Hugging Face's logo

Datasets:
HyperCactus0
/
LeanTransitionCorpus

Tasks:
Text Generation
Tags:
lean
lean4
automated-theorem-proving
theorem-proving
formal-mathematics
mathematics
License:
Dataset card Data Studio Files
xet
 Community
1
HyperCactus0 commited on
Commit
7b5e634
·
verified ·
1 Parent(s): 540aac4

Record 21 verified HPC batch manifests

Browse files
Files changed (21) hide show
  1. manifests/batches/mathlib/000613.json +133 -0
  2. manifests/batches/mathlib/000614.json +299 -0
  3. manifests/batches/mathlib/000615.json +179 -0
  4. manifests/batches/mathlib/000616.json +124 -0
  5. manifests/batches/mathlib/000617.json +135 -0
  6. manifests/batches/mathlib/000618.json +656 -0
  7. manifests/batches/mathlib/000619.json +245 -0
  8. manifests/batches/mathlib/000620.json +489 -0
  9. manifests/batches/mathlib/000621.json +634 -0
  10. manifests/batches/mathlib/000622.json +284 -0
  11. manifests/batches/mathlib/000623.json +761 -0
  12. manifests/batches/numina/001374.json +44 -0
  13. manifests/batches/numina/001375.json +79 -0
  14. manifests/batches/numina/001376.json +58 -0
  15. manifests/batches/numina/001377.json +44 -0
  16. manifests/batches/numina/001378.json +44 -0
  17. manifests/batches/numina/001379.json +51 -0
  18. manifests/batches/numina/001380.json +51 -0
  19. manifests/batches/numina/001381.json +51 -0
  20. manifests/batches/numina/001382.json +44 -0
  21. manifests/batches/numina/001383.json +73 -0
manifests/batches/mathlib/000613.json ADDED
@@ -0,0 +1,133 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000613",
4
+ "batch_fingerprint": "7425e03fe5f9f52de293f5e790410fc4d4d05885a3ddb7d484b0189e998e5a3d",
5
+ "evidence": {
6
+ "batch_fingerprint": "7425e03fe5f9f52de293f5e790410fc4d4d05885a3ddb7d484b0189e998e5a3d",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "no internal trace for tactic 'rw [\u2190 cancel_mono (B.map (L.functor.map (NatTrans.app L.unitIso.hom X)))]'",
11
+ "full_name": "CategoryTheory.CatCommSq.vInv_vInv",
12
+ "id": "CategoryTheory.CatCommSq.vInv_vInv",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 125,
18
+ 46
19
+ ],
20
+ "file_path": "Mathlib/CategoryTheory/CatCommSq.lean",
21
+ "full_name": "CategoryTheory.CatCommSq.vInv_vInv",
22
+ "start": [
23
+ 112,
24
+ 1
25
+ ],
26
+ "traced_tactics": [
27
+ {
28
+ "annotated_tactic": [
29
+ "\"ext X\"",
30
+ "[]"
31
+ ],
32
+ "state_after": "case iso'.w.w.h\nC\u2081 : Type u_1\nC\u2082 : Type u_2\nC\u2083 : Type u_3\nC\u2084 : Type u_4\nC\u2085 : Type u_5\nC\u2086 : Type u_6\ninst\u271d\u2075 : Category.{u_8, u_1} C\u2081\ninst\u271d\u2074 : Category.{u_9, u_2} C\u2082\ninst\u271d\u00b3 : Category.{u_10, u_3} C\u2083\ninst\u271d\u00b2 : Category.{u_7, u_4} C\u2084\ninst\u271d\u00b9 : Category.{?u.29698, u_5} C\u2085\ninst\u271d : Category.{?u.29702, u_6} C\u2086\nT\u271d : C\u2081 \u2964 C\u2082\nL\u271d : C\u2081 \u2964 C\u2083\nR\u271d : C\u2082 \u2964 C\u2084\nB\u271d : C\u2083 \u2964 C\u2084\nT : C\u2081 \u2964 C\u2082\nL : C\u2081 \u224c C\u2083\nR : C\u2082 \u224c C\u2084\nB : C\u2083 \u2964 C\u2084\nh : CatCommSq T L.functor R.functor B\nX : C\u2081\n\u22a2 iso'.hom.app X = iso'.hom.app X",
33
+ "state_before": "C\u2081 : Type u_1\nC\u2082 : Type u_2\nC\u2083 : Type u_3\nC\u2084 : Type u_4\nC\u2085 : Type u_5\nC\u2086 : Type u_6\ninst\u271d\u2075 : Category.{u_8, u_1} C\u2081\ninst\u271d\u2074 : Category.{u_9, u_2} C\u2082\ninst\u271d\u00b3 : Category.{u_10, u_3} C\u2083\ninst\u271d\u00b2 : Category.{u_7, u_4} C\u2084\ninst\u271d\u00b9 : Category.{?u.29698, u_5} C\u2085\ninst\u271d : Category.{?u.29702, u_6} C\u2086\nT\u271d : C\u2081 \u2964 C\u2082\nL\u271d : C\u2081 \u2964 C\u2083\nR\u271d : C\u2082 \u2964 C\u2084\nB\u271d : C\u2083 \u2964 C\u2084\nT : C\u2081 \u2964 C\u2082\nL : C\u2081 \u224c C\u2083\nR : C\u2082 \u224c C\u2084\nB : C\u2083 \u2964 C\u2084\nh : CatCommSq T L.functor R.functor B\n\u22a2 vInv B L.symm R.symm T (vInv T L R B h) = h",
34
+ "tactic": "ext X"
35
+ },
36
+ {
37
+ "annotated_tactic": [
38
+ "\"erw [<a>vInv_iso'_hom_app<\\/a>, <a>vInv_iso'_inv_app<\\/a>]\"",
39
+ "[{\"full_name\":\"CategoryTheory.CatCommSq.vInv_iso'_hom_app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/CatCommSq.lean\",\"def_pos\":[103,10],\"def_end_pos\":[103,22]},{\"full_name\":\"CategoryTheory.CatCommSq.vInv_iso'_inv_app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/CatCommSq.lean\",\"def_pos\":[103,23],\"def_end_pos\":[103,35]}]"
40
+ ],
41
+ "state_after": "case iso'.w.w.h\nC\u2081 : Type u_1\nC\u2082 : Type u_2\nC\u2083 : Type u_3\nC\u2084 : Type u_4\nC\u2085 : Type u_5\nC\u2086 : Type u_6\ninst\u271d\u2075 : Category.{u_8, u_1} C\u2081\ninst\u271d\u2074 : Category.{u_9, u_2} C\u2082\ninst\u271d\u00b3 : Category.{u_10, u_3} C\u2083\ninst\u271d\u00b2 : Category.{u_7, u_4} C\u2084\ninst\u271d\u00b9 : Category.{?u.29698, u_5} C\u2085\ninst\u271d : Category.{?u.29702, u_6} C\u2086\nT\u271d : C\u2081 \u2964 C\u2082\nL\u271d : C\u2081 \u2964 C\u2083\nR\u271d : C\u2082 \u2964 C\u2084\nB\u271d : C\u2083 \u2964 C\u2084\nT : C\u2081 \u2964 C\u2082\nL : C\u2081 \u224c C\u2083\nR : C\u2082 \u224c C\u2084\nB : C\u2083 \u2964 C\u2084\nh : CatCommSq T L.functor R.functor B\nX : C\u2081\n\u22a2 R.symm.inverse.map (T.map (L.symm.counitIso.inv.app X)) \u226b\n R.symm.inverse.map\n (R.unitIso.hom.app (T.obj (L.inverse.obj (L.symm.inverse.obj X))) \u226b\n R.inverse.map ((iso T L.functor R.functor B).hom.app (L.inverse.obj (L.symm.inverse.obj X))) \u226b\n R.inverse.map (B.map (L.counitIso.hom.app (L.symm.inverse.obj X)))) \u226b\n R.symm.unitIso.inv.app (B.obj (L.symm.inverse.obj X)) =\n iso'.hom.app X",
42
+ "state_before": "case iso'.w.w.h\nC\u2081 : Type u_1\nC\u2082 : Type u_2\nC\u2083 : Type u_3\nC\u2084 : Type u_4\nC\u2085 : Type u_5\nC\u2086 : Type u_6\ninst\u271d\u2075 : Category.{u_8, u_1} C\u2081\ninst\u271d\u2074 : Category.{u_9, u_2} C\u2082\ninst\u271d\u00b3 : Category.{u_10, u_3} C\u2083\ninst\u271d\u00b2 : Category.{u_7, u_4} C\u2084\ninst\u271d\u00b9 : Category.{?u.29698, u_5} C\u2085\ninst\u271d : Category.{?u.29702, u_6} C\u2086\nT\u271d : C\u2081 \u2964 C\u2082\nL\u271d : C\u2081 \u2964 C\u2083\nR\u271d : C\u2082 \u2964 C\u2084\nB\u271d : C\u2083 \u2964 C\u2084\nT : C\u2081 \u2964 C\u2082\nL : C\u2081 \u224c C\u2083\nR : C\u2082 \u224c C\u2084\nB : C\u2083 \u2964 C\u2084\nh : CatCommSq T L.functor R.functor B\nX : C\u2081\n\u22a2 iso'.hom.app X = iso'.hom.app X",
43
+ "tactic": "erw [vInv_iso'_hom_app, vInv_iso'_inv_app]"
44
+ },
45
+ {
46
+ "annotated_tactic": [
47
+ "\"dsimp\"",
48
+ "[]"
49
+ ],
50
+ "state_after": "case iso'.w.w.h\nC\u2081 : Type u_1\nC\u2082 : Type u_2\nC\u2083 : Type u_3\nC\u2084 : Type u_4\nC\u2085 : Type u_5\nC\u2086 : Type u_6\ninst\u271d\u2075 : Category.{u_8, u_1} C\u2081\ninst\u271d\u2074 : Category.{u_9, u_2} C\u2082\ninst\u271d\u00b3 : Category.{u_10, u_3} C\u2083\ninst\u271d\u00b2 : Category.{u_7, u_4} C\u2084\ninst\u271d\u00b9 : Category.{?u.29698, u_5} C\u2085\ninst\u271d : Category.{?u.29702, u_6} C\u2086\nT\u271d : C\u2081 \u2964 C\u2082\nL\u271d : C\u2081 \u2964 C\u2083\nR\u271d : C\u2082 \u2964 C\u2084\nB\u271d : C\u2083 \u2964 C\u2084\nT : C\u2081 \u2964 C\u2082\nL : C\u2081 \u224c C\u2083\nR : C\u2082 \u224c C\u2084\nB : C\u2083 \u2964 C\u2084\nh : CatCommSq T L.functor R.functor B\nX : C\u2081\n\u22a2 R.functor.map (T.map (L.unitIso.hom.app X)) \u226b\n R.functor.map\n (R.unitIso.hom.app (T.obj (L.inverse.obj (L.functor.obj X))) \u226b\n R.inverse.map ((iso T L.functor R.functor B).hom.app (L.inverse.obj (L.functor.obj X))) \u226b\n R.inverse.map (B.map (L.counitIso.hom.app (L.functor.obj X)))) \u226b\n R.counitIso.hom.app (B.obj (L.functor.obj X)) =\n iso'.hom.app X",
51
+ "state_before": "case iso'.w.w.h\nC\u2081 : Type u_1\nC\u2082 : Type u_2\nC\u2083 : Type u_3\nC\u2084 : Type u_4\nC\u2085 : Type u_5\nC\u2086 : Type u_6\ninst\u271d\u2075 : Category.{u_8, u_1} C\u2081\ninst\u271d\u2074 : Category.{u_9, u_2} C\u2082\ninst\u271d\u00b3 : Category.{u_10, u_3} C\u2083\ninst\u271d\u00b2 : Category.{u_7, u_4} C\u2084\ninst\u271d\u00b9 : Category.{?u.29698, u_5} C\u2085\ninst\u271d : Category.{?u.29702, u_6} C\u2086\nT\u271d : C\u2081 \u2964 C\u2082\nL\u271d : C\u2081 \u2964 C\u2083\nR\u271d : C\u2082 \u2964 C\u2084\nB\u271d : C\u2083 \u2964 C\u2084\nT : C\u2081 \u2964 C\u2082\nL : C\u2081 \u224c C\u2083\nR : C\u2082 \u224c C\u2084\nB : C\u2083 \u2964 C\u2084\nh : CatCommSq T L.functor R.functor B\nX : C\u2081\n\u22a2 R.symm.inverse.map (T.map (L.symm.counitIso.inv.app X)) \u226b\n R.symm.inverse.map\n (R.unitIso.hom.app (T.obj (L.inverse.obj (L.symm.inverse.obj X))) \u226b\n R.inverse.map ((iso T L.functor R.functor B).hom.app (L.inverse.obj (L.symm.inverse.obj X))) \u226b\n R.inverse.map (B.map (L.counitIso.hom.app (L.symm.inverse.obj X)))) \u226b\n R.symm.unitIso.inv.app (B.obj (L.symm.inverse.obj X)) =\n iso'.hom.app X",
52
+ "tactic": "dsimp"
53
+ },
54
+ {
55
+ "annotated_tactic": [
56
+ "\"rw [\\u2190 <a>cancel_mono<\\/a> (B.map (L.functor.map (<a>NatTrans.app<\\/a> L.unitIso.hom X)))]\"",
57
+ "[{\"full_name\":\"CategoryTheory.cancel_mono\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[310,9],\"def_end_pos\":[310,20]},{\"full_name\":\"CategoryTheory.NatTrans.app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/NatTrans.lean\",\"def_pos\":[50,3],\"def_end_pos\":[50,6]}]"
58
+ ],
59
+ "state_after": "case iso'.w.w.h\nC\u2081 : Type u_1\nC\u2082 : Type u_2\nC\u2083 : Type u_3\nC\u2084 : Type u_4\nC\u2085 : Type u_5\nC\u2086 : Type u_6\ninst\u271d\u2075 : Category.{u_8, u_1} C\u2081\ninst\u271d\u2074 : Category.{u_9, u_2} C\u2082\ninst\u271d\u00b3 : Category.{u_10, u_3} C\u2083\ninst\u271d\u00b2 : Category.{u_7, u_4} C\u2084\ninst\u271d\u00b9 : Category.{?u.29698, u_5} C\u2085\ninst\u271d : Category.{?u.29702, u_6} C\u2086\nT\u271d : C\u2081 \u2964 C\u2082\nL\u271d : C\u2081 \u2964 C\u2083\nR\u271d : C\u2082 \u2964 C\u2084\nB\u271d : C\u2083 \u2964 C\u2084\nT : C\u2081 \u2964 C\u2082\nL : C\u2081 \u224c C\u2083\nR : C\u2082 \u224c C\u2084\nB : C\u2083 \u2964 C\u2084\nh : CatCommSq T L.functor R.functor B\nX : C\u2081\n\u22a2 (R.functor.map (T.map (L.unitIso.hom.app X)) \u226b\n R.functor.map\n (R.unitIso.hom.app (T.obj (L.inverse.obj (L.functor.obj X))) \u226b\n R.inverse.map ((iso T L.functor R.functor B).hom.app (L.inverse.obj (L.functor.obj X))) \u226b\n R.inverse.map (B.map (L.counitIso.hom.app (L.functor.obj X)))) \u226b\n R.counitIso.hom.app (B.obj (L.functor.obj X))) \u226b\n B.map (L.functor.map (L.unitIso.hom.app X)) =\n iso'.hom.app X \u226b B.map (L.functor.map (L.unitIso.hom.app X))",
60
+ "state_before": "case iso'.w.w.h\nC\u2081 : Type u_1\nC\u2082 : Type u_2\nC\u2083 : Type u_3\nC\u2084 : Type u_4\nC\u2085 : Type u_5\nC\u2086 : Type u_6\ninst\u271d\u2075 : Category.{u_8, u_1} C\u2081\ninst\u271d\u2074 : Category.{u_9, u_2} C\u2082\ninst\u271d\u00b3 : Category.{u_10, u_3} C\u2083\ninst\u271d\u00b2 : Category.{u_7, u_4} C\u2084\ninst\u271d\u00b9 : Category.{?u.29698, u_5} C\u2085\ninst\u271d : Category.{?u.29702, u_6} C\u2086\nT\u271d : C\u2081 \u2964 C\u2082\nL\u271d : C\u2081 \u2964 C\u2083\nR\u271d : C\u2082 \u2964 C\u2084\nB\u271d : C\u2083 \u2964 C\u2084\nT : C\u2081 \u2964 C\u2082\nL : C\u2081 \u224c C\u2083\nR : C\u2082 \u224c C\u2084\nB : C\u2083 \u2964 C\u2084\nh : CatCommSq T L.functor R.functor B\nX : C\u2081\n\u22a2 R.functor.map (T.map (L.unitIso.hom.app X)) \u226b\n R.functor.map\n (R.unitIso.hom.app (T.obj (L.inverse.obj (L.functor.obj X))) \u226b\n R.inverse.map ((iso T L.functor R.functor B).hom.app (L.inverse.obj (L.functor.obj X))) \u226b\n R.inverse.map (B.map (L.counitIso.hom.app (L.functor.obj X)))) \u226b\n R.counitIso.hom.app (B.obj (L.functor.obj X)) =\n iso'.hom.app X",
61
+ "tactic": "rw [\u2190 cancel_mono (B.map (L.functor.map (NatTrans.app L.unitIso.hom X)))]"
62
+ },
63
+ {
64
+ "annotated_tactic": [
65
+ "\"erw [\\u2190 (<a>iso<\\/a> T L.functor R.functor B).hom.naturality (L.unitIso.hom.app X)]\"",
66
+ "[{\"full_name\":\"CategoryTheory.CatCommSq.iso\",\"def_path\":\"Mathlib\\/CategoryTheory\\/CatCommSq.lean\",\"def_pos\":[42,5],\"def_end_pos\":[42,8]}]"
67
+ ],
68
+ "state_after": "case iso'.w.w.h\nC\u2081 : Type u_1\nC\u2082 : Type u_2\nC\u2083 : Type u_3\nC\u2084 : Type u_4\nC\u2085 : Type u_5\nC\u2086 : Type u_6\ninst\u271d\u2075 : Category.{u_8, u_1} C\u2081\ninst\u271d\u2074 : Category.{u_9, u_2} C\u2082\ninst\u271d\u00b3 : Category.{u_10, u_3} C\u2083\ninst\u271d\u00b2 : Category.{u_7, u_4} C\u2084\ninst\u271d\u00b9 : Category.{?u.29698, u_5} C\u2085\ninst\u271d : Category.{?u.29702, u_6} C\u2086\nT\u271d : C\u2081 \u2964 C\u2082\nL\u271d : C\u2081 \u2964 C\u2083\nR\u271d : C\u2082 \u2964 C\u2084\nB\u271d : C\u2083 \u2964 C\u2084\nT : C\u2081 \u2964 C\u2082\nL : C\u2081 \u224c C\u2083\nR : C\u2082 \u224c C\u2084\nB : C\u2083 \u2964 C\u2084\nh : CatCommSq T L.functor R.functor B\nX : C\u2081\n\u22a2 (R.functor.map (T.map (L.unitIso.hom.app X)) \u226b\n R.functor.map\n (R.unitIso.hom.app (T.obj (L.inverse.obj (L.functor.obj X))) \u226b\n R.inverse.map ((iso T L.functor R.functor B).hom.app (L.inverse.obj (L.functor.obj X))) \u226b\n R.inverse.map (B.map (L.counitIso.hom.app (L.functor.obj X)))) \u226b\n R.counitIso.hom.app (B.obj (L.functor.obj X))) \u226b\n B.map (L.functor.map (L.unitIso.hom.app X)) =\n (T \u22d9 R.functor).map (L.unitIso.hom.app X) \u226b (iso T L.functor R.functor B).hom.app ((L.functor \u22d9 L.inverse).obj X)",
69
+ "state_before": "case iso'.w.w.h\nC\u2081 : Type u_1\nC\u2082 : Type u_2\nC\u2083 : Type u_3\nC\u2084 : Type u_4\nC\u2085 : Type u_5\nC\u2086 : Type u_6\ninst\u271d\u2075 : Category.{u_8, u_1} C\u2081\ninst\u271d\u2074 : Category.{u_9, u_2} C\u2082\ninst\u271d\u00b3 : Category.{u_10, u_3} C\u2083\ninst\u271d\u00b2 : Category.{u_7, u_4} C\u2084\ninst\u271d\u00b9 : Category.{?u.29698, u_5} C\u2085\ninst\u271d : Category.{?u.29702, u_6} C\u2086\nT\u271d : C\u2081 \u2964 C\u2082\nL\u271d : C\u2081 \u2964 C\u2083\nR\u271d : C\u2082 \u2964 C\u2084\nB\u271d : C\u2083 \u2964 C\u2084\nT : C\u2081 \u2964 C\u2082\nL : C\u2081 \u224c C\u2083\nR : C\u2082 \u224c C\u2084\nB : C\u2083 \u2964 C\u2084\nh : CatCommSq T L.functor R.functor B\nX : C\u2081\n\u22a2 (R.functor.map (T.map (L.unitIso.hom.app X)) \u226b\n R.functor.map\n (R.unitIso.hom.app (T.obj (L.inverse.obj (L.functor.obj X))) \u226b\n R.inverse.map ((iso T L.functor R.functor B).hom.app (L.inverse.obj (L.functor.obj X))) \u226b\n R.inverse.map (B.map (L.counitIso.hom.app (L.functor.obj X)))) \u226b\n R.counitIso.hom.app (B.obj (L.functor.obj X))) \u226b\n B.map (L.functor.map (L.unitIso.hom.app X)) =\n iso'.hom.app X \u226b B.map (L.functor.map (L.unitIso.hom.app X))",
70
+ "tactic": "erw [\u2190 (iso T L.functor R.functor B).hom.naturality (L.unitIso.hom.app X)]"
71
+ },
72
+ {
73
+ "annotated_tactic": [
74
+ "\"dsimp\"",
75
+ "[]"
76
+ ],
77
+ "state_after": "case iso'.w.w.h\nC\u2081 : Type u_1\nC\u2082 : Type u_2\nC\u2083 : Type u_3\nC\u2084 : Type u_4\nC\u2085 : Type u_5\nC\u2086 : Type u_6\ninst\u271d\u2075 : Category.{u_8, u_1} C\u2081\ninst\u271d\u2074 : Category.{u_9, u_2} C\u2082\ninst\u271d\u00b3 : Category.{u_10, u_3} C\u2083\ninst\u271d\u00b2 : Category.{u_7, u_4} C\u2084\ninst\u271d\u00b9 : Category.{?u.29698, u_5} C\u2085\ninst\u271d : Category.{?u.29702, u_6} C\u2086\nT\u271d : C\u2081 \u2964 C\u2082\nL\u271d : C\u2081 \u2964 C\u2083\nR\u271d : C\u2082 \u2964 C\u2084\nB\u271d : C\u2083 \u2964 C\u2084\nT : C\u2081 \u2964 C\u2082\nL : C\u2081 \u224c C\u2083\nR : C\u2082 \u224c C\u2084\nB : C\u2083 \u2964 C\u2084\nh : CatCommSq T L.functor R.functor B\nX : C\u2081\n\u22a2 (R.functor.map (T.map (L.unitIso.hom.app X)) \u226b\n R.functor.map\n (R.unitIso.hom.app (T.obj (L.inverse.obj (L.functor.obj X))) \u226b\n R.inverse.map ((iso T L.functor R.functor B).hom.app (L.inverse.obj (L.functor.obj X))) \u226b\n R.inverse.map (B.map (L.counitIso.hom.app (L.functor.obj X)))) \u226b\n R.counitIso.hom.app (B.obj (L.functor.obj X))) \u226b\n B.map (L.functor.map (L.unitIso.hom.app X)) =\n R.functor.map (T.map (L.unitIso.hom.app X)) \u226b\n (iso T L.functor R.functor B).hom.app (L.inverse.obj (L.functor.obj X))",
78
+ "state_before": "case iso'.w.w.h\nC\u2081 : Type u_1\nC\u2082 : Type u_2\nC\u2083 : Type u_3\nC\u2084 : Type u_4\nC\u2085 : Type u_5\nC\u2086 : Type u_6\ninst\u271d\u2075 : Category.{u_8, u_1} C\u2081\ninst\u271d\u2074 : Category.{u_9, u_2} C\u2082\ninst\u271d\u00b3 : Category.{u_10, u_3} C\u2083\ninst\u271d\u00b2 : Category.{u_7, u_4} C\u2084\ninst\u271d\u00b9 : Category.{?u.29698, u_5} C\u2085\ninst\u271d : Category.{?u.29702, u_6} C\u2086\nT\u271d : C\u2081 \u2964 C\u2082\nL\u271d : C\u2081 \u2964 C\u2083\nR\u271d : C\u2082 \u2964 C\u2084\nB\u271d : C\u2083 \u2964 C\u2084\nT : C\u2081 \u2964 C\u2082\nL : C\u2081 \u224c C\u2083\nR : C\u2082 \u224c C\u2084\nB : C\u2083 \u2964 C\u2084\nh : CatCommSq T L.functor R.functor B\nX : C\u2081\n\u22a2 (R.functor.map (T.map (L.unitIso.hom.app X)) \u226b\n R.functor.map\n (R.unitIso.hom.app (T.obj (L.inverse.obj (L.functor.obj X))) \u226b\n R.inverse.map ((iso T L.functor R.functor B).hom.app (L.inverse.obj (L.functor.obj X))) \u226b\n R.inverse.map (B.map (L.counitIso.hom.app (L.functor.obj X)))) \u226b\n R.counitIso.hom.app (B.obj (L.functor.obj X))) \u226b\n B.map (L.functor.map (L.unitIso.hom.app X)) =\n (T \u22d9 R.functor).map (L.unitIso.hom.app X) \u226b (iso T L.functor R.functor B).hom.app ((L.functor \u22d9 L.inverse).obj X)",
79
+ "tactic": "dsimp"
80
+ },
81
+ {
82
+ "annotated_tactic": [
83
+ "\"simp only [<a>Functor.map_comp<\\/a>, <a>Equivalence.fun_inv_map<\\/a>, <a>Functor.comp_obj<\\/a>,\\n <a>Functor.id_obj<\\/a>, <a>assoc<\\/a>, <a>Iso.inv_hom_id_app_assoc<\\/a>, <a>Iso.inv_hom_id_app<\\/a>, <a>comp_id<\\/a>]\"",
84
+ "[{\"full_name\":\"CategoryTheory.Functor.map_comp\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Basic.lean\",\"def_pos\":[43,3],\"def_end_pos\":[43,11]},{\"full_name\":\"CategoryTheory.Equivalence.fun_inv_map\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Equivalence.lean\",\"def_pos\":[228,9],\"def_end_pos\":[228,20]},{\"full_name\":\"CategoryTheory.Functor.comp_obj\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Basic.lean\",\"def_pos\":[110,9],\"def_end_pos\":[110,12]},{\"full_name\":\"CategoryTheory.Functor.id_obj\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Basic.lean\",\"def_pos\":[94,9],\"def_end_pos\":[94,15]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.Iso.inv_hom_id_app_assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/NatIso.lean\",\"def_pos\":[70,3],\"def_end_pos\":[70,25]},{\"full_name\":\"CategoryTheory.Iso.inv_hom_id_app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/NatIso.lean\",\"def_pos\":[71,9],\"def_end_pos\":[71,23]},{\"full_name\":\"CategoryTheory.Category.comp_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[179,3],\"def_end_pos\":[179,10]}]"
85
+ ],
86
+ "state_after": "case iso'.w.w.h\nC\u2081 : Type u_1\nC\u2082 : Type u_2\nC\u2083 : Type u_3\nC\u2084 : Type u_4\nC\u2085 : Type u_5\nC\u2086 : Type u_6\ninst\u271d\u2075 : Category.{u_8, u_1} C\u2081\ninst\u271d\u2074 : Category.{u_9, u_2} C\u2082\ninst\u271d\u00b3 : Category.{u_10, u_3} C\u2083\ninst\u271d\u00b2 : Category.{u_7, u_4} C\u2084\ninst\u271d\u00b9 : Category.{?u.29698, u_5} C\u2085\ninst\u271d : Category.{?u.29702, u_6} C\u2086\nT\u271d : C\u2081 \u2964 C\u2082\nL\u271d : C\u2081 \u2964 C\u2083\nR\u271d : C\u2082 \u2964 C\u2084\nB\u271d : C\u2083 \u2964 C\u2084\nT : C\u2081 \u2964 C\u2082\nL : C\u2081 \u224c C\u2083\nR : C\u2082 \u224c C\u2084\nB : C\u2083 \u2964 C\u2084\nh : CatCommSq T L.functor R.functor B\nX : C\u2081\n\u22a2 R.functor.map (T.map (L.unitIso.hom.app X)) \u226b\n R.functor.map (R.unitIso.hom.app (T.obj (L.inverse.obj (L.functor.obj X)))) \u226b\n R.counit.app (R.functor.obj (T.obj (L.inverse.obj (L.functor.obj X)))) \u226b\n (iso T L.functor R.functor B).hom.app (L.inverse.obj (L.functor.obj X)) \u226b\n B.map (L.counitIso.hom.app (L.functor.obj X)) \u226b B.map (L.functor.map (L.unitIso.hom.app X)) =\n R.functor.map (T.map (L.unitIso.hom.app X)) \u226b\n (iso T L.functor R.functor B).hom.app (L.inverse.obj (L.functor.obj X))",
87
+ "state_before": "case iso'.w.w.h\nC\u2081 : Type u_1\nC\u2082 : Type u_2\nC\u2083 : Type u_3\nC\u2084 : Type u_4\nC\u2085 : Type u_5\nC\u2086 : Type u_6\ninst\u271d\u2075 : Category.{u_8, u_1} C\u2081\ninst\u271d\u2074 : Category.{u_9, u_2} C\u2082\ninst\u271d\u00b3 : Category.{u_10, u_3} C\u2083\ninst\u271d\u00b2 : Category.{u_7, u_4} C\u2084\ninst\u271d\u00b9 : Category.{?u.29698, u_5} C\u2085\ninst\u271d : Category.{?u.29702, u_6} C\u2086\nT\u271d : C\u2081 \u2964 C\u2082\nL\u271d : C\u2081 \u2964 C\u2083\nR\u271d : C\u2082 \u2964 C\u2084\nB\u271d : C\u2083 \u2964 C\u2084\nT : C\u2081 \u2964 C\u2082\nL : C\u2081 \u224c C\u2083\nR : C\u2082 \u224c C\u2084\nB : C\u2083 \u2964 C\u2084\nh : CatCommSq T L.functor R.functor B\nX : C\u2081\n\u22a2 (R.functor.map (T.map (L.unitIso.hom.app X)) \u226b\n R.functor.map\n (R.unitIso.hom.app (T.obj (L.inverse.obj (L.functor.obj X))) \u226b\n R.inverse.map ((iso T L.functor R.functor B).hom.app (L.inverse.obj (L.functor.obj X))) \u226b\n R.inverse.map (B.map (L.counitIso.hom.app (L.functor.obj X)))) \u226b\n R.counitIso.hom.app (B.obj (L.functor.obj X))) \u226b\n B.map (L.functor.map (L.unitIso.hom.app X)) =\n R.functor.map (T.map (L.unitIso.hom.app X)) \u226b\n (iso T L.functor R.functor B).hom.app (L.inverse.obj (L.functor.obj X))",
88
+ "tactic": "simp only [Functor.map_comp, Equivalence.fun_inv_map, Functor.comp_obj,\n Functor.id_obj, assoc, Iso.inv_hom_id_app_assoc, Iso.inv_hom_id_app, comp_id]"
89
+ },
90
+ {
91
+ "annotated_tactic": [
92
+ "\"erw [\\u2190 B.map_comp, L.counit_app_functor, \\u2190 L.functor.map_comp, \\u2190 <a>NatTrans.comp_app<\\/a>,\\n <a>Iso.inv_hom_id<\\/a>, <a>NatTrans.id_app<\\/a>, L.functor.map_id, B.map_id, <a>comp_id<\\/a>, R.counit_app_functor,\\n \\u2190 R.functor.map_comp_assoc, \\u2190 R.functor.map_comp_assoc, <a>assoc<\\/a>, \\u2190 <a>NatTrans.comp_app<\\/a>,\\n <a>Iso.hom_inv_id<\\/a>, <a>NatTrans.id_app<\\/a>, <a>comp_id<\\/a>]\"",
93
+ "[{\"full_name\":\"CategoryTheory.NatTrans.comp_app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Category.lean\",\"def_pos\":[76,9],\"def_end_pos\":[76,17]},{\"full_name\":\"CategoryTheory.Iso.inv_hom_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[60,3],\"def_end_pos\":[60,13]},{\"full_name\":\"CategoryTheory.NatTrans.id_app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Category.lean\",\"def_pos\":[72,9],\"def_end_pos\":[72,15]},{\"full_name\":\"CategoryTheory.Category.comp_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[179,3],\"def_end_pos\":[179,10]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.NatTrans.comp_app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Category.lean\",\"def_pos\":[76,9],\"def_end_pos\":[76,17]},{\"full_name\":\"CategoryTheory.Iso.hom_inv_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[57,3],\"def_end_pos\":[57,13]},{\"full_name\":\"CategoryTheory.NatTrans.id_app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Category.lean\",\"def_pos\":[72,9],\"def_end_pos\":[72,15]},{\"full_name\":\"CategoryTheory.Category.comp_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[179,3],\"def_end_pos\":[179,10]}]"
94
+ ],
95
+ "state_after": "no goals",
96
+ "state_before": "case iso'.w.w.h\nC\u2081 : Type u_1\nC\u2082 : Type u_2\nC\u2083 : Type u_3\nC\u2084 : Type u_4\nC\u2085 : Type u_5\nC\u2086 : Type u_6\ninst\u271d\u2075 : Category.{u_8, u_1} C\u2081\ninst\u271d\u2074 : Category.{u_9, u_2} C\u2082\ninst\u271d\u00b3 : Category.{u_10, u_3} C\u2083\ninst\u271d\u00b2 : Category.{u_7, u_4} C\u2084\ninst\u271d\u00b9 : Category.{?u.29698, u_5} C\u2085\ninst\u271d : Category.{?u.29702, u_6} C\u2086\nT\u271d : C\u2081 \u2964 C\u2082\nL\u271d : C\u2081 \u2964 C\u2083\nR\u271d : C\u2082 \u2964 C\u2084\nB\u271d : C\u2083 \u2964 C\u2084\nT : C\u2081 \u2964 C\u2082\nL : C\u2081 \u224c C\u2083\nR : C\u2082 \u224c C\u2084\nB : C\u2083 \u2964 C\u2084\nh : CatCommSq T L.functor R.functor B\nX : C\u2081\n\u22a2 R.functor.map (T.map (L.unitIso.hom.app X)) \u226b\n R.functor.map (R.unitIso.hom.app (T.obj (L.inverse.obj (L.functor.obj X)))) \u226b\n R.counit.app (R.functor.obj (T.obj (L.inverse.obj (L.functor.obj X)))) \u226b\n (iso T L.functor R.functor B).hom.app (L.inverse.obj (L.functor.obj X)) \u226b\n B.map (L.counitIso.hom.app (L.functor.obj X)) \u226b B.map (L.functor.map (L.unitIso.hom.app X)) =\n R.functor.map (T.map (L.unitIso.hom.app X)) \u226b\n (iso T L.functor R.functor B).hom.app (L.inverse.obj (L.functor.obj X))",
97
+ "tactic": "erw [\u2190 B.map_comp, L.counit_app_functor, \u2190 L.functor.map_comp, \u2190 NatTrans.comp_app,\n Iso.inv_hom_id, NatTrans.id_app, L.functor.map_id, B.map_id, comp_id, R.counit_app_functor,\n \u2190 R.functor.map_comp_assoc, \u2190 R.functor.map_comp_assoc, assoc, \u2190 NatTrans.comp_app,\n Iso.hom_inv_id, NatTrans.id_app, comp_id]"
98
+ }
99
+ ],
100
+ "url": "https://github.com/leanprover-community/mathlib4"
101
+ },
102
+ "source_file": "Mathlib/CategoryTheory/CatCommSq.lean"
103
+ }
104
+ ],
105
+ "input_proofs": 3,
106
+ "input_units": 2,
107
+ "proofs": 2,
108
+ "published_proofs": 2,
109
+ "published_transitions": 4,
110
+ "replay_failures": [],
111
+ "transitions": 4,
112
+ "validation_failures": [],
113
+ "validation_rejected_proofs": 0,
114
+ "zero_transition_proofs": 0
115
+ },
116
+ "shards": [
117
+ {
118
+ "path": "data/train/mathlib-000613-0000-c57a257aa860a71e.parquet",
119
+ "sha256": "c57a257aa860a71e612cb3bbc21a7a65921e6383fc7c2b8c75292cca7b3e1503",
120
+ "bytes": 45026,
121
+ "rows": 4,
122
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
123
+ }
124
+ ],
125
+ "proof_ids": [
126
+ "mathlib:CategoryTheory.Bicategory.eqToHom_whiskerRight",
127
+ "mathlib:CategoryTheory.Bicategory.whiskerLeft_eqToHom"
128
+ ],
129
+ "proof_keys": [
130
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Bicategory/Strict.lean\",null,null,\"CategoryTheory.Bicategory.eqToHom_whiskerRight\"]",
131
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Bicategory/Strict.lean\",null,null,\"CategoryTheory.Bicategory.whiskerLeft_eqToHom\"]"
132
+ ]
133
+ }
manifests/batches/mathlib/000614.json ADDED
@@ -0,0 +1,299 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000614",
4
+ "batch_fingerprint": "64f24c2845cacc04302db0611157edcfd7c666edc561b8eabd4e16d273bddf67",
5
+ "evidence": {
6
+ "batch_fingerprint": "64f24c2845cacc04302db0611157edcfd7c666edc561b8eabd4e16d273bddf67",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "CategoryTheory.cancel_epi",
12
+ "id": "CategoryTheory.cancel_epi",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 307,
18
+ 54
19
+ ],
20
+ "file_path": "Mathlib/CategoryTheory/Category/Basic.lean",
21
+ "full_name": "CategoryTheory.cancel_epi",
22
+ "start": [
23
+ 306,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/CategoryTheory/Category/Basic.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "CategoryTheory.cancel_mono",
34
+ "id": "CategoryTheory.cancel_mono",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 312,
40
+ 71
41
+ ],
42
+ "file_path": "Mathlib/CategoryTheory/Category/Basic.lean",
43
+ "full_name": "CategoryTheory.cancel_mono",
44
+ "start": [
45
+ 310,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/CategoryTheory/Category/Basic.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "Bipointed.coe_of",
56
+ "id": "Bipointed.coe_of",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 48,
62
+ 6
63
+ ],
64
+ "file_path": "Mathlib/CategoryTheory/Category/Bipointed.lean",
65
+ "full_name": "Bipointed.coe_of",
66
+ "start": [
67
+ 47,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/CategoryTheory/Category/Bipointed.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "Bipointed.swapEquiv_symm",
78
+ "id": "Bipointed.swapEquiv_symm",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 121,
84
+ 6
85
+ ],
86
+ "file_path": "Mathlib/CategoryTheory/Category/Bipointed.lean",
87
+ "full_name": "Bipointed.swapEquiv_symm",
88
+ "start": [
89
+ 120,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/CategoryTheory/Category/Bipointed.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "bipointedToPointedFst_comp_forget",
100
+ "id": "bipointedToPointedFst_comp_forget",
101
+ "reason": "import_failure",
102
+ "selection": {
103
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
104
+ "end": [
105
+ 141,
106
+ 6
107
+ ],
108
+ "file_path": "Mathlib/CategoryTheory/Category/Bipointed.lean",
109
+ "full_name": "bipointedToPointedFst_comp_forget",
110
+ "start": [
111
+ 139,
112
+ 1
113
+ ],
114
+ "traced_tactics": [],
115
+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
+ "source_file": "Mathlib/CategoryTheory/Category/Bipointed.lean"
118
+ },
119
+ {
120
+ "error": "theorem has no selected tactic transitions",
121
+ "full_name": "bipointedToPointedSnd_comp_forget",
122
+ "id": "bipointedToPointedSnd_comp_forget",
123
+ "reason": "import_failure",
124
+ "selection": {
125
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
126
+ "end": [
127
+ 147,
128
+ 6
129
+ ],
130
+ "file_path": "Mathlib/CategoryTheory/Category/Bipointed.lean",
131
+ "full_name": "bipointedToPointedSnd_comp_forget",
132
+ "start": [
133
+ 145,
134
+ 1
135
+ ],
136
+ "traced_tactics": [],
137
+ "url": "https://github.com/leanprover-community/mathlib4"
138
+ },
139
+ "source_file": "Mathlib/CategoryTheory/Category/Bipointed.lean"
140
+ },
141
+ {
142
+ "error": "theorem has no selected tactic transitions",
143
+ "full_name": "pointedToBipointedFst_comp_swap",
144
+ "id": "pointedToBipointedFst_comp_swap",
145
+ "reason": "import_failure",
146
+ "selection": {
147
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
148
+ "end": [
149
+ 187,
150
+ 6
151
+ ],
152
+ "file_path": "Mathlib/CategoryTheory/Category/Bipointed.lean",
153
+ "full_name": "pointedToBipointedFst_comp_swap",
154
+ "start": [
155
+ 185,
156
+ 1
157
+ ],
158
+ "traced_tactics": [],
159
+ "url": "https://github.com/leanprover-community/mathlib4"
160
+ },
161
+ "source_file": "Mathlib/CategoryTheory/Category/Bipointed.lean"
162
+ },
163
+ {
164
+ "error": "theorem has no selected tactic transitions",
165
+ "full_name": "pointedToBipointedSnd_comp_swap",
166
+ "id": "pointedToBipointedSnd_comp_swap",
167
+ "reason": "import_failure",
168
+ "selection": {
169
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
170
+ "end": [
171
+ 193,
172
+ 6
173
+ ],
174
+ "file_path": "Mathlib/CategoryTheory/Category/Bipointed.lean",
175
+ "full_name": "pointedToBipointedSnd_comp_swap",
176
+ "start": [
177
+ 191,
178
+ 1
179
+ ],
180
+ "traced_tactics": [],
181
+ "url": "https://github.com/leanprover-community/mathlib4"
182
+ },
183
+ "source_file": "Mathlib/CategoryTheory/Category/Bipointed.lean"
184
+ },
185
+ {
186
+ "error": "theorem has no selected tactic transitions",
187
+ "full_name": "swap_comp_bipointedToPointedFst",
188
+ "id": "swap_comp_bipointedToPointedFst",
189
+ "reason": "import_failure",
190
+ "selection": {
191
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
192
+ "end": [
193
+ 153,
194
+ 6
195
+ ],
196
+ "file_path": "Mathlib/CategoryTheory/Category/Bipointed.lean",
197
+ "full_name": "swap_comp_bipointedToPointedFst",
198
+ "start": [
199
+ 151,
200
+ 1
201
+ ],
202
+ "traced_tactics": [],
203
+ "url": "https://github.com/leanprover-community/mathlib4"
204
+ },
205
+ "source_file": "Mathlib/CategoryTheory/Category/Bipointed.lean"
206
+ },
207
+ {
208
+ "error": "theorem has no selected tactic transitions",
209
+ "full_name": "swap_comp_bipointedToPointedSnd",
210
+ "id": "swap_comp_bipointedToPointedSnd",
211
+ "reason": "import_failure",
212
+ "selection": {
213
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
214
+ "end": [
215
+ 159,
216
+ 6
217
+ ],
218
+ "file_path": "Mathlib/CategoryTheory/Category/Bipointed.lean",
219
+ "full_name": "swap_comp_bipointedToPointedSnd",
220
+ "start": [
221
+ 157,
222
+ 1
223
+ ],
224
+ "traced_tactics": [],
225
+ "url": "https://github.com/leanprover-community/mathlib4"
226
+ },
227
+ "source_file": "Mathlib/CategoryTheory/Category/Bipointed.lean"
228
+ }
229
+ ],
230
+ "input_proofs": 29,
231
+ "input_units": 2,
232
+ "proofs": 19,
233
+ "published_proofs": 19,
234
+ "published_transitions": 43,
235
+ "replay_failures": [],
236
+ "transitions": 43,
237
+ "validation_failures": [],
238
+ "validation_rejected_proofs": 0,
239
+ "zero_transition_proofs": 0
240
+ },
241
+ "shards": [
242
+ {
243
+ "path": "data/train/mathlib-000614-0000-947bb41da0e44219.parquet",
244
+ "sha256": "947bb41da0e442194b722812c78eb2562e2f286c7536dda4dc79299431bee178",
245
+ "bytes": 122734,
246
+ "rows": 36,
247
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
248
+ },
249
+ {
250
+ "path": "data/internal_test/mathlib-000614-0000-494f57dfc73c8546.parquet",
251
+ "sha256": "494f57dfc73c8546e3aa8f6209e665444da67b39ebc506cfb55fa48d3c5e25b1",
252
+ "bytes": 52468,
253
+ "rows": 7,
254
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
255
+ }
256
+ ],
257
+ "proof_ids": [
258
+ "mathlib:CategoryTheory.cancel_epi_id",
259
+ "mathlib:CategoryTheory.cancel_mono_id",
260
+ "mathlib:CategoryTheory.comp_dite",
261
+ "mathlib:CategoryTheory.comp_ite",
262
+ "mathlib:CategoryTheory.dite_comp",
263
+ "mathlib:CategoryTheory.epi_comp",
264
+ "mathlib:CategoryTheory.epi_of_epi",
265
+ "mathlib:CategoryTheory.epi_of_epi_fac",
266
+ "mathlib:CategoryTheory.eq_of_comp_left_eq",
267
+ "mathlib:CategoryTheory.eq_of_comp_left_eq'",
268
+ "mathlib:CategoryTheory.eq_of_comp_right_eq",
269
+ "mathlib:CategoryTheory.eq_of_comp_right_eq'",
270
+ "mathlib:CategoryTheory.eq_whisker",
271
+ "mathlib:CategoryTheory.id_of_comp_left_id",
272
+ "mathlib:CategoryTheory.id_of_comp_right_id",
273
+ "mathlib:CategoryTheory.ite_comp",
274
+ "mathlib:CategoryTheory.mono_comp",
275
+ "mathlib:CategoryTheory.mono_of_mono",
276
+ "mathlib:CategoryTheory.mono_of_mono_fac"
277
+ ],
278
+ "proof_keys": [
279
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.cancel_epi_id\"]",
280
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.cancel_mono_id\"]",
281
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.comp_dite\"]",
282
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.comp_ite\"]",
283
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.dite_comp\"]",
284
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.epi_comp\"]",
285
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.epi_of_epi\"]",
286
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.epi_of_epi_fac\"]",
287
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.eq_of_comp_left_eq\"]",
288
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.eq_of_comp_left_eq'\"]",
289
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.eq_of_comp_right_eq\"]",
290
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.eq_of_comp_right_eq'\"]",
291
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.eq_whisker\"]",
292
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.id_of_comp_left_id\"]",
293
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.id_of_comp_right_id\"]",
294
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.ite_comp\"]",
295
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.mono_comp\"]",
296
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.mono_of_mono\"]",
297
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Basic.lean\",null,null,\"CategoryTheory.mono_of_mono_fac\"]"
298
+ ]
299
+ }
manifests/batches/mathlib/000615.json ADDED
@@ -0,0 +1,179 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000615",
4
+ "batch_fingerprint": "642f20cd1e991ffa9ad2e7f04c7335049cb078790a09a25cf02e39125b66cd6c",
5
+ "evidence": {
6
+ "batch_fingerprint": "642f20cd1e991ffa9ad2e7f04c7335049cb078790a09a25cf02e39125b66cd6c",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "CategoryTheory.Cat.comp_obj",
12
+ "id": "CategoryTheory.Cat.comp_obj",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 99,
18
+ 6
19
+ ],
20
+ "file_path": "Mathlib/CategoryTheory/Category/Cat.lean",
21
+ "full_name": "CategoryTheory.Cat.comp_obj",
22
+ "start": [
23
+ 98,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/CategoryTheory/Category/Cat.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "CategoryTheory.Cat.id_map",
34
+ "id": "CategoryTheory.Cat.id_map",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 93,
40
+ 6
41
+ ],
42
+ "file_path": "Mathlib/CategoryTheory/Category/Cat.lean",
43
+ "full_name": "CategoryTheory.Cat.id_map",
44
+ "start": [
45
+ 92,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/CategoryTheory/Category/Cat.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "CategoryTheory.Cat.whiskerLeft_app",
56
+ "id": "CategoryTheory.Cat.whiskerLeft_app",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 113,
62
+ 6
63
+ ],
64
+ "file_path": "Mathlib/CategoryTheory/Category/Cat.lean",
65
+ "full_name": "CategoryTheory.Cat.whiskerLeft_app",
66
+ "start": [
67
+ 110,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/CategoryTheory/Category/Cat.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "CategoryTheory.Cat.whiskerRight_app",
78
+ "id": "CategoryTheory.Cat.whiskerRight_app",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 118,
84
+ 6
85
+ ],
86
+ "file_path": "Mathlib/CategoryTheory/Category/Cat.lean",
87
+ "full_name": "CategoryTheory.Cat.whiskerRight_app",
88
+ "start": [
89
+ 115,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/CategoryTheory/Category/Cat.lean"
96
+ },
97
+ {
98
+ "full_name": "CategoryTheory.Cat.HasLimits.limit_\u03c0_homDiagram_eqToHom",
99
+ "id": "CategoryTheory.Cat.HasLimits.limit_\u03c0_homDiagram_eqToHom",
100
+ "reason": "missing_trace",
101
+ "selection": {
102
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
103
+ "end": [
104
+ 132,
105
+ 7
106
+ ],
107
+ "file_path": "Mathlib/CategoryTheory/Category/Cat/Limit.lean",
108
+ "full_name": "CategoryTheory.Cat.HasLimits.limit_\u03c0_homDiagram_eqToHom",
109
+ "start": [
110
+ 127,
111
+ 1
112
+ ],
113
+ "traced_tactics": [
114
+ {
115
+ "annotated_tactic": [
116
+ "\"subst h\"",
117
+ "[]"
118
+ ],
119
+ "state_after": "J : Type v\ninst\u271d : SmallCategory J\nF : J \u2964 Cat\nX : limit (F \u22d9 objects)\nj : J\n\u22a2 limit.\u03c0 (homDiagram X X) j (eqToHom \u22ef) = eqToHom \u22ef",
120
+ "state_before": "J : Type v\ninst\u271d : SmallCategory J\nF : J \u2964 Cat\nX Y : limit (F \u22d9 objects)\nj : J\nh : X = Y\n\u22a2 limit.\u03c0 (homDiagram X Y) j (eqToHom h) = eqToHom \u22ef",
121
+ "tactic": "subst h"
122
+ },
123
+ {
124
+ "annotated_tactic": [
125
+ "\"simp\"",
126
+ "[]"
127
+ ],
128
+ "state_after": "no goals",
129
+ "state_before": "J : Type v\ninst\u271d : SmallCategory J\nF : J \u2964 Cat\nX : limit (F \u22d9 objects)\nj : J\n\u22a2 limit.\u03c0 (homDiagram X X) j (eqToHom \u22ef) = eqToHom \u22ef",
130
+ "tactic": "simp"
131
+ }
132
+ ],
133
+ "url": "https://github.com/leanprover-community/mathlib4"
134
+ },
135
+ "source_file": "Mathlib/CategoryTheory/Category/Cat/Limit.lean"
136
+ }
137
+ ],
138
+ "input_proofs": 10,
139
+ "input_units": 2,
140
+ "proofs": 5,
141
+ "published_proofs": 5,
142
+ "published_transitions": 5,
143
+ "replay_failures": [],
144
+ "transitions": 5,
145
+ "validation_failures": [],
146
+ "validation_rejected_proofs": 0,
147
+ "zero_transition_proofs": 0
148
+ },
149
+ "shards": [
150
+ {
151
+ "path": "data/train/mathlib-000615-0000-833b0a4339f38357.parquet",
152
+ "sha256": "833b0a4339f38357b0bcb2fe4dbd550cf800c53d334cdaac14178c75bcfe849a",
153
+ "bytes": 29079,
154
+ "rows": 4,
155
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
156
+ },
157
+ {
158
+ "path": "data/internal_test/mathlib-000615-0000-dbf524373a4a9075.parquet",
159
+ "sha256": "dbf524373a4a907550b6e92154ddc4b6e13ead2392526dcc8aa6eed60ca3aa25",
160
+ "bytes": 24953,
161
+ "rows": 1,
162
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
163
+ }
164
+ ],
165
+ "proof_ids": [
166
+ "mathlib:CategoryTheory.Cat.associator_hom_app",
167
+ "mathlib:CategoryTheory.Cat.associator_inv_app",
168
+ "mathlib:CategoryTheory.Cat.leftUnitor_hom_app",
169
+ "mathlib:CategoryTheory.Cat.leftUnitor_inv_app",
170
+ "mathlib:CategoryTheory.Cat.rightUnitor_hom_app"
171
+ ],
172
+ "proof_keys": [
173
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Cat.lean\",null,null,\"CategoryTheory.Cat.associator_hom_app\"]",
174
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Cat.lean\",null,null,\"CategoryTheory.Cat.associator_inv_app\"]",
175
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Cat.lean\",null,null,\"CategoryTheory.Cat.leftUnitor_hom_app\"]",
176
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Cat.lean\",null,null,\"CategoryTheory.Cat.leftUnitor_inv_app\"]",
177
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Cat.lean\",null,null,\"CategoryTheory.Cat.rightUnitor_hom_app\"]"
178
+ ]
179
+ }
manifests/batches/mathlib/000616.json ADDED
@@ -0,0 +1,124 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000616",
4
+ "batch_fingerprint": "020e46c4fb6389f3053e037e924a7f7af00e9f2495dda94226f35b8e6014ae21",
5
+ "evidence": {
6
+ "batch_fingerprint": "020e46c4fb6389f3053e037e924a7f7af00e9f2495dda94226f35b8e6014ae21",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "CategoryTheory.Adjunction.gc",
12
+ "id": "CategoryTheory.Adjunction.gc",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 47,
18
+ 96
19
+ ],
20
+ "file_path": "Mathlib/CategoryTheory/Category/GaloisConnection.lean",
21
+ "full_name": "CategoryTheory.Adjunction.gc",
22
+ "start": [
23
+ 45,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/CategoryTheory/Category/GaloisConnection.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "CategoryTheory.Grpd.coe_of",
34
+ "id": "CategoryTheory.Grpd.coe_of",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 64,
40
+ 6
41
+ ],
42
+ "file_path": "Mathlib/CategoryTheory/Category/Grpd.lean",
43
+ "full_name": "CategoryTheory.Grpd.coe_of",
44
+ "start": [
45
+ 63,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/CategoryTheory/Category/Grpd.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "CategoryTheory.Grpd.hom_to_functor",
56
+ "id": "CategoryTheory.Grpd.hom_to_functor",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 105,
62
+ 6
63
+ ],
64
+ "file_path": "Mathlib/CategoryTheory/Category/Grpd.lean",
65
+ "full_name": "CategoryTheory.Grpd.hom_to_functor",
66
+ "start": [
67
+ 104,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/CategoryTheory/Category/Grpd.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "CategoryTheory.Grpd.id_to_functor",
78
+ "id": "CategoryTheory.Grpd.id_to_functor",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 111,
84
+ 6
85
+ ],
86
+ "file_path": "Mathlib/CategoryTheory/Category/Grpd.lean",
87
+ "full_name": "CategoryTheory.Grpd.id_to_functor",
88
+ "start": [
89
+ 110,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/CategoryTheory/Category/Grpd.lean"
96
+ }
97
+ ],
98
+ "input_proofs": 5,
99
+ "input_units": 2,
100
+ "proofs": 1,
101
+ "published_proofs": 1,
102
+ "published_transitions": 2,
103
+ "replay_failures": [],
104
+ "transitions": 2,
105
+ "validation_failures": [],
106
+ "validation_rejected_proofs": 0,
107
+ "zero_transition_proofs": 0
108
+ },
109
+ "shards": [
110
+ {
111
+ "path": "data/train/mathlib-000616-0000-78937ff471b68725.parquet",
112
+ "sha256": "78937ff471b687257e61796220bb96e395aa2a0531b1068da3883758c9ce58db",
113
+ "bytes": 34958,
114
+ "rows": 2,
115
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
116
+ }
117
+ ],
118
+ "proof_ids": [
119
+ "mathlib:CategoryTheory.Grpd.piIsoPi_hom_\u03c0"
120
+ ],
121
+ "proof_keys": [
122
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/Grpd.lean\",null,null,\"CategoryTheory.Grpd.piIsoPi_hom_\u03c0\"]"
123
+ ]
124
+ }
manifests/batches/mathlib/000617.json ADDED
@@ -0,0 +1,135 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000617",
4
+ "batch_fingerprint": "720dbd97791cb6d297ab77bf83e0b58b8fdbc9dbbdbead187e7e4b894a293493",
5
+ "evidence": {
6
+ "batch_fingerprint": "720dbd97791cb6d297ab77bf83e0b58b8fdbc9dbbdbead187e7e4b894a293493",
7
+ "batch_outcome": "all_inputs_failed_with_evidence",
8
+ "contamination_matches": [],
9
+ "failures": [
10
+ {
11
+ "error": "theorem has no selected tactic transitions",
12
+ "full_name": "CategoryTheory.KleisliCat.comp_def",
13
+ "id": "CategoryTheory.KleisliCat.comp_def",
14
+ "reason": "import_failure",
15
+ "selection": {
16
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
17
+ "end": [
18
+ 66,
19
+ 6
20
+ ],
21
+ "file_path": "Mathlib/CategoryTheory/Category/KleisliCat.lean",
22
+ "full_name": "CategoryTheory.KleisliCat.comp_def",
23
+ "start": [
24
+ 64,
25
+ 1
26
+ ],
27
+ "traced_tactics": [],
28
+ "url": "https://github.com/leanprover-community/mathlib4"
29
+ },
30
+ "source_file": "Mathlib/CategoryTheory/Category/KleisliCat.lean"
31
+ },
32
+ {
33
+ "error": "theorem has no selected tactic transitions",
34
+ "full_name": "CategoryTheory.KleisliCat.id_def",
35
+ "id": "CategoryTheory.KleisliCat.id_def",
36
+ "reason": "import_failure",
37
+ "selection": {
38
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
39
+ "end": [
40
+ 61,
41
+ 6
42
+ ],
43
+ "file_path": "Mathlib/CategoryTheory/Category/KleisliCat.lean",
44
+ "full_name": "CategoryTheory.KleisliCat.id_def",
45
+ "start": [
46
+ 60,
47
+ 1
48
+ ],
49
+ "traced_tactics": [],
50
+ "url": "https://github.com/leanprover-community/mathlib4"
51
+ },
52
+ "source_file": "Mathlib/CategoryTheory/Category/KleisliCat.lean"
53
+ },
54
+ {
55
+ "error": "theorem has no selected tactic transitions",
56
+ "full_name": "Pointed.Hom.comp_toFun'",
57
+ "id": "Pointed.Hom.comp_toFun'",
58
+ "reason": "import_failure",
59
+ "selection": {
60
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
61
+ "end": [
62
+ 106,
63
+ 45
64
+ ],
65
+ "file_path": "Mathlib/CategoryTheory/Category/Pointed.lean",
66
+ "full_name": "Pointed.Hom.comp_toFun'",
67
+ "start": [
68
+ 105,
69
+ 1
70
+ ],
71
+ "traced_tactics": [],
72
+ "url": "https://github.com/leanprover-community/mathlib4"
73
+ },
74
+ "source_file": "Mathlib/CategoryTheory/Category/Pointed.lean"
75
+ },
76
+ {
77
+ "error": "theorem has no selected tactic transitions",
78
+ "full_name": "Pointed.Hom.id_toFun'",
79
+ "id": "Pointed.Hom.id_toFun'",
80
+ "reason": "import_failure",
81
+ "selection": {
82
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
83
+ "end": [
84
+ 103,
85
+ 87
86
+ ],
87
+ "file_path": "Mathlib/CategoryTheory/Category/Pointed.lean",
88
+ "full_name": "Pointed.Hom.id_toFun'",
89
+ "start": [
90
+ 103,
91
+ 1
92
+ ],
93
+ "traced_tactics": [],
94
+ "url": "https://github.com/leanprover-community/mathlib4"
95
+ },
96
+ "source_file": "Mathlib/CategoryTheory/Category/Pointed.lean"
97
+ },
98
+ {
99
+ "error": "theorem has no selected tactic transitions",
100
+ "full_name": "Pointed.coe_of",
101
+ "id": "Pointed.coe_of",
102
+ "reason": "import_failure",
103
+ "selection": {
104
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
105
+ "end": [
106
+ 54,
107
+ 6
108
+ ],
109
+ "file_path": "Mathlib/CategoryTheory/Category/Pointed.lean",
110
+ "full_name": "Pointed.coe_of",
111
+ "start": [
112
+ 53,
113
+ 1
114
+ ],
115
+ "traced_tactics": [],
116
+ "url": "https://github.com/leanprover-community/mathlib4"
117
+ },
118
+ "source_file": "Mathlib/CategoryTheory/Category/Pointed.lean"
119
+ }
120
+ ],
121
+ "input_proofs": 5,
122
+ "input_units": 2,
123
+ "proofs": 0,
124
+ "published_proofs": 0,
125
+ "published_transitions": 0,
126
+ "replay_failures": [],
127
+ "transitions": 0,
128
+ "validation_failures": [],
129
+ "validation_rejected_proofs": 0,
130
+ "zero_transition_proofs": 0
131
+ },
132
+ "shards": [],
133
+ "proof_ids": [],
134
+ "proof_keys": []
135
+ }
manifests/batches/mathlib/000618.json ADDED
@@ -0,0 +1,656 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000618",
4
+ "batch_fingerprint": "034faae2086e2c1b5a1181a93d1f4a1e99c67bd25fade11706f40fea67caefaf",
5
+ "evidence": {
6
+ "batch_fingerprint": "034faae2086e2c1b5a1181a93d1f4a1e99c67bd25fade11706f40fea67caefaf",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "CategoryTheory.Equivalence.toOrderIso_symm_apply",
12
+ "id": "CategoryTheory.Equivalence.toOrderIso_symm_apply",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 222,
18
+ 6
19
+ ],
20
+ "file_path": "Mathlib/CategoryTheory/Category/Preorder.lean",
21
+ "full_name": "CategoryTheory.Equivalence.toOrderIso_symm_apply",
22
+ "start": [
23
+ 220,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/CategoryTheory/Category/Preorder.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "CategoryTheory.Functor.monotone",
34
+ "id": "CategoryTheory.Functor.monotone",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 186,
40
+ 91
41
+ ],
42
+ "file_path": "Mathlib/CategoryTheory/Category/Preorder.lean",
43
+ "full_name": "CategoryTheory.Functor.monotone",
44
+ "start": [
45
+ 186,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/CategoryTheory/Category/Preorder.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "CategoryTheory.Iso.to_eq",
56
+ "id": "CategoryTheory.Iso.to_eq",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 196,
62
+ 32
63
+ ],
64
+ "file_path": "Mathlib/CategoryTheory/Category/Preorder.lean",
65
+ "full_name": "CategoryTheory.Iso.to_eq",
66
+ "start": [
67
+ 195,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/CategoryTheory/Category/Preorder.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "CategoryTheory.homOfLE_comp",
78
+ "id": "CategoryTheory.homOfLE_comp",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 84,
84
+ 6
85
+ ],
86
+ "file_path": "Mathlib/CategoryTheory/Category/Preorder.lean",
87
+ "full_name": "CategoryTheory.homOfLE_comp",
88
+ "start": [
89
+ 82,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/CategoryTheory/Category/Preorder.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "CategoryTheory.homOfLE_leOfHom",
100
+ "id": "CategoryTheory.homOfLE_leOfHom",
101
+ "reason": "import_failure",
102
+ "selection": {
103
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
104
+ "end": [
105
+ 107,
106
+ 6
107
+ ],
108
+ "file_path": "Mathlib/CategoryTheory/Category/Preorder.lean",
109
+ "full_name": "CategoryTheory.homOfLE_leOfHom",
110
+ "start": [
111
+ 106,
112
+ 1
113
+ ],
114
+ "traced_tactics": [],
115
+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
+ "source_file": "Mathlib/CategoryTheory/Category/Preorder.lean"
118
+ },
119
+ {
120
+ "error": "theorem has no selected tactic transitions",
121
+ "full_name": "CategoryTheory.homOfLE_refl",
122
+ "id": "CategoryTheory.homOfLE_refl",
123
+ "reason": "import_failure",
124
+ "selection": {
125
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
126
+ "end": [
127
+ 78,
128
+ 6
129
+ ],
130
+ "file_path": "Mathlib/CategoryTheory/Category/Preorder.lean",
131
+ "full_name": "CategoryTheory.homOfLE_refl",
132
+ "start": [
133
+ 77,
134
+ 1
135
+ ],
136
+ "traced_tactics": [],
137
+ "url": "https://github.com/leanprover-community/mathlib4"
138
+ },
139
+ "source_file": "Mathlib/CategoryTheory/Category/Preorder.lean"
140
+ },
141
+ {
142
+ "error": "theorem has no selected tactic transitions",
143
+ "full_name": "CategoryTheory.leOfHom",
144
+ "id": "CategoryTheory.leOfHom",
145
+ "reason": "import_failure",
146
+ "selection": {
147
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
148
+ "end": [
149
+ 90,
150
+ 14
151
+ ],
152
+ "file_path": "Mathlib/CategoryTheory/Category/Preorder.lean",
153
+ "full_name": "CategoryTheory.leOfHom",
154
+ "start": [
155
+ 89,
156
+ 1
157
+ ],
158
+ "traced_tactics": [],
159
+ "url": "https://github.com/leanprover-community/mathlib4"
160
+ },
161
+ "source_file": "Mathlib/CategoryTheory/Category/Preorder.lean"
162
+ },
163
+ {
164
+ "error": "theorem has no selected tactic transitions",
165
+ "full_name": "CategoryTheory.leOfHom_homOfLE",
166
+ "id": "CategoryTheory.leOfHom_homOfLE",
167
+ "reason": "import_failure",
168
+ "selection": {
169
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
170
+ "end": [
171
+ 100,
172
+ 6
173
+ ],
174
+ "file_path": "Mathlib/CategoryTheory/Category/Preorder.lean",
175
+ "full_name": "CategoryTheory.leOfHom_homOfLE",
176
+ "start": [
177
+ 99,
178
+ 1
179
+ ],
180
+ "traced_tactics": [],
181
+ "url": "https://github.com/leanprover-community/mathlib4"
182
+ },
183
+ "source_file": "Mathlib/CategoryTheory/Category/Preorder.lean"
184
+ },
185
+ {
186
+ "error": "theorem has no selected tactic transitions",
187
+ "full_name": "CategoryTheory.le_of_op_hom",
188
+ "id": "CategoryTheory.le_of_op_hom",
189
+ "reason": "import_failure",
190
+ "selection": {
191
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
192
+ "end": [
193
+ 116,
194
+ 12
195
+ ],
196
+ "file_path": "Mathlib/CategoryTheory/Category/Preorder.lean",
197
+ "full_name": "CategoryTheory.le_of_op_hom",
198
+ "start": [
199
+ 115,
200
+ 1
201
+ ],
202
+ "traced_tactics": [],
203
+ "url": "https://github.com/leanprover-community/mathlib4"
204
+ },
205
+ "source_file": "Mathlib/CategoryTheory/Category/Preorder.lean"
206
+ },
207
+ {
208
+ "error": "theorem has no selected tactic transitions",
209
+ "full_name": "Monotone.functor_obj",
210
+ "id": "Monotone.functor_obj",
211
+ "reason": "import_failure",
212
+ "selection": {
213
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
214
+ "end": [
215
+ 160,
216
+ 6
217
+ ],
218
+ "file_path": "Mathlib/CategoryTheory/Category/Preorder.lean",
219
+ "full_name": "Monotone.functor_obj",
220
+ "start": [
221
+ 159,
222
+ 1
223
+ ],
224
+ "traced_tactics": [],
225
+ "url": "https://github.com/leanprover-community/mathlib4"
226
+ },
227
+ "source_file": "Mathlib/CategoryTheory/Category/Preorder.lean"
228
+ },
229
+ {
230
+ "error": "theorem has no selected tactic transitions",
231
+ "full_name": "CategoryTheory.RelCat.Hom.rel_comp",
232
+ "id": "CategoryTheory.RelCat.Hom.rel_comp",
233
+ "reason": "import_failure",
234
+ "selection": {
235
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
236
+ "end": [
237
+ 60,
238
+ 98
239
+ ],
240
+ "file_path": "Mathlib/CategoryTheory/Category/RelCat.lean",
241
+ "full_name": "CategoryTheory.RelCat.Hom.rel_comp",
242
+ "start": [
243
+ 60,
244
+ 11
245
+ ],
246
+ "traced_tactics": [],
247
+ "url": "https://github.com/leanprover-community/mathlib4"
248
+ },
249
+ "source_file": "Mathlib/CategoryTheory/Category/RelCat.lean"
250
+ },
251
+ {
252
+ "error": "theorem has no selected tactic transitions",
253
+ "full_name": "CategoryTheory.RelCat.Hom.rel_id",
254
+ "id": "CategoryTheory.RelCat.Hom.rel_id",
255
+ "reason": "import_failure",
256
+ "selection": {
257
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
258
+ "end": [
259
+ 58,
260
+ 61
261
+ ],
262
+ "file_path": "Mathlib/CategoryTheory/Category/RelCat.lean",
263
+ "full_name": "CategoryTheory.RelCat.Hom.rel_id",
264
+ "start": [
265
+ 58,
266
+ 11
267
+ ],
268
+ "traced_tactics": [],
269
+ "url": "https://github.com/leanprover-community/mathlib4"
270
+ },
271
+ "source_file": "Mathlib/CategoryTheory/Category/RelCat.lean"
272
+ },
273
+ {
274
+ "error": "theorem has no selected tactic transitions",
275
+ "full_name": "CategoryTheory.RelCat.graphFunctor_map",
276
+ "id": "CategoryTheory.RelCat.graphFunctor_map",
277
+ "reason": "import_failure",
278
+ "selection": {
279
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
280
+ "end": [
281
+ 83,
282
+ 56
283
+ ],
284
+ "file_path": "Mathlib/CategoryTheory/Category/RelCat.lean",
285
+ "full_name": "CategoryTheory.RelCat.graphFunctor_map",
286
+ "start": [
287
+ 82,
288
+ 9
289
+ ],
290
+ "traced_tactics": [],
291
+ "url": "https://github.com/leanprover-community/mathlib4"
292
+ },
293
+ "source_file": "Mathlib/CategoryTheory/Category/RelCat.lean"
294
+ },
295
+ {
296
+ "error": "theorem has no selected tactic transitions",
297
+ "full_name": "CategoryTheory.RelCat.hom_ext",
298
+ "id": "CategoryTheory.RelCat.hom_ext",
299
+ "reason": "import_failure",
300
+ "selection": {
301
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
302
+ "end": [
303
+ 54,
304
+ 39
305
+ ],
306
+ "file_path": "Mathlib/CategoryTheory/Category/RelCat.lean",
307
+ "full_name": "CategoryTheory.RelCat.hom_ext",
308
+ "start": [
309
+ 53,
310
+ 8
311
+ ],
312
+ "traced_tactics": [],
313
+ "url": "https://github.com/leanprover-community/mathlib4"
314
+ },
315
+ "source_file": "Mathlib/CategoryTheory/Category/RelCat.lean"
316
+ },
317
+ {
318
+ "error": "theorem has no selected tactic transitions",
319
+ "full_name": "CategoryTheory.RelCat.opFunctor_comp_unopFunctor_eq",
320
+ "id": "CategoryTheory.RelCat.opFunctor_comp_unopFunctor_eq",
321
+ "reason": "import_failure",
322
+ "selection": {
323
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
324
+ "end": [
325
+ 158,
326
+ 61
327
+ ],
328
+ "file_path": "Mathlib/CategoryTheory/Category/RelCat.lean",
329
+ "full_name": "CategoryTheory.RelCat.opFunctor_comp_unopFunctor_eq",
330
+ "start": [
331
+ 157,
332
+ 9
333
+ ],
334
+ "traced_tactics": [],
335
+ "url": "https://github.com/leanprover-community/mathlib4"
336
+ },
337
+ "source_file": "Mathlib/CategoryTheory/Category/RelCat.lean"
338
+ },
339
+ {
340
+ "error": "no internal trace for tactic 'intro h'",
341
+ "full_name": "CategoryTheory.RelCat.rel_iso_iff",
342
+ "id": "CategoryTheory.RelCat.rel_iso_iff",
343
+ "reason": "import_failure",
344
+ "selection": {
345
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
346
+ "end": [
347
+ 122,
348
+ 33
349
+ ],
350
+ "file_path": "Mathlib/CategoryTheory/Category/RelCat.lean",
351
+ "full_name": "CategoryTheory.RelCat.rel_iso_iff",
352
+ "start": [
353
+ 93,
354
+ 1
355
+ ],
356
+ "traced_tactics": [
357
+ {
358
+ "annotated_tactic": [
359
+ "\"constructor\"",
360
+ "[]"
361
+ ],
362
+ "state_after": "case mp\nX Y : RelCat\nr : X \u27f6 Y\n\u22a2 IsIso r \u2192 \u2203 f, graphFunctor.map f.hom = r\n\ncase mpr\nX Y : RelCat\nr : X \u27f6 Y\n\u22a2 (\u2203 f, graphFunctor.map f.hom = r) \u2192 IsIso r",
363
+ "state_before": "X Y : RelCat\nr : X \u27f6 Y\n\u22a2 IsIso r \u2194 \u2203 f, graphFunctor.map f.hom = r",
364
+ "tactic": "constructor"
365
+ },
366
+ {
367
+ "annotated_tactic": [
368
+ "\"intro h\"",
369
+ "[]"
370
+ ],
371
+ "state_after": "case mp\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\n\u22a2 \u2203 f, graphFunctor.map f.hom = r",
372
+ "state_before": "case mp\nX Y : RelCat\nr : X \u27f6 Y\n\u22a2 IsIso r \u2192 \u2203 f, graphFunctor.map f.hom = r",
373
+ "tactic": "intro h"
374
+ },
375
+ {
376
+ "annotated_tactic": [
377
+ "\"have h1 := <a>congr_fun\\u2082<\\/a> h.hom_inv_id\"",
378
+ "[{\"full_name\":\"congr_fun\\u2082\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Logic.lean\",\"def_pos\":[79,7],\"def_end_pos\":[79,17]}]"
379
+ ],
380
+ "state_after": "case mp\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (r \u226b inv r) a b = \ud835\udfd9 X a b\n\u22a2 \u2203 f, graphFunctor.map f.hom = r",
381
+ "state_before": "case mp\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\n\u22a2 \u2203 f, graphFunctor.map f.hom = r",
382
+ "tactic": "have h1 := congr_fun\u2082 h.hom_inv_id"
383
+ },
384
+ {
385
+ "annotated_tactic": [
386
+ "\"have h2 := <a>congr_fun\\u2082<\\/a> h.inv_hom_id\"",
387
+ "[{\"full_name\":\"congr_fun\\u2082\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Logic.lean\",\"def_pos\":[79,7],\"def_end_pos\":[79,17]}]"
388
+ ],
389
+ "state_after": "case mp\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (r \u226b inv r) a b = \ud835\udfd9 X a b\nh2 : \u2200 (a b : Y), (inv r \u226b r) a b = \ud835\udfd9 Y a b\n\u22a2 \u2203 f, graphFunctor.map f.hom = r",
390
+ "state_before": "case mp\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (r \u226b inv r) a b = \ud835\udfd9 X a b\n\u22a2 \u2203 f, graphFunctor.map f.hom = r",
391
+ "tactic": "have h2 := congr_fun\u2082 h.inv_hom_id"
392
+ },
393
+ {
394
+ "annotated_tactic": [
395
+ "\"simp only [<a>RelCat.Hom.rel_comp_apply\\u2082<\\/a>, <a>RelCat.Hom.rel_id_apply\\u2082<\\/a>, <a>eq_iff_iff<\\/a>] at h1 h2\"",
396
+ "[{\"full_name\":\"CategoryTheory.RelCat.Hom.rel_comp_apply\\u2082\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/RelCat.lean\",\"def_pos\":[65,9],\"def_end_pos\":[65,24]},{\"full_name\":\"CategoryTheory.RelCat.Hom.rel_id_apply\\u2082\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/RelCat.lean\",\"def_pos\":[62,9],\"def_end_pos\":[62,22]},{\"full_name\":\"eq_iff_iff\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1378,17],\"def_end_pos\":[1378,27]}]"
397
+ ],
398
+ "state_after": "case mp\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\n\u22a2 \u2203 f, graphFunctor.map f.hom = r",
399
+ "state_before": "case mp\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (r \u226b inv r) a b = \ud835\udfd9 X a b\nh2 : \u2200 (a b : Y), (inv r \u226b r) a b = \ud835\udfd9 Y a b\n\u22a2 \u2203 f, graphFunctor.map f.hom = r",
400
+ "tactic": "simp only [RelCat.Hom.rel_comp_apply\u2082, RelCat.Hom.rel_id_apply\u2082, eq_iff_iff] at h1 h2"
401
+ },
402
+ {
403
+ "annotated_tactic": [
404
+ "\"obtain \\u27e8f, hf\\u27e9 := <a>Classical.axiomOfChoice<\\/a> (fun a => (h1 a a).<a>mpr<\\/a> <a>rfl<\\/a>)\"",
405
+ "[{\"full_name\":\"Classical.axiomOfChoice\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Classical.lean\",\"def_pos\":[113,9],\"def_end_pos\":[113,22]},{\"full_name\":\"Iff.mpr\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[120,3],\"def_end_pos\":[120,6]},{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]}]"
406
+ ],
407
+ "state_after": "case mp.intro\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\n\u22a2 \u2203 f, graphFunctor.map f.hom = r",
408
+ "state_before": "case mp\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\n\u22a2 \u2203 f, graphFunctor.map f.hom = r",
409
+ "tactic": "obtain \u27e8f, hf\u27e9 := Classical.axiomOfChoice (fun a => (h1 a a).mpr rfl)"
410
+ },
411
+ {
412
+ "annotated_tactic": [
413
+ "\"obtain \\u27e8g, hg\\u27e9 := <a>Classical.axiomOfChoice<\\/a> (fun a => (h2 a a).<a>mpr<\\/a> <a>rfl<\\/a>)\"",
414
+ "[{\"full_name\":\"Classical.axiomOfChoice\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Classical.lean\",\"def_pos\":[113,9],\"def_end_pos\":[113,22]},{\"full_name\":\"Iff.mpr\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[120,3],\"def_end_pos\":[120,6]},{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]}]"
415
+ ],
416
+ "state_after": "case mp.intro.intro\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\n\u22a2 \u2203 f, graphFunctor.map f.hom = r",
417
+ "state_before": "case mp.intro\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\n\u22a2 \u2203 f, graphFunctor.map f.hom = r",
418
+ "tactic": "obtain \u27e8g, hg\u27e9 := Classical.axiomOfChoice (fun a => (h2 a a).mpr rfl)"
419
+ },
420
+ {
421
+ "annotated_tactic": [
422
+ "\"use g\"",
423
+ "[]"
424
+ ],
425
+ "state_after": "case h\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\n\u22a2 f \u226b g = \ud835\udfd9 X \u2227 g \u226b f = \ud835\udfd9 Y",
426
+ "state_before": "case mp.intro.intro\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\n\u22a2 IsIso f",
427
+ "tactic": "use g"
428
+ },
429
+ {
430
+ "annotated_tactic": [
431
+ "\"constructor\"",
432
+ "[]"
433
+ ],
434
+ "state_after": "case h.left\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\n\u22a2 f \u226b g = \ud835\udfd9 X\n\ncase h.right\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\n\u22a2 g \u226b f = \ud835\udfd9 Y",
435
+ "state_before": "case h\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\n\u22a2 f \u226b g = \ud835\udfd9 X \u2227 g \u226b f = \ud835\udfd9 Y",
436
+ "tactic": "constructor"
437
+ },
438
+ {
439
+ "annotated_tactic": [
440
+ "\"use <a>asIso<\\/a> f\"",
441
+ "[{\"full_name\":\"CategoryTheory.asIso\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[329,19],\"def_end_pos\":[329,24]}]"
442
+ ],
443
+ "state_after": "case h\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\n\u22a2 graphFunctor.map (asIso f).hom = r",
444
+ "state_before": "X Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\n\u22a2 \u2203 f, graphFunctor.map f.hom = r",
445
+ "tactic": "use asIso f"
446
+ },
447
+ {
448
+ "annotated_tactic": [
449
+ "\"ext x y\"",
450
+ "[]"
451
+ ],
452
+ "state_after": "case h.h\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\nx : graphFunctor.obj X\ny : graphFunctor.obj Y\n\u22a2 graphFunctor.map (asIso f).hom x y \u2194 r x y",
453
+ "state_before": "case h\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\n\u22a2 graphFunctor.map (asIso f).hom = r",
454
+ "tactic": "ext x y"
455
+ },
456
+ {
457
+ "annotated_tactic": [
458
+ "\"simp only [<a>asIso_hom<\\/a>, <a>graphFunctor_map<\\/a>]\"",
459
+ "[{\"full_name\":\"CategoryTheory.asIso_hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[337,9],\"def_end_pos\":[337,18]},{\"full_name\":\"CategoryTheory.RelCat.graphFunctor_map\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/RelCat.lean\",\"def_pos\":[82,17],\"def_end_pos\":[82,33]}]"
460
+ ],
461
+ "state_after": "case h.h\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\nx : graphFunctor.obj X\ny : graphFunctor.obj Y\n\u22a2 f x = y \u2194 r x y",
462
+ "state_before": "case h.h\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\nx : graphFunctor.obj X\ny : graphFunctor.obj Y\n\u22a2 graphFunctor.map (asIso f).hom x y \u2194 r x y",
463
+ "tactic": "simp only [asIso_hom, graphFunctor_map]"
464
+ },
465
+ {
466
+ "annotated_tactic": [
467
+ "\"constructor\"",
468
+ "[]"
469
+ ],
470
+ "state_after": "case h.h.mp\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\nx : graphFunctor.obj X\ny : graphFunctor.obj Y\n\u22a2 f x = y \u2192 r x y\n\ncase h.h.mpr\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\nx : graphFunctor.obj X\ny : graphFunctor.obj Y\n\u22a2 r x y \u2192 f x = y",
471
+ "state_before": "case h.h\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\nx : graphFunctor.obj X\ny : graphFunctor.obj Y\n\u22a2 f x = y \u2194 r x y",
472
+ "tactic": "constructor"
473
+ },
474
+ {
475
+ "annotated_tactic": [
476
+ "\"rintro rfl\"",
477
+ "[]"
478
+ ],
479
+ "state_after": "case h.h.mp\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\nx : graphFunctor.obj X\n\u22a2 r x (f x)",
480
+ "state_before": "case h.h.mp\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\nx : graphFunctor.obj X\ny : graphFunctor.obj Y\n\u22a2 f x = y \u2192 r x y",
481
+ "tactic": "rintro rfl"
482
+ },
483
+ {
484
+ "annotated_tactic": [
485
+ "\"exact (hf x).1\"",
486
+ "[]"
487
+ ],
488
+ "state_after": "no goals",
489
+ "state_before": "case h.h.mp\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\nx : graphFunctor.obj X\n\u22a2 r x (f x)",
490
+ "tactic": "exact (hf x).1"
491
+ },
492
+ {
493
+ "annotated_tactic": [
494
+ "\"intro hr\"",
495
+ "[]"
496
+ ],
497
+ "state_after": "case h.h.mpr\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\nx : graphFunctor.obj X\ny : graphFunctor.obj Y\nhr : r x y\n\u22a2 f x = y",
498
+ "state_before": "case h.h.mpr\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\nx : graphFunctor.obj X\ny : graphFunctor.obj Y\n\u22a2 r x y \u2192 f x = y",
499
+ "tactic": "intro hr"
500
+ },
501
+ {
502
+ "annotated_tactic": [
503
+ "\"specialize h2 (f x) y\"",
504
+ "[]"
505
+ ],
506
+ "state_after": "case h.h.mpr\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\nx : graphFunctor.obj X\ny : graphFunctor.obj Y\nhr : r x y\nh2 : (\u2203 y_1, inv r (f x) y_1 \u2227 r y_1 y) \u2194 f x = y\n\u22a2 f x = y",
507
+ "state_before": "case h.h.mpr\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\nx : graphFunctor.obj X\ny : graphFunctor.obj Y\nhr : r x y\n\u22a2 f x = y",
508
+ "tactic": "specialize h2 (f x) y"
509
+ },
510
+ {
511
+ "annotated_tactic": [
512
+ "\"rw [\\u2190 h2]\"",
513
+ "[]"
514
+ ],
515
+ "state_after": "case h.h.mpr\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\nx : graphFunctor.obj X\ny : graphFunctor.obj Y\nhr : r x y\nh2 : (\u2203 y_1, inv r (f x) y_1 \u2227 r y_1 y) \u2194 f x = y\n\u22a2 \u2203 y_1, inv r (f x) y_1 \u2227 r y_1 y",
516
+ "state_before": "case h.h.mpr\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\nx : graphFunctor.obj X\ny : graphFunctor.obj Y\nhr : r x y\nh2 : (\u2203 y_1, inv r (f x) y_1 \u2227 r y_1 y) \u2194 f x = y\n\u22a2 f x = y",
517
+ "tactic": "rw [\u2190 h2]"
518
+ },
519
+ {
520
+ "annotated_tactic": [
521
+ "\"use x, (hf x).2, hr\"",
522
+ "[]"
523
+ ],
524
+ "state_after": "no goals",
525
+ "state_before": "case h.h.mpr\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nhif : IsIso f\nx : graphFunctor.obj X\ny : graphFunctor.obj Y\nhr : r x y\nh2 : (\u2203 y_1, inv r (f x) y_1 \u2227 r y_1 y) \u2194 f x = y\n\u22a2 \u2203 y_1, inv r (f x) y_1 \u2227 r y_1 y",
526
+ "tactic": "use x, (hf x).2, hr"
527
+ },
528
+ {
529
+ "annotated_tactic": [
530
+ "\"ext x\"",
531
+ "[]"
532
+ ],
533
+ "state_after": "case h.left.h\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nx : X\n\u22a2 (f \u226b g) x = \ud835\udfd9 X x",
534
+ "state_before": "case h.left\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\n\u22a2 f \u226b g = \ud835\udfd9 X",
535
+ "tactic": "ext x"
536
+ },
537
+ {
538
+ "annotated_tactic": [
539
+ "\"apply (h1 _ _).<a>mp<\\/a>\"",
540
+ "[{\"full_name\":\"Iff.mp\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[118,3],\"def_end_pos\":[118,5]}]"
541
+ ],
542
+ "state_after": "case h.left.h\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nx : X\n\u22a2 \u2203 y, r ((f \u226b g) x) y \u2227 inv r y (\ud835\udfd9 X x)",
543
+ "state_before": "case h.left.h\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nx : X\n\u22a2 (f \u226b g) x = \ud835\udfd9 X x",
544
+ "tactic": "apply (h1 _ _).mp"
545
+ },
546
+ {
547
+ "annotated_tactic": [
548
+ "\"use f x, (hg _).2, (hf _).2\"",
549
+ "[]"
550
+ ],
551
+ "state_after": "no goals",
552
+ "state_before": "case h.left.h\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\nx : X\n\u22a2 \u2203 y, r ((f \u226b g) x) y \u2227 inv r y (\ud835\udfd9 X x)",
553
+ "tactic": "use f x, (hg _).2, (hf _).2"
554
+ },
555
+ {
556
+ "annotated_tactic": [
557
+ "\"ext y\"",
558
+ "[]"
559
+ ],
560
+ "state_after": "case h.right.h\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\ny : Y\n\u22a2 (g \u226b f) y = \ud835\udfd9 Y y",
561
+ "state_before": "case h.right\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\n\u22a2 g \u226b f = \ud835\udfd9 Y",
562
+ "tactic": "ext y"
563
+ },
564
+ {
565
+ "annotated_tactic": [
566
+ "\"apply (h2 _ _).<a>mp<\\/a>\"",
567
+ "[{\"full_name\":\"Iff.mp\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[118,3],\"def_end_pos\":[118,5]}]"
568
+ ],
569
+ "state_after": "case h.right.h\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\ny : Y\n\u22a2 \u2203 y_1, inv r ((g \u226b f) y) y_1 \u2227 r y_1 (\ud835\udfd9 Y y)",
570
+ "state_before": "case h.right.h\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\ny : Y\n\u22a2 (g \u226b f) y = \ud835\udfd9 Y y",
571
+ "tactic": "apply (h2 _ _).mp"
572
+ },
573
+ {
574
+ "annotated_tactic": [
575
+ "\"use g y, (hf (g y)).2, (hg y).2\"",
576
+ "[]"
577
+ ],
578
+ "state_after": "no goals",
579
+ "state_before": "case h.right.h\nX Y : RelCat\nr : X \u27f6 Y\nh : IsIso r\nh1 : \u2200 (a b : X), (\u2203 y, r a y \u2227 inv r y b) \u2194 a = b\nh2 : \u2200 (a b : Y), (\u2203 y, inv r a y \u2227 r y b) \u2194 a = b\nf : X \u2192 Y\nhf : \u2200 (x : X), r x (f x) \u2227 inv r (f x) x\ng : Y \u2192 X\nhg : \u2200 (x : Y), inv r x (g x) \u2227 r (g x) x\ny : Y\n\u22a2 \u2203 y_1, inv r ((g \u226b f) y) y_1 \u2227 r y_1 (\ud835\udfd9 Y y)",
580
+ "tactic": "use g y, (hf (g y)).2, (hg y).2"
581
+ },
582
+ {
583
+ "annotated_tactic": [
584
+ "\"rintro \\u27e8f, rfl\\u27e9\"",
585
+ "[]"
586
+ ],
587
+ "state_after": "case mpr.intro\nX Y : RelCat\nf : X \u2245 Y\n\u22a2 IsIso (graphFunctor.map f.hom)",
588
+ "state_before": "case mpr\nX Y : RelCat\nr : X \u27f6 Y\n\u22a2 (\u2203 f, graphFunctor.map f.hom = r) \u2192 IsIso r",
589
+ "tactic": "rintro \u27e8f, rfl\u27e9"
590
+ },
591
+ {
592
+ "annotated_tactic": [
593
+ "\"apply graphFunctor.map_isIso\"",
594
+ "[]"
595
+ ],
596
+ "state_after": "no goals",
597
+ "state_before": "case mpr.intro\nX Y : RelCat\nf : X \u2245 Y\n\u22a2 IsIso (graphFunctor.map f.hom)",
598
+ "tactic": "apply graphFunctor.map_isIso"
599
+ }
600
+ ],
601
+ "url": "https://github.com/leanprover-community/mathlib4"
602
+ },
603
+ "source_file": "Mathlib/CategoryTheory/Category/RelCat.lean"
604
+ },
605
+ {
606
+ "error": "theorem has no selected tactic transitions",
607
+ "full_name": "CategoryTheory.RelCat.unopFunctor_comp_opFunctor_eq",
608
+ "id": "CategoryTheory.RelCat.unopFunctor_comp_opFunctor_eq",
609
+ "reason": "import_failure",
610
+ "selection": {
611
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
612
+ "end": [
613
+ 161,
614
+ 61
615
+ ],
616
+ "file_path": "Mathlib/CategoryTheory/Category/RelCat.lean",
617
+ "full_name": "CategoryTheory.RelCat.unopFunctor_comp_opFunctor_eq",
618
+ "start": [
619
+ 160,
620
+ 9
621
+ ],
622
+ "traced_tactics": [],
623
+ "url": "https://github.com/leanprover-community/mathlib4"
624
+ },
625
+ "source_file": "Mathlib/CategoryTheory/Category/RelCat.lean"
626
+ }
627
+ ],
628
+ "input_proofs": 19,
629
+ "input_units": 2,
630
+ "proofs": 2,
631
+ "published_proofs": 2,
632
+ "published_transitions": 2,
633
+ "replay_failures": [],
634
+ "transitions": 2,
635
+ "validation_failures": [],
636
+ "validation_rejected_proofs": 0,
637
+ "zero_transition_proofs": 0
638
+ },
639
+ "shards": [
640
+ {
641
+ "path": "data/train/mathlib-000618-0000-314cdf7d43e597ea.parquet",
642
+ "sha256": "314cdf7d43e597ea8eb6bab905090df343889467465c6f74e232cb0eebc36a9c",
643
+ "bytes": 28270,
644
+ "rows": 2,
645
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
646
+ }
647
+ ],
648
+ "proof_ids": [
649
+ "mathlib:CategoryTheory.RelCat.Hom.rel_comp_apply\u2082",
650
+ "mathlib:CategoryTheory.RelCat.Hom.rel_id_apply\u2082"
651
+ ],
652
+ "proof_keys": [
653
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/RelCat.lean\",null,null,\"CategoryTheory.RelCat.Hom.rel_comp_apply\u2082\"]",
654
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Category/RelCat.lean\",null,null,\"CategoryTheory.RelCat.Hom.rel_id_apply\u2082\"]"
655
+ ]
656
+ }
manifests/batches/mathlib/000619.json ADDED
@@ -0,0 +1,245 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000619",
4
+ "batch_fingerprint": "714e79b2516c01683fbf194a292b90f0fca83d4c7fcc57070f1ddfd0f4fbdf93",
5
+ "evidence": {
6
+ "batch_fingerprint": "714e79b2516c01683fbf194a292b90f0fca83d4c7fcc57070f1ddfd0f4fbdf93",
7
+ "batch_outcome": "all_inputs_failed_with_evidence",
8
+ "contamination_matches": [],
9
+ "failures": [
10
+ {
11
+ "error": "theorem has no selected tactic transitions",
12
+ "full_name": "TwoP.coe_of",
13
+ "id": "TwoP.coe_of",
14
+ "reason": "import_failure",
15
+ "selection": {
16
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
17
+ "end": [
18
+ 51,
19
+ 6
20
+ ],
21
+ "file_path": "Mathlib/CategoryTheory/Category/TwoP.lean",
22
+ "full_name": "TwoP.coe_of",
23
+ "start": [
24
+ 50,
25
+ 1
26
+ ],
27
+ "traced_tactics": [],
28
+ "url": "https://github.com/leanprover-community/mathlib4"
29
+ },
30
+ "source_file": "Mathlib/CategoryTheory/Category/TwoP.lean"
31
+ },
32
+ {
33
+ "error": "theorem has no selected tactic transitions",
34
+ "full_name": "TwoP.coe_toBipointed",
35
+ "id": "TwoP.coe_toBipointed",
36
+ "reason": "import_failure",
37
+ "selection": {
38
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
39
+ "end": [
40
+ 68,
41
+ 6
42
+ ],
43
+ "file_path": "Mathlib/CategoryTheory/Category/TwoP.lean",
44
+ "full_name": "TwoP.coe_toBipointed",
45
+ "start": [
46
+ 67,
47
+ 1
48
+ ],
49
+ "traced_tactics": [],
50
+ "url": "https://github.com/leanprover-community/mathlib4"
51
+ },
52
+ "source_file": "Mathlib/CategoryTheory/Category/TwoP.lean"
53
+ },
54
+ {
55
+ "error": "theorem has no selected tactic transitions",
56
+ "full_name": "TwoP.swapEquiv_symm",
57
+ "id": "TwoP.swapEquiv_symm",
58
+ "reason": "import_failure",
59
+ "selection": {
60
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
61
+ "end": [
62
+ 105,
63
+ 6
64
+ ],
65
+ "file_path": "Mathlib/CategoryTheory/Category/TwoP.lean",
66
+ "full_name": "TwoP.swapEquiv_symm",
67
+ "start": [
68
+ 104,
69
+ 1
70
+ ],
71
+ "traced_tactics": [],
72
+ "url": "https://github.com/leanprover-community/mathlib4"
73
+ },
74
+ "source_file": "Mathlib/CategoryTheory/Category/TwoP.lean"
75
+ },
76
+ {
77
+ "error": "theorem has no selected tactic transitions",
78
+ "full_name": "TwoP_swap_comp_forget_to_Bipointed",
79
+ "id": "TwoP_swap_comp_forget_to_Bipointed",
80
+ "reason": "import_failure",
81
+ "selection": {
82
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
83
+ "end": [
84
+ 113,
85
+ 6
86
+ ],
87
+ "file_path": "Mathlib/CategoryTheory/Category/TwoP.lean",
88
+ "full_name": "TwoP_swap_comp_forget_to_Bipointed",
89
+ "start": [
90
+ 111,
91
+ 1
92
+ ],
93
+ "traced_tactics": [],
94
+ "url": "https://github.com/leanprover-community/mathlib4"
95
+ },
96
+ "source_file": "Mathlib/CategoryTheory/Category/TwoP.lean"
97
+ },
98
+ {
99
+ "error": "theorem has no selected tactic transitions",
100
+ "full_name": "pointedToTwoPFst_comp_forget_to_bipointed",
101
+ "id": "pointedToTwoPFst_comp_forget_to_bipointed",
102
+ "reason": "import_failure",
103
+ "selection": {
104
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
105
+ "end": [
106
+ 147,
107
+ 6
108
+ ],
109
+ "file_path": "Mathlib/CategoryTheory/Category/TwoP.lean",
110
+ "full_name": "pointedToTwoPFst_comp_forget_to_bipointed",
111
+ "start": [
112
+ 145,
113
+ 1
114
+ ],
115
+ "traced_tactics": [],
116
+ "url": "https://github.com/leanprover-community/mathlib4"
117
+ },
118
+ "source_file": "Mathlib/CategoryTheory/Category/TwoP.lean"
119
+ },
120
+ {
121
+ "error": "theorem has no selected tactic transitions",
122
+ "full_name": "pointedToTwoPFst_comp_swap",
123
+ "id": "pointedToTwoPFst_comp_swap",
124
+ "reason": "import_failure",
125
+ "selection": {
126
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
127
+ "end": [
128
+ 136,
129
+ 6
130
+ ],
131
+ "file_path": "Mathlib/CategoryTheory/Category/TwoP.lean",
132
+ "full_name": "pointedToTwoPFst_comp_swap",
133
+ "start": [
134
+ 135,
135
+ 1
136
+ ],
137
+ "traced_tactics": [],
138
+ "url": "https://github.com/leanprover-community/mathlib4"
139
+ },
140
+ "source_file": "Mathlib/CategoryTheory/Category/TwoP.lean"
141
+ },
142
+ {
143
+ "error": "theorem has no selected tactic transitions",
144
+ "full_name": "pointedToTwoPSnd_comp_forget_to_bipointed",
145
+ "id": "pointedToTwoPSnd_comp_forget_to_bipointed",
146
+ "reason": "import_failure",
147
+ "selection": {
148
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
149
+ "end": [
150
+ 153,
151
+ 6
152
+ ],
153
+ "file_path": "Mathlib/CategoryTheory/Category/TwoP.lean",
154
+ "full_name": "pointedToTwoPSnd_comp_forget_to_bipointed",
155
+ "start": [
156
+ 151,
157
+ 1
158
+ ],
159
+ "traced_tactics": [],
160
+ "url": "https://github.com/leanprover-community/mathlib4"
161
+ },
162
+ "source_file": "Mathlib/CategoryTheory/Category/TwoP.lean"
163
+ },
164
+ {
165
+ "error": "theorem has no selected tactic transitions",
166
+ "full_name": "pointedToTwoPSnd_comp_swap",
167
+ "id": "pointedToTwoPSnd_comp_swap",
168
+ "reason": "import_failure",
169
+ "selection": {
170
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
171
+ "end": [
172
+ 141,
173
+ 6
174
+ ],
175
+ "file_path": "Mathlib/CategoryTheory/Category/TwoP.lean",
176
+ "full_name": "pointedToTwoPSnd_comp_swap",
177
+ "start": [
178
+ 140,
179
+ 1
180
+ ],
181
+ "traced_tactics": [],
182
+ "url": "https://github.com/leanprover-community/mathlib4"
183
+ },
184
+ "source_file": "Mathlib/CategoryTheory/Category/TwoP.lean"
185
+ },
186
+ {
187
+ "error": "theorem has no selected tactic transitions",
188
+ "full_name": "CategoryTheory.objDown_objUp",
189
+ "id": "CategoryTheory.objDown_objUp",
190
+ "reason": "import_failure",
191
+ "selection": {
192
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
193
+ "end": [
194
+ 121,
195
+ 6
196
+ ],
197
+ "file_path": "Mathlib/CategoryTheory/Category/ULift.lean",
198
+ "full_name": "CategoryTheory.objDown_objUp",
199
+ "start": [
200
+ 120,
201
+ 1
202
+ ],
203
+ "traced_tactics": [],
204
+ "url": "https://github.com/leanprover-community/mathlib4"
205
+ },
206
+ "source_file": "Mathlib/CategoryTheory/Category/ULift.lean"
207
+ },
208
+ {
209
+ "error": "theorem has no selected tactic transitions",
210
+ "full_name": "CategoryTheory.objUp_objDown",
211
+ "id": "CategoryTheory.objUp_objDown",
212
+ "reason": "import_failure",
213
+ "selection": {
214
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
215
+ "end": [
216
+ 126,
217
+ 6
218
+ ],
219
+ "file_path": "Mathlib/CategoryTheory/Category/ULift.lean",
220
+ "full_name": "CategoryTheory.objUp_objDown",
221
+ "start": [
222
+ 125,
223
+ 1
224
+ ],
225
+ "traced_tactics": [],
226
+ "url": "https://github.com/leanprover-community/mathlib4"
227
+ },
228
+ "source_file": "Mathlib/CategoryTheory/Category/ULift.lean"
229
+ }
230
+ ],
231
+ "input_proofs": 10,
232
+ "input_units": 2,
233
+ "proofs": 0,
234
+ "published_proofs": 0,
235
+ "published_transitions": 0,
236
+ "replay_failures": [],
237
+ "transitions": 0,
238
+ "validation_failures": [],
239
+ "validation_rejected_proofs": 0,
240
+ "zero_transition_proofs": 0
241
+ },
242
+ "shards": [],
243
+ "proof_ids": [],
244
+ "proof_keys": []
245
+ }
manifests/batches/mathlib/000620.json ADDED
@@ -0,0 +1,489 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000620",
4
+ "batch_fingerprint": "f20bd6f556f6e5e0175f55879d8ead346812e0b8c056121f49a02e4865788ef7",
5
+ "evidence": {
6
+ "batch_fingerprint": "f20bd6f556f6e5e0175f55879d8ead346812e0b8c056121f49a02e4865788ef7",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "CategoryTheory.ChosenFiniteProducts.associator_hom_fst",
12
+ "id": "CategoryTheory.ChosenFiniteProducts.associator_hom_fst",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 143,
18
+ 65
19
+ ],
20
+ "file_path": "Mathlib/CategoryTheory/ChosenFiniteProducts.lean",
21
+ "full_name": "CategoryTheory.ChosenFiniteProducts.associator_hom_fst",
22
+ "start": [
23
+ 141,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/CategoryTheory/ChosenFiniteProducts.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "CategoryTheory.ChosenFiniteProducts.associator_inv_snd",
34
+ "id": "CategoryTheory.ChosenFiniteProducts.associator_inv_snd",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 171,
40
+ 65
41
+ ],
42
+ "file_path": "Mathlib/CategoryTheory/ChosenFiniteProducts.lean",
43
+ "full_name": "CategoryTheory.ChosenFiniteProducts.associator_inv_snd",
44
+ "start": [
45
+ 169,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/CategoryTheory/ChosenFiniteProducts.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "CategoryTheory.ChosenFiniteProducts.hom_ext",
56
+ "id": "CategoryTheory.ChosenFiniteProducts.hom_ext",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 111,
62
+ 63
63
+ ],
64
+ "file_path": "Mathlib/CategoryTheory/ChosenFiniteProducts.lean",
65
+ "full_name": "CategoryTheory.ChosenFiniteProducts.hom_ext",
66
+ "start": [
67
+ 106,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/CategoryTheory/ChosenFiniteProducts.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "CategoryTheory.ChosenFiniteProducts.tensorHom_fst",
78
+ "id": "CategoryTheory.ChosenFiniteProducts.tensorHom_fst",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 115,
84
+ 52
85
+ ],
86
+ "file_path": "Mathlib/CategoryTheory/ChosenFiniteProducts.lean",
87
+ "full_name": "CategoryTheory.ChosenFiniteProducts.tensorHom_fst",
88
+ "start": [
89
+ 113,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/CategoryTheory/ChosenFiniteProducts.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "CategoryTheory.ChosenFiniteProducts.tensorHom_snd",
100
+ "id": "CategoryTheory.ChosenFiniteProducts.tensorHom_snd",
101
+ "reason": "import_failure",
102
+ "selection": {
103
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
104
+ "end": [
105
+ 119,
106
+ 52
107
+ ],
108
+ "file_path": "Mathlib/CategoryTheory/ChosenFiniteProducts.lean",
109
+ "full_name": "CategoryTheory.ChosenFiniteProducts.tensorHom_snd",
110
+ "start": [
111
+ 117,
112
+ 1
113
+ ],
114
+ "traced_tactics": [],
115
+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
+ "source_file": "Mathlib/CategoryTheory/ChosenFiniteProducts.lean"
118
+ },
119
+ {
120
+ "error": "theorem has no selected tactic transitions",
121
+ "full_name": "CategoryTheory.ChosenFiniteProducts.toUnit_unique",
122
+ "id": "CategoryTheory.ChosenFiniteProducts.toUnit_unique",
123
+ "reason": "import_failure",
124
+ "selection": {
125
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
126
+ "end": [
127
+ 76,
128
+ 24
129
+ ],
130
+ "file_path": "Mathlib/CategoryTheory/ChosenFiniteProducts.lean",
131
+ "full_name": "CategoryTheory.ChosenFiniteProducts.toUnit_unique",
132
+ "start": [
133
+ 70,
134
+ 1
135
+ ],
136
+ "traced_tactics": [],
137
+ "url": "https://github.com/leanprover-community/mathlib4"
138
+ },
139
+ "source_file": "Mathlib/CategoryTheory/ChosenFiniteProducts.lean"
140
+ },
141
+ {
142
+ "error": "theorem has no selected tactic transitions",
143
+ "full_name": "CategoryTheory.ChosenFiniteProducts.whiskerLeft_snd",
144
+ "id": "CategoryTheory.ChosenFiniteProducts.whiskerLeft_snd",
145
+ "reason": "import_failure",
146
+ "selection": {
147
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
148
+ "end": [
149
+ 129,
150
+ 20
151
+ ],
152
+ "file_path": "Mathlib/CategoryTheory/ChosenFiniteProducts.lean",
153
+ "full_name": "CategoryTheory.ChosenFiniteProducts.whiskerLeft_snd",
154
+ "start": [
155
+ 126,
156
+ 1
157
+ ],
158
+ "traced_tactics": [],
159
+ "url": "https://github.com/leanprover-community/mathlib4"
160
+ },
161
+ "source_file": "Mathlib/CategoryTheory/ChosenFiniteProducts.lean"
162
+ },
163
+ {
164
+ "error": "theorem has no selected tactic transitions",
165
+ "full_name": "CategoryTheory.ChosenFiniteProducts.whiskerRight_fst",
166
+ "id": "CategoryTheory.ChosenFiniteProducts.whiskerRight_fst",
167
+ "reason": "import_failure",
168
+ "selection": {
169
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
170
+ "end": [
171
+ 134,
172
+ 20
173
+ ],
174
+ "file_path": "Mathlib/CategoryTheory/ChosenFiniteProducts.lean",
175
+ "full_name": "CategoryTheory.ChosenFiniteProducts.whiskerRight_fst",
176
+ "start": [
177
+ 131,
178
+ 1
179
+ ],
180
+ "traced_tactics": [],
181
+ "url": "https://github.com/leanprover-community/mathlib4"
182
+ },
183
+ "source_file": "Mathlib/CategoryTheory/ChosenFiniteProducts.lean"
184
+ },
185
+ {
186
+ "error": "no internal trace for tactic 'change _ \u226b (fst F\u2081 (F\u2082 \u2297 F\u2083)).app j = _'",
187
+ "full_name": "CategoryTheory.Functor.Monoidal.associator_hom_app",
188
+ "id": "CategoryTheory.Functor.Monoidal.associator_hom_app",
189
+ "reason": "import_failure",
190
+ "selection": {
191
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
192
+ "end": [
193
+ 147,
194
+ 10
195
+ ],
196
+ "file_path": "Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean",
197
+ "full_name": "CategoryTheory.Functor.Monoidal.associator_hom_app",
198
+ "start": [
199
+ 131,
200
+ 1
201
+ ],
202
+ "traced_tactics": [
203
+ {
204
+ "annotated_tactic": [
205
+ "\"apply <a>hom_ext<\\/a>\"",
206
+ "[{\"full_name\":\"CategoryTheory.ChosenFiniteProducts.hom_ext\",\"def_path\":\"Mathlib\\/CategoryTheory\\/ChosenFiniteProducts.lean\",\"def_pos\":[107,7],\"def_end_pos\":[107,14]}]"
207
+ ],
208
+ "state_after": "case h_fst\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (\u03b1_ F\u2081 F\u2082 F\u2083).hom.app j \u226b fst (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j) =\n (\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b fst (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)\n\ncase h_snd\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (\u03b1_ F\u2081 F\u2082 F\u2083).hom.app j \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j) =\n (\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)",
209
+ "state_before": "J : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (\u03b1_ F\u2081 F\u2082 F\u2083).hom.app j = (\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom",
210
+ "tactic": "apply hom_ext"
211
+ },
212
+ {
213
+ "annotated_tactic": [
214
+ "\"change _ \\u226b (<a>fst<\\/a> F\\u2081 (F\\u2082 \\u2297 F\\u2083)).<a>app<\\/a> j = _\"",
215
+ "[{\"full_name\":\"CategoryTheory.ChosenFiniteProducts.fst\",\"def_path\":\"Mathlib\\/CategoryTheory\\/ChosenFiniteProducts.lean\",\"def_pos\":[87,5],\"def_end_pos\":[87,8]},{\"full_name\":\"CategoryTheory.NatTrans.app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/NatTrans.lean\",\"def_pos\":[50,3],\"def_end_pos\":[50,6]}]"
216
+ ],
217
+ "state_after": "case h_fst\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (\u03b1_ F\u2081 F\u2082 F\u2083).hom.app j \u226b (fst F\u2081 (F\u2082 \u2297 F\u2083)).app j =\n (\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b fst (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)",
218
+ "state_before": "case h_fst\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (\u03b1_ F\u2081 F\u2082 F\u2083).hom.app j \u226b fst (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j) =\n (\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b fst (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)",
219
+ "tactic": "change _ \u226b (fst F\u2081 (F\u2082 \u2297 F\u2083)).app j = _"
220
+ },
221
+ {
222
+ "annotated_tactic": [
223
+ "\"rw [\\u2190 <a>NatTrans.comp_app<\\/a>, <a>associator_hom_fst<\\/a>]\"",
224
+ "[{\"full_name\":\"CategoryTheory.NatTrans.comp_app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Category.lean\",\"def_pos\":[76,9],\"def_end_pos\":[76,17]},{\"full_name\":\"CategoryTheory.ChosenFiniteProducts.associator_hom_fst\",\"def_path\":\"Mathlib\\/CategoryTheory\\/ChosenFiniteProducts.lean\",\"def_pos\":[142,7],\"def_end_pos\":[142,25]}]"
225
+ ],
226
+ "state_after": "case h_fst\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (fst (F\u2081 \u2297 F\u2082) F\u2083 \u226b fst F\u2081 F\u2082).app j = (\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b fst (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)",
227
+ "state_before": "case h_fst\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (\u03b1_ F\u2081 F\u2082 F\u2083).hom.app j \u226b (fst F\u2081 (F\u2082 \u2297 F\u2083)).app j =\n (\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b fst (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)",
228
+ "tactic": "rw [\u2190 NatTrans.comp_app, associator_hom_fst]"
229
+ },
230
+ {
231
+ "annotated_tactic": [
232
+ "\"erw [<a>associator_hom_fst<\\/a>]\"",
233
+ "[{\"full_name\":\"CategoryTheory.ChosenFiniteProducts.associator_hom_fst\",\"def_path\":\"Mathlib\\/CategoryTheory\\/ChosenFiniteProducts.lean\",\"def_pos\":[142,7],\"def_end_pos\":[142,25]}]"
234
+ ],
235
+ "state_after": "case h_fst\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (fst (F\u2081 \u2297 F\u2082) F\u2083 \u226b fst F\u2081 F\u2082).app j = fst (F\u2081.obj j \u2297 F\u2082.obj j) (F\u2083.obj j) \u226b fst (F\u2081.obj j) (F\u2082.obj j)",
236
+ "state_before": "case h_fst\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (fst (F\u2081 \u2297 F\u2082) F\u2083 \u226b fst F\u2081 F\u2082).app j = (\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b fst (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)",
237
+ "tactic": "erw [associator_hom_fst]"
238
+ },
239
+ {
240
+ "annotated_tactic": [
241
+ "\"rfl\"",
242
+ "[]"
243
+ ],
244
+ "state_after": "no goals",
245
+ "state_before": "case h_fst\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (fst (F\u2081 \u2297 F\u2082) F\u2083 \u226b fst F\u2081 F\u2082).app j = fst (F\u2081.obj j \u2297 F\u2082.obj j) (F\u2083.obj j) \u226b fst (F\u2081.obj j) (F\u2082.obj j)",
246
+ "tactic": "rfl"
247
+ },
248
+ {
249
+ "annotated_tactic": [
250
+ "\"apply <a>hom_ext<\\/a>\"",
251
+ "[{\"full_name\":\"CategoryTheory.ChosenFiniteProducts.hom_ext\",\"def_path\":\"Mathlib\\/CategoryTheory\\/ChosenFiniteProducts.lean\",\"def_pos\":[107,7],\"def_end_pos\":[107,14]}]"
252
+ ],
253
+ "state_after": "case h_snd.h_fst\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 ((\u03b1_ F\u2081 F\u2082 F\u2083).hom.app j \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)) \u226b fst (F\u2082.obj j) (F\u2083.obj j) =\n ((\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)) \u226b fst (F\u2082.obj j) (F\u2083.obj j)\n\ncase h_snd.h_snd\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 ((\u03b1_ F\u2081 F\u2082 F\u2083).hom.app j \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)) \u226b snd (F\u2082.obj j) (F\u2083.obj j) =\n ((\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)) \u226b snd (F\u2082.obj j) (F\u2083.obj j)",
254
+ "state_before": "case h_snd\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (\u03b1_ F\u2081 F\u2082 F\u2083).hom.app j \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j) =\n (\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)",
255
+ "tactic": "apply hom_ext"
256
+ },
257
+ {
258
+ "annotated_tactic": [
259
+ "\"change (_ \\u226b (<a>snd<\\/a> F\\u2081 (F\\u2082 \\u2297 F\\u2083)).<a>app<\\/a> j) \\u226b (<a>fst<\\/a> F\\u2082 F\\u2083).<a>app<\\/a> j = _\"",
260
+ "[{\"full_name\":\"CategoryTheory.ChosenFiniteProducts.snd\",\"def_path\":\"Mathlib\\/CategoryTheory\\/ChosenFiniteProducts.lean\",\"def_pos\":[94,5],\"def_end_pos\":[94,8]},{\"full_name\":\"CategoryTheory.NatTrans.app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/NatTrans.lean\",\"def_pos\":[50,3],\"def_end_pos\":[50,6]},{\"full_name\":\"CategoryTheory.ChosenFiniteProducts.fst\",\"def_path\":\"Mathlib\\/CategoryTheory\\/ChosenFiniteProducts.lean\",\"def_pos\":[87,5],\"def_end_pos\":[87,8]},{\"full_name\":\"CategoryTheory.NatTrans.app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/NatTrans.lean\",\"def_pos\":[50,3],\"def_end_pos\":[50,6]}]"
261
+ ],
262
+ "state_after": "case h_snd.h_fst\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 ((\u03b1_ F\u2081 F\u2082 F\u2083).hom.app j \u226b (snd F\u2081 (F\u2082 \u2297 F\u2083)).app j) \u226b (fst F\u2082 F\u2083).app j =\n ((\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)) \u226b fst (F\u2082.obj j) (F\u2083.obj j)",
263
+ "state_before": "case h_snd.h_fst\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 ((\u03b1_ F\u2081 F\u2082 F\u2083).hom.app j \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)) \u226b fst (F\u2082.obj j) (F\u2083.obj j) =\n ((\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)) \u226b fst (F\u2082.obj j) (F\u2083.obj j)",
264
+ "tactic": "change (_ \u226b (snd F\u2081 (F\u2082 \u2297 F\u2083)).app j) \u226b (fst F\u2082 F\u2083).app j = _"
265
+ },
266
+ {
267
+ "annotated_tactic": [
268
+ "\"rw [\\u2190 <a>NatTrans.comp_app<\\/a>, \\u2190 <a>NatTrans.comp_app<\\/a>, <a>assoc<\\/a>, <a>associator_hom_snd_fst<\\/a>, <a>assoc<\\/a>]\"",
269
+ "[{\"full_name\":\"CategoryTheory.NatTrans.comp_app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Category.lean\",\"def_pos\":[76,9],\"def_end_pos\":[76,17]},{\"full_name\":\"CategoryTheory.NatTrans.comp_app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Category.lean\",\"def_pos\":[76,9],\"def_end_pos\":[76,17]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.ChosenFiniteProducts.associator_hom_snd_fst\",\"def_path\":\"Mathlib\\/CategoryTheory\\/ChosenFiniteProducts.lean\",\"def_pos\":[146,7],\"def_end_pos\":[146,29]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]}]"
270
+ ],
271
+ "state_after": "case h_snd.h_fst\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (fst (F\u2081 \u2297 F\u2082) F\u2083 \u226b snd F\u2081 F\u2082).app j =\n (\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j) \u226b fst (F\u2082.obj j) (F\u2083.obj j)",
272
+ "state_before": "case h_snd.h_fst\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 ((\u03b1_ F\u2081 F\u2082 F\u2083).hom.app j \u226b (snd F\u2081 (F\u2082 \u2297 F\u2083)).app j) \u226b (fst F\u2082 F\u2083).app j =\n ((\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)) \u226b fst (F\u2082.obj j) (F\u2083.obj j)",
273
+ "tactic": "rw [\u2190 NatTrans.comp_app, \u2190 NatTrans.comp_app, assoc, associator_hom_snd_fst, assoc]"
274
+ },
275
+ {
276
+ "annotated_tactic": [
277
+ "\"erw [<a>associator_hom_snd_fst<\\/a>]\"",
278
+ "[{\"full_name\":\"CategoryTheory.ChosenFiniteProducts.associator_hom_snd_fst\",\"def_path\":\"Mathlib\\/CategoryTheory\\/ChosenFiniteProducts.lean\",\"def_pos\":[146,7],\"def_end_pos\":[146,29]}]"
279
+ ],
280
+ "state_after": "case h_snd.h_fst\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (fst (F\u2081 \u2297 F\u2082) F\u2083 \u226b snd F\u2081 F\u2082).app j = fst (F\u2081.obj j \u2297 F\u2082.obj j) (F\u2083.obj j) \u226b snd (F\u2081.obj j) (F\u2082.obj j)",
281
+ "state_before": "case h_snd.h_fst\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (fst (F\u2081 \u2297 F\u2082) F\u2083 \u226b snd F\u2081 F\u2082).app j =\n (\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j) \u226b fst (F\u2082.obj j) (F\u2083.obj j)",
282
+ "tactic": "erw [associator_hom_snd_fst]"
283
+ },
284
+ {
285
+ "annotated_tactic": [
286
+ "\"rfl\"",
287
+ "[]"
288
+ ],
289
+ "state_after": "no goals",
290
+ "state_before": "case h_snd.h_fst\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (fst (F\u2081 \u2297 F\u2082) F\u2083 \u226b snd F\u2081 F\u2082).app j = fst (F\u2081.obj j \u2297 F\u2082.obj j) (F\u2083.obj j) \u226b snd (F\u2081.obj j) (F\u2082.obj j)",
291
+ "tactic": "rfl"
292
+ },
293
+ {
294
+ "annotated_tactic": [
295
+ "\"change (_ \\u226b (<a>snd<\\/a> F\\u2081 (F\\u2082 \\u2297 F\\u2083)).<a>app<\\/a> j) \\u226b (<a>snd<\\/a> F\\u2082 F\\u2083).<a>app<\\/a> j = _\"",
296
+ "[{\"full_name\":\"CategoryTheory.ChosenFiniteProducts.snd\",\"def_path\":\"Mathlib\\/CategoryTheory\\/ChosenFiniteProducts.lean\",\"def_pos\":[94,5],\"def_end_pos\":[94,8]},{\"full_name\":\"CategoryTheory.NatTrans.app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/NatTrans.lean\",\"def_pos\":[50,3],\"def_end_pos\":[50,6]},{\"full_name\":\"CategoryTheory.ChosenFiniteProducts.snd\",\"def_path\":\"Mathlib\\/CategoryTheory\\/ChosenFiniteProducts.lean\",\"def_pos\":[94,5],\"def_end_pos\":[94,8]},{\"full_name\":\"CategoryTheory.NatTrans.app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/NatTrans.lean\",\"def_pos\":[50,3],\"def_end_pos\":[50,6]}]"
297
+ ],
298
+ "state_after": "case h_snd.h_snd\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 ((\u03b1_ F\u2081 F\u2082 F\u2083).hom.app j \u226b (snd F\u2081 (F\u2082 \u2297 F\u2083)).app j) \u226b (snd F\u2082 F\u2083).app j =\n ((\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)) \u226b snd (F\u2082.obj j) (F\u2083.obj j)",
299
+ "state_before": "case h_snd.h_snd\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 ((\u03b1_ F\u2081 F\u2082 F\u2083).hom.app j \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)) \u226b snd (F\u2082.obj j) (F\u2083.obj j) =\n ((\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)) \u226b snd (F\u2082.obj j) (F\u2083.obj j)",
300
+ "tactic": "change (_ \u226b (snd F\u2081 (F\u2082 \u2297 F\u2083)).app j) \u226b (snd F\u2082 F\u2083).app j = _"
301
+ },
302
+ {
303
+ "annotated_tactic": [
304
+ "\"rw [\\u2190 <a>NatTrans.comp_app<\\/a>, \\u2190 <a>NatTrans.comp_app<\\/a>, <a>assoc<\\/a>, <a>associator_hom_snd_snd<\\/a>, <a>assoc<\\/a>]\"",
305
+ "[{\"full_name\":\"CategoryTheory.NatTrans.comp_app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Category.lean\",\"def_pos\":[76,9],\"def_end_pos\":[76,17]},{\"full_name\":\"CategoryTheory.NatTrans.comp_app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Category.lean\",\"def_pos\":[76,9],\"def_end_pos\":[76,17]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.ChosenFiniteProducts.associator_hom_snd_snd\",\"def_path\":\"Mathlib\\/CategoryTheory\\/ChosenFiniteProducts.lean\",\"def_pos\":[152,7],\"def_end_pos\":[152,29]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]}]"
306
+ ],
307
+ "state_after": "case h_snd.h_snd\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (snd (F\u2081 \u2297 F\u2082) F\u2083).app j =\n (\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j) \u226b snd (F\u2082.obj j) (F\u2083.obj j)",
308
+ "state_before": "case h_snd.h_snd\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 ((\u03b1_ F\u2081 F\u2082 F\u2083).hom.app j \u226b (snd F\u2081 (F\u2082 \u2297 F\u2083)).app j) \u226b (snd F\u2082 F\u2083).app j =\n ((\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j)) \u226b snd (F\u2082.obj j) (F\u2083.obj j)",
309
+ "tactic": "rw [\u2190 NatTrans.comp_app, \u2190 NatTrans.comp_app, assoc, associator_hom_snd_snd, assoc]"
310
+ },
311
+ {
312
+ "annotated_tactic": [
313
+ "\"erw [<a>associator_hom_snd_snd<\\/a>]\"",
314
+ "[{\"full_name\":\"CategoryTheory.ChosenFiniteProducts.associator_hom_snd_snd\",\"def_path\":\"Mathlib\\/CategoryTheory\\/ChosenFiniteProducts.lean\",\"def_pos\":[152,7],\"def_end_pos\":[152,29]}]"
315
+ ],
316
+ "state_after": "case h_snd.h_snd\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (snd (F\u2081 \u2297 F\u2082) F\u2083).app j = snd (F\u2081.obj j \u2297 F\u2082.obj j) (F\u2083.obj j)",
317
+ "state_before": "case h_snd.h_snd\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (snd (F\u2081 \u2297 F\u2082) F\u2083).app j =\n (\u03b1_ (F\u2081.obj j) (F\u2082.obj j) (F\u2083.obj j)).hom \u226b snd (F\u2081.obj j) ((F\u2082 \u2297 F\u2083).obj j) \u226b snd (F\u2082.obj j) (F\u2083.obj j)",
318
+ "tactic": "erw [associator_hom_snd_snd]"
319
+ },
320
+ {
321
+ "annotated_tactic": [
322
+ "\"rfl\"",
323
+ "[]"
324
+ ],
325
+ "state_after": "no goals",
326
+ "state_before": "case h_snd.h_snd\nJ : Type u_1\nC : Type u_2\ninst\u271d\u00b2 : Category.{u_3, u_1} J\ninst\u271d\u00b9 : Category.{u_4, u_2} C\ninst\u271d : ChosenFiniteProducts C\nF\u2081 F\u2082 F\u2083 : J \u2964 C\nj : J\n\u22a2 (snd (F\u2081 \u2297 F\u2082) F\u2083).app j = snd (F\u2081.obj j \u2297 F\u2082.obj j) (F\u2083.obj j)",
327
+ "tactic": "rfl"
328
+ }
329
+ ],
330
+ "url": "https://github.com/leanprover-community/mathlib4"
331
+ },
332
+ "source_file": "Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean"
333
+ },
334
+ {
335
+ "error": "theorem has no selected tactic transitions",
336
+ "full_name": "CategoryTheory.Functor.Monoidal.leftUnitor_hom_app",
337
+ "id": "CategoryTheory.Functor.Monoidal.leftUnitor_hom_app",
338
+ "reason": "import_failure",
339
+ "selection": {
340
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
341
+ "end": [
342
+ 79,
343
+ 49
344
+ ],
345
+ "file_path": "Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean",
346
+ "full_name": "CategoryTheory.Functor.Monoidal.leftUnitor_hom_app",
347
+ "start": [
348
+ 77,
349
+ 1
350
+ ],
351
+ "traced_tactics": [],
352
+ "url": "https://github.com/leanprover-community/mathlib4"
353
+ },
354
+ "source_file": "Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean"
355
+ },
356
+ {
357
+ "error": "theorem has no selected tactic transitions",
358
+ "full_name": "CategoryTheory.Functor.Monoidal.rightUnitor_hom_app",
359
+ "id": "CategoryTheory.Functor.Monoidal.rightUnitor_hom_app",
360
+ "reason": "import_failure",
361
+ "selection": {
362
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
363
+ "end": [
364
+ 89,
365
+ 49
366
+ ],
367
+ "file_path": "Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean",
368
+ "full_name": "CategoryTheory.Functor.Monoidal.rightUnitor_hom_app",
369
+ "start": [
370
+ 87,
371
+ 1
372
+ ],
373
+ "traced_tactics": [],
374
+ "url": "https://github.com/leanprover-community/mathlib4"
375
+ },
376
+ "source_file": "Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean"
377
+ },
378
+ {
379
+ "error": "theorem has no selected tactic transitions",
380
+ "full_name": "CategoryTheory.Functor.Monoidal.whiskerLeft_app_snd",
381
+ "id": "CategoryTheory.Functor.Monoidal.whiskerLeft_app_snd",
382
+ "reason": "import_failure",
383
+ "selection": {
384
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
385
+ "end": [
386
+ 119,
387
+ 33
388
+ ],
389
+ "file_path": "Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean",
390
+ "full_name": "CategoryTheory.Functor.Monoidal.whiskerLeft_app_snd",
391
+ "start": [
392
+ 116,
393
+ 1
394
+ ],
395
+ "traced_tactics": [],
396
+ "url": "https://github.com/leanprover-community/mathlib4"
397
+ },
398
+ "source_file": "Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean"
399
+ },
400
+ {
401
+ "error": "theorem has no selected tactic transitions",
402
+ "full_name": "CategoryTheory.Functor.Monoidal.whiskerRight_app_fst",
403
+ "id": "CategoryTheory.Functor.Monoidal.whiskerRight_app_fst",
404
+ "reason": "import_failure",
405
+ "selection": {
406
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
407
+ "end": [
408
+ 124,
409
+ 33
410
+ ],
411
+ "file_path": "Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean",
412
+ "full_name": "CategoryTheory.Functor.Monoidal.whiskerRight_app_fst",
413
+ "start": [
414
+ 121,
415
+ 1
416
+ ],
417
+ "traced_tactics": [],
418
+ "url": "https://github.com/leanprover-community/mathlib4"
419
+ },
420
+ "source_file": "Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean"
421
+ }
422
+ ],
423
+ "input_proofs": 27,
424
+ "input_units": 2,
425
+ "proofs": 14,
426
+ "published_proofs": 14,
427
+ "published_transitions": 20,
428
+ "replay_failures": [],
429
+ "transitions": 20,
430
+ "validation_failures": [],
431
+ "validation_rejected_proofs": 0,
432
+ "zero_transition_proofs": 0
433
+ },
434
+ "shards": [
435
+ {
436
+ "path": "data/train/mathlib-000620-0000-1ef9eabb985c33ed.parquet",
437
+ "sha256": "1ef9eabb985c33ed153f8af313e829b572f3decf65e8e4b4bcd98db133d32003",
438
+ "bytes": 72750,
439
+ "rows": 15,
440
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
441
+ },
442
+ {
443
+ "path": "data/dev/mathlib-000620-0000-e1bc5f54662fc5f5.parquet",
444
+ "sha256": "e1bc5f54662fc5f50976419a78483cdc09f822968303d0502b68632ba8421f0e",
445
+ "bytes": 38342,
446
+ "rows": 1,
447
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
448
+ },
449
+ {
450
+ "path": "data/internal_test/mathlib-000620-0000-fa8f9fea856c907e.parquet",
451
+ "sha256": "fa8f9fea856c907eeefa51c379cee64f88b926de7e5509e993cce7b8d5957635",
452
+ "bytes": 49439,
453
+ "rows": 4,
454
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
455
+ }
456
+ ],
457
+ "proof_ids": [
458
+ "mathlib:CategoryTheory.ChosenFiniteProducts.associator_hom_snd_fst",
459
+ "mathlib:CategoryTheory.ChosenFiniteProducts.associator_hom_snd_snd",
460
+ "mathlib:CategoryTheory.ChosenFiniteProducts.associator_inv_fst",
461
+ "mathlib:CategoryTheory.ChosenFiniteProducts.associator_inv_fst_snd",
462
+ "mathlib:CategoryTheory.ChosenFiniteProducts.lift_fst",
463
+ "mathlib:CategoryTheory.ChosenFiniteProducts.lift_snd",
464
+ "mathlib:CategoryTheory.ChosenFiniteProducts.whiskerLeft_fst",
465
+ "mathlib:CategoryTheory.ChosenFiniteProducts.whiskerRight_snd",
466
+ "mathlib:CategoryTheory.Functor.Monoidal.associator_inv_app",
467
+ "mathlib:CategoryTheory.Functor.Monoidal.leftUnitor_inv_app",
468
+ "mathlib:CategoryTheory.Functor.Monoidal.rightUnitor_inv_app",
469
+ "mathlib:CategoryTheory.Functor.Monoidal.tensorHom_app_fst",
470
+ "mathlib:CategoryTheory.Functor.Monoidal.whiskerLeft_app_fst",
471
+ "mathlib:CategoryTheory.Functor.Monoidal.whiskerRight_app_snd"
472
+ ],
473
+ "proof_keys": [
474
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/ChosenFiniteProducts.lean\",null,null,\"CategoryTheory.ChosenFiniteProducts.associator_hom_snd_fst\"]",
475
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/ChosenFiniteProducts.lean\",null,null,\"CategoryTheory.ChosenFiniteProducts.associator_hom_snd_snd\"]",
476
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/ChosenFiniteProducts.lean\",null,null,\"CategoryTheory.ChosenFiniteProducts.associator_inv_fst\"]",
477
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/ChosenFiniteProducts.lean\",null,null,\"CategoryTheory.ChosenFiniteProducts.associator_inv_fst_snd\"]",
478
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/ChosenFiniteProducts.lean\",null,null,\"CategoryTheory.ChosenFiniteProducts.lift_fst\"]",
479
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/ChosenFiniteProducts.lean\",null,null,\"CategoryTheory.ChosenFiniteProducts.lift_snd\"]",
480
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/ChosenFiniteProducts.lean\",null,null,\"CategoryTheory.ChosenFiniteProducts.whiskerLeft_fst\"]",
481
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/ChosenFiniteProducts.lean\",null,null,\"CategoryTheory.ChosenFiniteProducts.whiskerRight_snd\"]",
482
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean\",null,null,\"CategoryTheory.Functor.Monoidal.associator_inv_app\"]",
483
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean\",null,null,\"CategoryTheory.Functor.Monoidal.leftUnitor_inv_app\"]",
484
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean\",null,null,\"CategoryTheory.Functor.Monoidal.rightUnitor_inv_app\"]",
485
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean\",null,null,\"CategoryTheory.Functor.Monoidal.tensorHom_app_fst\"]",
486
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean\",null,null,\"CategoryTheory.Functor.Monoidal.whiskerLeft_app_fst\"]",
487
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/ChosenFiniteProducts/FunctorCategory.lean\",null,null,\"CategoryTheory.Functor.Monoidal.whiskerRight_app_snd\"]"
488
+ ]
489
+ }
manifests/batches/mathlib/000621.json ADDED
@@ -0,0 +1,634 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000621",
4
+ "batch_fingerprint": "bfea9bd8c82bc9b40c6acbf3122c6ec2e56f24f30d8f15b26848441c6d666fd5",
5
+ "evidence": {
6
+ "batch_fingerprint": "bfea9bd8c82bc9b40c6acbf3122c6ec2e56f24f30d8f15b26848441c6d666fd5",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "CategoryTheory.CartesianClosed.curry_eq",
12
+ "id": "CategoryTheory.CartesianClosed.curry_eq",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 236,
18
+ 29
19
+ ],
20
+ "file_path": "Mathlib/CategoryTheory/Closed/Cartesian.lean",
21
+ "full_name": "CategoryTheory.CartesianClosed.curry_eq",
22
+ "start": [
23
+ 235,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/CategoryTheory/Closed/Cartesian.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "CategoryTheory.CartesianClosed.curry_eq_iff",
34
+ "id": "CategoryTheory.CartesianClosed.curry_eq_iff",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 222,
40
+ 54
41
+ ],
42
+ "file_path": "Mathlib/CategoryTheory/Closed/Cartesian.lean",
43
+ "full_name": "CategoryTheory.CartesianClosed.curry_eq_iff",
44
+ "start": [
45
+ 221,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/CategoryTheory/Closed/Cartesian.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "CategoryTheory.CartesianClosed.curry_injective",
56
+ "id": "CategoryTheory.CartesianClosed.curry_injective",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 248,
62
+ 38
63
+ ],
64
+ "file_path": "Mathlib/CategoryTheory/Closed/Cartesian.lean",
65
+ "full_name": "CategoryTheory.CartesianClosed.curry_injective",
66
+ "start": [
67
+ 247,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/CategoryTheory/Closed/Cartesian.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "CategoryTheory.CartesianClosed.curry_natural_left",
78
+ "id": "CategoryTheory.CartesianClosed.curry_natural_left",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 189,
84
+ 44
85
+ ],
86
+ "file_path": "Mathlib/CategoryTheory/Closed/Cartesian.lean",
87
+ "full_name": "CategoryTheory.CartesianClosed.curry_natural_left",
88
+ "start": [
89
+ 187,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/CategoryTheory/Closed/Cartesian.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "CategoryTheory.CartesianClosed.curry_natural_right",
100
+ "id": "CategoryTheory.CartesianClosed.curry_natural_right",
101
+ "reason": "import_failure",
102
+ "selection": {
103
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
104
+ "end": [
105
+ 195,
106
+ 45
107
+ ],
108
+ "file_path": "Mathlib/CategoryTheory/Closed/Cartesian.lean",
109
+ "full_name": "CategoryTheory.CartesianClosed.curry_natural_right",
110
+ "start": [
111
+ 193,
112
+ 1
113
+ ],
114
+ "traced_tactics": [],
115
+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
+ "source_file": "Mathlib/CategoryTheory/Closed/Cartesian.lean"
118
+ },
119
+ {
120
+ "error": "theorem has no selected tactic transitions",
121
+ "full_name": "CategoryTheory.CartesianClosed.curry_uncurry",
122
+ "id": "CategoryTheory.CartesianClosed.curry_uncurry",
123
+ "reason": "import_failure",
124
+ "selection": {
125
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
126
+ "end": [
127
+ 217,
128
+ 40
129
+ ],
130
+ "file_path": "Mathlib/CategoryTheory/Closed/Cartesian.lean",
131
+ "full_name": "CategoryTheory.CartesianClosed.curry_uncurry",
132
+ "start": [
133
+ 216,
134
+ 1
135
+ ],
136
+ "traced_tactics": [],
137
+ "url": "https://github.com/leanprover-community/mathlib4"
138
+ },
139
+ "source_file": "Mathlib/CategoryTheory/Closed/Cartesian.lean"
140
+ },
141
+ {
142
+ "error": "theorem has no selected tactic transitions",
143
+ "full_name": "CategoryTheory.CartesianClosed.eq_curry_iff",
144
+ "id": "CategoryTheory.CartesianClosed.eq_curry_iff",
145
+ "reason": "import_failure",
146
+ "selection": {
147
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
148
+ "end": [
149
+ 227,
150
+ 54
151
+ ],
152
+ "file_path": "Mathlib/CategoryTheory/Closed/Cartesian.lean",
153
+ "full_name": "CategoryTheory.CartesianClosed.eq_curry_iff",
154
+ "start": [
155
+ 226,
156
+ 1
157
+ ],
158
+ "traced_tactics": [],
159
+ "url": "https://github.com/leanprover-community/mathlib4"
160
+ },
161
+ "source_file": "Mathlib/CategoryTheory/Closed/Cartesian.lean"
162
+ },
163
+ {
164
+ "error": "theorem has no selected tactic transitions",
165
+ "full_name": "CategoryTheory.CartesianClosed.homEquiv_apply_eq",
166
+ "id": "CategoryTheory.CartesianClosed.homEquiv_apply_eq",
167
+ "reason": "import_failure",
168
+ "selection": {
169
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
170
+ "end": [
171
+ 176,
172
+ 6
173
+ ],
174
+ "file_path": "Mathlib/CategoryTheory/Closed/Cartesian.lean",
175
+ "full_name": "CategoryTheory.CartesianClosed.homEquiv_apply_eq",
176
+ "start": [
177
+ 175,
178
+ 1
179
+ ],
180
+ "traced_tactics": [],
181
+ "url": "https://github.com/leanprover-community/mathlib4"
182
+ },
183
+ "source_file": "Mathlib/CategoryTheory/Closed/Cartesian.lean"
184
+ },
185
+ {
186
+ "error": "theorem has no selected tactic transitions",
187
+ "full_name": "CategoryTheory.CartesianClosed.homEquiv_symm_apply_eq",
188
+ "id": "CategoryTheory.CartesianClosed.homEquiv_symm_apply_eq",
189
+ "reason": "import_failure",
190
+ "selection": {
191
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
192
+ "end": [
193
+ 183,
194
+ 6
195
+ ],
196
+ "file_path": "Mathlib/CategoryTheory/Closed/Cartesian.lean",
197
+ "full_name": "CategoryTheory.CartesianClosed.homEquiv_symm_apply_eq",
198
+ "start": [
199
+ 181,
200
+ 1
201
+ ],
202
+ "traced_tactics": [],
203
+ "url": "https://github.com/leanprover-community/mathlib4"
204
+ },
205
+ "source_file": "Mathlib/CategoryTheory/Closed/Cartesian.lean"
206
+ },
207
+ {
208
+ "error": "theorem has no selected tactic transitions",
209
+ "full_name": "CategoryTheory.CartesianClosed.uncurry_curry",
210
+ "id": "CategoryTheory.CartesianClosed.uncurry_curry",
211
+ "reason": "import_failure",
212
+ "selection": {
213
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
214
+ "end": [
215
+ 212,
216
+ 39
217
+ ],
218
+ "file_path": "Mathlib/CategoryTheory/Closed/Cartesian.lean",
219
+ "full_name": "CategoryTheory.CartesianClosed.uncurry_curry",
220
+ "start": [
221
+ 211,
222
+ 1
223
+ ],
224
+ "traced_tactics": [],
225
+ "url": "https://github.com/leanprover-community/mathlib4"
226
+ },
227
+ "source_file": "Mathlib/CategoryTheory/Closed/Cartesian.lean"
228
+ },
229
+ {
230
+ "error": "theorem has no selected tactic transitions",
231
+ "full_name": "CategoryTheory.CartesianClosed.uncurry_eq",
232
+ "id": "CategoryTheory.CartesianClosed.uncurry_eq",
233
+ "reason": "import_failure",
234
+ "selection": {
235
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
236
+ "end": [
237
+ 232,
238
+ 31
239
+ ],
240
+ "file_path": "Mathlib/CategoryTheory/Closed/Cartesian.lean",
241
+ "full_name": "CategoryTheory.CartesianClosed.uncurry_eq",
242
+ "start": [
243
+ 231,
244
+ 1
245
+ ],
246
+ "traced_tactics": [],
247
+ "url": "https://github.com/leanprover-community/mathlib4"
248
+ },
249
+ "source_file": "Mathlib/CategoryTheory/Closed/Cartesian.lean"
250
+ },
251
+ {
252
+ "error": "theorem has no selected tactic transitions",
253
+ "full_name": "CategoryTheory.CartesianClosed.uncurry_injective",
254
+ "id": "CategoryTheory.CartesianClosed.uncurry_injective",
255
+ "reason": "import_failure",
256
+ "selection": {
257
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
258
+ "end": [
259
+ 252,
260
+ 43
261
+ ],
262
+ "file_path": "Mathlib/CategoryTheory/Closed/Cartesian.lean",
263
+ "full_name": "CategoryTheory.CartesianClosed.uncurry_injective",
264
+ "start": [
265
+ 251,
266
+ 1
267
+ ],
268
+ "traced_tactics": [],
269
+ "url": "https://github.com/leanprover-community/mathlib4"
270
+ },
271
+ "source_file": "Mathlib/CategoryTheory/Closed/Cartesian.lean"
272
+ },
273
+ {
274
+ "error": "theorem has no selected tactic transitions",
275
+ "full_name": "CategoryTheory.CartesianClosed.uncurry_natural_left",
276
+ "id": "CategoryTheory.CartesianClosed.uncurry_natural_left",
277
+ "reason": "import_failure",
278
+ "selection": {
279
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
280
+ "end": [
281
+ 207,
282
+ 49
283
+ ],
284
+ "file_path": "Mathlib/CategoryTheory/Closed/Cartesian.lean",
285
+ "full_name": "CategoryTheory.CartesianClosed.uncurry_natural_left",
286
+ "start": [
287
+ 205,
288
+ 1
289
+ ],
290
+ "traced_tactics": [],
291
+ "url": "https://github.com/leanprover-community/mathlib4"
292
+ },
293
+ "source_file": "Mathlib/CategoryTheory/Closed/Cartesian.lean"
294
+ },
295
+ {
296
+ "error": "theorem has no selected tactic transitions",
297
+ "full_name": "CategoryTheory.CartesianClosed.uncurry_natural_right",
298
+ "id": "CategoryTheory.CartesianClosed.uncurry_natural_right",
299
+ "reason": "import_failure",
300
+ "selection": {
301
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
302
+ "end": [
303
+ 201,
304
+ 50
305
+ ],
306
+ "file_path": "Mathlib/CategoryTheory/Closed/Cartesian.lean",
307
+ "full_name": "CategoryTheory.CartesianClosed.uncurry_natural_right",
308
+ "start": [
309
+ 199,
310
+ 1
311
+ ],
312
+ "traced_tactics": [],
313
+ "url": "https://github.com/leanprover-community/mathlib4"
314
+ },
315
+ "source_file": "Mathlib/CategoryTheory/Closed/Cartesian.lean"
316
+ },
317
+ {
318
+ "error": "theorem has no selected tactic transitions",
319
+ "full_name": "CategoryTheory.coev_app_comp_pre_app",
320
+ "id": "CategoryTheory.coev_app_comp_pre_app",
321
+ "reason": "import_failure",
322
+ "selection": {
323
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
324
+ "end": [
325
+ 304,
326
+ 55
327
+ ],
328
+ "file_path": "Mathlib/CategoryTheory/Closed/Cartesian.lean",
329
+ "full_name": "CategoryTheory.coev_app_comp_pre_app",
330
+ "start": [
331
+ 301,
332
+ 1
333
+ ],
334
+ "traced_tactics": [],
335
+ "url": "https://github.com/leanprover-community/mathlib4"
336
+ },
337
+ "source_file": "Mathlib/CategoryTheory/Closed/Cartesian.lean"
338
+ },
339
+ {
340
+ "error": "theorem has no selected tactic transitions",
341
+ "full_name": "CategoryTheory.exp.coev_ev",
342
+ "id": "CategoryTheory.exp.coev_ev",
343
+ "reason": "import_failure",
344
+ "selection": {
345
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
346
+ "end": [
347
+ 150,
348
+ 19
349
+ ],
350
+ "file_path": "Mathlib/CategoryTheory/Closed/Cartesian.lean",
351
+ "full_name": "CategoryTheory.exp.coev_ev",
352
+ "start": [
353
+ 149,
354
+ 1
355
+ ],
356
+ "traced_tactics": [],
357
+ "url": "https://github.com/leanprover-community/mathlib4"
358
+ },
359
+ "source_file": "Mathlib/CategoryTheory/Closed/Cartesian.lean"
360
+ },
361
+ {
362
+ "error": "theorem has no selected tactic transitions",
363
+ "full_name": "CategoryTheory.exp.ev_coev",
364
+ "id": "CategoryTheory.exp.ev_coev",
365
+ "reason": "import_failure",
366
+ "selection": {
367
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
368
+ "end": [
369
+ 145,
370
+ 19
371
+ ],
372
+ "file_path": "Mathlib/CategoryTheory/Closed/Cartesian.lean",
373
+ "full_name": "CategoryTheory.exp.ev_coev",
374
+ "start": [
375
+ 144,
376
+ 1
377
+ ],
378
+ "traced_tactics": [],
379
+ "url": "https://github.com/leanprover-community/mathlib4"
380
+ },
381
+ "source_file": "Mathlib/CategoryTheory/Closed/Cartesian.lean"
382
+ },
383
+ {
384
+ "error": "theorem has no selected tactic transitions",
385
+ "full_name": "CategoryTheory.prod_map_pre_app_comp_ev",
386
+ "id": "CategoryTheory.prod_map_pre_app_comp_ev",
387
+ "reason": "import_failure",
388
+ "selection": {
389
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
390
+ "end": [
391
+ 293,
392
+ 57
393
+ ],
394
+ "file_path": "Mathlib/CategoryTheory/Closed/Cartesian.lean",
395
+ "full_name": "CategoryTheory.prod_map_pre_app_comp_ev",
396
+ "start": [
397
+ 290,
398
+ 1
399
+ ],
400
+ "traced_tactics": [],
401
+ "url": "https://github.com/leanprover-community/mathlib4"
402
+ },
403
+ "source_file": "Mathlib/CategoryTheory/Closed/Cartesian.lean"
404
+ },
405
+ {
406
+ "error": "theorem has no selected tactic transitions",
407
+ "full_name": "CategoryTheory.cartesianClosedFunctorOfLeftAdjointPreservesBinaryProducts",
408
+ "id": "CategoryTheory.cartesianClosedFunctorOfLeftAdjointPreservesBinaryProducts",
409
+ "reason": "import_failure",
410
+ "selection": {
411
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
412
+ "end": [
413
+ 179,
414
+ 71
415
+ ],
416
+ "file_path": "Mathlib/CategoryTheory/Closed/Functor.lean",
417
+ "full_name": "CategoryTheory.cartesianClosedFunctorOfLeftAdjointPreservesBinaryProducts",
418
+ "start": [
419
+ 177,
420
+ 1
421
+ ],
422
+ "traced_tactics": [],
423
+ "url": "https://github.com/leanprover-community/mathlib4"
424
+ },
425
+ "source_file": "Mathlib/CategoryTheory/Closed/Functor.lean"
426
+ },
427
+ {
428
+ "error": "no internal trace for tactic 'rw [assoc, assoc, \u2190 h.counit_naturality, \u2190 L.map_comp_assoc, assoc, inv_prodComparison_map_snd]'",
429
+ "full_name": "CategoryTheory.frobeniusMorphism_mate",
430
+ "id": "CategoryTheory.frobeniusMorphism_mate",
431
+ "reason": "import_failure",
432
+ "selection": {
433
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
434
+ "end": [
435
+ 149,
436
+ 9
437
+ ],
438
+ "file_path": "Mathlib/CategoryTheory/Closed/Functor.lean",
439
+ "full_name": "CategoryTheory.frobeniusMorphism_mate",
440
+ "start": [
441
+ 128,
442
+ 1
443
+ ],
444
+ "traced_tactics": [
445
+ {
446
+ "annotated_tactic": [
447
+ "\"rw [\\u2190 <a>Equiv.eq_symm_apply<\\/a>]\"",
448
+ "[{\"full_name\":\"Equiv.eq_symm_apply\",\"def_path\":\"Mathlib\\/Logic\\/Equiv\\/Defs.lean\",\"def_pos\":[346,9],\"def_end_pos\":[346,22]}]"
449
+ ],
450
+ "state_after": "C : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\n\u22a2 frobeniusMorphism F h A =\n (transferNatTransSelf (h.comp (exp.adjunction A)) ((exp.adjunction (F.obj A)).comp h)).symm (expComparison F A)",
451
+ "state_before": "C : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\n\u22a2 (transferNatTransSelf (h.comp (exp.adjunction A)) ((exp.adjunction (F.obj A)).comp h)) (frobeniusMorphism F h A) =\n expComparison F A",
452
+ "tactic": "rw [\u2190 Equiv.eq_symm_apply]"
453
+ },
454
+ {
455
+ "annotated_tactic": [
456
+ "\"ext B : 2\"",
457
+ "[]"
458
+ ],
459
+ "state_after": "case w.h\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 (frobeniusMorphism F h A).app B =\n ((transferNatTransSelf (h.comp (exp.adjunction A)) ((exp.adjunction (F.obj A)).comp h)).symm\n (expComparison F A)).app\n B",
460
+ "state_before": "C : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\n\u22a2 frobeniusMorphism F h A =\n (transferNatTransSelf (h.comp (exp.adjunction A)) ((exp.adjunction (F.obj A)).comp h)).symm (expComparison F A)",
461
+ "tactic": "ext B : 2"
462
+ },
463
+ {
464
+ "annotated_tactic": [
465
+ "\"dsimp [<a>frobeniusMorphism<\\/a>, <a>transferNatTransSelf<\\/a>, <a>transferNatTrans<\\/a>, <a>Adjunction.comp<\\/a>]\"",
466
+ "[{\"full_name\":\"CategoryTheory.frobeniusMorphism\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Closed\\/Functor.lean\",\"def_pos\":[58,5],\"def_end_pos\":[58,22]},{\"full_name\":\"CategoryTheory.transferNatTransSelf\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Adjunction\\/Mates.lean\",\"def_pos\":[146,5],\"def_end_pos\":[146,25]},{\"full_name\":\"CategoryTheory.transferNatTrans\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Adjunction\\/Mates.lean\",\"def_pos\":[76,5],\"def_end_pos\":[76,21]},{\"full_name\":\"CategoryTheory.Adjunction.comp\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Adjunction\\/Basic.lean\",\"def_pos\":[484,5],\"def_end_pos\":[484,9]}]"
467
+ ],
468
+ "state_after": "case w.h\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B)) =\n \ud835\udfd9 (L.obj (F.obj A \u2a2f B)) \u226b\n (L.map\n (prod.map (\ud835\udfd9 (F.obj A))\n ((h.unit.app B \u226b F.map ((ihom.coev A).app (L.obj B)) \u226b \ud835\udfd9 (F.obj (A \u27f9 A \u2a2f L.obj B))) \u226b\n \ud835\udfd9 (F.obj (A \u27f9 A \u2a2f L.obj B)) \u226b\n (expComparison F A).app (A \u2a2f L.obj B) \u226b \ud835\udfd9 (F.obj A \u27f9 F.obj (A \u2a2f L.obj B)))) \u226b\n \ud835\udfd9 (L.obj (F.obj A \u2a2f F.obj A \u27f9 F.obj (A \u2a2f L.obj B))) \u226b\n L.map ((ihom.ev (F.obj A)).app (F.obj (A \u2a2f L.obj B))) \u226b h.counit.app (A \u2a2f L.obj B)) \u226b\n \ud835\udfd9 (A \u2a2f L.obj B)",
469
+ "state_before": "case w.h\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 (frobeniusMorphism F h A).app B =\n ((transferNatTransSelf (h.comp (exp.adjunction A)) ((exp.adjunction (F.obj A)).comp h)).symm\n (expComparison F A)).app\n B",
470
+ "tactic": "dsimp [frobeniusMorphism, transferNatTransSelf, transferNatTrans, Adjunction.comp]"
471
+ },
472
+ {
473
+ "annotated_tactic": [
474
+ "\"simp only [<a>id_comp<\\/a>, <a>comp_id<\\/a>]\"",
475
+ "[{\"full_name\":\"CategoryTheory.Category.id_comp\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[177,3],\"def_end_pos\":[177,10]},{\"full_name\":\"CategoryTheory.Category.comp_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[179,3],\"def_end_pos\":[179,10]}]"
476
+ ],
477
+ "state_after": "case w.h\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B)) =\n L.map\n (prod.map (\ud835\udfd9 (F.obj A))\n ((h.unit.app B \u226b F.map ((ihom.coev A).app (L.obj B))) \u226b (expComparison F A).app (A \u2a2f L.obj B))) \u226b\n L.map ((ihom.ev (F.obj A)).app (F.obj (A \u2a2f L.obj B))) \u226b h.counit.app (A \u2a2f L.obj B)",
478
+ "state_before": "case w.h\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B)) =\n \ud835\udfd9 (L.obj (F.obj A \u2a2f B)) \u226b\n (L.map\n (prod.map (\ud835\udfd9 (F.obj A))\n ((h.unit.app B \u226b F.map ((ihom.coev A).app (L.obj B)) \u226b \ud835\udfd9 (F.obj (A \u27f9 A \u2a2f L.obj B))) \u226b\n \ud835\udfd9 (F.obj (A \u27f9 A \u2a2f L.obj B)) \u226b\n (expComparison F A).app (A \u2a2f L.obj B) \u226b \ud835\udfd9 (F.obj A \u27f9 F.obj (A \u2a2f L.obj B)))) \u226b\n \ud835\udfd9 (L.obj (F.obj A \u2a2f F.obj A \u27f9 F.obj (A \u2a2f L.obj B))) \u226b\n L.map ((ihom.ev (F.obj A)).app (F.obj (A \u2a2f L.obj B))) \u226b h.counit.app (A \u2a2f L.obj B)) \u226b\n \ud835\udfd9 (A \u2a2f L.obj B)",
479
+ "tactic": "simp only [id_comp, comp_id]"
480
+ },
481
+ {
482
+ "annotated_tactic": [
483
+ "\"rw [\\u2190 L.map_comp_assoc, <a>prod.map_id_comp<\\/a>, <a>assoc<\\/a>]\"",
484
+ "[{\"full_name\":\"CategoryTheory.Limits.prod.map_id_comp\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[779,9],\"def_end_pos\":[779,25]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]}]"
485
+ ],
486
+ "state_after": "case w.h\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B)) =\n L.map\n (prod.map (\ud835\udfd9 (F.obj A)) (h.unit.app B \u226b F.map ((ihom.coev A).app (L.obj B))) \u226b\n prod.map (\ud835\udfd9 (F.obj A)) ((expComparison F A).app (A \u2a2f L.obj B)) \u226b\n (ihom.ev (F.obj A)).app (F.obj (A \u2a2f L.obj B))) \u226b\n h.counit.app (A \u2a2f L.obj B)",
487
+ "state_before": "case w.h\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B)) =\n L.map\n (prod.map (\ud835\udfd9 (F.obj A))\n ((h.unit.app B \u226b F.map ((ihom.coev A).app (L.obj B))) \u226b (expComparison F A).app (A \u2a2f L.obj B))) \u226b\n L.map ((ihom.ev (F.obj A)).app (F.obj (A \u2a2f L.obj B))) \u226b h.counit.app (A \u2a2f L.obj B)",
488
+ "tactic": "rw [\u2190 L.map_comp_assoc, prod.map_id_comp, assoc]"
489
+ },
490
+ {
491
+ "annotated_tactic": [
492
+ "\"erw [<a>expComparison_ev<\\/a>]\"",
493
+ "[{\"full_name\":\"CategoryTheory.expComparison_ev\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Closed\\/Functor.lean\",\"def_pos\":[83,9],\"def_end_pos\":[83,25]}]"
494
+ ],
495
+ "state_after": "case w.h\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B)) =\n L.map\n (prod.map (\ud835\udfd9 (F.obj A)) (h.unit.app B \u226b F.map ((ihom.coev A).app (L.obj B))) \u226b\n inv (prodComparison F A (A \u27f9 A \u2a2f L.obj B)) \u226b F.map ((exp.ev A).app (A \u2a2f L.obj B))) \u226b\n h.counit.app (A \u2a2f L.obj B)",
496
+ "state_before": "case w.h\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B)) =\n L.map\n (prod.map (\ud835\udfd9 (F.obj A)) (h.unit.app B \u226b F.map ((ihom.coev A).app (L.obj B))) \u226b\n prod.map (\ud835\udfd9 (F.obj A)) ((expComparison F A).app (A \u2a2f L.obj B)) \u226b\n (ihom.ev (F.obj A)).app (F.obj (A \u2a2f L.obj B))) \u226b\n h.counit.app (A \u2a2f L.obj B)",
497
+ "tactic": "erw [expComparison_ev]"
498
+ },
499
+ {
500
+ "annotated_tactic": [
501
+ "\"rw [<a>prod.map_id_comp<\\/a>, <a>assoc<\\/a>, \\u2190 F.map_id, \\u2190 <a>prodComparison_inv_natural_assoc<\\/a>, \\u2190 F.map_comp]\"",
502
+ "[{\"full_name\":\"CategoryTheory.Limits.prod.map_id_comp\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[779,9],\"def_end_pos\":[779,25]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.Limits.prodComparison_inv_natural_assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[1306,3],\"def_end_pos\":[1306,10]}]"
503
+ ],
504
+ "state_after": "case w.h\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B)) =\n L.map\n (prod.map (F.map (\ud835\udfd9 A)) (h.unit.app B) \u226b\n inv (prodComparison F A (L.obj B)) \u226b\n F.map (prod.map (\ud835\udfd9 A) ((ihom.coev A).app (L.obj B)) \u226b (exp.ev A).app (A \u2a2f L.obj B))) \u226b\n h.counit.app (A \u2a2f L.obj B)",
505
+ "state_before": "case w.h\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B)) =\n L.map\n (prod.map (\ud835\udfd9 (F.obj A)) (h.unit.app B \u226b F.map ((ihom.coev A).app (L.obj B))) \u226b\n inv (prodComparison F A (A \u27f9 A \u2a2f L.obj B)) \u226b F.map ((exp.ev A).app (A \u2a2f L.obj B))) \u226b\n h.counit.app (A \u2a2f L.obj B)",
506
+ "tactic": "rw [prod.map_id_comp, assoc, \u2190 F.map_id, \u2190 prodComparison_inv_natural_assoc, \u2190 F.map_comp]"
507
+ },
508
+ {
509
+ "annotated_tactic": [
510
+ "\"erw [<a>exp.ev_coev<\\/a>]\"",
511
+ "[{\"full_name\":\"CategoryTheory.exp.ev_coev\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Closed\\/Cartesian.lean\",\"def_pos\":[144,9],\"def_end_pos\":[144,16]}]"
512
+ ],
513
+ "state_after": "case w.h\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B)) =\n L.map (prod.map (F.map (\ud835\udfd9 A)) (h.unit.app B) \u226b inv (prodComparison F A (L.obj B)) \u226b F.map (\ud835\udfd9 (A \u2a2f L.obj B))) \u226b\n h.counit.app (A \u2a2f L.obj B)",
514
+ "state_before": "case w.h\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B)) =\n L.map\n (prod.map (F.map (\ud835\udfd9 A)) (h.unit.app B) \u226b\n inv (prodComparison F A (L.obj B)) \u226b\n F.map (prod.map (\ud835\udfd9 A) ((ihom.coev A).app (L.obj B)) \u226b (exp.ev A).app (A \u2a2f L.obj B))) \u226b\n h.counit.app (A \u2a2f L.obj B)",
515
+ "tactic": "erw [exp.ev_coev]"
516
+ },
517
+ {
518
+ "annotated_tactic": [
519
+ "\"rw [F.map_id (A \\u2a2f L.obj B), <a>comp_id<\\/a>]\"",
520
+ "[{\"full_name\":\"CategoryTheory.Category.comp_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[179,3],\"def_end_pos\":[179,10]}]"
521
+ ],
522
+ "state_after": "case w.h\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B)) =\n L.map (prod.map (F.map (\ud835\udfd9 A)) (h.unit.app B) \u226b inv (prodComparison F A (L.obj B))) \u226b h.counit.app (A \u2a2f L.obj B)",
523
+ "state_before": "case w.h\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B)) =\n L.map (prod.map (F.map (\ud835\udfd9 A)) (h.unit.app B) \u226b inv (prodComparison F A (L.obj B)) \u226b F.map (\ud835\udfd9 (A \u2a2f L.obj B))) \u226b\n h.counit.app (A \u2a2f L.obj B)",
524
+ "tactic": "rw [F.map_id (A \u2a2f L.obj B), comp_id]"
525
+ },
526
+ {
527
+ "annotated_tactic": [
528
+ "\"ext\"",
529
+ "[]"
530
+ ],
531
+ "state_after": "case w.h.h\u2081\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 (prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B))) \u226b prod.fst =\n (L.map (prod.map (F.map (\ud835\udfd9 A)) (h.unit.app B) \u226b inv (prodComparison F A (L.obj B))) \u226b h.counit.app (A \u2a2f L.obj B)) \u226b\n prod.fst\n\ncase w.h.h\u2082\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 (prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B))) \u226b prod.snd =\n (L.map (prod.map (F.map (\ud835\udfd9 A)) (h.unit.app B) \u226b inv (prodComparison F A (L.obj B))) \u226b h.counit.app (A \u2a2f L.obj B)) \u226b\n prod.snd",
532
+ "state_before": "case w.h\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B)) =\n L.map (prod.map (F.map (\ud835\udfd9 A)) (h.unit.app B) \u226b inv (prodComparison F A (L.obj B))) \u226b h.counit.app (A \u2a2f L.obj B)",
533
+ "tactic": "ext"
534
+ },
535
+ {
536
+ "annotated_tactic": [
537
+ "\"rw [<a>assoc<\\/a>, <a>assoc<\\/a>, \\u2190 h.counit_naturality, \\u2190 L.map_comp_assoc, <a>assoc<\\/a>, <a>inv_prodComparison_map_fst<\\/a>]\"",
538
+ "[{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.Limits.inv_prodComparison_map_fst\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[1294,9],\"def_end_pos\":[1294,35]}]"
539
+ ],
540
+ "state_after": "case w.h.h\u2081\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B)) \u226b prod.fst =\n L.map (prod.map (F.map (\ud835\udfd9 A)) (h.unit.app B) \u226b prod.fst) \u226b h.counit.app A",
541
+ "state_before": "case w.h.h\u2081\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 (prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B))) \u226b prod.fst =\n (L.map (prod.map (F.map (\ud835\udfd9 A)) (h.unit.app B) \u226b inv (prodComparison F A (L.obj B))) \u226b h.counit.app (A \u2a2f L.obj B)) \u226b\n prod.fst",
542
+ "tactic": "rw [assoc, assoc, \u2190 h.counit_naturality, \u2190 L.map_comp_assoc, assoc, inv_prodComparison_map_fst]"
543
+ },
544
+ {
545
+ "annotated_tactic": [
546
+ "\"simp\"",
547
+ "[]"
548
+ ],
549
+ "state_after": "no goals",
550
+ "state_before": "case w.h.h\u2081\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B)) \u226b prod.fst =\n L.map (prod.map (F.map (\ud835\udfd9 A)) (h.unit.app B) \u226b prod.fst) \u226b h.counit.app A",
551
+ "tactic": "simp"
552
+ },
553
+ {
554
+ "annotated_tactic": [
555
+ "\"rw [<a>assoc<\\/a>, <a>assoc<\\/a>, \\u2190 h.counit_naturality, \\u2190 L.map_comp_assoc, <a>assoc<\\/a>, <a>inv_prodComparison_map_snd<\\/a>]\"",
556
+ "[{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.Limits.inv_prodComparison_map_snd\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[1300,9],\"def_end_pos\":[1300,35]}]"
557
+ ],
558
+ "state_after": "case w.h.h\u2082\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B)) \u226b prod.snd =\n L.map (prod.map (F.map (\ud835\udfd9 A)) (h.unit.app B) \u226b prod.snd) \u226b h.counit.app (L.obj B)",
559
+ "state_before": "case w.h.h\u2082\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 (prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B))) \u226b prod.snd =\n (L.map (prod.map (F.map (\ud835\udfd9 A)) (h.unit.app B) \u226b inv (prodComparison F A (L.obj B))) \u226b h.counit.app (A \u2a2f L.obj B)) \u226b\n prod.snd",
560
+ "tactic": "rw [assoc, assoc, \u2190 h.counit_naturality, \u2190 L.map_comp_assoc, assoc, inv_prodComparison_map_snd]"
561
+ },
562
+ {
563
+ "annotated_tactic": [
564
+ "\"simp\"",
565
+ "[]"
566
+ ],
567
+ "state_after": "no goals",
568
+ "state_before": "case w.h.h\u2082\nC : Type u\ninst\u271d\u2076 : Category.{v, u} C\nD : Type u'\ninst\u271d\u2075 : Category.{v, u'} D\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : HasFiniteProducts D\nF : C \u2964 D\nL : D \u2964 C\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : CartesianClosed D\ninst\u271d : PreservesLimitsOfShape (Discrete WalkingPair) F\nh : L \u22a3 F\nA : C\nB : D\n\u22a2 prodComparison L (F.obj A) B \u226b prod.map (h.counit.app A) (\ud835\udfd9 (L.obj B)) \u226b prod.snd =\n L.map (prod.map (F.map (\ud835\udfd9 A)) (h.unit.app B) \u226b prod.snd) \u226b h.counit.app (L.obj B)",
569
+ "tactic": "simp"
570
+ }
571
+ ],
572
+ "url": "https://github.com/leanprover-community/mathlib4"
573
+ },
574
+ "source_file": "Mathlib/CategoryTheory/Closed/Functor.lean"
575
+ }
576
+ ],
577
+ "input_proofs": 33,
578
+ "input_units": 2,
579
+ "proofs": 13,
580
+ "published_proofs": 13,
581
+ "published_transitions": 29,
582
+ "replay_failures": [],
583
+ "transitions": 29,
584
+ "validation_failures": [],
585
+ "validation_rejected_proofs": 0,
586
+ "zero_transition_proofs": 0
587
+ },
588
+ "shards": [
589
+ {
590
+ "path": "data/train/mathlib-000621-0000-f6d26bd96b9a79f1.parquet",
591
+ "sha256": "f6d26bd96b9a79f1d8bd25d998edf098ec1dc79c83e9eb2f20b20ecea6826ce9",
592
+ "bytes": 210541,
593
+ "rows": 28,
594
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
595
+ },
596
+ {
597
+ "path": "data/dev/mathlib-000621-0000-c9b928881b73ad4b.parquet",
598
+ "sha256": "c9b928881b73ad4b6f49ef11e870032e75575a75254f486de49b12e4d061c711",
599
+ "bytes": 41652,
600
+ "rows": 1,
601
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
602
+ }
603
+ ],
604
+ "proof_ids": [
605
+ "mathlib:CategoryTheory.CartesianClosed.curry_id_eq_coev",
606
+ "mathlib:CategoryTheory.CartesianClosed.uncurry_id_eq_ev",
607
+ "mathlib:CategoryTheory.coev_expComparison",
608
+ "mathlib:CategoryTheory.expComparison_ev",
609
+ "mathlib:CategoryTheory.expComparison_iso_of_frobeniusMorphism_iso",
610
+ "mathlib:CategoryTheory.expComparison_whiskerLeft",
611
+ "mathlib:CategoryTheory.frobeniusMorphism_iso_of_expComparison_iso",
612
+ "mathlib:CategoryTheory.initial_mono",
613
+ "mathlib:CategoryTheory.pre_id",
614
+ "mathlib:CategoryTheory.pre_map",
615
+ "mathlib:CategoryTheory.strict_initial",
616
+ "mathlib:CategoryTheory.uncurry_expComparison",
617
+ "mathlib:CategoryTheory.uncurry_pre"
618
+ ],
619
+ "proof_keys": [
620
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Cartesian.lean\",null,null,\"CategoryTheory.CartesianClosed.curry_id_eq_coev\"]",
621
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Cartesian.lean\",null,null,\"CategoryTheory.CartesianClosed.uncurry_id_eq_ev\"]",
622
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Cartesian.lean\",null,null,\"CategoryTheory.initial_mono\"]",
623
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Cartesian.lean\",null,null,\"CategoryTheory.pre_id\"]",
624
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Cartesian.lean\",null,null,\"CategoryTheory.pre_map\"]",
625
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Cartesian.lean\",null,null,\"CategoryTheory.strict_initial\"]",
626
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Cartesian.lean\",null,null,\"CategoryTheory.uncurry_pre\"]",
627
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Functor.lean\",null,null,\"CategoryTheory.coev_expComparison\"]",
628
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Functor.lean\",null,null,\"CategoryTheory.expComparison_ev\"]",
629
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Functor.lean\",null,null,\"CategoryTheory.expComparison_iso_of_frobeniusMorphism_iso\"]",
630
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Functor.lean\",null,null,\"CategoryTheory.expComparison_whiskerLeft\"]",
631
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Functor.lean\",null,null,\"CategoryTheory.frobeniusMorphism_iso_of_expComparison_iso\"]",
632
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Functor.lean\",null,null,\"CategoryTheory.uncurry_expComparison\"]"
633
+ ]
634
+ }
manifests/batches/mathlib/000622.json ADDED
@@ -0,0 +1,284 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000622",
4
+ "batch_fingerprint": "7eed7df7b63c93ca572baf75b1785b6be85c8c08264dfa9cab13a66ef67660ab",
5
+ "evidence": {
6
+ "batch_fingerprint": "7eed7df7b63c93ca572baf75b1785b6be85c8c08264dfa9cab13a66ef67660ab",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "CategoryTheory.Functor.ihom_coev_app",
12
+ "id": "CategoryTheory.Functor.ihom_coev_app",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 90,
18
+ 6
19
+ ],
20
+ "file_path": "Mathlib/CategoryTheory/Closed/FunctorCategory.lean",
21
+ "full_name": "CategoryTheory.Functor.ihom_coev_app",
22
+ "start": [
23
+ 89,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/CategoryTheory/Closed/FunctorCategory.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "CategoryTheory.Functor.ihom_ev_app",
34
+ "id": "CategoryTheory.Functor.ihom_ev_app",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 86,
40
+ 6
41
+ ],
42
+ "file_path": "Mathlib/CategoryTheory/Closed/FunctorCategory.lean",
43
+ "full_name": "CategoryTheory.Functor.ihom_ev_app",
44
+ "start": [
45
+ 85,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/CategoryTheory/Closed/FunctorCategory.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "CategoryTheory.Functor.ihom_map",
56
+ "id": "CategoryTheory.Functor.ihom_map",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 82,
62
+ 6
63
+ ],
64
+ "file_path": "Mathlib/CategoryTheory/Closed/FunctorCategory.lean",
65
+ "full_name": "CategoryTheory.Functor.ihom_map",
66
+ "start": [
67
+ 81,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/CategoryTheory/Closed/FunctorCategory.lean"
74
+ },
75
+ {
76
+ "error": "no internal trace for tactic 'rw [Limits.prod.map_snd, assoc, assoc, prodComparison_snd, \u2190 i.map_comp, prodComparison_snd]'",
77
+ "full_name": "CategoryTheory.bijection_symm_apply_id",
78
+ "id": "CategoryTheory.bijection_symm_apply_id",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 221,
84
+ 50
85
+ ],
86
+ "file_path": "Mathlib/CategoryTheory/Closed/Ideal.lean",
87
+ "full_name": "CategoryTheory.bijection_symm_apply_id",
88
+ "start": [
89
+ 204,
90
+ 1
91
+ ],
92
+ "traced_tactics": [
93
+ {
94
+ "annotated_tactic": [
95
+ "\"dsimp [<a>bijection<\\/a>]\"",
96
+ "[{\"full_name\":\"CategoryTheory.bijection\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Closed\\/Ideal.lean\",\"def_pos\":[180,19],\"def_end_pos\":[180,28]}]"
97
+ ],
98
+ "state_after": "C : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 ((reflectorAdjunction i).homEquiv (A \u2a2f B) ((reflector i).obj A \u2a2f (reflector i).obj B)).symm\n (prod.lift prod.snd prod.fst \u226b\n ((exp.adjunction B).homEquiv A (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B))).symm\n ((unitCompPartialBijective A \u22ef).symm\n (((exp.adjunction B).homEquiv (i.obj ((reflector i).obj A))\n (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B)))\n (prod.lift prod.snd prod.fst \u226b\n ((exp.adjunction (i.obj ((reflector i).obj A))).homEquiv B\n (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B))).symm\n ((unitCompPartialBijective B \u22ef).symm\n (((exp.adjunction (i.obj ((reflector i).obj A))).homEquiv (i.obj ((reflector i).obj B))\n (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B)))\n ((PreservesLimitPair.iso i ((reflector i).obj A) ((reflector i).obj B)).inv \u226b\n i.map (\ud835\udfd9 ((reflector i).obj A \u2a2f (reflector i).obj B)) \u226b\n \ud835\udfd9 (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B))))) \u226b\n \ud835\udfd9 (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B))))) \u226b\n \ud835\udfd9 (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B))) =\n prodComparison (reflector i) A B",
99
+ "state_before": "C : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 (bijection i A B ((reflector i).obj A \u2a2f (reflector i).obj B)).symm (\ud835\udfd9 ((reflector i).obj A \u2a2f (reflector i).obj B)) =\n prodComparison (reflector i) A B",
100
+ "tactic": "dsimp [bijection]"
101
+ },
102
+ {
103
+ "annotated_tactic": [
104
+ "\"erw [<a>homEquiv_symm_apply_eq<\\/a>, <a>homEquiv_symm_apply_eq<\\/a>, <a>homEquiv_apply_eq<\\/a>, <a>homEquiv_apply_eq<\\/a>]\"",
105
+ "[{\"full_name\":\"CategoryTheory.CartesianClosed.homEquiv_symm_apply_eq\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Closed\\/Cartesian.lean\",\"def_pos\":[181,9],\"def_end_pos\":[181,31]},{\"full_name\":\"CategoryTheory.CartesianClosed.homEquiv_symm_apply_eq\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Closed\\/Cartesian.lean\",\"def_pos\":[181,9],\"def_end_pos\":[181,31]},{\"full_name\":\"CategoryTheory.CartesianClosed.homEquiv_apply_eq\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Closed\\/Cartesian.lean\",\"def_pos\":[175,9],\"def_end_pos\":[175,26]},{\"full_name\":\"CategoryTheory.CartesianClosed.homEquiv_apply_eq\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Closed\\/Cartesian.lean\",\"def_pos\":[175,9],\"def_end_pos\":[175,26]}]"
106
+ ],
107
+ "state_after": "C : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 ((reflectorAdjunction i).homEquiv (A \u2a2f B) ((reflector i).obj A \u2a2f (reflector i).obj B)).symm\n (prod.lift prod.snd prod.fst \u226b\n uncurry\n ((unitCompPartialBijective A \u22ef).symm\n (curry\n (prod.lift prod.snd prod.fst \u226b\n uncurry\n ((unitCompPartialBijective B \u22ef).symm\n (curry\n ((PreservesLimitPair.iso i ((reflector i).obj A) ((reflector i).obj B)).inv \u226b\n i.map (\ud835\udfd9 ((reflector i).obj A \u2a2f (reflector i).obj B)) \u226b\n \ud835\udfd9 (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B))))) \u226b\n \ud835\udfd9 (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B))))) \u226b\n \ud835\udfd9 (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B))) =\n prodComparison (reflector i) A B",
108
+ "state_before": "C : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 ((reflectorAdjunction i).homEquiv (A \u2a2f B) ((reflector i).obj A \u2a2f (reflector i).obj B)).symm\n (prod.lift prod.snd prod.fst \u226b\n ((exp.adjunction B).homEquiv A (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B))).symm\n ((unitCompPartialBijective A \u22ef).symm\n (((exp.adjunction B).homEquiv (i.obj ((reflector i).obj A))\n (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B)))\n (prod.lift prod.snd prod.fst \u226b\n ((exp.adjunction (i.obj ((reflector i).obj A))).homEquiv B\n (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B))).symm\n ((unitCompPartialBijective B \u22ef).symm\n (((exp.adjunction (i.obj ((reflector i).obj A))).homEquiv (i.obj ((reflector i).obj B))\n (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B)))\n ((PreservesLimitPair.iso i ((reflector i).obj A) ((reflector i).obj B)).inv \u226b\n i.map (\ud835\udfd9 ((reflector i).obj A \u2a2f (reflector i).obj B)) \u226b\n \ud835\udfd9 (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B))))) \u226b\n \ud835\udfd9 (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B))))) \u226b\n \ud835\udfd9 (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B))) =\n prodComparison (reflector i) A B",
109
+ "tactic": "erw [homEquiv_symm_apply_eq, homEquiv_symm_apply_eq, homEquiv_apply_eq, homEquiv_apply_eq]"
110
+ },
111
+ {
112
+ "annotated_tactic": [
113
+ "\"rw [<a>comp_id<\\/a>, <a>comp_id<\\/a>, <a>comp_id<\\/a>, i.map_id, <a>comp_id<\\/a>, <a>unitCompPartialBijective_symm_apply<\\/a>,\\n <a>unitCompPartialBijective_symm_apply<\\/a>, <a>uncurry_natural_left<\\/a>, <a>uncurry_curry<\\/a>,\\n <a>uncurry_natural_left<\\/a>, <a>uncurry_curry<\\/a>, <a>prod.lift_map_assoc<\\/a>, <a>comp_id<\\/a>, <a>prod.lift_map_assoc<\\/a>, <a>comp_id<\\/a>]\"",
114
+ "[{\"full_name\":\"CategoryTheory.Category.comp_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[179,3],\"def_end_pos\":[179,10]},{\"full_name\":\"CategoryTheory.Category.comp_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[179,3],\"def_end_pos\":[179,10]},{\"full_name\":\"CategoryTheory.Category.comp_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[179,3],\"def_end_pos\":[179,10]},{\"full_name\":\"CategoryTheory.Category.comp_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[179,3],\"def_end_pos\":[179,10]},{\"full_name\":\"CategoryTheory.unitCompPartialBijective_symm_apply\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Adjunction\\/Reflective.lean\",\"def_pos\":[148,9],\"def_end_pos\":[148,44]},{\"full_name\":\"CategoryTheory.unitCompPartialBijective_symm_apply\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Adjunction\\/Reflective.lean\",\"def_pos\":[148,9],\"def_end_pos\":[148,44]},{\"full_name\":\"CategoryTheory.CartesianClosed.uncurry_natural_left\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Closed\\/Cartesian.lean\",\"def_pos\":[205,9],\"def_end_pos\":[205,29]},{\"full_name\":\"CategoryTheory.CartesianClosed.uncurry_curry\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Closed\\/Cartesian.lean\",\"def_pos\":[211,9],\"def_end_pos\":[211,22]},{\"full_name\":\"CategoryTheory.CartesianClosed.uncurry_natural_left\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Closed\\/Cartesian.lean\",\"def_pos\":[205,9],\"def_end_pos\":[205,29]},{\"full_name\":\"CategoryTheory.CartesianClosed.uncurry_curry\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Closed\\/Cartesian.lean\",\"def_pos\":[211,9],\"def_end_pos\":[211,22]},{\"full_name\":\"CategoryTheory.Limits.prod.lift_map_assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[739,3],\"def_end_pos\":[739,25]},{\"full_name\":\"CategoryTheory.Category.comp_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[179,3],\"def_end_pos\":[179,10]},{\"full_name\":\"CategoryTheory.Limits.prod.lift_map_assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[739,3],\"def_end_pos\":[739,25]},{\"full_name\":\"CategoryTheory.Category.comp_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[179,3],\"def_end_pos\":[179,10]}]"
115
+ ],
116
+ "state_after": "C : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 ((reflectorAdjunction i).homEquiv (A \u2a2f B) ((reflector i).obj A \u2a2f (reflector i).obj B)).symm\n (prod.lift prod.snd (prod.fst \u226b (reflectorAdjunction i).unit.app A) \u226b\n prod.lift prod.snd (prod.fst \u226b (reflectorAdjunction i).unit.app B) \u226b\n (PreservesLimitPair.iso i ((reflector i).obj A) ((reflector i).obj B)).inv) =\n prodComparison (reflector i) A B",
117
+ "state_before": "C : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 ((reflectorAdjunction i).homEquiv (A \u2a2f B) ((reflector i).obj A \u2a2f (reflector i).obj B)).symm\n (prod.lift prod.snd prod.fst \u226b\n uncurry\n ((unitCompPartialBijective A \u22ef).symm\n (curry\n (prod.lift prod.snd prod.fst \u226b\n uncurry\n ((unitCompPartialBijective B \u22ef).symm\n (curry\n ((PreservesLimitPair.iso i ((reflector i).obj A) ((reflector i).obj B)).inv \u226b\n i.map (\ud835\udfd9 ((reflector i).obj A \u2a2f (reflector i).obj B)) \u226b\n \ud835\udfd9 (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B))))) \u226b\n \ud835\udfd9 (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B))))) \u226b\n \ud835\udfd9 (i.obj ((reflector i).obj A \u2a2f (reflector i).obj B))) =\n prodComparison (reflector i) A B",
118
+ "tactic": "rw [comp_id, comp_id, comp_id, i.map_id, comp_id, unitCompPartialBijective_symm_apply,\n unitCompPartialBijective_symm_apply, uncurry_natural_left, uncurry_curry,\n uncurry_natural_left, uncurry_curry, prod.lift_map_assoc, comp_id, prod.lift_map_assoc, comp_id]"
119
+ },
120
+ {
121
+ "annotated_tactic": [
122
+ "\"rw [<a>prod.comp_lift_assoc<\\/a>, <a>prod.lift_snd<\\/a>, <a>prod.lift_fst_assoc<\\/a>, <a>prod.lift_fst_comp_snd_comp<\\/a>,\\n \\u2190 <a>Adjunction.eq_homEquiv_apply<\\/a>, <a>Adjunction.homEquiv_unit<\\/a>, <a>Iso.comp_inv_eq<\\/a>, <a>assoc<\\/a>]\"",
123
+ "[{\"full_name\":\"CategoryTheory.Limits.prod.comp_lift_assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[705,3],\"def_end_pos\":[705,10]},{\"full_name\":\"CategoryTheory.Limits.prod.lift_snd\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[629,9],\"def_end_pos\":[629,22]},{\"full_name\":\"CategoryTheory.Limits.prod.lift_fst_assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[620,3],\"def_end_pos\":[620,10]},{\"full_name\":\"CategoryTheory.Limits.prod.lift_fst_comp_snd_comp\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[747,9],\"def_end_pos\":[747,36]},{\"full_name\":\"CategoryTheory.Adjunction.eq_homEquiv_apply\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Adjunction\\/Basic.lean\",\"def_pos\":[264,9],\"def_end_pos\":[264,26]},{\"full_name\":\"CategoryTheory.Adjunction.homEquiv_unit\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Adjunction\\/Basic.lean\",\"def_pos\":[70,3],\"def_end_pos\":[70,16]},{\"full_name\":\"CategoryTheory.Iso.comp_inv_eq\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[219,9],\"def_end_pos\":[219,20]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]}]"
124
+ ],
125
+ "state_after": "C : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 prod.map ((reflectorAdjunction i).unit.app A) ((reflectorAdjunction i).unit.app B) =\n (reflectorAdjunction i).unit.app (A \u2a2f B) \u226b\n i.map (prodComparison (reflector i) A B) \u226b\n (PreservesLimitPair.iso i ((reflector i).obj A) ((reflector i).obj B)).hom",
126
+ "state_before": "C : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 ((reflectorAdjunction i).homEquiv (A \u2a2f B) ((reflector i).obj A \u2a2f (reflector i).obj B)).symm\n (prod.lift prod.snd (prod.fst \u226b (reflectorAdjunction i).unit.app A) \u226b\n prod.lift prod.snd (prod.fst \u226b (reflectorAdjunction i).unit.app B) \u226b\n (PreservesLimitPair.iso i ((reflector i).obj A) ((reflector i).obj B)).inv) =\n prodComparison (reflector i) A B",
127
+ "tactic": "rw [prod.comp_lift_assoc, prod.lift_snd, prod.lift_fst_assoc, prod.lift_fst_comp_snd_comp,\n \u2190 Adjunction.eq_homEquiv_apply, Adjunction.homEquiv_unit, Iso.comp_inv_eq, assoc]"
128
+ },
129
+ {
130
+ "annotated_tactic": [
131
+ "\"rw [<a>PreservesLimitPair.iso_hom<\\/a> i ((<a>reflector<\\/a> i).<a>obj<\\/a> A) ((<a>reflector<\\/a> i).<a>obj<\\/a> B)]\"",
132
+ "[{\"full_name\":\"CategoryTheory.Limits.PreservesLimitPair.iso_hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Preserves\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[96,9],\"def_end_pos\":[96,35]},{\"full_name\":\"CategoryTheory.reflector\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Adjunction\\/Reflective.lean\",\"def_pos\":[46,5],\"def_end_pos\":[46,14]},{\"full_name\":\"Prefunctor.obj\",\"def_path\":\"Mathlib\\/Combinatorics\\/Quiver\\/Basic.lean\",\"def_pos\":[59,3],\"def_end_pos\":[59,6]},{\"full_name\":\"CategoryTheory.reflector\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Adjunction\\/Reflective.lean\",\"def_pos\":[46,5],\"def_end_pos\":[46,14]},{\"full_name\":\"Prefunctor.obj\",\"def_path\":\"Mathlib\\/Combinatorics\\/Quiver\\/Basic.lean\",\"def_pos\":[59,3],\"def_end_pos\":[59,6]}]"
133
+ ],
134
+ "state_after": "C : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 prod.map ((reflectorAdjunction i).unit.app A) ((reflectorAdjunction i).unit.app B) =\n (reflectorAdjunction i).unit.app (A \u2a2f B) \u226b\n i.map (prodComparison (reflector i) A B) \u226b prodComparison i ((reflector i).obj A) ((reflector i).obj B)",
135
+ "state_before": "C : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 prod.map ((reflectorAdjunction i).unit.app A) ((reflectorAdjunction i).unit.app B) =\n (reflectorAdjunction i).unit.app (A \u2a2f B) \u226b\n i.map (prodComparison (reflector i) A B) \u226b\n (PreservesLimitPair.iso i ((reflector i).obj A) ((reflector i).obj B)).hom",
136
+ "tactic": "rw [PreservesLimitPair.iso_hom i ((reflector i).obj A) ((reflector i).obj B)]"
137
+ },
138
+ {
139
+ "annotated_tactic": [
140
+ "\"apply <a>prod.hom_ext<\\/a>\"",
141
+ "[{\"full_name\":\"CategoryTheory.Limits.prod.hom_ext\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[586,9],\"def_end_pos\":[586,21]}]"
142
+ ],
143
+ "state_after": "case h\u2081\nC : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 prod.map ((reflectorAdjunction i).unit.app A) ((reflectorAdjunction i).unit.app B) \u226b prod.fst =\n ((reflectorAdjunction i).unit.app (A \u2a2f B) \u226b\n i.map (prodComparison (reflector i) A B) \u226b prodComparison i ((reflector i).obj A) ((reflector i).obj B)) \u226b\n prod.fst\n\ncase h\u2082\nC : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 prod.map ((reflectorAdjunction i).unit.app A) ((reflectorAdjunction i).unit.app B) \u226b prod.snd =\n ((reflectorAdjunction i).unit.app (A \u2a2f B) \u226b\n i.map (prodComparison (reflector i) A B) \u226b prodComparison i ((reflector i).obj A) ((reflector i).obj B)) \u226b\n prod.snd",
144
+ "state_before": "C : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 prod.map ((reflectorAdjunction i).unit.app A) ((reflectorAdjunction i).unit.app B) =\n (reflectorAdjunction i).unit.app (A \u2a2f B) \u226b\n i.map (prodComparison (reflector i) A B) \u226b prodComparison i ((reflector i).obj A) ((reflector i).obj B)",
145
+ "tactic": "apply prod.hom_ext"
146
+ },
147
+ {
148
+ "annotated_tactic": [
149
+ "\"rw [<a>Limits.prod.map_fst<\\/a>, <a>assoc<\\/a>, <a>assoc<\\/a>, <a>prodComparison_fst<\\/a>, \\u2190 i.map_comp, <a>prodComparison_fst<\\/a>]\"",
150
+ "[{\"full_name\":\"CategoryTheory.Limits.prod.map_fst\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[716,9],\"def_end_pos\":[716,21]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.Limits.prodComparison_fst\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[1260,9],\"def_end_pos\":[1260,27]},{\"full_name\":\"CategoryTheory.Limits.prodComparison_fst\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[1260,9],\"def_end_pos\":[1260,27]}]"
151
+ ],
152
+ "state_after": "case h\u2081\nC : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 prod.fst \u226b (reflectorAdjunction i).unit.app A =\n (reflectorAdjunction i).unit.app (A \u2a2f B) \u226b i.map ((reflector i).map prod.fst)",
153
+ "state_before": "case h\u2081\nC : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 prod.map ((reflectorAdjunction i).unit.app A) ((reflectorAdjunction i).unit.app B) \u226b prod.fst =\n ((reflectorAdjunction i).unit.app (A \u2a2f B) \u226b\n i.map (prodComparison (reflector i) A B) \u226b prodComparison i ((reflector i).obj A) ((reflector i).obj B)) \u226b\n prod.fst",
154
+ "tactic": "rw [Limits.prod.map_fst, assoc, assoc, prodComparison_fst, \u2190 i.map_comp, prodComparison_fst]"
155
+ },
156
+ {
157
+ "annotated_tactic": [
158
+ "\"apply (<a>reflectorAdjunction<\\/a> i).unit.naturality\"",
159
+ "[{\"full_name\":\"CategoryTheory.reflectorAdjunction\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Adjunction\\/Reflective.lean\",\"def_pos\":[49,5],\"def_end_pos\":[49,24]}]"
160
+ ],
161
+ "state_after": "no goals",
162
+ "state_before": "case h\u2081\nC : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 prod.fst \u226b (reflectorAdjunction i).unit.app A =\n (reflectorAdjunction i).unit.app (A \u2a2f B) \u226b i.map ((reflector i).map prod.fst)",
163
+ "tactic": "apply (reflectorAdjunction i).unit.naturality"
164
+ },
165
+ {
166
+ "annotated_tactic": [
167
+ "\"rw [<a>Limits.prod.map_snd<\\/a>, <a>assoc<\\/a>, <a>assoc<\\/a>, <a>prodComparison_snd<\\/a>, \\u2190 i.map_comp, <a>prodComparison_snd<\\/a>]\"",
168
+ "[{\"full_name\":\"CategoryTheory.Limits.prod.map_snd\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[723,9],\"def_end_pos\":[723,21]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.Limits.prodComparison_snd\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[1266,9],\"def_end_pos\":[1266,27]},{\"full_name\":\"CategoryTheory.Limits.prodComparison_snd\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/BinaryProducts.lean\",\"def_pos\":[1266,9],\"def_end_pos\":[1266,27]}]"
169
+ ],
170
+ "state_after": "case h\u2082\nC : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 prod.snd \u226b (reflectorAdjunction i).unit.app B =\n (reflectorAdjunction i).unit.app (A \u2a2f B) \u226b i.map ((reflector i).map prod.snd)",
171
+ "state_before": "case h\u2082\nC : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 prod.map ((reflectorAdjunction i).unit.app A) ((reflectorAdjunction i).unit.app B) \u226b prod.snd =\n ((reflectorAdjunction i).unit.app (A \u2a2f B) \u226b\n i.map (prodComparison (reflector i) A B) \u226b prodComparison i ((reflector i).obj A) ((reflector i).obj B)) \u226b\n prod.snd",
172
+ "tactic": "rw [Limits.prod.map_snd, assoc, assoc, prodComparison_snd, \u2190 i.map_comp, prodComparison_snd]"
173
+ },
174
+ {
175
+ "annotated_tactic": [
176
+ "\"apply (<a>reflectorAdjunction<\\/a> i).unit.naturality\"",
177
+ "[{\"full_name\":\"CategoryTheory.reflectorAdjunction\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Adjunction\\/Reflective.lean\",\"def_pos\":[49,5],\"def_end_pos\":[49,24]}]"
178
+ ],
179
+ "state_after": "no goals",
180
+ "state_before": "case h\u2082\nC : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 prod.snd \u226b (reflectorAdjunction i).unit.app B =\n (reflectorAdjunction i).unit.app (A \u2a2f B) \u226b i.map ((reflector i).map prod.snd)",
181
+ "tactic": "apply (reflectorAdjunction i).unit.naturality"
182
+ }
183
+ ],
184
+ "url": "https://github.com/leanprover-community/mathlib4"
185
+ },
186
+ "source_file": "Mathlib/CategoryTheory/Closed/Ideal.lean"
187
+ },
188
+ {
189
+ "error": "theorem has no selected tactic transitions",
190
+ "full_name": "CategoryTheory.reflective_products",
191
+ "id": "CategoryTheory.reflective_products",
192
+ "reason": "import_failure",
193
+ "selection": {
194
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
195
+ "end": [
196
+ 112,
197
+ 46
198
+ ],
199
+ "file_path": "Mathlib/CategoryTheory/Closed/Ideal.lean",
200
+ "full_name": "CategoryTheory.reflective_products",
201
+ "start": [
202
+ 111,
203
+ 1
204
+ ],
205
+ "traced_tactics": [],
206
+ "url": "https://github.com/leanprover-community/mathlib4"
207
+ },
208
+ "source_file": "Mathlib/CategoryTheory/Closed/Ideal.lean"
209
+ }
210
+ ],
211
+ "input_proofs": 8,
212
+ "input_units": 2,
213
+ "proofs": 3,
214
+ "published_proofs": 2,
215
+ "published_transitions": 5,
216
+ "replay_failures": [],
217
+ "transitions": 7,
218
+ "validation_failures": [
219
+ {
220
+ "errors": [
221
+ "internal transition boundary mismatch"
222
+ ],
223
+ "file_path": "Mathlib/CategoryTheory/Closed/Ideal.lean",
224
+ "proof_id": "mathlib:CategoryTheory.prodComparison_iso",
225
+ "provenance": {
226
+ "selection": {
227
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
228
+ "end": [
229
+ 246,
230
+ 96
231
+ ],
232
+ "file_path": "Mathlib/CategoryTheory/Closed/Ideal.lean",
233
+ "full_name": "CategoryTheory.prodComparison_iso",
234
+ "start": [
235
+ 242,
236
+ 1
237
+ ],
238
+ "traced_tactics": [
239
+ {
240
+ "annotated_tactic": [
241
+ "\"rw [\\u2190 (<a>bijection<\\/a> i _ _ _).injective.eq_iff, <a>bijection_natural<\\/a>, \\u2190 <a>bijection_symm_apply_id<\\/a>,\\n <a>Equiv.apply_symm_apply<\\/a>, <a>id_comp<\\/a>]\"",
242
+ "[{\"full_name\":\"CategoryTheory.bijection\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Closed\\/Ideal.lean\",\"def_pos\":[180,19],\"def_end_pos\":[180,28]},{\"full_name\":\"CategoryTheory.bijection_natural\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Closed\\/Ideal.lean\",\"def_pos\":[224,9],\"def_end_pos\":[224,26]},{\"full_name\":\"CategoryTheory.bijection_symm_apply_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Closed\\/Ideal.lean\",\"def_pos\":[204,9],\"def_end_pos\":[204,32]},{\"full_name\":\"Equiv.apply_symm_apply\",\"def_path\":\"Mathlib\\/Logic\\/Equiv\\/Defs.lean\",\"def_pos\":[279,17],\"def_end_pos\":[279,33]},{\"full_name\":\"CategoryTheory.Category.id_comp\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[177,3],\"def_end_pos\":[177,10]}]"
243
+ ],
244
+ "state_after": "no goals",
245
+ "state_before": "C : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 prodComparison (reflector i) A B \u226b (bijection i A B ((reflector i).obj (A \u2a2f B))) (\ud835\udfd9 ((reflector i).obj (A \u2a2f B))) =\n \ud835\udfd9 ((reflector i).obj (A \u2a2f B))",
246
+ "tactic": "rw [\u2190 (bijection i _ _ _).injective.eq_iff, bijection_natural, \u2190 bijection_symm_apply_id,\n Equiv.apply_symm_apply, id_comp]"
247
+ },
248
+ {
249
+ "annotated_tactic": [
250
+ "\"rw [\\u2190 <a>bijection_natural<\\/a>, <a>id_comp<\\/a>, \\u2190 <a>bijection_symm_apply_id<\\/a>, <a>Equiv.apply_symm_apply<\\/a>]\"",
251
+ "[{\"full_name\":\"CategoryTheory.bijection_natural\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Closed\\/Ideal.lean\",\"def_pos\":[224,9],\"def_end_pos\":[224,26]},{\"full_name\":\"CategoryTheory.Category.id_comp\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[177,3],\"def_end_pos\":[177,10]},{\"full_name\":\"CategoryTheory.bijection_symm_apply_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Closed\\/Ideal.lean\",\"def_pos\":[204,9],\"def_end_pos\":[204,32]},{\"full_name\":\"Equiv.apply_symm_apply\",\"def_path\":\"Mathlib\\/Logic\\/Equiv\\/Defs.lean\",\"def_pos\":[279,17],\"def_end_pos\":[279,33]}]"
252
+ ],
253
+ "state_after": "no goals",
254
+ "state_before": "C : Type u\u2081\nD : Type u\u2082\ninst\u271d\u2076 : Category.{v\u2081, u\u2081} C\ninst\u271d\u2075 : Category.{v\u2081, u\u2082} D\ni : D \u2964 C\ninst\u271d\u2074 : HasFiniteProducts C\ninst\u271d\u00b3 : Reflective i\ninst\u271d\u00b2 : CartesianClosed C\ninst\u271d\u00b9 : HasFiniteProducts D\ninst\u271d : ExponentialIdeal i\nA B : C\n\u22a2 (bijection i A B ((reflector i).obj (A \u2a2f B))) (\ud835\udfd9 ((reflector i).obj (A \u2a2f B))) \u226b prodComparison (reflector i) A B =\n \ud835\udfd9 ((reflector i).obj A \u2a2f (reflector i).obj B)",
255
+ "tactic": "rw [\u2190 bijection_natural, id_comp, \u2190 bijection_symm_apply_id, Equiv.apply_symm_apply]"
256
+ }
257
+ ],
258
+ "url": "https://github.com/leanprover-community/mathlib4"
259
+ }
260
+ },
261
+ "theorem_name": "CategoryTheory.prodComparison_iso"
262
+ }
263
+ ],
264
+ "validation_rejected_proofs": 1,
265
+ "zero_transition_proofs": 0
266
+ },
267
+ "shards": [
268
+ {
269
+ "path": "data/train/mathlib-000622-0000-ad4282e3ec6a6d37.parquet",
270
+ "sha256": "ad4282e3ec6a6d3749218dd19113438fa89d27c94a3cc6661ef52f36316ab673",
271
+ "bytes": 63512,
272
+ "rows": 5,
273
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
274
+ }
275
+ ],
276
+ "proof_ids": [
277
+ "mathlib:CategoryTheory.ExponentialIdeal.mk'",
278
+ "mathlib:CategoryTheory.ExponentialIdeal.mk_of_iso"
279
+ ],
280
+ "proof_keys": [
281
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Ideal.lean\",null,null,\"CategoryTheory.ExponentialIdeal.mk'\"]",
282
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Ideal.lean\",null,null,\"CategoryTheory.ExponentialIdeal.mk_of_iso\"]"
283
+ ]
284
+ }
manifests/batches/mathlib/000623.json ADDED
@@ -0,0 +1,761 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000623",
4
+ "batch_fingerprint": "de3ea78f1c14a0db319b038b6cfc0e50a5b310054bd79254dbcbceed2783e8fb",
5
+ "evidence": {
6
+ "batch_fingerprint": "de3ea78f1c14a0db319b038b6cfc0e50a5b310054bd79254dbcbceed2783e8fb",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "CategoryTheory.MonoidalClosed.coev_app_comp_pre_app",
12
+ "id": "CategoryTheory.MonoidalClosed.coev_app_comp_pre_app",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 258,
18
+ 60
19
+ ],
20
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
21
+ "full_name": "CategoryTheory.MonoidalClosed.coev_app_comp_pre_app",
22
+ "start": [
23
+ 256,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "CategoryTheory.MonoidalClosed.curry_eq",
34
+ "id": "CategoryTheory.MonoidalClosed.curry_eq",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 211,
40
+ 29
41
+ ],
42
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
43
+ "full_name": "CategoryTheory.MonoidalClosed.curry_eq",
44
+ "start": [
45
+ 210,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "CategoryTheory.MonoidalClosed.curry_eq_iff",
56
+ "id": "CategoryTheory.MonoidalClosed.curry_eq_iff",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 198,
62
+ 55
63
+ ],
64
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
65
+ "full_name": "CategoryTheory.MonoidalClosed.curry_eq_iff",
66
+ "start": [
67
+ 197,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "CategoryTheory.MonoidalClosed.curry_injective",
78
+ "id": "CategoryTheory.MonoidalClosed.curry_injective",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 215,
84
+ 38
85
+ ],
86
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
87
+ "full_name": "CategoryTheory.MonoidalClosed.curry_injective",
88
+ "start": [
89
+ 214,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "CategoryTheory.MonoidalClosed.curry_natural_left",
100
+ "id": "CategoryTheory.MonoidalClosed.curry_natural_left",
101
+ "reason": "import_failure",
102
+ "selection": {
103
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
104
+ "end": [
105
+ 166,
106
+ 44
107
+ ],
108
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
109
+ "full_name": "CategoryTheory.MonoidalClosed.curry_natural_left",
110
+ "start": [
111
+ 165,
112
+ 1
113
+ ],
114
+ "traced_tactics": [],
115
+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
118
+ },
119
+ {
120
+ "error": "theorem has no selected tactic transitions",
121
+ "full_name": "CategoryTheory.MonoidalClosed.curry_natural_right",
122
+ "id": "CategoryTheory.MonoidalClosed.curry_natural_right",
123
+ "reason": "import_failure",
124
+ "selection": {
125
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
126
+ "end": [
127
+ 172,
128
+ 45
129
+ ],
130
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
131
+ "full_name": "CategoryTheory.MonoidalClosed.curry_natural_right",
132
+ "start": [
133
+ 170,
134
+ 1
135
+ ],
136
+ "traced_tactics": [],
137
+ "url": "https://github.com/leanprover-community/mathlib4"
138
+ },
139
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
140
+ },
141
+ {
142
+ "error": "theorem has no selected tactic transitions",
143
+ "full_name": "CategoryTheory.MonoidalClosed.curry_uncurry",
144
+ "id": "CategoryTheory.MonoidalClosed.curry_uncurry",
145
+ "reason": "import_failure",
146
+ "selection": {
147
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
148
+ "end": [
149
+ 194,
150
+ 40
151
+ ],
152
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
153
+ "full_name": "CategoryTheory.MonoidalClosed.curry_uncurry",
154
+ "start": [
155
+ 193,
156
+ 1
157
+ ],
158
+ "traced_tactics": [],
159
+ "url": "https://github.com/leanprover-community/mathlib4"
160
+ },
161
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
162
+ },
163
+ {
164
+ "error": "theorem has no selected tactic transitions",
165
+ "full_name": "CategoryTheory.MonoidalClosed.eq_curry_iff",
166
+ "id": "CategoryTheory.MonoidalClosed.eq_curry_iff",
167
+ "reason": "import_failure",
168
+ "selection": {
169
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
170
+ "end": [
171
+ 202,
172
+ 55
173
+ ],
174
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
175
+ "full_name": "CategoryTheory.MonoidalClosed.eq_curry_iff",
176
+ "start": [
177
+ 201,
178
+ 1
179
+ ],
180
+ "traced_tactics": [],
181
+ "url": "https://github.com/leanprover-community/mathlib4"
182
+ },
183
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
184
+ },
185
+ {
186
+ "error": "theorem has no selected tactic transitions",
187
+ "full_name": "CategoryTheory.MonoidalClosed.homEquiv_apply_eq",
188
+ "id": "CategoryTheory.MonoidalClosed.homEquiv_apply_eq",
189
+ "reason": "import_failure",
190
+ "selection": {
191
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
192
+ "end": [
193
+ 154,
194
+ 6
195
+ ],
196
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
197
+ "full_name": "CategoryTheory.MonoidalClosed.homEquiv_apply_eq",
198
+ "start": [
199
+ 153,
200
+ 1
201
+ ],
202
+ "traced_tactics": [],
203
+ "url": "https://github.com/leanprover-community/mathlib4"
204
+ },
205
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
206
+ },
207
+ {
208
+ "error": "theorem has no selected tactic transitions",
209
+ "full_name": "CategoryTheory.MonoidalClosed.homEquiv_symm_apply_eq",
210
+ "id": "CategoryTheory.MonoidalClosed.homEquiv_symm_apply_eq",
211
+ "reason": "import_failure",
212
+ "selection": {
213
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
214
+ "end": [
215
+ 161,
216
+ 6
217
+ ],
218
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
219
+ "full_name": "CategoryTheory.MonoidalClosed.homEquiv_symm_apply_eq",
220
+ "start": [
221
+ 159,
222
+ 1
223
+ ],
224
+ "traced_tactics": [],
225
+ "url": "https://github.com/leanprover-community/mathlib4"
226
+ },
227
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
228
+ },
229
+ {
230
+ "error": "theorem has no selected tactic transitions",
231
+ "full_name": "CategoryTheory.MonoidalClosed.id_tensor_pre_app_comp_ev",
232
+ "id": "CategoryTheory.MonoidalClosed.id_tensor_pre_app_comp_ev",
233
+ "reason": "import_failure",
234
+ "selection": {
235
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
236
+ "end": [
237
+ 246,
238
+ 62
239
+ ],
240
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
241
+ "full_name": "CategoryTheory.MonoidalClosed.id_tensor_pre_app_comp_ev",
242
+ "start": [
243
+ 244,
244
+ 1
245
+ ],
246
+ "traced_tactics": [],
247
+ "url": "https://github.com/leanprover-community/mathlib4"
248
+ },
249
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
250
+ },
251
+ {
252
+ "error": "theorem has no selected tactic transitions",
253
+ "full_name": "CategoryTheory.MonoidalClosed.ofEquiv_curry_def",
254
+ "id": "CategoryTheory.MonoidalClosed.ofEquiv_curry_def",
255
+ "reason": "import_failure",
256
+ "selection": {
257
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
258
+ "end": [
259
+ 313,
260
+ 6
261
+ ],
262
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
263
+ "full_name": "CategoryTheory.MonoidalClosed.ofEquiv_curry_def",
264
+ "start": [
265
+ 306,
266
+ 1
267
+ ],
268
+ "traced_tactics": [],
269
+ "url": "https://github.com/leanprover-community/mathlib4"
270
+ },
271
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
272
+ },
273
+ {
274
+ "error": "theorem has no selected tactic transitions",
275
+ "full_name": "CategoryTheory.MonoidalClosed.ofEquiv_uncurry_def",
276
+ "id": "CategoryTheory.MonoidalClosed.ofEquiv_uncurry_def",
277
+ "reason": "import_failure",
278
+ "selection": {
279
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
280
+ "end": [
281
+ 328,
282
+ 15
283
+ ],
284
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
285
+ "full_name": "CategoryTheory.MonoidalClosed.ofEquiv_uncurry_def",
286
+ "start": [
287
+ 321,
288
+ 1
289
+ ],
290
+ "traced_tactics": [],
291
+ "url": "https://github.com/leanprover-community/mathlib4"
292
+ },
293
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
294
+ },
295
+ {
296
+ "error": "theorem has no selected tactic transitions",
297
+ "full_name": "CategoryTheory.MonoidalClosed.uncurry_curry",
298
+ "id": "CategoryTheory.MonoidalClosed.uncurry_curry",
299
+ "reason": "import_failure",
300
+ "selection": {
301
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
302
+ "end": [
303
+ 189,
304
+ 39
305
+ ],
306
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
307
+ "full_name": "CategoryTheory.MonoidalClosed.uncurry_curry",
308
+ "start": [
309
+ 188,
310
+ 1
311
+ ],
312
+ "traced_tactics": [],
313
+ "url": "https://github.com/leanprover-community/mathlib4"
314
+ },
315
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
316
+ },
317
+ {
318
+ "error": "theorem has no selected tactic transitions",
319
+ "full_name": "CategoryTheory.MonoidalClosed.uncurry_eq",
320
+ "id": "CategoryTheory.MonoidalClosed.uncurry_eq",
321
+ "reason": "import_failure",
322
+ "selection": {
323
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
324
+ "end": [
325
+ 207,
326
+ 31
327
+ ],
328
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
329
+ "full_name": "CategoryTheory.MonoidalClosed.uncurry_eq",
330
+ "start": [
331
+ 206,
332
+ 1
333
+ ],
334
+ "traced_tactics": [],
335
+ "url": "https://github.com/leanprover-community/mathlib4"
336
+ },
337
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
338
+ },
339
+ {
340
+ "error": "theorem has no selected tactic transitions",
341
+ "full_name": "CategoryTheory.MonoidalClosed.uncurry_natural_left",
342
+ "id": "CategoryTheory.MonoidalClosed.uncurry_natural_left",
343
+ "reason": "import_failure",
344
+ "selection": {
345
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
346
+ "end": [
347
+ 184,
348
+ 49
349
+ ],
350
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
351
+ "full_name": "CategoryTheory.MonoidalClosed.uncurry_natural_left",
352
+ "start": [
353
+ 182,
354
+ 1
355
+ ],
356
+ "traced_tactics": [],
357
+ "url": "https://github.com/leanprover-community/mathlib4"
358
+ },
359
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
360
+ },
361
+ {
362
+ "error": "theorem has no selected tactic transitions",
363
+ "full_name": "CategoryTheory.MonoidalClosed.uncurry_natural_right",
364
+ "id": "CategoryTheory.MonoidalClosed.uncurry_natural_right",
365
+ "reason": "import_failure",
366
+ "selection": {
367
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
368
+ "end": [
369
+ 178,
370
+ 50
371
+ ],
372
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
373
+ "full_name": "CategoryTheory.MonoidalClosed.uncurry_natural_right",
374
+ "start": [
375
+ 176,
376
+ 1
377
+ ],
378
+ "traced_tactics": [],
379
+ "url": "https://github.com/leanprover-community/mathlib4"
380
+ },
381
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
382
+ },
383
+ {
384
+ "error": "theorem has no selected tactic transitions",
385
+ "full_name": "CategoryTheory.ihom.coev_ev",
386
+ "id": "CategoryTheory.ihom.coev_ev",
387
+ "reason": "import_failure",
388
+ "selection": {
389
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
390
+ "end": [
391
+ 126,
392
+ 61
393
+ ],
394
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
395
+ "full_name": "CategoryTheory.ihom.coev_ev",
396
+ "start": [
397
+ 125,
398
+ 1
399
+ ],
400
+ "traced_tactics": [],
401
+ "url": "https://github.com/leanprover-community/mathlib4"
402
+ },
403
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
404
+ },
405
+ {
406
+ "error": "theorem has no selected tactic transitions",
407
+ "full_name": "CategoryTheory.ihom.coev_naturality",
408
+ "id": "CategoryTheory.ihom.coev_naturality",
409
+ "reason": "import_failure",
410
+ "selection": {
411
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
412
+ "end": [
413
+ 112,
414
+ 24
415
+ ],
416
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
417
+ "full_name": "CategoryTheory.ihom.coev_naturality",
418
+ "start": [
419
+ 110,
420
+ 1
421
+ ],
422
+ "traced_tactics": [],
423
+ "url": "https://github.com/leanprover-community/mathlib4"
424
+ },
425
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
426
+ },
427
+ {
428
+ "error": "theorem has no selected tactic transitions",
429
+ "full_name": "CategoryTheory.ihom.ev_coev",
430
+ "id": "CategoryTheory.ihom.ev_coev",
431
+ "reason": "import_failure",
432
+ "selection": {
433
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
434
+ "end": [
435
+ 121,
436
+ 49
437
+ ],
438
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
439
+ "full_name": "CategoryTheory.ihom.ev_coev",
440
+ "start": [
441
+ 120,
442
+ 1
443
+ ],
444
+ "traced_tactics": [],
445
+ "url": "https://github.com/leanprover-community/mathlib4"
446
+ },
447
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
448
+ },
449
+ {
450
+ "error": "theorem has no selected tactic transitions",
451
+ "full_name": "CategoryTheory.ihom.ev_naturality",
452
+ "id": "CategoryTheory.ihom.ev_naturality",
453
+ "reason": "import_failure",
454
+ "selection": {
455
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
456
+ "end": [
457
+ 106,
458
+ 22
459
+ ],
460
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
461
+ "full_name": "CategoryTheory.ihom.ev_naturality",
462
+ "start": [
463
+ 104,
464
+ 1
465
+ ],
466
+ "traced_tactics": [],
467
+ "url": "https://github.com/leanprover-community/mathlib4"
468
+ },
469
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
470
+ },
471
+ {
472
+ "error": "theorem has no selected tactic transitions",
473
+ "full_name": "CategoryTheory.ihom.ihom_adjunction_counit",
474
+ "id": "CategoryTheory.ihom.ihom_adjunction_counit",
475
+ "reason": "import_failure",
476
+ "selection": {
477
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
478
+ "end": [
479
+ 95,
480
+ 6
481
+ ],
482
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
483
+ "full_name": "CategoryTheory.ihom.ihom_adjunction_counit",
484
+ "start": [
485
+ 94,
486
+ 1
487
+ ],
488
+ "traced_tactics": [],
489
+ "url": "https://github.com/leanprover-community/mathlib4"
490
+ },
491
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
492
+ },
493
+ {
494
+ "error": "theorem has no selected tactic transitions",
495
+ "full_name": "CategoryTheory.ihom.ihom_adjunction_unit",
496
+ "id": "CategoryTheory.ihom.ihom_adjunction_unit",
497
+ "reason": "import_failure",
498
+ "selection": {
499
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
500
+ "end": [
501
+ 100,
502
+ 6
503
+ ],
504
+ "file_path": "Mathlib/CategoryTheory/Closed/Monoidal.lean",
505
+ "full_name": "CategoryTheory.ihom.ihom_adjunction_unit",
506
+ "start": [
507
+ 99,
508
+ 1
509
+ ],
510
+ "traced_tactics": [],
511
+ "url": "https://github.com/leanprover-community/mathlib4"
512
+ },
513
+ "source_file": "Mathlib/CategoryTheory/Closed/Monoidal.lean"
514
+ },
515
+ {
516
+ "error": "theorem has no selected tactic transitions",
517
+ "full_name": "CategoryTheory.le_isoClosure",
518
+ "id": "CategoryTheory.le_isoClosure",
519
+ "reason": "import_failure",
520
+ "selection": {
521
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
522
+ "end": [
523
+ 48,
524
+ 36
525
+ ],
526
+ "file_path": "Mathlib/CategoryTheory/ClosedUnderIsomorphisms.lean",
527
+ "full_name": "CategoryTheory.le_isoClosure",
528
+ "start": [
529
+ 47,
530
+ 1
531
+ ],
532
+ "traced_tactics": [],
533
+ "url": "https://github.com/leanprover-community/mathlib4"
534
+ },
535
+ "source_file": "Mathlib/CategoryTheory/ClosedUnderIsomorphisms.lean"
536
+ },
537
+ {
538
+ "error": "theorem has no selected tactic transitions",
539
+ "full_name": "CategoryTheory.mem_iff_of_isIso",
540
+ "id": "CategoryTheory.mem_iff_of_isIso",
541
+ "reason": "import_failure",
542
+ "selection": {
543
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
544
+ "end": [
545
+ 35,
546
+ 29
547
+ ],
548
+ "file_path": "Mathlib/CategoryTheory/ClosedUnderIsomorphisms.lean",
549
+ "full_name": "CategoryTheory.mem_iff_of_isIso",
550
+ "start": [
551
+ 34,
552
+ 1
553
+ ],
554
+ "traced_tactics": [],
555
+ "url": "https://github.com/leanprover-community/mathlib4"
556
+ },
557
+ "source_file": "Mathlib/CategoryTheory/ClosedUnderIsomorphisms.lean"
558
+ },
559
+ {
560
+ "error": "theorem has no selected tactic transitions",
561
+ "full_name": "CategoryTheory.mem_iff_of_iso",
562
+ "id": "CategoryTheory.mem_iff_of_iso",
563
+ "reason": "import_failure",
564
+ "selection": {
565
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
566
+ "end": [
567
+ 29,
568
+ 40
569
+ ],
570
+ "file_path": "Mathlib/CategoryTheory/ClosedUnderIsomorphisms.lean",
571
+ "full_name": "CategoryTheory.mem_iff_of_iso",
572
+ "start": [
573
+ 28,
574
+ 1
575
+ ],
576
+ "traced_tactics": [],
577
+ "url": "https://github.com/leanprover-community/mathlib4"
578
+ },
579
+ "source_file": "Mathlib/CategoryTheory/ClosedUnderIsomorphisms.lean"
580
+ },
581
+ {
582
+ "error": "theorem has no selected tactic transitions",
583
+ "full_name": "CategoryTheory.mem_isoClosure",
584
+ "id": "CategoryTheory.mem_isoClosure",
585
+ "reason": "import_failure",
586
+ "selection": {
587
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
588
+ "end": [
589
+ 45,
590
+ 27
591
+ ],
592
+ "file_path": "Mathlib/CategoryTheory/ClosedUnderIsomorphisms.lean",
593
+ "full_name": "CategoryTheory.mem_isoClosure",
594
+ "start": [
595
+ 44,
596
+ 1
597
+ ],
598
+ "traced_tactics": [],
599
+ "url": "https://github.com/leanprover-community/mathlib4"
600
+ },
601
+ "source_file": "Mathlib/CategoryTheory/ClosedUnderIsomorphisms.lean"
602
+ },
603
+ {
604
+ "error": "theorem has no selected tactic transitions",
605
+ "full_name": "CategoryTheory.mem_of_isIso",
606
+ "id": "CategoryTheory.mem_of_isIso",
607
+ "reason": "import_failure",
608
+ "selection": {
609
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
610
+ "end": [
611
+ 32,
612
+ 28
613
+ ],
614
+ "file_path": "Mathlib/CategoryTheory/ClosedUnderIsomorphisms.lean",
615
+ "full_name": "CategoryTheory.mem_of_isIso",
616
+ "start": [
617
+ 31,
618
+ 1
619
+ ],
620
+ "traced_tactics": [],
621
+ "url": "https://github.com/leanprover-community/mathlib4"
622
+ },
623
+ "source_file": "Mathlib/CategoryTheory/ClosedUnderIsomorphisms.lean"
624
+ },
625
+ {
626
+ "error": "theorem has no selected tactic transitions",
627
+ "full_name": "CategoryTheory.mem_of_iso",
628
+ "id": "CategoryTheory.mem_of_iso",
629
+ "reason": "import_failure",
630
+ "selection": {
631
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
632
+ "end": [
633
+ 26,
634
+ 38
635
+ ],
636
+ "file_path": "Mathlib/CategoryTheory/ClosedUnderIsomorphisms.lean",
637
+ "full_name": "CategoryTheory.mem_of_iso",
638
+ "start": [
639
+ 25,
640
+ 1
641
+ ],
642
+ "traced_tactics": [],
643
+ "url": "https://github.com/leanprover-community/mathlib4"
644
+ },
645
+ "source_file": "Mathlib/CategoryTheory/ClosedUnderIsomorphisms.lean"
646
+ }
647
+ ],
648
+ "input_proofs": 39,
649
+ "input_units": 2,
650
+ "proofs": 10,
651
+ "published_proofs": 9,
652
+ "published_transitions": 12,
653
+ "replay_failures": [],
654
+ "transitions": 16,
655
+ "validation_failures": [
656
+ {
657
+ "errors": [
658
+ "internal transition boundary mismatch",
659
+ "internal transition boundary mismatch"
660
+ ],
661
+ "file_path": "Mathlib/CategoryTheory/ClosedUnderIsomorphisms.lean",
662
+ "proof_id": "mathlib:CategoryTheory.isoClosure_eq_self",
663
+ "provenance": {
664
+ "selection": {
665
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
666
+ "end": [
667
+ 59,
668
+ 26
669
+ ],
670
+ "file_path": "Mathlib/CategoryTheory/ClosedUnderIsomorphisms.lean",
671
+ "full_name": "CategoryTheory.isoClosure_eq_self",
672
+ "start": [
673
+ 55,
674
+ 1
675
+ ],
676
+ "traced_tactics": [
677
+ {
678
+ "annotated_tactic": [
679
+ "\"apply <a>le_antisymm<\\/a>\"",
680
+ "[{\"full_name\":\"le_antisymm\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[188,9],\"def_end_pos\":[188,20]}]"
681
+ ],
682
+ "state_after": "case a\nC : Type u_1\ninst\u271d\u00b9 : Category.{u_2, u_1} C\nP Q : C \u2192 Prop\ninst\u271d : ClosedUnderIsomorphisms P\n\u22a2 isoClosure P \u2264 P\n\ncase a\nC : Type u_1\ninst\u271d\u00b9 : Category.{u_2, u_1} C\nP Q : C \u2192 Prop\ninst\u271d : ClosedUnderIsomorphisms P\n\u22a2 P \u2264 isoClosure P",
683
+ "state_before": "C : Type u_1\ninst\u271d\u00b9 : Category.{u_2, u_1} C\nP Q : C \u2192 Prop\ninst\u271d : ClosedUnderIsomorphisms P\n\u22a2 isoClosure P = P",
684
+ "tactic": "apply le_antisymm"
685
+ },
686
+ {
687
+ "annotated_tactic": [
688
+ "\"intro X \\u27e8Y, hY, \\u27e8e\\u27e9\\u27e9\"",
689
+ "[]"
690
+ ],
691
+ "state_after": "case a\nC : Type u_1\ninst\u271d\u00b9 : Category.{u_2, u_1} C\nP Q : C \u2192 Prop\ninst\u271d : ClosedUnderIsomorphisms P\nX Y : C\nhY : P Y\ne : X \u2245 Y\n\u22a2 P X",
692
+ "state_before": "case a\nC : Type u_1\ninst\u271d\u00b9 : Category.{u_2, u_1} C\nP Q : C \u2192 Prop\ninst\u271d : ClosedUnderIsomorphisms P\n\u22a2 isoClosure P \u2264 P",
693
+ "tactic": "intro X \u27e8Y, hY, \u27e8e\u27e9\u27e9"
694
+ },
695
+ {
696
+ "annotated_tactic": [
697
+ "\"exact <a>mem_of_iso<\\/a> P e.symm hY\"",
698
+ "[{\"full_name\":\"CategoryTheory.mem_of_iso\",\"def_path\":\"Mathlib\\/CategoryTheory\\/ClosedUnderIsomorphisms.lean\",\"def_pos\":[25,7],\"def_end_pos\":[25,17]}]"
699
+ ],
700
+ "state_after": "no goals",
701
+ "state_before": "case a\nC : Type u_1\ninst\u271d\u00b9 : Category.{u_2, u_1} C\nP Q : C \u2192 Prop\ninst\u271d : ClosedUnderIsomorphisms P\nX Y : C\nhY : P Y\ne : X \u2245 Y\n\u22a2 P X",
702
+ "tactic": "exact mem_of_iso P e.symm hY"
703
+ },
704
+ {
705
+ "annotated_tactic": [
706
+ "\"exact <a>le_isoClosure<\\/a> P\"",
707
+ "[{\"full_name\":\"CategoryTheory.le_isoClosure\",\"def_path\":\"Mathlib\\/CategoryTheory\\/ClosedUnderIsomorphisms.lean\",\"def_pos\":[47,7],\"def_end_pos\":[47,20]}]"
708
+ ],
709
+ "state_after": "no goals",
710
+ "state_before": "case a\nC : Type u_1\ninst\u271d\u00b9 : Category.{u_2, u_1} C\nP Q : C \u2192 Prop\ninst\u271d : ClosedUnderIsomorphisms P\n\u22a2 P \u2264 isoClosure P",
711
+ "tactic": "exact le_isoClosure P"
712
+ }
713
+ ],
714
+ "url": "https://github.com/leanprover-community/mathlib4"
715
+ }
716
+ },
717
+ "theorem_name": "CategoryTheory.isoClosure_eq_self"
718
+ }
719
+ ],
720
+ "validation_rejected_proofs": 1,
721
+ "zero_transition_proofs": 0
722
+ },
723
+ "shards": [
724
+ {
725
+ "path": "data/train/mathlib-000623-0000-b3b0c558e36343dc.parquet",
726
+ "sha256": "b3b0c558e36343dcf3e7e9c11ba14fdfe327ca85bbfb9a56decc9eeefefef27f",
727
+ "bytes": 56946,
728
+ "rows": 10,
729
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
730
+ },
731
+ {
732
+ "path": "data/dev/mathlib-000623-0000-789ef7ca9525e6f7.parquet",
733
+ "sha256": "789ef7ca9525e6f7e093c5ecf5c9ca46cd6809ca3b5454748e68f535aee72cd9",
734
+ "bytes": 37116,
735
+ "rows": 2,
736
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
737
+ }
738
+ ],
739
+ "proof_ids": [
740
+ "mathlib:CategoryTheory.MonoidalClosed.curry_id_eq_coev",
741
+ "mathlib:CategoryTheory.MonoidalClosed.pre_comm_ihom_map",
742
+ "mathlib:CategoryTheory.MonoidalClosed.pre_id",
743
+ "mathlib:CategoryTheory.MonoidalClosed.pre_map",
744
+ "mathlib:CategoryTheory.MonoidalClosed.uncurry_id_eq_ev",
745
+ "mathlib:CategoryTheory.MonoidalClosed.uncurry_pre",
746
+ "mathlib:CategoryTheory.isoClosure_le_iff",
747
+ "mathlib:CategoryTheory.mem_isoClosure_iff",
748
+ "mathlib:CategoryTheory.monotone_isoClosure"
749
+ ],
750
+ "proof_keys": [
751
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Monoidal.lean\",null,null,\"CategoryTheory.MonoidalClosed.curry_id_eq_coev\"]",
752
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Monoidal.lean\",null,null,\"CategoryTheory.MonoidalClosed.pre_comm_ihom_map\"]",
753
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Monoidal.lean\",null,null,\"CategoryTheory.MonoidalClosed.pre_id\"]",
754
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Monoidal.lean\",null,null,\"CategoryTheory.MonoidalClosed.pre_map\"]",
755
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Monoidal.lean\",null,null,\"CategoryTheory.MonoidalClosed.uncurry_id_eq_ev\"]",
756
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Closed/Monoidal.lean\",null,null,\"CategoryTheory.MonoidalClosed.uncurry_pre\"]",
757
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/ClosedUnderIsomorphisms.lean\",null,null,\"CategoryTheory.isoClosure_le_iff\"]",
758
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/ClosedUnderIsomorphisms.lean\",null,null,\"CategoryTheory.mem_isoClosure_iff\"]",
759
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/ClosedUnderIsomorphisms.lean\",null,null,\"CategoryTheory.monotone_isoClosure\"]"
760
+ ]
761
+ }
manifests/batches/numina/001374.json ADDED
@@ -0,0 +1,44 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "numina/001374",
4
+ "batch_fingerprint": "e957381f68664deb47200918ffb75cc3eda07e51e70d4a84eda37c8f193254ac",
5
+ "evidence": {
6
+ "batch_fingerprint": "e957381f68664deb47200918ffb75cc3eda07e51e70d4a84eda37c8f193254ac",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 5,
10
+ "input_units": 5,
11
+ "proofs": 5,
12
+ "published_proofs": 5,
13
+ "published_transitions": 65,
14
+ "replay_failures": [],
15
+ "trace_mode": "bundle",
16
+ "transitions": 65,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/numina-001374-0000-b9693aca5669228a.parquet",
24
+ "sha256": "b9693aca5669228a1c827d36f4078f9da310df727191005f43c233c9e4096669",
25
+ "bytes": 702581,
26
+ "rows": 65,
27
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
28
+ }
29
+ ],
30
+ "proof_ids": [
31
+ "numina:250f12a2-1ac5-5bde-88f4-c266228d6e38",
32
+ "numina:46d7c1be-4553-5f85-bbbc-626d43dbbe5f",
33
+ "numina:472153da-16bb-5a6b-b5d8-c1266d562b3a",
34
+ "numina:6abeb42f-ffaf-519e-bd19-46f458674f0c",
35
+ "numina:de450765-0077-58f7-bd31-ae85c91ffc28"
36
+ ],
37
+ "proof_keys": [
38
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006870.lean\",\"6854ad8837e980fb2db7b17bb27ece9c4c11fc966b25c41487bafec58187ec4b\",0,\"algebra_758\"]",
39
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006871.lean\",\"87d78105a969073812cb677485d1058e9f396545d0d9ff8262def31ddd88a783\",0,\"algebra_96098\"]",
40
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006872.lean\",\"ff3f391b78cf6016f5ac92548f0a746d7ec9e2f96a33e69ee5e1abd1f29b1eba\",0,\"algebra_9080\"]",
41
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006873.lean\",\"69f44ca95893f6dad360e0865adffa517fc38aa6db42b5e48733ede2f0895742\",0,\"algebra_15897\"]",
42
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006874.lean\",\"e1699474376ceae3dbbdd1d22eb2362f3ef00ad908d788fe2726e085fa5cc749\",0,\"number_theory_257808\"]"
43
+ ]
44
+ }
manifests/batches/numina/001375.json ADDED
@@ -0,0 +1,79 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "numina/001375",
4
+ "batch_fingerprint": "d85690b44baf8cd38bdbf60b2acf44b13e118d000a537280f5aaa1f7c1d971ca",
5
+ "evidence": {
6
+ "batch_fingerprint": "d85690b44baf8cd38bdbf60b2acf44b13e118d000a537280f5aaa1f7c1d971ca",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 5,
10
+ "input_units": 5,
11
+ "proofs": 5,
12
+ "published_proofs": 4,
13
+ "published_transitions": 67,
14
+ "replay_failures": [],
15
+ "trace_mode": "bundle",
16
+ "transitions": 115,
17
+ "validation_failures": [
18
+ {
19
+ "errors": [
20
+ "internal transition boundary mismatch",
21
+ "internal transition boundary mismatch",
22
+ "internal transition boundary mismatch",
23
+ "internal transition boundary mismatch",
24
+ "internal transition boundary mismatch",
25
+ "internal transition boundary mismatch",
26
+ "internal transition boundary mismatch",
27
+ "internal transition boundary mismatch"
28
+ ],
29
+ "file_path": "Full/Proof_006879.lean",
30
+ "proof_id": "numina:f316b891-a721-52b3-b633-6555c0157c4d",
31
+ "provenance": {
32
+ "atomic_transition_count": 61,
33
+ "bundle_ordinal": 4,
34
+ "compound_transition_count": 18,
35
+ "declaration_kind": "theorem",
36
+ "metadata": {
37
+ "bundle_ordinal": 4,
38
+ "declaration_kind": "theorem",
39
+ "original_file_path": "Full/Proof_006879.lean",
40
+ "source_dataset": "numina",
41
+ "theorem_name": "algebra_162584",
42
+ "theorem_ordinal": 0
43
+ },
44
+ "original_file_path": "Full/Proof_006879.lean",
45
+ "selection_index": 6879,
46
+ "source_dataset": "numina",
47
+ "source_id": "f316b891-a721-52b3-b633-6555c0157c4d",
48
+ "source_sha256": "0f6a01b146255ce8fa5ff1fd31ca2f2b6631ea2ac0dbb02f71584189ab52054a",
49
+ "theorem_name": "algebra_162584",
50
+ "theorem_ordinal": 0
51
+ },
52
+ "theorem_name": "algebra_162584"
53
+ }
54
+ ],
55
+ "validation_rejected_proofs": 1,
56
+ "zero_transition_proofs": 0
57
+ },
58
+ "shards": [
59
+ {
60
+ "path": "data/train/numina-001375-0000-e66227cf946ea4a7.parquet",
61
+ "sha256": "e66227cf946ea4a724e85c958cd97b30d5ce82ed99f8ebc59e99636c3528c651",
62
+ "bytes": 569974,
63
+ "rows": 67,
64
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
65
+ }
66
+ ],
67
+ "proof_ids": [
68
+ "numina:30e13e32-25fe-5496-813e-6e35cb9963ed",
69
+ "numina:50792340-404d-5875-869e-10d2ba3afa67",
70
+ "numina:e04a9da9-4674-5625-8083-b7649c46bbc4",
71
+ "numina:e4f945e1-cdb4-57f6-882c-3e1430321cc5"
72
+ ],
73
+ "proof_keys": [
74
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006875.lean\",\"95cff18df52b2314ce7a7bdce7970b9a1a02c902bbbf2b2100a1ffd58ae6b64a\",0,\"number_theory_611197\"]",
75
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006876.lean\",\"403e48f29e61b8316942062f4ee557bfa895eb2f83fea01b15ebd5a0fd5049de\",0,\"algebra_607789\"]",
76
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006877.lean\",\"e448b62ca38b47b9d6acc46cd118dc4518437ae6e2757b963c6ee67dcc2a772e\",0,\"calculus_279245\"]",
77
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006878.lean\",\"00e2373a8e4b0ef8c469161bfc535bfebdec279fd92dc761a16c299880103f3e\",0,\"algebra_122634\"]"
78
+ ]
79
+ }
manifests/batches/numina/001376.json ADDED
@@ -0,0 +1,58 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "numina/001376",
4
+ "batch_fingerprint": "6079de85a769d831c2c1ff37adc605287b4604434e5737f90d49ddccb5f1af2b",
5
+ "evidence": {
6
+ "batch_fingerprint": "6079de85a769d831c2c1ff37adc605287b4604434e5737f90d49ddccb5f1af2b",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 5,
10
+ "input_units": 5,
11
+ "proofs": 5,
12
+ "published_proofs": 5,
13
+ "published_transitions": 27,
14
+ "replay_failures": [],
15
+ "trace_mode": "bundle",
16
+ "transitions": 27,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/numina-001376-0000-fd3a0d5bf8bcd9ff.parquet",
24
+ "sha256": "fd3a0d5bf8bcd9ffc657deeae08a70e4470e0860d3a26a564572bb1909ff8fb5",
25
+ "bytes": 197914,
26
+ "rows": 19,
27
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
28
+ },
29
+ {
30
+ "path": "data/dev/numina-001376-0000-090821d8c44ce5b5.parquet",
31
+ "sha256": "090821d8c44ce5b589804cd867bec0cf8490acbbe3283f075feece5de6e55f84",
32
+ "bytes": 38565,
33
+ "rows": 5,
34
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
35
+ },
36
+ {
37
+ "path": "data/internal_test/numina-001376-0000-1f12e2d10980bde2.parquet",
38
+ "sha256": "1f12e2d10980bde257298baf64136cc3ced64bbf6b0649010558e140c1b8375f",
39
+ "bytes": 38713,
40
+ "rows": 3,
41
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
42
+ }
43
+ ],
44
+ "proof_ids": [
45
+ "numina:0c27c9ce-1dae-5517-8b7a-f7d35eb83184",
46
+ "numina:13027763-160e-5d06-86d5-d59f00174ba2",
47
+ "numina:a0828d66-ec76-5205-a142-8712ec849017",
48
+ "numina:c6d53734-58b2-54e6-886d-2797457dfb81",
49
+ "numina:c81c873a-ee91-50f1-b6a4-c2b0e5faaef6"
50
+ ],
51
+ "proof_keys": [
52
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006880.lean\",\"c76bd1039a41974cd28578e77fb166a27f1a80a57b03e2ce913f021126b3896e\",0,\"number_theory_704\"]",
53
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006881.lean\",\"7ab1ac96d2c44a267c61f385d4df45beba4c52295fa952938fa8d35c51933362\",0,\"algebra_21329\"]",
54
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006882.lean\",\"18cb1ac1ffd2213a3721c4fbe93f108886aafa04eaecb20044016af15761c9fe\",0,\"algebra_9081\"]",
55
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006883.lean\",\"8bfeb1ed10495ba00b683f892cf884cd8d4d71610462f5262a08876f0d277ef1\",0,\"Other_5738\"]",
56
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006884.lean\",\"684e97ed55b79b4d785ab38d947c6f3fef1bf307c5ce9e01ae64745183d0876f\",0,\"algebra_611198\"]"
57
+ ]
58
+ }
manifests/batches/numina/001377.json ADDED
@@ -0,0 +1,44 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "numina/001377",
4
+ "batch_fingerprint": "95fcbb8f42fabb12772f05ad9ece723c4199b1c22f4442b995666fa83d855d63",
5
+ "evidence": {
6
+ "batch_fingerprint": "95fcbb8f42fabb12772f05ad9ece723c4199b1c22f4442b995666fa83d855d63",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 5,
10
+ "input_units": 5,
11
+ "proofs": 5,
12
+ "published_proofs": 5,
13
+ "published_transitions": 33,
14
+ "replay_failures": [],
15
+ "trace_mode": "bundle",
16
+ "transitions": 33,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/numina-001377-0000-745d7cc4c4be2957.parquet",
24
+ "sha256": "745d7cc4c4be2957baba172c7da4c9cd6704b25e20e8e40b880f25d1e4e0f838",
25
+ "bytes": 337109,
26
+ "rows": 33,
27
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
28
+ }
29
+ ],
30
+ "proof_ids": [
31
+ "numina:722331ce-4ae5-5521-9412-bd1f8bbf32c9",
32
+ "numina:99ea5bb6-c6a7-5f34-b810-6ee8211251f1",
33
+ "numina:b486394c-a53a-5dc4-9833-e296cd2cff47",
34
+ "numina:b5980783-aa08-5153-a419-758aba7c3b89",
35
+ "numina:ec6f6ea2-e1cd-5c06-9359-38d8b7284185"
36
+ ],
37
+ "proof_keys": [
38
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006885.lean\",\"87a9115b239ea09391f4285d49e95881011b4ddbaf0dd9b9a45fe8ae51d1c0d9\",0,\"number_theory_276074\"]",
39
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006886.lean\",\"bf06e3176e4c493dda8e26d8311f542a8182e5a6783502055b73b6a471b38e9d\",0,\"algebra_122683\"]",
40
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006887.lean\",\"c58926d5ed4ad5bc8020aa12f0a6f0865f31123cc4dd3aa57c6f92f789e07c19\",0,\"number_theory_162159\"]",
41
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006888.lean\",\"e2a6e2b78dffaa08b7eedbe4efe5a33d717cd4102ddeca199152065f2032cc12\",0,\"algebra_12265\"]",
42
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006889.lean\",\"19a040d2dfdccdfc54e4ffd5b4512f4c7eb70b7b7cddc0adfb6048c35793dcce\",0,\"Algebra_1165\"]"
43
+ ]
44
+ }
manifests/batches/numina/001378.json ADDED
@@ -0,0 +1,44 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "numina/001378",
4
+ "batch_fingerprint": "6e83966b8f4ec53f6050cea95feed0386498dbe85293074691edba860c5ba947",
5
+ "evidence": {
6
+ "batch_fingerprint": "6e83966b8f4ec53f6050cea95feed0386498dbe85293074691edba860c5ba947",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 5,
10
+ "input_units": 5,
11
+ "proofs": 5,
12
+ "published_proofs": 5,
13
+ "published_transitions": 50,
14
+ "replay_failures": [],
15
+ "trace_mode": "bundle",
16
+ "transitions": 50,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/numina-001378-0000-77b4e322f2688929.parquet",
24
+ "sha256": "77b4e322f26889299f2d65e626fc1e7881807f51b8cb2b5ed94776e58489f87e",
25
+ "bytes": 491480,
26
+ "rows": 50,
27
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
28
+ }
29
+ ],
30
+ "proof_ids": [
31
+ "numina:268e3447-5628-5e63-8cdd-a39869373b54",
32
+ "numina:4fec34ed-2289-5911-8109-e0e9d8f93515",
33
+ "numina:640bca89-132d-57ff-9419-3109cbd0e5ff",
34
+ "numina:d5d6474a-ca90-511f-bb42-f8b478303b0f",
35
+ "numina:f2f9e4a9-8200-524b-a0b1-d88201f849b8"
36
+ ],
37
+ "proof_keys": [
38
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006890.lean\",\"e333a4aca776f7e66e7f744d06eaa7d2af523a8a2ab052d379469fc40b4ea605\",0,\"algebra_21331\"]",
39
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006891.lean\",\"f0075e03aaee9b917b8ed2393a323595e03c4333cd94c224b8b63d6301c921c4\",0,\"number_theory_24693\"]",
40
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006892.lean\",\"f93be5bf66decba8fff62b78437dd7c011076501ae2a77dca2ea9c883a3805ed\",0,\"number_theory_182650\"]",
41
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006893.lean\",\"adde04a4dca2c1c7ef3f2e8a22a0b4b5293902f07b55ba2ba0ec89e6d69ae24c\",0,\"algebra_9082\"]",
42
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006894.lean\",\"c8784e2b1c33c7753a6e275a9e7f8bc1c0447f7918becc0e4a8df1e6d9cba700\",0,\"algebra_606369\"]"
43
+ ]
44
+ }
manifests/batches/numina/001379.json ADDED
@@ -0,0 +1,51 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "numina/001379",
4
+ "batch_fingerprint": "47718d34f2a0164ec8704394618e4c1403d0b40f02642a013e5fcfcfc55ed792",
5
+ "evidence": {
6
+ "batch_fingerprint": "47718d34f2a0164ec8704394618e4c1403d0b40f02642a013e5fcfcfc55ed792",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 5,
10
+ "input_units": 5,
11
+ "proofs": 5,
12
+ "published_proofs": 5,
13
+ "published_transitions": 37,
14
+ "replay_failures": [],
15
+ "trace_mode": "bundle",
16
+ "transitions": 37,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/numina-001379-0000-883244cff4e77a2a.parquet",
24
+ "sha256": "883244cff4e77a2ae31348ec682a85f3c49990a330cd76de774e492d2e254b77",
25
+ "bytes": 367353,
26
+ "rows": 28,
27
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
28
+ },
29
+ {
30
+ "path": "data/internal_test/numina-001379-0000-b56e9b19a72419de.parquet",
31
+ "sha256": "b56e9b19a72419de3dcbd17355d9b69eee2e506f1e82ff0073de03df737e3774",
32
+ "bytes": 99976,
33
+ "rows": 9,
34
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
35
+ }
36
+ ],
37
+ "proof_ids": [
38
+ "numina:27dfdba3-2fae-5bc9-a556-3aaa16237858",
39
+ "numina:4662d1d5-5090-52af-bf73-2b20c8c3166d",
40
+ "numina:e056ae60-6a50-5ba3-90be-3554850a8f6d",
41
+ "numina:eeaaf587-62d6-5a9c-bc3c-dce0a7557ddc",
42
+ "numina:f10fdcfe-1ed9-5aac-8f7e-19212254ec01"
43
+ ],
44
+ "proof_keys": [
45
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006895.lean\",\"31b8cd5a0204fabd3763176e4901050094f3626edbca51d2260fcdc606fb8e1f\",0,\"number_theory_122359\"]",
46
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006896.lean\",\"262003e9b8dc31ea8c8f6abfd0e69097ca2840acbc2c355f6418d90907cda01e\",0,\"inequalities_162237\"]",
47
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006897.lean\",\"621e38e7d48b7b819ddedd7c9ec24913d1ccfaa4cf331295cfa3d54ea5fb0e97\",0,\"algebra_16021\"]",
48
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006898.lean\",\"fa3c95510e4d065331f880ad0eef3d1ae2dab8a396effb741da4828e310f9454\",0,\"algebra_9086\"]",
49
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006899.lean\",\"289e382537923df1a0dddf18cf5d93abece608b5273227ee74e256e28747dec5\",0,\"calculus_611202\"]"
50
+ ]
51
+ }
manifests/batches/numina/001380.json ADDED
@@ -0,0 +1,51 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "numina/001380",
4
+ "batch_fingerprint": "158743aa5e2568b1031adf16e6541fa28bb79d698298a2a6932de57bbf7a04f0",
5
+ "evidence": {
6
+ "batch_fingerprint": "158743aa5e2568b1031adf16e6541fa28bb79d698298a2a6932de57bbf7a04f0",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 5,
10
+ "input_units": 5,
11
+ "proofs": 5,
12
+ "published_proofs": 5,
13
+ "published_transitions": 36,
14
+ "replay_failures": [],
15
+ "trace_mode": "bundle",
16
+ "transitions": 36,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/numina-001380-0000-fc36373ded23061f.parquet",
24
+ "sha256": "fc36373ded23061f48b2490088895f21b47f8e7cbc1ac436baa8a2de26bce902",
25
+ "bytes": 261400,
26
+ "rows": 32,
27
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
28
+ },
29
+ {
30
+ "path": "data/internal_test/numina-001380-0000-51438c0365f8faba.parquet",
31
+ "sha256": "51438c0365f8faba7ed5aa93717c671c109dfc23216618036218d1486ce8d233",
32
+ "bytes": 74594,
33
+ "rows": 4,
34
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
35
+ }
36
+ ],
37
+ "proof_ids": [
38
+ "numina:4c7ab903-d067-5c2d-9deb-217c9f69bcaa",
39
+ "numina:7b88bf15-8d37-513f-aa03-3986cb49e2b7",
40
+ "numina:acf0ea64-4949-5d56-9aa9-6137247b48eb",
41
+ "numina:ca2ed0ca-51b6-5739-bd67-1dccdba1944c",
42
+ "numina:d19c4998-2415-5656-9e7d-add8680efb33"
43
+ ],
44
+ "proof_keys": [
45
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006900.lean\",\"c54a2a133e3aeeef0587f4c29611811fa663b5cdf5e9232a9cc2b7a5eb64b792\",0,\"number_theory_113479\"]",
46
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006901.lean\",\"13b36be424aeac7ed3225b80e9cc3405afad8ab3d3f96f8a4a059be2ac693596\",0,\"algebra_162284\"]",
47
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006902.lean\",\"f9c517aa722383a262dce2f171625d651c4a3509ac907c0b4385d8e5f82da032\",0,\"algebra_100084\"]",
48
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006903.lean\",\"ca301f29d9895a435f2d7be98aab9520a31f5cd74ec198a912063d4a4b86ed41\",0,\"algebra_21335\"]",
49
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006904.lean\",\"195a580340370d56380880634f008fedbffc7edafb1156491a53d90ed8525a61\",0,\"algebra_9077\"]"
50
+ ]
51
+ }
manifests/batches/numina/001381.json ADDED
@@ -0,0 +1,51 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "numina/001381",
4
+ "batch_fingerprint": "2928fd940b7032238a05e2437bd59c65a1feeecae2a04361ff11f8004c677328",
5
+ "evidence": {
6
+ "batch_fingerprint": "2928fd940b7032238a05e2437bd59c65a1feeecae2a04361ff11f8004c677328",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 5,
10
+ "input_units": 5,
11
+ "proofs": 5,
12
+ "published_proofs": 5,
13
+ "published_transitions": 22,
14
+ "replay_failures": [],
15
+ "trace_mode": "bundle",
16
+ "transitions": 22,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/numina-001381-0000-4df30e1412635d2e.parquet",
24
+ "sha256": "4df30e1412635d2e534bf050b34a9f80492c0dd0bfd8accf208ffa345262cdf5",
25
+ "bytes": 91715,
26
+ "rows": 15,
27
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
28
+ },
29
+ {
30
+ "path": "data/internal_test/numina-001381-0000-2f9a80c2e1babd02.parquet",
31
+ "sha256": "2f9a80c2e1babd0239db21fbf040f8d41124130b89678f042080ea79ab26ee65",
32
+ "bytes": 33195,
33
+ "rows": 7,
34
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
35
+ }
36
+ ],
37
+ "proof_ids": [
38
+ "numina:1d6ed093-b983-525b-b4f3-7ea9d48d1eb5",
39
+ "numina:67c890a5-bb06-5772-9b96-c7a0180bdf0c",
40
+ "numina:a1d6e2de-ed4e-53af-acea-4ce063b9dcbf",
41
+ "numina:bb608080-dd6f-5eb9-b9db-fed5a738625d",
42
+ "numina:fb2b316d-12d1-56e4-9440-37088aef78a4"
43
+ ],
44
+ "proof_keys": [
45
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006905.lean\",\"04bef05017f1b7a5c603b2a9d413586137c51931969069564d84672431ef9064\",0,\"number_theory_328315\"]",
46
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006906.lean\",\"eadf13e97a4f06bd1741cf984ad53866ce463cc84ab67b80efc3029e8f5c2fdb\",0,\"number_theory_53999\"]",
47
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006907.lean\",\"8898e6ffa79751eb926319185e0cfcb22473ce82d193cbc076869844671cfe43\",0,\"number_theory_255863\"]",
48
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006908.lean\",\"07cca347a737443993b3303efdb2e2ba5e21092de9835385893704b7df130f40\",0,\"algebra_276215\"]",
49
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006909.lean\",\"fae5bb672088fa1755671378335c463eee598d1153f0c4fcfde4f48f77edcaf8\",0,\"number_theory_218634\"]"
50
+ ]
51
+ }
manifests/batches/numina/001382.json ADDED
@@ -0,0 +1,44 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "numina/001382",
4
+ "batch_fingerprint": "387a5981efa69ce2e6f57133719b1ada2b1a1f455abc0b118e00d1afb5ea9a9a",
5
+ "evidence": {
6
+ "batch_fingerprint": "387a5981efa69ce2e6f57133719b1ada2b1a1f455abc0b118e00d1afb5ea9a9a",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 5,
10
+ "input_units": 5,
11
+ "proofs": 5,
12
+ "published_proofs": 5,
13
+ "published_transitions": 47,
14
+ "replay_failures": [],
15
+ "trace_mode": "bundle",
16
+ "transitions": 47,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/numina-001382-0000-c4af0b8f6336948e.parquet",
24
+ "sha256": "c4af0b8f6336948e6431e4241e9e7927f2d1a0fb298759a264a2f47f0cb0a869",
25
+ "bytes": 225451,
26
+ "rows": 47,
27
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
28
+ }
29
+ ],
30
+ "proof_ids": [
31
+ "numina:007c64c7-fa77-5f6d-aa7b-e1f2ca56d174",
32
+ "numina:64aa7d91-062c-5a96-9102-6f1c30ac8bee",
33
+ "numina:9aafd3b4-560b-59dd-b7a1-e484db180a1c",
34
+ "numina:a732a901-52db-5c50-ab16-a6c00fa40ed7",
35
+ "numina:b5f029c9-b543-5c42-b6c8-4df73522f163"
36
+ ],
37
+ "proof_keys": [
38
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006910.lean\",\"0d37400544b51ef1ee56a0168ab0dedb61ec7105df47ae3bfae6725b00b40182\",0,\"algebra_95734\"]",
39
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006911.lean\",\"da9af6cd1ad2767d8d12816dd58301d98c6986af1da89fde24a5044121c37f70\",0,\"algebra_12272\"]",
40
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006912.lean\",\"afe4e3c5ed1d75cbca24b0af91ecba90382c86c0ed987002192d9d7cbd097077\",0,\"algebra_21342\"]",
41
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006913.lean\",\"19de904b8984be722f14036241b3c639b70a7bd9f7a19bad9a17a8ced43eb7b6\",0,\"inequalities_45542\"]",
42
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006914.lean\",\"ee43ad11e838b08da880f8b77e258f04d6323845d933f308067d345dccabdb43\",0,\"algebra_182688\"]"
43
+ ]
44
+ }
manifests/batches/numina/001383.json ADDED
@@ -0,0 +1,73 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "numina/001383",
4
+ "batch_fingerprint": "8b75a6de94332ba22cd3f9b212a42e1407e8be03bf1600e83967a3d0b07b2a8d",
5
+ "evidence": {
6
+ "batch_fingerprint": "8b75a6de94332ba22cd3f9b212a42e1407e8be03bf1600e83967a3d0b07b2a8d",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 5,
10
+ "input_units": 5,
11
+ "proofs": 5,
12
+ "published_proofs": 4,
13
+ "published_transitions": 36,
14
+ "replay_failures": [],
15
+ "trace_mode": "bundle",
16
+ "transitions": 45,
17
+ "validation_failures": [
18
+ {
19
+ "errors": [
20
+ "internal transition boundary mismatch",
21
+ "internal transition boundary mismatch"
22
+ ],
23
+ "file_path": "Full/Proof_006918.lean",
24
+ "proof_id": "numina:8b9fa763-80ea-5f99-945e-8c9a782624fb",
25
+ "provenance": {
26
+ "atomic_transition_count": 49,
27
+ "bundle_ordinal": 3,
28
+ "compound_transition_count": 13,
29
+ "declaration_kind": "theorem",
30
+ "metadata": {
31
+ "bundle_ordinal": 3,
32
+ "declaration_kind": "theorem",
33
+ "original_file_path": "Full/Proof_006918.lean",
34
+ "source_dataset": "numina",
35
+ "theorem_name": "number_theory_328431",
36
+ "theorem_ordinal": 0
37
+ },
38
+ "original_file_path": "Full/Proof_006918.lean",
39
+ "selection_index": 6918,
40
+ "source_dataset": "numina",
41
+ "source_id": "8b9fa763-80ea-5f99-945e-8c9a782624fb",
42
+ "source_sha256": "0597cde842baa3ff96682ba8626f1a2ea46c48431f1ed59601ad5c974395d37e",
43
+ "theorem_name": "number_theory_328431",
44
+ "theorem_ordinal": 0
45
+ },
46
+ "theorem_name": "number_theory_328431"
47
+ }
48
+ ],
49
+ "validation_rejected_proofs": 1,
50
+ "zero_transition_proofs": 0
51
+ },
52
+ "shards": [
53
+ {
54
+ "path": "data/train/numina-001383-0000-01a11fcbe36d05f5.parquet",
55
+ "sha256": "01a11fcbe36d05f5be8dcda1e9288e3c7bdb017593828e89634e97b8458d7c5c",
56
+ "bytes": 175932,
57
+ "rows": 36,
58
+ "revision": "540aac416fcf8bc27a29108551aa515caf5e35da"
59
+ }
60
+ ],
61
+ "proof_ids": [
62
+ "numina:28c94c33-a016-5f64-8ebb-a9a61a6ffa95",
63
+ "numina:7ae312c7-ad06-50bf-8e73-fecab5440cf4",
64
+ "numina:e32dc9a2-dede-5c26-ba6a-321ca0169e25",
65
+ "numina:ec4fddb9-ec25-547f-b5da-54cf57a08685"
66
+ ],
67
+ "proof_keys": [
68
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006915.lean\",\"b985f7801181afa062a9a083e0e5a4ebea520327ee8e4608f1494b3e3c3cd0ce\",0,\"algebra_9078\"]",
69
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006916.lean\",\"9241e5a07ca41a5c893229f5385a99d9d3ffae06b38b56a44c0ab564daf9f4fc\",0,\"algebra_16029\"]",
70
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006917.lean\",\"3e607735c65cc9a21947489c659cd0a1d956bc89e3eb5ce1c9bbaa9c30517059\",0,\"algebra_231255\"]",
71
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_006919.lean\",\"4198b0271a7ce3e6a14e7f11f8c9818d1a66accc40b8f5a7c8aabc91cbe696c8\",0,\"number_theory_19475\"]"
72
+ ]
73
+ }