]",
+              "state_before": "case inr.refine_2\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nhroot : (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)\nhpb : \u00acp \u2223 b\nhdiv : orderOf \u2191b \u2223 p - 1\n\u22a2 p \u2261 1 [MOD k]",
+              "tactic": "haveI : NeZero (k : ZMod p) :=\n  NeZero.of_not_dvd (ZMod p) fun hpk => hpb (dvd_mul_of_dvd_left hpk _)"
+            },
+            {
+              "annotated_tactic": [
+                "\"have : k = <a>orderOf<\\/a> (b : <a>ZMod<\\/a> p) := (isRoot_cyclotomic_iff.mp hroot).<a>eq_orderOf<\\/a>\"",
+                "[{\"full_name\":\"orderOf\",\"def_path\":\"Mathlib\\/GroupTheory\\/OrderOfElement.lean\",\"def_pos\":[155,19],\"def_end_pos\":[155,26]},{\"full_name\":\"ZMod\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Defs.lean\",\"def_pos\":[95,5],\"def_end_pos\":[95,9]},{\"full_name\":\"IsPrimitiveRoot.eq_orderOf\",\"def_path\":\"Mathlib\\/RingTheory\\/RootsOfUnity\\/Basic.lean\",\"def_pos\":[461,9],\"def_end_pos\":[461,19]}]"
+              ],
+              "state_after": "case inr.refine_2\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nhroot : (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)\nhpb : \u00acp \u2223 b\nhdiv : orderOf \u2191b \u2223 p - 1\nthis\u271d : NeZero \u2191k\nthis : k = orderOf \u2191b\n\u22a2 p \u2261 1 [MOD k]",
+              "state_before": "case inr.refine_2\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nhroot : (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)\nhpb : \u00acp \u2223 b\nhdiv : orderOf \u2191b \u2223 p - 1\nthis : NeZero \u2191k\n\u22a2 p \u2261 1 [MOD k]",
+              "tactic": "have : k = orderOf (b : ZMod p) := (isRoot_cyclotomic_iff.mp hroot).eq_orderOf"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 this] at hdiv\"",
+                "[]"
+              ],
+              "state_after": "case inr.refine_2\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nhroot : (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)\nhpb : \u00acp \u2223 b\nhdiv : k \u2223 p - 1\nthis\u271d : NeZero \u2191k\nthis : k = orderOf \u2191b\n\u22a2 p \u2261 1 [MOD k]",
+              "state_before": "case inr.refine_2\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nhroot : (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)\nhpb : \u00acp \u2223 b\nhdiv : orderOf \u2191b \u2223 p - 1\nthis\u271d : NeZero \u2191k\nthis : k = orderOf \u2191b\n\u22a2 p \u2261 1 [MOD k]",
+              "tactic": "rw [\u2190 this] at hdiv"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact ((<a>modEq_iff_dvd'<\\/a> hprime.1.<a>pos<\\/a>).2 hdiv).<a>symm<\\/a>\"",
+                "[{\"full_name\":\"Nat.modEq_iff_dvd'\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/ModEq.lean\",\"def_pos\":[99,9],\"def_end_pos\":[99,23]},{\"full_name\":\"Nat.Prime.pos\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Prime.lean\",\"def_pos\":[65,9],\"def_end_pos\":[65,18]},{\"full_name\":\"Nat.ModEq.symm\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/ModEq.lean\",\"def_pos\":[60,19],\"def_end_pos\":[60,23]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inr.refine_2\nk n : \u2115\nhk0 : k \u2260 0\nhk1 : 1 < k\nb : \u2115 := k * n !\nhgt : 1 < (eval (\u2191b) (cyclotomic k \u2124)).natAbs\np : \u2115 := (eval (\u2191b) (cyclotomic k \u2124)).natAbs.minFac\nhprime : Fact (Prime p)\nhroot : (cyclotomic k (ZMod p)).IsRoot ((castRingHom (ZMod p)) b)\nhpb : \u00acp \u2223 b\nhdiv : k \u2223 p - 1\nthis\u271d : NeZero \u2191k\nthis : k = orderOf \u2191b\n\u22a2 p \u2261 1 [MOD k]",
+              "tactic": "exact ((modEq_iff_dvd' hprime.1.pos).2 hdiv).symm"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/NumberTheory/PrimesCongruentOne.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Nat.infinite_setOf_prime_modEq_one",
+        "id": "Nat.infinite_setOf_prime_modEq_one",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            70,
+            67
+          ],
+          "file_path": "Mathlib/NumberTheory/PrimesCongruentOne.lean",
+          "full_name": "Nat.infinite_setOf_prime_modEq_one",
+          "start": [
+            68,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/NumberTheory/PrimesCongruentOne.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "primorial_add_le",
+        "id": "primorial_add_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            70,
+            99
+          ],
+          "file_path": "Mathlib/NumberTheory/Primorial.lean",
+          "full_name": "primorial_add_le",
+          "start": [
+            69,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/NumberTheory/Primorial.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rfl'",
+        "full_name": "primorial_le_4_pow",
+        "id": "primorial_le_4_pow",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            91,
+            69
+          ],
+          "file_path": "Mathlib/NumberTheory/Primorial.lean",
+          "full_name": "primorial_le_4_pow",
+          "start": [
+            73,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"induction' n using <a>Nat.strong_induction_on<\\/a> with n ihn\"",
+                "[{\"full_name\":\"Nat.strong_induction_on\",\"def_path\":\"Mathlib\\/Init\\/Data\\/Nat\\/Lemmas.lean\",\"def_pos\":[490,19],\"def_end_pos\":[490,38]}]"
+              ],
+              "state_after": "case h\nn : \u2115\nihn : \u2200 m < n, m# \u2264 4 ^ m\n\u22a2 n# \u2264 4 ^ n",
+              "state_before": "n : \u2115\n\u22a2 n# \u2264 4 ^ n",
+              "tactic": "induction' n using Nat.strong_induction_on with n ihn"
+            },
+            {
+              "annotated_tactic": [
+                "\"cases' n with n\"",
+                "[]"
+              ],
+              "state_after": "case h.zero\nihn : \u2200 m < 0, m# \u2264 4 ^ m\n\u22a2 0# \u2264 4 ^ 0\n\ncase h.succ\nn : \u2115\nihn : \u2200 m < n + 1, m# \u2264 4 ^ m\n\u22a2 (n + 1)# \u2264 4 ^ (n + 1)",
+              "state_before": "case h\nn : \u2115\nihn : \u2200 m < n, m# \u2264 4 ^ m\n\u22a2 n# \u2264 4 ^ n",
+              "tactic": "cases' n with n"
+            },
+            {
+              "annotated_tactic": [
+                "\"rcases n.even_or_odd with (\\u27e8m, rfl\\u27e9 | ho)\"",
+                "[]"
+              ],
+              "state_after": "case h.succ.inl.intro\nm : \u2115\nihn : \u2200 m_1 < m + m + 1, m_1# \u2264 4 ^ m_1\n\u22a2 (m + m + 1)# \u2264 4 ^ (m + m + 1)\n\ncase h.succ.inr\nn : \u2115\nihn : \u2200 m < n + 1, m# \u2264 4 ^ m\nho : Odd n\n\u22a2 (n + 1)# \u2264 4 ^ (n + 1)",
+              "state_before": "case h.succ\nn : \u2115\nihn : \u2200 m < n + 1, m# \u2264 4 ^ m\n\u22a2 (n + 1)# \u2264 4 ^ (n + 1)",
+              "tactic": "rcases n.even_or_odd with (\u27e8m, rfl\u27e9 | ho)"
+            },
+            {
+              "annotated_tactic": [
+                "\"rfl\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.zero\nihn : \u2200 m < 0, m# \u2264 4 ^ m\n\u22a2 0# \u2264 4 ^ 0",
+              "tactic": "rfl"
+            },
+            {
+              "annotated_tactic": [
+                "\"rcases m.eq_zero_or_pos with (rfl | hm)\"",
+                "[]"
+              ],
+              "state_after": "case h.succ.inl.intro.inl\nihn : \u2200 m < 0 + 0 + 1, m# \u2264 4 ^ m\n\u22a2 (0 + 0 + 1)# \u2264 4 ^ (0 + 0 + 1)\n\ncase h.succ.inl.intro.inr\nm : \u2115\nihn : \u2200 m_1 < m + m + 1, m_1# \u2264 4 ^ m_1\nhm : m > 0\n\u22a2 (m + m + 1)# \u2264 4 ^ (m + m + 1)",
+              "state_before": "case h.succ.inl.intro\nm : \u2115\nihn : \u2200 m_1 < m + m + 1, m_1# \u2264 4 ^ m_1\n\u22a2 (m + m + 1)# \u2264 4 ^ (m + m + 1)",
+              "tactic": "rcases m.eq_zero_or_pos with (rfl | hm)"
+            },
+            {
+              "annotated_tactic": [
+                "\"calc\\n      (m + m + 1)# = (m + 1 + m)# := by rw [<a>add_right_comm<\\/a>]\\n      _ \\u2264 (m + 1)# * <a>choose<\\/a> (m + 1 + m) (m + 1) := <a>primorial_add_le<\\/a> m.le_succ\\n      _ = (m + 1)# * <a>choose<\\/a> (2 * m + 1) m := by rw [<a>choose_symm_add<\\/a>, <a>two_mul<\\/a>, <a>add_right_comm<\\/a>]\\n      _ \\u2264 4 ^ (m + 1) * 4 ^ m :=\\n        <a>mul_le_mul'<\\/a> (ihn _ <| <a>succ_lt_succ<\\/a> <| (<a>lt_add_iff_pos_left<\\/a> _).2 hm) (<a>choose_middle_le_pow<\\/a> _)\\n      _ \\u2264 4 ^ (m + m + 1) := by rw [\\u2190 <a>pow_add<\\/a>, <a>add_right_comm<\\/a>]\"",
+                "[{\"full_name\":\"add_right_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[189,3],\"def_end_pos\":[189,14]},{\"full_name\":\"Nat.choose\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Choose\\/Basic.lean\",\"def_pos\":[47,5],\"def_end_pos\":[47,11]},{\"full_name\":\"primorial_add_le\",\"def_path\":\"Mathlib\\/NumberTheory\\/Primorial.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,25]},{\"full_name\":\"Nat.choose\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Choose\\/Basic.lean\",\"def_pos\":[47,5],\"def_end_pos\":[47,11]},{\"full_name\":\"Nat.choose_symm_add\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Choose\\/Basic.lean\",\"def_pos\":[203,9],\"def_end_pos\":[203,24]},{\"full_name\":\"two_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[179,9],\"def_end_pos\":[179,16]},{\"full_name\":\"add_right_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[189,3],\"def_end_pos\":[189,14]},{\"full_name\":\"mul_le_mul'\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Unbundled\\/Basic.lean\",\"def_pos\":[206,9],\"def_end_pos\":[206,20]},{\"full_name\":\"Nat.succ_lt_succ\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[260,9],\"def_end_pos\":[260,21]},{\"full_name\":\"lt_add_iff_pos_left\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Unbundled\\/Basic.lean\",\"def_pos\":[571,30],\"def_end_pos\":[571,49]},{\"full_name\":\"Nat.choose_middle_le_pow\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Choose\\/Sum.lean\",\"def_pos\":[118,9],\"def_end_pos\":[118,29]},{\"full_name\":\"pow_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[703,7],\"def_end_pos\":[703,14]},{\"full_name\":\"add_right_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[189,3],\"def_end_pos\":[189,14]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.succ.inl.intro.inr\nm : \u2115\nihn : \u2200 m_1 < m + m + 1, m_1# \u2264 4 ^ m_1\nhm : m > 0\n\u22a2 (m + m + 1)# \u2264 4 ^ (m + m + 1)",
+              "tactic": "calc\n  (m + m + 1)# = (m + 1 + m)# := by rw [add_right_comm]\n  _ \u2264 (m + 1)# * choose (m + 1 + m) (m + 1) := primorial_add_le m.le_succ\n  _ = (m + 1)# * choose (2 * m + 1) m := by rw [choose_symm_add, two_mul, add_right_comm]\n  _ \u2264 4 ^ (m + 1) * 4 ^ m :=\n    mul_le_mul' (ihn _ <| succ_lt_succ <| (lt_add_iff_pos_left _).2 hm) (choose_middle_le_pow _)\n  _ \u2264 4 ^ (m + m + 1) := by rw [\u2190 pow_add, add_right_comm]"
+            },
+            {
+              "annotated_tactic": [
+                "\"decide\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.succ.inl.intro.inl\nihn : \u2200 m < 0 + 0 + 1, m# \u2264 4 ^ m\n\u22a2 (0 + 0 + 1)# \u2264 4 ^ (0 + 0 + 1)",
+              "tactic": "decide"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>add_right_comm<\\/a>]\"",
+                "[{\"full_name\":\"add_right_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[189,3],\"def_end_pos\":[189,14]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "m : \u2115\nihn : \u2200 m_1 < m + m + 1, m_1# \u2264 4 ^ m_1\nhm : m > 0\n\u22a2 (m + m + 1)# = (m + 1 + m)#",
+              "tactic": "rw [add_right_comm]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>choose_symm_add<\\/a>, <a>two_mul<\\/a>, <a>add_right_comm<\\/a>]\"",
+                "[{\"full_name\":\"Nat.choose_symm_add\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Choose\\/Basic.lean\",\"def_pos\":[203,9],\"def_end_pos\":[203,24]},{\"full_name\":\"two_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[179,9],\"def_end_pos\":[179,16]},{\"full_name\":\"add_right_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[189,3],\"def_end_pos\":[189,14]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "m : \u2115\nihn : \u2200 m_1 < m + m + 1, m_1# \u2264 4 ^ m_1\nhm : m > 0\n\u22a2 (m + 1)# * (m + 1 + m).choose (m + 1) = (m + 1)# * (2 * m + 1).choose m",
+              "tactic": "rw [choose_symm_add, two_mul, add_right_comm]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>pow_add<\\/a>, <a>add_right_comm<\\/a>]\"",
+                "[{\"full_name\":\"pow_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[703,7],\"def_end_pos\":[703,14]},{\"full_name\":\"add_right_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[189,3],\"def_end_pos\":[189,14]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "m : \u2115\nihn : \u2200 m_1 < m + m + 1, m_1# \u2264 4 ^ m_1\nhm : m > 0\n\u22a2 4 ^ (m + 1) * 4 ^ m \u2264 4 ^ (m + m + 1)",
+              "tactic": "rw [\u2190 pow_add, add_right_comm]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rcases <a>Decidable.eq_or_ne<\\/a> n 1 with (rfl | hn)\"",
+                "[{\"full_name\":\"Decidable.eq_or_ne\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[204,9],\"def_end_pos\":[204,27]}]"
+              ],
+              "state_after": "case h.succ.inr.inl\nihn : \u2200 m < 1 + 1, m# \u2264 4 ^ m\nho : Odd 1\n\u22a2 (1 + 1)# \u2264 4 ^ (1 + 1)\n\ncase h.succ.inr.inr\nn : \u2115\nihn : \u2200 m < n + 1, m# \u2264 4 ^ m\nho : Odd n\nhn : n \u2260 1\n\u22a2 (n + 1)# \u2264 4 ^ (n + 1)",
+              "state_before": "case h.succ.inr\nn : \u2115\nihn : \u2200 m < n + 1, m# \u2264 4 ^ m\nho : Odd n\n\u22a2 (n + 1)# \u2264 4 ^ (n + 1)",
+              "tactic": "rcases Decidable.eq_or_ne n 1 with (rfl | hn)"
+            },
+            {
+              "annotated_tactic": [
+                "\"decide\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.succ.inr.inl\nihn : \u2200 m < 1 + 1, m# \u2264 4 ^ m\nho : Odd 1\n\u22a2 (1 + 1)# \u2264 4 ^ (1 + 1)",
+              "tactic": "decide"
+            },
+            {
+              "annotated_tactic": [
+                "\"calc\\n        (n + 1)# = n# := <a>primorial_succ<\\/a> hn ho\\n        _ \\u2264 4 ^ n := ihn n n.lt_succ_self\\n        _ \\u2264 4 ^ (n + 1) := <a>pow_le_pow_of_le_right<\\/a> <a>four_pos<\\/a> n.le_succ\"",
+                "[{\"full_name\":\"primorial_succ\",\"def_path\":\"Mathlib\\/NumberTheory\\/Primorial.lean\",\"def_pos\":[45,9],\"def_end_pos\":[45,23]},{\"full_name\":\"Nat.pow_le_pow_of_le_right\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[761,9],\"def_end_pos\":[761,31]},{\"full_name\":\"four_pos\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/NatCast.lean\",\"def_pos\":[119,7],\"def_end_pos\":[119,15]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h.succ.inr.inr\nn : \u2115\nihn : \u2200 m < n + 1, m# \u2264 4 ^ m\nho : Odd n\nhn : n \u2260 1\n\u22a2 (n + 1)# \u2264 4 ^ (n + 1)",
+              "tactic": "calc\n  (n + 1)# = n# := primorial_succ hn ho\n  _ \u2264 4 ^ n := ihn n n.lt_succ_self\n  _ \u2264 4 ^ (n + 1) := pow_le_pow_of_le_right four_pos n.le_succ"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/NumberTheory/Primorial.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "primorial_pos",
+        "id": "primorial_pos",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            42,
+            47
+          ],
+          "file_path": "Mathlib/NumberTheory/Primorial.lean",
+          "full_name": "primorial_pos",
+          "start": [
+            41,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/NumberTheory/Primorial.lean"
+      }
+    ],
+    "input_proofs": 9,
+    "input_units": 2,
+    "proofs": 4,
+    "published_proofs": 4,
+    "published_transitions": 10,
+    "replay_failures": [],
+    "transitions": 10,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001507-0000-70c205e2e24ae9e4.parquet",
+      "sha256": "70c205e2e24ae9e419e51a34254e4eb0260db15d797b8ddfad9baf3fa66b19e8",
+      "bytes": 64275,
+      "rows": 10,
+      "revision": "504ada6ade9a708ef0393868f005bf429a0291c6"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Nat.frequently_atTop_modEq_one",
+    "mathlib:primorial_add",
+    "mathlib:primorial_add_dvd",
+    "mathlib:primorial_succ"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/NumberTheory/PrimesCongruentOne.lean\",null,null,\"Nat.frequently_atTop_modEq_one\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/NumberTheory/Primorial.lean\",null,null,\"primorial_add\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/NumberTheory/Primorial.lean\",null,null,\"primorial_add_dvd\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/NumberTheory/Primorial.lean\",null,null,\"primorial_succ\"]"
+  ]
+}

manifests/batches/mathlib/001515.json

@@ -0,0 +1,514 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001515",
+  "batch_fingerprint": "e952d42ce556eefe116a3699900374c9a46b1449b993391381ab4ff6dea77c68",
+  "evidence": {
+    "batch_fingerprint": "e952d42ce556eefe116a3699900374c9a46b1449b993391381ab4ff6dea77c68",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "no internal trace for tactic 'have hp41 : p % 4 = 1 := by\\n  rw [\u2190 Nat.mod_mul_left_mod p 2 2, show 2 * 2 = 4 from rfl] at hp1\\n  have := Nat.mod_lt p (show 0 < 4 by decide)\\n  revert this hp3 hp1\\n  generalize p % 4 = m\\n  intros; interval_cases m <;> simp_all'",
+        "full_name": "GaussianInt.mod_four_eq_three_of_nat_prime_of_prime",
+        "id": "GaussianInt.mod_four_eq_three_of_nat_prime_of_prime",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            83,
+            12
+          ],
+          "file_path": "Mathlib/NumberTheory/Zsqrtd/QuadraticReciprocity.lean",
+          "full_name": "GaussianInt.mod_four_eq_three_of_nat_prime_of_prime",
+          "start": [
+            33,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"have := h \\u27e81, 1\\u27e9 \\u27e81, -1\\u27e9 (hp2.symm \\u25b8 <a>rfl<\\/a>)\"",
+                "[{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]}]"
+              ],
+              "state_after": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp2 : p = 2\nx\u271d : Irreducible \u2191p\nnot_unit\u271d : \u00acIsUnit \u2191p\nh : \u2200 (a b : \u2124[i]), \u2191p = a * b \u2192 IsUnit a \u2228 IsUnit b\nthis : IsUnit { re := 1, im := 1 } \u2228 IsUnit { re := 1, im := -1 }\n\u22a2 False",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp2 : p = 2\nx\u271d : Irreducible \u2191p\nnot_unit\u271d : \u00acIsUnit \u2191p\nh : \u2200 (a b : \u2124[i]), \u2191p = a * b \u2192 IsUnit a \u2228 IsUnit b\n\u22a2 False",
+              "tactic": "have := h \u27e81, 1\u27e9 \u27e81, -1\u27e9 (hp2.symm \u25b8 rfl)"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>norm_eq_one_iff<\\/a>, \\u2190 <a>norm_eq_one_iff<\\/a>] at this\"",
+                "[{\"full_name\":\"Zsqrtd.norm_eq_one_iff\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/Basic.lean\",\"def_pos\":[569,9],\"def_end_pos\":[569,24]},{\"full_name\":\"Zsqrtd.norm_eq_one_iff\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/Basic.lean\",\"def_pos\":[569,9],\"def_end_pos\":[569,24]}]"
+              ],
+              "state_after": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp2 : p = 2\nx\u271d : Irreducible \u2191p\nnot_unit\u271d : \u00acIsUnit \u2191p\nh : \u2200 (a b : \u2124[i]), \u2191p = a * b \u2192 IsUnit a \u2228 IsUnit b\nthis : { re := 1, im := 1 }.norm.natAbs = 1 \u2228 { re := 1, im := -1 }.norm.natAbs = 1\n\u22a2 False",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp2 : p = 2\nx\u271d : Irreducible \u2191p\nnot_unit\u271d : \u00acIsUnit \u2191p\nh : \u2200 (a b : \u2124[i]), \u2191p = a * b \u2192 IsUnit a \u2228 IsUnit b\nthis : IsUnit { re := 1, im := 1 } \u2228 IsUnit { re := 1, im := -1 }\n\u22a2 False",
+              "tactic": "rw [\u2190 norm_eq_one_iff, \u2190 norm_eq_one_iff] at this"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>absurd<\\/a> this (by decide)\"",
+                "[{\"full_name\":\"absurd\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[246,21],\"def_end_pos\":[246,27]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp2 : p = 2\nx\u271d : Irreducible \u2191p\nnot_unit\u271d : \u00acIsUnit \u2191p\nh : \u2200 (a b : \u2124[i]), \u2191p = a * b \u2192 IsUnit a \u2228 IsUnit b\nthis : { re := 1, im := 1 }.norm.natAbs = 1 \u2228 { re := 1, im := -1 }.norm.natAbs = 1\n\u22a2 False",
+              "tactic": "exact absurd this (by decide)"
+            },
+            {
+              "annotated_tactic": [
+                "\"decide\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp2 : p = 2\nx\u271d : Irreducible \u2191p\nnot_unit\u271d : \u00acIsUnit \u2191p\nh : \u2200 (a b : \u2124[i]), \u2191p = a * b \u2192 IsUnit a \u2228 IsUnit b\nthis : { re := 1, im := 1 }.norm.natAbs = 1 \u2228 { re := 1, im := -1 }.norm.natAbs = 1\n\u22a2 \u00ac({ re := 1, im := 1 }.norm.natAbs = 1 \u2228 { re := 1, im := -1 }.norm.natAbs = 1)",
+              "tactic": "decide"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hp41 : p % 4 = 1 := by\\n        rw [\\u2190 <a>Nat.mod_mul_left_mod<\\/a> p 2 2, show 2 * 2 = 4 from <a>rfl<\\/a>] at hp1\\n        have := <a>Nat.mod_lt<\\/a> p (show 0 < 4 by decide)\\n        revert this hp3 hp1\\n        generalize p % 4 = m\\n        intros; interval_cases m <;> simp_all\"",
+                "[{\"full_name\":\"Nat.mod_mul_left_mod\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Mod.lean\",\"def_pos\":[65,9],\"def_end_pos\":[65,25]},{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]},{\"full_name\":\"Nat.mod_lt\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Div.lean\",\"def_pos\":[142,9],\"def_end_pos\":[142,15]}]"
+              ],
+              "state_after": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\n\u22a2 False",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\n\u22a2 False",
+              "tactic": "have hp41 : p % 4 = 1 := by\n  rw [\u2190 Nat.mod_mul_left_mod p 2 2, show 2 * 2 = 4 from rfl] at hp1\n  have := Nat.mod_lt p (show 0 < 4 by decide)\n  revert this hp3 hp1\n  generalize p % 4 = m\n  intros; interval_cases m <;> simp_all"
+            },
+            {
+              "annotated_tactic": [
+                "\"let \\u27e8k, hk\\u27e9 := (<a>ZMod.exists_sq_eq_neg_one_iff<\\/a> (p := p)).2 <| by rw [hp41]; decide\"",
+                "[{\"full_name\":\"ZMod.exists_sq_eq_neg_one_iff\",\"def_path\":\"Mathlib\\/NumberTheory\\/LegendreSymbol\\/Basic.lean\",\"def_pos\":[302,9],\"def_end_pos\":[302,33]}]"
+              ],
+              "state_after": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : ZMod p\nhk : -1 = k * k\n\u22a2 False",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\n\u22a2 False",
+              "tactic": "let \u27e8k, hk\u27e9 := (ZMod.exists_sq_eq_neg_one_iff (p := p)).2 <| by rw [hp41]; decide"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8k, k_lt_p, rfl\\u27e9 : \\u2203 (k' : \\u2115) (_ : k' < p), (k' : <a>ZMod<\\/a> p) = k := by\\n        exact \\u27e8k.val, k.val_lt, <a>ZMod.natCast_zmod_val<\\/a> k\\u27e9\"",
+                "[{\"full_name\":\"ZMod\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Defs.lean\",\"def_pos\":[95,5],\"def_end_pos\":[95,9]},{\"full_name\":\"ZMod.natCast_zmod_val\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Basic.lean\",\"def_pos\":[209,9],\"def_end_pos\":[209,25]}]"
+              ],
+              "state_after": "case intro.intro\np : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\n\u22a2 False",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : ZMod p\nhk : -1 = k * k\n\u22a2 False",
+              "tactic": "obtain \u27e8k, k_lt_p, rfl\u27e9 : \u2203 (k' : \u2115) (_ : k' < p), (k' : ZMod p) = k := by\n  exact \u27e8k.val, k.val_lt, ZMod.natCast_zmod_val k\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hpk : p \\u2223 k ^ 2 + 1 := by\\n        rw [<a>pow_two<\\/a>, \\u2190 <a>CharP.cast_eq_zero_iff<\\/a> (<a>ZMod<\\/a> p) p, <a>Nat.cast_add<\\/a>, <a>Nat.cast_mul<\\/a>, <a>Nat.cast_one<\\/a>,\\n          \\u2190 hk, <a>add_left_neg<\\/a>]\"",
+                "[{\"full_name\":\"pow_two\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[679,32],\"def_end_pos\":[679,39]},{\"full_name\":\"CharP.cast_eq_zero_iff\",\"def_path\":\"Mathlib\\/Algebra\\/CharP\\/Defs.lean\",\"def_pos\":[48,7],\"def_end_pos\":[48,23]},{\"full_name\":\"ZMod\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Defs.lean\",\"def_pos\":[95,5],\"def_end_pos\":[95,9]},{\"full_name\":\"Nat.cast_add\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Defs.lean\",\"def_pos\":[159,9],\"def_end_pos\":[159,17]},{\"full_name\":\"Nat.cast_mul\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Basic.lean\",\"def_pos\":[62,26],\"def_end_pos\":[62,34]},{\"full_name\":\"Nat.cast_one\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Defs.lean\",\"def_pos\":[154,9],\"def_end_pos\":[154,17]},{\"full_name\":\"add_left_neg\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1221,3],\"def_end_pos\":[1221,14]}]"
+              ],
+              "state_after": "case intro.intro\np : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\n\u22a2 False",
+              "state_before": "case intro.intro\np : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\n\u22a2 False",
+              "tactic": "have hpk : p \u2223 k ^ 2 + 1 := by\n  rw [pow_two, \u2190 CharP.cast_eq_zero_iff (ZMod p) p, Nat.cast_add, Nat.cast_mul, Nat.cast_one,\n    \u2190 hk, add_left_neg]"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hkmul : (k ^ 2 + 1 : \\u2124[i]) = \\u27e8k, 1\\u27e9 * \\u27e8k, -1\\u27e9 := by ext <;> simp [<a>sq<\\/a>]\"",
+                "[{\"full_name\":\"sq\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[684,41],\"def_end_pos\":[684,43]}]"
+              ],
+              "state_after": "case intro.intro\np : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\n\u22a2 False",
+              "state_before": "case intro.intro\np : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\n\u22a2 False",
+              "tactic": "have hkmul : (k ^ 2 + 1 : \u2124[i]) = \u27e8k, 1\u27e9 * \u27e8k, -1\u27e9 := by ext <;> simp [sq]"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hkltp : 1 + k * k < p * p :=\\n        calc\\n          1 + k * k \\u2264 k + k * k := by\\n            apply <a>add_le_add_right<\\/a>\\n            exact (<a>Nat.pos_of_ne_zero<\\/a> fun (hk0 : k = 0) => by clear_aux_decl; simp_all [<a>pow_succ'<\\/a>])\\n          _ = k * (k + 1) := by simp [<a>add_comm<\\/a>, <a>mul_add<\\/a>]\\n          _ < p * p := <a>mul_lt_mul<\\/a> k_lt_p k_lt_p (<a>Nat.succ_pos<\\/a> _) (<a>Nat.zero_le<\\/a> _)\"",
+                "[{\"full_name\":\"add_le_add_right\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Unbundled\\/Basic.lean\",\"def_pos\":[66,32],\"def_end_pos\":[66,48]},{\"full_name\":\"Nat.pos_of_ne_zero\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[354,19],\"def_end_pos\":[354,33]},{\"full_name\":\"pow_succ'\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[667,34],\"def_end_pos\":[667,43]},{\"full_name\":\"add_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[331,3],\"def_end_pos\":[331,14]},{\"full_name\":\"mul_add\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[83,7],\"def_end_pos\":[83,14]},{\"full_name\":\"mul_lt_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Ring\\/Defs.lean\",\"def_pos\":[543,9],\"def_end_pos\":[543,19]},{\"full_name\":\"Nat.succ_pos\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1693,9],\"def_end_pos\":[1693,21]},{\"full_name\":\"Nat.zero_le\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1663,9],\"def_end_pos\":[1663,20]}]"
+              ],
+              "state_after": "case intro.intro\np : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\n\u22a2 False",
+              "state_before": "case intro.intro\np : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\n\u22a2 False",
+              "tactic": "have hkltp : 1 + k * k < p * p :=\n  calc\n    1 + k * k \u2264 k + k * k := by\n      apply add_le_add_right\n      exact (Nat.pos_of_ne_zero fun (hk0 : k = 0) => by clear_aux_decl; simp_all [pow_succ'])\n    _ = k * (k + 1) := by simp [add_comm, mul_add]\n    _ < p * p := mul_lt_mul k_lt_p k_lt_p (Nat.succ_pos _) (Nat.zero_le _)"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hpk\\u2081 : \\u00ac(p : \\u2124[i]) \\u2223 \\u27e8k, -1\\u27e9 := fun \\u27e8x, hx\\u27e9 =>\\n        <a>lt_irrefl<\\/a> (p * x : \\u2124[i]).norm.natAbs <|\\n          calc\\n            (<a>norm<\\/a> (p * x : \\u2124[i])).<a>natAbs<\\/a> = (<a>Zsqrtd.norm<\\/a> \\u27e8k, -1\\u27e9).<a>natAbs<\\/a> := by rw [hx]\\n            _ < (<a>norm<\\/a> (p : \\u2124[i])).<a>natAbs<\\/a> := by simpa [<a>add_comm<\\/a>, <a>Zsqrtd.norm<\\/a>] using hkltp\\n            _ \\u2264 (<a>norm<\\/a> (p * x : \\u2124[i])).<a>natAbs<\\/a> :=\\n              <a>norm_le_norm_mul_left<\\/a> _ fun hx0 =>\\n                show (-1 : \\u2124) \\u2260 0 by decide <| by simpa [hx0] using <a>congr_arg<\\/a> <a>Zsqrtd.im<\\/a> hx\"",
+                "[{\"full_name\":\"lt_irrefl\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[79,9],\"def_end_pos\":[79,18]},{\"full_name\":\"Zsqrtd.norm\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/Basic.lean\",\"def_pos\":[500,5],\"def_end_pos\":[500,9]},{\"full_name\":\"Int.natAbs\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Basic.lean\",\"def_pos\":[262,5],\"def_end_pos\":[262,11]},{\"full_name\":\"Zsqrtd.norm\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/Basic.lean\",\"def_pos\":[500,5],\"def_end_pos\":[500,9]},{\"full_name\":\"Int.natAbs\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Basic.lean\",\"def_pos\":[262,5],\"def_end_pos\":[262,11]},{\"full_name\":\"Zsqrtd.norm\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/Basic.lean\",\"def_pos\":[500,5],\"def_end_pos\":[500,9]},{\"full_name\":\"Int.natAbs\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Basic.lean\",\"def_pos\":[262,5],\"def_end_pos\":[262,11]},{\"full_name\":\"add_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[331,3],\"def_end_pos\":[331,14]},{\"full_name\":\"Zsqrtd.norm\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/Basic.lean\",\"def_pos\":[500,5],\"def_end_pos\":[500,9]},{\"full_name\":\"Zsqrtd.norm\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/Basic.lean\",\"def_pos\":[500,5],\"def_end_pos\":[500,9]},{\"full_name\":\"Int.natAbs\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Basic.lean\",\"def_pos\":[262,5],\"def_end_pos\":[262,11]},{\"full_name\":\"GaussianInt.norm_le_norm_mul_left\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/GaussianInt.lean\",\"def_pos\":[270,9],\"def_end_pos\":[270,30]},{\"full_name\":\"congr_arg\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Logic.lean\",\"def_pos\":[76,7],\"def_end_pos\":[76,16]},{\"full_name\":\"Zsqrtd.im\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/Basic.lean\",\"def_pos\":[33,3],\"def_end_pos\":[33,5]}]"
+              ],
+              "state_after": "case intro.intro\np : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nhpk\u2081 : \u00ac\u2191p \u2223 { re := \u2191k, im := -1 }\n\u22a2 False",
+              "state_before": "case intro.intro\np : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\n\u22a2 False",
+              "tactic": "have hpk\u2081 : \u00ac(p : \u2124[i]) \u2223 \u27e8k, -1\u27e9 := fun \u27e8x, hx\u27e9 =>\n  lt_irrefl (p * x : \u2124[i]).norm.natAbs <|\n    calc\n      (norm (p * x : \u2124[i])).natAbs = (Zsqrtd.norm \u27e8k, -1\u27e9).natAbs := by rw [hx]\n      _ < (norm (p : \u2124[i])).natAbs := by simpa [add_comm, Zsqrtd.norm] using hkltp\n      _ \u2264 (norm (p * x : \u2124[i])).natAbs :=\n        norm_le_norm_mul_left _ fun hx0 =>\n          show (-1 : \u2124) \u2260 0 by decide <| by simpa [hx0] using congr_arg Zsqrtd.im hx"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hpk\\u2082 : \\u00ac(p : \\u2124[i]) \\u2223 \\u27e8k, 1\\u27e9 := fun \\u27e8x, hx\\u27e9 =>\\n        <a>lt_irrefl<\\/a> (p * x : \\u2124[i]).norm.natAbs <|\\n          calc\\n            (<a>norm<\\/a> (p * x : \\u2124[i])).<a>natAbs<\\/a> = (<a>Zsqrtd.norm<\\/a> \\u27e8k, 1\\u27e9).<a>natAbs<\\/a> := by rw [hx]\\n            _ < (<a>norm<\\/a> (p : \\u2124[i])).<a>natAbs<\\/a> := by simpa [<a>add_comm<\\/a>, <a>Zsqrtd.norm<\\/a>] using hkltp\\n            _ \\u2264 (<a>norm<\\/a> (p * x : \\u2124[i])).<a>natAbs<\\/a> :=\\n              <a>norm_le_norm_mul_left<\\/a> _ fun hx0 =>\\n                show (1 : \\u2124) \\u2260 0 by decide <| by simpa [hx0] using <a>congr_arg<\\/a> <a>Zsqrtd.im<\\/a> hx\"",
+                "[{\"full_name\":\"lt_irrefl\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[79,9],\"def_end_pos\":[79,18]},{\"full_name\":\"Zsqrtd.norm\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/Basic.lean\",\"def_pos\":[500,5],\"def_end_pos\":[500,9]},{\"full_name\":\"Int.natAbs\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Basic.lean\",\"def_pos\":[262,5],\"def_end_pos\":[262,11]},{\"full_name\":\"Zsqrtd.norm\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/Basic.lean\",\"def_pos\":[500,5],\"def_end_pos\":[500,9]},{\"full_name\":\"Int.natAbs\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Basic.lean\",\"def_pos\":[262,5],\"def_end_pos\":[262,11]},{\"full_name\":\"Zsqrtd.norm\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/Basic.lean\",\"def_pos\":[500,5],\"def_end_pos\":[500,9]},{\"full_name\":\"Int.natAbs\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Basic.lean\",\"def_pos\":[262,5],\"def_end_pos\":[262,11]},{\"full_name\":\"add_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[331,3],\"def_end_pos\":[331,14]},{\"full_name\":\"Zsqrtd.norm\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/Basic.lean\",\"def_pos\":[500,5],\"def_end_pos\":[500,9]},{\"full_name\":\"Zsqrtd.norm\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/Basic.lean\",\"def_pos\":[500,5],\"def_end_pos\":[500,9]},{\"full_name\":\"Int.natAbs\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Basic.lean\",\"def_pos\":[262,5],\"def_end_pos\":[262,11]},{\"full_name\":\"GaussianInt.norm_le_norm_mul_left\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/GaussianInt.lean\",\"def_pos\":[270,9],\"def_end_pos\":[270,30]},{\"full_name\":\"congr_arg\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Logic.lean\",\"def_pos\":[76,7],\"def_end_pos\":[76,16]},{\"full_name\":\"Zsqrtd.im\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/Basic.lean\",\"def_pos\":[33,3],\"def_end_pos\":[33,5]}]"
+              ],
+              "state_after": "case intro.intro\np : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nhpk\u2081 : \u00ac\u2191p \u2223 { re := \u2191k, im := -1 }\nhpk\u2082 : \u00ac\u2191p \u2223 { re := \u2191k, im := 1 }\n\u22a2 False",
+              "state_before": "case intro.intro\np : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nhpk\u2081 : \u00ac\u2191p \u2223 { re := \u2191k, im := -1 }\n\u22a2 False",
+              "tactic": "have hpk\u2082 : \u00ac(p : \u2124[i]) \u2223 \u27e8k, 1\u27e9 := fun \u27e8x, hx\u27e9 =>\n  lt_irrefl (p * x : \u2124[i]).norm.natAbs <|\n    calc\n      (norm (p * x : \u2124[i])).natAbs = (Zsqrtd.norm \u27e8k, 1\u27e9).natAbs := by rw [hx]\n      _ < (norm (p : \u2124[i])).natAbs := by simpa [add_comm, Zsqrtd.norm] using hkltp\n      _ \u2264 (norm (p * x : \u2124[i])).natAbs :=\n        norm_le_norm_mul_left _ fun hx0 =>\n          show (1 : \u2124) \u2260 0 by decide <| by simpa [hx0] using congr_arg Zsqrtd.im hx"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8y, hy\\u27e9 := hpk\"",
+                "[]"
+              ],
+              "state_after": "case intro.intro.intro\np : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nhpk\u2081 : \u00ac\u2191p \u2223 { re := \u2191k, im := -1 }\nhpk\u2082 : \u00ac\u2191p \u2223 { re := \u2191k, im := 1 }\ny : \u2115\nhy : k ^ 2 + 1 = p * y\n\u22a2 False",
+              "state_before": "case intro.intro\np : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nhpk\u2081 : \u00ac\u2191p \u2223 { re := \u2191k, im := -1 }\nhpk\u2082 : \u00ac\u2191p \u2223 { re := \u2191k, im := 1 }\n\u22a2 False",
+              "tactic": "obtain \u27e8y, hy\u27e9 := hpk"
+            },
+            {
+              "annotated_tactic": [
+                "\"have := hpi.2.2 \\u27e8k, 1\\u27e9 \\u27e8k, -1\\u27e9 \\u27e8y, by rw [\\u2190 hkmul, \\u2190 <a>Nat.cast_mul<\\/a> p, \\u2190 hy]; simp\\u27e9\"",
+                "[{\"full_name\":\"Nat.cast_mul\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Basic.lean\",\"def_pos\":[62,26],\"def_end_pos\":[62,34]}]"
+              ],
+              "state_after": "case intro.intro.intro\np : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nhpk\u2081 : \u00ac\u2191p \u2223 { re := \u2191k, im := -1 }\nhpk\u2082 : \u00ac\u2191p \u2223 { re := \u2191k, im := 1 }\ny : \u2115\nhy : k ^ 2 + 1 = p * y\nthis : \u2191p \u2223 { re := \u2191k, im := 1 } \u2228 \u2191p \u2223 { re := \u2191k, im := -1 }\n\u22a2 False",
+              "state_before": "case intro.intro.intro\np : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nhpk\u2081 : \u00ac\u2191p \u2223 { re := \u2191k, im := -1 }\nhpk\u2082 : \u00ac\u2191p \u2223 { re := \u2191k, im := 1 }\ny : \u2115\nhy : k ^ 2 + 1 = p * y\n\u22a2 False",
+              "tactic": "have := hpi.2.2 \u27e8k, 1\u27e9 \u27e8k, -1\u27e9 \u27e8y, by rw [\u2190 hkmul, \u2190 Nat.cast_mul p, \u2190 hy]; simp\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"tauto\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case intro.intro.intro\np : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nhpk\u2081 : \u00ac\u2191p \u2223 { re := \u2191k, im := -1 }\nhpk\u2082 : \u00ac\u2191p \u2223 { re := \u2191k, im := 1 }\ny : \u2115\nhy : k ^ 2 + 1 = p * y\nthis : \u2191p \u2223 { re := \u2191k, im := 1 } \u2228 \u2191p \u2223 { re := \u2191k, im := -1 }\n\u22a2 False",
+              "tactic": "tauto"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>Nat.mod_mul_left_mod<\\/a> p 2 2, show 2 * 2 = 4 from <a>rfl<\\/a>] at hp1\"",
+                "[{\"full_name\":\"Nat.mod_mul_left_mod\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Mod.lean\",\"def_pos\":[65,9],\"def_end_pos\":[65,25]},{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]}]"
+              ],
+              "state_after": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 4 % 2 = 1\nhp3 : p % 4 \u2260 3\n\u22a2 p % 4 = 1",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\n\u22a2 p % 4 = 1",
+              "tactic": "rw [\u2190 Nat.mod_mul_left_mod p 2 2, show 2 * 2 = 4 from rfl] at hp1"
+            },
+            {
+              "annotated_tactic": [
+                "\"have := <a>Nat.mod_lt<\\/a> p (show 0 < 4 by decide)\"",
+                "[{\"full_name\":\"Nat.mod_lt\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Div.lean\",\"def_pos\":[142,9],\"def_end_pos\":[142,15]}]"
+              ],
+              "state_after": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 4 % 2 = 1\nhp3 : p % 4 \u2260 3\nthis : p % 4 < 4\n\u22a2 p % 4 = 1",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 4 % 2 = 1\nhp3 : p % 4 \u2260 3\n\u22a2 p % 4 = 1",
+              "tactic": "have := Nat.mod_lt p (show 0 < 4 by decide)"
+            },
+            {
+              "annotated_tactic": [
+                "\"revert this hp3 hp1\"",
+                "[]"
+              ],
+              "state_after": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\n\u22a2 p % 4 % 2 = 1 \u2192 p % 4 \u2260 3 \u2192 p % 4 < 4 \u2192 p % 4 = 1",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 4 % 2 = 1\nhp3 : p % 4 \u2260 3\nthis : p % 4 < 4\n\u22a2 p % 4 = 1",
+              "tactic": "revert this hp3 hp1"
+            },
+            {
+              "annotated_tactic": [
+                "\"generalize p % 4 = m\"",
+                "[]"
+              ],
+              "state_after": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nm : \u2115\n\u22a2 m % 2 = 1 \u2192 m \u2260 3 \u2192 m < 4 \u2192 m = 1",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\n\u22a2 p % 4 % 2 = 1 \u2192 p % 4 \u2260 3 \u2192 p % 4 < 4 \u2192 p % 4 = 1",
+              "tactic": "generalize p % 4 = m"
+            },
+            {
+              "annotated_tactic": [
+                "\"intros\"",
+                "[]"
+              ],
+              "state_after": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nm : \u2115\nhp1\u271d : m % 2 = 1\nhp3\u271d : m \u2260 3\nthis\u271d : m < 4\n\u22a2 m = 1",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nm : \u2115\n\u22a2 m % 2 = 1 \u2192 m \u2260 3 \u2192 m < 4 \u2192 m = 1",
+              "tactic": "intros"
+            },
+            {
+              "annotated_tactic": [
+                "\"interval_cases m <;> simp_all\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nm : \u2115\nhp1\u271d : m % 2 = 1\nhp3\u271d : m \u2260 3\nthis\u271d : m < 4\n\u22a2 m = 1",
+              "tactic": "interval_cases m <;> simp_all"
+            },
+            {
+              "annotated_tactic": [
+                "\"decide\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 4 % 2 = 1\nhp3 : p % 4 \u2260 3\n\u22a2 0 < 4",
+              "tactic": "decide"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [hp41]\"",
+                "[]"
+              ],
+              "state_after": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\n\u22a2 1 \u2260 3",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\n\u22a2 p % 4 \u2260 3",
+              "tactic": "rw [hp41]"
+            },
+            {
+              "annotated_tactic": [
+                "\"decide\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\n\u22a2 1 \u2260 3",
+              "tactic": "decide"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact \\u27e8k.val, k.val_lt, <a>ZMod.natCast_zmod_val<\\/a> k\\u27e9\"",
+                "[{\"full_name\":\"ZMod.natCast_zmod_val\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Basic.lean\",\"def_pos\":[209,9],\"def_end_pos\":[209,25]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : ZMod p\nhk : -1 = k * k\n\u22a2 \u2203 k', \u2203 (_ : k' < p), \u2191k' = k",
+              "tactic": "exact \u27e8k.val, k.val_lt, ZMod.natCast_zmod_val k\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>pow_two<\\/a>, \\u2190 <a>CharP.cast_eq_zero_iff<\\/a> (<a>ZMod<\\/a> p) p, <a>Nat.cast_add<\\/a>, <a>Nat.cast_mul<\\/a>, <a>Nat.cast_one<\\/a>,\\n          \\u2190 hk, <a>add_left_neg<\\/a>]\"",
+                "[{\"full_name\":\"pow_two\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[679,32],\"def_end_pos\":[679,39]},{\"full_name\":\"CharP.cast_eq_zero_iff\",\"def_path\":\"Mathlib\\/Algebra\\/CharP\\/Defs.lean\",\"def_pos\":[48,7],\"def_end_pos\":[48,23]},{\"full_name\":\"ZMod\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Defs.lean\",\"def_pos\":[95,5],\"def_end_pos\":[95,9]},{\"full_name\":\"Nat.cast_add\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Defs.lean\",\"def_pos\":[159,9],\"def_end_pos\":[159,17]},{\"full_name\":\"Nat.cast_mul\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Basic.lean\",\"def_pos\":[62,26],\"def_end_pos\":[62,34]},{\"full_name\":\"Nat.cast_one\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Defs.lean\",\"def_pos\":[154,9],\"def_end_pos\":[154,17]},{\"full_name\":\"add_left_neg\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1221,3],\"def_end_pos\":[1221,14]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\n\u22a2 p \u2223 k ^ 2 + 1",
+              "tactic": "rw [pow_two, \u2190 CharP.cast_eq_zero_iff (ZMod p) p, Nat.cast_add, Nat.cast_mul, Nat.cast_one,\n  \u2190 hk, add_left_neg]"
+            },
+            {
+              "annotated_tactic": [
+                "\"ext <;> simp [<a>sq<\\/a>]\"",
+                "[{\"full_name\":\"sq\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[684,41],\"def_end_pos\":[684,43]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\n\u22a2 \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }",
+              "tactic": "ext <;> simp [sq]"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>add_le_add_right<\\/a>\"",
+                "[{\"full_name\":\"add_le_add_right\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Unbundled\\/Basic.lean\",\"def_pos\":[66,32],\"def_end_pos\":[66,48]}]"
+              ],
+              "state_after": "case bc\np : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\n\u22a2 1 \u2264 k",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\n\u22a2 1 + k * k \u2264 k + k * k",
+              "tactic": "apply add_le_add_right"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact (<a>Nat.pos_of_ne_zero<\\/a> fun (hk0 : k = 0) => by clear_aux_decl; simp_all [<a>pow_succ'<\\/a>])\"",
+                "[{\"full_name\":\"Nat.pos_of_ne_zero\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[354,19],\"def_end_pos\":[354,33]},{\"full_name\":\"pow_succ'\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[667,34],\"def_end_pos\":[667,43]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case bc\np : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\n\u22a2 1 \u2264 k",
+              "tactic": "exact (Nat.pos_of_ne_zero fun (hk0 : k = 0) => by clear_aux_decl; simp_all [pow_succ'])"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp_all [<a>pow_succ'<\\/a>]\"",
+                "[{\"full_name\":\"pow_succ'\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[667,34],\"def_end_pos\":[667,43]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhk0 : k = 0\n\u22a2 False",
+              "tactic": "simp_all [pow_succ']"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [<a>add_comm<\\/a>, <a>mul_add<\\/a>]\"",
+                "[{\"full_name\":\"add_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[331,3],\"def_end_pos\":[331,14]},{\"full_name\":\"mul_add\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[83,7],\"def_end_pos\":[83,14]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\n\u22a2 k + k * k = k * (k + 1)",
+              "tactic": "simp [add_comm, mul_add]"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [hx]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nx\u271d : \u2191p \u2223 { re := \u2191k, im := -1 }\nx : \u2124[i]\nhx : { re := \u2191k, im := -1 } = \u2191p * x\n\u22a2 (Zsqrtd.norm (\u2191p * x)).natAbs = { re := \u2191k, im := -1 }.norm.natAbs",
+              "tactic": "rw [hx]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simpa [<a>add_comm<\\/a>, <a>Zsqrtd.norm<\\/a>] using hkltp\"",
+                "[{\"full_name\":\"add_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[331,3],\"def_end_pos\":[331,14]},{\"full_name\":\"Zsqrtd.norm\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/Basic.lean\",\"def_pos\":[500,5],\"def_end_pos\":[500,9]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nx\u271d : \u2191p \u2223 { re := \u2191k, im := -1 }\nx : \u2124[i]\nhx : { re := \u2191k, im := -1 } = \u2191p * x\n\u22a2 { re := \u2191k, im := -1 }.norm.natAbs < (Zsqrtd.norm \u2191p).natAbs",
+              "tactic": "simpa [add_comm, Zsqrtd.norm] using hkltp"
+            },
+            {
+              "annotated_tactic": [
+                "\"decide\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nx\u271d : \u2191p \u2223 { re := \u2191k, im := -1 }\nx : \u2124[i]\nhx : { re := \u2191k, im := -1 } = \u2191p * x\nhx0 : x = 0\n\u22a2 -1 \u2260 0",
+              "tactic": "decide"
+            },
+            {
+              "annotated_tactic": [
+                "\"simpa [hx0] using <a>congr_arg<\\/a> <a>Zsqrtd.im<\\/a> hx\"",
+                "[{\"full_name\":\"congr_arg\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Logic.lean\",\"def_pos\":[76,7],\"def_end_pos\":[76,16]},{\"full_name\":\"Zsqrtd.im\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/Basic.lean\",\"def_pos\":[33,3],\"def_end_pos\":[33,5]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nx\u271d : \u2191p \u2223 { re := \u2191k, im := -1 }\nx : \u2124[i]\nhx : { re := \u2191k, im := -1 } = \u2191p * x\nhx0 : x = 0\n\u22a2 -1 = 0",
+              "tactic": "simpa [hx0] using congr_arg Zsqrtd.im hx"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [hx]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nhpk\u2081 : \u00ac\u2191p \u2223 { re := \u2191k, im := -1 }\nx\u271d : \u2191p \u2223 { re := \u2191k, im := 1 }\nx : \u2124[i]\nhx : { re := \u2191k, im := 1 } = \u2191p * x\n\u22a2 (Zsqrtd.norm (\u2191p * x)).natAbs = { re := \u2191k, im := 1 }.norm.natAbs",
+              "tactic": "rw [hx]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simpa [<a>add_comm<\\/a>, <a>Zsqrtd.norm<\\/a>] using hkltp\"",
+                "[{\"full_name\":\"add_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[331,3],\"def_end_pos\":[331,14]},{\"full_name\":\"Zsqrtd.norm\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/Basic.lean\",\"def_pos\":[500,5],\"def_end_pos\":[500,9]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nhpk\u2081 : \u00ac\u2191p \u2223 { re := \u2191k, im := -1 }\nx\u271d : \u2191p \u2223 { re := \u2191k, im := 1 }\nx : \u2124[i]\nhx : { re := \u2191k, im := 1 } = \u2191p * x\n\u22a2 { re := \u2191k, im := 1 }.norm.natAbs < (Zsqrtd.norm \u2191p).natAbs",
+              "tactic": "simpa [add_comm, Zsqrtd.norm] using hkltp"
+            },
+            {
+              "annotated_tactic": [
+                "\"decide\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nhpk\u2081 : \u00ac\u2191p \u2223 { re := \u2191k, im := -1 }\nx\u271d : \u2191p \u2223 { re := \u2191k, im := 1 }\nx : \u2124[i]\nhx : { re := \u2191k, im := 1 } = \u2191p * x\nhx0 : x = 0\n\u22a2 1 \u2260 0",
+              "tactic": "decide"
+            },
+            {
+              "annotated_tactic": [
+                "\"simpa [hx0] using <a>congr_arg<\\/a> <a>Zsqrtd.im<\\/a> hx\"",
+                "[{\"full_name\":\"congr_arg\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Logic.lean\",\"def_pos\":[76,7],\"def_end_pos\":[76,16]},{\"full_name\":\"Zsqrtd.im\",\"def_path\":\"Mathlib\\/NumberTheory\\/Zsqrtd\\/Basic.lean\",\"def_pos\":[33,3],\"def_end_pos\":[33,5]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhpk : p \u2223 k ^ 2 + 1\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nhpk\u2081 : \u00ac\u2191p \u2223 { re := \u2191k, im := -1 }\nx\u271d : \u2191p \u2223 { re := \u2191k, im := 1 }\nx : \u2124[i]\nhx : { re := \u2191k, im := 1 } = \u2191p * x\nhx0 : x = 0\n\u22a2 1 = 0",
+              "tactic": "simpa [hx0] using congr_arg Zsqrtd.im hx"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 hkmul, \\u2190 <a>Nat.cast_mul<\\/a> p, \\u2190 hy]\"",
+                "[{\"full_name\":\"Nat.cast_mul\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Cast\\/Basic.lean\",\"def_pos\":[62,26],\"def_end_pos\":[62,34]}]"
+              ],
+              "state_after": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nhpk\u2081 : \u00ac\u2191p \u2223 { re := \u2191k, im := -1 }\nhpk\u2082 : \u00ac\u2191p \u2223 { re := \u2191k, im := 1 }\ny : \u2115\nhy : k ^ 2 + 1 = p * y\n\u22a2 \u2191k ^ 2 + 1 = \u2191(k ^ 2 + 1)",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nhpk\u2081 : \u00ac\u2191p \u2223 { re := \u2191k, im := -1 }\nhpk\u2082 : \u00ac\u2191p \u2223 { re := \u2191k, im := 1 }\ny : \u2115\nhy : k ^ 2 + 1 = p * y\n\u22a2 { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 } = \u2191p * \u2191y",
+              "tactic": "rw [\u2190 hkmul, \u2190 Nat.cast_mul p, \u2190 hy]"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhpi : Prime \u2191p\nhp1 : p % 2 = 1\nhp3 : p % 4 \u2260 3\nhp41 : p % 4 = 1\nk : \u2115\nk_lt_p : k < p\nhk : -1 = \u2191k * \u2191k\nhkmul : \u2191k ^ 2 + 1 = { re := \u2191k, im := 1 } * { re := \u2191k, im := -1 }\nhkltp : 1 + k * k < p * p\nhpk\u2081 : \u00ac\u2191p \u2223 { re := \u2191k, im := -1 }\nhpk\u2082 : \u00ac\u2191p \u2223 { re := \u2191k, im := 1 }\ny : \u2115\nhy : k ^ 2 + 1 = p * y\n\u22a2 \u2191k ^ 2 + 1 = \u2191(k ^ 2 + 1)",
+              "tactic": "simp"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/NumberTheory/Zsqrtd/QuadraticReciprocity.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "GaussianInt.prime_iff_mod_four_eq_three_of_nat_prime",
+        "id": "GaussianInt.prime_iff_mod_four_eq_three_of_nat_prime",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            99,
+            89
+          ],
+          "file_path": "Mathlib/NumberTheory/Zsqrtd/QuadraticReciprocity.lean",
+          "full_name": "GaussianInt.prime_iff_mod_four_eq_three_of_nat_prime",
+          "start": [
+            97,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/NumberTheory/Zsqrtd/QuadraticReciprocity.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Zsqrtd.toReal_injective",
+        "id": "Zsqrtd.toReal_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            31,
+            22
+          ],
+          "file_path": "Mathlib/NumberTheory/Zsqrtd/ToReal.lean",
+          "full_name": "Zsqrtd.toReal_injective",
+          "start": [
+            29,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/NumberTheory/Zsqrtd/ToReal.lean"
+      }
+    ],
+    "input_proofs": 4,
+    "input_units": 2,
+    "proofs": 1,
+    "published_proofs": 0,
+    "published_transitions": 0,
+    "replay_failures": [],
+    "transitions": 3,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/NumberTheory/Zsqrtd/QuadraticReciprocity.lean",
+        "proof_id": "mathlib:GaussianInt.prime_of_nat_prime_of_mod_four_eq_three",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              93,
+              31
+            ],
+            "file_path": "Mathlib/NumberTheory/Zsqrtd/QuadraticReciprocity.lean",
+            "full_name": "GaussianInt.prime_of_nat_prime_of_mod_four_eq_three",
+            "start": [
+              86,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"erw [\\u2190 <a>ZMod.natCast_mod<\\/a> p 4, hp3]\"",
+                  "[{\"full_name\":\"ZMod.natCast_mod\",\"def_path\":\"Mathlib\\/Data\\/ZMod\\/Basic.lean\",\"def_pos\":[851,9],\"def_end_pos\":[851,20]}]"
+                ],
+                "state_after": "p : \u2115\nhp : Fact (Nat.Prime p)\nhp3 : p % 4 = 3\nhpi : \u00acIrreducible \u2191p\na b : \u2115\nhab : a ^ 2 + b ^ 2 = p\n\u22a2 \u2200 (a b : ZMod 4), a ^ 2 + b ^ 2 \u2260 \u21913",
+                "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhp3 : p % 4 = 3\nhpi : \u00acIrreducible \u2191p\na b : \u2115\nhab : a ^ 2 + b ^ 2 = p\n\u22a2 \u2200 (a b : ZMod 4), a ^ 2 + b ^ 2 \u2260 \u2191p",
+                "tactic": "erw [\u2190 ZMod.natCast_mod p 4, hp3]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"decide\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhp3 : p % 4 = 3\nhpi : \u00acIrreducible \u2191p\na b : \u2115\nhab : a ^ 2 + b ^ 2 = p\n\u22a2 \u2200 (a b : ZMod 4), a ^ 2 + b ^ 2 \u2260 \u21913",
+                "tactic": "decide"
+              },
+              {
+                "annotated_tactic": [
+                  "\"simp\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "p : \u2115\nhp : Fact (Nat.Prime p)\nhp3 : p % 4 = 3\nhpi : \u00acIrreducible \u2191p\na b : \u2115\nhab : a ^ 2 + b ^ 2 = p\nthis : \u2200 (a b : ZMod 4), a ^ 2 + b ^ 2 \u2260 \u2191p\n\u22a2 \u2191a ^ 2 + \u2191b ^ 2 = \u2191(a ^ 2 + b ^ 2)",
+                "tactic": "simp"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "GaussianInt.prime_of_nat_prime_of_mod_four_eq_three"
+      }
+    ],
+    "validation_rejected_proofs": 1,
+    "zero_transition_proofs": 0
+  },
+  "shards": [],
+  "proof_ids": [],
+  "proof_keys": []
+}

manifests/batches/mathlib/001516.json

@@ -0,0 +1,1924 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001516",
+  "batch_fingerprint": "57ef86b8d3e98a3a43604b80c84749d827875a9e4973e2ffb6969a8c41af4af9",
+  "evidence": {
+    "batch_fingerprint": "57ef86b8d3e98a3a43604b80c84749d827875a9e4973e2ffb6969a8c41af4af9",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.bot_mem_iff",
+        "id": "IsAntichain.bot_mem_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            250,
+            42
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.bot_mem_iff",
+          "start": [
+            249,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.eq",
+        "id": "IsAntichain.eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            61,
+            46
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.eq",
+          "start": [
+            59,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.eq'",
+        "id": "IsAntichain.eq'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            66,
+            23
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.eq'",
+          "start": [
+            64,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.flip",
+        "id": "IsAntichain.flip",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            82,
+            18
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.flip",
+          "start": [
+            81,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.greatest_iff",
+        "id": "IsAntichain.greatest_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            238,
+            61
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.greatest_iff",
+          "start": [
+            237,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.image_compl",
+        "id": "IsAntichain.image_compl",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            195,
+            64
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.image_compl",
+          "start": [
+            193,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.image_embedding",
+        "id": "IsAntichain.image_embedding",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            152,
+            26
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.image_embedding",
+          "start": [
+            150,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.image_embedding_iff",
+        "id": "IsAntichain.image_embedding_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            162,
+            25
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.image_embedding_iff",
+          "start": [
+            160,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.image_iso",
+        "id": "IsAntichain.image_iso",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            167,
+            26
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.image_iso",
+          "start": [
+            165,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.image_iso_iff",
+        "id": "IsAntichain.image_iso_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            172,
+            25
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.image_iso_iff",
+          "start": [
+            170,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "no internal trace for tactic \"rw [haa']\"",
+        "full_name": "IsAntichain.image_relEmbedding",
+        "id": "IsAntichain.image_relEmbedding",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            124,
+            74
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.image_relEmbedding",
+          "start": [
+            120,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"intro b hb b' hb' h\\u2081 h\\u2082\"",
+                "[]"
+              ],
+              "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr r\u2081 r\u2082 : \u03b1 \u2192 \u03b1 \u2192 Prop\nr' : \u03b2 \u2192 \u03b2 \u2192 Prop\ns t : Set \u03b1\na b\u271d : \u03b1\nhs : IsAntichain r s\n\u03c6 : r \u21aar r'\nb : \u03b2\nhb : b \u2208 \u21d1\u03c6 '' s\nb' : \u03b2\nhb' : b' \u2208 \u21d1\u03c6 '' s\nh\u2081 : b \u2260 b'\nh\u2082 : r' b b'\n\u22a2 False",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr r\u2081 r\u2082 : \u03b1 \u2192 \u03b1 \u2192 Prop\nr' : \u03b2 \u2192 \u03b2 \u2192 Prop\ns t : Set \u03b1\na b : \u03b1\nhs : IsAntichain r s\n\u03c6 : r \u21aar r'\n\u22a2 IsAntichain r' (\u21d1\u03c6 '' s)",
+              "tactic": "intro b hb b' hb' h\u2081 h\u2082"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>Set.mem_image<\\/a>] at hb hb'\"",
+                "[{\"full_name\":\"Set.mem_image\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Defs.lean\",\"def_pos\":[127,9],\"def_end_pos\":[127,18]}]"
+              ],
+              "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr r\u2081 r\u2082 : \u03b1 \u2192 \u03b1 \u2192 Prop\nr' : \u03b2 \u2192 \u03b2 \u2192 Prop\ns t : Set \u03b1\na b\u271d : \u03b1\nhs : IsAntichain r s\n\u03c6 : r \u21aar r'\nb : \u03b2\nhb : \u2203 x \u2208 s, \u03c6 x = b\nb' : \u03b2\nhb' : \u2203 x \u2208 s, \u03c6 x = b'\nh\u2081 : b \u2260 b'\nh\u2082 : r' b b'\n\u22a2 False",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr r\u2081 r\u2082 : \u03b1 \u2192 \u03b1 \u2192 Prop\nr' : \u03b2 \u2192 \u03b2 \u2192 Prop\ns t : Set \u03b1\na b\u271d : \u03b1\nhs : IsAntichain r s\n\u03c6 : r \u21aar r'\nb : \u03b2\nhb : b \u2208 \u21d1\u03c6 '' s\nb' : \u03b2\nhb' : b' \u2208 \u21d1\u03c6 '' s\nh\u2081 : b \u2260 b'\nh\u2082 : r' b b'\n\u22a2 False",
+              "tactic": "rw [Set.mem_image] at hb hb'"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8\\u27e8a, has, rfl\\u27e9, \\u27e8a', has', rfl\\u27e9\\u27e9 := hb, hb'\"",
+                "[]"
+              ],
+              "state_after": "case intro.intro.intro.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr r\u2081 r\u2082 : \u03b1 \u2192 \u03b1 \u2192 Prop\nr' : \u03b2 \u2192 \u03b2 \u2192 Prop\ns t : Set \u03b1\na\u271d b : \u03b1\nhs : IsAntichain r s\n\u03c6 : r \u21aar r'\na : \u03b1\nhas : a \u2208 s\na' : \u03b1\nhas' : a' \u2208 s\nh\u2081 : \u03c6 a \u2260 \u03c6 a'\nh\u2082 : r' (\u03c6 a) (\u03c6 a')\n\u22a2 False",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr r\u2081 r\u2082 : \u03b1 \u2192 \u03b1 \u2192 Prop\nr' : \u03b2 \u2192 \u03b2 \u2192 Prop\ns t : Set \u03b1\na b\u271d : \u03b1\nhs : IsAntichain r s\n\u03c6 : r \u21aar r'\nb : \u03b2\nhb : \u2203 x \u2208 s, \u03c6 x = b\nb' : \u03b2\nhb' : \u2203 x \u2208 s, \u03c6 x = b'\nh\u2081 : b \u2260 b'\nh\u2082 : r' b b'\n\u22a2 False",
+              "tactic": "obtain \u27e8\u27e8a, has, rfl\u27e9, \u27e8a', has', rfl\u27e9\u27e9 := hb, hb'"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact hs has has' (fun haa' => h\\u2081 (by rw [haa'])) (\\u03c6.map_rel_iff.mp h\\u2082)\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case intro.intro.intro.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr r\u2081 r\u2082 : \u03b1 \u2192 \u03b1 \u2192 Prop\nr' : \u03b2 \u2192 \u03b2 \u2192 Prop\ns t : Set \u03b1\na\u271d b : \u03b1\nhs : IsAntichain r s\n\u03c6 : r \u21aar r'\na : \u03b1\nhas : a \u2208 s\na' : \u03b1\nhas' : a' \u2208 s\nh\u2081 : \u03c6 a \u2260 \u03c6 a'\nh\u2082 : r' (\u03c6 a) (\u03c6 a')\n\u22a2 False",
+              "tactic": "exact hs has has' (fun haa' => h\u2081 (by rw [haa'])) (\u03c6.map_rel_iff.mp h\u2082)"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [haa']\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr r\u2081 r\u2082 : \u03b1 \u2192 \u03b1 \u2192 Prop\nr' : \u03b2 \u2192 \u03b2 \u2192 Prop\ns t : Set \u03b1\na\u271d b : \u03b1\nhs : IsAntichain r s\n\u03c6 : r \u21aar r'\na : \u03b1\nhas : a \u2208 s\na' : \u03b1\nhas' : a' \u2208 s\nh\u2081 : \u03c6 a \u2260 \u03c6 a'\nh\u2082 : r' (\u03c6 a) (\u03c6 a')\nhaa' : a = a'\n\u22a2 \u03c6 a = \u03c6 a'",
+              "tactic": "rw [haa']"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.image_relEmbedding_iff",
+        "id": "IsAntichain.image_relEmbedding_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            143,
+            28
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.image_relEmbedding_iff",
+          "start": [
+            141,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.image_relIso",
+        "id": "IsAntichain.image_relIso",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            133,
+            26
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.image_relIso",
+          "start": [
+            132,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.image_relIso_iff",
+        "id": "IsAntichain.image_relIso_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            147,
+            50
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.image_relIso_iff",
+          "start": [
+            146,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.insert",
+        "id": "IsAntichain.insert",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            107,
+            68
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.insert",
+          "start": [
+            105,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.insert_of_symmetric",
+        "id": "IsAntichain.insert_of_symmetric",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            117,
+            49
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.insert_of_symmetric",
+          "start": [
+            115,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.isAntisymm",
+        "id": "IsAntichain.isAntisymm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            70,
+            44
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.isAntisymm",
+          "start": [
+            69,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.isWeakAntichain",
+        "id": "IsAntichain.isWeakAntichain",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            397,
+            36
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.isWeakAntichain",
+          "start": [
+            396,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.least_iff",
+        "id": "IsAntichain.least_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            234,
+            58
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.least_iff",
+          "start": [
+            233,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.mono",
+        "id": "IsAntichain.mono",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            51,
+            31
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.mono",
+          "start": [
+            50,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.mono_on",
+        "id": "IsAntichain.mono_on",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            56,
+            51
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.mono_on",
+          "start": [
+            54,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.not_lt",
+        "id": "IsAntichain.not_lt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            218,
+            30
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.not_lt",
+          "start": [
+            217,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.of_monotoneOn_strictAntiOn",
+        "id": "IsAntichain.of_monotoneOn_strictAntiOn",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            351,
+            83
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.of_monotoneOn_strictAntiOn",
+          "start": [
+            349,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.of_strictMonoOn_antitoneOn",
+        "id": "IsAntichain.of_strictMonoOn_antitoneOn",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            347,
+            83
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.of_strictMonoOn_antitoneOn",
+          "start": [
+            345,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.preimage",
+        "id": "IsAntichain.preimage",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            97,
+            31
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.preimage",
+          "start": [
+            95,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.preimage_compl",
+        "id": "IsAntichain.preimage_compl",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            200,
+            74
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.preimage_compl",
+          "start": [
+            198,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.preimage_embedding",
+        "id": "IsAntichain.preimage_embedding",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            157,
+            29
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.preimage_embedding",
+          "start": [
+            155,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.preimage_iso",
+        "id": "IsAntichain.preimage_iso",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            177,
+            29
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.preimage_iso",
+          "start": [
+            175,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.preimage_iso_iff",
+        "id": "IsAntichain.preimage_iso_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            182,
+            83
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.preimage_iso_iff",
+          "start": [
+            180,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.preimage_relEmbedding",
+        "id": "IsAntichain.preimage_relEmbedding",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            129,
+            67
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.preimage_relEmbedding",
+          "start": [
+            127,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.preimage_relIso",
+        "id": "IsAntichain.preimage_relIso",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            138,
+            29
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.preimage_relIso",
+          "start": [
+            136,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.subset",
+        "id": "IsAntichain.subset",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            47,
+            12
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.subset",
+          "start": [
+            46,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.swap",
+        "id": "IsAntichain.swap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            86,
+            10
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.swap",
+          "start": [
+            85,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.to_dual",
+        "id": "IsAntichain.to_dual",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            186,
+            41
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.to_dual",
+          "start": [
+            185,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.to_dual_iff",
+        "id": "IsAntichain.to_dual_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            190,
+            21
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.to_dual_iff",
+          "start": [
+            189,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsAntichain.top_mem_iff",
+        "id": "IsAntichain.top_mem_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            254,
+            48
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsAntichain.top_mem_iff",
+          "start": [
+            253,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsGreatest.antichain_iff",
+        "id": "IsGreatest.antichain_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            246,
+            60
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsGreatest.antichain_iff",
+          "start": [
+            245,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsLeast.antichain_iff",
+        "id": "IsLeast.antichain_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            242,
+            57
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsLeast.antichain_iff",
+          "start": [
+            241,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsStrongAntichain.eq",
+        "id": "IsStrongAntichain.eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            292,
+            69
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsStrongAntichain.eq",
+          "start": [
+            289,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsStrongAntichain.flip",
+        "id": "IsStrongAntichain.flip",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            306,
+            78
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsStrongAntichain.flip",
+          "start": [
+            305,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsStrongAntichain.insert",
+        "id": "IsStrongAntichain.insert",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            333,
+            37
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsStrongAntichain.insert",
+          "start": [
+            331,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsStrongAntichain.isAntichain",
+        "id": "IsStrongAntichain.isAntichain",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            296,
+            71
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsStrongAntichain.isAntichain",
+          "start": [
+            295,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsStrongAntichain.mono",
+        "id": "IsStrongAntichain.mono",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            286,
+            86
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsStrongAntichain.mono",
+          "start": [
+            285,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsStrongAntichain.preimage",
+        "id": "IsStrongAntichain.preimage",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            322,
+            59
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsStrongAntichain.preimage",
+          "start": [
+            320,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsStrongAntichain.subset",
+        "id": "IsStrongAntichain.subset",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            282,
+            12
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsStrongAntichain.subset",
+          "start": [
+            281,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsStrongAntichain.subsingleton",
+        "id": "IsStrongAntichain.subsingleton",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            302,
+            21
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsStrongAntichain.subsingleton",
+          "start": [
+            299,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsStrongAntichain.swap",
+        "id": "IsStrongAntichain.swap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            310,
+            10
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsStrongAntichain.swap",
+          "start": [
+            309,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsWeakAntichain.eq",
+        "id": "IsWeakAntichain.eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            380,
+            20
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsWeakAntichain.eq",
+          "start": [
+            379,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsWeakAntichain.insert",
+        "id": "IsWeakAntichain.insert",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            386,
+            24
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsWeakAntichain.insert",
+          "start": [
+            383,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsWeakAntichain.subset",
+        "id": "IsWeakAntichain.subset",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            376,
+            24
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "IsWeakAntichain.subset",
+          "start": [
+            375,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.Subsingleton.isAntichain",
+        "id": "Set.Subsingleton.isAntichain",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            210,
+            16
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "Set.Subsingleton.isAntichain",
+          "start": [
+            209,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.Subsingleton.isStrongAntichain",
+        "id": "Set.Subsingleton.isStrongAntichain",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            340,
+            16
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "Set.Subsingleton.isStrongAntichain",
+          "start": [
+            338,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.Subsingleton.isWeakAntichain",
+        "id": "Set.Subsingleton.isWeakAntichain",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            401,
+            19
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "Set.Subsingleton.isWeakAntichain",
+          "start": [
+            400,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Symmetric.compl",
+        "id": "Symmetric.compl",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            36,
+            14
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "Symmetric.compl",
+          "start": [
+            35,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "isAntichain_iff_forall_not_lt",
+        "id": "isAntichain_iff_forall_not_lt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            265,
+            86
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "isAntichain_iff_forall_not_lt",
+          "start": [
+            263,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "isAntichain_insert",
+        "id": "isAntichain_insert",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            102,
+            22
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "isAntichain_insert",
+          "start": [
+            100,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "isAntichain_insert_of_symmetric",
+        "id": "isAntichain_insert_of_symmetric",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            112,
+            40
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "isAntichain_insert_of_symmetric",
+          "start": [
+            110,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "isAntichain_singleton",
+        "id": "isAntichain_singleton",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            206,
+            25
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "isAntichain_singleton",
+          "start": [
+            205,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "isStrongAntichain_insert",
+        "id": "isStrongAntichain_insert",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            328,
+            61
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "isStrongAntichain_insert",
+          "start": [
+            325,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "isWeakAntichain_insert",
+        "id": "isWeakAntichain_insert",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            393,
+            21
+          ],
+          "file_path": "Mathlib/Order/Antichain.lean",
+          "full_name": "isWeakAntichain_insert",
+          "start": [
+            391,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antichain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "AntisymmRel.symm",
+        "id": "AntisymmRel.symm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            56,
+            11
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "AntisymmRel.symm",
+          "start": [
+            55,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "AntisymmRel.trans",
+        "id": "AntisymmRel.trans",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            62,
+            55
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "AntisymmRel.trans",
+          "start": [
+            60,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Antisymmetrization.induction_on",
+        "id": "Antisymmetrization.induction_on",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            120,
+            28
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "Antisymmetrization.induction_on",
+          "start": [
+            118,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "OrderHom.antisymmetrization_apply",
+        "id": "OrderHom.antisymmetrization_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            229,
+            6
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "OrderHom.antisymmetrization_apply",
+          "start": [
+            227,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "OrderHom.antisymmetrization_apply_mk",
+        "id": "OrderHom.antisymmetrization_apply_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            235,
+            79
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "OrderHom.antisymmetrization_apply_mk",
+          "start": [
+            233,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "OrderHom.coe_antisymmetrization",
+        "id": "OrderHom.coe_antisymmetrization",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            222,
+            6
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "OrderHom.coe_antisymmetrization",
+          "start": [
+            220,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "OrderIso.dualAntisymmetrization_apply",
+        "id": "OrderIso.dualAntisymmetrization_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            261,
+            6
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "OrderIso.dualAntisymmetrization_apply",
+          "start": [
+            258,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "OrderIso.dualAntisymmetrization_symm_apply",
+        "id": "OrderIso.dualAntisymmetrization_symm_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            268,
+            6
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "OrderIso.dualAntisymmetrization_symm_apply",
+          "start": [
+            265,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "acc_antisymmetrization_iff",
+        "id": "acc_antisymmetrization_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            161,
+            19
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "acc_antisymmetrization_iff",
+          "start": [
+            159,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "antisymmRel_iff_eq",
+        "id": "antisymmRel_iff_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            71,
+            15
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "antisymmRel_iff_eq",
+          "start": [
+            70,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "antisymmRel_refl",
+        "id": "antisymmRel_refl",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            49,
+            19
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "antisymmRel_refl",
+          "start": [
+            48,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "antisymmRel_swap",
+        "id": "antisymmRel_swap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            44,
+            51
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "antisymmRel_swap",
+          "start": [
+            43,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "liftFun_antisymmRel",
+        "id": "liftFun_antisymmRel",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            209,
+            27
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "liftFun_antisymmRel",
+          "start": [
+            207,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ofAntisymmetrization_le_ofAntisymmetrization_iff",
+        "id": "ofAntisymmetrization_le_ofAntisymmetrization_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            194,
+            44
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "ofAntisymmetrization_le_ofAntisymmetrization_iff",
+          "start": [
+            192,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ofAntisymmetrization_lt_ofAntisymmetrization_iff",
+        "id": "ofAntisymmetrization_lt_ofAntisymmetrization_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            200,
+            44
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "ofAntisymmetrization_lt_ofAntisymmetrization_iff",
+          "start": [
+            198,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "toAntisymmetrization_le_toAntisymmetrization_iff",
+        "id": "toAntisymmetrization_le_toAntisymmetrization_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            182,
+            10
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "toAntisymmetrization_le_toAntisymmetrization_iff",
+          "start": [
+            180,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "toAntisymmetrization_lt_toAntisymmetrization_iff",
+        "id": "toAntisymmetrization_lt_toAntisymmetrization_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            188,
+            10
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "toAntisymmetrization_lt_toAntisymmetrization_iff",
+          "start": [
+            186,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "toAntisymmetrization_mono",
+        "id": "toAntisymmetrization_mono",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            204,
+            98
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "toAntisymmetrization_mono",
+          "start": [
+            204,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "toAntisymmetrization_ofAntisymmetrization",
+        "id": "toAntisymmetrization_ofAntisymmetrization",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            126,
+            21
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "toAntisymmetrization_ofAntisymmetrization",
+          "start": [
+            124,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "wellFounded_antisymmetrization_iff",
+        "id": "wellFounded_antisymmetrization_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            166,
+            27
+          ],
+          "file_path": "Mathlib/Order/Antisymmetrization.lean",
+          "full_name": "wellFounded_antisymmetrization_iff",
+          "start": [
+            164,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Antisymmetrization.lean"
+      }
+    ],
+    "input_proofs": 86,
+    "input_units": 2,
+    "proofs": 6,
+    "published_proofs": 5,
+    "published_transitions": 11,
+    "replay_failures": [],
+    "transitions": 16,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Order/Antichain.lean",
+        "proof_id": "mathlib:IsAntichain.subsingleton",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              78,
+              26
+            ],
+            "file_path": "Mathlib/Order/Antichain.lean",
+            "full_name": "IsAntichain.subsingleton",
+            "start": [
+              73,
+              11
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"rintro a ha b hb\"",
+                  "[]"
+                ],
+                "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr r\u2081 r\u2082 : \u03b1 \u2192 \u03b1 \u2192 Prop\nr' : \u03b2 \u2192 \u03b2 \u2192 Prop\ns t : Set \u03b1\na\u271d b\u271d : \u03b1\ninst\u271d : IsTrichotomous \u03b1 r\nh : IsAntichain r s\na : \u03b1\nha : a \u2208 s\nb : \u03b1\nhb : b \u2208 s\n\u22a2 a = b",
+                "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr r\u2081 r\u2082 : \u03b1 \u2192 \u03b1 \u2192 Prop\nr' : \u03b2 \u2192 \u03b2 \u2192 Prop\ns t : Set \u03b1\na b : \u03b1\ninst\u271d : IsTrichotomous \u03b1 r\nh : IsAntichain r s\n\u22a2 s.Subsingleton",
+                "tactic": "rintro a ha b hb"
+              },
+              {
+                "annotated_tactic": [
+                  "\"obtain hab | hab | hab := <a>trichotomous_of<\\/a> r a b\"",
+                  "[{\"full_name\":\"trichotomous_of\",\"def_path\":\"Mathlib\\/Init\\/Algebra\\/Classes.lean\",\"def_pos\":[364,9],\"def_end_pos\":[364,24]}]"
+                ],
+                "state_after": "case inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr r\u2081 r\u2082 : \u03b1 \u2192 \u03b1 \u2192 Prop\nr' : \u03b2 \u2192 \u03b2 \u2192 Prop\ns t : Set \u03b1\na\u271d b\u271d : \u03b1\ninst\u271d : IsTrichotomous \u03b1 r\nh : IsAntichain r s\na : \u03b1\nha : a \u2208 s\nb : \u03b1\nhb : b \u2208 s\nhab : r a b\n\u22a2 a = b\n\ncase inr.inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr r\u2081 r\u2082 : \u03b1 \u2192 \u03b1 \u2192 Prop\nr' : \u03b2 \u2192 \u03b2 \u2192 Prop\ns t : Set \u03b1\na\u271d b\u271d : \u03b1\ninst\u271d : IsTrichotomous \u03b1 r\nh : IsAntichain r s\na : \u03b1\nha : a \u2208 s\nb : \u03b1\nhb : b \u2208 s\nhab : a = b\n\u22a2 a = b\n\ncase inr.inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr r\u2081 r\u2082 : \u03b1 \u2192 \u03b1 \u2192 Prop\nr' : \u03b2 \u2192 \u03b2 \u2192 Prop\ns t : Set \u03b1\na\u271d b\u271d : \u03b1\ninst\u271d : IsTrichotomous \u03b1 r\nh : IsAntichain r s\na : \u03b1\nha : a \u2208 s\nb : \u03b1\nhb : b \u2208 s\nhab : r b a\n\u22a2 a = b",
+                "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr r\u2081 r\u2082 : \u03b1 \u2192 \u03b1 \u2192 Prop\nr' : \u03b2 \u2192 \u03b2 \u2192 Prop\ns t : Set \u03b1\na\u271d b\u271d : \u03b1\ninst\u271d : IsTrichotomous \u03b1 r\nh : IsAntichain r s\na : \u03b1\nha : a \u2208 s\nb : \u03b1\nhb : b \u2208 s\n\u22a2 a = b",
+                "tactic": "obtain hab | hab | hab := trichotomous_of r a b"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact h.eq ha hb hab\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr r\u2081 r\u2082 : \u03b1 \u2192 \u03b1 \u2192 Prop\nr' : \u03b2 \u2192 \u03b2 \u2192 Prop\ns t : Set \u03b1\na\u271d b\u271d : \u03b1\ninst\u271d : IsTrichotomous \u03b1 r\nh : IsAntichain r s\na : \u03b1\nha : a \u2208 s\nb : \u03b1\nhb : b \u2208 s\nhab : r a b\n\u22a2 a = b",
+                "tactic": "exact h.eq ha hb hab"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact hab\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case inr.inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr r\u2081 r\u2082 : \u03b1 \u2192 \u03b1 \u2192 Prop\nr' : \u03b2 \u2192 \u03b2 \u2192 Prop\ns t : Set \u03b1\na\u271d b\u271d : \u03b1\ninst\u271d : IsTrichotomous \u03b1 r\nh : IsAntichain r s\na : \u03b1\nha : a \u2208 s\nb : \u03b1\nhb : b \u2208 s\nhab : a = b\n\u22a2 a = b",
+                "tactic": "exact hab"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact h.eq' ha hb hab\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case inr.inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr r\u2081 r\u2082 : \u03b1 \u2192 \u03b1 \u2192 Prop\nr' : \u03b2 \u2192 \u03b2 \u2192 Prop\ns t : Set \u03b1\na\u271d b\u271d : \u03b1\ninst\u271d : IsTrichotomous \u03b1 r\nh : IsAntichain r s\na : \u03b1\nha : a \u2208 s\nb : \u03b1\nhb : b \u2208 s\nhab : r b a\n\u22a2 a = b",
+                "tactic": "exact h.eq' ha hb hab"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "IsAntichain.subsingleton"
+      }
+    ],
+    "validation_rejected_proofs": 1,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001516-0000-70b30e25dbc9e9fe.parquet",
+      "sha256": "70b30e25dbc9e9feffb6565b0afa4a04f3a923ffe871abaed6339c64373fa543",
+      "bytes": 57009,
+      "rows": 11,
+      "revision": "504ada6ade9a708ef0393868f005bf429a0291c6"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:IsAntichain.image",
+    "mathlib:IsStrongAntichain.image",
+    "mathlib:antisymmetrization_fibration",
+    "mathlib:isAntichain_and_greatest_iff",
+    "mathlib:isAntichain_and_least_iff"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Antichain.lean\",null,null,\"IsAntichain.image\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Antichain.lean\",null,null,\"IsStrongAntichain.image\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Antichain.lean\",null,null,\"isAntichain_and_greatest_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Antichain.lean\",null,null,\"isAntichain_and_least_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Antisymmetrization.lean\",null,null,\"antisymmetrization_fibration\"]"
+  ]
+}

manifests/batches/mathlib/001520.json

@@ -0,0 +1,1808 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001520",
+  "batch_fingerprint": "25758e148f07db35480a19ae15b89ccfbee74fbb178562fe3ac29f172798b969",
+  "evidence": {
+    "batch_fingerprint": "25758e148f07db35480a19ae15b89ccfbee74fbb178562fe3ac29f172798b969",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.comp_bot",
+        "id": "Booleanisation.comp_bot",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            153,
+            49
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.comp_bot",
+          "start": [
+            153,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.comp_inf_comp",
+        "id": "Booleanisation.comp_inf_comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            150,
+            78
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.comp_inf_comp",
+          "start": [
+            150,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.comp_inf_lift",
+        "id": "Booleanisation.comp_inf_lift",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            149,
+            78
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.comp_inf_lift",
+          "start": [
+            149,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.comp_sdiff_comp",
+        "id": "Booleanisation.comp_sdiff_comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            161,
+            80
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.comp_sdiff_comp",
+          "start": [
+            161,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.comp_sdiff_lift",
+        "id": "Booleanisation.comp_sdiff_lift",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            160,
+            80
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.comp_sdiff_lift",
+          "start": [
+            160,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.comp_sup_comp",
+        "id": "Booleanisation.comp_sup_comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            145,
+            78
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.comp_sup_comp",
+          "start": [
+            145,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.comp_sup_lift",
+        "id": "Booleanisation.comp_sup_lift",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            144,
+            78
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.comp_sup_lift",
+          "start": [
+            144,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.compl_comp",
+        "id": "Booleanisation.compl_comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            156,
+            61
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.compl_comp",
+          "start": [
+            156,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.compl_lift",
+        "id": "Booleanisation.compl_lift",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            155,
+            61
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.compl_lift",
+          "start": [
+            155,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.liftLatticeHom_injective",
+        "id": "Booleanisation.liftLatticeHom_injective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            270,
+            90
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.liftLatticeHom_injective",
+          "start": [
+            270,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.lift_bot",
+        "id": "Booleanisation.lift_bot",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            152,
+            49
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.lift_bot",
+          "start": [
+            152,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.lift_inf_comp",
+        "id": "Booleanisation.lift_inf_comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            148,
+            78
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.lift_inf_comp",
+          "start": [
+            148,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.lift_inf_lift",
+        "id": "Booleanisation.lift_inf_lift",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            147,
+            78
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.lift_inf_lift",
+          "start": [
+            147,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.lift_sdiff_comp",
+        "id": "Booleanisation.lift_sdiff_comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            159,
+            80
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.lift_sdiff_comp",
+          "start": [
+            159,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.lift_sdiff_lift",
+        "id": "Booleanisation.lift_sdiff_lift",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            158,
+            80
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.lift_sdiff_lift",
+          "start": [
+            158,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.lift_sup_comp",
+        "id": "Booleanisation.lift_sup_comp",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            143,
+            78
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.lift_sup_comp",
+          "start": [
+            143,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.lift_sup_lift",
+        "id": "Booleanisation.lift_sup_lift",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            142,
+            78
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.lift_sup_lift",
+          "start": [
+            142,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.not_comp_le_lift",
+        "id": "Booleanisation.not_comp_le_lift",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            135,
+            72
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.not_comp_le_lift",
+          "start": [
+            135,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Booleanisation.not_comp_lt_lift",
+        "id": "Booleanisation.not_comp_lt_lift",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            140,
+            72
+          ],
+          "file_path": "Mathlib/Order/Booleanisation.lean",
+          "full_name": "Booleanisation.not_comp_lt_lift",
+          "start": [
+            140,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Booleanisation.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.Bounded.mono",
+        "id": "Set.Bounded.mono",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            27,
+            40
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.Bounded.mono",
+          "start": [
+            26,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.Bounded.rel_mono",
+        "id": "Set.Bounded.rel_mono",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            91,
+            38
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.Bounded.rel_mono",
+          "start": [
+            89,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.Unbounded.mono",
+        "id": "Set.Unbounded.mono",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            32,
+            19
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.Unbounded.mono",
+          "start": [
+            30,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.Unbounded.rel_mono",
+        "id": "Set.Unbounded.rel_mono",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            101,
+            41
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.Unbounded.rel_mono",
+          "start": [
+            98,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_ge_Icc",
+        "id": "Set.bounded_ge_Icc",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            272,
+            50
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_ge_Icc",
+          "start": [
+            271,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_ge_Ici",
+        "id": "Set.bounded_ge_Ici",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            201,
+            17
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_ge_Ici",
+          "start": [
+            200,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_ge_Ico",
+        "id": "Set.bounded_ge_Ico",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            268,
+            50
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_ge_Ico",
+          "start": [
+            267,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_ge_Ioc",
+        "id": "Set.bounded_ge_Ioc",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            264,
+            50
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_ge_Ioc",
+          "start": [
+            263,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_ge_Ioi",
+        "id": "Set.bounded_ge_Ioi",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            197,
+            46
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_ge_Ioi",
+          "start": [
+            196,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_ge_Ioo",
+        "id": "Set.bounded_ge_Ioo",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            260,
+            50
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_ge_Ioo",
+          "start": [
+            259,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_ge_iff_bounded_gt",
+        "id": "Set.bounded_ge_iff_bounded_gt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            137,
+            39
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_ge_iff_bounded_gt",
+          "start": [
+            135,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_ge_inter_ge",
+        "id": "Set.bounded_ge_inter_ge",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            415,
+            33
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_ge_inter_ge",
+          "start": [
+            413,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_ge_inter_gt",
+        "id": "Set.bounded_ge_inter_gt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            405,
+            33
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_ge_inter_gt",
+          "start": [
+            403,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_ge_inter_not_ge",
+        "id": "Set.bounded_ge_inter_not_ge",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            395,
+            37
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_ge_inter_not_ge",
+          "start": [
+            393,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_ge_of_bounded_gt",
+        "id": "Set.bounded_ge_of_bounded_gt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            126,
+            38
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_ge_of_bounded_gt",
+          "start": [
+            124,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_gt_Icc",
+        "id": "Set.bounded_gt_Icc",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            256,
+            50
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_gt_Icc",
+          "start": [
+            255,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_gt_Ico",
+        "id": "Set.bounded_gt_Ico",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            252,
+            50
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_gt_Ico",
+          "start": [
+            251,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_gt_Ioc",
+        "id": "Set.bounded_gt_Ioc",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            248,
+            50
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_gt_Ioc",
+          "start": [
+            247,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_gt_Ioi",
+        "id": "Set.bounded_gt_Ioi",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            193,
+            17
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_gt_Ioi",
+          "start": [
+            192,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_gt_Ioo",
+        "id": "Set.bounded_gt_Ioo",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            244,
+            50
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_gt_Ioo",
+          "start": [
+            243,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_gt_inter_ge",
+        "id": "Set.bounded_gt_inter_ge",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            438,
+            33
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_gt_inter_ge",
+          "start": [
+            436,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_gt_inter_gt",
+        "id": "Set.bounded_gt_inter_gt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            448,
+            35
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_gt_inter_gt",
+          "start": [
+            446,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_le_Icc",
+        "id": "Set.bounded_le_Icc",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            240,
+            50
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_le_Icc",
+          "start": [
+            239,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_le_Ico",
+        "id": "Set.bounded_le_Ico",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            232,
+            50
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_le_Ico",
+          "start": [
+            231,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_le_Iic",
+        "id": "Set.bounded_le_Iic",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            185,
+            17
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_le_Iic",
+          "start": [
+            184,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_le_Iio",
+        "id": "Set.bounded_le_Iio",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            181,
+            46
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_le_Iio",
+          "start": [
+            180,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_le_Ioc",
+        "id": "Set.bounded_le_Ioc",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            236,
+            50
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_le_Ioc",
+          "start": [
+            235,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_le_Ioo",
+        "id": "Set.bounded_le_Ioo",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            228,
+            50
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_le_Ioo",
+          "start": [
+            227,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_le_inter_not_le",
+        "id": "Set.bounded_le_inter_not_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            319,
+            99
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_le_inter_not_le",
+          "start": [
+            317,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_le_of_bounded_lt",
+        "id": "Set.bounded_le_of_bounded_lt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            95,
+            33
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_le_of_bounded_lt",
+          "start": [
+            94,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_lt_Ico",
+        "id": "Set.bounded_lt_Ico",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            216,
+            50
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_lt_Ico",
+          "start": [
+            215,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_lt_Iio",
+        "id": "Set.bounded_lt_Iio",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            177,
+            17
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_lt_Iio",
+          "start": [
+            176,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_lt_Ioc",
+        "id": "Set.bounded_lt_Ioc",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            220,
+            50
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_lt_Ioc",
+          "start": [
+            219,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_lt_Ioo",
+        "id": "Set.bounded_lt_Ioo",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            212,
+            50
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_lt_Ioo",
+          "start": [
+            211,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_lt_inter_not_lt",
+        "id": "Set.bounded_lt_inter_not_lt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            357,
+            99
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_lt_inter_not_lt",
+          "start": [
+            355,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.bounded_self",
+        "id": "Set.bounded_self",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            170,
+            19
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.bounded_self",
+          "start": [
+            169,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_ge_iff",
+        "id": "Set.unbounded_ge_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            67,
+            38
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_ge_iff",
+          "start": [
+            63,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_ge_iff_unbounded_inter_ge",
+        "id": "Set.unbounded_ge_iff_unbounded_inter_ge",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            420,
+            35
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_ge_iff_unbounded_inter_ge",
+          "start": [
+            418,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_ge_inter_gt",
+        "id": "Set.unbounded_ge_inter_gt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            410,
+            35
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_ge_inter_gt",
+          "start": [
+            408,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_ge_inter_not_ge",
+        "id": "Set.unbounded_ge_inter_not_ge",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            400,
+            39
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_ge_inter_not_ge",
+          "start": [
+            398,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_ge_of_forall_exists_gt",
+        "id": "Set.unbounded_ge_of_forall_exists_gt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            60,
+            46
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_ge_of_forall_exists_gt",
+          "start": [
+            58,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_ge_univ",
+        "id": "Set.unbounded_ge_univ",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            159,
+            14
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_ge_univ",
+          "start": [
+            157,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_gt_iff",
+        "id": "Set.unbounded_gt_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            80,
+            38
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_gt_iff",
+          "start": [
+            76,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_gt_iff_unbounded_ge",
+        "id": "Set.unbounded_gt_iff_unbounded_ge",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            142,
+            43
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_gt_iff_unbounded_ge",
+          "start": [
+            140,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_gt_inter_gt",
+        "id": "Set.unbounded_gt_inter_gt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            453,
+            37
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_gt_inter_gt",
+          "start": [
+            451,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_gt_inter_not_gt",
+        "id": "Set.unbounded_gt_inter_not_gt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            433,
+            39
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_gt_inter_not_gt",
+          "start": [
+            431,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_gt_of_forall_exists_ge",
+        "id": "Set.unbounded_gt_of_forall_exists_ge",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            73,
+            43
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_gt_of_forall_exists_ge",
+          "start": [
+            70,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_gt_of_unbounded_ge",
+        "id": "Set.unbounded_gt_of_unbounded_ge",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            132,
+            43
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_gt_of_unbounded_ge",
+          "start": [
+            129,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_gt_univ",
+        "id": "Set.unbounded_gt_univ",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            163,
+            49
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_gt_univ",
+          "start": [
+            162,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_inter_ge",
+        "id": "Set.unbounded_inter_ge",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            443,
+            35
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_inter_ge",
+          "start": [
+            441,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_le_Ici",
+        "id": "Set.unbounded_le_Ici",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            286,
+            52
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_le_Ici",
+          "start": [
+            284,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_le_Ioi",
+        "id": "Set.unbounded_le_Ioi",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            281,
+            66
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_le_Ioi",
+          "start": [
+            278,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_le_of_forall_exists_lt",
+        "id": "Set.unbounded_le_of_forall_exists_lt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            41,
+            37
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_le_of_forall_exists_lt",
+          "start": [
+            38,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_le_univ",
+        "id": "Set.unbounded_le_univ",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            150,
+            14
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_le_univ",
+          "start": [
+            148,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_lt_Ici",
+        "id": "Set.unbounded_lt_Ici",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            295,
+            44
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_lt_Ici",
+          "start": [
+            294,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_lt_Ioi",
+        "id": "Set.unbounded_lt_Ioi",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            291,
+            52
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_lt_Ioi",
+          "start": [
+            289,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_lt_of_forall_exists_le",
+        "id": "Set.unbounded_lt_of_forall_exists_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            51,
+            37
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_lt_of_forall_exists_le",
+          "start": [
+            48,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_lt_of_unbounded_le",
+        "id": "Set.unbounded_lt_of_unbounded_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            105,
+            33
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_lt_of_unbounded_le",
+          "start": [
+            104,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.unbounded_lt_univ",
+        "id": "Set.unbounded_lt_univ",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            154,
+            49
+          ],
+          "file_path": "Mathlib/Order/Bounded.lean",
+          "full_name": "Set.unbounded_lt_univ",
+          "start": [
+            153,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounded.lean"
+      }
+    ],
+    "input_proofs": 100,
+    "input_units": 2,
+    "proofs": 22,
+    "published_proofs": 22,
+    "published_transitions": 43,
+    "replay_failures": [],
+    "transitions": 43,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001520-0000-7751f50c0a949796.parquet",
+      "sha256": "7751f50c0a949796133d97aaa45a9067efa648fc4f7465562eb28050f48f5db7",
+      "bytes": 114821,
+      "rows": 37,
+      "revision": "504ada6ade9a708ef0393868f005bf429a0291c6"
+    },
+    {
+      "path": "data/dev/mathlib-001520-0000-0cf3b258ed3d974a.parquet",
+      "sha256": "0cf3b258ed3d974a5167478456941b1e34a4f63aa65fa0e7ca3caf0b9990f8e5",
+      "bytes": 44110,
+      "rows": 2,
+      "revision": "504ada6ade9a708ef0393868f005bf429a0291c6"
+    },
+    {
+      "path": "data/internal_test/mathlib-001520-0000-4cfdf466047da93b.parquet",
+      "sha256": "4cfdf466047da93b73e9fd411f650c759b060615ff77b6c2c5f35d74341e287f",
+      "bytes": 44231,
+      "rows": 4,
+      "revision": "504ada6ade9a708ef0393868f005bf429a0291c6"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Booleanisation.comp_le_comp",
+    "mathlib:Booleanisation.comp_lt_comp",
+    "mathlib:Booleanisation.lift_le_comp",
+    "mathlib:Booleanisation.lift_lt_comp",
+    "mathlib:Booleanisation.lift_lt_lift",
+    "mathlib:Set.bounded_gt_Ici",
+    "mathlib:Set.bounded_inter_not",
+    "mathlib:Set.bounded_le_iff_bounded_lt",
+    "mathlib:Set.bounded_le_inter_le",
+    "mathlib:Set.bounded_le_inter_lt",
+    "mathlib:Set.bounded_lt_Iic",
+    "mathlib:Set.bounded_lt_inter_le",
+    "mathlib:Set.bounded_lt_inter_lt",
+    "mathlib:Set.unbounded_le_iff",
+    "mathlib:Set.unbounded_le_inter_le",
+    "mathlib:Set.unbounded_le_inter_lt",
+    "mathlib:Set.unbounded_le_inter_not_le",
+    "mathlib:Set.unbounded_lt_iff",
+    "mathlib:Set.unbounded_lt_iff_unbounded_le",
+    "mathlib:Set.unbounded_lt_inter_le",
+    "mathlib:Set.unbounded_lt_inter_lt",
+    "mathlib:Set.unbounded_lt_inter_not_lt"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Booleanisation.lean\",null,null,\"Booleanisation.comp_le_comp\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Booleanisation.lean\",null,null,\"Booleanisation.comp_lt_comp\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Booleanisation.lean\",null,null,\"Booleanisation.lift_le_comp\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Booleanisation.lean\",null,null,\"Booleanisation.lift_lt_comp\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Booleanisation.lean\",null,null,\"Booleanisation.lift_lt_lift\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounded.lean\",null,null,\"Set.bounded_gt_Ici\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounded.lean\",null,null,\"Set.bounded_inter_not\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounded.lean\",null,null,\"Set.bounded_le_iff_bounded_lt\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounded.lean\",null,null,\"Set.bounded_le_inter_le\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounded.lean\",null,null,\"Set.bounded_le_inter_lt\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounded.lean\",null,null,\"Set.bounded_lt_Iic\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounded.lean\",null,null,\"Set.bounded_lt_inter_le\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounded.lean\",null,null,\"Set.bounded_lt_inter_lt\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounded.lean\",null,null,\"Set.unbounded_le_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounded.lean\",null,null,\"Set.unbounded_le_inter_le\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounded.lean\",null,null,\"Set.unbounded_le_inter_lt\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounded.lean\",null,null,\"Set.unbounded_le_inter_not_le\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounded.lean\",null,null,\"Set.unbounded_lt_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounded.lean\",null,null,\"Set.unbounded_lt_iff_unbounded_le\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounded.lean\",null,null,\"Set.unbounded_lt_inter_le\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounded.lean\",null,null,\"Set.unbounded_lt_inter_lt\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounded.lean\",null,null,\"Set.unbounded_lt_inter_not_lt\"]"
+  ]
+}

manifests/batches/mathlib/001522.json

@@ -0,0 +1,301 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001522",
+  "batch_fingerprint": "e4decfde26e480a9f3f6a4106763a2fb5de60522b3e98b3395d204a9fa408e89",
+  "evidence": {
+    "batch_fingerprint": "e4decfde26e480a9f3f6a4106763a2fb5de60522b3e98b3395d204a9fa408e89",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "OrderIso.isGLB_image",
+        "id": "OrderIso.isGLB_image",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            45,
+            21
+          ],
+          "file_path": "Mathlib/Order/Bounds/OrderIso.lean",
+          "full_name": "OrderIso.isGLB_image",
+          "start": [
+            44,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounds/OrderIso.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "OrderIso.isGLB_image'",
+        "id": "OrderIso.isGLB_image'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            49,
+            22
+          ],
+          "file_path": "Mathlib/Order/Bounds/OrderIso.lean",
+          "full_name": "OrderIso.isGLB_image'",
+          "start": [
+            48,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounds/OrderIso.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "OrderIso.isGLB_preimage",
+        "id": "OrderIso.isGLB_preimage",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            63,
+            24
+          ],
+          "file_path": "Mathlib/Order/Bounds/OrderIso.lean",
+          "full_name": "OrderIso.isGLB_preimage",
+          "start": [
+            62,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounds/OrderIso.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "OrderIso.isGLB_preimage'",
+        "id": "OrderIso.isGLB_preimage'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            67,
+            25
+          ],
+          "file_path": "Mathlib/Order/Bounds/OrderIso.lean",
+          "full_name": "OrderIso.isGLB_preimage'",
+          "start": [
+            66,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounds/OrderIso.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'simp'",
+        "full_name": "OrderIso.isLUB_image",
+        "id": "OrderIso.isLUB_image",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            36,
+            67
+          ],
+          "file_path": "Mathlib/Order/Bounds/OrderIso.lean",
+          "full_name": "OrderIso.isLUB_image",
+          "start": [
+            34,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"simp\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : Preorder \u03b1\ninst\u271d : Preorder \u03b2\nf : \u03b1 \u2243o \u03b2\ns : Set \u03b1\nx : \u03b2\nh : IsLUB (\u21d1f '' s) x\n\u22a2 \u2200 {x y : \u03b1}, f x \u2264 f y \u2194 x \u2264 y",
+              "tactic": "simp"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : Preorder \u03b1\ninst\u271d : Preorder \u03b2\nf : \u03b1 \u2243o \u03b2\ns : Set \u03b1\nx : \u03b2\nh : IsLUB s (f.symm x)\n\u22a2 \u2200 {x y : \u03b2}, f.symm x \u2264 f.symm y \u2194 x \u2264 y",
+              "tactic": "simp"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounds/OrderIso.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "OrderIso.lowerBounds_image",
+        "id": "OrderIso.lowerBounds_image",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            29,
+            42
+          ],
+          "file_path": "Mathlib/Order/Bounds/OrderIso.lean",
+          "full_name": "OrderIso.lowerBounds_image",
+          "start": [
+            28,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounds/OrderIso.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "OrderIso.upperBounds_image",
+        "id": "OrderIso.upperBounds_image",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            25,
+            58
+          ],
+          "file_path": "Mathlib/Order/Bounds/OrderIso.lean",
+          "full_name": "OrderIso.upperBounds_image",
+          "start": [
+            21,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Bounds/OrderIso.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BddDistLat.coe_of",
+        "id": "BddDistLat.coe_of",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            52,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddDistLat.lean",
+          "full_name": "BddDistLat.coe_of",
+          "start": [
+            51,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddDistLat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BddDistLat.coe_toBddLat",
+        "id": "BddDistLat.coe_toBddLat",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            65,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddDistLat.lean",
+          "full_name": "BddDistLat.coe_toBddLat",
+          "start": [
+            64,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddDistLat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BddDistLat.forget_bddLat_lat_eq_forget_distLat_lat",
+        "id": "BddDistLat.forget_bddLat_lat_eq_forget_distLat_lat",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            89,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddDistLat.lean",
+          "full_name": "BddDistLat.forget_bddLat_lat_eq_forget_distLat_lat",
+          "start": [
+            86,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddDistLat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "bddDistLat_dual_comp_forget_to_distLat",
+        "id": "bddDistLat_dual_comp_forget_to_distLat",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            123,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddDistLat.lean",
+          "full_name": "bddDistLat_dual_comp_forget_to_distLat",
+          "start": [
+            120,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddDistLat.lean"
+      }
+    ],
+    "input_proofs": 14,
+    "input_units": 2,
+    "proofs": 3,
+    "published_proofs": 3,
+    "published_transitions": 3,
+    "replay_failures": [],
+    "transitions": 3,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001522-0000-463332a3c0154d73.parquet",
+      "sha256": "463332a3c0154d73eb55742a1c4f3d2dfa2c0bd1b4c27c3a7646b90faf1ce365",
+      "bytes": 38496,
+      "rows": 3,
+      "revision": "504ada6ade9a708ef0393868f005bf429a0291c6"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:OrderIso.isLUB_image'",
+    "mathlib:OrderIso.isLUB_preimage",
+    "mathlib:OrderIso.isLUB_preimage'"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounds/OrderIso.lean\",null,null,\"OrderIso.isLUB_image'\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounds/OrderIso.lean\",null,null,\"OrderIso.isLUB_preimage\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Bounds/OrderIso.lean\",null,null,\"OrderIso.isLUB_preimage'\"]"
+  ]
+}

manifests/batches/mathlib/001523.json

@@ -0,0 +1,355 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001523",
+  "batch_fingerprint": "920a19c6f47422058c0c102425f2f4f07d99161f9811f1cbc58b741040f1eb95",
+  "evidence": {
+    "batch_fingerprint": "920a19c6f47422058c0c102425f2f4f07d99161f9811f1cbc58b741040f1eb95",
+    "batch_outcome": "all_inputs_failed_with_evidence",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BddLat.coe_forget_to_bddOrd",
+        "id": "BddLat.coe_forget_to_bddOrd",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            104,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddLat.lean",
+          "full_name": "BddLat.coe_forget_to_bddOrd",
+          "start": [
+            103,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddLat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BddLat.coe_forget_to_lat",
+        "id": "BddLat.coe_forget_to_lat",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            109,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddLat.lean",
+          "full_name": "BddLat.coe_forget_to_lat",
+          "start": [
+            108,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddLat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BddLat.coe_forget_to_semilatInf",
+        "id": "BddLat.coe_forget_to_semilatInf",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            121,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddLat.lean",
+          "full_name": "BddLat.coe_forget_to_semilatInf",
+          "start": [
+            119,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddLat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BddLat.coe_forget_to_semilatSup",
+        "id": "BddLat.coe_forget_to_semilatSup",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            115,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddLat.lean",
+          "full_name": "BddLat.coe_forget_to_semilatSup",
+          "start": [
+            113,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddLat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BddLat.coe_of",
+        "id": "BddLat.coe_of",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            53,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddLat.lean",
+          "full_name": "BddLat.coe_of",
+          "start": [
+            52,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddLat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BddLat.forget_lat_partOrd_eq_forget_bddOrd_partOrd",
+        "id": "BddLat.forget_lat_partOrd_eq_forget_bddOrd_partOrd",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            127,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddLat.lean",
+          "full_name": "BddLat.forget_lat_partOrd_eq_forget_bddOrd_partOrd",
+          "start": [
+            124,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddLat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BddLat.forget_semilatInf_partOrd_eq_forget_bddOrd_partOrd",
+        "id": "BddLat.forget_semilatInf_partOrd_eq_forget_bddOrd_partOrd",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            139,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddLat.lean",
+          "full_name": "BddLat.forget_semilatInf_partOrd_eq_forget_bddOrd_partOrd",
+          "start": [
+            136,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddLat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BddLat.forget_semilatSup_partOrd_eq_forget_bddOrd_partOrd",
+        "id": "BddLat.forget_semilatSup_partOrd_eq_forget_bddOrd_partOrd",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            133,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddLat.lean",
+          "full_name": "BddLat.forget_semilatSup_partOrd_eq_forget_bddOrd_partOrd",
+          "start": [
+            130,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddLat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "bddLat_dual_comp_forget_to_bddOrd",
+        "id": "bddLat_dual_comp_forget_to_bddOrd",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            173,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddLat.lean",
+          "full_name": "bddLat_dual_comp_forget_to_bddOrd",
+          "start": [
+            170,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddLat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "bddLat_dual_comp_forget_to_lat",
+        "id": "bddLat_dual_comp_forget_to_lat",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            178,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddLat.lean",
+          "full_name": "bddLat_dual_comp_forget_to_lat",
+          "start": [
+            176,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddLat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "bddLat_dual_comp_forget_to_semilatInfCat",
+        "id": "bddLat_dual_comp_forget_to_semilatInfCat",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            190,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddLat.lean",
+          "full_name": "bddLat_dual_comp_forget_to_semilatInfCat",
+          "start": [
+            187,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddLat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "bddLat_dual_comp_forget_to_semilatSupCat",
+        "id": "bddLat_dual_comp_forget_to_semilatSupCat",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            184,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddLat.lean",
+          "full_name": "bddLat_dual_comp_forget_to_semilatSupCat",
+          "start": [
+            181,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddLat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BddOrd.coe_of",
+        "id": "BddOrd.coe_of",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            49,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddOrd.lean",
+          "full_name": "BddOrd.coe_of",
+          "start": [
+            48,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddOrd.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "bddOrd_dual_comp_forget_to_bipointed",
+        "id": "bddOrd_dual_comp_forget_to_bipointed",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            125,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddOrd.lean",
+          "full_name": "bddOrd_dual_comp_forget_to_bipointed",
+          "start": [
+            122,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddOrd.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "bddOrd_dual_comp_forget_to_partOrd",
+        "id": "bddOrd_dual_comp_forget_to_partOrd",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            119,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BddOrd.lean",
+          "full_name": "bddOrd_dual_comp_forget_to_partOrd",
+          "start": [
+            116,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BddOrd.lean"
+      }
+    ],
+    "input_proofs": 15,
+    "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/001524.json

@@ -0,0 +1,135 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001524",
+  "batch_fingerprint": "37093c84a9ad038e93a7692d7241060dea044f8b4fc5f200a0822a298ef7addd",
+  "evidence": {
+    "batch_fingerprint": "37093c84a9ad038e93a7692d7241060dea044f8b4fc5f200a0822a298ef7addd",
+    "batch_outcome": "all_inputs_failed_with_evidence",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BoolAlg.coe_of",
+        "id": "BoolAlg.coe_of",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            45,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BoolAlg.lean",
+          "full_name": "BoolAlg.coe_of",
+          "start": [
+            44,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BoolAlg.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "BoolAlg.coe_toBddDistLat",
+        "id": "BoolAlg.coe_toBddDistLat",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            58,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BoolAlg.lean",
+          "full_name": "BoolAlg.coe_toBddDistLat",
+          "start": [
+            57,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BoolAlg.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "boolAlg_dual_comp_forget_to_bddDistLat",
+        "id": "boolAlg_dual_comp_forget_to_bddDistLat",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            117,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/BoolAlg.lean",
+          "full_name": "boolAlg_dual_comp_forget_to_bddDistLat",
+          "start": [
+            114,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/BoolAlg.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CompleteLat.coe_of",
+        "id": "CompleteLat.coe_of",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            43,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/CompleteLat.lean",
+          "full_name": "CompleteLat.coe_of",
+          "start": [
+            42,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/CompleteLat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "completeLat_dual_comp_forget_to_bddLat",
+        "id": "completeLat_dual_comp_forget_to_bddLat",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            97,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/CompleteLat.lean",
+          "full_name": "completeLat_dual_comp_forget_to_bddLat",
+          "start": [
+            94,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/CompleteLat.lean"
+      }
+    ],
+    "input_proofs": 5,
+    "input_units": 2,
+    "proofs": 0,
+    "published_proofs": 0,
+    "published_transitions": 0,
+    "replay_failures": [],
+    "transitions": 0,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [],
+  "proof_ids": [],
+  "proof_keys": []
+}

manifests/batches/mathlib/001525.json

@@ -0,0 +1,91 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001525",
+  "batch_fingerprint": "e3bde3228f1f32162f28e1f21f85472e70c6b8ec94d781519992631b7920f6ad",
+  "evidence": {
+    "batch_fingerprint": "e3bde3228f1f32162f28e1f21f85472e70c6b8ec94d781519992631b7920f6ad",
+    "batch_outcome": "all_inputs_failed_with_evidence",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DistLat.coe_of",
+        "id": "DistLat.coe_of",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            47,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/DistLat.lean",
+          "full_name": "DistLat.coe_of",
+          "start": [
+            46,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/DistLat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "distLat_dual_comp_forget_to_Lat",
+        "id": "distLat_dual_comp_forget_to_Lat",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            99,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/DistLat.lean",
+          "full_name": "distLat_dual_comp_forget_to_Lat",
+          "start": [
+            97,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/DistLat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "finBddDistLat_dual_comp_forget_to_bddDistLat",
+        "id": "finBddDistLat_dual_comp_forget_to_bddDistLat",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            113,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/FinBddDistLat.lean",
+          "full_name": "finBddDistLat_dual_comp_forget_to_bddDistLat",
+          "start": [
+            110,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/FinBddDistLat.lean"
+      }
+    ],
+    "input_proofs": 3,
+    "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/001526.json

@@ -0,0 +1,113 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001526",
+  "batch_fingerprint": "84e287a86253e51dee913b5643438d8434a6ce19369d87c9f70823e73316a2d4",
+  "evidence": {
+    "batch_fingerprint": "84e287a86253e51dee913b5643438d8434a6ce19369d87c9f70823e73316a2d4",
+    "batch_outcome": "all_inputs_failed_with_evidence",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "FinBoolAlg.coe_of",
+        "id": "FinBoolAlg.coe_of",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            68,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/FinBoolAlg.lean",
+          "full_name": "FinBoolAlg.coe_of",
+          "start": [
+            67,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/FinBoolAlg.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "finBoolAlg_dual_comp_forget_to_finBddDistLat",
+        "id": "finBoolAlg_dual_comp_forget_to_finBddDistLat",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            163,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/FinBoolAlg.lean",
+          "full_name": "finBoolAlg_dual_comp_forget_to_finBddDistLat",
+          "start": [
+            160,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/FinBoolAlg.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "FinPartOrd.coe_of",
+        "id": "FinPartOrd.coe_of",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            56,
+            77
+          ],
+          "file_path": "Mathlib/Order/Category/FinPartOrd.lean",
+          "full_name": "FinPartOrd.coe_of",
+          "start": [
+            56,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/FinPartOrd.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "FinPartOrd_dual_comp_forget_to_partOrd",
+        "id": "FinPartOrd_dual_comp_forget_to_partOrd",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            113,
+            55
+          ],
+          "file_path": "Mathlib/Order/Category/FinPartOrd.lean",
+          "full_name": "FinPartOrd_dual_comp_forget_to_partOrd",
+          "start": [
+            111,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/FinPartOrd.lean"
+      }
+    ],
+    "input_proofs": 4,
+    "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/001527.json

@@ -0,0 +1,69 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001527",
+  "batch_fingerprint": "e5a6a041094ee9f6f59ff968878c2f0bad3ea62eb5c926ae0afad155f6cc7fc8",
+  "evidence": {
+    "batch_fingerprint": "e5a6a041094ee9f6f59ff968878c2f0bad3ea62eb5c926ae0afad155f6cc7fc8",
+    "batch_outcome": "all_inputs_failed_with_evidence",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Frm.coe_of",
+        "id": "Frm.coe_of",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            49,
+            58
+          ],
+          "file_path": "Mathlib/Order/Category/Frm.lean",
+          "full_name": "Frm.coe_of",
+          "start": [
+            49,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/Frm.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "HeytAlg.coe_of",
+        "id": "HeytAlg.coe_of",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            43,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/HeytAlg.lean",
+          "full_name": "HeytAlg.coe_of",
+          "start": [
+            42,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/HeytAlg.lean"
+      }
+    ],
+    "input_proofs": 2,
+    "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/001528.json

@@ -0,0 +1,113 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001528",
+  "batch_fingerprint": "83068c04869c5c567981fb4d6d8245b44d35c7ef2c2edf4e256ada86158c0730",
+  "evidence": {
+    "batch_fingerprint": "83068c04869c5c567981fb4d6d8245b44d35c7ef2c2edf4e256ada86158c0730",
+    "batch_outcome": "all_inputs_failed_with_evidence",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Lat.coe_of",
+        "id": "Lat.coe_of",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            51,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/Lat.lean",
+          "full_name": "Lat.coe_of",
+          "start": [
+            50,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/Lat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Lat_dual_comp_forget_to_partOrd",
+        "id": "Lat_dual_comp_forget_to_partOrd",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            108,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/Lat.lean",
+          "full_name": "Lat_dual_comp_forget_to_partOrd",
+          "start": [
+            106,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/Lat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LinOrd.coe_of",
+        "id": "LinOrd.coe_of",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            49,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/LinOrd.lean",
+          "full_name": "LinOrd.coe_of",
+          "start": [
+            48,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/LinOrd.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "linOrd_dual_comp_forget_to_Lat",
+        "id": "linOrd_dual_comp_forget_to_Lat",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            102,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/LinOrd.lean",
+          "full_name": "linOrd_dual_comp_forget_to_Lat",
+          "start": [
+            100,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/LinOrd.lean"
+      }
+    ],
+    "input_proofs": 4,
+    "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/001529.json

@@ -0,0 +1,451 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001529",
+  "batch_fingerprint": "254bd245e2a3b876e9b8f8afc19889c795e13253114b16fb50b2f4bfb08a4bde",
+  "evidence": {
+    "batch_fingerprint": "254bd245e2a3b876e9b8f8afc19889c795e13253114b16fb50b2f4bfb08a4bde",
+    "batch_outcome": "all_inputs_failed_with_evidence",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "NonemptyFinLinOrd.coe_of",
+        "id": "NonemptyFinLinOrd.coe_of",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            86,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/NonemptyFinLinOrd.lean",
+          "full_name": "NonemptyFinLinOrd.coe_of",
+          "start": [
+            85,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/NonemptyFinLinOrd.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'simp only'",
+        "full_name": "NonemptyFinLinOrd.epi_iff_surjective",
+        "id": "NonemptyFinLinOrd.epi_iff_surjective",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            210,
+            49
+          ],
+          "file_path": "Mathlib/Order/Category/NonemptyFinLinOrd.lean",
+          "full_name": "NonemptyFinLinOrd.epi_iff_surjective",
+          "start": [
+            172,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"constructor\"",
+                "[]"
+              ],
+              "state_after": "case mp\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\n\u22a2 Epi f \u2192 Function.Surjective \u21d1f\n\ncase mpr\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\n\u22a2 Function.Surjective \u21d1f \u2192 Epi f",
+              "state_before": "A B : NonemptyFinLinOrd\nf : A \u27f6 B\n\u22a2 Epi f \u2194 Function.Surjective \u21d1f",
+              "tactic": "constructor"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro\"",
+                "[]"
+              ],
+              "state_after": "case mp\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\n\u22a2 Function.Surjective \u21d1f",
+              "state_before": "case mp\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\n\u22a2 Epi f \u2192 Function.Surjective \u21d1f",
+              "tactic": "intro"
+            },
+            {
+              "annotated_tactic": [
+                "\"dsimp only [<a>Function.Surjective<\\/a>]\"",
+                "[{\"full_name\":\"Function.Surjective\",\"def_path\":\"Mathlib\\/Init\\/Function.lean\",\"def_pos\":[133,5],\"def_end_pos\":[133,15]}]"
+              ],
+              "state_after": "case mp\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\n\u22a2 \u2200 (b : \u2191B), \u2203 a, f a = b",
+              "state_before": "case mp\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\n\u22a2 Function.Surjective \u21d1f",
+              "tactic": "dsimp only [Function.Surjective]"
+            },
+            {
+              "annotated_tactic": [
+                "\"by_contra! hf'\"",
+                "[]"
+              ],
+              "state_after": "case mp\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nhf' : \u2203 b, \u2200 (a : \u2191A), f a \u2260 b\n\u22a2 False",
+              "state_before": "case mp\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\n\u22a2 \u2200 (b : \u2191B), \u2203 a, f a = b",
+              "tactic": "by_contra! hf'"
+            },
+            {
+              "annotated_tactic": [
+                "\"rcases hf' with \\u27e8m, hm\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "case mp.intro\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\n\u22a2 False",
+              "state_before": "case mp\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nhf' : \u2203 b, \u2200 (a : \u2191A), f a \u2260 b\n\u22a2 False",
+              "tactic": "rcases hf' with \u27e8m, hm\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"let Y := <a>NonemptyFinLinOrd.of<\\/a> (<a>ULift<\\/a> (<a>Fin<\\/a> 2))\"",
+                "[{\"full_name\":\"NonemptyFinLinOrd.of\",\"def_path\":\"Mathlib\\/Order\\/Category\\/NonemptyFinLinOrd.lean\",\"def_pos\":[79,5],\"def_end_pos\":[79,7]},{\"full_name\":\"ULift\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[809,11],\"def_end_pos\":[809,16]},{\"full_name\":\"Fin\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1831,11],\"def_end_pos\":[1831,14]}]"
+              ],
+              "state_after": "case mp.intro\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{?u.21080, 0} (Fin 2))\n\u22a2 False",
+              "state_before": "case mp.intro\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\n\u22a2 False",
+              "tactic": "let Y := NonemptyFinLinOrd.of (ULift (Fin 2))"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp [Y, <a>DFunLike.coe<\\/a>] at h\"",
+                "[{\"full_name\":\"DFunLike.coe\",\"def_path\":\"Mathlib\\/Data\\/FunLike\\/Basic.lean\",\"def_pos\":[147,3],\"def_end_pos\":[147,6]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case mp.intro\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nh : p\u2081 m = p\u2082 m\n\u22a2 False",
+              "tactic": "simp [Y, DFunLike.coe] at h"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only\"",
+                "[]"
+              ],
+              "state_after": "A B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\n\u22a2 (if x\u2081 < m then { down := 0 } else { down := 1 }) \u2264 if x\u2082 < m then { down := 0 } else { down := 1 }",
+              "state_before": "A B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\n\u22a2 (fun b => if b < m then { down := 0 } else { down := 1 }) x\u2081 \u2264\n    (fun b => if b < m then { down := 0 } else { down := 1 }) x\u2082",
+              "tactic": "simp only"
+            },
+            {
+              "annotated_tactic": [
+                "\"split_ifs with h\\u2081 h\\u2082 h\\u2082\"",
+                "[]"
+              ],
+              "state_after": "case pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : x\u2081 < m\nh\u2082 : x\u2082 < m\n\u22a2 { down := 0 } \u2264 { down := 0 }\n\ncase neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : x\u2081 < m\nh\u2082 : \u00acx\u2082 < m\n\u22a2 { down := 0 } \u2264 { down := 1 }\n\ncase pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 < m\nh\u2082 : x\u2082 < m\n\u22a2 { down := 1 } \u2264 { down := 0 }\n\ncase neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 < m\nh\u2082 : \u00acx\u2082 < m\n\u22a2 { down := 1 } \u2264 { down := 1 }",
+              "state_before": "A B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\n\u22a2 (if x\u2081 < m then { down := 0 } else { down := 1 }) \u2264 if x\u2082 < m then { down := 0 } else { down := 1 }",
+              "tactic": "split_ifs with h\u2081 h\u2082 h\u2082"
+            },
+            {
+              "annotated_tactic": [
+                "\"any_goals apply <a>Fin.zero_le<\\/a>\"",
+                "[{\"full_name\":\"Fin.zero_le\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[130,17],\"def_end_pos\":[130,24]}]"
+              ],
+              "state_after": "case pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 < m\nh\u2082 : x\u2082 < m\n\u22a2 { down := 1 } \u2264 { down := 0 }\n\ncase neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 < m\nh\u2082 : \u00acx\u2082 < m\n\u22a2 { down := 1 } \u2264 { down := 1 }",
+              "state_before": "case pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : x\u2081 < m\nh\u2082 : x\u2082 < m\n\u22a2 { down := 0 } \u2264 { down := 0 }\n\ncase neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : x\u2081 < m\nh\u2082 : \u00acx\u2082 < m\n\u22a2 { down := 0 } \u2264 { down := 1 }\n\ncase pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 < m\nh\u2082 : x\u2082 < m\n\u22a2 { down := 1 } \u2264 { down := 0 }\n\ncase neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 < m\nh\u2082 : \u00acx\u2082 < m\n\u22a2 { down := 1 } \u2264 { down := 1 }",
+              "tactic": "any_goals apply Fin.zero_le"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Fin.zero_le<\\/a>\"",
+                "[{\"full_name\":\"Fin.zero_le\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[130,17],\"def_end_pos\":[130,24]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : x\u2081 < m\nh\u2082 : \u00acx\u2082 < m\n\u22a2 { down := 0 } \u2264 { down := 1 }",
+              "tactic": "apply Fin.zero_le"
+            },
+            {
+              "annotated_tactic": [
+                "\"exfalso\"",
+                "[]"
+              ],
+              "state_after": "case pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 < m\nh\u2082 : x\u2082 < m\n\u22a2 False",
+              "state_before": "case pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 < m\nh\u2082 : x\u2082 < m\n\u22a2 { down := 1 } \u2264 { down := 0 }",
+              "tactic": "exfalso"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact h\\u2081 (<a>lt_of_le_of_lt<\\/a> h h\\u2082)\"",
+                "[{\"full_name\":\"lt_of_le_of_lt\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[122,9],\"def_end_pos\":[122,23]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 < m\nh\u2082 : x\u2082 < m\n\u22a2 False",
+              "tactic": "exact h\u2081 (lt_of_le_of_lt h h\u2082)"
+            },
+            {
+              "annotated_tactic": [
+                "\"rfl\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 < m\nh\u2082 : \u00acx\u2082 < m\n\u22a2 { down := 1 } \u2264 { down := 1 }",
+              "tactic": "rfl"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only\"",
+                "[]"
+              ],
+              "state_after": "A B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\n\u22a2 (if x\u2081 \u2264 m then { down := 0 } else { down := 1 }) \u2264 if x\u2082 \u2264 m then { down := 0 } else { down := 1 }",
+              "state_before": "A B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\n\u22a2 (fun b => if b \u2264 m then { down := 0 } else { down := 1 }) x\u2081 \u2264\n    (fun b => if b \u2264 m then { down := 0 } else { down := 1 }) x\u2082",
+              "tactic": "simp only"
+            },
+            {
+              "annotated_tactic": [
+                "\"split_ifs with h\\u2081 h\\u2082 h\\u2082\"",
+                "[]"
+              ],
+              "state_after": "case pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : x\u2081 \u2264 m\nh\u2082 : x\u2082 \u2264 m\n\u22a2 { down := 0 } \u2264 { down := 0 }\n\ncase neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : x\u2081 \u2264 m\nh\u2082 : \u00acx\u2082 \u2264 m\n\u22a2 { down := 0 } \u2264 { down := 1 }\n\ncase pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 \u2264 m\nh\u2082 : x\u2082 \u2264 m\n\u22a2 { down := 1 } \u2264 { down := 0 }\n\ncase neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 \u2264 m\nh\u2082 : \u00acx\u2082 \u2264 m\n\u22a2 { down := 1 } \u2264 { down := 1 }",
+              "state_before": "A B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\n\u22a2 (if x\u2081 \u2264 m then { down := 0 } else { down := 1 }) \u2264 if x\u2082 \u2264 m then { down := 0 } else { down := 1 }",
+              "tactic": "split_ifs with h\u2081 h\u2082 h\u2082"
+            },
+            {
+              "annotated_tactic": [
+                "\"any_goals apply <a>Fin.zero_le<\\/a>\"",
+                "[{\"full_name\":\"Fin.zero_le\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[130,17],\"def_end_pos\":[130,24]}]"
+              ],
+              "state_after": "case pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 \u2264 m\nh\u2082 : x\u2082 \u2264 m\n\u22a2 { down := 1 } \u2264 { down := 0 }\n\ncase neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 \u2264 m\nh\u2082 : \u00acx\u2082 \u2264 m\n\u22a2 { down := 1 } \u2264 { down := 1 }",
+              "state_before": "case pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : x\u2081 \u2264 m\nh\u2082 : x\u2082 \u2264 m\n\u22a2 { down := 0 } \u2264 { down := 0 }\n\ncase neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : x\u2081 \u2264 m\nh\u2082 : \u00acx\u2082 \u2264 m\n\u22a2 { down := 0 } \u2264 { down := 1 }\n\ncase pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 \u2264 m\nh\u2082 : x\u2082 \u2264 m\n\u22a2 { down := 1 } \u2264 { down := 0 }\n\ncase neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 \u2264 m\nh\u2082 : \u00acx\u2082 \u2264 m\n\u22a2 { down := 1 } \u2264 { down := 1 }",
+              "tactic": "any_goals apply Fin.zero_le"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Fin.zero_le<\\/a>\"",
+                "[{\"full_name\":\"Fin.zero_le\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[130,17],\"def_end_pos\":[130,24]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : x\u2081 \u2264 m\nh\u2082 : \u00acx\u2082 \u2264 m\n\u22a2 { down := 0 } \u2264 { down := 1 }",
+              "tactic": "apply Fin.zero_le"
+            },
+            {
+              "annotated_tactic": [
+                "\"exfalso\"",
+                "[]"
+              ],
+              "state_after": "case pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 \u2264 m\nh\u2082 : x\u2082 \u2264 m\n\u22a2 False",
+              "state_before": "case pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 \u2264 m\nh\u2082 : x\u2082 \u2264 m\n\u22a2 { down := 1 } \u2264 { down := 0 }",
+              "tactic": "exfalso"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact h\\u2081 (h.trans h\\u2082)\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 \u2264 m\nh\u2082 : x\u2082 \u2264 m\n\u22a2 False",
+              "tactic": "exact h\u2081 (h.trans h\u2082)"
+            },
+            {
+              "annotated_tactic": [
+                "\"rfl\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\nx\u2081 x\u2082 : \u2191B\nh : x\u2081 \u2264 x\u2082\nh\u2081 : \u00acx\u2081 \u2264 m\nh\u2082 : \u00acx\u2082 \u2264 m\n\u22a2 { down := 1 } \u2264 { down := 1 }",
+              "tactic": "rfl"
+            },
+            {
+              "annotated_tactic": [
+                "\"congr\"",
+                "[]"
+              ],
+              "state_after": "case e_a\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\n\u22a2 p\u2081 = p\u2082",
+              "state_before": "A B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\n\u22a2 p\u2081 m = p\u2082 m",
+              "tactic": "congr"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>cancel_epi<\\/a> f]\"",
+                "[{\"full_name\":\"CategoryTheory.cancel_epi\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[306,9],\"def_end_pos\":[306,19]}]"
+              ],
+              "state_after": "case e_a\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\n\u22a2 f \u226b p\u2081 = f \u226b p\u2082",
+              "state_before": "case e_a\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\n\u22a2 p\u2081 = p\u2082",
+              "tactic": "rw [\u2190 cancel_epi f]"
+            },
+            {
+              "annotated_tactic": [
+                "\"ext a\"",
+                "[]"
+              ],
+              "state_after": "case e_a.w\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\n\u22a2 (f \u226b p\u2081) a = (f \u226b p\u2082) a",
+              "state_before": "case e_a\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\n\u22a2 f \u226b p\u2081 = f \u226b p\u2082",
+              "tactic": "ext a"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>coe_of<\\/a>, <a>comp_apply<\\/a>]\"",
+                "[{\"full_name\":\"NonemptyFinLinOrd.coe_of\",\"def_path\":\"Mathlib\\/Order\\/Category\\/NonemptyFinLinOrd.lean\",\"def_pos\":[85,9],\"def_end_pos\":[85,15]},{\"full_name\":\"CategoryTheory.comp_apply\",\"def_path\":\"Mathlib\\/CategoryTheory\\/ConcreteCategory\\/Basic.lean\",\"def_pos\":[134,17],\"def_end_pos\":[134,27]}]"
+              ],
+              "state_after": "case e_a.w\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\n\u22a2 p\u2081 (f a) = p\u2082 (f a)",
+              "state_before": "case e_a.w\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\n\u22a2 (f \u226b p\u2081) a = (f \u226b p\u2082) a",
+              "tactic": "simp only [coe_of, comp_apply]"
+            },
+            {
+              "annotated_tactic": [
+                "\"change <a>ite<\\/a> _ _ _ = <a>ite<\\/a> _ _ _\"",
+                "[{\"full_name\":\"ite\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[970,21],\"def_end_pos\":[970,24]},{\"full_name\":\"ite\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[970,21],\"def_end_pos\":[970,24]}]"
+              ],
+              "state_after": "case e_a.w\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\n\u22a2 (if f a < m then { down := 0 } else { down := 1 }) = if f a \u2264 m then { down := 0 } else { down := 1 }",
+              "state_before": "case e_a.w\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\n\u22a2 p\u2081 (f a) = p\u2082 (f a)",
+              "tactic": "change ite _ _ _ = ite _ _ _"
+            },
+            {
+              "annotated_tactic": [
+                "\"split_ifs with h\\u2081 h\\u2082 h\\u2082\"",
+                "[]"
+              ],
+              "state_after": "case pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\nh\u2081 : f a < m\nh\u2082 : f a \u2264 m\n\u22a2 { down := 0 } = { down := 0 }\n\ncase neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\nh\u2081 : f a < m\nh\u2082 : \u00acf a \u2264 m\n\u22a2 { down := 0 } = { down := 1 }\n\ncase pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\nh\u2081 : \u00acf a < m\nh\u2082 : f a \u2264 m\n\u22a2 { down := 1 } = { down := 0 }\n\ncase neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\nh\u2081 : \u00acf a < m\nh\u2082 : \u00acf a \u2264 m\n\u22a2 { down := 1 } = { down := 1 }",
+              "state_before": "case e_a.w\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\n\u22a2 (if f a < m then { down := 0 } else { down := 1 }) = if f a \u2264 m then { down := 0 } else { down := 1 }",
+              "tactic": "split_ifs with h\u2081 h\u2082 h\u2082"
+            },
+            {
+              "annotated_tactic": [
+                "\"any_goals rfl\"",
+                "[]"
+              ],
+              "state_after": "case neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\nh\u2081 : f a < m\nh\u2082 : \u00acf a \u2264 m\n\u22a2 { down := 0 } = { down := 1 }\n\ncase pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\nh\u2081 : \u00acf a < m\nh\u2082 : f a \u2264 m\n\u22a2 { down := 1 } = { down := 0 }",
+              "state_before": "case pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\nh\u2081 : f a < m\nh\u2082 : f a \u2264 m\n\u22a2 { down := 0 } = { down := 0 }\n\ncase neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\nh\u2081 : f a < m\nh\u2082 : \u00acf a \u2264 m\n\u22a2 { down := 0 } = { down := 1 }\n\ncase pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\nh\u2081 : \u00acf a < m\nh\u2082 : f a \u2264 m\n\u22a2 { down := 1 } = { down := 0 }\n\ncase neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\nh\u2081 : \u00acf a < m\nh\u2082 : \u00acf a \u2264 m\n\u22a2 { down := 1 } = { down := 1 }",
+              "tactic": "any_goals rfl"
+            },
+            {
+              "annotated_tactic": [
+                "\"rfl\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\nh\u2081 : \u00acf a < m\nh\u2082 : \u00acf a \u2264 m\n\u22a2 { down := 1 } = { down := 1 }",
+              "tactic": "rfl"
+            },
+            {
+              "annotated_tactic": [
+                "\"exfalso\"",
+                "[]"
+              ],
+              "state_after": "case neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\nh\u2081 : f a < m\nh\u2082 : \u00acf a \u2264 m\n\u22a2 False",
+              "state_before": "case neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\nh\u2081 : f a < m\nh\u2082 : \u00acf a \u2264 m\n\u22a2 { down := 0 } = { down := 1 }",
+              "tactic": "exfalso"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact h\\u2082 (<a>le_of_lt<\\/a> h\\u2081)\"",
+                "[{\"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 neg\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\nh\u2081 : f a < m\nh\u2082 : \u00acf a \u2264 m\n\u22a2 False",
+              "tactic": "exact h\u2082 (le_of_lt h\u2081)"
+            },
+            {
+              "annotated_tactic": [
+                "\"exfalso\"",
+                "[]"
+              ],
+              "state_after": "case pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\nh\u2081 : \u00acf a < m\nh\u2082 : f a \u2264 m\n\u22a2 False",
+              "state_before": "case pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\nh\u2081 : \u00acf a < m\nh\u2082 : f a \u2264 m\n\u22a2 { down := 1 } = { down := 0 }",
+              "tactic": "exfalso"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact hm a (<a>eq_of_le_of_not_lt<\\/a> h\\u2082 h\\u2081)\"",
+                "[{\"full_name\":\"eq_of_le_of_not_lt\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[404,9],\"def_end_pos\":[404,27]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case pos\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\na\u271d : Epi f\nm : \u2191B\nhm : \u2200 (a : \u2191A), f a \u2260 m\nY : NonemptyFinLinOrd := of (ULift.{u, 0} (Fin 2))\np\u2081 : B \u27f6 Y := { toFun := fun b => if b < m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\np\u2082 : B \u27f6 Y := { toFun := fun b => if b \u2264 m then { down := 0 } else { down := 1 }, monotone' := \u22ef }\na : (forget NonemptyFinLinOrd).obj A\nh\u2081 : \u00acf a < m\nh\u2082 : f a \u2264 m\n\u22a2 False",
+              "tactic": "exact hm a (eq_of_le_of_not_lt h\u2082 h\u2081)"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro h\"",
+                "[]"
+              ],
+              "state_after": "case mpr\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\nh : Function.Surjective \u21d1f\n\u22a2 Epi f",
+              "state_before": "case mpr\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\n\u22a2 Function.Surjective \u21d1f \u2192 Epi f",
+              "tactic": "intro h"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>ConcreteCategory.epi_of_surjective<\\/a> f h\"",
+                "[{\"full_name\":\"CategoryTheory.ConcreteCategory.epi_of_surjective\",\"def_path\":\"Mathlib\\/CategoryTheory\\/ConcreteCategory\\/EpiMono.lean\",\"def_pos\":[153,9],\"def_end_pos\":[153,26]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case mpr\nA B : NonemptyFinLinOrd\nf : A \u27f6 B\nh : Function.Surjective \u21d1f\n\u22a2 Epi f",
+              "tactic": "exact ConcreteCategory.epi_of_surjective f h"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/NonemptyFinLinOrd.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "NonemptyFinLinOrd.forget_map_apply",
+        "id": "NonemptyFinLinOrd.forget_map_apply",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            170,
+            75
+          ],
+          "file_path": "Mathlib/Order/Category/NonemptyFinLinOrd.lean",
+          "full_name": "NonemptyFinLinOrd.forget_map_apply",
+          "start": [
+            169,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/NonemptyFinLinOrd.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "nonemptyFinLinOrd_dual_comp_forget_to_linOrd",
+        "id": "nonemptyFinLinOrd_dual_comp_forget_to_linOrd",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            257,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/NonemptyFinLinOrd.lean",
+          "full_name": "nonemptyFinLinOrd_dual_comp_forget_to_linOrd",
+          "start": [
+            254,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/NonemptyFinLinOrd.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "\u03c9CPO.coe_of",
+        "id": "\u03c9CPO.coe_of",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            64,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/OmegaCompletePartialOrder.lean",
+          "full_name": "\u03c9CPO.coe_of",
+          "start": [
+            63,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/OmegaCompletePartialOrder.lean"
+      }
+    ],
+    "input_proofs": 5,
+    "input_units": 2,
+    "proofs": 0,
+    "published_proofs": 0,
+    "published_transitions": 0,
+    "replay_failures": [],
+    "transitions": 0,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [],
+  "proof_ids": [],
+  "proof_keys": []
+}

manifests/batches/mathlib/001530.json

@@ -0,0 +1,91 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001530",
+  "batch_fingerprint": "aa66c9d8646f4bff68d592658106322954eefdb8ed14340f6e9245a3b7958d5e",
+  "evidence": {
+    "batch_fingerprint": "aa66c9d8646f4bff68d592658106322954eefdb8ed14340f6e9245a3b7958d5e",
+    "batch_outcome": "all_inputs_failed_with_evidence",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "PartOrd.coe_of",
+        "id": "PartOrd.coe_of",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            51,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/PartOrd.lean",
+          "full_name": "PartOrd.coe_of",
+          "start": [
+            50,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/PartOrd.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "partOrd_dual_comp_forget_to_preord",
+        "id": "partOrd_dual_comp_forget_to_preord",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            103,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/PartOrd.lean",
+          "full_name": "partOrd_dual_comp_forget_to_preord",
+          "start": [
+            100,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/PartOrd.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Preord.coe_of",
+        "id": "Preord.coe_of",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            56,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/Preord.lean",
+          "full_name": "Preord.coe_of",
+          "start": [
+            55,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/Preord.lean"
+      }
+    ],
+    "input_proofs": 3,
+    "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/001531.json

@@ -0,0 +1,1151 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001531",
+  "batch_fingerprint": "ac0ff6b05f8bc17cc638a5aa0ff7b69893d45d7ea3b3f8aed9460af816fd11bd",
+  "evidence": {
+    "batch_fingerprint": "ac0ff6b05f8bc17cc638a5aa0ff7b69893d45d7ea3b3f8aed9460af816fd11bd",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SemilatInfCat.coe_forget_to_partOrd",
+        "id": "SemilatInfCat.coe_forget_to_partOrd",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            147,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/Semilat.lean",
+          "full_name": "SemilatInfCat.coe_forget_to_partOrd",
+          "start": [
+            145,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/Semilat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SemilatInfCat.coe_of",
+        "id": "SemilatInfCat.coe_of",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            113,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/Semilat.lean",
+          "full_name": "SemilatInfCat.coe_of",
+          "start": [
+            112,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/Semilat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SemilatInfCat_dual_comp_forget_to_partOrd",
+        "id": "SemilatInfCat_dual_comp_forget_to_partOrd",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            212,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/Semilat.lean",
+          "full_name": "SemilatInfCat_dual_comp_forget_to_partOrd",
+          "start": [
+            209,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/Semilat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SemilatSupCat.coe_forget_to_partOrd",
+        "id": "SemilatSupCat.coe_forget_to_partOrd",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            94,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/Semilat.lean",
+          "full_name": "SemilatSupCat.coe_forget_to_partOrd",
+          "start": [
+            92,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/Semilat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SemilatSupCat.coe_of",
+        "id": "SemilatSupCat.coe_of",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            58,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/Semilat.lean",
+          "full_name": "SemilatSupCat.coe_of",
+          "start": [
+            57,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/Semilat.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SemilatSupCat_dual_comp_forget_to_partOrd",
+        "id": "SemilatSupCat_dual_comp_forget_to_partOrd",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            206,
+            6
+          ],
+          "file_path": "Mathlib/Order/Category/Semilat.lean",
+          "full_name": "SemilatSupCat_dual_comp_forget_to_partOrd",
+          "start": [
+            203,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Category/Semilat.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'exact h.succ'",
+        "full_name": "ChainClosure.isChain",
+        "id": "ChainClosure.isChain",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            275,
+            35
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "ChainClosure.isChain",
+          "start": [
+            269,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"induction hc with\\n  | <a>succ<\\/a> _ h => exact h.succ\\n  | <a>union<\\/a> hs h =>\\n    exact fun c\\u2081 \\u27e8t\\u2081, ht\\u2081, (hc\\u2081 : c\\u2081 \\u2208 t\\u2081)\\u27e9 c\\u2082 \\u27e8t\\u2082, ht\\u2082, (hc\\u2082 : c\\u2082 \\u2208 t\\u2082)\\u27e9 hneq =>\\n      ((hs _ ht\\u2081).<a>total<\\/a> <| hs _ ht\\u2082).<a>elim<\\/a> (fun ht => h t\\u2082 ht\\u2082 (ht hc\\u2081) hc\\u2082 hneq) fun ht =>\\n        h t\\u2081 ht\\u2081 hc\\u2081 (ht hc\\u2082) hneq\"",
+                "[{\"full_name\":\"ChainClosure.succ\",\"def_path\":\"Mathlib\\/Order\\/Chain.lean\",\"def_pos\":[200,5],\"def_end_pos\":[200,9]},{\"full_name\":\"ChainClosure.union\",\"def_path\":\"Mathlib\\/Order\\/Chain.lean\",\"def_pos\":[201,5],\"def_end_pos\":[201,10]},{\"full_name\":\"ChainClosure.total\",\"def_path\":\"Mathlib\\/Order\\/Chain.lean\",\"def_pos\":[250,9],\"def_end_pos\":[250,27]},{\"full_name\":\"Or.elim\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[550,9],\"def_end_pos\":[550,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2081 c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\nhc : ChainClosure r c\n\u22a2 IsChain r c",
+              "tactic": "induction hc with\n| succ _ h => exact h.succ\n| union hs h =>\n  exact fun c\u2081 \u27e8t\u2081, ht\u2081, (hc\u2081 : c\u2081 \u2208 t\u2081)\u27e9 c\u2082 \u27e8t\u2082, ht\u2082, (hc\u2082 : c\u2082 \u2208 t\u2082)\u27e9 hneq =>\n    ((hs _ ht\u2081).total <| hs _ ht\u2082).elim (fun ht => h t\u2082 ht\u2082 (ht hc\u2081) hc\u2082 hneq) fun ht =>\n      h t\u2081 ht\u2081 hc\u2081 (ht hc\u2082) hneq"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact h.succ\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case succ\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2081 c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set \u03b1\na\u271d : ChainClosure r s\u271d\nh : IsChain r s\u271d\n\u22a2 IsChain r (SuccChain r s\u271d)",
+              "tactic": "exact h.succ"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact fun c\\u2081 \\u27e8t\\u2081, ht\\u2081, (hc\\u2081 : c\\u2081 \\u2208 t\\u2081)\\u27e9 c\\u2082 \\u27e8t\\u2082, ht\\u2082, (hc\\u2082 : c\\u2082 \\u2208 t\\u2082)\\u27e9 hneq =>\\n      ((hs _ ht\\u2081).<a>total<\\/a> <| hs _ ht\\u2082).<a>elim<\\/a> (fun ht => h t\\u2082 ht\\u2082 (ht hc\\u2081) hc\\u2082 hneq) fun ht =>\\n        h t\\u2081 ht\\u2081 hc\\u2081 (ht hc\\u2082) hneq\"",
+                "[{\"full_name\":\"ChainClosure.total\",\"def_path\":\"Mathlib\\/Order\\/Chain.lean\",\"def_pos\":[250,9],\"def_end_pos\":[250,27]},{\"full_name\":\"Or.elim\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[550,9],\"def_end_pos\":[550,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case union\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2081 c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set (Set \u03b1)\nhs : \u2200 a \u2208 s\u271d, ChainClosure r a\nh : \u2200 a \u2208 s\u271d, IsChain r a\n\u22a2 IsChain r (\u22c3\u2080 s\u271d)",
+              "tactic": "exact fun c\u2081 \u27e8t\u2081, ht\u2081, (hc\u2081 : c\u2081 \u2208 t\u2081)\u27e9 c\u2082 \u27e8t\u2082, ht\u2082, (hc\u2082 : c\u2082 \u2208 t\u2082)\u27e9 hneq =>\n  ((hs _ ht\u2081).total <| hs _ ht\u2082).elim (fun ht => h t\u2082 ht\u2082 (ht hc\u2081) hc\u2082 hneq) fun ht =>\n    h t\u2081 ht\u2081 hc\u2081 (ht hc\u2082) hneq"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'exact (chainClosure_succ_total hc\u2081 hc\u2082 h).elim (fun h => h \u25b8 hc.subset) id'",
+        "full_name": "ChainClosure.succ_fixpoint",
+        "id": "ChainClosure.succ_fixpoint",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            260,
+            41
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "ChainClosure.succ_fixpoint",
+          "start": [
+            256,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"induction hc\\u2081 with\\n  | <a>succ<\\/a> hc\\u2081 h => exact (<a>chainClosure_succ_total<\\/a> hc\\u2081 hc\\u2082 h).<a>elim<\\/a> (fun h => h \\u25b8 hc.subset) <a>id<\\/a>\\n  | <a>union<\\/a> _ ih => exact <a>sUnion_subset<\\/a> ih\"",
+                "[{\"full_name\":\"ChainClosure.succ\",\"def_path\":\"Mathlib\\/Order\\/Chain.lean\",\"def_pos\":[200,5],\"def_end_pos\":[200,9]},{\"full_name\":\"_private.Mathlib.Order.Chain.0.chainClosure_succ_total\",\"def_path\":\"Mathlib\\/Order\\/Chain.lean\",\"def_pos\":[231,17],\"def_end_pos\":[231,40]},{\"full_name\":\"Or.elim\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[550,9],\"def_end_pos\":[550,16]},{\"full_name\":\"id\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[33,15],\"def_end_pos\":[33,17]},{\"full_name\":\"ChainClosure.union\",\"def_path\":\"Mathlib\\/Order\\/Chain.lean\",\"def_pos\":[201,5],\"def_end_pos\":[201,10]},{\"full_name\":\"Set.sUnion_subset\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Lattice.lean\",\"def_pos\":[1018,9],\"def_end_pos\":[1018,22]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2081 c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\nhc\u2081 : ChainClosure r c\u2081\nhc\u2082 : ChainClosure r c\u2082\nhc : SuccChain r c\u2082 = c\u2082\n\u22a2 c\u2081 \u2286 c\u2082",
+              "tactic": "induction hc\u2081 with\n| succ hc\u2081 h => exact (chainClosure_succ_total hc\u2081 hc\u2082 h).elim (fun h => h \u25b8 hc.subset) id\n| union _ ih => exact sUnion_subset ih"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact (<a>chainClosure_succ_total<\\/a> hc\\u2081 hc\\u2082 h).<a>elim<\\/a> (fun h => h \\u25b8 hc.subset) <a>id<\\/a>\"",
+                "[{\"full_name\":\"_private.Mathlib.Order.Chain.0.chainClosure_succ_total\",\"def_path\":\"Mathlib\\/Order\\/Chain.lean\",\"def_pos\":[231,17],\"def_end_pos\":[231,40]},{\"full_name\":\"Or.elim\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[550,9],\"def_end_pos\":[550,16]},{\"full_name\":\"id\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[33,15],\"def_end_pos\":[33,17]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case succ\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2081 c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\nhc\u2082 : ChainClosure r c\u2082\nhc : SuccChain r c\u2082 = c\u2082\ns\u271d : Set \u03b1\nhc\u2081 : ChainClosure r s\u271d\nh : s\u271d \u2286 c\u2082\n\u22a2 SuccChain r s\u271d \u2286 c\u2082",
+              "tactic": "exact (chainClosure_succ_total hc\u2081 hc\u2082 h).elim (fun h => h \u25b8 hc.subset) id"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>sUnion_subset<\\/a> ih\"",
+                "[{\"full_name\":\"Set.sUnion_subset\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Lattice.lean\",\"def_pos\":[1018,9],\"def_end_pos\":[1018,22]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case union\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2081 c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\nhc\u2082 : ChainClosure r c\u2082\nhc : SuccChain r c\u2082 = c\u2082\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, a \u2286 c\u2082\n\u22a2 \u22c3\u2080 s\u271d \u2286 c\u2082",
+              "tactic": "exact sUnion_subset ih"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ChainClosure.succ_fixpoint_iff",
+        "id": "ChainClosure.succ_fixpoint_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            266,
+            95
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "ChainClosure.succ_fixpoint_iff",
+          "start": [
+            263,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Flag.bot_mem",
+        "id": "Flag.bot_mem",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            350,
+            21
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "Flag.bot_mem",
+          "start": [
+            349,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Flag.chain_le",
+        "id": "Flag.chain_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            338,
+            11
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "Flag.chain_le",
+          "start": [
+            337,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Flag.chain_lt",
+        "id": "Flag.chain_lt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            378,
+            83
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "Flag.chain_lt",
+          "start": [
+            378,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Flag.coe_mk",
+        "id": "Flag.coe_mk",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            329,
+            6
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "Flag.coe_mk",
+          "start": [
+            328,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Flag.ext",
+        "id": "Flag.ext",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            318,
+            15
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "Flag.ext",
+          "start": [
+            317,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Flag.le_or_le",
+        "id": "Flag.le_or_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            360,
+            25
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "Flag.le_or_le",
+          "start": [
+            359,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Flag.maxChain",
+        "id": "Flag.maxChain",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            342,
+            29
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "Flag.maxChain",
+          "start": [
+            341,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Flag.mem_coe_iff",
+        "id": "Flag.mem_coe_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            324,
+            10
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "Flag.mem_coe_iff",
+          "start": [
+            323,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Flag.mk_coe",
+        "id": "Flag.mk_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            334,
+            10
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "Flag.mk_coe",
+          "start": [
+            333,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Flag.top_mem",
+        "id": "Flag.top_mem",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            346,
+            21
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "Flag.top_mem",
+          "start": [
+            345,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsChain.directedOn",
+        "id": "IsChain.directedOn",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            125,
+            81
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "IsChain.directedOn",
+          "start": [
+            124,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsChain.image",
+        "id": "IsChain.image",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            104,
+            83
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "IsChain.image",
+          "start": [
+            101,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsChain.insert",
+        "id": "IsChain.insert",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            92,
+            49
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "IsChain.insert",
+          "start": [
+            90,
+            11
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsChain.lt_of_le",
+        "id": "IsChain.lt_of_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            114,
+            47
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "IsChain.lt_of_le",
+          "start": [
+            112,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsChain.mono",
+        "id": "IsChain.mono",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            73,
+            20
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "IsChain.mono",
+          "start": [
+            72,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsChain.mono_rel",
+        "id": "IsChain.mono_rel",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            78,
+            52
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "IsChain.mono_rel",
+          "start": [
+            76,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsChain.symm",
+        "id": "IsChain.symm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            83,
+            29
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "IsChain.symm",
+          "start": [
+            82,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsChain.total",
+        "id": "IsChain.total",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            121,
+            64
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "IsChain.total",
+          "start": [
+            120,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsMaxChain.bot_mem",
+        "id": "IsMaxChain.bot_mem",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            156,
+            91
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "IsMaxChain.bot_mem",
+          "start": [
+            155,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsMaxChain.isChain",
+        "id": "IsMaxChain.isChain",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            148,
+            6
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "IsMaxChain.isChain",
+          "start": [
+            147,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsMaxChain.not_superChain",
+        "id": "IsMaxChain.not_superChain",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            152,
+            29
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "IsMaxChain.not_superChain",
+          "start": [
+            151,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "IsMaxChain.top_mem",
+        "id": "IsMaxChain.top_mem",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            160,
+            91
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "IsMaxChain.top_mem",
+          "start": [
+            159,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "final tactic does not close all goals",
+        "full_name": "Monotone.isChain_range",
+        "id": "Monotone.isChain_range",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            110,
+            57
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "Monotone.isChain_range",
+          "start": [
+            107,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"rw [\\u2190 <a>image_univ<\\/a>]\"",
+                "[{\"full_name\":\"Set.image_univ\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Image.lean\",\"def_pos\":[701,9],\"def_end_pos\":[701,19]}]"
+              ],
+              "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2081 c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\nf : \u03b1 \u2192 \u03b2\nhf : Monotone f\n\u22a2 IsChain (fun x x_1 => x \u2264 x_1) (f '' univ)",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2081 c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\nf : \u03b1 \u2192 \u03b2\nhf : Monotone f\n\u22a2 IsChain (fun x x_1 => x \u2264 x_1) (range f)",
+              "tactic": "rw [\u2190 image_univ]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.Subsingleton.isChain",
+        "id": "Set.Subsingleton.isChain",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            69,
+            16
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "Set.Subsingleton.isChain",
+          "start": [
+            68,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "chainClosure_maxChain",
+        "id": "chainClosure_maxChain",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            216,
+            33
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "chainClosure_maxChain",
+          "start": [
+            215,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'exact h\u2081 (subset_succChain.trans h)'",
+        "full_name": "chainClosure_succ_total",
+        "id": "chainClosure_succ_total",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            248,
+            54
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "chainClosure_succ_total",
+          "start": [
+            231,
+            9
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"refine ((<a>chainClosure_succ_total_aux<\\/a> hc\\u2081) fun c\\u2081 => ih).<a>imp<\\/a> h.antisymm' fun h\\u2081 => ?_\"",
+                "[{\"full_name\":\"_private.Mathlib.Order.Chain.0.chainClosure_succ_total_aux\",\"def_path\":\"Mathlib\\/Order\\/Chain.lean\",\"def_pos\":[219,17],\"def_end_pos\":[219,44]},{\"full_name\":\"Or.imp\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[172,9],\"def_end_pos\":[172,15]}]"
+              ],
+              "state_after": "case succ\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set \u03b1\na\u271d : ChainClosure r s\u271d\nih : \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 s\u271d \u2192 s\u271d = c\u2081 \u2228 SuccChain r c\u2081 \u2286 s\u271d\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh : c\u2081 \u2286 SuccChain r s\u271d\nh\u2081 : c\u2081 \u2286 s\u271d\n\u22a2 SuccChain r c\u2081 \u2286 SuccChain r s\u271d",
+              "state_before": "case succ\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set \u03b1\na\u271d : ChainClosure r s\u271d\nih : \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 s\u271d \u2192 s\u271d = c\u2081 \u2228 SuccChain r c\u2081 \u2286 s\u271d\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh : c\u2081 \u2286 SuccChain r s\u271d\n\u22a2 SuccChain r s\u271d = c\u2081 \u2228 SuccChain r c\u2081 \u2286 SuccChain r s\u271d",
+              "tactic": "refine ((chainClosure_succ_total_aux hc\u2081) fun c\u2081 => ih).imp h.antisymm' fun h\u2081 => ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain rfl | h\\u2082 := ih hc\\u2081 h\\u2081\"",
+                "[]"
+              ],
+              "state_after": "case succ.inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set \u03b1\na\u271d : ChainClosure r s\u271d\nih : \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 s\u271d \u2192 s\u271d = c\u2081 \u2228 SuccChain r c\u2081 \u2286 s\u271d\nhc\u2081 : ChainClosure r s\u271d\nh : s\u271d \u2286 SuccChain r s\u271d\nh\u2081 : s\u271d \u2286 s\u271d\n\u22a2 SuccChain r s\u271d \u2286 SuccChain r s\u271d\n\ncase succ.inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set \u03b1\na\u271d : ChainClosure r s\u271d\nih : \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 s\u271d \u2192 s\u271d = c\u2081 \u2228 SuccChain r c\u2081 \u2286 s\u271d\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh : c\u2081 \u2286 SuccChain r s\u271d\nh\u2081 : c\u2081 \u2286 s\u271d\nh\u2082 : SuccChain r c\u2081 \u2286 s\u271d\n\u22a2 SuccChain r c\u2081 \u2286 SuccChain r s\u271d",
+              "state_before": "case succ\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set \u03b1\na\u271d : ChainClosure r s\u271d\nih : \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 s\u271d \u2192 s\u271d = c\u2081 \u2228 SuccChain r c\u2081 \u2286 s\u271d\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh : c\u2081 \u2286 SuccChain r s\u271d\nh\u2081 : c\u2081 \u2286 s\u271d\n\u22a2 SuccChain r c\u2081 \u2286 SuccChain r s\u271d",
+              "tactic": "obtain rfl | h\u2082 := ih hc\u2081 h\u2081"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>Subset.rfl<\\/a>\"",
+                "[{\"full_name\":\"Set.Subset.rfl\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[334,9],\"def_end_pos\":[334,19]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case succ.inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set \u03b1\na\u271d : ChainClosure r s\u271d\nih : \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 s\u271d \u2192 s\u271d = c\u2081 \u2228 SuccChain r c\u2081 \u2286 s\u271d\nhc\u2081 : ChainClosure r s\u271d\nh : s\u271d \u2286 SuccChain r s\u271d\nh\u2081 : s\u271d \u2286 s\u271d\n\u22a2 SuccChain r s\u271d \u2286 SuccChain r s\u271d",
+              "tactic": "exact Subset.rfl"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact h\\u2082.trans <a>subset_succChain<\\/a>\"",
+                "[{\"full_name\":\"subset_succChain\",\"def_path\":\"Mathlib\\/Order\\/Chain.lean\",\"def_pos\":[191,9],\"def_end_pos\":[191,25]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case succ.inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set \u03b1\na\u271d : ChainClosure r s\u271d\nih : \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 s\u271d \u2192 s\u271d = c\u2081 \u2228 SuccChain r c\u2081 \u2286 s\u271d\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh : c\u2081 \u2286 SuccChain r s\u271d\nh\u2081 : c\u2081 \u2286 s\u271d\nh\u2082 : SuccChain r c\u2081 \u2286 s\u271d\n\u22a2 SuccChain r c\u2081 \u2286 SuccChain r s\u271d",
+              "tactic": "exact h\u2082.trans subset_succChain"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>Or.imp_left<\\/a> h.antisymm'\"",
+                "[{\"full_name\":\"Or.imp_left\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[173,9],\"def_end_pos\":[173,20]}]"
+              ],
+              "state_after": "case union\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 a \u2192 a = c\u2081 \u2228 SuccChain r c\u2081 \u2286 a\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh : c\u2081 \u2286 \u22c3\u2080 s\u271d\n\u22a2 \u22c3\u2080 s\u271d \u2286 c\u2081 \u2228 SuccChain r c\u2081 \u2286 \u22c3\u2080 s\u271d",
+              "state_before": "case union\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 a \u2192 a = c\u2081 \u2228 SuccChain r c\u2081 \u2286 a\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh : c\u2081 \u2286 \u22c3\u2080 s\u271d\n\u22a2 \u22c3\u2080 s\u271d = c\u2081 \u2228 SuccChain r c\u2081 \u2286 \u22c3\u2080 s\u271d",
+              "tactic": "apply Or.imp_left h.antisymm'"
+            },
+            {
+              "annotated_tactic": [
+                "\"apply <a>by_contradiction<\\/a>\"",
+                "[{\"full_name\":\"by_contradiction\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[218,9],\"def_end_pos\":[218,25]}]"
+              ],
+              "state_after": "case union.a\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 a \u2192 a = c\u2081 \u2228 SuccChain r c\u2081 \u2286 a\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh : c\u2081 \u2286 \u22c3\u2080 s\u271d\n\u22a2 \u00ac(\u22c3\u2080 s\u271d \u2286 c\u2081 \u2228 SuccChain r c\u2081 \u2286 \u22c3\u2080 s\u271d) \u2192 False",
+              "state_before": "case union\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 a \u2192 a = c\u2081 \u2228 SuccChain r c\u2081 \u2286 a\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh : c\u2081 \u2286 \u22c3\u2080 s\u271d\n\u22a2 \u22c3\u2080 s\u271d \u2286 c\u2081 \u2228 SuccChain r c\u2081 \u2286 \u22c3\u2080 s\u271d",
+              "tactic": "apply by_contradiction"
+            },
+            {
+              "annotated_tactic": [
+                "\"simp only [<a>sUnion_subset_iff<\\/a>, <a>not_or<\\/a>, <a>not_forall<\\/a>, <a>exists_prop<\\/a>, <a>and_imp<\\/a>, <a>forall_exists_index<\\/a>]\"",
+                "[{\"full_name\":\"Set.sUnion_subset_iff\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Lattice.lean\",\"def_pos\":[1023,9],\"def_end_pos\":[1023,26]},{\"full_name\":\"not_or\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/PropLemmas.lean\",\"def_pos\":[134,17],\"def_end_pos\":[134,23]},{\"full_name\":\"Classical.not_forall\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Classical.lean\",\"def_pos\":[137,21],\"def_end_pos\":[137,31]},{\"full_name\":\"exists_prop\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/PropLemmas.lean\",\"def_pos\":[307,17],\"def_end_pos\":[307,28]},{\"full_name\":\"and_imp\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[115,17],\"def_end_pos\":[115,24]},{\"full_name\":\"forall_exists_index\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/PropLemmas.lean\",\"def_pos\":[189,17],\"def_end_pos\":[189,36]}]"
+              ],
+              "state_after": "case union.a\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 a \u2192 a = c\u2081 \u2228 SuccChain r c\u2081 \u2286 a\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh : c\u2081 \u2286 \u22c3\u2080 s\u271d\n\u22a2 \u2200 x \u2208 s\u271d, \u00acx \u2286 c\u2081 \u2192 \u00acSuccChain r c\u2081 \u2286 \u22c3\u2080 s\u271d \u2192 False",
+              "state_before": "case union.a\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 a \u2192 a = c\u2081 \u2228 SuccChain r c\u2081 \u2286 a\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh : c\u2081 \u2286 \u22c3\u2080 s\u271d\n\u22a2 \u00ac(\u22c3\u2080 s\u271d \u2286 c\u2081 \u2228 SuccChain r c\u2081 \u2286 \u22c3\u2080 s\u271d) \u2192 False",
+              "tactic": "simp only [sUnion_subset_iff, not_or, not_forall, exists_prop, and_imp, forall_exists_index]"
+            },
+            {
+              "annotated_tactic": [
+                "\"intro c\\u2083 hc\\u2083 h\\u2081 h\\u2082\"",
+                "[]"
+              ],
+              "state_after": "case union.a\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083\u271d s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 a \u2192 a = c\u2081 \u2228 SuccChain r c\u2081 \u2286 a\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh : c\u2081 \u2286 \u22c3\u2080 s\u271d\nc\u2083 : Set \u03b1\nhc\u2083 : c\u2083 \u2208 s\u271d\nh\u2081 : \u00acc\u2083 \u2286 c\u2081\nh\u2082 : \u00acSuccChain r c\u2081 \u2286 \u22c3\u2080 s\u271d\n\u22a2 False",
+              "state_before": "case union.a\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 a \u2192 a = c\u2081 \u2228 SuccChain r c\u2081 \u2286 a\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh : c\u2081 \u2286 \u22c3\u2080 s\u271d\n\u22a2 \u2200 x \u2208 s\u271d, \u00acx \u2286 c\u2081 \u2192 \u00acSuccChain r c\u2081 \u2286 \u22c3\u2080 s\u271d \u2192 False",
+              "tactic": "intro c\u2083 hc\u2083 h\u2081 h\u2082"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain h | h := <a>chainClosure_succ_total_aux<\\/a> hc\\u2081 fun c\\u2084 => ih _ hc\\u2083\"",
+                "[{\"full_name\":\"_private.Mathlib.Order.Chain.0.chainClosure_succ_total_aux\",\"def_path\":\"Mathlib\\/Order\\/Chain.lean\",\"def_pos\":[219,17],\"def_end_pos\":[219,44]}]"
+              ],
+              "state_after": "case union.a.inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083\u271d s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 a \u2192 a = c\u2081 \u2228 SuccChain r c\u2081 \u2286 a\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh\u271d : c\u2081 \u2286 \u22c3\u2080 s\u271d\nc\u2083 : Set \u03b1\nhc\u2083 : c\u2083 \u2208 s\u271d\nh\u2081 : \u00acc\u2083 \u2286 c\u2081\nh\u2082 : \u00acSuccChain r c\u2081 \u2286 \u22c3\u2080 s\u271d\nh : SuccChain r c\u2083 \u2286 c\u2081\n\u22a2 False\n\ncase union.a.inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083\u271d s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 a \u2192 a = c\u2081 \u2228 SuccChain r c\u2081 \u2286 a\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh\u271d : c\u2081 \u2286 \u22c3\u2080 s\u271d\nc\u2083 : Set \u03b1\nhc\u2083 : c\u2083 \u2208 s\u271d\nh\u2081 : \u00acc\u2083 \u2286 c\u2081\nh\u2082 : \u00acSuccChain r c\u2081 \u2286 \u22c3\u2080 s\u271d\nh : c\u2081 \u2286 c\u2083\n\u22a2 False",
+              "state_before": "case union.a\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083\u271d s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 a \u2192 a = c\u2081 \u2228 SuccChain r c\u2081 \u2286 a\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh : c\u2081 \u2286 \u22c3\u2080 s\u271d\nc\u2083 : Set \u03b1\nhc\u2083 : c\u2083 \u2208 s\u271d\nh\u2081 : \u00acc\u2083 \u2286 c\u2081\nh\u2082 : \u00acSuccChain r c\u2081 \u2286 \u22c3\u2080 s\u271d\n\u22a2 False",
+              "tactic": "obtain h | h := chainClosure_succ_total_aux hc\u2081 fun c\u2084 => ih _ hc\u2083"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain h' | h' := ih c\\u2083 hc\\u2083 hc\\u2081 h\"",
+                "[]"
+              ],
+              "state_after": "case union.a.inr.inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083\u271d s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 a \u2192 a = c\u2081 \u2228 SuccChain r c\u2081 \u2286 a\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh\u271d : c\u2081 \u2286 \u22c3\u2080 s\u271d\nc\u2083 : Set \u03b1\nhc\u2083 : c\u2083 \u2208 s\u271d\nh\u2081 : \u00acc\u2083 \u2286 c\u2081\nh\u2082 : \u00acSuccChain r c\u2081 \u2286 \u22c3\u2080 s\u271d\nh : c\u2081 \u2286 c\u2083\nh' : c\u2083 = c\u2081\n\u22a2 False\n\ncase union.a.inr.inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083\u271d s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 a \u2192 a = c\u2081 \u2228 SuccChain r c\u2081 \u2286 a\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh\u271d : c\u2081 \u2286 \u22c3\u2080 s\u271d\nc\u2083 : Set \u03b1\nhc\u2083 : c\u2083 \u2208 s\u271d\nh\u2081 : \u00acc\u2083 \u2286 c\u2081\nh\u2082 : \u00acSuccChain r c\u2081 \u2286 \u22c3\u2080 s\u271d\nh : c\u2081 \u2286 c\u2083\nh' : SuccChain r c\u2081 \u2286 c\u2083\n\u22a2 False",
+              "state_before": "case union.a.inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083\u271d s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 a \u2192 a = c\u2081 \u2228 SuccChain r c\u2081 \u2286 a\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh\u271d : c\u2081 \u2286 \u22c3\u2080 s\u271d\nc\u2083 : Set \u03b1\nhc\u2083 : c\u2083 \u2208 s\u271d\nh\u2081 : \u00acc\u2083 \u2286 c\u2081\nh\u2082 : \u00acSuccChain r c\u2081 \u2286 \u22c3\u2080 s\u271d\nh : c\u2081 \u2286 c\u2083\n\u22a2 False",
+              "tactic": "obtain h' | h' := ih c\u2083 hc\u2083 hc\u2081 h"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact h\\u2081 (subset_succChain.trans h)\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case union.a.inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083\u271d s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 a \u2192 a = c\u2081 \u2228 SuccChain r c\u2081 \u2286 a\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh\u271d : c\u2081 \u2286 \u22c3\u2080 s\u271d\nc\u2083 : Set \u03b1\nhc\u2083 : c\u2083 \u2208 s\u271d\nh\u2081 : \u00acc\u2083 \u2286 c\u2081\nh\u2082 : \u00acSuccChain r c\u2081 \u2286 \u22c3\u2080 s\u271d\nh : SuccChain r c\u2083 \u2286 c\u2081\n\u22a2 False",
+              "tactic": "exact h\u2081 (subset_succChain.trans h)"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact h\\u2081 h'.subset\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case union.a.inr.inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083\u271d s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 a \u2192 a = c\u2081 \u2228 SuccChain r c\u2081 \u2286 a\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh\u271d : c\u2081 \u2286 \u22c3\u2080 s\u271d\nc\u2083 : Set \u03b1\nhc\u2083 : c\u2083 \u2208 s\u271d\nh\u2081 : \u00acc\u2083 \u2286 c\u2081\nh\u2082 : \u00acSuccChain r c\u2081 \u2286 \u22c3\u2080 s\u271d\nh : c\u2081 \u2286 c\u2083\nh' : c\u2083 = c\u2081\n\u22a2 False",
+              "tactic": "exact h\u2081 h'.subset"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact h\\u2082 (h'.trans <| <a>subset_sUnion_of_mem<\\/a> hc\\u2083)\"",
+                "[{\"full_name\":\"Set.subset_sUnion_of_mem\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Lattice.lean\",\"def_pos\":[1009,9],\"def_end_pos\":[1009,29]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case union.a.inr.inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2082 c\u2083\u271d s t : Set \u03b1\na b x y : \u03b1\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, \u2200 {c\u2081 : Set \u03b1}, ChainClosure r c\u2081 \u2192 c\u2081 \u2286 a \u2192 a = c\u2081 \u2228 SuccChain r c\u2081 \u2286 a\nc\u2081 : Set \u03b1\nhc\u2081 : ChainClosure r c\u2081\nh\u271d : c\u2081 \u2286 \u22c3\u2080 s\u271d\nc\u2083 : Set \u03b1\nhc\u2083 : c\u2083 \u2208 s\u271d\nh\u2081 : \u00acc\u2083 \u2286 c\u2081\nh\u2082 : \u00acSuccChain r c\u2081 \u2286 \u22c3\u2080 s\u271d\nh : c\u2081 \u2286 c\u2083\nh' : SuccChain r c\u2081 \u2286 c\u2083\n\u22a2 False",
+              "tactic": "exact h\u2082 (h'.trans <| subset_sUnion_of_mem hc\u2083)"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "isChain_empty",
+        "id": "isChain_empty",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            65,
+            23
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "isChain_empty",
+          "start": [
+            64,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "isChain_of_trichotomous",
+        "id": "isChain_of_trichotomous",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            87,
+            83
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "isChain_of_trichotomous",
+          "start": [
+            86,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "maxChain_spec",
+        "id": "maxChain_spec",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            285,
+            64
+          ],
+          "file_path": "Mathlib/Order/Chain.lean",
+          "full_name": "maxChain_spec",
+          "start": [
+            282,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Chain.lean"
+      }
+    ],
+    "input_proofs": 47,
+    "input_units": 2,
+    "proofs": 9,
+    "published_proofs": 8,
+    "published_transitions": 19,
+    "replay_failures": [],
+    "transitions": 24,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Order/Chain.lean",
+        "proof_id": "mathlib:chainClosure_succ_total_aux",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              229,
+              83
+            ],
+            "file_path": "Mathlib/Order/Chain.lean",
+            "full_name": "chainClosure_succ_total_aux",
+            "start": [
+              219,
+              9
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"cases' ih with ih ih\"",
+                  "[]"
+                ],
+                "state_after": "case succ.inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2081 c\u2082 c\u2083\u271d s t : Set \u03b1\na b x y : \u03b1\nh : \u2200 \u2983c\u2083 : Set \u03b1\u2984, ChainClosure r c\u2083 \u2192 c\u2083 \u2286 c\u2082 \u2192 c\u2082 = c\u2083 \u2228 SuccChain r c\u2083 \u2286 c\u2082\nc\u2083 : Set \u03b1\nhc\u2083 : ChainClosure r c\u2083\nih : SuccChain r c\u2082 \u2286 c\u2083\n\u22a2 SuccChain r c\u2082 \u2286 SuccChain r c\u2083 \u2228 SuccChain r c\u2083 \u2286 c\u2082\n\ncase succ.inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2081 c\u2082 c\u2083\u271d s t : Set \u03b1\na b x y : \u03b1\nh : \u2200 \u2983c\u2083 : Set \u03b1\u2984, ChainClosure r c\u2083 \u2192 c\u2083 \u2286 c\u2082 \u2192 c\u2082 = c\u2083 \u2228 SuccChain r c\u2083 \u2286 c\u2082\nc\u2083 : Set \u03b1\nhc\u2083 : ChainClosure r c\u2083\nih : c\u2083 \u2286 c\u2082\n\u22a2 SuccChain r c\u2082 \u2286 SuccChain r c\u2083 \u2228 SuccChain r c\u2083 \u2286 c\u2082",
+                "state_before": "case succ\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2081 c\u2082 c\u2083\u271d s t : Set \u03b1\na b x y : \u03b1\nh : \u2200 \u2983c\u2083 : Set \u03b1\u2984, ChainClosure r c\u2083 \u2192 c\u2083 \u2286 c\u2082 \u2192 c\u2082 = c\u2083 \u2228 SuccChain r c\u2083 \u2286 c\u2082\nc\u2083 : Set \u03b1\nhc\u2083 : ChainClosure r c\u2083\nih : SuccChain r c\u2082 \u2286 c\u2083 \u2228 c\u2083 \u2286 c\u2082\n\u22a2 SuccChain r c\u2082 \u2286 SuccChain r c\u2083 \u2228 SuccChain r c\u2083 \u2286 c\u2082",
+                "tactic": "cases' ih with ih ih"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact <a>Or.inl<\\/a> (ih.trans <a>subset_succChain<\\/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\":\"subset_succChain\",\"def_path\":\"Mathlib\\/Order\\/Chain.lean\",\"def_pos\":[191,9],\"def_end_pos\":[191,25]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case succ.inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2081 c\u2082 c\u2083\u271d s t : Set \u03b1\na b x y : \u03b1\nh : \u2200 \u2983c\u2083 : Set \u03b1\u2984, ChainClosure r c\u2083 \u2192 c\u2083 \u2286 c\u2082 \u2192 c\u2082 = c\u2083 \u2228 SuccChain r c\u2083 \u2286 c\u2082\nc\u2083 : Set \u03b1\nhc\u2083 : ChainClosure r c\u2083\nih : SuccChain r c\u2082 \u2286 c\u2083\n\u22a2 SuccChain r c\u2082 \u2286 SuccChain r c\u2083 \u2228 SuccChain r c\u2083 \u2286 c\u2082",
+                "tactic": "exact Or.inl (ih.trans subset_succChain)"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact (h hc\\u2083 ih).<a>imp_left<\\/a> fun (h : c\\u2082 = c\\u2083) => h \\u25b8 <a>Subset.rfl<\\/a>\"",
+                  "[{\"full_name\":\"Or.imp_left\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[173,9],\"def_end_pos\":[173,20]},{\"full_name\":\"Set.Subset.rfl\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[334,9],\"def_end_pos\":[334,19]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case succ.inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2081 c\u2082 c\u2083\u271d s t : Set \u03b1\na b x y : \u03b1\nh : \u2200 \u2983c\u2083 : Set \u03b1\u2984, ChainClosure r c\u2083 \u2192 c\u2083 \u2286 c\u2082 \u2192 c\u2082 = c\u2083 \u2228 SuccChain r c\u2083 \u2286 c\u2082\nc\u2083 : Set \u03b1\nhc\u2083 : ChainClosure r c\u2083\nih : c\u2083 \u2286 c\u2082\n\u22a2 SuccChain r c\u2082 \u2286 SuccChain r c\u2083 \u2228 SuccChain r c\u2083 \u2286 c\u2082",
+                "tactic": "exact (h hc\u2083 ih).imp_left fun (h : c\u2082 = c\u2083) => h \u25b8 Subset.rfl"
+              },
+              {
+                "annotated_tactic": [
+                  "\"refine <a>or_iff_not_imp_left<\\/a>.2 fun hn => <a>sUnion_subset<\\/a> fun a ha => ?_\"",
+                  "[{\"full_name\":\"Classical.or_iff_not_imp_left\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Classical.lean\",\"def_pos\":[147,9],\"def_end_pos\":[147,28]},{\"full_name\":\"Set.sUnion_subset\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Lattice.lean\",\"def_pos\":[1018,9],\"def_end_pos\":[1018,22]}]"
+                ],
+                "state_after": "case union\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2081 c\u2082 c\u2083 s t : Set \u03b1\na\u271d\u00b9 b x y : \u03b1\nh : \u2200 \u2983c\u2083 : Set \u03b1\u2984, ChainClosure r c\u2083 \u2192 c\u2083 \u2286 c\u2082 \u2192 c\u2082 = c\u2083 \u2228 SuccChain r c\u2083 \u2286 c\u2082\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, SuccChain r c\u2082 \u2286 a \u2228 a \u2286 c\u2082\nhn : \u00acSuccChain r c\u2082 \u2286 \u22c3\u2080 s\u271d\na : Set \u03b1\nha : a \u2208 s\u271d\n\u22a2 a \u2286 c\u2082",
+                "state_before": "case union\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2081 c\u2082 c\u2083 s t : Set \u03b1\na b x y : \u03b1\nh : \u2200 \u2983c\u2083 : Set \u03b1\u2984, ChainClosure r c\u2083 \u2192 c\u2083 \u2286 c\u2082 \u2192 c\u2082 = c\u2083 \u2228 SuccChain r c\u2083 \u2286 c\u2082\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, SuccChain r c\u2082 \u2286 a \u2228 a \u2286 c\u2082\n\u22a2 SuccChain r c\u2082 \u2286 \u22c3\u2080 s\u271d \u2228 \u22c3\u2080 s\u271d \u2286 c\u2082",
+                "tactic": "refine or_iff_not_imp_left.2 fun hn => sUnion_subset fun a ha => ?_"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact (ih a ha).<a>resolve_left<\\/a> fun h => hn <| h.trans <| <a>subset_sUnion_of_mem<\\/a> ha\"",
+                  "[{\"full_name\":\"Or.resolve_left\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[555,9],\"def_end_pos\":[555,24]},{\"full_name\":\"Set.subset_sUnion_of_mem\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Lattice.lean\",\"def_pos\":[1009,9],\"def_end_pos\":[1009,29]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case union\n\u03b1 : Type u_1\n\u03b2 : Type u_2\nr : \u03b1 \u2192 \u03b1 \u2192 Prop\nc c\u2081 c\u2082 c\u2083 s t : Set \u03b1\na\u271d\u00b9 b x y : \u03b1\nh : \u2200 \u2983c\u2083 : Set \u03b1\u2984, ChainClosure r c\u2083 \u2192 c\u2083 \u2286 c\u2082 \u2192 c\u2082 = c\u2083 \u2228 SuccChain r c\u2083 \u2286 c\u2082\ns\u271d : Set (Set \u03b1)\na\u271d : \u2200 a \u2208 s\u271d, ChainClosure r a\nih : \u2200 a \u2208 s\u271d, SuccChain r c\u2082 \u2286 a \u2228 a \u2286 c\u2082\nhn : \u00acSuccChain r c\u2082 \u2286 \u22c3\u2080 s\u271d\na : Set \u03b1\nha : a \u2208 s\u271d\n\u22a2 a \u2286 c\u2082",
+                "tactic": "exact (ih a ha).resolve_left fun h => hn <| h.trans <| subset_sUnion_of_mem ha"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "chainClosure_succ_total_aux"
+      }
+    ],
+    "validation_rejected_proofs": 1,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001531-0000-705026028bf4b028.parquet",
+      "sha256": "705026028bf4b028e3b2f5f81f6b5065c45d78ff9dd102dbb550188ed369cd15",
+      "bytes": 75752,
+      "rows": 16,
+      "revision": "504ada6ade9a708ef0393868f005bf429a0291c6"
+    },
+    {
+      "path": "data/internal_test/mathlib-001531-0000-5baf86a7fefbb345.parquet",
+      "sha256": "5baf86a7fefbb345e055accd1095ce946866f921f495412107b688a9d3fb48a0",
+      "bytes": 64886,
+      "rows": 3,
+      "revision": "504ada6ade9a708ef0393868f005bf429a0291c6"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:IsChain.directed",
+    "mathlib:IsChain.exists3",
+    "mathlib:IsChain.succ",
+    "mathlib:IsChain.superChain_succChain",
+    "mathlib:chainClosure_empty",
+    "mathlib:isChain_univ_iff",
+    "mathlib:subset_succChain",
+    "mathlib:succChain_spec"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Chain.lean\",null,null,\"IsChain.directed\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Chain.lean\",null,null,\"IsChain.exists3\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Chain.lean\",null,null,\"IsChain.succ\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Chain.lean\",null,null,\"IsChain.superChain_succChain\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Chain.lean\",null,null,\"chainClosure_empty\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Chain.lean\",null,null,\"isChain_univ_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Chain.lean\",null,null,\"subset_succChain\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Chain.lean\",null,null,\"succChain_spec\"]"
+  ]
+}

manifests/batches/mathlib/001532.json

@@ -0,0 +1,1794 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001532",
+  "batch_fingerprint": "23ef13cc7e9af3304584d12bb60341ff7a8cf8040473ced6fcfa2665d846eeb8",
+  "evidence": {
+    "batch_fingerprint": "23ef13cc7e9af3304584d12bb60341ff7a8cf8040473ced6fcfa2665d846eeb8",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Btw.btw.antisymm",
+        "id": "Btw.btw.antisymm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            279,
+            17
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "Btw.btw.antisymm",
+          "start": [
+            278,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Btw.btw.cyclic_left",
+        "id": "Btw.btw.cyclic_left",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            167,
+            20
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "Btw.btw.cyclic_left",
+          "start": [
+            166,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "SBtw.sbtw.trans_left",
+        "id": "SBtw.sbtw.trans_left",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            237,
+            20
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "SBtw.sbtw.trans_left",
+          "start": [
+            236,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.left_mem_cIcc",
+        "id": "Set.left_mem_cIcc",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            362,
+            15
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "Set.left_mem_cIcc",
+          "start": [
+            361,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.mem_cIcc",
+        "id": "Set.mem_cIcc",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            347,
+            10
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "Set.mem_cIcc",
+          "start": [
+            346,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Set.mem_cIoo",
+        "id": "Set.mem_cIoo",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            352,
+            10
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "Set.mem_cIoo",
+          "start": [
+            351,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "btw_cyclic",
+        "id": "btw_cyclic",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            180,
+            38
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "btw_cyclic",
+          "start": [
+            179,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "btw_cyclic_right",
+        "id": "btw_cyclic_right",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            171,
+            28
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "btw_cyclic_right",
+          "start": [
+            170,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "btw_iff_not_sbtw",
+        "id": "btw_iff_not_sbtw",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            321,
+            34
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "btw_iff_not_sbtw",
+          "start": [
+            320,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "btw_of_sbtw",
+        "id": "btw_of_sbtw",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            188,
+            31
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "btw_of_sbtw",
+          "start": [
+            187,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "btw_refl_left",
+        "id": "btw_refl_left",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            300,
+            34
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "btw_refl_left",
+          "start": [
+            299,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "btw_refl_left_right",
+        "id": "btw_refl_left_right",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            292,
+            34
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "btw_refl_left_right",
+          "start": [
+            291,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "btw_refl_right",
+        "id": "btw_refl_right",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            308,
+            33
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "btw_refl_right",
+          "start": [
+            307,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "btw_rfl",
+        "id": "btw_rfl",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            161,
+            13
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "btw_rfl",
+          "start": [
+            160,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "btw_rfl_left",
+        "id": "btw_rfl_left",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            304,
+            20
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "btw_rfl_left",
+          "start": [
+            303,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "btw_rfl_left_right",
+        "id": "btw_rfl_left_right",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            296,
+            26
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "btw_rfl_left_right",
+          "start": [
+            295,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "btw_rfl_right",
+        "id": "btw_rfl_right",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            312,
+            21
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "btw_rfl_right",
+          "start": [
+            311,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "not_btw_of_sbtw",
+        "id": "not_btw_of_sbtw",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            195,
+            31
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "not_btw_of_sbtw",
+          "start": [
+            194,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "not_sbtw_of_btw",
+        "id": "not_sbtw_of_btw",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            201,
+            92
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "not_sbtw_of_btw",
+          "start": [
+            201,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "sbtw_asymm",
+        "id": "sbtw_asymm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            248,
+            17
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "sbtw_asymm",
+          "start": [
+            247,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "sbtw_cyclic",
+        "id": "sbtw_cyclic",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            231,
+            40
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "sbtw_cyclic",
+          "start": [
+            230,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "sbtw_cyclic_left",
+        "id": "sbtw_cyclic_left",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            215,
+            71
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "sbtw_cyclic_left",
+          "start": [
+            214,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "sbtw_irrefl",
+        "id": "sbtw_irrefl",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            264,
+            25
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "sbtw_irrefl",
+          "start": [
+            263,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "sbtw_irrefl_left",
+        "id": "sbtw_irrefl_left",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            257,
+            98
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "sbtw_irrefl_left",
+          "start": [
+            257,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "sbtw_irrefl_left_right",
+        "id": "sbtw_irrefl_left_right",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            254,
+            83
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "sbtw_irrefl_left_right",
+          "start": [
+            254,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "sbtw_irrefl_right",
+        "id": "sbtw_irrefl_right",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            260,
+            100
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "sbtw_irrefl_right",
+          "start": [
+            260,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "sbtw_of_btw_not_btw",
+        "id": "sbtw_of_btw_not_btw",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            208,
+            38
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "sbtw_of_btw_not_btw",
+          "start": [
+            207,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "sbtw_trans_right",
+        "id": "sbtw_trans_right",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            241,
+            60
+          ],
+          "file_path": "Mathlib/Order/Circular.lean",
+          "full_name": "sbtw_trans_right",
+          "start": [
+            240,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Circular.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.IsClosed.closure_eq",
+        "id": "ClosureOperator.IsClosed.closure_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            196,
+            73
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.IsClosed.closure_eq",
+          "start": [
+            196,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.closure_iSup_closure",
+        "id": "ClosureOperator.closure_iSup_closure",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            303,
+            52
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.closure_iSup_closure",
+          "start": [
+            301,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.closure_inf_le",
+        "id": "ClosureOperator.closure_inf_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            256,
+            28
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.closure_inf_le",
+          "start": [
+            254,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.closure_isGLB",
+        "id": "ClosureOperator.closure_isGLB",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            221,
+            56
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.closure_isGLB",
+          "start": [
+            219,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.closure_min",
+        "id": "ClosureOperator.closure_min",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            217,
+            89
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.closure_min",
+          "start": [
+            217,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.closure_sup_closure_le",
+        "id": "ClosureOperator.closure_sup_closure_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            264,
+            28
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.closure_sup_closure_le",
+          "start": [
+            263,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.closure_sup_closure_left",
+        "id": "ClosureOperator.closure_sup_closure_left",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            270,
+            55
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.closure_sup_closure_left",
+          "start": [
+            267,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.closure_top",
+        "id": "ClosureOperator.closure_top",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            246,
+            35
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.closure_top",
+          "start": [
+            245,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.conjBy_refl",
+        "id": "ClosureOperator.conjBy_refl",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            99,
+            42
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.conjBy_refl",
+          "start": [
+            98,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.conjBy_trans",
+        "id": "ClosureOperator.conjBy_trans",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            103,
+            60
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.conjBy_trans",
+          "start": [
+            101,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.ext",
+        "id": "ClosureOperator.ext",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            128,
+            15
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.ext",
+          "start": [
+            127,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.ext_isClosed",
+        "id": "ClosureOperator.ext_isClosed",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            226,
+            68
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.ext_isClosed",
+          "start": [
+            223,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.idempotent",
+        "id": "ClosureOperator.idempotent",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            181,
+            18
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.idempotent",
+          "start": [
+            180,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.isClosed_closure",
+        "id": "ClosureOperator.isClosed_closure",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            184,
+            96
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.isClosed_closure",
+          "start": [
+            184,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.isClosed_iff_closure_le",
+        "id": "ClosureOperator.isClosed_iff_closure_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            200,
+            86
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.isClosed_iff_closure_le",
+          "start": [
+            199,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.isClosed_top",
+        "id": "ClosureOperator.isClosed_top",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            249,
+            76
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.isClosed_top",
+          "start": [
+            249,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.le_closure",
+        "id": "ClosureOperator.le_closure",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            176,
+            18
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.le_closure",
+          "start": [
+            175,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.le_closure_iff",
+        "id": "ClosureOperator.le_closure_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            209,
+            66
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.le_closure_iff",
+          "start": [
+            208,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.monotone",
+        "id": "ClosureOperator.monotone",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            170,
+            14
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.monotone",
+          "start": [
+            169,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "ClosureOperator.sInf_isClosed",
+        "id": "ClosureOperator.sInf_isClosed",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            298,
+            74
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.sInf_isClosed",
+          "start": [
+            295,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'rintro \u27e8y, rfl\u27e9'",
+        "full_name": "ClosureOperator.setOf_isClosed_eq_range_closure",
+        "id": "ClosureOperator.setOf_isClosed_eq_range_closure",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            205,
+            93
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "ClosureOperator.setOf_isClosed_eq_range_closure",
+          "start": [
+            204,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"ext x\"",
+                "[]"
+              ],
+              "state_after": "case h\n\u03b1 : Type u_1\n\u03b9 : Sort u_2\n\u03ba : \u03b9 \u2192 Sort u_3\ninst\u271d\u00b9 inst\u271d : PartialOrder \u03b1\nc : ClosureOperator \u03b1\nx\u271d y x : \u03b1\n\u22a2 x \u2208 {x | c.IsClosed x} \u2194 x \u2208 range \u21d1c",
+              "state_before": "\u03b1 : Type u_1\n\u03b9 : Sort u_2\n\u03ba : \u03b9 \u2192 Sort u_3\ninst\u271d\u00b9 inst\u271d : PartialOrder \u03b1\nc : ClosureOperator \u03b1\nx y : \u03b1\n\u22a2 {x | c.IsClosed x} = range \u21d1c",
+              "tactic": "ext x"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact \\u27e8fun hx \\u21a6 \\u27e8x, hx.closure_eq\\u27e9, by rintro \\u27e8y, rfl\\u27e9; exact c.isClosed_closure _\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case h\n\u03b1 : Type u_1\n\u03b9 : Sort u_2\n\u03ba : \u03b9 \u2192 Sort u_3\ninst\u271d\u00b9 inst\u271d : PartialOrder \u03b1\nc : ClosureOperator \u03b1\nx\u271d y x : \u03b1\n\u22a2 x \u2208 {x | c.IsClosed x} \u2194 x \u2208 range \u21d1c",
+              "tactic": "exact \u27e8fun hx \u21a6 \u27e8x, hx.closure_eq\u27e9, by rintro \u27e8y, rfl\u27e9; exact c.isClosed_closure _\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"rintro \\u27e8y, rfl\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "case intro\n\u03b1 : Type u_1\n\u03b9 : Sort u_2\n\u03ba : \u03b9 \u2192 Sort u_3\ninst\u271d\u00b9 inst\u271d : PartialOrder \u03b1\nc : ClosureOperator \u03b1\nx y\u271d y : \u03b1\n\u22a2 c y \u2208 {x | c.IsClosed x}",
+              "state_before": "\u03b1 : Type u_1\n\u03b9 : Sort u_2\n\u03ba : \u03b9 \u2192 Sort u_3\ninst\u271d\u00b9 inst\u271d : PartialOrder \u03b1\nc : ClosureOperator \u03b1\nx\u271d y x : \u03b1\n\u22a2 x \u2208 range \u21d1c \u2192 x \u2208 {x | c.IsClosed x}",
+              "tactic": "rintro \u27e8y, rfl\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact c.isClosed_closure _\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case intro\n\u03b1 : Type u_1\n\u03b9 : Sort u_2\n\u03ba : \u03b9 \u2192 Sort u_3\ninst\u271d\u00b9 inst\u271d : PartialOrder \u03b1\nc : ClosureOperator \u03b1\nx y\u271d y : \u03b1\n\u22a2 c y \u2208 {x | c.IsClosed x}",
+              "tactic": "exact c.isClosed_closure _"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.closed_eq_range_close",
+        "id": "LowerAdjoint.closed_eq_range_close",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            448,
+            52
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.closed_eq_range_close",
+          "start": [
+            447,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.closure_eq_self_of_mem_closed",
+        "id": "LowerAdjoint.closure_eq_self_of_mem_closed",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            428,
+            4
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.closure_eq_self_of_mem_closed",
+          "start": [
+            427,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.closure_iSup_closure",
+        "id": "LowerAdjoint.closure_iSup_closure",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            500,
+            43
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.closure_iSup_closure",
+          "start": [
+            499,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.closure_iSup\u2082_closure",
+        "id": "LowerAdjoint.closure_iSup\u2082_closure",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            505,
+            44
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.closure_iSup\u2082_closure",
+          "start": [
+            503,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.closure_iUnion_closure",
+        "id": "LowerAdjoint.closure_iUnion_closure",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            556,
+            52
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.closure_iUnion_closure",
+          "start": [
+            555,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.closure_iUnion\u2082_closure",
+        "id": "LowerAdjoint.closure_iUnion\u2082_closure",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            564,
+            53
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.closure_iUnion\u2082_closure",
+          "start": [
+            562,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.closure_inf_le",
+        "id": "LowerAdjoint.closure_inf_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            470,
+            39
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.closure_inf_le",
+          "start": [
+            468,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.closure_is_closed",
+        "id": "LowerAdjoint.closure_is_closed",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            443,
+            17
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.closure_is_closed",
+          "start": [
+            442,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.closure_le_closed_iff_le",
+        "id": "LowerAdjoint.closure_le_closed_iff_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            458,
+            61
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.closure_le_closed_iff_le",
+          "start": [
+            457,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.closure_sup_closure",
+        "id": "LowerAdjoint.closure_sup_closure",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            490,
+            44
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.closure_sup_closure",
+          "start": [
+            489,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.closure_sup_closure_le",
+        "id": "LowerAdjoint.closure_sup_closure_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            478,
+            47
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.closure_sup_closure_le",
+          "start": [
+            477,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.closure_sup_closure_left",
+        "id": "LowerAdjoint.closure_sup_closure_left",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            482,
+            49
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.closure_sup_closure_left",
+          "start": [
+            481,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.closure_sup_closure_right",
+        "id": "LowerAdjoint.closure_sup_closure_right",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            486,
+            50
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.closure_sup_closure_right",
+          "start": [
+            485,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.closure_top",
+        "id": "LowerAdjoint.closure_top",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            465,
+            32
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.closure_top",
+          "start": [
+            463,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.closure_union_closure_left",
+        "id": "LowerAdjoint.closure_union_closure_left",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            542,
+            57
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.closure_union_closure_left",
+          "start": [
+            541,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.closure_union_closure_right",
+        "id": "LowerAdjoint.closure_union_closure_right",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            547,
+            58
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.closure_union_closure_right",
+          "start": [
+            546,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.closure_union_closure_subset",
+        "id": "LowerAdjoint.closure_union_closure_subset",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            537,
+            31
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.closure_union_closure_subset",
+          "start": [
+            536,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.eq_of_le",
+        "id": "LowerAdjoint.eq_of_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            533,
+            43
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.eq_of_le",
+          "start": [
+            532,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.gc",
+        "id": "LowerAdjoint.gc",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            368,
+            8
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.gc",
+          "start": [
+            367,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.idempotent",
+        "id": "LowerAdjoint.idempotent",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            406,
+            33
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.idempotent",
+          "start": [
+            405,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.le_closure",
+        "id": "LowerAdjoint.le_closure",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            385,
+            16
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.le_closure",
+          "start": [
+            384,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.le_closure_iff",
+        "id": "LowerAdjoint.le_closure_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            410,
+            35
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.le_closure_iff",
+          "start": [
+            409,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.le_iff_subset",
+        "id": "LowerAdjoint.le_iff_subset",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            524,
+            11
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.le_iff_subset",
+          "start": [
+            523,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.mem_closed_iff",
+        "id": "LowerAdjoint.mem_closed_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            424,
+            10
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.mem_closed_iff",
+          "start": [
+            423,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.mem_closed_iff_closure_le",
+        "id": "LowerAdjoint.mem_closed_iff_closure_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            438,
+            44
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.mem_closed_iff_closure_le",
+          "start": [
+            437,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.monotone",
+        "id": "LowerAdjoint.monotone",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            379,
+            39
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.monotone",
+          "start": [
+            378,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.not_mem_of_not_mem_closure",
+        "id": "LowerAdjoint.not_mem_of_not_mem_closure",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            520,
+            28
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.not_mem_of_not_mem_closure",
+          "start": [
+            519,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LowerAdjoint.subset_closure",
+        "id": "LowerAdjoint.subset_closure",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            516,
+            17
+          ],
+          "file_path": "Mathlib/Order/Closure.lean",
+          "full_name": "LowerAdjoint.subset_closure",
+          "start": [
+            515,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Closure.lean"
+      }
+    ],
+    "input_proofs": 88,
+    "input_units": 2,
+    "proofs": 11,
+    "published_proofs": 11,
+    "published_transitions": 17,
+    "replay_failures": [],
+    "transitions": 17,
+    "validation_failures": [],
+    "validation_rejected_proofs": 0,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001532-0000-b10c71f68aa08795.parquet",
+      "sha256": "b10c71f68aa0879575543e31a1c4b4992b88c7e5484edcf8e225b7410029bf18",
+      "bytes": 65275,
+      "rows": 15,
+      "revision": "504ada6ade9a708ef0393868f005bf429a0291c6"
+    },
+    {
+      "path": "data/dev/mathlib-001532-0000-0ffed2d716491e81.parquet",
+      "sha256": "0ffed2d716491e8196ba1f56ac4528e816e340a316807fb91275d2a183f343d5",
+      "bytes": 39332,
+      "rows": 2,
+      "revision": "504ada6ade9a708ef0393868f005bf429a0291c6"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:ClosureOperator.IsClosed.closure_le_iff",
+    "mathlib:ClosureOperator.closure_sup_closure",
+    "mathlib:ClosureOperator.closure_sup_closure_right",
+    "mathlib:ClosureOperator.eq_ofPred_closed",
+    "mathlib:LowerAdjoint.closure_union_closure",
+    "mathlib:LowerAdjoint.ext",
+    "mathlib:LowerAdjoint.mem_iff",
+    "mathlib:Set.compl_cIcc",
+    "mathlib:Set.compl_cIoo",
+    "mathlib:closureOperator_gi_self",
+    "mathlib:sbtw_iff_not_btw"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Circular.lean\",null,null,\"Set.compl_cIcc\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Circular.lean\",null,null,\"Set.compl_cIoo\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Circular.lean\",null,null,\"sbtw_iff_not_btw\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Closure.lean\",null,null,\"ClosureOperator.IsClosed.closure_le_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Closure.lean\",null,null,\"ClosureOperator.closure_sup_closure\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Closure.lean\",null,null,\"ClosureOperator.closure_sup_closure_right\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Closure.lean\",null,null,\"ClosureOperator.eq_ofPred_closed\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Closure.lean\",null,null,\"LowerAdjoint.closure_union_closure\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Closure.lean\",null,null,\"LowerAdjoint.ext\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Closure.lean\",null,null,\"LowerAdjoint.mem_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Closure.lean\",null,null,\"closureOperator_gi_self\"]"
+  ]
+}

manifests/batches/mathlib/001534.json

@@ -0,0 +1,1574 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001534",
+  "batch_fingerprint": "1f182205b844a5379ab8eeb93ff24400471adcf7729ab7b5a2008dc53e3aaa0d",
+  "evidence": {
+    "batch_fingerprint": "1f182205b844a5379ab8eeb93ff24400471adcf7729ab7b5a2008dc53e3aaa0d",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Eq.cmp_eq_eq",
+        "id": "Eq.cmp_eq_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            274,
+            26
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "Eq.cmp_eq_eq",
+          "start": [
+            273,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Eq.cmp_eq_eq'",
+        "id": "Eq.cmp_eq_eq'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            278,
+            19
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "Eq.cmp_eq_eq'",
+          "start": [
+            277,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LT.lt.cmp_eq_gt",
+        "id": "LT.lt.cmp_eq_gt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            271,
+            26
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "LT.lt.cmp_eq_gt",
+          "start": [
+            270,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "LT.lt.cmp_eq_lt",
+        "id": "LT.lt.cmp_eq_lt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            268,
+            26
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "LT.lt.cmp_eq_lt",
+          "start": [
+            267,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Ordering.Compares.cmp_eq",
+        "id": "Ordering.Compares.cmp_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            173,
+            27
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "Ordering.Compares.cmp_eq",
+          "start": [
+            171,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'injection h'",
+        "full_name": "Ordering.Compares.eq_eq",
+        "id": "Ordering.Compares.eq_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            97,
+            77
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "Ordering.Compares.eq_eq",
+          "start": [
+            94,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"injection h\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : Preorder \u03b1\na b : \u03b1\nh\u271d : lt.Compares a b\nh : lt = eq\n\u22a2 a = b",
+              "tactic": "injection h"
+            },
+            {
+              "annotated_tactic": [
+                "\"injection h\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : Preorder \u03b1\na b : \u03b1\nh\u271d : gt.Compares a b\nh : gt = eq\n\u22a2 a = b",
+              "tactic": "injection h"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Ordering.Compares.eq_gt",
+        "id": "Ordering.Compares.eq_gt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            101,
+            46
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "Ordering.Compares.eq_gt",
+          "start": [
+            100,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'injection h'",
+        "full_name": "Ordering.Compares.eq_lt",
+        "id": "Ordering.Compares.eq_lt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            85,
+            77
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "Ordering.Compares.eq_lt",
+          "start": [
+            82,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"injection h\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : Preorder \u03b1\na b : \u03b1\nh\u271d : eq.Compares a b\nh : eq = lt\n\u22a2 a < b",
+              "tactic": "injection h"
+            },
+            {
+              "annotated_tactic": [
+                "\"injection h\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : Preorder \u03b1\na b : \u03b1\nh\u271d : gt.Compares a b\nh : gt = lt\n\u22a2 a < b",
+              "tactic": "injection h"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Ordering.Compares.inj",
+        "id": "Ordering.Compares.inj",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            124,
+            38
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "Ordering.Compares.inj",
+          "start": [
+            120,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Ordering.Compares.le_antisymm",
+        "id": "Ordering.Compares.le_antisymm",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            117,
+            47
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "Ordering.Compares.le_antisymm",
+          "start": [
+            114,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Ordering.Compares.le_total",
+        "id": "Ordering.Compares.le_total",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            111,
+            33
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "Ordering.Compares.le_total",
+          "start": [
+            108,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Ordering.Compares.ne_gt",
+        "id": "Ordering.Compares.ne_gt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            105,
+            58
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "Ordering.Compares.ne_gt",
+          "start": [
+            104,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'injection h'",
+        "full_name": "Ordering.Compares.ne_lt",
+        "id": "Ordering.Compares.ne_lt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            91,
+            68
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "Ordering.Compares.ne_lt",
+          "start": [
+            88,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"injection h\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : Preorder \u03b1\na b : \u03b1\nh\u271d : eq.Compares a b\nx\u271d : b \u2264 a\nh : eq = lt\n\u22a2 False",
+              "tactic": "injection h"
+            },
+            {
+              "annotated_tactic": [
+                "\"injection h\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : Preorder \u03b1\na b : \u03b1\nh\u271d : gt.Compares a b\nx\u271d : b \u2264 a\nh : gt = lt\n\u22a2 False",
+              "tactic": "injection h"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Ordering.compares_eq",
+        "id": "Ordering.compares_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            62,
+            70
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "Ordering.compares_eq",
+          "start": [
+            61,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Ordering.compares_gt",
+        "id": "Ordering.compares_gt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            65,
+            70
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "Ordering.compares_gt",
+          "start": [
+            64,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "no internal trace for tactic \"cases' hab with hab hab\"",
+        "full_name": "Ordering.compares_iff_of_compares_impl",
+        "id": "Ordering.compares_iff_of_compares_impl",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            138,
+            27
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "Ordering.compares_iff_of_compares_impl",
+          "start": [
+            128,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"refine \\u27e8h, fun ho => ?_\\u27e9\"",
+                "[]"
+              ],
+              "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\na b : \u03b1\na' b' : \u03b2\nh : \u2200 {o : Ordering}, o.Compares a b \u2192 o.Compares a' b'\no : Ordering\nho : o.Compares a' b'\n\u22a2 o.Compares a b",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\na b : \u03b1\na' b' : \u03b2\nh : \u2200 {o : Ordering}, o.Compares a b \u2192 o.Compares a' b'\no : Ordering\n\u22a2 o.Compares a b \u2194 o.Compares a' b'",
+              "tactic": "refine \u27e8h, fun ho => ?_\u27e9"
+            },
+            {
+              "annotated_tactic": [
+                "\"cases' <a>lt_trichotomy<\\/a> a b with hab hab\"",
+                "[{\"full_name\":\"lt_trichotomy\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[313,9],\"def_end_pos\":[313,22]}]"
+              ],
+              "state_after": "case inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\na b : \u03b1\na' b' : \u03b2\nh : \u2200 {o : Ordering}, o.Compares a b \u2192 o.Compares a' b'\no : Ordering\nho : o.Compares a' b'\nhab : a < b\n\u22a2 o.Compares a b\n\ncase inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\na b : \u03b1\na' b' : \u03b2\nh : \u2200 {o : Ordering}, o.Compares a b \u2192 o.Compares a' b'\no : Ordering\nho : o.Compares a' b'\nhab : a = b \u2228 b < a\n\u22a2 o.Compares a b",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\na b : \u03b1\na' b' : \u03b2\nh : \u2200 {o : Ordering}, o.Compares a b \u2192 o.Compares a' b'\no : Ordering\nho : o.Compares a' b'\n\u22a2 o.Compares a b",
+              "tactic": "cases' lt_trichotomy a b with hab hab"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hab : <a>Compares<\\/a> <a>Ordering.lt<\\/a> a b := hab\"",
+                "[{\"full_name\":\"Ordering.Compares\",\"def_path\":\"Mathlib\\/Order\\/Compare.lean\",\"def_pos\":[52,5],\"def_end_pos\":[52,13]},{\"full_name\":\"Ordering.lt\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Ord.lean\",\"def_pos\":[12,5],\"def_end_pos\":[12,7]}]"
+              ],
+              "state_after": "case inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\na b : \u03b1\na' b' : \u03b2\nh : \u2200 {o : Ordering}, o.Compares a b \u2192 o.Compares a' b'\no : Ordering\nho : o.Compares a' b'\nhab\u271d : a < b\nhab : lt.Compares a b\n\u22a2 o.Compares a b",
+              "state_before": "case inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\na b : \u03b1\na' b' : \u03b2\nh : \u2200 {o : Ordering}, o.Compares a b \u2192 o.Compares a' b'\no : Ordering\nho : o.Compares a' b'\nhab : a < b\n\u22a2 o.Compares a b",
+              "tactic": "have hab : Compares Ordering.lt a b := hab"
+            },
+            {
+              "annotated_tactic": [
+                "\"rwa [ho.inj (h hab)]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\na b : \u03b1\na' b' : \u03b2\nh : \u2200 {o : Ordering}, o.Compares a b \u2192 o.Compares a' b'\no : Ordering\nho : o.Compares a' b'\nhab\u271d : a < b\nhab : lt.Compares a b\n\u22a2 o.Compares a b",
+              "tactic": "rwa [ho.inj (h hab)]"
+            },
+            {
+              "annotated_tactic": [
+                "\"cases' hab with hab hab\"",
+                "[]"
+              ],
+              "state_after": "case inr.inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\na b : \u03b1\na' b' : \u03b2\nh : \u2200 {o : Ordering}, o.Compares a b \u2192 o.Compares a' b'\no : Ordering\nho : o.Compares a' b'\nhab : a = b\n\u22a2 o.Compares a b\n\ncase inr.inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\na b : \u03b1\na' b' : \u03b2\nh : \u2200 {o : Ordering}, o.Compares a b \u2192 o.Compares a' b'\no : Ordering\nho : o.Compares a' b'\nhab : b < a\n\u22a2 o.Compares a b",
+              "state_before": "case inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\na b : \u03b1\na' b' : \u03b2\nh : \u2200 {o : Ordering}, o.Compares a b \u2192 o.Compares a' b'\no : Ordering\nho : o.Compares a' b'\nhab : a = b \u2228 b < a\n\u22a2 o.Compares a b",
+              "tactic": "cases' hab with hab hab"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hab : <a>Compares<\\/a> <a>Ordering.eq<\\/a> a b := hab\"",
+                "[{\"full_name\":\"Ordering.Compares\",\"def_path\":\"Mathlib\\/Order\\/Compare.lean\",\"def_pos\":[52,5],\"def_end_pos\":[52,13]},{\"full_name\":\"Ordering.eq\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Ord.lean\",\"def_pos\":[12,10],\"def_end_pos\":[12,12]}]"
+              ],
+              "state_after": "case inr.inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\na b : \u03b1\na' b' : \u03b2\nh : \u2200 {o : Ordering}, o.Compares a b \u2192 o.Compares a' b'\no : Ordering\nho : o.Compares a' b'\nhab\u271d : a = b\nhab : eq.Compares a b\n\u22a2 o.Compares a b",
+              "state_before": "case inr.inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\na b : \u03b1\na' b' : \u03b2\nh : \u2200 {o : Ordering}, o.Compares a b \u2192 o.Compares a' b'\no : Ordering\nho : o.Compares a' b'\nhab : a = b\n\u22a2 o.Compares a b",
+              "tactic": "have hab : Compares Ordering.eq a b := hab"
+            },
+            {
+              "annotated_tactic": [
+                "\"rwa [ho.inj (h hab)]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inr.inl\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\na b : \u03b1\na' b' : \u03b2\nh : \u2200 {o : Ordering}, o.Compares a b \u2192 o.Compares a' b'\no : Ordering\nho : o.Compares a' b'\nhab\u271d : a = b\nhab : eq.Compares a b\n\u22a2 o.Compares a b",
+              "tactic": "rwa [ho.inj (h hab)]"
+            },
+            {
+              "annotated_tactic": [
+                "\"have hab : <a>Compares<\\/a> <a>Ordering.gt<\\/a> a b := hab\"",
+                "[{\"full_name\":\"Ordering.Compares\",\"def_path\":\"Mathlib\\/Order\\/Compare.lean\",\"def_pos\":[52,5],\"def_end_pos\":[52,13]},{\"full_name\":\"Ordering.gt\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Ord.lean\",\"def_pos\":[12,15],\"def_end_pos\":[12,17]}]"
+              ],
+              "state_after": "case inr.inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\na b : \u03b1\na' b' : \u03b2\nh : \u2200 {o : Ordering}, o.Compares a b \u2192 o.Compares a' b'\no : Ordering\nho : o.Compares a' b'\nhab\u271d : b < a\nhab : gt.Compares a b\n\u22a2 o.Compares a b",
+              "state_before": "case inr.inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\na b : \u03b1\na' b' : \u03b2\nh : \u2200 {o : Ordering}, o.Compares a b \u2192 o.Compares a' b'\no : Ordering\nho : o.Compares a' b'\nhab : b < a\n\u22a2 o.Compares a b",
+              "tactic": "have hab : Compares Ordering.gt a b := hab"
+            },
+            {
+              "annotated_tactic": [
+                "\"rwa [ho.inj (h hab)]\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case inr.inr\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\ninst\u271d : Preorder \u03b2\na b : \u03b1\na' b' : \u03b2\nh : \u2200 {o : Ordering}, o.Compares a b \u2192 o.Compares a' b'\no : Ordering\nho : o.Compares a' b'\nhab\u271d : b < a\nhab : gt.Compares a b\n\u22a2 o.Compares a b",
+              "tactic": "rwa [ho.inj (h hab)]"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Ordering.compares_lt",
+        "id": "Ordering.compares_lt",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            59,
+            70
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "Ordering.compares_lt",
+          "start": [
+            58,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'exact eq_comm'",
+        "full_name": "Ordering.compares_swap",
+        "id": "Ordering.compares_swap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            71,
+            18
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "Ordering.compares_swap",
+          "start": [
+            67,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"cases o\"",
+                "[]"
+              ],
+              "state_after": "case lt\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : LT \u03b1\na b : \u03b1\n\u22a2 lt.swap.Compares a b \u2194 lt.Compares b a\n\ncase eq\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : LT \u03b1\na b : \u03b1\n\u22a2 eq.swap.Compares a b \u2194 eq.Compares b a\n\ncase gt\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : LT \u03b1\na b : \u03b1\n\u22a2 gt.swap.Compares a b \u2194 gt.Compares b a",
+              "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : LT \u03b1\na b : \u03b1\no : Ordering\n\u22a2 o.swap.Compares a b \u2194 o.Compares b a",
+              "tactic": "cases o"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>Iff.rfl<\\/a>\"",
+                "[{\"full_name\":\"Iff.rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[796,19],\"def_end_pos\":[796,26]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case lt\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : LT \u03b1\na b : \u03b1\n\u22a2 lt.swap.Compares a b \u2194 lt.Compares b a",
+              "tactic": "exact Iff.rfl"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <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 eq\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : LT \u03b1\na b : \u03b1\n\u22a2 eq.swap.Compares a b \u2194 eq.Compares b a",
+              "tactic": "exact eq_comm"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>Iff.rfl<\\/a>\"",
+                "[{\"full_name\":\"Iff.rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[796,19],\"def_end_pos\":[796,26]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case gt\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : LT \u03b1\na b : \u03b1\n\u22a2 gt.swap.Compares a b \u2194 gt.Compares b a",
+              "tactic": "exact Iff.rfl"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "cmpLE_ofDual",
+        "id": "cmpLE_ofDual",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            193,
+            6
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "cmpLE_ofDual",
+          "start": [
+            191,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "cmpLE_toDual",
+        "id": "cmpLE_toDual",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            187,
+            6
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "cmpLE_toDual",
+          "start": [
+            185,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "cmp_eq_eq_iff",
+        "id": "cmp_eq_eq_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            232,
+            45
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "cmp_eq_eq_iff",
+          "start": [
+            231,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "cmp_eq_lt_iff",
+        "id": "cmp_eq_lt_iff",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            227,
+            45
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "cmp_eq_lt_iff",
+          "start": [
+            226,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "cmp_ofDual",
+        "id": "cmp_ofDual",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            206,
+            6
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "cmp_ofDual",
+          "start": [
+            204,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "cmp_toDual",
+        "id": "cmp_toDual",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            200,
+            6
+          ],
+          "file_path": "Mathlib/Order/Compare.lean",
+          "full_name": "cmp_toDual",
+          "start": [
+            198,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/Compare.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "PUnit.sInf_eq",
+        "id": "PUnit.sInf_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            608,
+            6
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "PUnit.sInf_eq",
+          "start": [
+            607,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "PUnit.sSup_eq",
+        "id": "PUnit.sSup_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            603,
+            6
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "PUnit.sSup_eq",
+          "start": [
+            602,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "biInf_sup_biInf",
+        "id": "biInf_sup_biInf",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            321,
+            37
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "biInf_sup_biInf",
+          "start": [
+            319,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "biSup_symmDiff_biSup_le",
+        "id": "biSup_symmDiff_biSup_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            464,
+            75
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "biSup_symmDiff_biSup_le",
+          "start": [
+            461,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "compl_iInf",
+        "id": "compl_iInf",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            431,
+            53
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "compl_iInf",
+          "start": [
+            427,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "compl_sInf'",
+        "id": "compl_sInf'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            445,
+            35
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "compl_sInf'",
+          "start": [
+            444,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "compl_sSup'",
+        "id": "compl_sSup'",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            449,
+            35
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "compl_sSup'",
+          "start": [
+            448,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "iInf_sup_eq",
+        "id": "iInf_sup_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            299,
+            27
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "iInf_sup_eq",
+          "start": [
+            298,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "iInf_sup_iInf",
+        "id": "iInf_sup_iInf",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            316,
+            31
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "iInf_sup_iInf",
+          "start": [
+            314,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "iInf_sup_of_antitone",
+        "id": "iInf_sup_of_antitone",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            335,
+            68
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "iInf_sup_of_antitone",
+          "start": [
+            333,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "iInf_sup_of_monotone",
+        "id": "iInf_sup_of_monotone",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            330,
+            68
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "iInf_sup_of_monotone",
+          "start": [
+            328,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "iInf\u2082_sup_eq",
+        "id": "iInf\u2082_sup_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            307,
+            30
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "iInf\u2082_sup_eq",
+          "start": [
+            306,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "no internal trace for tactic 'push_neg at h'",
+        "full_name": "iSup_iInf_eq",
+        "id": "iSup_iInf_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            120,
+            20
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "iSup_iInf_eq",
+          "start": [
+            107,
+            1
+          ],
+          "traced_tactics": [
+            {
+              "annotated_tactic": [
+                "\"refine <a>le_antisymm<\\/a> <a>iSup_iInf_le<\\/a> ?_\"",
+                "[{\"full_name\":\"le_antisymm\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[188,9],\"def_end_pos\":[188,20]},{\"full_name\":\"iSup_iInf_le\",\"def_path\":\"Mathlib\\/Order\\/CompleteBooleanAlgebra.lean\",\"def_pos\":[103,9],\"def_end_pos\":[103,21]}]"
+              ],
+              "state_after": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\n\u22a2 \u2a05 g, \u2a06 a, f a (g a) \u2264 \u2a06 a, \u2a05 b, f a b",
+              "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\n\u22a2 \u2a06 a, \u2a05 b, f a b = \u2a05 g, \u2a06 a, f a (g a)",
+              "tactic": "refine le_antisymm iSup_iInf_le ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"rw [<a>iInf_iSup_eq<\\/a>]\"",
+                "[{\"full_name\":\"iInf_iSup_eq\",\"def_path\":\"Mathlib\\/Order\\/CompleteBooleanAlgebra.lean\",\"def_pos\":[92,9],\"def_end_pos\":[92,21]}]"
+              ],
+              "state_after": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\n\u22a2 \u2a06 g, \u2a05 a, f (g a) (a (g a)) \u2264 \u2a06 a, \u2a05 b, f a b",
+              "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\n\u22a2 \u2a05 g, \u2a06 a, f a (g a) \u2264 \u2a06 a, \u2a05 b, f a b",
+              "tactic": "rw [iInf_iSup_eq]"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine <a>iSup_le<\\/a> fun g => ?_\"",
+                "[{\"full_name\":\"iSup_le\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[760,9],\"def_end_pos\":[760,16]}]"
+              ],
+              "state_after": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : ((a : \u03b9) \u2192 \u03ba a) \u2192 \u03b9\n\u22a2 \u2a05 a, f (g a) (a (g a)) \u2264 \u2a06 a, \u2a05 b, f a b",
+              "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\n\u22a2 \u2a06 g, \u2a05 a, f (g a) (a (g a)) \u2264 \u2a06 a, \u2a05 b, f a b",
+              "tactic": "refine iSup_le fun g => ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"have \\u27e8a, ha\\u27e9 : \\u2203 a, \\u2200 b, \\u2203 f, \\u2203 h : a = g f, h \\u25b8 b = f (g f) := <a>of_not_not<\\/a> fun h => by\\n    push_neg at h\\n    choose h hh using h\\n    have := hh _ h <a>rfl<\\/a>\\n    contradiction\"",
+                "[{\"full_name\":\"of_not_not\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[255,9],\"def_end_pos\":[255,19]},{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]}]"
+              ],
+              "state_after": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : ((a : \u03b9) \u2192 \u03ba a) \u2192 \u03b9\na : \u03b9\nha : \u2200 (b : \u03ba a), \u2203 f, \u2203 (h : a = g f), h \u25b8 b = f (g f)\n\u22a2 \u2a05 a, f (g a) (a (g a)) \u2264 \u2a06 a, \u2a05 b, f a b",
+              "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : ((a : \u03b9) \u2192 \u03ba a) \u2192 \u03b9\n\u22a2 \u2a05 a, f (g a) (a (g a)) \u2264 \u2a06 a, \u2a05 b, f a b",
+              "tactic": "have \u27e8a, ha\u27e9 : \u2203 a, \u2200 b, \u2203 f, \u2203 h : a = g f, h \u25b8 b = f (g f) := of_not_not fun h => by\n  push_neg at h\n  choose h hh using h\n  have := hh _ h rfl\n  contradiction"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine <a>le_trans<\\/a> ?_ (<a>le_iSup<\\/a> _ a)\"",
+                "[{\"full_name\":\"le_trans\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[56,9],\"def_end_pos\":[56,17]},{\"full_name\":\"le_iSup\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[702,9],\"def_end_pos\":[702,16]}]"
+              ],
+              "state_after": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : ((a : \u03b9) \u2192 \u03ba a) \u2192 \u03b9\na : \u03b9\nha : \u2200 (b : \u03ba a), \u2203 f, \u2203 (h : a = g f), h \u25b8 b = f (g f)\n\u22a2 \u2a05 a, f (g a) (a (g a)) \u2264 \u2a05 b, f a b",
+              "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : ((a : \u03b9) \u2192 \u03ba a) \u2192 \u03b9\na : \u03b9\nha : \u2200 (b : \u03ba a), \u2203 f, \u2203 (h : a = g f), h \u25b8 b = f (g f)\n\u22a2 \u2a05 a, f (g a) (a (g a)) \u2264 \u2a06 a, \u2a05 b, f a b",
+              "tactic": "refine le_trans ?_ (le_iSup _ a)"
+            },
+            {
+              "annotated_tactic": [
+                "\"refine <a>le_iInf<\\/a> fun b => ?_\"",
+                "[{\"full_name\":\"le_iInf\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[764,9],\"def_end_pos\":[764,16]}]"
+              ],
+              "state_after": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : ((a : \u03b9) \u2192 \u03ba a) \u2192 \u03b9\na : \u03b9\nha : \u2200 (b : \u03ba a), \u2203 f, \u2203 (h : a = g f), h \u25b8 b = f (g f)\nb : \u03ba a\n\u22a2 \u2a05 a, f (g a) (a (g a)) \u2264 f a b",
+              "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : ((a : \u03b9) \u2192 \u03ba a) \u2192 \u03b9\na : \u03b9\nha : \u2200 (b : \u03ba a), \u2203 f, \u2203 (h : a = g f), h \u25b8 b = f (g f)\n\u22a2 \u2a05 a, f (g a) (a (g a)) \u2264 \u2a05 b, f a b",
+              "tactic": "refine le_iInf fun b => ?_"
+            },
+            {
+              "annotated_tactic": [
+                "\"obtain \\u27e8h, rfl, rfl\\u27e9 := ha b\"",
+                "[]"
+              ],
+              "state_after": "case intro.intro\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : ((a : \u03b9) \u2192 \u03ba a) \u2192 \u03b9\nh : (a : \u03b9) \u2192 \u03ba a\nha : \u2200 (b : \u03ba (g h)), \u2203 f, \u2203 (h_1 : g h = g f), h_1 \u25b8 b = f (g f)\n\u22a2 \u2a05 a, f (g a) (a (g a)) \u2264 f (g h) (h (g h))",
+              "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : ((a : \u03b9) \u2192 \u03ba a) \u2192 \u03b9\na : \u03b9\nha : \u2200 (b : \u03ba a), \u2203 f, \u2203 (h : a = g f), h \u25b8 b = f (g f)\nb : \u03ba a\n\u22a2 \u2a05 a, f (g a) (a (g a)) \u2264 f a b",
+              "tactic": "obtain \u27e8h, rfl, rfl\u27e9 := ha b"
+            },
+            {
+              "annotated_tactic": [
+                "\"exact <a>iInf_le<\\/a> _ _\"",
+                "[{\"full_name\":\"iInf_le\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[706,9],\"def_end_pos\":[706,16]}]"
+              ],
+              "state_after": "no goals",
+              "state_before": "case intro.intro\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : ((a : \u03b9) \u2192 \u03ba a) \u2192 \u03b9\nh : (a : \u03b9) \u2192 \u03ba a\nha : \u2200 (b : \u03ba (g h)), \u2203 f, \u2203 (h_1 : g h = g f), h_1 \u25b8 b = f (g f)\n\u22a2 \u2a05 a, f (g a) (a (g a)) \u2264 f (g h) (h (g h))",
+              "tactic": "exact iInf_le _ _"
+            },
+            {
+              "annotated_tactic": [
+                "\"push_neg at h\"",
+                "[]"
+              ],
+              "state_after": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : ((a : \u03b9) \u2192 \u03ba a) \u2192 \u03b9\nh : \u2200 (a : \u03b9), \u2203 b, \u2200 (f : (a : \u03b9) \u2192 \u03ba a) (h : a = g f), h \u25b8 b \u2260 f (g f)\n\u22a2 False",
+              "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : ((a : \u03b9) \u2192 \u03ba a) \u2192 \u03b9\nh : \u00ac\u2203 a, \u2200 (b : \u03ba a), \u2203 f, \u2203 (h : a = g f), h \u25b8 b = f (g f)\n\u22a2 False",
+              "tactic": "push_neg at h"
+            },
+            {
+              "annotated_tactic": [
+                "\"choose h hh using h\"",
+                "[]"
+              ],
+              "state_after": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : ((a : \u03b9) \u2192 \u03ba a) \u2192 \u03b9\nh : (a : \u03b9) \u2192 \u03ba a\nhh : \u2200 (a : \u03b9) (f : (a : \u03b9) \u2192 \u03ba a) (h_1 : a = g f), h_1 \u25b8 h a \u2260 f (g f)\n\u22a2 False",
+              "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : ((a : \u03b9) \u2192 \u03ba a) \u2192 \u03b9\nh : \u2200 (a : \u03b9), \u2203 b, \u2200 (f : (a : \u03b9) \u2192 \u03ba a) (h : a = g f), h \u25b8 b \u2260 f (g f)\n\u22a2 False",
+              "tactic": "choose h hh using h"
+            },
+            {
+              "annotated_tactic": [
+                "\"have := hh _ h <a>rfl<\\/a>\"",
+                "[{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]}]"
+              ],
+              "state_after": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : ((a : \u03b9) \u2192 \u03ba a) \u2192 \u03b9\nh : (a : \u03b9) \u2192 \u03ba a\nhh : \u2200 (a : \u03b9) (f : (a : \u03b9) \u2192 \u03ba a) (h_1 : a = g f), h_1 \u25b8 h a \u2260 f (g f)\nthis : \u22ef \u25b8 h (g h) \u2260 h (g h)\n\u22a2 False",
+              "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : ((a : \u03b9) \u2192 \u03ba a) \u2192 \u03b9\nh : (a : \u03b9) \u2192 \u03ba a\nhh : \u2200 (a : \u03b9) (f : (a : \u03b9) \u2192 \u03ba a) (h_1 : a = g f), h_1 \u25b8 h a \u2260 f (g f)\n\u22a2 False",
+              "tactic": "have := hh _ h rfl"
+            },
+            {
+              "annotated_tactic": [
+                "\"contradiction\"",
+                "[]"
+              ],
+              "state_after": "no goals",
+              "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : ((a : \u03b9) \u2192 \u03ba a) \u2192 \u03b9\nh : (a : \u03b9) \u2192 \u03ba a\nhh : \u2200 (a : \u03b9) (f : (a : \u03b9) \u2192 \u03ba a) (h_1 : a = g f), h_1 \u25b8 h a \u2260 f (g f)\nthis : \u22ef \u25b8 h (g h) \u2260 h (g h)\n\u22a2 False",
+              "tactic": "contradiction"
+            }
+          ],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "iSup_iInf_le",
+        "id": "iSup_iInf_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            105,
+            26
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "iSup_iInf_le",
+          "start": [
+            103,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "iSup_inf_of_antitone",
+        "id": "iSup_inf_of_antitone",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            259,
+            66
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "iSup_inf_of_antitone",
+          "start": [
+            257,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "inf_sSup_eq",
+        "id": "inf_sSup_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            182,
+            65
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "inf_sSup_eq",
+          "start": [
+            181,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "le_iInf_iSup",
+        "id": "le_iInf_iSup",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            90,
+            73
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "le_iInf_iSup",
+          "start": [
+            88,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "sInf_sup_eq",
+        "id": "sInf_sup_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            295,
+            25
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "sInf_sup_eq",
+          "start": [
+            294,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "sInf_sup_sInf",
+        "id": "sInf_sup_sInf",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            325,
+            27
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "sInf_sup_sInf",
+          "start": [
+            324,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "sup_iInf_eq",
+        "id": "sup_iInf_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            303,
+            27
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "sup_iInf_eq",
+          "start": [
+            302,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "sup_iInf\u2082_eq",
+        "id": "sup_iInf\u2082_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            311,
+            30
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "sup_iInf\u2082_eq",
+          "start": [
+            310,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "sup_sInf_eq",
+        "id": "sup_sInf_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            291,
+            25
+          ],
+          "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+          "full_name": "sup_sInf_eq",
+          "start": [
+            290,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteBooleanAlgebra.lean"
+      }
+    ],
+    "input_proofs": 79,
+    "input_units": 2,
+    "proofs": 33,
+    "published_proofs": 30,
+    "published_transitions": 41,
+    "replay_failures": [],
+    "transitions": 51,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Order/Compare.lean",
+        "proof_id": "mathlib:cmp_eq_cmp_symm",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              248,
+              58
+            ],
+            "file_path": "Mathlib/Order/Compare.lean",
+            "full_name": "cmp_eq_cmp_symm",
+            "start": [
+              246,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"rwa [\\u2190 <a>cmp_swap<\\/a> x', \\u2190 <a>cmp_swap<\\/a>, <a>swap_inj<\\/a>]\"",
+                  "[{\"full_name\":\"cmp_swap\",\"def_path\":\"Mathlib\\/Order\\/Compare.lean\",\"def_pos\":[177,9],\"def_end_pos\":[177,17]},{\"full_name\":\"cmp_swap\",\"def_path\":\"Mathlib\\/Order\\/Compare.lean\",\"def_pos\":[177,9],\"def_end_pos\":[177,17]},{\"full_name\":\"Ordering.swap_inj\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Classes\\/Order.lean\",\"def_pos\":[14,17],\"def_end_pos\":[14,25]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "\u03b1 : Type u_1\n\u03b2\u271d : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\nx y : \u03b1\n\u03b2 : Type u_3\ninst\u271d : LinearOrder \u03b2\nx' y' : \u03b2\nh : cmp x y = cmp x' y'\n\u22a2 cmp y x = cmp y' x'",
+                "tactic": "rwa [\u2190 cmp_swap x', \u2190 cmp_swap, swap_inj]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rwa [\\u2190 <a>cmp_swap<\\/a> y', \\u2190 <a>cmp_swap<\\/a>, <a>swap_inj<\\/a>]\"",
+                  "[{\"full_name\":\"cmp_swap\",\"def_path\":\"Mathlib\\/Order\\/Compare.lean\",\"def_pos\":[177,9],\"def_end_pos\":[177,17]},{\"full_name\":\"cmp_swap\",\"def_path\":\"Mathlib\\/Order\\/Compare.lean\",\"def_pos\":[177,9],\"def_end_pos\":[177,17]},{\"full_name\":\"Ordering.swap_inj\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Classes\\/Order.lean\",\"def_pos\":[14,17],\"def_end_pos\":[14,25]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "\u03b1 : Type u_1\n\u03b2\u271d : Type u_2\ninst\u271d\u00b9 : LinearOrder \u03b1\nx y : \u03b1\n\u03b2 : Type u_3\ninst\u271d : LinearOrder \u03b2\nx' y' : \u03b2\nh : cmp y x = cmp y' x'\n\u22a2 cmp x y = cmp x' y'",
+                "tactic": "rwa [\u2190 cmp_swap y', \u2190 cmp_swap, swap_inj]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "cmp_eq_cmp_symm"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+        "proof_id": "mathlib:iInf_iSup_eq",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              101,
+              53
+            ],
+            "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+            "full_name": "iInf_iSup_eq",
+            "start": [
+              92,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"simp_rw [<a>iInf_subtype<\\/a>, <a>iInf_range<\\/a>, <a>iSup_subtype<\\/a>, <a>iSup_range<\\/a>]\"",
+                  "[{\"full_name\":\"iInf_subtype\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[1145,9],\"def_end_pos\":[1145,21]},{\"full_name\":\"iInf_range\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[1345,9],\"def_end_pos\":[1345,19]},{\"full_name\":\"iSup_subtype\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[1140,9],\"def_end_pos\":[1140,21]},{\"full_name\":\"iSup_range\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[1341,9],\"def_end_pos\":[1341,19]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\n\u22a2 \u2a05 a, \u2a06 b, f a b = \u2a05 a, \u2a06 b, \u2191b",
+                "tactic": "simp_rw [iInf_subtype, iInf_range, iSup_subtype, iSup_range]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"refine <a>le_trans<\\/a> ?_ <| <a>le_iSup<\\/a> _ fun a => <a>Classical.choose<\\/a> (g \\u27e8_, a, <a>rfl<\\/a>\\u27e9).2\"",
+                  "[{\"full_name\":\"le_trans\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[56,9],\"def_end_pos\":[56,17]},{\"full_name\":\"le_iSup\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[702,9],\"def_end_pos\":[702,16]},{\"full_name\":\"Classical.choose\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Classical.lean\",\"def_pos\":[25,19],\"def_end_pos\":[25,25]},{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]}]"
+                ],
+                "state_after": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : (a : \u2191(range fun x => range (f x))) \u2192 \u2191\u2191a\n\u22a2 \u2a05 a, \u2191(g a) \u2264 \u2a05 a, f a ((fun a => Classical.choose \u22ef) a)",
+                "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : (a : \u2191(range fun x => range (f x))) \u2192 \u2191\u2191a\n\u22a2 \u2a05 a, \u2191(g a) \u2264 \u2a06 g, \u2a05 a, f a (g a)",
+                "tactic": "refine le_trans ?_ <| le_iSup _ fun a => Classical.choose (g \u27e8_, a, rfl\u27e9).2"
+              },
+              {
+                "annotated_tactic": [
+                  "\"refine <a>le_iInf<\\/a> fun a => <a>le_trans<\\/a> (<a>iInf_le<\\/a> _ \\u27e8<a>range<\\/a> (f a), a, <a>rfl<\\/a>\\u27e9) ?_\"",
+                  "[{\"full_name\":\"le_iInf\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[764,9],\"def_end_pos\":[764,16]},{\"full_name\":\"le_trans\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[56,9],\"def_end_pos\":[56,17]},{\"full_name\":\"iInf_le\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[706,9],\"def_end_pos\":[706,16]},{\"full_name\":\"Set.range\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Defs.lean\",\"def_pos\":[157,5],\"def_end_pos\":[157,10]},{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]}]"
+                ],
+                "state_after": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : (a : \u2191(range fun x => range (f x))) \u2192 \u2191\u2191a\na : \u03b9\n\u22a2 \u2191(g \u27e8range (f a), \u22ef\u27e9) \u2264 f a ((fun a => Classical.choose \u22ef) a)",
+                "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : (a : \u2191(range fun x => range (f x))) \u2192 \u2191\u2191a\n\u22a2 \u2a05 a, \u2191(g a) \u2264 \u2a05 a, f a ((fun a => Classical.choose \u22ef) a)",
+                "tactic": "refine le_iInf fun a => le_trans (iInf_le _ \u27e8range (f a), a, rfl\u27e9) ?_"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [\\u2190 <a>Classical.choose_spec<\\/a> (g \\u27e8_, a, <a>rfl<\\/a>\\u27e9).2]\"",
+                  "[{\"full_name\":\"Classical.choose_spec\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Classical.lean\",\"def_pos\":[28,9],\"def_end_pos\":[28,20]},{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9 : Sort w\n\u03ba : \u03b9 \u2192 Sort w'\ninst\u271d : CompletelyDistribLattice \u03b1\nf : (a : \u03b9) \u2192 \u03ba a \u2192 \u03b1\ng : (a : \u2191(range fun x => range (f x))) \u2192 \u2191\u2191a\na : \u03b9\n\u22a2 \u2191(g \u27e8range (f a), \u22ef\u27e9) \u2264 f a ((fun a => Classical.choose \u22ef) a)",
+                "tactic": "rw [\u2190 Classical.choose_spec (g \u27e8_, a, rfl\u27e9).2]"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "iInf_iSup_eq"
+      },
+      {
+        "errors": [
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+        "proof_id": "mathlib:iSup_inf_of_monotone",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              254,
+              40
+            ],
+            "file_path": "Mathlib/Order/CompleteBooleanAlgebra.lean",
+            "full_name": "iSup_inf_of_monotone",
+            "start": [
+              248,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"refine (<a>le_iSup_inf_iSup<\\/a> f g).<a>antisymm<\\/a> ?_\"",
+                  "[{\"full_name\":\"le_iSup_inf_iSup\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[1923,9],\"def_end_pos\":[1923,25]},{\"full_name\":\"LE.le.antisymm\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[123,7],\"def_end_pos\":[123,21]}]"
+                ],
+                "state_after": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9\u271d : Sort w\n\u03ba : \u03b9\u271d \u2192 Sort w'\ninst\u271d\u00b2 : Frame \u03b1\ns t : Set \u03b1\na b : \u03b1\n\u03b9 : Type u_1\ninst\u271d\u00b9 : Preorder \u03b9\ninst\u271d : IsDirected \u03b9 fun x x_1 => x \u2264 x_1\nf g : \u03b9 \u2192 \u03b1\nhf : Monotone f\nhg : Monotone g\n\u22a2 (\u2a06 i, f i) \u2293 \u2a06 i, g i \u2264 \u2a06 i, f i \u2293 g i",
+                "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9\u271d : Sort w\n\u03ba : \u03b9\u271d \u2192 Sort w'\ninst\u271d\u00b2 : Frame \u03b1\ns t : Set \u03b1\na b : \u03b1\n\u03b9 : Type u_1\ninst\u271d\u00b9 : Preorder \u03b9\ninst\u271d : IsDirected \u03b9 fun x x_1 => x \u2264 x_1\nf g : \u03b9 \u2192 \u03b1\nhf : Monotone f\nhg : Monotone g\n\u22a2 \u2a06 i, f i \u2293 g i = (\u2a06 i, f i) \u2293 \u2a06 i, g i",
+                "tactic": "refine (le_iSup_inf_iSup f g).antisymm ?_"
+              },
+              {
+                "annotated_tactic": [
+                  "\"rw [<a>iSup_inf_iSup<\\/a>]\"",
+                  "[{\"full_name\":\"iSup_inf_iSup\",\"def_path\":\"Mathlib\\/Order\\/CompleteBooleanAlgebra.lean\",\"def_pos\":[207,9],\"def_end_pos\":[207,22]}]"
+                ],
+                "state_after": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9\u271d : Sort w\n\u03ba : \u03b9\u271d \u2192 Sort w'\ninst\u271d\u00b2 : Frame \u03b1\ns t : Set \u03b1\na b : \u03b1\n\u03b9 : Type u_1\ninst\u271d\u00b9 : Preorder \u03b9\ninst\u271d : IsDirected \u03b9 fun x x_1 => x \u2264 x_1\nf g : \u03b9 \u2192 \u03b1\nhf : Monotone f\nhg : Monotone g\n\u22a2 \u2a06 i, f i.1 \u2293 g i.2 \u2264 \u2a06 i, f i \u2293 g i",
+                "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9\u271d : Sort w\n\u03ba : \u03b9\u271d \u2192 Sort w'\ninst\u271d\u00b2 : Frame \u03b1\ns t : Set \u03b1\na b : \u03b1\n\u03b9 : Type u_1\ninst\u271d\u00b9 : Preorder \u03b9\ninst\u271d : IsDirected \u03b9 fun x x_1 => x \u2264 x_1\nf g : \u03b9 \u2192 \u03b1\nhf : Monotone f\nhg : Monotone g\n\u22a2 (\u2a06 i, f i) \u2293 \u2a06 i, g i \u2264 \u2a06 i, f i \u2293 g i",
+                "tactic": "rw [iSup_inf_iSup]"
+              },
+              {
+                "annotated_tactic": [
+                  "\"refine <a>iSup_mono'<\\/a> fun i => ?_\"",
+                  "[{\"full_name\":\"iSup_mono'\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[804,9],\"def_end_pos\":[804,19]}]"
+                ],
+                "state_after": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9\u271d : Sort w\n\u03ba : \u03b9\u271d \u2192 Sort w'\ninst\u271d\u00b2 : Frame \u03b1\ns t : Set \u03b1\na b : \u03b1\n\u03b9 : Type u_1\ninst\u271d\u00b9 : Preorder \u03b9\ninst\u271d : IsDirected \u03b9 fun x x_1 => x \u2264 x_1\nf g : \u03b9 \u2192 \u03b1\nhf : Monotone f\nhg : Monotone g\ni : \u03b9 \u00d7 \u03b9\n\u22a2 \u2203 i', f i.1 \u2293 g i.2 \u2264 f i' \u2293 g i'",
+                "state_before": "\u03b1 : Type u\n\u03b2 : Type v\n\u03b9\u271d : Sort w\n\u03ba : \u03b9\u271d \u2192 Sort w'\ninst\u271d\u00b2 : Frame \u03b1\ns t : Set \u03b1\na b : \u03b1\n\u03b9 : Type u_1\ninst\u271d\u00b9 : Preorder \u03b9\ninst\u271d : IsDirected \u03b9 fun x x_1 => x \u2264 x_1\nf g : \u03b9 \u2192 \u03b1\nhf : Monotone f\nhg : Monotone g\n\u22a2 \u2a06 i, f i.1 \u2293 g i.2 \u2264 \u2a06 i, f i \u2293 g i",
+                "tactic": "refine iSup_mono' fun i => ?_"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact \\u27e8j, <a>inf_le_inf<\\/a> (hf h\\u2081) (hg h\\u2082)\\u27e9\"",
+                  "[{\"full_name\":\"inf_le_inf\",\"def_path\":\"Mathlib\\/Order\\/Lattice.lean\",\"def_pos\":[442,9],\"def_end_pos\":[442,19]}]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case intro.intro\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b9\u271d : Sort w\n\u03ba : \u03b9\u271d \u2192 Sort w'\ninst\u271d\u00b2 : Frame \u03b1\ns t : Set \u03b1\na b : \u03b1\n\u03b9 : Type u_1\ninst\u271d\u00b9 : Preorder \u03b9\ninst\u271d : IsDirected \u03b9 fun x x_1 => x \u2264 x_1\nf g : \u03b9 \u2192 \u03b1\nhf : Monotone f\nhg : Monotone g\ni : \u03b9 \u00d7 \u03b9\nj : \u03b9\nh\u2081 : i.1 \u2264 j\nh\u2082 : i.2 \u2264 j\n\u22a2 \u2203 i', f i.1 \u2293 g i.2 \u2264 f i' \u2293 g i'",
+                "tactic": "exact \u27e8j, inf_le_inf (hf h\u2081) (hg h\u2082)\u27e9"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "iSup_inf_of_monotone"
+      }
+    ],
+    "validation_rejected_proofs": 3,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001534-0000-892e16e523f0ca69.parquet",
+      "sha256": "892e16e523f0ca69cd33828bb8360d70c5bfe8975054f871a11cf7fcea99e4ae",
+      "bytes": 125432,
+      "rows": 35,
+      "revision": "504ada6ade9a708ef0393868f005bf429a0291c6"
+    },
+    {
+      "path": "data/dev/mathlib-001534-0000-f0ba226665fae4d4.parquet",
+      "sha256": "f0ba226665fae4d4b79a851831d8e4ea11a30f5f622bd6693ae90b6f950fb867",
+      "bytes": 42560,
+      "rows": 1,
+      "revision": "504ada6ade9a708ef0393868f005bf429a0291c6"
+    },
+    {
+      "path": "data/internal_test/mathlib-001534-0000-37c609c7bcf9fdb2.parquet",
+      "sha256": "37c609c7bcf9fdb21aa81a35f24e6458f07b0a3fe723eddbda2424d165c01530",
+      "bytes": 47132,
+      "rows": 5,
+      "revision": "504ada6ade9a708ef0393868f005bf429a0291c6"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:Ordering.orElse_eq_lt",
+    "mathlib:Ordering.swap_eq_iff_eq_swap",
+    "mathlib:Ordering.swap_orElse",
+    "mathlib:biSup_inf_biSup",
+    "mathlib:cmpLE_eq_cmp",
+    "mathlib:cmpLE_swap",
+    "mathlib:cmp_compares",
+    "mathlib:cmp_self_eq_eq",
+    "mathlib:cmp_swap",
+    "mathlib:compl_iSup",
+    "mathlib:compl_sInf",
+    "mathlib:compl_sSup",
+    "mathlib:disjoint_iSup_iff",
+    "mathlib:disjoint_iSup\u2082_iff",
+    "mathlib:disjoint_sSup_iff",
+    "mathlib:eq_iff_eq_of_cmp_eq_cmp",
+    "mathlib:iSup_disjoint_iff",
+    "mathlib:iSup_inf_eq",
+    "mathlib:iSup_inf_iSup",
+    "mathlib:iSup_symmDiff_iSup_le",
+    "mathlib:iSup\u2082_inf_eq",
+    "mathlib:inf_iSup_eq",
+    "mathlib:inf_iSup\u2082_eq",
+    "mathlib:le_iff_le_of_cmp_eq_cmp",
+    "mathlib:lt_iff_lt_of_cmp_eq_cmp",
+    "mathlib:ofDual_compares_ofDual",
+    "mathlib:sSup_disjoint_iff",
+    "mathlib:sSup_inf_eq",
+    "mathlib:sSup_inf_sSup",
+    "mathlib:toDual_compares_toDual"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Compare.lean\",null,null,\"Ordering.orElse_eq_lt\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Compare.lean\",null,null,\"Ordering.swap_eq_iff_eq_swap\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Compare.lean\",null,null,\"Ordering.swap_orElse\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Compare.lean\",null,null,\"cmpLE_eq_cmp\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Compare.lean\",null,null,\"cmpLE_swap\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Compare.lean\",null,null,\"cmp_compares\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Compare.lean\",null,null,\"cmp_self_eq_eq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Compare.lean\",null,null,\"cmp_swap\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Compare.lean\",null,null,\"eq_iff_eq_of_cmp_eq_cmp\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Compare.lean\",null,null,\"le_iff_le_of_cmp_eq_cmp\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Compare.lean\",null,null,\"lt_iff_lt_of_cmp_eq_cmp\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Compare.lean\",null,null,\"ofDual_compares_ofDual\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/Compare.lean\",null,null,\"toDual_compares_toDual\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteBooleanAlgebra.lean\",null,null,\"biSup_inf_biSup\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteBooleanAlgebra.lean\",null,null,\"compl_iSup\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteBooleanAlgebra.lean\",null,null,\"compl_sInf\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteBooleanAlgebra.lean\",null,null,\"compl_sSup\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteBooleanAlgebra.lean\",null,null,\"disjoint_iSup_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteBooleanAlgebra.lean\",null,null,\"disjoint_iSup\u2082_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteBooleanAlgebra.lean\",null,null,\"disjoint_sSup_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteBooleanAlgebra.lean\",null,null,\"iSup_disjoint_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteBooleanAlgebra.lean\",null,null,\"iSup_inf_eq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteBooleanAlgebra.lean\",null,null,\"iSup_inf_iSup\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteBooleanAlgebra.lean\",null,null,\"iSup_symmDiff_iSup_le\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteBooleanAlgebra.lean\",null,null,\"iSup\u2082_inf_eq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteBooleanAlgebra.lean\",null,null,\"inf_iSup_eq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteBooleanAlgebra.lean\",null,null,\"inf_iSup\u2082_eq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteBooleanAlgebra.lean\",null,null,\"sSup_disjoint_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteBooleanAlgebra.lean\",null,null,\"sSup_inf_eq\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteBooleanAlgebra.lean\",null,null,\"sSup_inf_sSup\"]"
+  ]
+}

manifests/batches/mathlib/001536.json

@@ -0,0 +1,449 @@
+{
+  "format": "leangpt-parquet-v2",
+  "batch": "mathlib/001536",
+  "batch_fingerprint": "6f22107389561e197c05da7e707b81571d934d8be654437a51c5f60ffc47c5c0",
+  "evidence": {
+    "batch_fingerprint": "6f22107389561e197c05da7e707b81571d934d8be654437a51c5f60ffc47c5c0",
+    "contamination_matches": [],
+    "failures": [
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "Directed.iSup_le",
+        "id": "Directed.iSup_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            59,
+            57
+          ],
+          "file_path": "Mathlib/Order/CompletePartialOrder.lean",
+          "full_name": "Directed.iSup_le",
+          "start": [
+            58,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompletePartialOrder.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DirectedOn.isLUB_sSup",
+        "id": "DirectedOn.isLUB_sSup",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            47,
+            37
+          ],
+          "file_path": "Mathlib/Order/CompletePartialOrder.lean",
+          "full_name": "DirectedOn.isLUB_sSup",
+          "start": [
+            46,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompletePartialOrder.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DirectedOn.le_sSup",
+        "id": "DirectedOn.le_sSup",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            50,
+            19
+          ],
+          "file_path": "Mathlib/Order/CompletePartialOrder.lean",
+          "full_name": "DirectedOn.le_sSup",
+          "start": [
+            49,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompletePartialOrder.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "DirectedOn.sSup_le",
+        "id": "DirectedOn.sSup_le",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            53,
+            19
+          ],
+          "file_path": "Mathlib/Order/CompletePartialOrder.lean",
+          "full_name": "DirectedOn.sSup_le",
+          "start": [
+            52,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompletePartialOrder.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CompleteLatticeHom.range_coe",
+        "id": "CompleteLatticeHom.range_coe",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            169,
+            55
+          ],
+          "file_path": "Mathlib/Order/CompleteSublattice.lean",
+          "full_name": "CompleteLatticeHom.range_coe",
+          "start": [
+            169,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteSublattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CompleteSublattice.coe_bot",
+        "id": "CompleteSublattice.coe_bot",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            78,
+            52
+          ],
+          "file_path": "Mathlib/Order/CompleteSublattice.lean",
+          "full_name": "CompleteSublattice.coe_bot",
+          "start": [
+            78,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteSublattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CompleteSublattice.coe_copy",
+        "id": "CompleteSublattice.coe_copy",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            155,
+            76
+          ],
+          "file_path": "Mathlib/Order/CompleteSublattice.lean",
+          "full_name": "CompleteSublattice.coe_copy",
+          "start": [
+            155,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteSublattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CompleteSublattice.coe_sInf",
+        "id": "CompleteSublattice.coe_sInf",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            87,
+            87
+          ],
+          "file_path": "Mathlib/Order/CompleteSublattice.lean",
+          "full_name": "CompleteSublattice.coe_sInf",
+          "start": [
+            87,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteSublattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CompleteSublattice.coe_sSup",
+        "id": "CompleteSublattice.coe_sSup",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            82,
+            87
+          ],
+          "file_path": "Mathlib/Order/CompleteSublattice.lean",
+          "full_name": "CompleteSublattice.coe_sSup",
+          "start": [
+            82,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteSublattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CompleteSublattice.coe_top",
+        "id": "CompleteSublattice.coe_top",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            80,
+            52
+          ],
+          "file_path": "Mathlib/Order/CompleteSublattice.lean",
+          "full_name": "CompleteSublattice.coe_top",
+          "start": [
+            80,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteSublattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CompleteSublattice.copy_eq",
+        "id": "CompleteSublattice.copy_eq",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            157,
+            77
+          ],
+          "file_path": "Mathlib/Order/CompleteSublattice.lean",
+          "full_name": "CompleteSublattice.copy_eq",
+          "start": [
+            157,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteSublattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CompleteSublattice.mem_comap",
+        "id": "CompleteSublattice.mem_comap",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            123,
+            98
+          ],
+          "file_path": "Mathlib/Order/CompleteSublattice.lean",
+          "full_name": "CompleteSublattice.mem_comap",
+          "start": [
+            123,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteSublattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CompleteSublattice.mem_map",
+        "id": "CompleteSublattice.mem_map",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            111,
+            76
+          ],
+          "file_path": "Mathlib/Order/CompleteSublattice.lean",
+          "full_name": "CompleteSublattice.mem_map",
+          "start": [
+            111,
+            9
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteSublattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CompleteSublattice.sInfClosed",
+        "id": "CompleteSublattice.sInfClosed",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            76,
+            75
+          ],
+          "file_path": "Mathlib/Order/CompleteSublattice.lean",
+          "full_name": "CompleteSublattice.sInfClosed",
+          "start": [
+            76,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteSublattice.lean"
+      },
+      {
+        "error": "theorem has no selected tactic transitions",
+        "full_name": "CompleteSublattice.sSupClosed",
+        "id": "CompleteSublattice.sSupClosed",
+        "reason": "import_failure",
+        "selection": {
+          "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+          "end": [
+            74,
+            75
+          ],
+          "file_path": "Mathlib/Order/CompleteSublattice.lean",
+          "full_name": "CompleteSublattice.sSupClosed",
+          "start": [
+            74,
+            1
+          ],
+          "traced_tactics": [],
+          "url": "https://github.com/leanprover-community/mathlib4"
+        },
+        "source_file": "Mathlib/Order/CompleteSublattice.lean"
+      }
+    ],
+    "input_proofs": 22,
+    "input_units": 2,
+    "proofs": 7,
+    "published_proofs": 6,
+    "published_transitions": 8,
+    "replay_failures": [],
+    "transitions": 13,
+    "validation_failures": [
+      {
+        "errors": [
+          "internal transition boundary mismatch",
+          "internal transition boundary mismatch"
+        ],
+        "file_path": "Mathlib/Order/CompleteSublattice.lean",
+        "proof_id": "mathlib:CompleteSublattice.isComplemented_iff",
+        "provenance": {
+          "selection": {
+            "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
+            "end": [
+              144,
+              60
+            ],
+            "file_path": "Mathlib/Order/CompleteSublattice.lean",
+            "full_name": "CompleteSublattice.isComplemented_iff",
+            "start": [
+              139,
+              1
+            ],
+            "traced_tactics": [
+              {
+                "annotated_tactic": [
+                  "\"refine \\u27e8fun \\u27e8h\\u27e9 a ha \\u21a6 ?_, fun h \\u21a6 \\u27e8fun \\u27e8a, ha\\u27e9 \\u21a6 ?_\\u27e9\\u27e9\"",
+                  "[]"
+                ],
+                "state_after": "case refine_1\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : CompleteLattice \u03b1\ninst\u271d : CompleteLattice \u03b2\nf : CompleteLatticeHom \u03b1 \u03b2\nL : CompleteSublattice \u03b1\nx\u271d : ComplementedLattice \u21a5L\na : \u03b1\nha : a \u2208 L\nh : \u2200 (a : \u21a5L), \u2203 b, IsCompl a b\n\u22a2 \u2203 b \u2208 L, IsCompl a b\n\ncase refine_2\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : CompleteLattice \u03b1\ninst\u271d : CompleteLattice \u03b2\nf : CompleteLatticeHom \u03b1 \u03b2\nL : CompleteSublattice \u03b1\nh : \u2200 a \u2208 L, \u2203 b \u2208 L, IsCompl a b\nx\u271d : \u21a5L\na : \u03b1\nha : a \u2208 L\n\u22a2 \u2203 b, IsCompl \u27e8a, ha\u27e9 b",
+                "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : CompleteLattice \u03b1\ninst\u271d : CompleteLattice \u03b2\nf : CompleteLatticeHom \u03b1 \u03b2\nL : CompleteSublattice \u03b1\n\u22a2 ComplementedLattice \u21a5L \u2194 \u2200 a \u2208 L, \u2203 b \u2208 L, IsCompl a b",
+                "tactic": "refine \u27e8fun \u27e8h\u27e9 a ha \u21a6 ?_, fun h \u21a6 \u27e8fun \u27e8a, ha\u27e9 \u21a6 ?_\u27e9\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"obtain \\u27e8b, hb\\u27e9 := h \\u27e8a, ha\\u27e9\"",
+                  "[]"
+                ],
+                "state_after": "case refine_1.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : CompleteLattice \u03b1\ninst\u271d : CompleteLattice \u03b2\nf : CompleteLatticeHom \u03b1 \u03b2\nL : CompleteSublattice \u03b1\nx\u271d : ComplementedLattice \u21a5L\na : \u03b1\nha : a \u2208 L\nh : \u2200 (a : \u21a5L), \u2203 b, IsCompl a b\nb : \u21a5L\nhb : IsCompl \u27e8a, ha\u27e9 b\n\u22a2 \u2203 b \u2208 L, IsCompl a b",
+                "state_before": "case refine_1\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : CompleteLattice \u03b1\ninst\u271d : CompleteLattice \u03b2\nf : CompleteLatticeHom \u03b1 \u03b2\nL : CompleteSublattice \u03b1\nx\u271d : ComplementedLattice \u21a5L\na : \u03b1\nha : a \u2208 L\nh : \u2200 (a : \u21a5L), \u2203 b, IsCompl a b\n\u22a2 \u2203 b \u2208 L, IsCompl a b",
+                "tactic": "obtain \u27e8b, hb\u27e9 := h \u27e8a, ha\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact \\u27e8b, b.property, CompleteSublattice.isCompl_iff.mp hb\\u27e9\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case refine_1.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : CompleteLattice \u03b1\ninst\u271d : CompleteLattice \u03b2\nf : CompleteLatticeHom \u03b1 \u03b2\nL : CompleteSublattice \u03b1\nx\u271d : ComplementedLattice \u21a5L\na : \u03b1\nha : a \u2208 L\nh : \u2200 (a : \u21a5L), \u2203 b, IsCompl a b\nb : \u21a5L\nhb : IsCompl \u27e8a, ha\u27e9 b\n\u22a2 \u2203 b \u2208 L, IsCompl a b",
+                "tactic": "exact \u27e8b, b.property, CompleteSublattice.isCompl_iff.mp hb\u27e9"
+              },
+              {
+                "annotated_tactic": [
+                  "\"obtain \\u27e8b, hb, hb'\\u27e9 := h a ha\"",
+                  "[]"
+                ],
+                "state_after": "case refine_2.intro.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : CompleteLattice \u03b1\ninst\u271d : CompleteLattice \u03b2\nf : CompleteLatticeHom \u03b1 \u03b2\nL : CompleteSublattice \u03b1\nh : \u2200 a \u2208 L, \u2203 b \u2208 L, IsCompl a b\nx\u271d : \u21a5L\na : \u03b1\nha : a \u2208 L\nb : \u03b1\nhb : b \u2208 L\nhb' : IsCompl a b\n\u22a2 \u2203 b, IsCompl \u27e8a, ha\u27e9 b",
+                "state_before": "case refine_2\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : CompleteLattice \u03b1\ninst\u271d : CompleteLattice \u03b2\nf : CompleteLatticeHom \u03b1 \u03b2\nL : CompleteSublattice \u03b1\nh : \u2200 a \u2208 L, \u2203 b \u2208 L, IsCompl a b\nx\u271d : \u21a5L\na : \u03b1\nha : a \u2208 L\n\u22a2 \u2203 b, IsCompl \u27e8a, ha\u27e9 b",
+                "tactic": "obtain \u27e8b, hb, hb'\u27e9 := h a ha"
+              },
+              {
+                "annotated_tactic": [
+                  "\"exact \\u27e8\\u27e8b, hb\\u27e9, CompleteSublattice.isCompl_iff.mpr hb'\\u27e9\"",
+                  "[]"
+                ],
+                "state_after": "no goals",
+                "state_before": "case refine_2.intro.intro\n\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b9 : CompleteLattice \u03b1\ninst\u271d : CompleteLattice \u03b2\nf : CompleteLatticeHom \u03b1 \u03b2\nL : CompleteSublattice \u03b1\nh : \u2200 a \u2208 L, \u2203 b \u2208 L, IsCompl a b\nx\u271d : \u21a5L\na : \u03b1\nha : a \u2208 L\nb : \u03b1\nhb : b \u2208 L\nhb' : IsCompl a b\n\u22a2 \u2203 b, IsCompl \u27e8a, ha\u27e9 b",
+                "tactic": "exact \u27e8\u27e8b, hb\u27e9, CompleteSublattice.isCompl_iff.mpr hb'\u27e9"
+              }
+            ],
+            "url": "https://github.com/leanprover-community/mathlib4"
+          }
+        },
+        "theorem_name": "CompleteSublattice.isComplemented_iff"
+      }
+    ],
+    "validation_rejected_proofs": 1,
+    "zero_transition_proofs": 0
+  },
+  "shards": [
+    {
+      "path": "data/train/mathlib-001536-0000-3ccd3179ba2e04a6.parquet",
+      "sha256": "3ccd3179ba2e04a633b928b37120dff73fbfaca138a025c11ad73bfebed7e9fc",
+      "bytes": 62897,
+      "rows": 8,
+      "revision": "504ada6ade9a708ef0393868f005bf429a0291c6"
+    }
+  ],
+  "proof_ids": [
+    "mathlib:CompletePartialOrder.scottContinuous",
+    "mathlib:CompleteSublattice.codisjoint_iff",
+    "mathlib:CompleteSublattice.coe_sInf'",
+    "mathlib:CompleteSublattice.coe_sSup'",
+    "mathlib:CompleteSublattice.disjoint_iff",
+    "mathlib:CompleteSublattice.isCompl_iff"
+  ],
+  "proof_keys": [
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompletePartialOrder.lean\",null,null,\"CompletePartialOrder.scottContinuous\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteSublattice.lean\",null,null,\"CompleteSublattice.codisjoint_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteSublattice.lean\",null,null,\"CompleteSublattice.coe_sInf'\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteSublattice.lean\",null,null,\"CompleteSublattice.coe_sSup'\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteSublattice.lean\",null,null,\"CompleteSublattice.disjoint_iff\"]",
+    "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Order/CompleteSublattice.lean\",null,null,\"CompleteSublattice.isCompl_iff\"]"
+  ]
+}