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
52bb2cb
·
verified ·
1 Parent(s): 9aefeac

Record 20 verified HPC batch manifests

Browse files
Files changed (20) hide show
  1. manifests/batches/deepseek/000322.json +148 -0
  2. manifests/batches/deepseek/000324.json +141 -0
  3. manifests/batches/deepseek/000326.json +148 -0
  4. manifests/batches/deepseek/000327.json +141 -0
  5. manifests/batches/deepseek/000329.json +148 -0
  6. manifests/batches/mathlib/000252.json +0 -0
  7. manifests/batches/mathlib/000253.json +423 -0
  8. manifests/batches/mathlib/000254.json +1084 -0
  9. manifests/batches/mathlib/000255.json +1114 -0
  10. manifests/batches/mathlib/000256.json +541 -0
  11. manifests/batches/mathlib/000257.json +148 -0
  12. manifests/batches/mathlib/000258.json +1022 -0
  13. manifests/batches/mathlib/000259.json +1012 -0
  14. manifests/batches/numina/001012.json +44 -0
  15. manifests/batches/numina/001014.json +44 -0
  16. manifests/batches/numina/001015.json +44 -0
  17. manifests/batches/numina/001016.json +51 -0
  18. manifests/batches/numina/001017.json +51 -0
  19. manifests/batches/numina/001018.json +51 -0
  20. manifests/batches/numina/001019.json +51 -0
manifests/batches/deepseek/000322.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "deepseek/000322",
4
+ "batch_fingerprint": "e0e83c74bce009fa92dc334b39ec195e9a13d77af8726a1c7667549f0d7eb71a",
5
+ "evidence": {
6
+ "batch_fingerprint": "e0e83c74bce009fa92dc334b39ec195e9a13d77af8726a1c7667549f0d7eb71a",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 50,
10
+ "input_units": 50,
11
+ "proofs": 50,
12
+ "published_proofs": 50,
13
+ "published_transitions": 113,
14
+ "replay_failures": [],
15
+ "trace_mode": "individual",
16
+ "transitions": 113,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/deepseek-000322-0000-0682089f0549e62c.parquet",
24
+ "sha256": "0682089f0549e62c2c171e04cc92cdb7972265992b3d095c6ac3b3ad87536a35",
25
+ "bytes": 323489,
26
+ "rows": 90,
27
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
28
+ },
29
+ {
30
+ "path": "data/dev/deepseek-000322-0000-3d4e6162646e4db6.parquet",
31
+ "sha256": "3d4e6162646e4db61de59c18b8d99faa506e4cf2838d003800dcd4d3cd75a2a3",
32
+ "bytes": 48330,
33
+ "rows": 9,
34
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
35
+ },
36
+ {
37
+ "path": "data/internal_test/deepseek-000322-0000-fed8e8582082d9fa.parquet",
38
+ "sha256": "fed8e8582082d9fa556f0b9d3758ff4c7d341f1c735cdc10227432507e2bbc4d",
39
+ "bytes": 55049,
40
+ "rows": 14,
41
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
42
+ }
43
+ ],
44
+ "proof_ids": [
45
+ "deepseek:thm_16143",
46
+ "deepseek:thm_16144",
47
+ "deepseek:thm_16145",
48
+ "deepseek:thm_16146",
49
+ "deepseek:thm_16147",
50
+ "deepseek:thm_16148",
51
+ "deepseek:thm_16149",
52
+ "deepseek:thm_16150",
53
+ "deepseek:thm_16151",
54
+ "deepseek:thm_16152",
55
+ "deepseek:thm_16153",
56
+ "deepseek:thm_16154",
57
+ "deepseek:thm_16155",
58
+ "deepseek:thm_16156",
59
+ "deepseek:thm_16157",
60
+ "deepseek:thm_16158",
61
+ "deepseek:thm_16159",
62
+ "deepseek:thm_16160",
63
+ "deepseek:thm_16161",
64
+ "deepseek:thm_16162",
65
+ "deepseek:thm_16163",
66
+ "deepseek:thm_16164",
67
+ "deepseek:thm_16165",
68
+ "deepseek:thm_16166",
69
+ "deepseek:thm_16167",
70
+ "deepseek:thm_16168",
71
+ "deepseek:thm_16169",
72
+ "deepseek:thm_16170",
73
+ "deepseek:thm_16171",
74
+ "deepseek:thm_16172",
75
+ "deepseek:thm_16173",
76
+ "deepseek:thm_16174",
77
+ "deepseek:thm_16175",
78
+ "deepseek:thm_16176",
79
+ "deepseek:thm_16177",
80
+ "deepseek:thm_16178",
81
+ "deepseek:thm_16179",
82
+ "deepseek:thm_16180",
83
+ "deepseek:thm_16181",
84
+ "deepseek:thm_16182",
85
+ "deepseek:thm_16183",
86
+ "deepseek:thm_16184",
87
+ "deepseek:thm_16185",
88
+ "deepseek:thm_16186",
89
+ "deepseek:thm_16187",
90
+ "deepseek:thm_16188",
91
+ "deepseek:thm_16189",
92
+ "deepseek:thm_16190",
93
+ "deepseek:thm_16191",
94
+ "deepseek:thm_16192"
95
+ ],
96
+ "proof_keys": [
97
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016100.lean\",\"7b13638341ad2d75fe6574b565134fca983d5c6b5fe883bd4bcf6974f50692f6\",0,\"thm_16143\"]",
98
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016101.lean\",\"ef084bb2f4ecc498d664fe1c7398511ce1408796837a273efed8b2e03e9017de\",0,\"thm_16144\"]",
99
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016102.lean\",\"c4da7f2ef67e6e74b44790246e5bdab58825a11db13b033f93386f67d75c2c63\",0,\"thm_16145\"]",
100
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016103.lean\",\"843f2714ae2dec2cc9154d1c8caed1146155996760f8dc354c7dc59edbfe713e\",0,\"thm_16146\"]",
101
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016104.lean\",\"c3a65b9bcbf74b9cec9fad650ddd2587e2849b2c993d2ed9a648453633c1f45c\",0,\"thm_16147\"]",
102
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016105.lean\",\"e5f59cdb41f295171224b4ec580007d4e24d228858d05d1c5d70fa7f7a1c51c4\",0,\"thm_16148\"]",
103
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016106.lean\",\"e321b9ecaa4307d6dc5cbddaa74fb0c347cb5399f108cd7715d3806dcf9d4098\",0,\"thm_16149\"]",
104
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016107.lean\",\"a903a5acff7b06c29eb65970ffa0a4cfac6aa14c717b7d3cc8cf5ee477dfa8d8\",0,\"thm_16150\"]",
105
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016108.lean\",\"ad24bcb479598ef56b9f80e6be659dfa9bb10409fdee86896329b90082864a38\",0,\"thm_16151\"]",
106
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016109.lean\",\"5df6aa9cf7b2f34453140b80322fa53a1cf00770f784d3f120b64760d451d5f6\",0,\"thm_16152\"]",
107
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016110.lean\",\"ab65f75afaceb856f2422f5b43b449b5614b2e258a415c979501c183e630a103\",0,\"thm_16153\"]",
108
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016111.lean\",\"b3d4e8037eadaa5c7bc92ea38d64fb03c399c30e8623cf761b2c0b31a17e3ae4\",0,\"thm_16154\"]",
109
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016112.lean\",\"c3b2b9b285f793ce651cac0e64e81fd0a634895a7426da0a9737ebacf12dcd6b\",0,\"thm_16155\"]",
110
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016113.lean\",\"7c91b2a9af3f036018fe02a48676786365b4913a5bf987d5c6b723f8c03f8e5e\",0,\"thm_16156\"]",
111
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016114.lean\",\"154a0998b9164de4e0e65a53a2d52b65bce3180132acd9168ff98bfa1f40a116\",0,\"thm_16157\"]",
112
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016115.lean\",\"ba14434eac9d8af1f5c32898b618cddfabb830cefcbff06abad2a485df32ded0\",0,\"thm_16158\"]",
113
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016116.lean\",\"114fa61f00998cc67498679c50755ab706177883e46bed8a3b349d6c721c77d5\",0,\"thm_16159\"]",
114
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016117.lean\",\"aeff2a3086cc219c9033f1dd3e22c6327a78cabf4bdb2c69363c2b9ac696fbaf\",0,\"thm_16160\"]",
115
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016118.lean\",\"7daebe70a295117db1343b367f9e4f78eb4e1b361c74dfdbb44abee0fc54a7f4\",0,\"thm_16161\"]",
116
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016119.lean\",\"ed176b87868b147c1166bcea8cf95041389e120147fe3d105f524a99d66ddac8\",0,\"thm_16162\"]",
117
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016120.lean\",\"b3b82635cb4168525d5a680173b5376bf56bd1cce46ff4b9fe20bcd6a05a87c9\",0,\"thm_16163\"]",
118
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016121.lean\",\"c8f4106d576aad396a455e0450fce235fa3b191bea33ef03fa47c6919baad970\",0,\"thm_16164\"]",
119
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016122.lean\",\"519372e913ed67d9d6adbff01a635d97c1f74141f91b816d7e0c8b8e21909475\",0,\"thm_16165\"]",
120
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016123.lean\",\"32c98c07349aee81f828943122d3b01a30945942fb5e9e3c6172485d99660352\",0,\"thm_16166\"]",
121
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016124.lean\",\"35201225efa845323de4d95c0dc6f81be39cfc5843cb426cd4788633cab9f025\",0,\"thm_16167\"]",
122
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016125.lean\",\"d7e4f8d4ff449b8f148da0df6547f402b13e037b8ec29ee782c7d275f4efc0b8\",0,\"thm_16168\"]",
123
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016126.lean\",\"9499bcf46540e45e79790ed965b4392d8a67cf364755cceaa4e9a36596f94240\",0,\"thm_16169\"]",
124
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016127.lean\",\"46d85fcf24e0d2398f0cda2ed8ab0f0f4fa1bcdcb242d540b88a1473b1b84195\",0,\"thm_16170\"]",
125
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016128.lean\",\"d0847ce72a173fa086f6c56b5fd6b12c273517d1fdd8cf4dc9ff0c40f5c683d6\",0,\"thm_16171\"]",
126
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016129.lean\",\"b547032989e113249fa74ff3c972ce627cfa40b5b5b8a54077190ddb10b3be62\",0,\"thm_16172\"]",
127
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016130.lean\",\"4938972eb10a2e303c3eee1c214cde39ae360ea57a08fdb81ac858791062fff3\",0,\"thm_16173\"]",
128
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016131.lean\",\"300e588db48c36fdf4a63e29d7a0eb198793099b2afdb3f5ea9b5728ecec5935\",0,\"thm_16174\"]",
129
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016132.lean\",\"8387546df173a2e6592de63d4da80daa9e2f18ad548f6353655702aac650c7db\",0,\"thm_16175\"]",
130
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016133.lean\",\"deaf05cac8efdb8f5fee91001e4e9a4dbeb275d4994b1121a637a6fe1841160c\",0,\"thm_16176\"]",
131
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016134.lean\",\"6713edf9e3ee3103c12260e0981f929701eaf213c6f2932cbd4023c2a344c8ca\",0,\"thm_16177\"]",
132
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016135.lean\",\"815694d47b1953dfa9112c55f1a87a6f45cb57dca4d159899908e6dc45e37276\",0,\"thm_16178\"]",
133
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016136.lean\",\"d087add5dfdec7670297948b938341343fd1158a22c3563d67c1e5ba680b719d\",0,\"thm_16179\"]",
134
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016137.lean\",\"fce5c5f7ff41e9c85a89c783a7f4a3bcc5b01e91b005ee934f42e0bd85ed9ab3\",0,\"thm_16180\"]",
135
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016138.lean\",\"417ab0a2890cd5e3f1af58142665fa254dd5baaff3af19158b9f208004e8df76\",0,\"thm_16181\"]",
136
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016139.lean\",\"1beee8ea94f1129dce51fbe0ca62db96349bca964df73785d958ebfdcb905b3e\",0,\"thm_16182\"]",
137
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016140.lean\",\"d6b7dce6f258f5746f073edea5837e1e10cee1b033c4a6dcc490086e7fffd220\",0,\"thm_16183\"]",
138
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016141.lean\",\"e066bf53d653ea4dbf70a33ada7aa8dfebb7cd1739065ffab9705b9ee9f21baf\",0,\"thm_16184\"]",
139
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016142.lean\",\"a57a8f05c96d2cbddf306eb25649ecc73e28533a42d907812b922a8d73d38d8d\",0,\"thm_16185\"]",
140
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016143.lean\",\"8772387a24b393f51b9877731c0e3e31835842c4a80bfb74288d994891646354\",0,\"thm_16186\"]",
141
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016144.lean\",\"de190428552372e188d6c0cc779e189fe692146b2b08ae99cdaceacb72ef0c47\",0,\"thm_16187\"]",
142
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016145.lean\",\"e9f4d6342238d24b323dda48de9042e76f70eee35755e35cdd5b12d7f6cf1310\",0,\"thm_16188\"]",
143
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016146.lean\",\"ef40d951fe9295494950cda0609c228dfbb895068c930a713953b29d962da52a\",0,\"thm_16189\"]",
144
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016147.lean\",\"99a3a767ff6d3130f51a320931664af87755f985fd435cff58815ab07e1daf0c\",0,\"thm_16190\"]",
145
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016148.lean\",\"2e2f118dc44aabf47caa329e3c9214c01e4f82240182922c1e90d54ee7b8fb0a\",0,\"thm_16191\"]",
146
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016149.lean\",\"2700a2ab7af9e4ec88f6b1fd1209589fd6cea55b264fc1a141e4fd58154ee8df\",0,\"thm_16192\"]"
147
+ ]
148
+ }
manifests/batches/deepseek/000324.json ADDED
@@ -0,0 +1,141 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "deepseek/000324",
4
+ "batch_fingerprint": "a615b2ff459e1c93f01dd42673f119bdabf740eab8404de48d3795f53a33f432",
5
+ "evidence": {
6
+ "batch_fingerprint": "a615b2ff459e1c93f01dd42673f119bdabf740eab8404de48d3795f53a33f432",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 50,
10
+ "input_units": 50,
11
+ "proofs": 50,
12
+ "published_proofs": 50,
13
+ "published_transitions": 120,
14
+ "replay_failures": [],
15
+ "trace_mode": "individual",
16
+ "transitions": 120,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/deepseek-000324-0000-8d1c8c7f89785565.parquet",
24
+ "sha256": "8d1c8c7f89785565a4dff734f14756fcc82fb57f733a9e547eba051a22e531d6",
25
+ "bytes": 349926,
26
+ "rows": 105,
27
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
28
+ },
29
+ {
30
+ "path": "data/internal_test/deepseek-000324-0000-e09f4213337db2bc.parquet",
31
+ "sha256": "e09f4213337db2bc802bacce330361ee780ad45878e18dc912268c7cf1693ca6",
32
+ "bytes": 55192,
33
+ "rows": 15,
34
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
35
+ }
36
+ ],
37
+ "proof_ids": [
38
+ "deepseek:thm_16243",
39
+ "deepseek:thm_16244",
40
+ "deepseek:thm_16245",
41
+ "deepseek:thm_16246",
42
+ "deepseek:thm_16247",
43
+ "deepseek:thm_16248",
44
+ "deepseek:thm_16249",
45
+ "deepseek:thm_16250",
46
+ "deepseek:thm_16251",
47
+ "deepseek:thm_16252",
48
+ "deepseek:thm_16253",
49
+ "deepseek:thm_16254",
50
+ "deepseek:thm_16255",
51
+ "deepseek:thm_16256",
52
+ "deepseek:thm_16257",
53
+ "deepseek:thm_16258",
54
+ "deepseek:thm_16259",
55
+ "deepseek:thm_16260",
56
+ "deepseek:thm_16261",
57
+ "deepseek:thm_16262",
58
+ "deepseek:thm_16263",
59
+ "deepseek:thm_16264",
60
+ "deepseek:thm_16265",
61
+ "deepseek:thm_16266",
62
+ "deepseek:thm_16267",
63
+ "deepseek:thm_16268",
64
+ "deepseek:thm_16269",
65
+ "deepseek:thm_16270",
66
+ "deepseek:thm_16271",
67
+ "deepseek:thm_16272",
68
+ "deepseek:thm_16273",
69
+ "deepseek:thm_16274",
70
+ "deepseek:thm_16275",
71
+ "deepseek:thm_16276",
72
+ "deepseek:thm_16277",
73
+ "deepseek:thm_16278",
74
+ "deepseek:thm_16279",
75
+ "deepseek:thm_16280",
76
+ "deepseek:thm_16281",
77
+ "deepseek:thm_16282",
78
+ "deepseek:thm_16283",
79
+ "deepseek:thm_16284",
80
+ "deepseek:thm_16285",
81
+ "deepseek:thm_16286",
82
+ "deepseek:thm_16287",
83
+ "deepseek:thm_16288",
84
+ "deepseek:thm_16289",
85
+ "deepseek:thm_16290",
86
+ "deepseek:thm_16291",
87
+ "deepseek:thm_16292"
88
+ ],
89
+ "proof_keys": [
90
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016200.lean\",\"d24b71c2a887edda8a2db7c360bdace8212b50cd8cc7cd4fc3e3d0150aa0bb68\",0,\"thm_16243\"]",
91
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016201.lean\",\"eba97cafdb088eabbe8b0bab5b35aaa759307917eb444bfe5ca470886d721bb7\",0,\"thm_16244\"]",
92
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016202.lean\",\"9089eee65b7930f5974b47420db45349ea174ae8b1be252e483455ee4c248aac\",0,\"thm_16245\"]",
93
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016203.lean\",\"3817b3e911922f5aefe4fbf8fbe5c15c92dc4665503145afc1efda21f5a151b5\",0,\"thm_16246\"]",
94
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016204.lean\",\"41f1af7898f039b91ab77a8065516be4a0b11ef6ab90827fa3c277c3c945e19b\",0,\"thm_16247\"]",
95
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016205.lean\",\"12de4d0134b15a2cef0da051c443e6755ea8701448ca3121222949e2fc541c7e\",0,\"thm_16248\"]",
96
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016206.lean\",\"2f9a4b7a7bb13b3635acaccc4cf9fab4d1b99c55f3c079989d50a4077aeac861\",0,\"thm_16249\"]",
97
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016207.lean\",\"15a948d96343715de62a79e017705de899ea509675c92f0940787240efcbfacd\",0,\"thm_16250\"]",
98
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016208.lean\",\"2650b2b3c826a9cb26dd1893fbe59cbdd9de8583cd8a3e751e95bb1ec1bdeb6f\",0,\"thm_16251\"]",
99
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016209.lean\",\"6787084b4529d6f228b5c1179c6ae151f54f3d35f2285815588fa4753962b5a0\",0,\"thm_16252\"]",
100
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016210.lean\",\"f0cf184e2de5580bf4a74cc016e16e9fd3f5a3f5aab6f3ac2fea7f180ea21474\",0,\"thm_16253\"]",
101
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016211.lean\",\"ba06dd0a827cdb8c6c7ac6bf158e313336c7157f93814f99be5eaf5090f81a4b\",0,\"thm_16254\"]",
102
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016212.lean\",\"8e484526dcdd6f410e615fab65e5d9bae2ae5aa47cef82921bbefd65bf00bcbb\",0,\"thm_16255\"]",
103
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016213.lean\",\"22981429c79eeb65eaee0361ade0799cbd0d4c508dc156d0b8f1b0525eb05492\",0,\"thm_16256\"]",
104
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016214.lean\",\"38d520e9483d3ea59b098923ca97baeb6d65f935d43a2248707d632e37d956c5\",0,\"thm_16257\"]",
105
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016215.lean\",\"81411b463036ef653c41ecab0a44374d9cc43a51093ae3444d004b732cadb82c\",0,\"thm_16258\"]",
106
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016216.lean\",\"906a5e4f7f5ac68c47e610395a8a49bcab739ee28937af4cb03d45def35bd7b7\",0,\"thm_16259\"]",
107
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016217.lean\",\"6aeecb7e81512cd99c9e2c9959287f7a8c8ec1522286668820a2039f55809598\",0,\"thm_16260\"]",
108
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016218.lean\",\"062245fb59c3dc4c7a97c9388b396a6dc441cd56d0d0e6d32122ef70130a6455\",0,\"thm_16261\"]",
109
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016219.lean\",\"595a370d8929a3c6353492a45c00d1487811b63a9fe1dbbb66a907539d8af2d3\",0,\"thm_16262\"]",
110
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016220.lean\",\"b72a08775e396e78fa4a460ddbce78273817206ab0c5b21224d90646a670b585\",0,\"thm_16263\"]",
111
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016221.lean\",\"8bb85d7a019e2d761763f04c2523dce066fb66894d01317f39522027c036cc3c\",0,\"thm_16264\"]",
112
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016222.lean\",\"3f0bc76fe02a2f9d0e17ec596611abc2d859908fbcc6d2a1fbfee67507a82a84\",0,\"thm_16265\"]",
113
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016223.lean\",\"e5d54a26f47034e291667986e1709342cbdb1ed1aaac858957764c61589058b1\",0,\"thm_16266\"]",
114
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016224.lean\",\"6a39510db96ce08195632cac20a83eae83f256b450b48dd1e00f766f70ef2225\",0,\"thm_16267\"]",
115
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016225.lean\",\"9159fecd27cc9b8593d826302059763d9095c2fadb71d49221b64900588dde9d\",0,\"thm_16268\"]",
116
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016226.lean\",\"0520c05eb3b6a500c39e966c75f504278a3c0f3bcf935a5064b8003f5b38f5f9\",0,\"thm_16269\"]",
117
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016227.lean\",\"bed85468dfef07003637a8aaf206d9f27ee98d4e96d9f5d40f40f65e361d5768\",0,\"thm_16270\"]",
118
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016228.lean\",\"43e3a55a56f85ad0605be0f5980a7f204538399d2e1e9a9bbc584f4159ee4d77\",0,\"thm_16271\"]",
119
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016229.lean\",\"6e790df8b5f5f9a3dfeb3c5a0b58205acfc8a55cea30d6186379c7708c7683df\",0,\"thm_16272\"]",
120
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016230.lean\",\"46130586e5c7db436ec44ab5de52d5741b85472d8538e289e600b3a3ec98354c\",0,\"thm_16273\"]",
121
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016231.lean\",\"7d5c6cdef51a450be8c646f88336a248376f3a9d999ae82c8359d89667c7e2e3\",0,\"thm_16274\"]",
122
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016232.lean\",\"688fe633ad878171b6032c4a2bc71449de04981fc664ef0bc4214a451577aaf2\",0,\"thm_16275\"]",
123
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016233.lean\",\"e2f38c2ab2f291ffa7132a2498c39d2a825116776512399538148d5301e1f263\",0,\"thm_16276\"]",
124
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016234.lean\",\"12b2371b6fc2dfb9bd3e8bcda3d8ad3e8b36f72a975759357b191a90e9281e8e\",0,\"thm_16277\"]",
125
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016235.lean\",\"c5d7f82b950a7e8a9b062937200a4c4d0a18dee9c3389da31c0710e21571e387\",0,\"thm_16278\"]",
126
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016236.lean\",\"05cd6c580b47a6e16a811ce99914de1240323227e32e0fa9b4a659783ee223d9\",0,\"thm_16279\"]",
127
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016237.lean\",\"dffc3d0f18e6a3a9ed1bf1fcc0e4c5d793fa8e64c7269ec8497a2e90bf343d21\",0,\"thm_16280\"]",
128
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016238.lean\",\"7b0c05a94bcc0df58bb2a60f2285c2ee9d9619af2de6f52b140426ded277fb61\",0,\"thm_16281\"]",
129
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016239.lean\",\"cc75a8c96423581df7e04b181f0a64465254f167b33e02564e2ca0d5b563e3d1\",0,\"thm_16282\"]",
130
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016240.lean\",\"754b6f7addcc7d8646460faf2b110a8907f6d3e4162badda3235b403148a4c5b\",0,\"thm_16283\"]",
131
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016241.lean\",\"0f1a5f0c4bfb012a8197584909433f58ce1943166a3ca41102cf924eb793eb44\",0,\"thm_16284\"]",
132
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016242.lean\",\"8e097bb2cd7c9d2cf10471bab3cdba5adf45cd0ad894dc7f1ddcbae863501c36\",0,\"thm_16285\"]",
133
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016243.lean\",\"fd1d8a6d8483f4f057daed114e54cee73a7775e38dd3012d6b1da64a8548b701\",0,\"thm_16286\"]",
134
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016244.lean\",\"4835c00c32ff6bf06db4ab38794d02dca54fc687a023931d72d62c2f6e3ecf16\",0,\"thm_16287\"]",
135
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016245.lean\",\"02623feba615e738e3b51a236742ba197ae6a92c7b08dc7ac6ca40ad34f17645\",0,\"thm_16288\"]",
136
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016246.lean\",\"6def3c3f1b4d6beb3794f2a7fcfdea3415788eb4822b6e2861d9e9ee162f645d\",0,\"thm_16289\"]",
137
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016247.lean\",\"922eed452f8e135f051cd20ee2c83cc3438098df5e87e2e43042a7d5431d85e9\",0,\"thm_16290\"]",
138
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016248.lean\",\"8378dcc82de8fffc41dd907ff4fcf242291b511c6cf475d31f7063673dbe7f0d\",0,\"thm_16291\"]",
139
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016249.lean\",\"acb75876d2aad250aa4fe15b549ccfb8162a7fecedafd2848f2cf3d9e0730bfd\",0,\"thm_16292\"]"
140
+ ]
141
+ }
manifests/batches/deepseek/000326.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "deepseek/000326",
4
+ "batch_fingerprint": "c9f02f4e48221d4181bd138f36a939e506861fea130d89b0f1c710d2eafaaa16",
5
+ "evidence": {
6
+ "batch_fingerprint": "c9f02f4e48221d4181bd138f36a939e506861fea130d89b0f1c710d2eafaaa16",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 50,
10
+ "input_units": 50,
11
+ "proofs": 50,
12
+ "published_proofs": 50,
13
+ "published_transitions": 110,
14
+ "replay_failures": [],
15
+ "trace_mode": "individual",
16
+ "transitions": 110,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/deepseek-000326-0000-7cd8b88affd346bf.parquet",
24
+ "sha256": "7cd8b88affd346bf994cd94fa4e639f2db07f55e9959a8bf08101eb2bdf03ba3",
25
+ "bytes": 263441,
26
+ "rows": 95,
27
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
28
+ },
29
+ {
30
+ "path": "data/dev/deepseek-000326-0000-68ab76a463ab3e9e.parquet",
31
+ "sha256": "68ab76a463ab3e9e20ee6318c8ce683420e0d9c3fd913f239dd8aeaee8186b0b",
32
+ "bytes": 39823,
33
+ "rows": 3,
34
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
35
+ },
36
+ {
37
+ "path": "data/internal_test/deepseek-000326-0000-c52a49b304f73f75.parquet",
38
+ "sha256": "c52a49b304f73f75ca48093ee7575734769eedd165f9aea66c0ec92785c50452",
39
+ "bytes": 50848,
40
+ "rows": 12,
41
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
42
+ }
43
+ ],
44
+ "proof_ids": [
45
+ "deepseek:thm_16343",
46
+ "deepseek:thm_16344",
47
+ "deepseek:thm_16345",
48
+ "deepseek:thm_16346",
49
+ "deepseek:thm_16347",
50
+ "deepseek:thm_16348",
51
+ "deepseek:thm_16349",
52
+ "deepseek:thm_16350",
53
+ "deepseek:thm_16351",
54
+ "deepseek:thm_16352",
55
+ "deepseek:thm_16353",
56
+ "deepseek:thm_16354",
57
+ "deepseek:thm_16355",
58
+ "deepseek:thm_16356",
59
+ "deepseek:thm_16357",
60
+ "deepseek:thm_16358",
61
+ "deepseek:thm_16359",
62
+ "deepseek:thm_16360",
63
+ "deepseek:thm_16361",
64
+ "deepseek:thm_16362",
65
+ "deepseek:thm_16363",
66
+ "deepseek:thm_16364",
67
+ "deepseek:thm_16365",
68
+ "deepseek:thm_16366",
69
+ "deepseek:thm_16367",
70
+ "deepseek:thm_16368",
71
+ "deepseek:thm_16369",
72
+ "deepseek:thm_16370",
73
+ "deepseek:thm_16371",
74
+ "deepseek:thm_16372",
75
+ "deepseek:thm_16373",
76
+ "deepseek:thm_16374",
77
+ "deepseek:thm_16375",
78
+ "deepseek:thm_16376",
79
+ "deepseek:thm_16377",
80
+ "deepseek:thm_16378",
81
+ "deepseek:thm_16379",
82
+ "deepseek:thm_16380",
83
+ "deepseek:thm_16381",
84
+ "deepseek:thm_16382",
85
+ "deepseek:thm_16383",
86
+ "deepseek:thm_16384",
87
+ "deepseek:thm_16385",
88
+ "deepseek:thm_16386",
89
+ "deepseek:thm_16387",
90
+ "deepseek:thm_16388",
91
+ "deepseek:thm_16389",
92
+ "deepseek:thm_16390",
93
+ "deepseek:thm_16391",
94
+ "deepseek:thm_16392"
95
+ ],
96
+ "proof_keys": [
97
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016300.lean\",\"e7dec12f99f5f52ce44d74d422290eaaa649ecfb67f02f0bb9bbb61d5f414d3d\",0,\"thm_16343\"]",
98
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016301.lean\",\"167370a2abaca11f5a60cad298a7f3175e75bae1178149a069fdd7f914e9c7e0\",0,\"thm_16344\"]",
99
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016302.lean\",\"6a3d2da7e046dc8702a9cd5f03085c6779366c00c18b2b12cc9db5f54260c65c\",0,\"thm_16345\"]",
100
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016303.lean\",\"5d42635a03379855e2dd22b302090779749319e5dda234f58c3ab0251c4777df\",0,\"thm_16346\"]",
101
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016304.lean\",\"446b6a18a285432143dfd571ef8cf195ab5dbf740aa3bdbbd0b441cd9ec47aed\",0,\"thm_16347\"]",
102
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016305.lean\",\"9cbda08401fa31d7e75132d3f14177207824c25cd67f3ac641b6de8874f84a6f\",0,\"thm_16348\"]",
103
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016306.lean\",\"0b007fc4b3ae9dae50730dc69c887e7f1743c4c496c8170abba97297599b2e34\",0,\"thm_16349\"]",
104
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016307.lean\",\"7bc643a914a56890815e3e94818704ad2881e2e9da655ec1875590fdee9f89fd\",0,\"thm_16350\"]",
105
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016308.lean\",\"254f55127b8fa3d34a3d80367e07256a65225af066f3366a916ad1013b0bd409\",0,\"thm_16351\"]",
106
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016309.lean\",\"67723246cc57576ccff43984c29465c2225a614d3f2ed05ff395c139eadc6572\",0,\"thm_16352\"]",
107
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016310.lean\",\"24c275630a4ba53162c24440a9df3c549b226a0e5f658f865dd31881f9596f6d\",0,\"thm_16353\"]",
108
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016311.lean\",\"a324dfdb3b0aa74f4a7e22c76505fef609aacec790cbb95ff6f84cc2c94a33a9\",0,\"thm_16354\"]",
109
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016312.lean\",\"3c36a65ad39412bf719130d84120a470b9e6071500d8e33d7c60b93efe108f4e\",0,\"thm_16355\"]",
110
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016313.lean\",\"a512c0e33a71123a4cb5f21788e4e1fc7a4db4492a7f067142cde3509a49f4fb\",0,\"thm_16356\"]",
111
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016314.lean\",\"f69f649b3e9497eb928cbf60fd9579e69e71de440fd2a27a43b1d06998ad2cc6\",0,\"thm_16357\"]",
112
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016315.lean\",\"36c8ec70b5d9bc89fb411ed4a68003161dddf9671f70573d6cd71c4b004d77fb\",0,\"thm_16358\"]",
113
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016316.lean\",\"061b511d79f28d6caa42e9b595f35086017a71c6fc36032f04bb6c53eab62da3\",0,\"thm_16359\"]",
114
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016317.lean\",\"381d91fc7735a7d19f340fc975afa958780ed6924dfd29f8072ca423f5c80842\",0,\"thm_16360\"]",
115
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016318.lean\",\"3ce91aa3c32fe58e2fb5b40ba4d0266d9dc57ac6d9ecfcbaa9b320826c0b8e6b\",0,\"thm_16361\"]",
116
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016319.lean\",\"3196491337004279d2a4e040ff95f4892fc1ce736c7b407c342f0bdef4665815\",0,\"thm_16362\"]",
117
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016320.lean\",\"694f0e7edd9c8b6695177924bb76cc6095a45b17a00574883ffcc09ef926287a\",0,\"thm_16363\"]",
118
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016321.lean\",\"3ff95475fa0c108aeb89b19c46c5318b208cb92456c5fb15ec26e0a5621557ee\",0,\"thm_16364\"]",
119
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016322.lean\",\"25607cb2b43129418b3b90c3f1600b31ade4dc9effefb5213745aa6852585bc7\",0,\"thm_16365\"]",
120
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016323.lean\",\"40c7121ec364cdf6255dd6b89a954eaca2d1118a5b194c3fceab8b8c3c5542f3\",0,\"thm_16366\"]",
121
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016324.lean\",\"87c16fe03ecf1a88259d80b1c11700fe3ee91363da729fc813f2f357c3076ff1\",0,\"thm_16367\"]",
122
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016325.lean\",\"da07719eca2a5c6a7bf4da49c082f5eb8ce9a5dc2583bb5a914b634c406e018a\",0,\"thm_16368\"]",
123
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016326.lean\",\"fa513eb1356270854bb2b68f211236ba15392e4542d916ff082563db49247f84\",0,\"thm_16369\"]",
124
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016327.lean\",\"f718349ba8247fdd0bfb914bf2ddc80331b9306796546a1308e3b76fa3b3f12c\",0,\"thm_16370\"]",
125
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016328.lean\",\"32f156e450a9d6415d8db09d134c7e160f20d0a76d44d4763f0ba0b935053d1c\",0,\"thm_16371\"]",
126
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016329.lean\",\"e9dfdb3fc33488ce684c8b8c2962ea3fd945f5c4e9d441b90c812679c8a95642\",0,\"thm_16372\"]",
127
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016330.lean\",\"cf95e214a25fb4732a24afe2595f265d537316c0c0c8496d863f013d775f804d\",0,\"thm_16373\"]",
128
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016331.lean\",\"f11c002e4e8a5e23beb335cced2c2e4fa6606dbeb30cf5e6a2f64435e18b1528\",0,\"thm_16374\"]",
129
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016332.lean\",\"785dfdd1a7a54bd3bfd0d25a9ef3461cf651bd7852afe5343f6571eab0771838\",0,\"thm_16375\"]",
130
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016333.lean\",\"5608fdb408bac13635f217b21cc55d592638ce0b5451a5781fa063dc239584fc\",0,\"thm_16376\"]",
131
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016334.lean\",\"b352252b676a85633da86182162b708b9a4e42b8a7a157372b27347830330d69\",0,\"thm_16377\"]",
132
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016335.lean\",\"7af1404856f323140e3ff34a93ba136ad49a9bb6fe8058db5c2205189f7bbe7f\",0,\"thm_16378\"]",
133
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016336.lean\",\"f0a2fc7f8720ab0e0a7ed22ab7aad391e7fbf5014aba2bbed5518632acf755d8\",0,\"thm_16379\"]",
134
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016337.lean\",\"b0f09032715dcbc781834d9eda348ef9fa05dc4fef8b3ba85d351df901ff706a\",0,\"thm_16380\"]",
135
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016338.lean\",\"42f6ec088f4c9a005a415e904a0e57e4aa1c55bfe88171ec2c66dc45f2520ddb\",0,\"thm_16381\"]",
136
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016339.lean\",\"ebc7731cb5b84bda6d80283de826e819533d30f68ded353bf1223cf3f8251347\",0,\"thm_16382\"]",
137
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016340.lean\",\"f5986b2b874b1e30d903f926b1e8bc070c4abd31a7b2b6c89fa98079f3154f05\",0,\"thm_16383\"]",
138
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016341.lean\",\"2bd7e49fae3d6c5dcefffbc6e4e8b913a0c9176ba6bf6e8fac4af6b5c0185212\",0,\"thm_16384\"]",
139
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016342.lean\",\"858ea6e15b6d7d77b2a86a1a411477e70055c0e6adec145da91200a45b0c450d\",0,\"thm_16385\"]",
140
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016343.lean\",\"0df2cdc28c528c357edaf4fcb98a80c1bd88567090c0c6e4a89b184636a33937\",0,\"thm_16386\"]",
141
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016344.lean\",\"b92da2d1056f5b63490d9f57dbd0dd9bf55b3a7222abbf0050e7d101a428c43b\",0,\"thm_16387\"]",
142
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016345.lean\",\"b4485423bb1fb72c28a7a6f3ff1ec089611cac0ecd53759f51dc162e15c874ba\",0,\"thm_16388\"]",
143
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016346.lean\",\"ff36b5407441c909d96b0d8690a97578f06f22b291f35d940440f9d69952e9aa\",0,\"thm_16389\"]",
144
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016347.lean\",\"1b92193269a52c3d5a9fa2e52fb0f7d8b79d1969c1b2a3398529b07bbec9772c\",0,\"thm_16390\"]",
145
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016348.lean\",\"f5df42d6563f2ed66c510f7f7a80e407691cc5e2573c64b57ba24d9b0349a479\",0,\"thm_16391\"]",
146
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016349.lean\",\"3ad39ec303f6842bb92f4b8e0eabd381b74e3640323f6dfc1e13c25565bd119e\",0,\"thm_16392\"]"
147
+ ]
148
+ }
manifests/batches/deepseek/000327.json ADDED
@@ -0,0 +1,141 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "deepseek/000327",
4
+ "batch_fingerprint": "fbd6d6ead687a508ed9b2033cdc77f5671ff3e39d040a2b5e578ca8daded3712",
5
+ "evidence": {
6
+ "batch_fingerprint": "fbd6d6ead687a508ed9b2033cdc77f5671ff3e39d040a2b5e578ca8daded3712",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 50,
10
+ "input_units": 50,
11
+ "proofs": 50,
12
+ "published_proofs": 50,
13
+ "published_transitions": 129,
14
+ "replay_failures": [],
15
+ "trace_mode": "individual",
16
+ "transitions": 129,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/deepseek-000327-0000-40057ad14499253d.parquet",
24
+ "sha256": "40057ad14499253d4ac52ff542922e1d92cb8ce5cd1888c155bc0bad8c2b589e",
25
+ "bytes": 351909,
26
+ "rows": 112,
27
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
28
+ },
29
+ {
30
+ "path": "data/internal_test/deepseek-000327-0000-295c0901b4538b57.parquet",
31
+ "sha256": "295c0901b4538b57399b76e4a0c7c08148a17ea68c502d111f72120abe381de7",
32
+ "bytes": 63734,
33
+ "rows": 17,
34
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
35
+ }
36
+ ],
37
+ "proof_ids": [
38
+ "deepseek:thm_16393",
39
+ "deepseek:thm_16394",
40
+ "deepseek:thm_16395",
41
+ "deepseek:thm_16396",
42
+ "deepseek:thm_16397",
43
+ "deepseek:thm_16398",
44
+ "deepseek:thm_16399",
45
+ "deepseek:thm_16400",
46
+ "deepseek:thm_16401",
47
+ "deepseek:thm_16402",
48
+ "deepseek:thm_16403",
49
+ "deepseek:thm_16404",
50
+ "deepseek:thm_16405",
51
+ "deepseek:thm_16406",
52
+ "deepseek:thm_16407",
53
+ "deepseek:thm_16408",
54
+ "deepseek:thm_16409",
55
+ "deepseek:thm_16410",
56
+ "deepseek:thm_16411",
57
+ "deepseek:thm_16412",
58
+ "deepseek:thm_16413",
59
+ "deepseek:thm_16414",
60
+ "deepseek:thm_16415",
61
+ "deepseek:thm_16416",
62
+ "deepseek:thm_16417",
63
+ "deepseek:thm_16418",
64
+ "deepseek:thm_16419",
65
+ "deepseek:thm_16420",
66
+ "deepseek:thm_16421",
67
+ "deepseek:thm_16422",
68
+ "deepseek:thm_16423",
69
+ "deepseek:thm_16424",
70
+ "deepseek:thm_16425",
71
+ "deepseek:thm_16426",
72
+ "deepseek:thm_16427",
73
+ "deepseek:thm_16428",
74
+ "deepseek:thm_16429",
75
+ "deepseek:thm_16430",
76
+ "deepseek:thm_16431",
77
+ "deepseek:thm_16432",
78
+ "deepseek:thm_16433",
79
+ "deepseek:thm_16434",
80
+ "deepseek:thm_16435",
81
+ "deepseek:thm_16436",
82
+ "deepseek:thm_16437",
83
+ "deepseek:thm_16438",
84
+ "deepseek:thm_16439",
85
+ "deepseek:thm_16440",
86
+ "deepseek:thm_16441",
87
+ "deepseek:thm_16442"
88
+ ],
89
+ "proof_keys": [
90
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016350.lean\",\"6204d10931993b4d8ccf5fe3f4b11ac2f8646af8246de6b29d94255fad8ec086\",0,\"thm_16393\"]",
91
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016351.lean\",\"0e42990e842084c4b0cd76169a1bd6d00fa79576eabdf7573ec0960a4bd7f9ab\",0,\"thm_16394\"]",
92
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016352.lean\",\"ad3e5d3ab140fd80b2a9a6ccd89568a9d95e15913eb2261127d067028449ff96\",0,\"thm_16395\"]",
93
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016353.lean\",\"3b80e2a2637dc6d665bb98ae38b49e1bebbfdb0e1e8ba56d74d55380f322a9f5\",0,\"thm_16396\"]",
94
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016354.lean\",\"0e82b612605a08d7a0bfc63377edecf18074d822ea1e18c217cefbf8d4bf228f\",0,\"thm_16397\"]",
95
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016355.lean\",\"5c0959a34141f88ca4b044db9f74b4a7b483cdfb09314498d152ae34dcc0e9d3\",0,\"thm_16398\"]",
96
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016356.lean\",\"477d44cf15ff7e8ff28ee83624882056a786cbaa37ba9abd1ed2ac37264e4a9d\",0,\"thm_16399\"]",
97
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016357.lean\",\"87330d3113118ceed77ebf4075f52c1f870e4a54b9dbe6d067965dd36f0e91e8\",0,\"thm_16400\"]",
98
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016358.lean\",\"1b0d2edfa122cccf915fc9cabcea55f1b4ff104f0775959a55db184abe8ef83c\",0,\"thm_16401\"]",
99
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016359.lean\",\"4f3b48541731d7bf7388384c5d1256ecd8123add9a5a1e492c1b1f6e0c67cae8\",0,\"thm_16402\"]",
100
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016360.lean\",\"b5d0cdfa5e833d836320af7c6a3aaf2eb22dfaa9f3331fdbdc570a00776f378d\",0,\"thm_16403\"]",
101
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016361.lean\",\"45eb5295d17bf4b63cc176d3d8bde055522c2893cf99e9d565a729f156bf8fc6\",0,\"thm_16404\"]",
102
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016362.lean\",\"8e118ca8d7b92b26271973a7b339e74271961f4cacb00772e3e516e49b8726a7\",0,\"thm_16405\"]",
103
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016363.lean\",\"4d2c2a1e9fb92125190cf994646012b46273c6255d27db30a0f405b8c8621e3d\",0,\"thm_16406\"]",
104
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016364.lean\",\"e92c42969281325e4c9355440d5c10d1f3b3e49359db272688dab31c6f3a69e8\",0,\"thm_16407\"]",
105
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016365.lean\",\"a2689ce19b25516af8edb633b34c9c28080af7b8a0b66bafe753d1e70873d3e7\",0,\"thm_16408\"]",
106
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016366.lean\",\"3ca543229fc10384765e3dcb06b83aabca94609712271ff46a7f6bfc2a65667a\",0,\"thm_16409\"]",
107
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016367.lean\",\"118505b925db2a9d894d0ca3e510930b462005c6b2d56400078b0edb3725c017\",0,\"thm_16410\"]",
108
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016368.lean\",\"945b730fe5ccc2f06fcc69e509158667e6515dacbdc55c33b16805d50632e0aa\",0,\"thm_16411\"]",
109
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016369.lean\",\"f599f0566b88dba6d495bb1cde402f047cb6bf3c2bbbe1e5fc4fae4dd53fbb5c\",0,\"thm_16412\"]",
110
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016370.lean\",\"d92aeddd56ed5b1e1751b1116da70b3ba29c03a5b875ff7d5ad9b8726a857298\",0,\"thm_16413\"]",
111
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016371.lean\",\"978d506fd82c0be8f9093d6898945654ad94d274296db1bb48a8d2e7230de152\",0,\"thm_16414\"]",
112
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016372.lean\",\"1a6a9982d692c961e2b451423673be5752b68d64c394e5f47f738559b7b6aa85\",0,\"thm_16415\"]",
113
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016373.lean\",\"f4a074334d4eeb19a3dbd25bd47b7c1d2bcb37e6527426b7db8450037e2324c3\",0,\"thm_16416\"]",
114
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016374.lean\",\"d07735a7098f1288bdbce0834f813b260369d33d0310534f991ca9847b93c410\",0,\"thm_16417\"]",
115
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016375.lean\",\"ccb6e560bf0aaa2a50433ebd86cba138c1bd4eb090102f1526729cfe47827972\",0,\"thm_16418\"]",
116
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016376.lean\",\"0d70f811d335af4c1c2945cf7a14ac56cef719e60ab9de7ddab0ad6c7de588e3\",0,\"thm_16419\"]",
117
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016377.lean\",\"b546b717ec7a84d27b656a081c7353c1b50107081110810674089be85c3a2ddd\",0,\"thm_16420\"]",
118
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016378.lean\",\"4004f59db24c5c1596c038f12867bc8f3dd7be71bab0417168243f98ca75ab97\",0,\"thm_16421\"]",
119
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016379.lean\",\"76a0c9e47f1aa638ca57d372c44c0c9ec4a41d3f5f3d96dd1ea517dd8ccff6cc\",0,\"thm_16422\"]",
120
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016380.lean\",\"994018add41e4f380caaa87229dbae93c8b2d77e3af5409e37cb54bf805768aa\",0,\"thm_16423\"]",
121
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016381.lean\",\"031648ec79f2365a23571a32870f461c9614dabd05c6644890d58aa1d37f1d71\",0,\"thm_16424\"]",
122
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016382.lean\",\"2298824de764d8e2a900c5fc2d10d221e2d7d5d147b1ea0238672d03da35b0b7\",0,\"thm_16425\"]",
123
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016383.lean\",\"72fa040100976f26f68f95692efce13d614c1fe0601901e571d1b5a0d952d6ca\",0,\"thm_16426\"]",
124
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016384.lean\",\"6d79ede8b98d65e8f7dd7b4c71e8f8b677e95f8d00a55afba0be8a9e7c150a28\",0,\"thm_16427\"]",
125
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016385.lean\",\"095feefb80e5f9cb87727f7956f255173f3e3101a9e2985083a3a60f836fcb0f\",0,\"thm_16428\"]",
126
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016386.lean\",\"ba4f2910c8ca3df4fa0468f445f4dea73c0e9615ac65e3a8a8bd8348a6ac5fa7\",0,\"thm_16429\"]",
127
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016387.lean\",\"69f655b651600a955ba1ac5cc45160651eacbef3b084a9b9c44c7b5a5cd7fc7a\",0,\"thm_16430\"]",
128
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016388.lean\",\"acd9d1e42f2696a71c9e823115b817efdb483ca346e070ec107865c37c0f82be\",0,\"thm_16431\"]",
129
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016389.lean\",\"91581ff2f349670b9ee3dfec6f6d4999991093b74f0729607ffc5d12ee779671\",0,\"thm_16432\"]",
130
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016390.lean\",\"67912682667df3d82186bf59d094e9c228bfb9ad7ce5a251c764915d40603ccb\",0,\"thm_16433\"]",
131
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016391.lean\",\"f9a561711a478661d49bfabeec629a09c954100f0b908eb704258b89ead64747\",0,\"thm_16434\"]",
132
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016392.lean\",\"17ad235de117c4e2d1c3afedeb0d8c7d6d1261ac1956d7ffb92aa9777c93f266\",0,\"thm_16435\"]",
133
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016393.lean\",\"2d77ae19b8ae00c6397a2c54680e94ffed7d9d15bb8b7542ecd4897d5dd4a162\",0,\"thm_16436\"]",
134
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016394.lean\",\"8621e4c7a61e478498e18ca33f8d2646b7ad9e97f1cbb09ab5ad855788baf03b\",0,\"thm_16437\"]",
135
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016395.lean\",\"6b0219b72af1ac47b4582e66f60297c195ebe9e98b7ac3b8860e3e69dd6b7f31\",0,\"thm_16438\"]",
136
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016396.lean\",\"77270931e052f73863e108de7cb1390864b0b389015545d943e41a922fbf247c\",0,\"thm_16439\"]",
137
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016397.lean\",\"24080faf6de9d3c7258d4665c459058b740c6aca8b8db31602b796610fe8a6d3\",0,\"thm_16440\"]",
138
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016398.lean\",\"52afa6f812f1e2598f9de3d6ab5cc7a60dd4d7b8533b9d5f95dd85cfafc7c1a9\",0,\"thm_16441\"]",
139
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016399.lean\",\"65df39202ecb7bac3747d13f11dbbe11fcba143e796f66b6ce6addbd268f0fc7\",0,\"thm_16442\"]"
140
+ ]
141
+ }
manifests/batches/deepseek/000329.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "deepseek/000329",
4
+ "batch_fingerprint": "cbf1e25a11e61ed929d11409d506ef86ee541a53ff8febebd762db2b8a1b90dd",
5
+ "evidence": {
6
+ "batch_fingerprint": "cbf1e25a11e61ed929d11409d506ef86ee541a53ff8febebd762db2b8a1b90dd",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 50,
10
+ "input_units": 50,
11
+ "proofs": 50,
12
+ "published_proofs": 50,
13
+ "published_transitions": 117,
14
+ "replay_failures": [],
15
+ "trace_mode": "individual",
16
+ "transitions": 117,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/deepseek-000329-0000-41da7a2e235313ae.parquet",
24
+ "sha256": "41da7a2e235313ae23acc3a682d87139cc3209760317e2ee7542249cb0689651",
25
+ "bytes": 346038,
26
+ "rows": 103,
27
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
28
+ },
29
+ {
30
+ "path": "data/dev/deepseek-000329-0000-ca749609bb1781ba.parquet",
31
+ "sha256": "ca749609bb1781ba21088166353635fddd1910e8a150599bf962806210fd81a8",
32
+ "bytes": 35843,
33
+ "rows": 5,
34
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
35
+ },
36
+ {
37
+ "path": "data/internal_test/deepseek-000329-0000-be0c54ff62c36d74.parquet",
38
+ "sha256": "be0c54ff62c36d74b8bcd72d68fcd971ee4b09971076002dd41c6baab5fd2d09",
39
+ "bytes": 46567,
40
+ "rows": 9,
41
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
42
+ }
43
+ ],
44
+ "proof_ids": [
45
+ "deepseek:thm_16493",
46
+ "deepseek:thm_16494",
47
+ "deepseek:thm_16495",
48
+ "deepseek:thm_16496",
49
+ "deepseek:thm_16497",
50
+ "deepseek:thm_16498",
51
+ "deepseek:thm_16499",
52
+ "deepseek:thm_16500",
53
+ "deepseek:thm_16501",
54
+ "deepseek:thm_16502",
55
+ "deepseek:thm_16503",
56
+ "deepseek:thm_16504",
57
+ "deepseek:thm_16505",
58
+ "deepseek:thm_16506",
59
+ "deepseek:thm_16507",
60
+ "deepseek:thm_16508",
61
+ "deepseek:thm_16509",
62
+ "deepseek:thm_16510",
63
+ "deepseek:thm_16511",
64
+ "deepseek:thm_16512",
65
+ "deepseek:thm_16513",
66
+ "deepseek:thm_16514",
67
+ "deepseek:thm_16515",
68
+ "deepseek:thm_16516",
69
+ "deepseek:thm_16517",
70
+ "deepseek:thm_16518",
71
+ "deepseek:thm_16519",
72
+ "deepseek:thm_16520",
73
+ "deepseek:thm_16521",
74
+ "deepseek:thm_16522",
75
+ "deepseek:thm_16523",
76
+ "deepseek:thm_16524",
77
+ "deepseek:thm_16525",
78
+ "deepseek:thm_16526",
79
+ "deepseek:thm_16527",
80
+ "deepseek:thm_16528",
81
+ "deepseek:thm_16529",
82
+ "deepseek:thm_16530",
83
+ "deepseek:thm_16531",
84
+ "deepseek:thm_16532",
85
+ "deepseek:thm_16533",
86
+ "deepseek:thm_16534",
87
+ "deepseek:thm_16535",
88
+ "deepseek:thm_16536",
89
+ "deepseek:thm_16537",
90
+ "deepseek:thm_16538",
91
+ "deepseek:thm_16539",
92
+ "deepseek:thm_16540",
93
+ "deepseek:thm_16541",
94
+ "deepseek:thm_16542"
95
+ ],
96
+ "proof_keys": [
97
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016450.lean\",\"c5fd5b4b9a418f63eefaf668305f9864e3fa19f6f086f3b6def62ff3c6728aad\",0,\"thm_16493\"]",
98
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016451.lean\",\"bb4cb31c033aabc2fef6842b9611bc3cc757291186d66a17ddea3635566bf160\",0,\"thm_16494\"]",
99
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016452.lean\",\"2f0bb59a74f33b635bcd3548f4165fd98af56659f52111de1a5c419b3d9305df\",0,\"thm_16495\"]",
100
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016453.lean\",\"847c98f1a04784f181b64eef7b45783b19d916967cbf546516b78f5084476458\",0,\"thm_16496\"]",
101
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016454.lean\",\"eabdcf2337ae9e873e0d785b008b89c643eda1ccb025e6cd12b10acb217dbe1a\",0,\"thm_16497\"]",
102
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016455.lean\",\"57a16329304abb38d76554372b91620c8268599897a64fcbd040f3a396c94e6d\",0,\"thm_16498\"]",
103
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016456.lean\",\"dccd191772e1b1d630474d32445227f47be7b44efb43d050c43be326baee7fe0\",0,\"thm_16499\"]",
104
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016457.lean\",\"103d40125d5105fb8f222a87d2ebcebaf4d8291aa3f3849f874a8cd6ae972ffb\",0,\"thm_16500\"]",
105
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016458.lean\",\"5cbb90c4e35cfe065beb6b0385b3c55980e6371060270c738df90342aa7287a3\",0,\"thm_16501\"]",
106
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016459.lean\",\"64d03c06adc81440b3c208feb8c6185b9245b8e88ce62eb71b2af243b274be0b\",0,\"thm_16502\"]",
107
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016460.lean\",\"4764e29b3b7ff97c4ed112bd4ee6bb7e0cdc68a8472eb9d6154ee257f43e6e2f\",0,\"thm_16503\"]",
108
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016461.lean\",\"76bf2a079ed87ff8c0e3e751a40ed1352dfacfd5667bea92905af31b327d7cb2\",0,\"thm_16504\"]",
109
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016462.lean\",\"1d9d8f0c15ac7d1308ebb49929113e88f8ac62dc0f6c2f729cac5ebbfcaef913\",0,\"thm_16505\"]",
110
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016463.lean\",\"8d42b23a071a2b3a84ded6eff98669884094f975614fa266612d03d0ee3012ce\",0,\"thm_16506\"]",
111
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016464.lean\",\"93e5d182df221392ee9b30584434a0ae7fb7e3a5e12292ee86a229203b9075f8\",0,\"thm_16507\"]",
112
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016465.lean\",\"edd044f3146af49eccca3b32255c59f813a8391f0cfa00592d804fba8df57799\",0,\"thm_16508\"]",
113
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016466.lean\",\"d5e289d2ac60015c244c907a3c9d4e108e915d48a5994aafb46518091fc66ad9\",0,\"thm_16509\"]",
114
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016467.lean\",\"40bda4fe92c93c4e7b49a2d033d416405a2083088201d5d0db29ebbd0f7f4ea3\",0,\"thm_16510\"]",
115
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016468.lean\",\"ed76a46ac4d3dc5c0e21c160a0578024057f13e293384b9c0e474b324d247339\",0,\"thm_16511\"]",
116
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016469.lean\",\"53fa09a7c8eb0d0d0b2dab97b9e4eddc46991ac2f6ab84687fa26ebd2e2a332d\",0,\"thm_16512\"]",
117
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016470.lean\",\"991baa0a1e3cb598d0301a0660c982f82ff8e0396eb67e066ac700beaa7f184e\",0,\"thm_16513\"]",
118
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016471.lean\",\"9d1ed1dbe32c3857fcd2246e5b2a15f09d373b09532ffeaedaa5ce6bcaf63e70\",0,\"thm_16514\"]",
119
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016472.lean\",\"f6a050a6a89e31292df55a4fd856cd9832d1eeaa5f1e8c8695542b10af207919\",0,\"thm_16515\"]",
120
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016473.lean\",\"7b9db14fce1ebb9a6148e73129128034c61dc4f80ee4a96a762a2520092941e1\",0,\"thm_16516\"]",
121
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016474.lean\",\"045ddd77b3d1f122d20063ba653fb117b5b8c60af9952c47f4b4873b0d021d28\",0,\"thm_16517\"]",
122
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016475.lean\",\"c759d1c076908de45064138e3dc36f136714fc5ecbbadb539b0c38f7bfbe587f\",0,\"thm_16518\"]",
123
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016476.lean\",\"c8f6c1d34e60b18c1b414f086470f73c27618e9165d81bcd09164acc75744829\",0,\"thm_16519\"]",
124
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016477.lean\",\"0546abd7fed6ec32a2996d446e23273db4cf94db8907e4c560911145f630d795\",0,\"thm_16520\"]",
125
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016478.lean\",\"8efd43c177d874ba9942722af8f08afb3ca0435dd7923554732e004f1d41e0f5\",0,\"thm_16521\"]",
126
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016479.lean\",\"ddd1307b29ad7768e6df048fff80b70169e9288a1906e9403fee106b044ca0d4\",0,\"thm_16522\"]",
127
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016480.lean\",\"996d1ae1f5d5f7ec71460163db2a55c843e81ffccba67cb85427a5bf26701086\",0,\"thm_16523\"]",
128
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016481.lean\",\"9691345099fa8070e118b02869fff73f8f29515df18c9c9dd4e58b806db02430\",0,\"thm_16524\"]",
129
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016482.lean\",\"e3b78b7f638d9bda84357285ce45437c32bdb3581d4c074ed711a48da4fc4295\",0,\"thm_16525\"]",
130
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016483.lean\",\"9485b42041edff7bb0e3b1f0eb4ff6410b69a59a8974169a1f063d63ba9cb962\",0,\"thm_16526\"]",
131
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016484.lean\",\"3e66983f5128410b8e13075013605acf531fb07938ebb0aa9509b640c79c38cc\",0,\"thm_16527\"]",
132
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016485.lean\",\"5f641bf8771f9a9414573aa68678a66b8c57d56e6a202dd5ba28c2f6523bc2c7\",0,\"thm_16528\"]",
133
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016486.lean\",\"7702fd46d9ec2f4622c756f97313fbafb6511660e8dc7664d5e34b89a427c76f\",0,\"thm_16529\"]",
134
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016487.lean\",\"f5bd2011fd430044df220505779634f3a73a4c866464e9066c72a7848fa01ee9\",0,\"thm_16530\"]",
135
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016488.lean\",\"e204987edc1559c1d225eaf2a2f516d428fa68526374b1a6246df8be50716d84\",0,\"thm_16531\"]",
136
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016489.lean\",\"15b0f24f76aa62e6e2bd8f10fafb5169cd1d822a97878a0218c7fff2f63ef013\",0,\"thm_16532\"]",
137
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016490.lean\",\"bb1a54af6d5132b4c1d82e25d13a0e581af5e1019015892f7cff787b5a6ae9cf\",0,\"thm_16533\"]",
138
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016491.lean\",\"bbe036ff654bbfe01d97e03e877e27a7642004acb4a4a773e3b766ea9348ca16\",0,\"thm_16534\"]",
139
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016492.lean\",\"4e4f96f0141b5f3c6e5829415e4bc3ec8279d56129f7199c7996fc5886e79dcf\",0,\"thm_16535\"]",
140
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016493.lean\",\"4a67edb3e49a97c0bb3e4c8d5687a03a7f5e891b5d2a87a8712c1df7a4d1d22a\",0,\"thm_16536\"]",
141
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016494.lean\",\"fb3470e566d7cd20fc30315e282d0dacfb770a7bcb12fc27e18864d180457370\",0,\"thm_16537\"]",
142
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016495.lean\",\"fdc5a02ff599b04e807df91978ee5fb523b8a9b4cf9b0569ed347ab8a288a140\",0,\"thm_16538\"]",
143
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016496.lean\",\"fe730ed33ee0cd7a5e187099258c485850f3293191c7b74fdc3cd44667c9b69e\",0,\"thm_16539\"]",
144
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016497.lean\",\"03b4c2f14fa40258e4a08b86eeb05810abb257fd78866da9e142c2361edbba2c\",0,\"thm_16540\"]",
145
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016498.lean\",\"3a0dbef2f217b68f6cab2625962b41b2d2bbe8c9b7d6e178e2bdb5d92988adc2\",0,\"thm_16541\"]",
146
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_016499.lean\",\"2e8e3f4a6e3b188f6fc0de73b44e2a0111f4cdc79a5d0bc56b2bc3d1f7c9de1b\",0,\"thm_16542\"]"
147
+ ]
148
+ }
manifests/batches/mathlib/000252.json ADDED
The diff for this file is too large to render. See raw diff
 
manifests/batches/mathlib/000253.json ADDED
@@ -0,0 +1,423 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000253",
4
+ "batch_fingerprint": "6f008cd39f6d991da4743bfd9ce9c015964a4e7bd47a32382c95b01b49e58b60",
5
+ "evidence": {
6
+ "batch_fingerprint": "6f008cd39f6d991da4743bfd9ce9c015964a4e7bd47a32382c95b01b49e58b60",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "zpow_eq_zpow_iff'",
12
+ "id": "zpow_eq_zpow_iff'",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 135,
18
+ 81
19
+ ],
20
+ "file_path": "Mathlib/Algebra/Order/Group/Basic.lean",
21
+ "full_name": "zpow_eq_zpow_iff'",
22
+ "start": [
23
+ 131,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/Algebra/Order/Group/Basic.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "zpow_le_zpow",
34
+ "id": "zpow_le_zpow",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 53,
40
+ 84
41
+ ],
42
+ "file_path": "Mathlib/Algebra/Order/Group/Basic.lean",
43
+ "full_name": "zpow_le_zpow",
44
+ "start": [
45
+ 52,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/Algebra/Order/Group/Basic.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "zpow_le_zpow'",
56
+ "id": "zpow_le_zpow'",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 89,
62
+ 86
63
+ ],
64
+ "file_path": "Mathlib/Algebra/Order/Group/Basic.lean",
65
+ "full_name": "zpow_le_zpow'",
66
+ "start": [
67
+ 88,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/Algebra/Order/Group/Basic.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "zpow_le_zpow_iff",
78
+ "id": "zpow_le_zpow_iff",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 63,
84
+ 100
85
+ ],
86
+ "file_path": "Mathlib/Algebra/Order/Group/Basic.lean",
87
+ "full_name": "zpow_le_zpow_iff",
88
+ "start": [
89
+ 62,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/Algebra/Order/Group/Basic.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "zpow_le_zpow_iff'",
100
+ "id": "zpow_le_zpow_iff'",
101
+ "reason": "import_failure",
102
+ "selection": {
103
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
104
+ "end": [
105
+ 105,
106
+ 40
107
+ ],
108
+ "file_path": "Mathlib/Algebra/Order/Group/Basic.lean",
109
+ "full_name": "zpow_le_zpow_iff'",
110
+ "start": [
111
+ 104,
112
+ 1
113
+ ],
114
+ "traced_tactics": [],
115
+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
+ "source_file": "Mathlib/Algebra/Order/Group/Basic.lean"
118
+ },
119
+ {
120
+ "error": "theorem has no selected tactic transitions",
121
+ "full_name": "zpow_left_inj",
122
+ "id": "zpow_left_inj",
123
+ "reason": "import_failure",
124
+ "selection": {
125
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
126
+ "end": [
127
+ 127,
128
+ 92
129
+ ],
130
+ "file_path": "Mathlib/Algebra/Order/Group/Basic.lean",
131
+ "full_name": "zpow_left_inj",
132
+ "start": [
133
+ 126,
134
+ 1
135
+ ],
136
+ "traced_tactics": [],
137
+ "url": "https://github.com/leanprover-community/mathlib4"
138
+ },
139
+ "source_file": "Mathlib/Algebra/Order/Group/Basic.lean"
140
+ },
141
+ {
142
+ "error": "theorem has no selected tactic transitions",
143
+ "full_name": "zpow_lt_zpow",
144
+ "id": "zpow_lt_zpow",
145
+ "reason": "import_failure",
146
+ "selection": {
147
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
148
+ "end": [
149
+ 58,
150
+ 90
151
+ ],
152
+ "file_path": "Mathlib/Algebra/Order/Group/Basic.lean",
153
+ "full_name": "zpow_lt_zpow",
154
+ "start": [
155
+ 57,
156
+ 1
157
+ ],
158
+ "traced_tactics": [],
159
+ "url": "https://github.com/leanprover-community/mathlib4"
160
+ },
161
+ "source_file": "Mathlib/Algebra/Order/Group/Basic.lean"
162
+ },
163
+ {
164
+ "error": "theorem has no selected tactic transitions",
165
+ "full_name": "zpow_lt_zpow'",
166
+ "id": "zpow_lt_zpow'",
167
+ "reason": "import_failure",
168
+ "selection": {
169
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
170
+ "end": [
171
+ 94,
172
+ 92
173
+ ],
174
+ "file_path": "Mathlib/Algebra/Order/Group/Basic.lean",
175
+ "full_name": "zpow_lt_zpow'",
176
+ "start": [
177
+ 93,
178
+ 1
179
+ ],
180
+ "traced_tactics": [],
181
+ "url": "https://github.com/leanprover-community/mathlib4"
182
+ },
183
+ "source_file": "Mathlib/Algebra/Order/Group/Basic.lean"
184
+ },
185
+ {
186
+ "error": "theorem has no selected tactic transitions",
187
+ "full_name": "zpow_lt_zpow_iff",
188
+ "id": "zpow_lt_zpow_iff",
189
+ "reason": "import_failure",
190
+ "selection": {
191
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
192
+ "end": [
193
+ 68,
194
+ 100
195
+ ],
196
+ "file_path": "Mathlib/Algebra/Order/Group/Basic.lean",
197
+ "full_name": "zpow_lt_zpow_iff",
198
+ "start": [
199
+ 67,
200
+ 1
201
+ ],
202
+ "traced_tactics": [],
203
+ "url": "https://github.com/leanprover-community/mathlib4"
204
+ },
205
+ "source_file": "Mathlib/Algebra/Order/Group/Basic.lean"
206
+ },
207
+ {
208
+ "error": "theorem has no selected tactic transitions",
209
+ "full_name": "zpow_lt_zpow_iff'",
210
+ "id": "zpow_lt_zpow_iff'",
211
+ "reason": "import_failure",
212
+ "selection": {
213
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
214
+ "end": [
215
+ 110,
216
+ 40
217
+ ],
218
+ "file_path": "Mathlib/Algebra/Order/Group/Basic.lean",
219
+ "full_name": "zpow_lt_zpow_iff'",
220
+ "start": [
221
+ 109,
222
+ 1
223
+ ],
224
+ "traced_tactics": [],
225
+ "url": "https://github.com/leanprover-community/mathlib4"
226
+ },
227
+ "source_file": "Mathlib/Algebra/Order/Group/Basic.lean"
228
+ },
229
+ {
230
+ "error": "theorem has no selected tactic transitions",
231
+ "full_name": "IsGLB.exists_between_self_add",
232
+ "id": "IsGLB.exists_between_self_add",
233
+ "reason": "import_failure",
234
+ "selection": {
235
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
236
+ "end": [
237
+ 20,
238
+ 47
239
+ ],
240
+ "file_path": "Mathlib/Algebra/Order/Group/Bounds.lean",
241
+ "full_name": "IsGLB.exists_between_self_add",
242
+ "start": [
243
+ 19,
244
+ 1
245
+ ],
246
+ "traced_tactics": [],
247
+ "url": "https://github.com/leanprover-community/mathlib4"
248
+ },
249
+ "source_file": "Mathlib/Algebra/Order/Group/Bounds.lean"
250
+ },
251
+ {
252
+ "error": "theorem has no selected tactic transitions",
253
+ "full_name": "IsGLB.exists_between_self_add'",
254
+ "id": "IsGLB.exists_between_self_add'",
255
+ "reason": "import_failure",
256
+ "selection": {
257
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
258
+ "end": [
259
+ 25,
260
+ 51
261
+ ],
262
+ "file_path": "Mathlib/Algebra/Order/Group/Bounds.lean",
263
+ "full_name": "IsGLB.exists_between_self_add'",
264
+ "start": [
265
+ 23,
266
+ 1
267
+ ],
268
+ "traced_tactics": [],
269
+ "url": "https://github.com/leanprover-community/mathlib4"
270
+ },
271
+ "source_file": "Mathlib/Algebra/Order/Group/Bounds.lean"
272
+ },
273
+ {
274
+ "error": "theorem has no selected tactic transitions",
275
+ "full_name": "IsLUB.exists_between_sub_self",
276
+ "id": "IsLUB.exists_between_sub_self",
277
+ "reason": "import_failure",
278
+ "selection": {
279
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
280
+ "end": [
281
+ 29,
282
+ 39
283
+ ],
284
+ "file_path": "Mathlib/Algebra/Order/Group/Bounds.lean",
285
+ "full_name": "IsLUB.exists_between_sub_self",
286
+ "start": [
287
+ 28,
288
+ 1
289
+ ],
290
+ "traced_tactics": [],
291
+ "url": "https://github.com/leanprover-community/mathlib4"
292
+ },
293
+ "source_file": "Mathlib/Algebra/Order/Group/Bounds.lean"
294
+ },
295
+ {
296
+ "error": "theorem has no selected tactic transitions",
297
+ "full_name": "IsLUB.exists_between_sub_self'",
298
+ "id": "IsLUB.exists_between_sub_self'",
299
+ "reason": "import_failure",
300
+ "selection": {
301
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
302
+ "end": [
303
+ 34,
304
+ 43
305
+ ],
306
+ "file_path": "Mathlib/Algebra/Order/Group/Bounds.lean",
307
+ "full_name": "IsLUB.exists_between_sub_self'",
308
+ "start": [
309
+ 32,
310
+ 1
311
+ ],
312
+ "traced_tactics": [],
313
+ "url": "https://github.com/leanprover-community/mathlib4"
314
+ },
315
+ "source_file": "Mathlib/Algebra/Order/Group/Bounds.lean"
316
+ }
317
+ ],
318
+ "input_proofs": 20,
319
+ "input_units": 2,
320
+ "proofs": 6,
321
+ "published_proofs": 5,
322
+ "published_transitions": 11,
323
+ "replay_failures": [],
324
+ "transitions": 15,
325
+ "validation_failures": [
326
+ {
327
+ "errors": [
328
+ "internal transition boundary mismatch",
329
+ "internal transition boundary mismatch"
330
+ ],
331
+ "file_path": "Mathlib/Algebra/Order/Group/Basic.lean",
332
+ "proof_id": "mathlib:zpow_left_injective",
333
+ "provenance": {
334
+ "selection": {
335
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
336
+ "end": [
337
+ 122,
338
+ 48
339
+ ],
340
+ "file_path": "Mathlib/Algebra/Order/Group/Basic.lean",
341
+ "full_name": "zpow_left_injective",
342
+ "start": [
343
+ 114,
344
+ 1
345
+ ],
346
+ "traced_tactics": [
347
+ {
348
+ "annotated_tactic": [
349
+ "\"obtain hn | hn := hn.lt_or_lt\"",
350
+ "[]"
351
+ ],
352
+ "state_after": "case inl\n\u03b1 : Type u_1\nM : Type u_2\nR : Type u_3\ninst\u271d : LinearOrderedCommGroup \u03b1\nn : \u2124\na b : \u03b1\nhn\u271d : n \u2260 0\nhn : n < 0\n\u22a2 Injective fun x => x ^ n\n\ncase inr\n\u03b1 : Type u_1\nM : Type u_2\nR : Type u_3\ninst\u271d : LinearOrderedCommGroup \u03b1\nn : \u2124\na b : \u03b1\nhn\u271d : n \u2260 0\nhn : 0 < n\n\u22a2 Injective fun x => x ^ n",
353
+ "state_before": "\u03b1 : Type u_1\nM : Type u_2\nR : Type u_3\ninst\u271d : LinearOrderedCommGroup \u03b1\nn : \u2124\na b : \u03b1\nhn : n \u2260 0\n\u22a2 Injective fun x => x ^ n",
354
+ "tactic": "obtain hn | hn := hn.lt_or_lt"
355
+ },
356
+ {
357
+ "annotated_tactic": [
358
+ "\"refine fun a b (hab : a ^ n = b ^ n) \\u21a6\\n (<a>zpow_strictMono_left<\\/a> _ $ <a>Int.neg_pos_of_neg<\\/a> hn).<a>injective<\\/a> ?_\"",
359
+ "[{\"full_name\":\"zpow_strictMono_left\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Basic.lean\",\"def_pos\":[75,7],\"def_end_pos\":[75,27]},{\"full_name\":\"Int.neg_pos_of_neg\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Order.lean\",\"def_pos\":[310,19],\"def_end_pos\":[310,33]},{\"full_name\":\"StrictMono.injective\",\"def_path\":\"Mathlib\\/Order\\/Monotone\\/Basic.lean\",\"def_pos\":[899,9],\"def_end_pos\":[899,29]}]"
360
+ ],
361
+ "state_after": "case inl\n\u03b1 : Type u_1\nM : Type u_2\nR : Type u_3\ninst\u271d : LinearOrderedCommGroup \u03b1\nn : \u2124\na\u271d b\u271d : \u03b1\nhn\u271d : n \u2260 0\nhn : n < 0\na b : \u03b1\nhab : a ^ n = b ^ n\n\u22a2 a ^ (-n) = b ^ (-n)",
362
+ "state_before": "case inl\n\u03b1 : Type u_1\nM : Type u_2\nR : Type u_3\ninst\u271d : LinearOrderedCommGroup \u03b1\nn : \u2124\na b : \u03b1\nhn\u271d : n \u2260 0\nhn : n < 0\n\u22a2 Injective fun x => x ^ n",
363
+ "tactic": "refine fun a b (hab : a ^ n = b ^ n) \u21a6\n (zpow_strictMono_left _ $ Int.neg_pos_of_neg hn).injective ?_"
364
+ },
365
+ {
366
+ "annotated_tactic": [
367
+ "\"rw [<a>zpow_neg<\\/a>, <a>zpow_neg<\\/a>, hab]\"",
368
+ "[{\"full_name\":\"zpow_neg\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[593,7],\"def_end_pos\":[593,15]},{\"full_name\":\"zpow_neg\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[593,7],\"def_end_pos\":[593,15]}]"
369
+ ],
370
+ "state_after": "no goals",
371
+ "state_before": "case inl\n\u03b1 : Type u_1\nM : Type u_2\nR : Type u_3\ninst\u271d : LinearOrderedCommGroup \u03b1\nn : \u2124\na\u271d b\u271d : \u03b1\nhn\u271d : n \u2260 0\nhn : n < 0\na b : \u03b1\nhab : a ^ n = b ^ n\n\u22a2 a ^ (-n) = b ^ (-n)",
372
+ "tactic": "rw [zpow_neg, zpow_neg, hab]"
373
+ },
374
+ {
375
+ "annotated_tactic": [
376
+ "\"exact (<a>zpow_strictMono_left<\\/a> _ hn).<a>injective<\\/a>\"",
377
+ "[{\"full_name\":\"zpow_strictMono_left\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Basic.lean\",\"def_pos\":[75,7],\"def_end_pos\":[75,27]},{\"full_name\":\"StrictMono.injective\",\"def_path\":\"Mathlib\\/Order\\/Monotone\\/Basic.lean\",\"def_pos\":[899,9],\"def_end_pos\":[899,29]}]"
378
+ ],
379
+ "state_after": "no goals",
380
+ "state_before": "case inr\n\u03b1 : Type u_1\nM : Type u_2\nR : Type u_3\ninst\u271d : LinearOrderedCommGroup \u03b1\nn : \u2124\na b : \u03b1\nhn\u271d : n \u2260 0\nhn : 0 < n\n\u22a2 Injective fun x => x ^ n",
381
+ "tactic": "exact (zpow_strictMono_left _ hn).injective"
382
+ }
383
+ ],
384
+ "url": "https://github.com/leanprover-community/mathlib4"
385
+ }
386
+ },
387
+ "theorem_name": "zpow_left_injective"
388
+ }
389
+ ],
390
+ "validation_rejected_proofs": 1,
391
+ "zero_transition_proofs": 0
392
+ },
393
+ "shards": [
394
+ {
395
+ "path": "data/train/mathlib-000253-0000-f7e8c787245aa968.parquet",
396
+ "sha256": "f7e8c787245aa968bba89793cf790bd98773820aea72d4a59a233d34d20d2862",
397
+ "bytes": 56008,
398
+ "rows": 9,
399
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
400
+ },
401
+ {
402
+ "path": "data/dev/mathlib-000253-0000-c3e9cc0e260cfd0b.parquet",
403
+ "sha256": "c3e9cc0e260cfd0b2b65e138f8f16cabd3e3974a06ab6f6ecf550bf1675dd18f",
404
+ "bytes": 46378,
405
+ "rows": 2,
406
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
407
+ }
408
+ ],
409
+ "proof_ids": [
410
+ "mathlib:one_lt_zpow'",
411
+ "mathlib:zpow_mono_left",
412
+ "mathlib:zpow_mono_right",
413
+ "mathlib:zpow_right_strictMono",
414
+ "mathlib:zpow_strictMono_left"
415
+ ],
416
+ "proof_keys": [
417
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Basic.lean\",null,null,\"one_lt_zpow'\"]",
418
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Basic.lean\",null,null,\"zpow_mono_left\"]",
419
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Basic.lean\",null,null,\"zpow_mono_right\"]",
420
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Basic.lean\",null,null,\"zpow_right_strictMono\"]",
421
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Basic.lean\",null,null,\"zpow_strictMono_left\"]"
422
+ ]
423
+ }
manifests/batches/mathlib/000254.json ADDED
@@ -0,0 +1,1084 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000254",
4
+ "batch_fingerprint": "f65cacbad343d171ac5e013ed53ce618876663c2b449f8551d3c256f11c7a31b",
5
+ "evidence": {
6
+ "batch_fingerprint": "f65cacbad343d171ac5e013ed53ce618876663c2b449f8551d3c256f11c7a31b",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "Antitone.inv",
12
+ "id": "Antitone.inv",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 1245,
18
+ 28
19
+ ],
20
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
21
+ "full_name": "Antitone.inv",
22
+ "start": [
23
+ 1244,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "AntitoneOn.inv",
34
+ "id": "AntitoneOn.inv",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 1257,
40
+ 55
41
+ ],
42
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
43
+ "full_name": "AntitoneOn.inv",
44
+ "start": [
45
+ 1256,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "Left.inv_le_self",
56
+ "id": "Left.inv_le_self",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 438,
62
+ 41
63
+ ],
64
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
65
+ "full_name": "Left.inv_le_self",
66
+ "start": [
67
+ 437,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "Left.inv_lt_self",
78
+ "id": "Left.inv_lt_self",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 459,
84
+ 38
85
+ ],
86
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
87
+ "full_name": "Left.inv_lt_self",
88
+ "start": [
89
+ 458,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "Left.self_le_inv",
100
+ "id": "Left.self_le_inv",
101
+ "reason": "import_failure",
102
+ "selection": {
103
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
104
+ "end": [
105
+ 447,
106
+ 41
107
+ ],
108
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
109
+ "full_name": "Left.self_le_inv",
110
+ "start": [
111
+ 446,
112
+ 1
113
+ ],
114
+ "traced_tactics": [],
115
+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
118
+ },
119
+ {
120
+ "error": "theorem has no selected tactic transitions",
121
+ "full_name": "Left.self_lt_inv",
122
+ "id": "Left.self_lt_inv",
123
+ "reason": "import_failure",
124
+ "selection": {
125
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
126
+ "end": [
127
+ 468,
128
+ 41
129
+ ],
130
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
131
+ "full_name": "Left.self_lt_inv",
132
+ "start": [
133
+ 467,
134
+ 1
135
+ ],
136
+ "traced_tactics": [],
137
+ "url": "https://github.com/leanprover-community/mathlib4"
138
+ },
139
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
140
+ },
141
+ {
142
+ "error": "theorem has no selected tactic transitions",
143
+ "full_name": "LinearOrderedCommGroup.mul_lt_mul_left'",
144
+ "id": "LinearOrderedCommGroup.mul_lt_mul_left'",
145
+ "reason": "import_failure",
146
+ "selection": {
147
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
148
+ "end": [
149
+ 1120,
150
+ 30
151
+ ],
152
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
153
+ "full_name": "LinearOrderedCommGroup.mul_lt_mul_left'",
154
+ "start": [
155
+ 1119,
156
+ 1
157
+ ],
158
+ "traced_tactics": [],
159
+ "url": "https://github.com/leanprover-community/mathlib4"
160
+ },
161
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
162
+ },
163
+ {
164
+ "error": "theorem has no selected tactic transitions",
165
+ "full_name": "Monotone.inv",
166
+ "id": "Monotone.inv",
167
+ "reason": "import_failure",
168
+ "selection": {
169
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
170
+ "end": [
171
+ 1239,
172
+ 28
173
+ ],
174
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
175
+ "full_name": "Monotone.inv",
176
+ "start": [
177
+ 1238,
178
+ 1
179
+ ],
180
+ "traced_tactics": [],
181
+ "url": "https://github.com/leanprover-community/mathlib4"
182
+ },
183
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
184
+ },
185
+ {
186
+ "error": "theorem has no selected tactic transitions",
187
+ "full_name": "MonotoneOn.inv",
188
+ "id": "MonotoneOn.inv",
189
+ "reason": "import_failure",
190
+ "selection": {
191
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
192
+ "end": [
193
+ 1251,
194
+ 55
195
+ ],
196
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
197
+ "full_name": "MonotoneOn.inv",
198
+ "start": [
199
+ 1250,
200
+ 1
201
+ ],
202
+ "traced_tactics": [],
203
+ "url": "https://github.com/leanprover-community/mathlib4"
204
+ },
205
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
206
+ },
207
+ {
208
+ "error": "theorem has no selected tactic transitions",
209
+ "full_name": "Right.inv_le_self",
210
+ "id": "Right.inv_le_self",
211
+ "reason": "import_failure",
212
+ "selection": {
213
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
214
+ "end": [
215
+ 480,
216
+ 42
217
+ ],
218
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
219
+ "full_name": "Right.inv_le_self",
220
+ "start": [
221
+ 479,
222
+ 1
223
+ ],
224
+ "traced_tactics": [],
225
+ "url": "https://github.com/leanprover-community/mathlib4"
226
+ },
227
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
228
+ },
229
+ {
230
+ "error": "theorem has no selected tactic transitions",
231
+ "full_name": "Right.inv_lt_self",
232
+ "id": "Right.inv_lt_self",
233
+ "reason": "import_failure",
234
+ "selection": {
235
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
236
+ "end": [
237
+ 498,
238
+ 39
239
+ ],
240
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
241
+ "full_name": "Right.inv_lt_self",
242
+ "start": [
243
+ 497,
244
+ 1
245
+ ],
246
+ "traced_tactics": [],
247
+ "url": "https://github.com/leanprover-community/mathlib4"
248
+ },
249
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
250
+ },
251
+ {
252
+ "error": "theorem has no selected tactic transitions",
253
+ "full_name": "Right.self_le_inv",
254
+ "id": "Right.self_le_inv",
255
+ "reason": "import_failure",
256
+ "selection": {
257
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
258
+ "end": [
259
+ 486,
260
+ 42
261
+ ],
262
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
263
+ "full_name": "Right.self_le_inv",
264
+ "start": [
265
+ 485,
266
+ 1
267
+ ],
268
+ "traced_tactics": [],
269
+ "url": "https://github.com/leanprover-community/mathlib4"
270
+ },
271
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
272
+ },
273
+ {
274
+ "error": "theorem has no selected tactic transitions",
275
+ "full_name": "Right.self_lt_inv",
276
+ "id": "Right.self_lt_inv",
277
+ "reason": "import_failure",
278
+ "selection": {
279
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
280
+ "end": [
281
+ 504,
282
+ 42
283
+ ],
284
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
285
+ "full_name": "Right.self_lt_inv",
286
+ "start": [
287
+ 503,
288
+ 1
289
+ ],
290
+ "traced_tactics": [],
291
+ "url": "https://github.com/leanprover-community/mathlib4"
292
+ },
293
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
294
+ },
295
+ {
296
+ "error": "theorem has no selected tactic transitions",
297
+ "full_name": "StrictAnti.inv",
298
+ "id": "StrictAnti.inv",
299
+ "reason": "import_failure",
300
+ "selection": {
301
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
302
+ "end": [
303
+ 1276,
304
+ 28
305
+ ],
306
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
307
+ "full_name": "StrictAnti.inv",
308
+ "start": [
309
+ 1275,
310
+ 1
311
+ ],
312
+ "traced_tactics": [],
313
+ "url": "https://github.com/leanprover-community/mathlib4"
314
+ },
315
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
316
+ },
317
+ {
318
+ "error": "theorem has no selected tactic transitions",
319
+ "full_name": "StrictAntiOn.inv",
320
+ "id": "StrictAntiOn.inv",
321
+ "reason": "import_failure",
322
+ "selection": {
323
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
324
+ "end": [
325
+ 1288,
326
+ 55
327
+ ],
328
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
329
+ "full_name": "StrictAntiOn.inv",
330
+ "start": [
331
+ 1287,
332
+ 1
333
+ ],
334
+ "traced_tactics": [],
335
+ "url": "https://github.com/leanprover-community/mathlib4"
336
+ },
337
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
338
+ },
339
+ {
340
+ "error": "theorem has no selected tactic transitions",
341
+ "full_name": "StrictMono.inv",
342
+ "id": "StrictMono.inv",
343
+ "reason": "import_failure",
344
+ "selection": {
345
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
346
+ "end": [
347
+ 1270,
348
+ 28
349
+ ],
350
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
351
+ "full_name": "StrictMono.inv",
352
+ "start": [
353
+ 1269,
354
+ 1
355
+ ],
356
+ "traced_tactics": [],
357
+ "url": "https://github.com/leanprover-community/mathlib4"
358
+ },
359
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
360
+ },
361
+ {
362
+ "error": "theorem has no selected tactic transitions",
363
+ "full_name": "StrictMonoOn.inv",
364
+ "id": "StrictMonoOn.inv",
365
+ "reason": "import_failure",
366
+ "selection": {
367
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
368
+ "end": [
369
+ 1282,
370
+ 55
371
+ ],
372
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
373
+ "full_name": "StrictMonoOn.inv",
374
+ "start": [
375
+ 1281,
376
+ 1
377
+ ],
378
+ "traced_tactics": [],
379
+ "url": "https://github.com/leanprover-community/mathlib4"
380
+ },
381
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
382
+ },
383
+ {
384
+ "error": "theorem has no selected tactic transitions",
385
+ "full_name": "div_le_comm",
386
+ "id": "div_le_comm",
387
+ "reason": "import_failure",
388
+ "selection": {
389
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
390
+ "end": [
391
+ 837,
392
+ 50
393
+ ],
394
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
395
+ "full_name": "div_le_comm",
396
+ "start": [
397
+ 836,
398
+ 1
399
+ ],
400
+ "traced_tactics": [],
401
+ "url": "https://github.com/leanprover-community/mathlib4"
402
+ },
403
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
404
+ },
405
+ {
406
+ "error": "theorem has no selected tactic transitions",
407
+ "full_name": "div_le_div_left'",
408
+ "id": "div_le_div_left'",
409
+ "reason": "import_failure",
410
+ "selection": {
411
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
412
+ "end": [
413
+ 784,
414
+ 30
415
+ ],
416
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
417
+ "full_name": "div_le_div_left'",
418
+ "start": [
419
+ 783,
420
+ 1
421
+ ],
422
+ "traced_tactics": [],
423
+ "url": "https://github.com/leanprover-community/mathlib4"
424
+ },
425
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
426
+ },
427
+ {
428
+ "error": "theorem has no selected tactic transitions",
429
+ "full_name": "div_le_div_right'",
430
+ "id": "div_le_div_right'",
431
+ "reason": "import_failure",
432
+ "selection": {
433
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
434
+ "end": [
435
+ 716,
436
+ 31
437
+ ],
438
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
439
+ "full_name": "div_le_div_right'",
440
+ "start": [
441
+ 715,
442
+ 1
443
+ ],
444
+ "traced_tactics": [],
445
+ "url": "https://github.com/leanprover-community/mathlib4"
446
+ },
447
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
448
+ },
449
+ {
450
+ "error": "theorem has no selected tactic transitions",
451
+ "full_name": "div_lt_comm",
452
+ "id": "div_lt_comm",
453
+ "reason": "import_failure",
454
+ "selection": {
455
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
456
+ "end": [
457
+ 999,
458
+ 50
459
+ ],
460
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
461
+ "full_name": "div_lt_comm",
462
+ "start": [
463
+ 998,
464
+ 1
465
+ ],
466
+ "traced_tactics": [],
467
+ "url": "https://github.com/leanprover-community/mathlib4"
468
+ },
469
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
470
+ },
471
+ {
472
+ "error": "theorem has no selected tactic transitions",
473
+ "full_name": "div_lt_div_left'",
474
+ "id": "div_lt_div_left'",
475
+ "reason": "import_failure",
476
+ "selection": {
477
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
478
+ "end": [
479
+ 951,
480
+ 30
481
+ ],
482
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
483
+ "full_name": "div_lt_div_left'",
484
+ "start": [
485
+ 950,
486
+ 1
487
+ ],
488
+ "traced_tactics": [],
489
+ "url": "https://github.com/leanprover-community/mathlib4"
490
+ },
491
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
492
+ },
493
+ {
494
+ "error": "theorem has no selected tactic transitions",
495
+ "full_name": "div_lt_div_right'",
496
+ "id": "div_lt_div_right'",
497
+ "reason": "import_failure",
498
+ "selection": {
499
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
500
+ "end": [
501
+ 882,
502
+ 31
503
+ ],
504
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
505
+ "full_name": "div_lt_div_right'",
506
+ "start": [
507
+ 881,
508
+ 1
509
+ ],
510
+ "traced_tactics": [],
511
+ "url": "https://github.com/leanprover-community/mathlib4"
512
+ },
513
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
514
+ },
515
+ {
516
+ "error": "theorem has no selected tactic transitions",
517
+ "full_name": "eq_one_of_inv_eq'",
518
+ "id": "eq_one_of_inv_eq'",
519
+ "reason": "import_failure",
520
+ "selection": {
521
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
522
+ "end": [
523
+ 1133,
524
+ 25
525
+ ],
526
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
527
+ "full_name": "eq_one_of_inv_eq'",
528
+ "start": [
529
+ 1125,
530
+ 1
531
+ ],
532
+ "traced_tactics": [],
533
+ "url": "https://github.com/leanprover-community/mathlib4"
534
+ },
535
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
536
+ },
537
+ {
538
+ "error": "theorem has no selected tactic transitions",
539
+ "full_name": "inv_le_div_iff_le_mul",
540
+ "id": "inv_le_div_iff_le_mul",
541
+ "reason": "import_failure",
542
+ "selection": {
543
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
544
+ "end": [
545
+ 826,
546
+ 49
547
+ ],
548
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
549
+ "full_name": "inv_le_div_iff_le_mul",
550
+ "start": [
551
+ 825,
552
+ 1
553
+ ],
554
+ "traced_tactics": [],
555
+ "url": "https://github.com/leanprover-community/mathlib4"
556
+ },
557
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
558
+ },
559
+ {
560
+ "error": "theorem has no selected tactic transitions",
561
+ "full_name": "inv_le_inv'",
562
+ "id": "inv_le_inv'",
563
+ "reason": "import_failure",
564
+ "selection": {
565
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
566
+ "end": [
567
+ 1199,
568
+ 29
569
+ ],
570
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
571
+ "full_name": "inv_le_inv'",
572
+ "start": [
573
+ 1197,
574
+ 1
575
+ ],
576
+ "traced_tactics": [],
577
+ "url": "https://github.com/leanprover-community/mathlib4"
578
+ },
579
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
580
+ },
581
+ {
582
+ "error": "theorem has no selected tactic transitions",
583
+ "full_name": "inv_le_one_of_one_le",
584
+ "id": "inv_le_one_of_one_le",
585
+ "reason": "import_failure",
586
+ "selection": {
587
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
588
+ "end": [
589
+ 1220,
590
+ 18
591
+ ],
592
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
593
+ "full_name": "inv_le_one_of_one_le",
594
+ "start": [
595
+ 1219,
596
+ 1
597
+ ],
598
+ "traced_tactics": [],
599
+ "url": "https://github.com/leanprover-community/mathlib4"
600
+ },
601
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
602
+ },
603
+ {
604
+ "error": "theorem has no selected tactic transitions",
605
+ "full_name": "inv_lt_div_iff_lt_mul'",
606
+ "id": "inv_lt_div_iff_lt_mul'",
607
+ "reason": "import_failure",
608
+ "selection": {
609
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
610
+ "end": [
611
+ 993,
612
+ 49
613
+ ],
614
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
615
+ "full_name": "inv_lt_div_iff_lt_mul'",
616
+ "start": [
617
+ 992,
618
+ 1
619
+ ],
620
+ "traced_tactics": [],
621
+ "url": "https://github.com/leanprover-community/mathlib4"
622
+ },
623
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
624
+ },
625
+ {
626
+ "error": "theorem has no selected tactic transitions",
627
+ "full_name": "inv_lt_inv'",
628
+ "id": "inv_lt_inv'",
629
+ "reason": "import_failure",
630
+ "selection": {
631
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
632
+ "end": [
633
+ 1206,
634
+ 29
635
+ ],
636
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
637
+ "full_name": "inv_lt_inv'",
638
+ "start": [
639
+ 1204,
640
+ 1
641
+ ],
642
+ "traced_tactics": [],
643
+ "url": "https://github.com/leanprover-community/mathlib4"
644
+ },
645
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
646
+ },
647
+ {
648
+ "error": "theorem has no selected tactic transitions",
649
+ "full_name": "inv_lt_one_of_one_lt",
650
+ "id": "inv_lt_one_of_one_lt",
651
+ "reason": "import_failure",
652
+ "selection": {
653
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
654
+ "end": [
655
+ 1213,
656
+ 28
657
+ ],
658
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
659
+ "full_name": "inv_lt_one_of_one_lt",
660
+ "start": [
661
+ 1212,
662
+ 1
663
+ ],
664
+ "traced_tactics": [],
665
+ "url": "https://github.com/leanprover-community/mathlib4"
666
+ },
667
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
668
+ },
669
+ {
670
+ "error": "theorem has no selected tactic transitions",
671
+ "full_name": "le_div_comm",
672
+ "id": "le_div_comm",
673
+ "reason": "import_failure",
674
+ "selection": {
675
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
676
+ "end": [
677
+ 843,
678
+ 50
679
+ ],
680
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
681
+ "full_name": "le_div_comm",
682
+ "start": [
683
+ 842,
684
+ 1
685
+ ],
686
+ "traced_tactics": [],
687
+ "url": "https://github.com/leanprover-community/mathlib4"
688
+ },
689
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
690
+ },
691
+ {
692
+ "error": "theorem has no selected tactic transitions",
693
+ "full_name": "le_iff_forall_one_lt_lt_mul",
694
+ "id": "le_iff_forall_one_lt_lt_mul",
695
+ "reason": "import_failure",
696
+ "selection": {
697
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
698
+ "end": [
699
+ 1057,
700
+ 68
701
+ ],
702
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
703
+ "full_name": "le_iff_forall_one_lt_lt_mul",
704
+ "start": [
705
+ 1056,
706
+ 1
707
+ ],
708
+ "traced_tactics": [],
709
+ "url": "https://github.com/leanprover-community/mathlib4"
710
+ },
711
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
712
+ },
713
+ {
714
+ "error": "theorem has no selected tactic transitions",
715
+ "full_name": "lt_div_comm",
716
+ "id": "lt_div_comm",
717
+ "reason": "import_failure",
718
+ "selection": {
719
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
720
+ "end": [
721
+ 1005,
722
+ 50
723
+ ],
724
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
725
+ "full_name": "lt_div_comm",
726
+ "start": [
727
+ 1004,
728
+ 1
729
+ ],
730
+ "traced_tactics": [],
731
+ "url": "https://github.com/leanprover-community/mathlib4"
732
+ },
733
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
734
+ },
735
+ {
736
+ "error": "theorem has no selected tactic transitions",
737
+ "full_name": "one_le_inv_of_le_one",
738
+ "id": "one_le_inv_of_le_one",
739
+ "reason": "import_failure",
740
+ "selection": {
741
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
742
+ "end": [
743
+ 1226,
744
+ 18
745
+ ],
746
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
747
+ "full_name": "one_le_inv_of_le_one",
748
+ "start": [
749
+ 1225,
750
+ 1
751
+ ],
752
+ "traced_tactics": [],
753
+ "url": "https://github.com/leanprover-community/mathlib4"
754
+ },
755
+ "source_file": "Mathlib/Algebra/Order/Group/Defs.lean"
756
+ },
757
+ {
758
+ "error": "theorem has no selected tactic transitions",
759
+ "full_name": "le_iff_forall_lt_one_mul_le",
760
+ "id": "le_iff_forall_lt_one_mul_le",
761
+ "reason": "import_failure",
762
+ "selection": {
763
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
764
+ "end": [
765
+ 46,
766
+ 41
767
+ ],
768
+ "file_path": "Mathlib/Algebra/Order/Group/DenselyOrdered.lean",
769
+ "full_name": "le_iff_forall_lt_one_mul_le",
770
+ "start": [
771
+ 45,
772
+ 1
773
+ ],
774
+ "traced_tactics": [],
775
+ "url": "https://github.com/leanprover-community/mathlib4"
776
+ },
777
+ "source_file": "Mathlib/Algebra/Order/Group/DenselyOrdered.lean"
778
+ },
779
+ {
780
+ "error": "theorem has no selected tactic transitions",
781
+ "full_name": "le_iff_forall_one_lt_le_mul",
782
+ "id": "le_iff_forall_one_lt_le_mul",
783
+ "reason": "import_failure",
784
+ "selection": {
785
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
786
+ "end": [
787
+ 40,
788
+ 83
789
+ ],
790
+ "file_path": "Mathlib/Algebra/Order/Group/DenselyOrdered.lean",
791
+ "full_name": "le_iff_forall_one_lt_le_mul",
792
+ "start": [
793
+ 39,
794
+ 1
795
+ ],
796
+ "traced_tactics": [],
797
+ "url": "https://github.com/leanprover-community/mathlib4"
798
+ },
799
+ "source_file": "Mathlib/Algebra/Order/Group/DenselyOrdered.lean"
800
+ },
801
+ {
802
+ "error": "theorem has no selected tactic transitions",
803
+ "full_name": "le_of_forall_lt_one_mul_le",
804
+ "id": "le_of_forall_lt_one_mul_le",
805
+ "reason": "import_failure",
806
+ "selection": {
807
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
808
+ "end": [
809
+ 27,
810
+ 42
811
+ ],
812
+ "file_path": "Mathlib/Algebra/Order/Group/DenselyOrdered.lean",
813
+ "full_name": "le_of_forall_lt_one_mul_le",
814
+ "start": [
815
+ 26,
816
+ 1
817
+ ],
818
+ "traced_tactics": [],
819
+ "url": "https://github.com/leanprover-community/mathlib4"
820
+ },
821
+ "source_file": "Mathlib/Algebra/Order/Group/DenselyOrdered.lean"
822
+ }
823
+ ],
824
+ "input_proofs": 117,
825
+ "input_units": 2,
826
+ "proofs": 80,
827
+ "published_proofs": 79,
828
+ "published_transitions": 91,
829
+ "replay_failures": [],
830
+ "transitions": 95,
831
+ "validation_failures": [
832
+ {
833
+ "errors": [
834
+ "internal transition boundary mismatch",
835
+ "internal transition boundary mismatch"
836
+ ],
837
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
838
+ "proof_id": "mathlib:exists_one_lt'",
839
+ "provenance": {
840
+ "selection": {
841
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
842
+ "end": [
843
+ 1142,
844
+ 17
845
+ ],
846
+ "file_path": "Mathlib/Algebra/Order/Group/Defs.lean",
847
+ "full_name": "exists_one_lt'",
848
+ "start": [
849
+ 1138,
850
+ 1
851
+ ],
852
+ "traced_tactics": [
853
+ {
854
+ "annotated_tactic": [
855
+ "\"obtain \\u27e8y, hy\\u27e9 := <a>Decidable.exists_ne<\\/a> (1 : \\u03b1)\"",
856
+ "[{\"full_name\":\"Decidable.exists_ne\",\"def_path\":\"Mathlib\\/Logic\\/Nontrivial\\/Defs.lean\",\"def_pos\":[45,19],\"def_end_pos\":[45,38]}]"
857
+ ],
858
+ "state_after": "case intro\n\u03b1 : Type u\ninst\u271d\u00b9 : LinearOrderedCommGroup \u03b1\na b c : \u03b1\ninst\u271d : Nontrivial \u03b1\ny : \u03b1\nhy : y \u2260 1\n\u22a2 \u2203 a, 1 < a",
859
+ "state_before": "\u03b1 : Type u\ninst\u271d\u00b9 : LinearOrderedCommGroup \u03b1\na b c : \u03b1\ninst\u271d : Nontrivial \u03b1\n\u22a2 \u2203 a, 1 < a",
860
+ "tactic": "obtain \u27e8y, hy\u27e9 := Decidable.exists_ne (1 : \u03b1)"
861
+ },
862
+ {
863
+ "annotated_tactic": [
864
+ "\"obtain h|h := hy.lt_or_lt\"",
865
+ "[]"
866
+ ],
867
+ "state_after": "case intro.inl\n\u03b1 : Type u\ninst\u271d\u00b9 : LinearOrderedCommGroup \u03b1\na b c : \u03b1\ninst\u271d : Nontrivial \u03b1\ny : \u03b1\nhy : y \u2260 1\nh : y < 1\n\u22a2 \u2203 a, 1 < a\n\ncase intro.inr\n\u03b1 : Type u\ninst\u271d\u00b9 : LinearOrderedCommGroup \u03b1\na b c : \u03b1\ninst\u271d : Nontrivial \u03b1\ny : \u03b1\nhy : y \u2260 1\nh : 1 < y\n\u22a2 \u2203 a, 1 < a",
868
+ "state_before": "case intro\n\u03b1 : Type u\ninst\u271d\u00b9 : LinearOrderedCommGroup \u03b1\na b c : \u03b1\ninst\u271d : Nontrivial \u03b1\ny : \u03b1\nhy : y \u2260 1\n\u22a2 \u2203 a, 1 < a",
869
+ "tactic": "obtain h|h := hy.lt_or_lt"
870
+ },
871
+ {
872
+ "annotated_tactic": [
873
+ "\"exact \\u27e8y\\u207b\\u00b9, one_lt_inv'.mpr h\\u27e9\"",
874
+ "[]"
875
+ ],
876
+ "state_after": "no goals",
877
+ "state_before": "case intro.inl\n\u03b1 : Type u\ninst\u271d\u00b9 : LinearOrderedCommGroup \u03b1\na b c : \u03b1\ninst\u271d : Nontrivial \u03b1\ny : \u03b1\nhy : y \u2260 1\nh : y < 1\n\u22a2 \u2203 a, 1 < a",
878
+ "tactic": "exact \u27e8y\u207b\u00b9, one_lt_inv'.mpr h\u27e9"
879
+ },
880
+ {
881
+ "annotated_tactic": [
882
+ "\"exact \\u27e8y, h\\u27e9\"",
883
+ "[]"
884
+ ],
885
+ "state_after": "no goals",
886
+ "state_before": "case intro.inr\n\u03b1 : Type u\ninst\u271d\u00b9 : LinearOrderedCommGroup \u03b1\na b c : \u03b1\ninst\u271d : Nontrivial \u03b1\ny : \u03b1\nhy : y \u2260 1\nh : 1 < y\n\u22a2 \u2203 a, 1 < a",
887
+ "tactic": "exact \u27e8y, h\u27e9"
888
+ }
889
+ ],
890
+ "url": "https://github.com/leanprover-community/mathlib4"
891
+ }
892
+ },
893
+ "theorem_name": "exists_one_lt'"
894
+ }
895
+ ],
896
+ "validation_rejected_proofs": 1,
897
+ "zero_transition_proofs": 0
898
+ },
899
+ "shards": [
900
+ {
901
+ "path": "data/train/mathlib-000254-0000-e6301bc0dcfd5d87.parquet",
902
+ "sha256": "e6301bc0dcfd5d876d26618250773c5c56a4f4b9168357c7ac2cb4d0095d00ba",
903
+ "bytes": 200180,
904
+ "rows": 79,
905
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
906
+ },
907
+ {
908
+ "path": "data/dev/mathlib-000254-0000-c146dc9774f446d4.parquet",
909
+ "sha256": "c146dc9774f446d4491a13800c2159afb7658185ad4c43c1f2d8affc2115551e",
910
+ "bytes": 44602,
911
+ "rows": 4,
912
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
913
+ },
914
+ {
915
+ "path": "data/internal_test/mathlib-000254-0000-b8cedcf990478ca4.parquet",
916
+ "sha256": "b8cedcf990478ca467184f85b74445a8eac2909b3655798064bcf7b42f56e3a7",
917
+ "bytes": 46350,
918
+ "rows": 8,
919
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
920
+ }
921
+ ],
922
+ "proof_ids": [
923
+ "mathlib:Left.inv_le_one_iff",
924
+ "mathlib:Left.inv_lt_one_iff",
925
+ "mathlib:Left.one_le_inv_iff",
926
+ "mathlib:Left.one_lt_inv_iff",
927
+ "mathlib:OrderedCommGroup.to_contravariantClass_left_le",
928
+ "mathlib:OrderedCommGroup.to_contravariantClass_right_le",
929
+ "mathlib:Right.inv_le_one_iff",
930
+ "mathlib:Right.inv_lt_one_iff",
931
+ "mathlib:Right.one_le_inv_iff",
932
+ "mathlib:Right.one_lt_inv_iff",
933
+ "mathlib:cmp_div_one'",
934
+ "mathlib:div_le_div''",
935
+ "mathlib:div_le_div_flip",
936
+ "mathlib:div_le_div_iff'",
937
+ "mathlib:div_le_div_iff_left",
938
+ "mathlib:div_le_div_iff_right",
939
+ "mathlib:div_le_iff_le_mul",
940
+ "mathlib:div_le_iff_le_mul'",
941
+ "mathlib:div_le_inv_mul_iff",
942
+ "mathlib:div_le_one'",
943
+ "mathlib:div_le_self_iff",
944
+ "mathlib:div_lt_div''",
945
+ "mathlib:div_lt_div_iff'",
946
+ "mathlib:div_lt_div_iff_left",
947
+ "mathlib:div_lt_div_iff_right",
948
+ "mathlib:div_lt_iff_lt_mul",
949
+ "mathlib:div_lt_iff_lt_mul'",
950
+ "mathlib:div_lt_one'",
951
+ "mathlib:div_lt_self_iff",
952
+ "mathlib:inv_le_div_iff_le_mul'",
953
+ "mathlib:inv_le_iff_one_le_mul",
954
+ "mathlib:inv_le_iff_one_le_mul'",
955
+ "mathlib:inv_le_inv_iff",
956
+ "mathlib:inv_le_self_iff",
957
+ "mathlib:inv_lt'",
958
+ "mathlib:inv_lt_div_iff_lt_mul",
959
+ "mathlib:inv_lt_iff_one_lt_mul",
960
+ "mathlib:inv_lt_iff_one_lt_mul'",
961
+ "mathlib:inv_lt_inv_iff",
962
+ "mathlib:inv_lt_self_iff",
963
+ "mathlib:inv_mul_le_iff_le_mul",
964
+ "mathlib:inv_mul_le_iff_le_mul'",
965
+ "mathlib:inv_mul_le_one_iff",
966
+ "mathlib:inv_mul_lt_iff_lt_mul",
967
+ "mathlib:inv_mul_lt_iff_lt_mul'",
968
+ "mathlib:inv_mul_lt_one_iff",
969
+ "mathlib:inv_mul_lt_one_iff_lt",
970
+ "mathlib:le_div_iff_mul_le",
971
+ "mathlib:le_div_iff_mul_le'",
972
+ "mathlib:le_div_self_iff",
973
+ "mathlib:le_inv_iff_mul_le_one_left",
974
+ "mathlib:le_inv_mul_iff_le",
975
+ "mathlib:le_inv_mul_iff_mul_le",
976
+ "mathlib:le_inv_self_iff",
977
+ "mathlib:le_mul_inv_iff_le",
978
+ "mathlib:le_mul_inv_iff_mul_le",
979
+ "mathlib:le_of_forall_one_lt_lt_mul",
980
+ "mathlib:lt_div_iff_mul_lt",
981
+ "mathlib:lt_div_iff_mul_lt'",
982
+ "mathlib:lt_inv'",
983
+ "mathlib:lt_inv_iff_mul_lt_one",
984
+ "mathlib:lt_inv_iff_mul_lt_one'",
985
+ "mathlib:lt_inv_mul_iff_lt",
986
+ "mathlib:lt_inv_mul_iff_mul_lt",
987
+ "mathlib:lt_inv_self_iff",
988
+ "mathlib:lt_mul_inv_iff_lt",
989
+ "mathlib:lt_mul_inv_iff_mul_lt",
990
+ "mathlib:mul_inv_le_iff_le_mul",
991
+ "mathlib:mul_inv_le_iff_le_mul'",
992
+ "mathlib:mul_inv_le_inv_mul_iff",
993
+ "mathlib:mul_inv_le_mul_inv_iff'",
994
+ "mathlib:mul_inv_le_one_iff",
995
+ "mathlib:mul_inv_le_one_iff_le",
996
+ "mathlib:mul_inv_lt_iff_le_mul'",
997
+ "mathlib:mul_inv_lt_iff_lt_mul",
998
+ "mathlib:mul_inv_lt_mul_inv_iff'",
999
+ "mathlib:mul_inv_lt_one_iff",
1000
+ "mathlib:one_le_div'",
1001
+ "mathlib:one_lt_div'"
1002
+ ],
1003
+ "proof_keys": [
1004
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"Left.inv_le_one_iff\"]",
1005
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"Left.inv_lt_one_iff\"]",
1006
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"Left.one_le_inv_iff\"]",
1007
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"Left.one_lt_inv_iff\"]",
1008
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"OrderedCommGroup.to_contravariantClass_left_le\"]",
1009
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"OrderedCommGroup.to_contravariantClass_right_le\"]",
1010
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"Right.inv_le_one_iff\"]",
1011
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"Right.inv_lt_one_iff\"]",
1012
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"Right.one_le_inv_iff\"]",
1013
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"Right.one_lt_inv_iff\"]",
1014
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"cmp_div_one'\"]",
1015
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"div_le_div''\"]",
1016
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"div_le_div_flip\"]",
1017
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"div_le_div_iff'\"]",
1018
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"div_le_div_iff_left\"]",
1019
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"div_le_div_iff_right\"]",
1020
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"div_le_iff_le_mul\"]",
1021
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"div_le_iff_le_mul'\"]",
1022
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"div_le_inv_mul_iff\"]",
1023
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"div_le_one'\"]",
1024
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"div_le_self_iff\"]",
1025
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"div_lt_div''\"]",
1026
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"div_lt_div_iff'\"]",
1027
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"div_lt_div_iff_left\"]",
1028
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"div_lt_div_iff_right\"]",
1029
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"div_lt_iff_lt_mul\"]",
1030
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"div_lt_iff_lt_mul'\"]",
1031
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"div_lt_one'\"]",
1032
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"div_lt_self_iff\"]",
1033
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"inv_le_div_iff_le_mul'\"]",
1034
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"inv_le_iff_one_le_mul\"]",
1035
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"inv_le_iff_one_le_mul'\"]",
1036
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"inv_le_inv_iff\"]",
1037
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"inv_le_self_iff\"]",
1038
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"inv_lt'\"]",
1039
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"inv_lt_div_iff_lt_mul\"]",
1040
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"inv_lt_iff_one_lt_mul\"]",
1041
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"inv_lt_iff_one_lt_mul'\"]",
1042
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"inv_lt_inv_iff\"]",
1043
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"inv_lt_self_iff\"]",
1044
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"inv_mul_le_iff_le_mul\"]",
1045
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"inv_mul_le_iff_le_mul'\"]",
1046
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"inv_mul_le_one_iff\"]",
1047
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"inv_mul_lt_iff_lt_mul\"]",
1048
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"inv_mul_lt_iff_lt_mul'\"]",
1049
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"inv_mul_lt_one_iff\"]",
1050
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"inv_mul_lt_one_iff_lt\"]",
1051
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"le_div_iff_mul_le\"]",
1052
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"le_div_iff_mul_le'\"]",
1053
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"le_div_self_iff\"]",
1054
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"le_inv_iff_mul_le_one_left\"]",
1055
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"le_inv_mul_iff_le\"]",
1056
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"le_inv_mul_iff_mul_le\"]",
1057
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"le_inv_self_iff\"]",
1058
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"le_mul_inv_iff_le\"]",
1059
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"le_mul_inv_iff_mul_le\"]",
1060
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"le_of_forall_one_lt_lt_mul\"]",
1061
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"lt_div_iff_mul_lt\"]",
1062
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"lt_div_iff_mul_lt'\"]",
1063
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"lt_inv'\"]",
1064
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"lt_inv_iff_mul_lt_one\"]",
1065
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"lt_inv_iff_mul_lt_one'\"]",
1066
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"lt_inv_mul_iff_lt\"]",
1067
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"lt_inv_mul_iff_mul_lt\"]",
1068
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"lt_inv_self_iff\"]",
1069
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"lt_mul_inv_iff_lt\"]",
1070
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"lt_mul_inv_iff_mul_lt\"]",
1071
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"mul_inv_le_iff_le_mul\"]",
1072
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"mul_inv_le_iff_le_mul'\"]",
1073
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"mul_inv_le_inv_mul_iff\"]",
1074
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"mul_inv_le_mul_inv_iff'\"]",
1075
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"mul_inv_le_one_iff\"]",
1076
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"mul_inv_le_one_iff_le\"]",
1077
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"mul_inv_lt_iff_le_mul'\"]",
1078
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"mul_inv_lt_iff_lt_mul\"]",
1079
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"mul_inv_lt_mul_inv_iff'\"]",
1080
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"mul_inv_lt_one_iff\"]",
1081
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"one_le_div'\"]",
1082
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Defs.lean\",null,null,\"one_lt_div'\"]"
1083
+ ]
1084
+ }
manifests/batches/mathlib/000255.json ADDED
@@ -0,0 +1,1114 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000255",
4
+ "batch_fingerprint": "2a4d1a4bb6809c9a2685769c3a20a5ff33baf18afb1f778946a333d8093d5199",
5
+ "evidence": {
6
+ "batch_fingerprint": "2a4d1a4bb6809c9a2685769c3a20a5ff33baf18afb1f778946a333d8093d5199",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "Function.mulSupport_iInf",
12
+ "id": "Function.mulSupport_iInf",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 63,
18
+ 92
19
+ ],
20
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
21
+ "full_name": "Function.mulSupport_iInf",
22
+ "start": [
23
+ 61,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "Function.mulSupport_inf",
34
+ "id": "Function.mulSupport_inf",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 36,
40
+ 51
41
+ ],
42
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
43
+ "full_name": "Function.mulSupport_inf",
44
+ "start": [
45
+ 33,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "Function.mulSupport_max",
56
+ "id": "Function.mulSupport_max",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 42,
62
+ 93
63
+ ],
64
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
65
+ "full_name": "Function.mulSupport_max",
66
+ "start": [
67
+ 40,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "Function.mulSupport_min",
78
+ "id": "Function.mulSupport_min",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 48,
84
+ 93
85
+ ],
86
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
87
+ "full_name": "Function.mulSupport_min",
88
+ "start": [
89
+ 46,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "Function.mulSupport_sup",
100
+ "id": "Function.mulSupport_sup",
101
+ "reason": "import_failure",
102
+ "selection": {
103
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
104
+ "end": [
105
+ 29,
106
+ 51
107
+ ],
108
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
109
+ "full_name": "Function.mulSupport_sup",
110
+ "start": [
111
+ 26,
112
+ 1
113
+ ],
114
+ "traced_tactics": [],
115
+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
118
+ },
119
+ {
120
+ "error": "no internal trace for tactic 'simp_rw [indicator_apply]'",
121
+ "full_name": "Set.indicator_le_indicator_nonneg",
122
+ "id": "Set.indicator_le_indicator_nonneg",
123
+ "reason": "import_failure",
124
+ "selection": {
125
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
126
+ "end": [
127
+ 164,
128
+ 50
129
+ ],
130
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
131
+ "full_name": "Set.indicator_le_indicator_nonneg",
132
+ "start": [
133
+ 158,
134
+ 1
135
+ ],
136
+ "traced_tactics": [
137
+ {
138
+ "annotated_tactic": [
139
+ "\"intro a\"",
140
+ "[]"
141
+ ],
142
+ "state_after": "\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : Zero M\ninst\u271d : LinearOrder M\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\n\u22a2 s.indicator f a \u2264 {a | 0 \u2264 f a}.indicator f a",
143
+ "state_before": "\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : Zero M\ninst\u271d : LinearOrder M\ns : Set \u03b1\nf : \u03b1 \u2192 M\n\u22a2 s.indicator f \u2264 {a | 0 \u2264 f a}.indicator f",
144
+ "tactic": "intro a"
145
+ },
146
+ {
147
+ "annotated_tactic": [
148
+ "\"classical\\n simp_rw [<a>indicator_apply<\\/a>]\\n split_ifs\\n exacts [<a>le_rfl<\\/a>, (<a>not_le<\\/a>.1 \\u2039_\\u203a).<a>le<\\/a>, \\u2039_\\u203a, <a>le_rfl<\\/a>]\"",
149
+ "[{\"full_name\":\"Set.indicator_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[60,3],\"def_end_pos\":[60,14]},{\"full_name\":\"le_rfl\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[50,9],\"def_end_pos\":[50,15]},{\"full_name\":\"not_le\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[375,9],\"def_end_pos\":[375,15]},{\"full_name\":\"LT.lt.le\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[137,7],\"def_end_pos\":[137,15]},{\"full_name\":\"le_rfl\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[50,9],\"def_end_pos\":[50,15]}]"
150
+ ],
151
+ "state_after": "no goals",
152
+ "state_before": "\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : Zero M\ninst\u271d : LinearOrder M\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\n\u22a2 s.indicator f a \u2264 {a | 0 \u2264 f a}.indicator f a",
153
+ "tactic": "classical\nsimp_rw [indicator_apply]\nsplit_ifs\nexacts [le_rfl, (not_le.1 \u2039_\u203a).le, \u2039_\u203a, le_rfl]"
154
+ },
155
+ {
156
+ "annotated_tactic": [
157
+ "\"simp_rw [<a>indicator_apply<\\/a>]\"",
158
+ "[{\"full_name\":\"Set.indicator_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[60,3],\"def_end_pos\":[60,14]}]"
159
+ ],
160
+ "state_after": "\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : Zero M\ninst\u271d : LinearOrder M\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\n\u22a2 (if a \u2208 s then f a else 0) \u2264 if a \u2208 {a | 0 \u2264 f a} then f a else 0",
161
+ "state_before": "\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : Zero M\ninst\u271d : LinearOrder M\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\n\u22a2 s.indicator f a \u2264 {a | 0 \u2264 f a}.indicator f a",
162
+ "tactic": "simp_rw [indicator_apply]"
163
+ },
164
+ {
165
+ "annotated_tactic": [
166
+ "\"split_ifs\"",
167
+ "[]"
168
+ ],
169
+ "state_after": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : Zero M\ninst\u271d : LinearOrder M\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\nh\u271d\u00b9 : a \u2208 s\nh\u271d : a \u2208 {a | 0 \u2264 f a}\n\u22a2 f a \u2264 f a\n\ncase neg\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : Zero M\ninst\u271d : LinearOrder M\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\nh\u271d\u00b9 : a \u2208 s\nh\u271d : a \u2209 {a | 0 \u2264 f a}\n\u22a2 f a \u2264 0\n\ncase pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : Zero M\ninst\u271d : LinearOrder M\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\nh\u271d\u00b9 : a \u2209 s\nh\u271d : a \u2208 {a | 0 \u2264 f a}\n\u22a2 0 \u2264 f a\n\ncase neg\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : Zero M\ninst\u271d : LinearOrder M\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\nh\u271d\u00b9 : a \u2209 s\nh\u271d : a \u2209 {a | 0 \u2264 f a}\n\u22a2 0 \u2264 0",
170
+ "state_before": "\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : Zero M\ninst\u271d : LinearOrder M\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\n\u22a2 (if a \u2208 s then f a else 0) \u2264 if a \u2208 {a | 0 \u2264 f a} then f a else 0",
171
+ "tactic": "split_ifs"
172
+ },
173
+ {
174
+ "annotated_tactic": [
175
+ "\"exacts [<a>le_rfl<\\/a>, (<a>not_le<\\/a>.1 \\u2039_\\u203a).<a>le<\\/a>, \\u2039_\\u203a, <a>le_rfl<\\/a>]\"",
176
+ "[{\"full_name\":\"le_rfl\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[50,9],\"def_end_pos\":[50,15]},{\"full_name\":\"not_le\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[375,9],\"def_end_pos\":[375,15]},{\"full_name\":\"LT.lt.le\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[137,7],\"def_end_pos\":[137,15]},{\"full_name\":\"le_rfl\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[50,9],\"def_end_pos\":[50,15]}]"
177
+ ],
178
+ "state_after": "no goals",
179
+ "state_before": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : Zero M\ninst\u271d : LinearOrder M\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\nh\u271d\u00b9 : a \u2208 s\nh\u271d : a \u2208 {a | 0 \u2264 f a}\n\u22a2 f a \u2264 f a\n\ncase neg\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : Zero M\ninst\u271d : LinearOrder M\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\nh\u271d\u00b9 : a \u2208 s\nh\u271d : a \u2209 {a | 0 \u2264 f a}\n\u22a2 f a \u2264 0\n\ncase pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : Zero M\ninst\u271d : LinearOrder M\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\nh\u271d\u00b9 : a \u2209 s\nh\u271d : a \u2208 {a | 0 \u2264 f a}\n\u22a2 0 \u2264 f a\n\ncase neg\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : Zero M\ninst\u271d : LinearOrder M\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\nh\u271d\u00b9 : a \u2209 s\nh\u271d : a \u2209 {a | 0 \u2264 f a}\n\u22a2 0 \u2264 0",
180
+ "tactic": "exacts [le_rfl, (not_le.1 \u2039_\u203a).le, \u2039_\u203a, le_rfl]"
181
+ }
182
+ ],
183
+ "url": "https://github.com/leanprover-community/mathlib4"
184
+ },
185
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
186
+ },
187
+ {
188
+ "error": "theorem has no selected tactic transitions",
189
+ "full_name": "Set.indicator_nonpos_le_indicator",
190
+ "id": "Set.indicator_nonpos_le_indicator",
191
+ "reason": "import_failure",
192
+ "selection": {
193
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
194
+ "end": [
195
+ 169,
196
+ 47
197
+ ],
198
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
199
+ "full_name": "Set.indicator_nonpos_le_indicator",
200
+ "start": [
201
+ 167,
202
+ 1
203
+ ],
204
+ "traced_tactics": [],
205
+ "url": "https://github.com/leanprover-community/mathlib4"
206
+ },
207
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
208
+ },
209
+ {
210
+ "error": "theorem has no selected tactic transitions",
211
+ "full_name": "Set.le_mulIndicator",
212
+ "id": "Set.le_mulIndicator",
213
+ "reason": "import_failure",
214
+ "selection": {
215
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
216
+ "end": [
217
+ 97,
218
+ 73
219
+ ],
220
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
221
+ "full_name": "Set.le_mulIndicator",
222
+ "start": [
223
+ 95,
224
+ 1
225
+ ],
226
+ "traced_tactics": [],
227
+ "url": "https://github.com/leanprover-community/mathlib4"
228
+ },
229
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
230
+ },
231
+ {
232
+ "error": "theorem has no selected tactic transitions",
233
+ "full_name": "Set.le_mulIndicator_apply",
234
+ "id": "Set.le_mulIndicator_apply",
235
+ "reason": "import_failure",
236
+ "selection": {
237
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
238
+ "end": [
239
+ 91,
240
+ 71
241
+ ],
242
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
243
+ "full_name": "Set.le_mulIndicator_apply",
244
+ "start": [
245
+ 89,
246
+ 1
247
+ ],
248
+ "traced_tactics": [],
249
+ "url": "https://github.com/leanprover-community/mathlib4"
250
+ },
251
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
252
+ },
253
+ {
254
+ "error": "theorem has no selected tactic transitions",
255
+ "full_name": "Set.mabs_mulIndicator_symmDiff",
256
+ "id": "Set.mabs_mulIndicator_symmDiff",
257
+ "reason": "import_failure",
258
+ "selection": {
259
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
260
+ "end": [
261
+ 244,
262
+ 47
263
+ ],
264
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
265
+ "full_name": "Set.mabs_mulIndicator_symmDiff",
266
+ "start": [
267
+ 241,
268
+ 1
269
+ ],
270
+ "traced_tactics": [],
271
+ "url": "https://github.com/leanprover-community/mathlib4"
272
+ },
273
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
274
+ },
275
+ {
276
+ "error": "theorem has no selected tactic transitions",
277
+ "full_name": "Set.mulIndicator_apply_le",
278
+ "id": "Set.mulIndicator_apply_le",
279
+ "reason": "import_failure",
280
+ "selection": {
281
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
282
+ "end": [
283
+ 223,
284
+ 46
285
+ ],
286
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
287
+ "full_name": "Set.mulIndicator_apply_le",
288
+ "start": [
289
+ 220,
290
+ 1
291
+ ],
292
+ "traced_tactics": [],
293
+ "url": "https://github.com/leanprover-community/mathlib4"
294
+ },
295
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
296
+ },
297
+ {
298
+ "error": "theorem has no selected tactic transitions",
299
+ "full_name": "Set.mulIndicator_apply_le_one",
300
+ "id": "Set.mulIndicator_apply_le_one",
301
+ "reason": "import_failure",
302
+ "selection": {
303
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
304
+ "end": [
305
+ 120,
306
+ 42
307
+ ],
308
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
309
+ "full_name": "Set.mulIndicator_apply_le_one",
310
+ "start": [
311
+ 118,
312
+ 1
313
+ ],
314
+ "traced_tactics": [],
315
+ "url": "https://github.com/leanprover-community/mathlib4"
316
+ },
317
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
318
+ },
319
+ {
320
+ "error": "no internal trace for tactic 'simp only [mulIndicator_of_mem (hx _), ciInf_const, le_refl]'",
321
+ "full_name": "Set.mulIndicator_iInter_apply",
322
+ "id": "Set.mulIndicator_iInter_apply",
323
+ "reason": "import_failure",
324
+ "selection": {
325
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
326
+ "end": [
327
+ 206,
328
+ 90
329
+ ],
330
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
331
+ "full_name": "Set.mulIndicator_iInter_apply",
332
+ "start": [
333
+ 194,
334
+ 1
335
+ ],
336
+ "traced_tactics": [
337
+ {
338
+ "annotated_tactic": [
339
+ "\"by_cases hx : x \\u2208 \\u22c2 i, s i\"",
340
+ "[]"
341
+ ],
342
+ "state_after": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : x \u2208 \u22c2 i, s i\n\u22a2 (\u22c2 i, s i).mulIndicator f x = \u2a05 i, (s i).mulIndicator f x\n\ncase neg\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : x \u2209 \u22c2 i, s i\n\u22a2 (\u22c2 i, s i).mulIndicator f x = \u2a05 i, (s i).mulIndicator f x",
343
+ "state_before": "\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\n\u22a2 (\u22c2 i, s i).mulIndicator f x = \u2a05 i, (s i).mulIndicator f x",
344
+ "tactic": "by_cases hx : x \u2208 \u22c2 i, s i"
345
+ },
346
+ {
347
+ "annotated_tactic": [
348
+ "\"rw [<a>mulIndicator_of_mem<\\/a> hx]\"",
349
+ "[{\"full_name\":\"Set.mulIndicator_of_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,28]}]"
350
+ ],
351
+ "state_after": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : x \u2208 \u22c2 i, s i\n\u22a2 f x = \u2a05 i, (s i).mulIndicator f x",
352
+ "state_before": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : x \u2208 \u22c2 i, s i\n\u22a2 (\u22c2 i, s i).mulIndicator f x = \u2a05 i, (s i).mulIndicator f x",
353
+ "tactic": "rw [mulIndicator_of_mem hx]"
354
+ },
355
+ {
356
+ "annotated_tactic": [
357
+ "\"rw [<a>mem_iInter<\\/a>] at hx\"",
358
+ "[{\"full_name\":\"Set.mem_iInter\",\"def_path\":\"Mathlib\\/Order\\/SetNotation.lean\",\"def_pos\":[274,9],\"def_end_pos\":[274,19]}]"
359
+ ],
360
+ "state_after": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : \u2200 (i : \u03b9), x \u2208 s i\n\u22a2 f x = \u2a05 i, (s i).mulIndicator f x",
361
+ "state_before": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : x \u2208 \u22c2 i, s i\n\u22a2 f x = \u2a05 i, (s i).mulIndicator f x",
362
+ "tactic": "rw [mem_iInter] at hx"
363
+ },
364
+ {
365
+ "annotated_tactic": [
366
+ "\"refine <a>le_antisymm<\\/a> ?_ (by simp only [<a>mulIndicator_of_mem<\\/a> (hx _), <a>ciInf_const<\\/a>, <a>le_refl<\\/a>])\"",
367
+ "[{\"full_name\":\"le_antisymm\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[188,9],\"def_end_pos\":[188,20]},{\"full_name\":\"Set.mulIndicator_of_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,28]},{\"full_name\":\"ciInf_const\",\"def_path\":\"Mathlib\\/Order\\/ConditionallyCompleteLattice\\/Basic.lean\",\"def_pos\":[853,9],\"def_end_pos\":[853,20]},{\"full_name\":\"le_refl\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[45,9],\"def_end_pos\":[45,16]}]"
368
+ ],
369
+ "state_after": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : \u2200 (i : \u03b9), x \u2208 s i\n\u22a2 f x \u2264 \u2a05 i, (s i).mulIndicator f x",
370
+ "state_before": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : \u2200 (i : \u03b9), x \u2208 s i\n\u22a2 f x = \u2a05 i, (s i).mulIndicator f x",
371
+ "tactic": "refine le_antisymm ?_ (by simp only [mulIndicator_of_mem (hx _), ciInf_const, le_refl])"
372
+ },
373
+ {
374
+ "annotated_tactic": [
375
+ "\"exact <a>le_iInf<\\/a> (fun j \\u21a6 by simp only [<a>mulIndicator_of_mem<\\/a> (hx j), <a>le_refl<\\/a>])\"",
376
+ "[{\"full_name\":\"le_iInf\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[764,9],\"def_end_pos\":[764,16]},{\"full_name\":\"Set.mulIndicator_of_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,28]},{\"full_name\":\"le_refl\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[45,9],\"def_end_pos\":[45,16]}]"
377
+ ],
378
+ "state_after": "no goals",
379
+ "state_before": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : \u2200 (i : \u03b9), x \u2208 s i\n\u22a2 f x \u2264 \u2a05 i, (s i).mulIndicator f x",
380
+ "tactic": "exact le_iInf (fun j \u21a6 by simp only [mulIndicator_of_mem (hx j), le_refl])"
381
+ },
382
+ {
383
+ "annotated_tactic": [
384
+ "\"simp only [<a>mulIndicator_of_mem<\\/a> (hx _), <a>ciInf_const<\\/a>, <a>le_refl<\\/a>]\"",
385
+ "[{\"full_name\":\"Set.mulIndicator_of_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,28]},{\"full_name\":\"ciInf_const\",\"def_path\":\"Mathlib\\/Order\\/ConditionallyCompleteLattice\\/Basic.lean\",\"def_pos\":[853,9],\"def_end_pos\":[853,20]},{\"full_name\":\"le_refl\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[45,9],\"def_end_pos\":[45,16]}]"
386
+ ],
387
+ "state_after": "no goals",
388
+ "state_before": "\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : \u2200 (i : \u03b9), x \u2208 s i\n\u22a2 \u2a05 i, (s i).mulIndicator f x \u2264 f x",
389
+ "tactic": "simp only [mulIndicator_of_mem (hx _), ciInf_const, le_refl]"
390
+ },
391
+ {
392
+ "annotated_tactic": [
393
+ "\"simp only [<a>mulIndicator_of_mem<\\/a> (hx j), <a>le_refl<\\/a>]\"",
394
+ "[{\"full_name\":\"Set.mulIndicator_of_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,28]},{\"full_name\":\"le_refl\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[45,9],\"def_end_pos\":[45,16]}]"
395
+ ],
396
+ "state_after": "no goals",
397
+ "state_before": "\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : \u2200 (i : \u03b9), x \u2208 s i\nj : \u03b9\n\u22a2 f x \u2264 (s j).mulIndicator f x",
398
+ "tactic": "simp only [mulIndicator_of_mem (hx j), le_refl]"
399
+ },
400
+ {
401
+ "annotated_tactic": [
402
+ "\"rw [<a>mulIndicator_of_not_mem<\\/a> hx]\"",
403
+ "[{\"full_name\":\"Set.mulIndicator_of_not_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[75,9],\"def_end_pos\":[75,32]}]"
404
+ ],
405
+ "state_after": "case neg\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : x \u2209 \u22c2 i, s i\n\u22a2 1 = \u2a05 i, (s i).mulIndicator f x",
406
+ "state_before": "case neg\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : x \u2209 \u22c2 i, s i\n\u22a2 (\u22c2 i, s i).mulIndicator f x = \u2a05 i, (s i).mulIndicator f x",
407
+ "tactic": "rw [mulIndicator_of_not_mem hx]"
408
+ },
409
+ {
410
+ "annotated_tactic": [
411
+ "\"simp only [<a>mem_iInter<\\/a>, <a>not_exists<\\/a>, <a>not_forall<\\/a>] at hx\"",
412
+ "[{\"full_name\":\"Set.mem_iInter\",\"def_path\":\"Mathlib\\/Order\\/SetNotation.lean\",\"def_pos\":[274,9],\"def_end_pos\":[274,19]},{\"full_name\":\"not_exists\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/PropLemmas.lean\",\"def_pos\":[254,17],\"def_end_pos\":[254,27]},{\"full_name\":\"Classical.not_forall\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Classical.lean\",\"def_pos\":[137,21],\"def_end_pos\":[137,31]}]"
413
+ ],
414
+ "state_after": "case neg\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : \u2203 x_1, x \u2209 s x_1\n\u22a2 1 = \u2a05 i, (s i).mulIndicator f x",
415
+ "state_before": "case neg\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : x \u2209 \u22c2 i, s i\n\u22a2 1 = \u2a05 i, (s i).mulIndicator f x",
416
+ "tactic": "simp only [mem_iInter, not_exists, not_forall] at hx"
417
+ },
418
+ {
419
+ "annotated_tactic": [
420
+ "\"rcases hx with \\u27e8j, hj\\u27e9\"",
421
+ "[]"
422
+ ],
423
+ "state_after": "case neg.intro\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nj : \u03b9\nhj : x \u2209 s j\n\u22a2 1 = \u2a05 i, (s i).mulIndicator f x",
424
+ "state_before": "case neg\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : \u2203 x_1, x \u2209 s x_1\n\u22a2 1 = \u2a05 i, (s i).mulIndicator f x",
425
+ "tactic": "rcases hx with \u27e8j, hj\u27e9"
426
+ },
427
+ {
428
+ "annotated_tactic": [
429
+ "\"refine <a>le_antisymm<\\/a> (by simp only [\\u2190 h1, <a>le_iInf_iff<\\/a>, <a>bot_le<\\/a>, <a>forall_const<\\/a>]) ?_\"",
430
+ "[{\"full_name\":\"le_antisymm\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[188,9],\"def_end_pos\":[188,20]},{\"full_name\":\"le_iInf_iff\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[854,9],\"def_end_pos\":[854,20]},{\"full_name\":\"bot_le\",\"def_path\":\"Mathlib\\/Order\\/BoundedOrder.lean\",\"def_pos\":[224,9],\"def_end_pos\":[224,15]},{\"full_name\":\"forall_const\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/PropLemmas.lean\",\"def_pos\":[265,17],\"def_end_pos\":[265,29]}]"
431
+ ],
432
+ "state_after": "case neg.intro\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nj : \u03b9\nhj : x \u2209 s j\n\u22a2 \u2a05 i, (s i).mulIndicator f x \u2264 1",
433
+ "state_before": "case neg.intro\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nj : \u03b9\nhj : x \u2209 s j\n\u22a2 1 = \u2a05 i, (s i).mulIndicator f x",
434
+ "tactic": "refine le_antisymm (by simp only [\u2190 h1, le_iInf_iff, bot_le, forall_const]) ?_"
435
+ },
436
+ {
437
+ "annotated_tactic": [
438
+ "\"simpa [<a>mulIndicator_of_not_mem<\\/a> hj] using (<a>iInf_le<\\/a> (fun i \\u21a6 (s i).<a>mulIndicator<\\/a> f) j) x\"",
439
+ "[{\"full_name\":\"Set.mulIndicator_of_not_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[75,9],\"def_end_pos\":[75,32]},{\"full_name\":\"iInf_le\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[706,9],\"def_end_pos\":[706,16]},{\"full_name\":\"Set.mulIndicator\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[48,19],\"def_end_pos\":[48,31]}]"
440
+ ],
441
+ "state_after": "no goals",
442
+ "state_before": "case neg.intro\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nj : \u03b9\nhj : x \u2209 s j\n\u22a2 \u2a05 i, (s i).mulIndicator f x \u2264 1",
443
+ "tactic": "simpa [mulIndicator_of_not_mem hj] using (iInf_le (fun i \u21a6 (s i).mulIndicator f) j) x"
444
+ },
445
+ {
446
+ "annotated_tactic": [
447
+ "\"simp only [\\u2190 h1, <a>le_iInf_iff<\\/a>, <a>bot_le<\\/a>, <a>forall_const<\\/a>]\"",
448
+ "[{\"full_name\":\"le_iInf_iff\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[854,9],\"def_end_pos\":[854,20]},{\"full_name\":\"bot_le\",\"def_path\":\"Mathlib\\/Order\\/BoundedOrder.lean\",\"def_pos\":[224,9],\"def_end_pos\":[224,15]},{\"full_name\":\"forall_const\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/PropLemmas.lean\",\"def_pos\":[265,17],\"def_end_pos\":[265,29]}]"
449
+ ],
450
+ "state_after": "no goals",
451
+ "state_before": "\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b2 : CompleteLattice M\ninst\u271d\u00b9 : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\ninst\u271d : Nonempty \u03b9\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nj : \u03b9\nhj : x \u2209 s j\n\u22a2 1 \u2264 \u2a05 i, (s i).mulIndicator f x",
452
+ "tactic": "simp only [\u2190 h1, le_iInf_iff, bot_le, forall_const]"
453
+ }
454
+ ],
455
+ "url": "https://github.com/leanprover-community/mathlib4"
456
+ },
457
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
458
+ },
459
+ {
460
+ "error": "theorem has no selected tactic transitions",
461
+ "full_name": "Set.mulIndicator_le",
462
+ "id": "Set.mulIndicator_le",
463
+ "reason": "import_failure",
464
+ "selection": {
465
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
466
+ "end": [
467
+ 230,
468
+ 42
469
+ ],
470
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
471
+ "full_name": "Set.mulIndicator_le",
472
+ "start": [
473
+ 227,
474
+ 1
475
+ ],
476
+ "traced_tactics": [],
477
+ "url": "https://github.com/leanprover-community/mathlib4"
478
+ },
479
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
480
+ },
481
+ {
482
+ "error": "theorem has no selected tactic transitions",
483
+ "full_name": "Set.mulIndicator_le'",
484
+ "id": "Set.mulIndicator_le'",
485
+ "reason": "import_failure",
486
+ "selection": {
487
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
488
+ "end": [
489
+ 85,
490
+ 74
491
+ ],
492
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
493
+ "full_name": "Set.mulIndicator_le'",
494
+ "start": [
495
+ 83,
496
+ 1
497
+ ],
498
+ "traced_tactics": [],
499
+ "url": "https://github.com/leanprover-community/mathlib4"
500
+ },
501
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
502
+ },
503
+ {
504
+ "error": "theorem has no selected tactic transitions",
505
+ "full_name": "Set.mulIndicator_le_mulIndicator",
506
+ "id": "Set.mulIndicator_le_mulIndicator",
507
+ "reason": "import_failure",
508
+ "selection": {
509
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
510
+ "end": [
511
+ 132,
512
+ 49
513
+ ],
514
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
515
+ "full_name": "Set.mulIndicator_le_mulIndicator",
516
+ "start": [
517
+ 130,
518
+ 1
519
+ ],
520
+ "traced_tactics": [],
521
+ "url": "https://github.com/leanprover-community/mathlib4"
522
+ },
523
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
524
+ },
525
+ {
526
+ "error": "theorem has no selected tactic transitions",
527
+ "full_name": "Set.mulIndicator_le_mulIndicator_of_subset",
528
+ "id": "Set.mulIndicator_le_mulIndicator_of_subset",
529
+ "reason": "import_failure",
530
+ "selection": {
531
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
532
+ "end": [
533
+ 143,
534
+ 43
535
+ ],
536
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
537
+ "full_name": "Set.mulIndicator_le_mulIndicator_of_subset",
538
+ "start": [
539
+ 138,
540
+ 1
541
+ ],
542
+ "traced_tactics": [],
543
+ "url": "https://github.com/leanprover-community/mathlib4"
544
+ },
545
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
546
+ },
547
+ {
548
+ "error": "theorem has no selected tactic transitions",
549
+ "full_name": "Set.mulIndicator_le_one",
550
+ "id": "Set.mulIndicator_le_one",
551
+ "reason": "import_failure",
552
+ "selection": {
553
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
554
+ "end": [
555
+ 126,
556
+ 34
557
+ ],
558
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
559
+ "full_name": "Set.mulIndicator_le_one",
560
+ "start": [
561
+ 124,
562
+ 1
563
+ ],
564
+ "traced_tactics": [],
565
+ "url": "https://github.com/leanprover-community/mathlib4"
566
+ },
567
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
568
+ },
569
+ {
570
+ "error": "theorem has no selected tactic transitions",
571
+ "full_name": "Set.mulIndicator_le_self",
572
+ "id": "Set.mulIndicator_le_self",
573
+ "reason": "import_failure",
574
+ "selection": {
575
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
576
+ "end": [
577
+ 216,
578
+ 43
579
+ ],
580
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
581
+ "full_name": "Set.mulIndicator_le_self",
582
+ "start": [
583
+ 214,
584
+ 1
585
+ ],
586
+ "traced_tactics": [],
587
+ "url": "https://github.com/leanprover-community/mathlib4"
588
+ },
589
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
590
+ },
591
+ {
592
+ "error": "theorem has no selected tactic transitions",
593
+ "full_name": "Set.mulIndicator_le_self'",
594
+ "id": "Set.mulIndicator_le_self'",
595
+ "reason": "import_failure",
596
+ "selection": {
597
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
598
+ "end": [
599
+ 149,
600
+ 41
601
+ ],
602
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
603
+ "full_name": "Set.mulIndicator_le_self'",
604
+ "start": [
605
+ 147,
606
+ 1
607
+ ],
608
+ "traced_tactics": [],
609
+ "url": "https://github.com/leanprover-community/mathlib4"
610
+ },
611
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
612
+ },
613
+ {
614
+ "error": "theorem has no selected tactic transitions",
615
+ "full_name": "Set.one_le_mulIndicator",
616
+ "id": "Set.one_le_mulIndicator",
617
+ "reason": "import_failure",
618
+ "selection": {
619
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
620
+ "end": [
621
+ 114,
622
+ 34
623
+ ],
624
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
625
+ "full_name": "Set.one_le_mulIndicator",
626
+ "start": [
627
+ 112,
628
+ 1
629
+ ],
630
+ "traced_tactics": [],
631
+ "url": "https://github.com/leanprover-community/mathlib4"
632
+ },
633
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
634
+ },
635
+ {
636
+ "error": "theorem has no selected tactic transitions",
637
+ "full_name": "Set.one_le_mulIndicator_apply",
638
+ "id": "Set.one_le_mulIndicator_apply",
639
+ "reason": "import_failure",
640
+ "selection": {
641
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
642
+ "end": [
643
+ 108,
644
+ 41
645
+ ],
646
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
647
+ "full_name": "Set.one_le_mulIndicator_apply",
648
+ "start": [
649
+ 106,
650
+ 1
651
+ ],
652
+ "traced_tactics": [],
653
+ "url": "https://github.com/leanprover-community/mathlib4"
654
+ },
655
+ "source_file": "Mathlib/Algebra/Order/Group/Indicator.lean"
656
+ },
657
+ {
658
+ "error": "theorem has no selected tactic transitions",
659
+ "full_name": "Int.abs_eq_natAbs",
660
+ "id": "Int.abs_eq_natAbs",
661
+ "reason": "import_failure",
662
+ "selection": {
663
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
664
+ "end": [
665
+ 51,
666
+ 61
667
+ ],
668
+ "file_path": "Mathlib/Algebra/Order/Group/Int.lean",
669
+ "full_name": "Int.abs_eq_natAbs",
670
+ "start": [
671
+ 49,
672
+ 1
673
+ ],
674
+ "traced_tactics": [],
675
+ "url": "https://github.com/leanprover-community/mathlib4"
676
+ },
677
+ "source_file": "Mathlib/Algebra/Order/Group/Int.lean"
678
+ },
679
+ {
680
+ "error": "theorem has no selected tactic transitions",
681
+ "full_name": "Int.abs_natCast",
682
+ "id": "Int.abs_natCast",
683
+ "reason": "import_failure",
684
+ "selection": {
685
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
686
+ "end": [
687
+ 78,
688
+ 91
689
+ ],
690
+ "file_path": "Mathlib/Algebra/Order/Group/Int.lean",
691
+ "full_name": "Int.abs_natCast",
692
+ "start": [
693
+ 78,
694
+ 1
695
+ ],
696
+ "traced_tactics": [],
697
+ "url": "https://github.com/leanprover-community/mathlib4"
698
+ },
699
+ "source_file": "Mathlib/Algebra/Order/Group/Int.lean"
700
+ },
701
+ {
702
+ "error": "theorem has no selected tactic transitions",
703
+ "full_name": "Int.emod_abs",
704
+ "id": "Int.emod_abs",
705
+ "reason": "import_failure",
706
+ "selection": {
707
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
708
+ "end": [
709
+ 112,
710
+ 59
711
+ ],
712
+ "file_path": "Mathlib/Algebra/Order/Group/Int.lean",
713
+ "full_name": "Int.emod_abs",
714
+ "start": [
715
+ 111,
716
+ 1
717
+ ],
718
+ "traced_tactics": [],
719
+ "url": "https://github.com/leanprover-community/mathlib4"
720
+ },
721
+ "source_file": "Mathlib/Algebra/Order/Group/Int.lean"
722
+ },
723
+ {
724
+ "error": "theorem has no selected tactic transitions",
725
+ "full_name": "Int.le_self_sq",
726
+ "id": "Int.le_self_sq",
727
+ "reason": "import_failure",
728
+ "selection": {
729
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
730
+ "end": [
731
+ 72,
732
+ 81
733
+ ],
734
+ "file_path": "Mathlib/Algebra/Order/Group/Int.lean",
735
+ "full_name": "Int.le_self_sq",
736
+ "start": [
737
+ 72,
738
+ 1
739
+ ],
740
+ "traced_tactics": [],
741
+ "url": "https://github.com/leanprover-community/mathlib4"
742
+ },
743
+ "source_file": "Mathlib/Algebra/Order/Group/Int.lean"
744
+ },
745
+ {
746
+ "error": "theorem has no selected tactic transitions",
747
+ "full_name": "Int.natAbs_sub_ne_zero_iff",
748
+ "id": "Int.natAbs_sub_ne_zero_iff",
749
+ "reason": "import_failure",
750
+ "selection": {
751
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
752
+ "end": [
753
+ 85,
754
+ 51
755
+ ],
756
+ "file_path": "Mathlib/Algebra/Order/Group/Int.lean",
757
+ "full_name": "Int.natAbs_sub_ne_zero_iff",
758
+ "start": [
759
+ 84,
760
+ 1
761
+ ],
762
+ "traced_tactics": [],
763
+ "url": "https://github.com/leanprover-community/mathlib4"
764
+ },
765
+ "source_file": "Mathlib/Algebra/Order/Group/Int.lean"
766
+ },
767
+ {
768
+ "error": "theorem has no selected tactic transitions",
769
+ "full_name": "Int.natCast_natAbs",
770
+ "id": "Int.natCast_natAbs",
771
+ "reason": "import_failure",
772
+ "selection": {
773
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
774
+ "end": [
775
+ 54,
776
+ 95
777
+ ],
778
+ "file_path": "Mathlib/Algebra/Order/Group/Int.lean",
779
+ "full_name": "Int.natCast_natAbs",
780
+ "start": [
781
+ 54,
782
+ 1
783
+ ],
784
+ "traced_tactics": [],
785
+ "url": "https://github.com/leanprover-community/mathlib4"
786
+ },
787
+ "source_file": "Mathlib/Algebra/Order/Group/Int.lean"
788
+ },
789
+ {
790
+ "error": "theorem has no selected tactic transitions",
791
+ "full_name": "Int.natCast_strictMono",
792
+ "id": "Int.natCast_strictMono",
793
+ "reason": "import_failure",
794
+ "selection": {
795
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
796
+ "end": [
797
+ 37,
798
+ 80
799
+ ],
800
+ "file_path": "Mathlib/Algebra/Order/Group/Int.lean",
801
+ "full_name": "Int.natCast_strictMono",
802
+ "start": [
803
+ 37,
804
+ 1
805
+ ],
806
+ "traced_tactics": [],
807
+ "url": "https://github.com/leanprover-community/mathlib4"
808
+ },
809
+ "source_file": "Mathlib/Algebra/Order/Group/Int.lean"
810
+ },
811
+ {
812
+ "error": "theorem has no selected tactic transitions",
813
+ "full_name": "Int.one_le_abs",
814
+ "id": "Int.one_le_abs",
815
+ "reason": "import_failure",
816
+ "selection": {
817
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
818
+ "end": [
819
+ 97,
820
+ 38
821
+ ],
822
+ "file_path": "Mathlib/Algebra/Order/Group/Int.lean",
823
+ "full_name": "Int.one_le_abs",
824
+ "start": [
825
+ 96,
826
+ 1
827
+ ],
828
+ "traced_tactics": [],
829
+ "url": "https://github.com/leanprover-community/mathlib4"
830
+ },
831
+ "source_file": "Mathlib/Algebra/Order/Group/Int.lean"
832
+ }
833
+ ],
834
+ "input_proofs": 45,
835
+ "input_units": 2,
836
+ "proofs": 15,
837
+ "published_proofs": 12,
838
+ "published_transitions": 19,
839
+ "replay_failures": [],
840
+ "transitions": 35,
841
+ "validation_failures": [
842
+ {
843
+ "errors": [
844
+ "internal transition boundary mismatch",
845
+ "internal transition boundary mismatch"
846
+ ],
847
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
848
+ "proof_id": "mathlib:Set.mulIndicator_apply_le'",
849
+ "provenance": {
850
+ "selection": {
851
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
852
+ "end": [
853
+ 79,
854
+ 27
855
+ ],
856
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
857
+ "full_name": "Set.mulIndicator_apply_le'",
858
+ "start": [
859
+ 74,
860
+ 1
861
+ ],
862
+ "traced_tactics": [
863
+ {
864
+ "annotated_tactic": [
865
+ "\"by_cases ha : a \\u2208 s\"",
866
+ "[]"
867
+ ],
868
+ "state_after": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : LE M\ninst\u271d : One M\ns t : Set \u03b1\nf g : \u03b1 \u2192 M\na : \u03b1\ny : M\nhfg : a \u2208 s \u2192 f a \u2264 y\nhg : a \u2209 s \u2192 1 \u2264 y\nha : a \u2208 s\n\u22a2 s.mulIndicator f a \u2264 y\n\ncase neg\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : LE M\ninst\u271d : One M\ns t : Set \u03b1\nf g : \u03b1 \u2192 M\na : \u03b1\ny : M\nhfg : a \u2208 s \u2192 f a \u2264 y\nhg : a \u2209 s \u2192 1 \u2264 y\nha : a \u2209 s\n\u22a2 s.mulIndicator f a \u2264 y",
869
+ "state_before": "\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : LE M\ninst\u271d : One M\ns t : Set \u03b1\nf g : \u03b1 \u2192 M\na : \u03b1\ny : M\nhfg : a \u2208 s \u2192 f a \u2264 y\nhg : a \u2209 s \u2192 1 \u2264 y\n\u22a2 s.mulIndicator f a \u2264 y",
870
+ "tactic": "by_cases ha : a \u2208 s"
871
+ },
872
+ {
873
+ "annotated_tactic": [
874
+ "\"simpa [ha] using hfg ha\"",
875
+ "[]"
876
+ ],
877
+ "state_after": "no goals",
878
+ "state_before": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : LE M\ninst\u271d : One M\ns t : Set \u03b1\nf g : \u03b1 \u2192 M\na : \u03b1\ny : M\nhfg : a \u2208 s \u2192 f a \u2264 y\nhg : a \u2209 s \u2192 1 \u2264 y\nha : a \u2208 s\n\u22a2 s.mulIndicator f a \u2264 y",
879
+ "tactic": "simpa [ha] using hfg ha"
880
+ },
881
+ {
882
+ "annotated_tactic": [
883
+ "\"simpa [ha] using hg ha\"",
884
+ "[]"
885
+ ],
886
+ "state_after": "no goals",
887
+ "state_before": "case neg\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : LE M\ninst\u271d : One M\ns t : Set \u03b1\nf g : \u03b1 \u2192 M\na : \u03b1\ny : M\nhfg : a \u2208 s \u2192 f a \u2264 y\nhg : a \u2209 s \u2192 1 \u2264 y\nha : a \u2209 s\n\u22a2 s.mulIndicator f a \u2264 y",
888
+ "tactic": "simpa [ha] using hg ha"
889
+ }
890
+ ],
891
+ "url": "https://github.com/leanprover-community/mathlib4"
892
+ }
893
+ },
894
+ "theorem_name": "Set.mulIndicator_apply_le'"
895
+ },
896
+ {
897
+ "errors": [
898
+ "internal transition boundary mismatch",
899
+ "internal transition boundary mismatch"
900
+ ],
901
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
902
+ "proof_id": "mathlib:Set.mulIndicator_iUnion_apply",
903
+ "provenance": {
904
+ "selection": {
905
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
906
+ "end": [
907
+ 188,
908
+ 20
909
+ ],
910
+ "file_path": "Mathlib/Algebra/Order/Group/Indicator.lean",
911
+ "full_name": "Set.mulIndicator_iUnion_apply",
912
+ "start": [
913
+ 177,
914
+ 1
915
+ ],
916
+ "traced_tactics": [
917
+ {
918
+ "annotated_tactic": [
919
+ "\"by_cases hx : x \\u2208 \\u22c3 i, s i\"",
920
+ "[]"
921
+ ],
922
+ "state_after": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : CompleteLattice M\ninst\u271d : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : x \u2208 \u22c3 i, s i\n\u22a2 (\u22c3 i, s i).mulIndicator f x = \u2a06 i, (s i).mulIndicator f x\n\ncase neg\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : CompleteLattice M\ninst\u271d : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : x \u2209 \u22c3 i, s i\n\u22a2 (\u22c3 i, s i).mulIndicator f x = \u2a06 i, (s i).mulIndicator f x",
923
+ "state_before": "\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : CompleteLattice M\ninst\u271d : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\n\u22a2 (\u22c3 i, s i).mulIndicator f x = \u2a06 i, (s i).mulIndicator f x",
924
+ "tactic": "by_cases hx : x \u2208 \u22c3 i, s i"
925
+ },
926
+ {
927
+ "annotated_tactic": [
928
+ "\"rw [<a>mulIndicator_of_mem<\\/a> hx]\"",
929
+ "[{\"full_name\":\"Set.mulIndicator_of_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,28]}]"
930
+ ],
931
+ "state_after": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : CompleteLattice M\ninst\u271d : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : x \u2208 \u22c3 i, s i\n\u22a2 f x = \u2a06 i, (s i).mulIndicator f x",
932
+ "state_before": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : CompleteLattice M\ninst\u271d : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : x \u2208 \u22c3 i, s i\n\u22a2 (\u22c3 i, s i).mulIndicator f x = \u2a06 i, (s i).mulIndicator f x",
933
+ "tactic": "rw [mulIndicator_of_mem hx]"
934
+ },
935
+ {
936
+ "annotated_tactic": [
937
+ "\"rw [<a>mem_iUnion<\\/a>] at hx\"",
938
+ "[{\"full_name\":\"Set.mem_iUnion\",\"def_path\":\"Mathlib\\/Order\\/SetNotation.lean\",\"def_pos\":[268,9],\"def_end_pos\":[268,19]}]"
939
+ ],
940
+ "state_after": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : CompleteLattice M\ninst\u271d : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : \u2203 i, x \u2208 s i\n\u22a2 f x = \u2a06 i, (s i).mulIndicator f x",
941
+ "state_before": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : CompleteLattice M\ninst\u271d : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : x \u2208 \u22c3 i, s i\n\u22a2 f x = \u2a06 i, (s i).mulIndicator f x",
942
+ "tactic": "rw [mem_iUnion] at hx"
943
+ },
944
+ {
945
+ "annotated_tactic": [
946
+ "\"refine <a>le_antisymm<\\/a> ?_ (<a>iSup_le<\\/a> fun i \\u21a6 <a>mulIndicator_le_self'<\\/a> (fun x _ \\u21a6 h1 \\u25b8 <a>bot_le<\\/a>) x)\"",
947
+ "[{\"full_name\":\"le_antisymm\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[188,9],\"def_end_pos\":[188,20]},{\"full_name\":\"iSup_le\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[760,9],\"def_end_pos\":[760,16]},{\"full_name\":\"Set.mulIndicator_le_self'\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Indicator.lean\",\"def_pos\":[148,7],\"def_end_pos\":[148,28]},{\"full_name\":\"bot_le\",\"def_path\":\"Mathlib\\/Order\\/BoundedOrder.lean\",\"def_pos\":[224,9],\"def_end_pos\":[224,15]}]"
948
+ ],
949
+ "state_after": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : CompleteLattice M\ninst\u271d : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : \u2203 i, x \u2208 s i\n\u22a2 f x \u2264 \u2a06 i, (s i).mulIndicator f x",
950
+ "state_before": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : CompleteLattice M\ninst\u271d : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : \u2203 i, x \u2208 s i\n\u22a2 f x = \u2a06 i, (s i).mulIndicator f x",
951
+ "tactic": "refine le_antisymm ?_ (iSup_le fun i \u21a6 mulIndicator_le_self' (fun x _ \u21a6 h1 \u25b8 bot_le) x)"
952
+ },
953
+ {
954
+ "annotated_tactic": [
955
+ "\"rcases hx with \\u27e8i, hi\\u27e9\"",
956
+ "[]"
957
+ ],
958
+ "state_after": "case pos.intro\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : CompleteLattice M\ninst\u271d : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\ni : \u03b9\nhi : x \u2208 s i\n\u22a2 f x \u2264 \u2a06 i, (s i).mulIndicator f x",
959
+ "state_before": "case pos\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : CompleteLattice M\ninst\u271d : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : \u2203 i, x \u2208 s i\n\u22a2 f x \u2264 \u2a06 i, (s i).mulIndicator f x",
960
+ "tactic": "rcases hx with \u27e8i, hi\u27e9"
961
+ },
962
+ {
963
+ "annotated_tactic": [
964
+ "\"exact <a>le_iSup_of_le<\\/a> i (<a>ge_of_eq<\\/a> <| <a>mulIndicator_of_mem<\\/a> hi _)\"",
965
+ "[{\"full_name\":\"le_iSup_of_le\",\"def_path\":\"Mathlib\\/Order\\/CompleteLattice.lean\",\"def_pos\":[734,9],\"def_end_pos\":[734,22]},{\"full_name\":\"ge_of_eq\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[330,9],\"def_end_pos\":[330,17]},{\"full_name\":\"Set.mulIndicator_of_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,28]}]"
966
+ ],
967
+ "state_after": "no goals",
968
+ "state_before": "case pos.intro\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : CompleteLattice M\ninst\u271d : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\ni : \u03b9\nhi : x \u2208 s i\n\u22a2 f x \u2264 \u2a06 i, (s i).mulIndicator f x",
969
+ "tactic": "exact le_iSup_of_le i (ge_of_eq <| mulIndicator_of_mem hi _)"
970
+ },
971
+ {
972
+ "annotated_tactic": [
973
+ "\"rw [<a>mulIndicator_of_not_mem<\\/a> hx]\"",
974
+ "[{\"full_name\":\"Set.mulIndicator_of_not_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[75,9],\"def_end_pos\":[75,32]}]"
975
+ ],
976
+ "state_after": "case neg\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : CompleteLattice M\ninst\u271d : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : x \u2209 \u22c3 i, s i\n\u22a2 1 = \u2a06 i, (s i).mulIndicator f x",
977
+ "state_before": "case neg\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : CompleteLattice M\ninst\u271d : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : x \u2209 \u22c3 i, s i\n\u22a2 (\u22c3 i, s i).mulIndicator f x = \u2a06 i, (s i).mulIndicator f x",
978
+ "tactic": "rw [mulIndicator_of_not_mem hx]"
979
+ },
980
+ {
981
+ "annotated_tactic": [
982
+ "\"simp only [<a>mem_iUnion<\\/a>, <a>not_exists<\\/a>] at hx\"",
983
+ "[{\"full_name\":\"Set.mem_iUnion\",\"def_path\":\"Mathlib\\/Order\\/SetNotation.lean\",\"def_pos\":[268,9],\"def_end_pos\":[268,19]},{\"full_name\":\"not_exists\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/PropLemmas.lean\",\"def_pos\":[254,17],\"def_end_pos\":[254,27]}]"
984
+ ],
985
+ "state_after": "case neg\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : CompleteLattice M\ninst\u271d : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : \u2200 (x_1 : \u03b9), x \u2209 s x_1\n\u22a2 1 = \u2a06 i, (s i).mulIndicator f x",
986
+ "state_before": "case neg\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : CompleteLattice M\ninst\u271d : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : x \u2209 \u22c3 i, s i\n\u22a2 1 = \u2a06 i, (s i).mulIndicator f x",
987
+ "tactic": "simp only [mem_iUnion, not_exists] at hx"
988
+ },
989
+ {
990
+ "annotated_tactic": [
991
+ "\"simp [hx, \\u2190 h1]\"",
992
+ "[]"
993
+ ],
994
+ "state_after": "no goals",
995
+ "state_before": "case neg\n\u03b9 : Sort u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\ninst\u271d\u00b9 : CompleteLattice M\ninst\u271d : One M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na : \u03b1\ny : M\nh1 : \u22a5 = 1\ns : \u03b9 \u2192 Set \u03b1\nf : \u03b1 \u2192 M\nx : \u03b1\nhx : \u2200 (x_1 : \u03b9), x \u2209 s x_1\n\u22a2 1 = \u2a06 i, (s i).mulIndicator f x",
996
+ "tactic": "simp [hx, \u2190 h1]"
997
+ }
998
+ ],
999
+ "url": "https://github.com/leanprover-community/mathlib4"
1000
+ }
1001
+ },
1002
+ "theorem_name": "Set.mulIndicator_iUnion_apply"
1003
+ },
1004
+ {
1005
+ "errors": [
1006
+ "internal transition boundary mismatch"
1007
+ ],
1008
+ "file_path": "Mathlib/Algebra/Order/Group/Int.lean",
1009
+ "proof_id": "mathlib:Int.abs_ediv_le_abs",
1010
+ "provenance": {
1011
+ "selection": {
1012
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1013
+ "end": [
1014
+ 133,
1015
+ 67
1016
+ ],
1017
+ "file_path": "Mathlib/Algebra/Order/Group/Int.lean",
1018
+ "full_name": "Int.abs_ediv_le_abs",
1019
+ "start": [
1020
+ 121,
1021
+ 1
1022
+ ],
1023
+ "traced_tactics": [
1024
+ {
1025
+ "annotated_tactic": [
1026
+ "\"rw [<a>Int.ediv_neg<\\/a>, <a>abs_neg<\\/a>]\"",
1027
+ "[{\"full_name\":\"Int.ediv_neg\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/DivModLemmas.lean\",\"def_pos\":[292,27],\"def_end_pos\":[292,35]},{\"full_name\":\"abs_neg\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Abs.lean\",\"def_pos\":[87,3],\"def_end_pos\":[87,14]}]"
1028
+ ],
1029
+ "state_after": "this : \u2200 (a : \u2124) (n : \u2115), |a / \u2191n| \u2264 |a|\na b : \u2124\nn : \u2115\n\u22a2 |a / \u2191n| \u2264 |a|",
1030
+ "state_before": "this : \u2200 (a : \u2124) (n : \u2115), |a / \u2191n| \u2264 |a|\na b : \u2124\nn : \u2115\n\u22a2 |a / -\u2191n| \u2264 |a|",
1031
+ "tactic": "rw [Int.ediv_neg, abs_neg]"
1032
+ },
1033
+ {
1034
+ "annotated_tactic": [
1035
+ "\"apply this\"",
1036
+ "[]"
1037
+ ],
1038
+ "state_after": "no goals",
1039
+ "state_before": "this : \u2200 (a : \u2124) (n : \u2115), |a / \u2191n| \u2264 |a|\na b : \u2124\nn : \u2115\n\u22a2 |a / \u2191n| \u2264 |a|",
1040
+ "tactic": "apply this"
1041
+ },
1042
+ {
1043
+ "annotated_tactic": [
1044
+ "\"rw [<a>abs_eq_natAbs<\\/a>, <a>abs_eq_natAbs<\\/a>]\"",
1045
+ "[{\"full_name\":\"Int.abs_eq_natAbs\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Int.lean\",\"def_pos\":[49,9],\"def_end_pos\":[49,22]},{\"full_name\":\"Int.abs_eq_natAbs\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Int.lean\",\"def_pos\":[49,9],\"def_end_pos\":[49,22]}]"
1046
+ ],
1047
+ "state_after": "a : \u2124\nn : \u2115\n\u22a2 \u2191(a / \u2191n).natAbs \u2264 \u2191a.natAbs",
1048
+ "state_before": "a : \u2124\nn : \u2115\n\u22a2 |a / \u2191n| \u2264 |a|",
1049
+ "tactic": "rw [abs_eq_natAbs, abs_eq_natAbs]"
1050
+ },
1051
+ {
1052
+ "annotated_tactic": [
1053
+ "\"exact\\n <a>ofNat_le_ofNat_of_le<\\/a>\\n (match a, n with\\n | (m : \\u2115), n => <a>Nat.div_le_self<\\/a> _ _\\n | -[m+1], 0 => <a>Nat.zero_le<\\/a> _\\n | -[m+1], n + 1 => <a>Nat.succ_le_succ<\\/a> (<a>Nat.div_le_self<\\/a> _ _))\"",
1054
+ "[{\"full_name\":\"Int.ofNat_le_ofNat_of_le\",\"def_path\":\"Mathlib\\/Init\\/Data\\/Int\\/Order.lean\",\"def_pos\":[29,30],\"def_end_pos\":[29,50]},{\"full_name\":\"Nat.div_le_self\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Div.lean\",\"def_pos\":[50,9],\"def_end_pos\":[50,20]},{\"full_name\":\"Nat.zero_le\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1663,9],\"def_end_pos\":[1663,20]},{\"full_name\":\"Nat.succ_le_succ\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1667,9],\"def_end_pos\":[1667,25]},{\"full_name\":\"Nat.div_le_self\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Div.lean\",\"def_pos\":[50,9],\"def_end_pos\":[50,20]}]"
1055
+ ],
1056
+ "state_after": "no goals",
1057
+ "state_before": "a : \u2124\nn : \u2115\n\u22a2 \u2191(a / \u2191n).natAbs \u2264 \u2191a.natAbs",
1058
+ "tactic": "exact\n ofNat_le_ofNat_of_le\n (match a, n with\n | (m : \u2115), n => Nat.div_le_self _ _\n | -[m+1], 0 => Nat.zero_le _\n | -[m+1], n + 1 => Nat.succ_le_succ (Nat.div_le_self _ _))"
1059
+ }
1060
+ ],
1061
+ "url": "https://github.com/leanprover-community/mathlib4"
1062
+ }
1063
+ },
1064
+ "theorem_name": "Int.abs_ediv_le_abs"
1065
+ }
1066
+ ],
1067
+ "validation_rejected_proofs": 3,
1068
+ "zero_transition_proofs": 0
1069
+ },
1070
+ "shards": [
1071
+ {
1072
+ "path": "data/train/mathlib-000255-0000-8239c3bb5cc98959.parquet",
1073
+ "sha256": "8239c3bb5cc98959b51d0ffcb28a960d157d74b06ed4e0692cccb47ade98532a",
1074
+ "bytes": 50745,
1075
+ "rows": 15,
1076
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
1077
+ },
1078
+ {
1079
+ "path": "data/internal_test/mathlib-000255-0000-df355184aa326da2.parquet",
1080
+ "sha256": "df355184aa326da29cb708bb2f16a1d768904fe32a82e5856d35083656a41c64",
1081
+ "bytes": 48401,
1082
+ "rows": 4,
1083
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
1084
+ }
1085
+ ],
1086
+ "proof_ids": [
1087
+ "mathlib:Function.mulSupport_iSup",
1088
+ "mathlib:Int.abs_le_one_iff",
1089
+ "mathlib:Int.abs_lt_one_iff",
1090
+ "mathlib:Int.abs_sign_of_nonzero",
1091
+ "mathlib:Int.ediv_eq_zero_of_lt_abs",
1092
+ "mathlib:Int.emod_lt",
1093
+ "mathlib:Int.natAbs_abs",
1094
+ "mathlib:Int.natAbs_le_self_sq",
1095
+ "mathlib:Int.natAbs_sub_pos_iff",
1096
+ "mathlib:Int.sign_eq_ediv_abs",
1097
+ "mathlib:Int.sign_mul_abs",
1098
+ "mathlib:zpow_abs_eq_one"
1099
+ ],
1100
+ "proof_keys": [
1101
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Indicator.lean\",null,null,\"Function.mulSupport_iSup\"]",
1102
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Int.lean\",null,null,\"Int.abs_le_one_iff\"]",
1103
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Int.lean\",null,null,\"Int.abs_lt_one_iff\"]",
1104
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Int.lean\",null,null,\"Int.abs_sign_of_nonzero\"]",
1105
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Int.lean\",null,null,\"Int.ediv_eq_zero_of_lt_abs\"]",
1106
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Int.lean\",null,null,\"Int.emod_lt\"]",
1107
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Int.lean\",null,null,\"Int.natAbs_abs\"]",
1108
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Int.lean\",null,null,\"Int.natAbs_le_self_sq\"]",
1109
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Int.lean\",null,null,\"Int.natAbs_sub_pos_iff\"]",
1110
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Int.lean\",null,null,\"Int.sign_eq_ediv_abs\"]",
1111
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Int.lean\",null,null,\"Int.sign_mul_abs\"]",
1112
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/Int.lean\",null,null,\"zpow_abs_eq_one\"]"
1113
+ ]
1114
+ }
manifests/batches/mathlib/000256.json ADDED
@@ -0,0 +1,541 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000256",
4
+ "batch_fingerprint": "96699280848cd3b10c102dd0cbbe12c52df8bd61a02db44dad9aa44b90d89b0f",
5
+ "evidence": {
6
+ "batch_fingerprint": "96699280848cd3b10c102dd0cbbe12c52df8bd61a02db44dad9aa44b90d89b0f",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "div_inf",
12
+ "id": "div_inf",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 87,
18
+ 92
19
+ ],
20
+ "file_path": "Mathlib/Algebra/Order/Group/Lattice.lean",
21
+ "full_name": "div_inf",
22
+ "start": [
23
+ 86,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/Algebra/Order/Group/Lattice.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "div_sup",
34
+ "id": "div_sup",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 81,
40
+ 92
41
+ ],
42
+ "file_path": "Mathlib/Algebra/Order/Group/Lattice.lean",
43
+ "full_name": "div_sup",
44
+ "start": [
45
+ 80,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/Algebra/Order/Group/Lattice.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "inf_div",
56
+ "id": "inf_div",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 90,
62
+ 93
63
+ ],
64
+ "file_path": "Mathlib/Algebra/Order/Group/Lattice.lean",
65
+ "full_name": "inf_div",
66
+ "start": [
67
+ 89,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/Algebra/Order/Group/Lattice.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "inf_mul",
78
+ "id": "inf_mul",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 67,
84
+ 93
85
+ ],
86
+ "file_path": "Mathlib/Algebra/Order/Group/Lattice.lean",
87
+ "full_name": "inf_mul",
88
+ "start": [
89
+ 66,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/Algebra/Order/Group/Lattice.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "inv_inf",
100
+ "id": "inv_inf",
101
+ "reason": "import_failure",
102
+ "selection": {
103
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
104
+ "end": [
105
+ 76,
106
+ 95
107
+ ],
108
+ "file_path": "Mathlib/Algebra/Order/Group/Lattice.lean",
109
+ "full_name": "inv_inf",
110
+ "start": [
111
+ 76,
112
+ 1
113
+ ],
114
+ "traced_tactics": [],
115
+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
+ "source_file": "Mathlib/Algebra/Order/Group/Lattice.lean"
118
+ },
119
+ {
120
+ "error": "theorem has no selected tactic transitions",
121
+ "full_name": "inv_sup",
122
+ "id": "inv_sup",
123
+ "reason": "import_failure",
124
+ "selection": {
125
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
126
+ "end": [
127
+ 72,
128
+ 95
129
+ ],
130
+ "file_path": "Mathlib/Algebra/Order/Group/Lattice.lean",
131
+ "full_name": "inv_sup",
132
+ "start": [
133
+ 72,
134
+ 1
135
+ ],
136
+ "traced_tactics": [],
137
+ "url": "https://github.com/leanprover-community/mathlib4"
138
+ },
139
+ "source_file": "Mathlib/Algebra/Order/Group/Lattice.lean"
140
+ },
141
+ {
142
+ "error": "theorem has no selected tactic transitions",
143
+ "full_name": "mul_inf",
144
+ "id": "mul_inf",
145
+ "reason": "import_failure",
146
+ "selection": {
147
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
148
+ "end": [
149
+ 60,
150
+ 92
151
+ ],
152
+ "file_path": "Mathlib/Algebra/Order/Group/Lattice.lean",
153
+ "full_name": "mul_inf",
154
+ "start": [
155
+ 59,
156
+ 1
157
+ ],
158
+ "traced_tactics": [],
159
+ "url": "https://github.com/leanprover-community/mathlib4"
160
+ },
161
+ "source_file": "Mathlib/Algebra/Order/Group/Lattice.lean"
162
+ },
163
+ {
164
+ "error": "theorem has no selected tactic transitions",
165
+ "full_name": "mul_sup",
166
+ "id": "mul_sup",
167
+ "reason": "import_failure",
168
+ "selection": {
169
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
170
+ "end": [
171
+ 50,
172
+ 92
173
+ ],
174
+ "file_path": "Mathlib/Algebra/Order/Group/Lattice.lean",
175
+ "full_name": "mul_sup",
176
+ "start": [
177
+ 49,
178
+ 1
179
+ ],
180
+ "traced_tactics": [],
181
+ "url": "https://github.com/leanprover-community/mathlib4"
182
+ },
183
+ "source_file": "Mathlib/Algebra/Order/Group/Lattice.lean"
184
+ },
185
+ {
186
+ "error": "no internal trace for tactic 'rwa [\u2190 inf_eq_right, \u2190 mul_right_eq_self]'",
187
+ "full_name": "pow_two_semiclosed",
188
+ "id": "pow_two_semiclosed",
189
+ "reason": "import_failure",
190
+ "selection": {
191
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
192
+ "end": [
193
+ 101,
194
+ 34
195
+ ],
196
+ "file_path": "Mathlib/Algebra/Order/Group/Lattice.lean",
197
+ "full_name": "pow_two_semiclosed",
198
+ "start": [
199
+ 95,
200
+ 1
201
+ ],
202
+ "traced_tactics": [
203
+ {
204
+ "annotated_tactic": [
205
+ "\"suffices this : (a \\u2293 1) * (a \\u2293 1) = a \\u2293 1 by\\n rwa [\\u2190 <a>inf_eq_right<\\/a>, \\u2190 <a>mul_right_eq_self<\\/a>]\"",
206
+ "[{\"full_name\":\"inf_eq_right\",\"def_path\":\"Mathlib\\/Order\\/Lattice.lean\",\"def_pos\":[404,9],\"def_end_pos\":[404,21]},{\"full_name\":\"mul_right_eq_self\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[323,9],\"def_end_pos\":[323,26]}]"
207
+ ],
208
+ "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u2074 : Lattice \u03b1\ninst\u271d\u00b3 : Group \u03b1\ninst\u271d\u00b2 : CovariantClass \u03b1 \u03b1 (fun x x_1 => x * x_1) fun x x_1 => x \u2264 x_1\ninst\u271d\u00b9 inst\u271d : CovariantClass \u03b1 \u03b1 (swap fun x x_1 => x * x_1) fun x x_1 => x \u2264 x_1\na : \u03b1\nha : 1 \u2264 a ^ 2\n\u22a2 (a \u2293 1) * (a \u2293 1) = a \u2293 1",
209
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u2074 : Lattice \u03b1\ninst\u271d\u00b3 : Group \u03b1\ninst\u271d\u00b2 : CovariantClass \u03b1 \u03b1 (fun x x_1 => x * x_1) fun x x_1 => x \u2264 x_1\ninst\u271d\u00b9 inst\u271d : CovariantClass \u03b1 \u03b1 (swap fun x x_1 => x * x_1) fun x x_1 => x \u2264 x_1\na : \u03b1\nha : 1 \u2264 a ^ 2\n\u22a2 1 \u2264 a",
210
+ "tactic": "suffices this : (a \u2293 1) * (a \u2293 1) = a \u2293 1 by\n rwa [\u2190 inf_eq_right, \u2190 mul_right_eq_self]"
211
+ },
212
+ {
213
+ "annotated_tactic": [
214
+ "\"rw [<a>mul_inf<\\/a>, <a>inf_mul<\\/a>, \\u2190 <a>pow_two<\\/a>, <a>mul_one<\\/a>, <a>one_mul<\\/a>, <a>inf_assoc<\\/a>, <a>inf_left_idem<\\/a>, <a>inf_comm<\\/a>,\\n <a>inf_assoc<\\/a>, <a>inf_of_le_left<\\/a> ha]\"",
215
+ "[{\"full_name\":\"mul_inf\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Lattice.lean\",\"def_pos\":[60,7],\"def_end_pos\":[60,14]},{\"full_name\":\"inf_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Lattice.lean\",\"def_pos\":[67,7],\"def_end_pos\":[67,14]},{\"full_name\":\"pow_two\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[679,32],\"def_end_pos\":[679,39]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"one_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[477,9],\"def_end_pos\":[477,16]},{\"full_name\":\"inf_assoc\",\"def_path\":\"Mathlib\\/Order\\/Lattice.lean\",\"def_pos\":[466,9],\"def_end_pos\":[466,18]},{\"full_name\":\"inf_left_idem\",\"def_path\":\"Mathlib\\/Order\\/Lattice.lean\",\"def_pos\":[475,9],\"def_end_pos\":[475,22]},{\"full_name\":\"inf_comm\",\"def_path\":\"Mathlib\\/Order\\/Lattice.lean\",\"def_pos\":[461,9],\"def_end_pos\":[461,17]},{\"full_name\":\"inf_assoc\",\"def_path\":\"Mathlib\\/Order\\/Lattice.lean\",\"def_pos\":[466,9],\"def_end_pos\":[466,18]},{\"full_name\":\"inf_of_le_left\",\"def_path\":\"Mathlib\\/Order\\/Lattice.lean\",\"def_pos\":[418,22],\"def_end_pos\":[418,36]}]"
216
+ ],
217
+ "state_after": "no goals",
218
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u2074 : Lattice \u03b1\ninst\u271d\u00b3 : Group \u03b1\ninst\u271d\u00b2 : CovariantClass \u03b1 \u03b1 (fun x x_1 => x * x_1) fun x x_1 => x \u2264 x_1\ninst\u271d\u00b9 inst\u271d : CovariantClass \u03b1 \u03b1 (swap fun x x_1 => x * x_1) fun x x_1 => x \u2264 x_1\na : \u03b1\nha : 1 \u2264 a ^ 2\n\u22a2 (a \u2293 1) * (a \u2293 1) = a \u2293 1",
219
+ "tactic": "rw [mul_inf, inf_mul, \u2190 pow_two, mul_one, one_mul, inf_assoc, inf_left_idem, inf_comm,\n inf_assoc, inf_of_le_left ha]"
220
+ },
221
+ {
222
+ "annotated_tactic": [
223
+ "\"rwa [\\u2190 <a>inf_eq_right<\\/a>, \\u2190 <a>mul_right_eq_self<\\/a>]\"",
224
+ "[{\"full_name\":\"inf_eq_right\",\"def_path\":\"Mathlib\\/Order\\/Lattice.lean\",\"def_pos\":[404,9],\"def_end_pos\":[404,21]},{\"full_name\":\"mul_right_eq_self\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[323,9],\"def_end_pos\":[323,26]}]"
225
+ ],
226
+ "state_after": "no goals",
227
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u2074 : Lattice \u03b1\ninst\u271d\u00b3 : Group \u03b1\ninst\u271d\u00b2 : CovariantClass \u03b1 \u03b1 (fun x x_1 => x * x_1) fun x x_1 => x \u2264 x_1\ninst\u271d\u00b9 inst\u271d : CovariantClass \u03b1 \u03b1 (swap fun x x_1 => x * x_1) fun x x_1 => x \u2264 x_1\na : \u03b1\nha : 1 \u2264 a ^ 2\nthis : (a \u2293 1) * (a \u2293 1) = a \u2293 1\n\u22a2 1 \u2264 a",
228
+ "tactic": "rwa [\u2190 inf_eq_right, \u2190 mul_right_eq_self]"
229
+ }
230
+ ],
231
+ "url": "https://github.com/leanprover-community/mathlib4"
232
+ },
233
+ "source_file": "Mathlib/Algebra/Order/Group/Lattice.lean"
234
+ },
235
+ {
236
+ "error": "theorem has no selected tactic transitions",
237
+ "full_name": "sup_div",
238
+ "id": "sup_div",
239
+ "reason": "import_failure",
240
+ "selection": {
241
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
242
+ "end": [
243
+ 84,
244
+ 93
245
+ ],
246
+ "file_path": "Mathlib/Algebra/Order/Group/Lattice.lean",
247
+ "full_name": "sup_div",
248
+ "start": [
249
+ 83,
250
+ 1
251
+ ],
252
+ "traced_tactics": [],
253
+ "url": "https://github.com/leanprover-community/mathlib4"
254
+ },
255
+ "source_file": "Mathlib/Algebra/Order/Group/Lattice.lean"
256
+ },
257
+ {
258
+ "error": "theorem has no selected tactic transitions",
259
+ "full_name": "sup_mul",
260
+ "id": "sup_mul",
261
+ "reason": "import_failure",
262
+ "selection": {
263
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
264
+ "end": [
265
+ 55,
266
+ 93
267
+ ],
268
+ "file_path": "Mathlib/Algebra/Order/Group/Lattice.lean",
269
+ "full_name": "sup_mul",
270
+ "start": [
271
+ 54,
272
+ 1
273
+ ],
274
+ "traced_tactics": [],
275
+ "url": "https://github.com/leanprover-community/mathlib4"
276
+ },
277
+ "source_file": "Mathlib/Algebra/Order/Group/Lattice.lean"
278
+ },
279
+ {
280
+ "error": "no internal trace for tactic 'rw [abs_sub_comm a c, abs_sub_comm b d]'",
281
+ "full_name": "abs_max_sub_max_le_max",
282
+ "id": "abs_max_sub_max_le_max",
283
+ "reason": "import_failure",
284
+ "selection": {
285
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
286
+ "end": [
287
+ 100,
288
+ 90
289
+ ],
290
+ "file_path": "Mathlib/Algebra/Order/Group/MinMax.lean",
291
+ "full_name": "abs_max_sub_max_le_max",
292
+ "start": [
293
+ 96,
294
+ 1
295
+ ],
296
+ "traced_tactics": [
297
+ {
298
+ "annotated_tactic": [
299
+ "\"refine <a>abs_sub_le_iff<\\/a>.2 \\u27e8?_, ?_\\u27e9\"",
300
+ "[{\"full_name\":\"abs_sub_le_iff\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Abs.lean\",\"def_pos\":[429,9],\"def_end_pos\":[429,23]}]"
301
+ ],
302
+ "state_after": "case refine_1\n\u03b1 : Type u_1\ninst\u271d : LinearOrderedAddCommGroup \u03b1\na\u271d b\u271d c\u271d a b c d : \u03b1\n\u22a2 max a b - max c d \u2264 max |a - c| |b - d|\n\ncase refine_2\n\u03b1 : Type u_1\ninst\u271d : LinearOrderedAddCommGroup \u03b1\na\u271d b\u271d c\u271d a b c d : \u03b1\n\u22a2 max c d - max a b \u2264 max |a - c| |b - d|",
303
+ "state_before": "\u03b1 : Type u_1\ninst\u271d : LinearOrderedAddCommGroup \u03b1\na\u271d b\u271d c\u271d a b c d : \u03b1\n\u22a2 |max a b - max c d| \u2264 max |a - c| |b - d|",
304
+ "tactic": "refine abs_sub_le_iff.2 \u27e8?_, ?_\u27e9"
305
+ },
306
+ {
307
+ "annotated_tactic": [
308
+ "\"exact (<a>max_sub_max_le_max<\\/a> _ _ _ _).<a>trans<\\/a> (<a>max_le_max<\\/a> (<a>le_abs_self<\\/a> _) (<a>le_abs_self<\\/a> _))\"",
309
+ "[{\"full_name\":\"max_sub_max_le_max\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/MinMax.lean\",\"def_pos\":[86,9],\"def_end_pos\":[86,27]},{\"full_name\":\"LE.le.trans\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[115,7],\"def_end_pos\":[115,18]},{\"full_name\":\"max_le_max\",\"def_path\":\"Mathlib\\/Order\\/MinMax.lean\",\"def_pos\":[73,9],\"def_end_pos\":[73,19]},{\"full_name\":\"le_abs_self\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Abs.lean\",\"def_pos\":[73,3],\"def_end_pos\":[73,14]},{\"full_name\":\"le_abs_self\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Abs.lean\",\"def_pos\":[73,3],\"def_end_pos\":[73,14]}]"
310
+ ],
311
+ "state_after": "no goals",
312
+ "state_before": "case refine_1\n\u03b1 : Type u_1\ninst\u271d : LinearOrderedAddCommGroup \u03b1\na\u271d b\u271d c\u271d a b c d : \u03b1\n\u22a2 max a b - max c d \u2264 max |a - c| |b - d|",
313
+ "tactic": "exact (max_sub_max_le_max _ _ _ _).trans (max_le_max (le_abs_self _) (le_abs_self _))"
314
+ },
315
+ {
316
+ "annotated_tactic": [
317
+ "\"rw [<a>abs_sub_comm<\\/a> a c, <a>abs_sub_comm<\\/a> b d]\"",
318
+ "[{\"full_name\":\"abs_sub_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Abs.lean\",\"def_pos\":[90,3],\"def_end_pos\":[90,14]},{\"full_name\":\"abs_sub_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Abs.lean\",\"def_pos\":[90,3],\"def_end_pos\":[90,14]}]"
319
+ ],
320
+ "state_after": "case refine_2\n\u03b1 : Type u_1\ninst\u271d : LinearOrderedAddCommGroup \u03b1\na\u271d b\u271d c\u271d a b c d : \u03b1\n\u22a2 max c d - max a b \u2264 max |c - a| |d - b|",
321
+ "state_before": "case refine_2\n\u03b1 : Type u_1\ninst\u271d : LinearOrderedAddCommGroup \u03b1\na\u271d b\u271d c\u271d a b c d : \u03b1\n\u22a2 max c d - max a b \u2264 max |a - c| |b - d|",
322
+ "tactic": "rw [abs_sub_comm a c, abs_sub_comm b d]"
323
+ },
324
+ {
325
+ "annotated_tactic": [
326
+ "\"exact (<a>max_sub_max_le_max<\\/a> _ _ _ _).<a>trans<\\/a> (<a>max_le_max<\\/a> (<a>le_abs_self<\\/a> _) (<a>le_abs_self<\\/a> _))\"",
327
+ "[{\"full_name\":\"max_sub_max_le_max\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/MinMax.lean\",\"def_pos\":[86,9],\"def_end_pos\":[86,27]},{\"full_name\":\"LE.le.trans\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[115,7],\"def_end_pos\":[115,18]},{\"full_name\":\"max_le_max\",\"def_path\":\"Mathlib\\/Order\\/MinMax.lean\",\"def_pos\":[73,9],\"def_end_pos\":[73,19]},{\"full_name\":\"le_abs_self\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Abs.lean\",\"def_pos\":[73,3],\"def_end_pos\":[73,14]},{\"full_name\":\"le_abs_self\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Abs.lean\",\"def_pos\":[73,3],\"def_end_pos\":[73,14]}]"
328
+ ],
329
+ "state_after": "no goals",
330
+ "state_before": "case refine_2\n\u03b1 : Type u_1\ninst\u271d : LinearOrderedAddCommGroup \u03b1\na\u271d b\u271d c\u271d a b c d : \u03b1\n\u22a2 max c d - max a b \u2264 max |c - a| |d - b|",
331
+ "tactic": "exact (max_sub_max_le_max _ _ _ _).trans (max_le_max (le_abs_self _) (le_abs_self _))"
332
+ }
333
+ ],
334
+ "url": "https://github.com/leanprover-community/mathlib4"
335
+ },
336
+ "source_file": "Mathlib/Algebra/Order/Group/MinMax.lean"
337
+ },
338
+ {
339
+ "error": "theorem has no selected tactic transitions",
340
+ "full_name": "max_inv_inv'",
341
+ "id": "max_inv_inv'",
342
+ "reason": "import_failure",
343
+ "selection": {
344
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
345
+ "end": [
346
+ 52,
347
+ 34
348
+ ],
349
+ "file_path": "Mathlib/Algebra/Order/Group/MinMax.lean",
350
+ "full_name": "max_inv_inv'",
351
+ "start": [
352
+ 49,
353
+ 1
354
+ ],
355
+ "traced_tactics": [],
356
+ "url": "https://github.com/leanprover-community/mathlib4"
357
+ },
358
+ "source_file": "Mathlib/Algebra/Order/Group/MinMax.lean"
359
+ },
360
+ {
361
+ "error": "theorem has no selected tactic transitions",
362
+ "full_name": "min_inv_inv'",
363
+ "id": "min_inv_inv'",
364
+ "reason": "import_failure",
365
+ "selection": {
366
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
367
+ "end": [
368
+ 44,
369
+ 34
370
+ ],
371
+ "file_path": "Mathlib/Algebra/Order/Group/MinMax.lean",
372
+ "full_name": "min_inv_inv'",
373
+ "start": [
374
+ 41,
375
+ 1
376
+ ],
377
+ "traced_tactics": [],
378
+ "url": "https://github.com/leanprover-community/mathlib4"
379
+ },
380
+ "source_file": "Mathlib/Algebra/Order/Group/MinMax.lean"
381
+ }
382
+ ],
383
+ "input_proofs": 24,
384
+ "input_units": 2,
385
+ "proofs": 10,
386
+ "published_proofs": 8,
387
+ "published_transitions": 8,
388
+ "replay_failures": [],
389
+ "transitions": 15,
390
+ "validation_failures": [
391
+ {
392
+ "errors": [
393
+ "internal transition boundary mismatch",
394
+ "internal transition boundary mismatch"
395
+ ],
396
+ "file_path": "Mathlib/Algebra/Order/Group/Lattice.lean",
397
+ "proof_id": "mathlib:inf_mul_sup",
398
+ "provenance": {
399
+ "selection": {
400
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
401
+ "end": [
402
+ 115,
403
+ 56
404
+ ],
405
+ "file_path": "Mathlib/Algebra/Order/Group/Lattice.lean",
406
+ "full_name": "inf_mul_sup",
407
+ "start": [
408
+ 109,
409
+ 1
410
+ ],
411
+ "traced_tactics": [
412
+ {
413
+ "annotated_tactic": [
414
+ "\"rw [<a>mul_sup<\\/a> b\\u207b\\u00b9 a\\u207b\\u00b9 (a * b), <a>mul_inv_cancel_right<\\/a>, <a>mul_inv_cancel_comm<\\/a>]\"",
415
+ "[{\"full_name\":\"mul_sup\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Lattice.lean\",\"def_pos\":[50,7],\"def_end_pos\":[50,14]},{\"full_name\":\"mul_inv_cancel_right\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1262,9],\"def_end_pos\":[1262,29]},{\"full_name\":\"mul_inv_cancel_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1320,7],\"def_end_pos\":[1320,26]}]"
416
+ ],
417
+ "state_after": "no goals",
418
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b2 : Lattice \u03b1\ninst\u271d\u00b9 : CommGroup \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x * x_1) fun x x_1 => x \u2264 x_1\na b : \u03b1\n\u22a2 (a \u2293 b) * (a \u2294 b) = (a \u2293 b) * (a * b * (b\u207b\u00b9 \u2294 a\u207b\u00b9))",
419
+ "tactic": "rw [mul_sup b\u207b\u00b9 a\u207b\u00b9 (a * b), mul_inv_cancel_right, mul_inv_cancel_comm]"
420
+ },
421
+ {
422
+ "annotated_tactic": [
423
+ "\"rw [<a>inv_inf<\\/a>, <a>sup_comm<\\/a>]\"",
424
+ "[{\"full_name\":\"inv_inf\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Lattice.lean\",\"def_pos\":[76,22],\"def_end_pos\":[76,29]},{\"full_name\":\"sup_comm\",\"def_path\":\"Mathlib\\/Order\\/Lattice.lean\",\"def_pos\":[224,9],\"def_end_pos\":[224,17]}]"
425
+ ],
426
+ "state_after": "no goals",
427
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b2 : Lattice \u03b1\ninst\u271d\u00b9 : CommGroup \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x * x_1) fun x x_1 => x \u2264 x_1\na b : \u03b1\n\u22a2 (a \u2293 b) * (a * b * (b\u207b\u00b9 \u2294 a\u207b\u00b9)) = (a \u2293 b) * (a * b * (a \u2293 b)\u207b\u00b9)",
428
+ "tactic": "rw [inv_inf, sup_comm]"
429
+ },
430
+ {
431
+ "annotated_tactic": [
432
+ "\"rw [<a>mul_comm<\\/a>, <a>inv_mul_cancel_right<\\/a>]\"",
433
+ "[{\"full_name\":\"mul_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[332,9],\"def_end_pos\":[332,17]},{\"full_name\":\"inv_mul_cancel_right\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1268,9],\"def_end_pos\":[1268,29]}]"
434
+ ],
435
+ "state_after": "no goals",
436
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d\u00b2 : Lattice \u03b1\ninst\u271d\u00b9 : CommGroup \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x * x_1) fun x x_1 => x \u2264 x_1\na b : \u03b1\n\u22a2 (a \u2293 b) * (a * b * (a \u2293 b)\u207b\u00b9) = a * b",
437
+ "tactic": "rw [mul_comm, inv_mul_cancel_right]"
438
+ }
439
+ ],
440
+ "url": "https://github.com/leanprover-community/mathlib4"
441
+ }
442
+ },
443
+ "theorem_name": "inf_mul_sup"
444
+ },
445
+ {
446
+ "errors": [
447
+ "internal transition boundary mismatch",
448
+ "internal transition boundary mismatch"
449
+ ],
450
+ "file_path": "Mathlib/Algebra/Order/Group/MinMax.lean",
451
+ "proof_id": "mathlib:max_sub_max_le_max",
452
+ "provenance": {
453
+ "selection": {
454
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
455
+ "end": [
456
+ 93,
457
+ 90
458
+ ],
459
+ "file_path": "Mathlib/Algebra/Order/Group/MinMax.lean",
460
+ "full_name": "max_sub_max_le_max",
461
+ "start": [
462
+ 86,
463
+ 1
464
+ ],
465
+ "traced_tactics": [
466
+ {
467
+ "annotated_tactic": [
468
+ "\"simp only [<a>sub_le_iff_le_add<\\/a>, <a>max_le_iff<\\/a>]\"",
469
+ "[{\"full_name\":\"sub_le_iff_le_add\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Defs.lean\",\"def_pos\":[750,3],\"def_end_pos\":[750,14]},{\"full_name\":\"max_le_iff\",\"def_path\":\"Mathlib\\/Order\\/MinMax.lean\",\"def_pos\":[48,9],\"def_end_pos\":[48,19]}]"
470
+ ],
471
+ "state_after": "\u03b1 : Type u_1\ninst\u271d : LinearOrderedAddCommGroup \u03b1\na\u271d b\u271d c\u271d a b c d : \u03b1\n\u22a2 a \u2264 max (a - c) (b - d) + max c d \u2227 b \u2264 max (a - c) (b - d) + max c d",
472
+ "state_before": "\u03b1 : Type u_1\ninst\u271d : LinearOrderedAddCommGroup \u03b1\na\u271d b\u271d c\u271d a b c d : \u03b1\n\u22a2 max a b - max c d \u2264 max (a - c) (b - d)",
473
+ "tactic": "simp only [sub_le_iff_le_add, max_le_iff]"
474
+ },
475
+ {
476
+ "annotated_tactic": [
477
+ "\"constructor\"",
478
+ "[]"
479
+ ],
480
+ "state_after": "case left\n\u03b1 : Type u_1\ninst\u271d : LinearOrderedAddCommGroup \u03b1\na\u271d b\u271d c\u271d a b c d : \u03b1\n\u22a2 a \u2264 max (a - c) (b - d) + max c d\n\ncase right\n\u03b1 : Type u_1\ninst\u271d : LinearOrderedAddCommGroup \u03b1\na\u271d b\u271d c\u271d a b c d : \u03b1\n\u22a2 b \u2264 max (a - c) (b - d) + max c d",
481
+ "state_before": "\u03b1 : Type u_1\ninst\u271d : LinearOrderedAddCommGroup \u03b1\na\u271d b\u271d c\u271d a b c d : \u03b1\n\u22a2 a \u2264 max (a - c) (b - d) + max c d \u2227 b \u2264 max (a - c) (b - d) + max c d",
482
+ "tactic": "constructor"
483
+ },
484
+ {
485
+ "annotated_tactic": [
486
+ "\"calc\\n a = a - c + c := (<a>sub_add_cancel<\\/a> a c).<a>symm<\\/a>\\n _ \\u2264 <a>max<\\/a> (a - c) (b - d) + <a>max<\\/a> c d := <a>add_le_add<\\/a> (<a>le_max_left<\\/a> _ _) (<a>le_max_left<\\/a> _ _)\"",
487
+ "[{\"full_name\":\"sub_add_cancel\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[997,3],\"def_end_pos\":[997,14]},{\"full_name\":\"Eq.symm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[323,9],\"def_end_pos\":[323,16]},{\"full_name\":\"Max.max\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1129,3],\"def_end_pos\":[1129,6]},{\"full_name\":\"Max.max\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1129,3],\"def_end_pos\":[1129,6]},{\"full_name\":\"add_le_add\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Unbundled\\/Basic.lean\",\"def_pos\":[205,32],\"def_end_pos\":[205,42]},{\"full_name\":\"le_max_left\",\"def_path\":\"Mathlib\\/Init\\/Order\\/LinearOrder.lean\",\"def_pos\":[54,9],\"def_end_pos\":[54,20]},{\"full_name\":\"le_max_left\",\"def_path\":\"Mathlib\\/Init\\/Order\\/LinearOrder.lean\",\"def_pos\":[54,9],\"def_end_pos\":[54,20]}]"
488
+ ],
489
+ "state_after": "no goals",
490
+ "state_before": "case left\n\u03b1 : Type u_1\ninst\u271d : LinearOrderedAddCommGroup \u03b1\na\u271d b\u271d c\u271d a b c d : \u03b1\n\u22a2 a \u2264 max (a - c) (b - d) + max c d",
491
+ "tactic": "calc\na = a - c + c := (sub_add_cancel a c).symm\n_ \u2264 max (a - c) (b - d) + max c d := add_le_add (le_max_left _ _) (le_max_left _ _)"
492
+ },
493
+ {
494
+ "annotated_tactic": [
495
+ "\"calc\\n b = b - d + d := (<a>sub_add_cancel<\\/a> b d).<a>symm<\\/a>\\n _ \\u2264 <a>max<\\/a> (a - c) (b - d) + <a>max<\\/a> c d := <a>add_le_add<\\/a> (<a>le_max_right<\\/a> _ _) (<a>le_max_right<\\/a> _ _)\"",
496
+ "[{\"full_name\":\"sub_add_cancel\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[997,3],\"def_end_pos\":[997,14]},{\"full_name\":\"Eq.symm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[323,9],\"def_end_pos\":[323,16]},{\"full_name\":\"Max.max\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1129,3],\"def_end_pos\":[1129,6]},{\"full_name\":\"Max.max\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1129,3],\"def_end_pos\":[1129,6]},{\"full_name\":\"add_le_add\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Unbundled\\/Basic.lean\",\"def_pos\":[205,32],\"def_end_pos\":[205,42]},{\"full_name\":\"le_max_right\",\"def_path\":\"Mathlib\\/Init\\/Order\\/LinearOrder.lean\",\"def_pos\":[61,9],\"def_end_pos\":[61,21]},{\"full_name\":\"le_max_right\",\"def_path\":\"Mathlib\\/Init\\/Order\\/LinearOrder.lean\",\"def_pos\":[61,9],\"def_end_pos\":[61,21]}]"
497
+ ],
498
+ "state_after": "no goals",
499
+ "state_before": "case right\n\u03b1 : Type u_1\ninst\u271d : LinearOrderedAddCommGroup \u03b1\na\u271d b\u271d c\u271d a b c d : \u03b1\n\u22a2 b \u2264 max (a - c) (b - d) + max c d",
500
+ "tactic": "calc\nb = b - d + d := (sub_add_cancel b d).symm\n_ \u2264 max (a - c) (b - d) + max c d := add_le_add (le_max_right _ _) (le_max_right _ _)"
501
+ }
502
+ ],
503
+ "url": "https://github.com/leanprover-community/mathlib4"
504
+ }
505
+ },
506
+ "theorem_name": "max_sub_max_le_max"
507
+ }
508
+ ],
509
+ "validation_rejected_proofs": 2,
510
+ "zero_transition_proofs": 0
511
+ },
512
+ "shards": [
513
+ {
514
+ "path": "data/train/mathlib-000256-0000-471e9d0f007653f5.parquet",
515
+ "sha256": "471e9d0f007653f53b8b7f8b3413931737b4d9dfd1eb4d0d9b505fb22b3c74e8",
516
+ "bytes": 49083,
517
+ "rows": 8,
518
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
519
+ }
520
+ ],
521
+ "proof_ids": [
522
+ "mathlib:abs_max_sub_max_le_abs",
523
+ "mathlib:abs_min_sub_min_le_max",
524
+ "mathlib:max_div_div_left'",
525
+ "mathlib:max_div_div_right'",
526
+ "mathlib:max_inv_one",
527
+ "mathlib:max_one_div_max_inv_one_eq_self",
528
+ "mathlib:min_div_div_left'",
529
+ "mathlib:min_div_div_right'"
530
+ ],
531
+ "proof_keys": [
532
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/MinMax.lean\",null,null,\"abs_max_sub_max_le_abs\"]",
533
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/MinMax.lean\",null,null,\"abs_min_sub_min_le_max\"]",
534
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/MinMax.lean\",null,null,\"max_div_div_left'\"]",
535
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/MinMax.lean\",null,null,\"max_div_div_right'\"]",
536
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/MinMax.lean\",null,null,\"max_inv_one\"]",
537
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/MinMax.lean\",null,null,\"max_one_div_max_inv_one_eq_self\"]",
538
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/MinMax.lean\",null,null,\"min_div_div_left'\"]",
539
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/MinMax.lean\",null,null,\"min_div_div_right'\"]"
540
+ ]
541
+ }
manifests/batches/mathlib/000257.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000257",
4
+ "batch_fingerprint": "9b91325160c276ca87e15a72432f87bd8934299078682e52c3e109b22104d2db",
5
+ "evidence": {
6
+ "batch_fingerprint": "9b91325160c276ca87e15a72432f87bd8934299078682e52c3e109b22104d2db",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "Nat.pow_left_strictMono",
12
+ "id": "Nat.pow_left_strictMono",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 56,
18
+ 39
19
+ ],
20
+ "file_path": "Mathlib/Algebra/Order/Group/Nat.lean",
21
+ "full_name": "Nat.pow_left_strictMono",
22
+ "start": [
23
+ 54,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/Algebra/Order/Group/Nat.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "NeZero.one_le",
34
+ "id": "NeZero.one_le",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 50,
40
+ 96
41
+ ],
42
+ "file_path": "Mathlib/Algebra/Order/Group/Nat.lean",
43
+ "full_name": "NeZero.one_le",
44
+ "start": [
45
+ 50,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/Algebra/Order/Group/Nat.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "StrictMono.nat_pow",
56
+ "id": "StrictMono.nat_pow",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 60,
62
+ 65
63
+ ],
64
+ "file_path": "Mathlib/Algebra/Order/Group/Nat.lean",
65
+ "full_name": "StrictMono.nat_pow",
66
+ "start": [
67
+ 59,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/Algebra/Order/Group/Nat.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "inv_le'",
78
+ "id": "inv_le'",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 50,
84
+ 33
85
+ ],
86
+ "file_path": "Mathlib/Algebra/Order/Group/OrderIso.lean",
87
+ "full_name": "inv_le'",
88
+ "start": [
89
+ 49,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/Algebra/Order/Group/OrderIso.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "le_inv'",
100
+ "id": "le_inv'",
101
+ "reason": "import_failure",
102
+ "selection": {
103
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
104
+ "end": [
105
+ 62,
106
+ 33
107
+ ],
108
+ "file_path": "Mathlib/Algebra/Order/Group/OrderIso.lean",
109
+ "full_name": "le_inv'",
110
+ "start": [
111
+ 61,
112
+ 1
113
+ ],
114
+ "traced_tactics": [],
115
+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
+ "source_file": "Mathlib/Algebra/Order/Group/OrderIso.lean"
118
+ }
119
+ ],
120
+ "input_proofs": 7,
121
+ "input_units": 2,
122
+ "proofs": 2,
123
+ "published_proofs": 2,
124
+ "published_transitions": 4,
125
+ "replay_failures": [],
126
+ "transitions": 4,
127
+ "validation_failures": [],
128
+ "validation_rejected_proofs": 0,
129
+ "zero_transition_proofs": 0
130
+ },
131
+ "shards": [
132
+ {
133
+ "path": "data/train/mathlib-000257-0000-0acf39e5dcecd3db.parquet",
134
+ "sha256": "0acf39e5dcecd3dbd48acaff85bbe97b090520104d08d5f805b378a79e268203",
135
+ "bytes": 39198,
136
+ "rows": 4,
137
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
138
+ }
139
+ ],
140
+ "proof_ids": [
141
+ "mathlib:OrderIso.mulLeft_symm",
142
+ "mathlib:OrderIso.mulRight_symm"
143
+ ],
144
+ "proof_keys": [
145
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/OrderIso.lean\",null,null,\"OrderIso.mulLeft_symm\"]",
146
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/OrderIso.lean\",null,null,\"OrderIso.mulRight_symm\"]"
147
+ ]
148
+ }
manifests/batches/mathlib/000258.json ADDED
@@ -0,0 +1,1022 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000258",
4
+ "batch_fingerprint": "a8f0c19e95a6f28514fcd582a843e711036e8a089f8752745fbfee894f91180c",
5
+ "evidence": {
6
+ "batch_fingerprint": "a8f0c19e95a6f28514fcd582a843e711036e8a089f8752745fbfee894f91180c",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "Pi.leOnePart_apply",
12
+ "id": "Pi.leOnePart_apply",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 293,
18
+ 98
19
+ ],
20
+ "file_path": "Mathlib/Algebra/Order/Group/PosPart.lean",
21
+ "full_name": "Pi.leOnePart_apply",
22
+ "start": [
23
+ 293,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/Algebra/Order/Group/PosPart.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "Pi.leOnePart_def",
34
+ "id": "Pi.leOnePart_def",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 296,
40
+ 79
41
+ ],
42
+ "file_path": "Mathlib/Algebra/Order/Group/PosPart.lean",
43
+ "full_name": "Pi.leOnePart_def",
44
+ "start": [
45
+ 296,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/Algebra/Order/Group/PosPart.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "Pi.oneLePart_apply",
56
+ "id": "Pi.oneLePart_apply",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 292,
62
+ 98
63
+ ],
64
+ "file_path": "Mathlib/Algebra/Order/Group/PosPart.lean",
65
+ "full_name": "Pi.oneLePart_apply",
66
+ "start": [
67
+ 292,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/Algebra/Order/Group/PosPart.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "Pi.oneLePart_def",
78
+ "id": "Pi.oneLePart_def",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 295,
84
+ 79
85
+ ],
86
+ "file_path": "Mathlib/Algebra/Order/Group/PosPart.lean",
87
+ "full_name": "Pi.oneLePart_def",
88
+ "start": [
89
+ 295,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/Algebra/Order/Group/PosPart.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "inv_le_leOnePart",
100
+ "id": "inv_le_leOnePart",
101
+ "reason": "import_failure",
102
+ "selection": {
103
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
104
+ "end": [
105
+ 114,
106
+ 73
107
+ ],
108
+ "file_path": "Mathlib/Algebra/Order/Group/PosPart.lean",
109
+ "full_name": "inv_le_leOnePart",
110
+ "start": [
111
+ 114,
112
+ 1
113
+ ],
114
+ "traced_tactics": [],
115
+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
+ "source_file": "Mathlib/Algebra/Order/Group/PosPart.lean"
118
+ },
119
+ {
120
+ "error": "theorem has no selected tactic transitions",
121
+ "full_name": "leOnePart_anti",
122
+ "id": "leOnePart_anti",
123
+ "reason": "import_failure",
124
+ "selection": {
125
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
126
+ "end": [
127
+ 91,
128
+ 60
129
+ ],
130
+ "file_path": "Mathlib/Algebra/Order/Group/PosPart.lean",
131
+ "full_name": "leOnePart_anti",
132
+ "start": [
133
+ 90,
134
+ 1
135
+ ],
136
+ "traced_tactics": [],
137
+ "url": "https://github.com/leanprover-community/mathlib4"
138
+ },
139
+ "source_file": "Mathlib/Algebra/Order/Group/PosPart.lean"
140
+ },
141
+ {
142
+ "error": "theorem has no selected tactic transitions",
143
+ "full_name": "leOnePart_eq_inv'",
144
+ "id": "leOnePart_eq_inv'",
145
+ "reason": "import_failure",
146
+ "selection": {
147
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
148
+ "end": [
149
+ 130,
150
+ 61
151
+ ],
152
+ "file_path": "Mathlib/Algebra/Order/Group/PosPart.lean",
153
+ "full_name": "leOnePart_eq_inv'",
154
+ "start": [
155
+ 128,
156
+ 1
157
+ ],
158
+ "traced_tactics": [],
159
+ "url": "https://github.com/leanprover-community/mathlib4"
160
+ },
161
+ "source_file": "Mathlib/Algebra/Order/Group/PosPart.lean"
162
+ },
163
+ {
164
+ "error": "theorem has no selected tactic transitions",
165
+ "full_name": "leOnePart_eq_one'",
166
+ "id": "leOnePart_eq_one'",
167
+ "reason": "import_failure",
168
+ "selection": {
169
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
170
+ "end": [
171
+ 140,
172
+ 60
173
+ ],
174
+ "file_path": "Mathlib/Algebra/Order/Group/PosPart.lean",
175
+ "full_name": "leOnePart_eq_one'",
176
+ "start": [
177
+ 138,
178
+ 1
179
+ ],
180
+ "traced_tactics": [],
181
+ "url": "https://github.com/leanprover-community/mathlib4"
182
+ },
183
+ "source_file": "Mathlib/Algebra/Order/Group/PosPart.lean"
184
+ },
185
+ {
186
+ "error": "theorem has no selected tactic transitions",
187
+ "full_name": "le_oneLePart",
188
+ "id": "le_oneLePart",
189
+ "reason": "import_failure",
190
+ "selection": {
191
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
192
+ "end": [
193
+ 110,
194
+ 78
195
+ ],
196
+ "file_path": "Mathlib/Algebra/Order/Group/PosPart.lean",
197
+ "full_name": "le_oneLePart",
198
+ "start": [
199
+ 110,
200
+ 1
201
+ ],
202
+ "traced_tactics": [],
203
+ "url": "https://github.com/leanprover-community/mathlib4"
204
+ },
205
+ "source_file": "Mathlib/Algebra/Order/Group/PosPart.lean"
206
+ },
207
+ {
208
+ "error": "theorem has no selected tactic transitions",
209
+ "full_name": "oneLePart_eq_one",
210
+ "id": "oneLePart_eq_one",
211
+ "reason": "import_failure",
212
+ "selection": {
213
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
214
+ "end": [
215
+ 122,
216
+ 72
217
+ ],
218
+ "file_path": "Mathlib/Algebra/Order/Group/PosPart.lean",
219
+ "full_name": "oneLePart_eq_one",
220
+ "start": [
221
+ 122,
222
+ 1
223
+ ],
224
+ "traced_tactics": [],
225
+ "url": "https://github.com/leanprover-community/mathlib4"
226
+ },
227
+ "source_file": "Mathlib/Algebra/Order/Group/PosPart.lean"
228
+ },
229
+ {
230
+ "error": "theorem has no selected tactic transitions",
231
+ "full_name": "oneLePart_eq_self",
232
+ "id": "oneLePart_eq_self",
233
+ "reason": "import_failure",
234
+ "selection": {
235
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
236
+ "end": [
237
+ 118,
238
+ 87
239
+ ],
240
+ "file_path": "Mathlib/Algebra/Order/Group/PosPart.lean",
241
+ "full_name": "oneLePart_eq_self",
242
+ "start": [
243
+ 118,
244
+ 1
245
+ ],
246
+ "traced_tactics": [],
247
+ "url": "https://github.com/leanprover-community/mathlib4"
248
+ },
249
+ "source_file": "Mathlib/Algebra/Order/Group/PosPart.lean"
250
+ },
251
+ {
252
+ "error": "theorem has no selected tactic transitions",
253
+ "full_name": "oneLePart_inv",
254
+ "id": "oneLePart_inv",
255
+ "reason": "import_failure",
256
+ "selection": {
257
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
258
+ "end": [
259
+ 171,
260
+ 79
261
+ ],
262
+ "file_path": "Mathlib/Algebra/Order/Group/PosPart.lean",
263
+ "full_name": "oneLePart_inv",
264
+ "start": [
265
+ 171,
266
+ 1
267
+ ],
268
+ "traced_tactics": [],
269
+ "url": "https://github.com/leanprover-community/mathlib4"
270
+ },
271
+ "source_file": "Mathlib/Algebra/Order/Group/PosPart.lean"
272
+ },
273
+ {
274
+ "error": "theorem has no selected tactic transitions",
275
+ "full_name": "oneLePart_mono",
276
+ "id": "oneLePart_mono",
277
+ "reason": "import_failure",
278
+ "selection": {
279
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
280
+ "end": [
281
+ 88,
282
+ 41
283
+ ],
284
+ "file_path": "Mathlib/Algebra/Order/Group/PosPart.lean",
285
+ "full_name": "oneLePart_mono",
286
+ "start": [
287
+ 87,
288
+ 1
289
+ ],
290
+ "traced_tactics": [],
291
+ "url": "https://github.com/leanprover-community/mathlib4"
292
+ },
293
+ "source_file": "Mathlib/Algebra/Order/Group/PosPart.lean"
294
+ },
295
+ {
296
+ "error": "theorem has no selected tactic transitions",
297
+ "full_name": "oneLePart_one",
298
+ "id": "oneLePart_one",
299
+ "reason": "import_failure",
300
+ "selection": {
301
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
302
+ "end": [
303
+ 93,
304
+ 80
305
+ ],
306
+ "file_path": "Mathlib/Algebra/Order/Group/PosPart.lean",
307
+ "full_name": "oneLePart_one",
308
+ "start": [
309
+ 93,
310
+ 1
311
+ ],
312
+ "traced_tactics": [],
313
+ "url": "https://github.com/leanprover-community/mathlib4"
314
+ },
315
+ "source_file": "Mathlib/Algebra/Order/Group/PosPart.lean"
316
+ },
317
+ {
318
+ "error": "theorem has no selected tactic transitions",
319
+ "full_name": "one_le_leOnePart",
320
+ "id": "one_le_leOnePart",
321
+ "reason": "import_failure",
322
+ "selection": {
323
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
324
+ "end": [
325
+ 105,
326
+ 87
327
+ ],
328
+ "file_path": "Mathlib/Algebra/Order/Group/PosPart.lean",
329
+ "full_name": "one_le_leOnePart",
330
+ "start": [
331
+ 105,
332
+ 1
333
+ ],
334
+ "traced_tactics": [],
335
+ "url": "https://github.com/leanprover-community/mathlib4"
336
+ },
337
+ "source_file": "Mathlib/Algebra/Order/Group/PosPart.lean"
338
+ },
339
+ {
340
+ "error": "theorem has no selected tactic transitions",
341
+ "full_name": "one_le_oneLePart",
342
+ "id": "one_le_oneLePart",
343
+ "reason": "import_failure",
344
+ "selection": {
345
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
346
+ "end": [
347
+ 101,
348
+ 87
349
+ ],
350
+ "file_path": "Mathlib/Algebra/Order/Group/PosPart.lean",
351
+ "full_name": "one_le_oneLePart",
352
+ "start": [
353
+ 101,
354
+ 1
355
+ ],
356
+ "traced_tactics": [],
357
+ "url": "https://github.com/leanprover-community/mathlib4"
358
+ },
359
+ "source_file": "Mathlib/Algebra/Order/Group/PosPart.lean"
360
+ },
361
+ {
362
+ "error": "theorem has no selected tactic transitions",
363
+ "full_name": "one_lt_ltOnePart_iff",
364
+ "id": "one_lt_ltOnePart_iff",
365
+ "reason": "import_failure",
366
+ "selection": {
367
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
368
+ "end": [
369
+ 279,
370
+ 81
371
+ ],
372
+ "file_path": "Mathlib/Algebra/Order/Group/PosPart.lean",
373
+ "full_name": "one_lt_ltOnePart_iff",
374
+ "start": [
375
+ 278,
376
+ 1
377
+ ],
378
+ "traced_tactics": [],
379
+ "url": "https://github.com/leanprover-community/mathlib4"
380
+ },
381
+ "source_file": "Mathlib/Algebra/Order/Group/PosPart.lean"
382
+ },
383
+ {
384
+ "error": "theorem has no selected tactic transitions",
385
+ "full_name": "one_lt_oneLePart_iff",
386
+ "id": "one_lt_oneLePart_iff",
387
+ "reason": "import_failure",
388
+ "selection": {
389
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
390
+ "end": [
391
+ 276,
392
+ 81
393
+ ],
394
+ "file_path": "Mathlib/Algebra/Order/Group/PosPart.lean",
395
+ "full_name": "one_lt_oneLePart_iff",
396
+ "start": [
397
+ 275,
398
+ 1
399
+ ],
400
+ "traced_tactics": [],
401
+ "url": "https://github.com/leanprover-community/mathlib4"
402
+ },
403
+ "source_file": "Mathlib/Algebra/Order/Group/PosPart.lean"
404
+ },
405
+ {
406
+ "error": "theorem has no selected tactic transitions",
407
+ "full_name": "ofDual_div",
408
+ "id": "ofDual_div",
409
+ "reason": "import_failure",
410
+ "selection": {
411
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
412
+ "end": [
413
+ 145,
414
+ 85
415
+ ],
416
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
417
+ "full_name": "ofDual_div",
418
+ "start": [
419
+ 145,
420
+ 1
421
+ ],
422
+ "traced_tactics": [],
423
+ "url": "https://github.com/leanprover-community/mathlib4"
424
+ },
425
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
426
+ },
427
+ {
428
+ "error": "theorem has no selected tactic transitions",
429
+ "full_name": "ofDual_inv",
430
+ "id": "ofDual_inv",
431
+ "reason": "import_failure",
432
+ "selection": {
433
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
434
+ "end": [
435
+ 135,
436
+ 72
437
+ ],
438
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
439
+ "full_name": "ofDual_inv",
440
+ "start": [
441
+ 135,
442
+ 1
443
+ ],
444
+ "traced_tactics": [],
445
+ "url": "https://github.com/leanprover-community/mathlib4"
446
+ },
447
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
448
+ },
449
+ {
450
+ "error": "theorem has no selected tactic transitions",
451
+ "full_name": "ofDual_mul",
452
+ "id": "ofDual_mul",
453
+ "reason": "import_failure",
454
+ "selection": {
455
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
456
+ "end": [
457
+ 125,
458
+ 85
459
+ ],
460
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
461
+ "full_name": "ofDual_mul",
462
+ "start": [
463
+ 125,
464
+ 1
465
+ ],
466
+ "traced_tactics": [],
467
+ "url": "https://github.com/leanprover-community/mathlib4"
468
+ },
469
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
470
+ },
471
+ {
472
+ "error": "theorem has no selected tactic transitions",
473
+ "full_name": "ofDual_one",
474
+ "id": "ofDual_one",
475
+ "reason": "import_failure",
476
+ "selection": {
477
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
478
+ "end": [
479
+ 115,
480
+ 55
481
+ ],
482
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
483
+ "full_name": "ofDual_one",
484
+ "start": [
485
+ 115,
486
+ 1
487
+ ],
488
+ "traced_tactics": [],
489
+ "url": "https://github.com/leanprover-community/mathlib4"
490
+ },
491
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
492
+ },
493
+ {
494
+ "error": "theorem has no selected tactic transitions",
495
+ "full_name": "ofDual_pow",
496
+ "id": "ofDual_pow",
497
+ "reason": "import_failure",
498
+ "selection": {
499
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
500
+ "end": [
501
+ 156,
502
+ 86
503
+ ],
504
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
505
+ "full_name": "ofDual_pow",
506
+ "start": [
507
+ 156,
508
+ 1
509
+ ],
510
+ "traced_tactics": [],
511
+ "url": "https://github.com/leanprover-community/mathlib4"
512
+ },
513
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
514
+ },
515
+ {
516
+ "error": "theorem has no selected tactic transitions",
517
+ "full_name": "ofLex_div",
518
+ "id": "ofLex_div",
519
+ "reason": "import_failure",
520
+ "selection": {
521
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
522
+ "end": [
523
+ 285,
524
+ 83
525
+ ],
526
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
527
+ "full_name": "ofLex_div",
528
+ "start": [
529
+ 285,
530
+ 1
531
+ ],
532
+ "traced_tactics": [],
533
+ "url": "https://github.com/leanprover-community/mathlib4"
534
+ },
535
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
536
+ },
537
+ {
538
+ "error": "theorem has no selected tactic transitions",
539
+ "full_name": "ofLex_inv",
540
+ "id": "ofLex_inv",
541
+ "reason": "import_failure",
542
+ "selection": {
543
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
544
+ "end": [
545
+ 275,
546
+ 71
547
+ ],
548
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
549
+ "full_name": "ofLex_inv",
550
+ "start": [
551
+ 275,
552
+ 1
553
+ ],
554
+ "traced_tactics": [],
555
+ "url": "https://github.com/leanprover-community/mathlib4"
556
+ },
557
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
558
+ },
559
+ {
560
+ "error": "theorem has no selected tactic transitions",
561
+ "full_name": "ofLex_mul",
562
+ "id": "ofLex_mul",
563
+ "reason": "import_failure",
564
+ "selection": {
565
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
566
+ "end": [
567
+ 265,
568
+ 83
569
+ ],
570
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
571
+ "full_name": "ofLex_mul",
572
+ "start": [
573
+ 265,
574
+ 1
575
+ ],
576
+ "traced_tactics": [],
577
+ "url": "https://github.com/leanprover-community/mathlib4"
578
+ },
579
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
580
+ },
581
+ {
582
+ "error": "theorem has no selected tactic transitions",
583
+ "full_name": "ofLex_one",
584
+ "id": "ofLex_one",
585
+ "reason": "import_failure",
586
+ "selection": {
587
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
588
+ "end": [
589
+ 255,
590
+ 53
591
+ ],
592
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
593
+ "full_name": "ofLex_one",
594
+ "start": [
595
+ 255,
596
+ 1
597
+ ],
598
+ "traced_tactics": [],
599
+ "url": "https://github.com/leanprover-community/mathlib4"
600
+ },
601
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
602
+ },
603
+ {
604
+ "error": "theorem has no selected tactic transitions",
605
+ "full_name": "ofLex_pow",
606
+ "id": "ofLex_pow",
607
+ "reason": "import_failure",
608
+ "selection": {
609
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
610
+ "end": [
611
+ 296,
612
+ 85
613
+ ],
614
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
615
+ "full_name": "ofLex_pow",
616
+ "start": [
617
+ 296,
618
+ 1
619
+ ],
620
+ "traced_tactics": [],
621
+ "url": "https://github.com/leanprover-community/mathlib4"
622
+ },
623
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
624
+ },
625
+ {
626
+ "error": "theorem has no selected tactic transitions",
627
+ "full_name": "pow_ofDual",
628
+ "id": "pow_ofDual",
629
+ "reason": "import_failure",
630
+ "selection": {
631
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
632
+ "end": [
633
+ 168,
634
+ 77
635
+ ],
636
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
637
+ "full_name": "pow_ofDual",
638
+ "start": [
639
+ 168,
640
+ 1
641
+ ],
642
+ "traced_tactics": [],
643
+ "url": "https://github.com/leanprover-community/mathlib4"
644
+ },
645
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
646
+ },
647
+ {
648
+ "error": "theorem has no selected tactic transitions",
649
+ "full_name": "pow_ofLex",
650
+ "id": "pow_ofLex",
651
+ "reason": "import_failure",
652
+ "selection": {
653
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
654
+ "end": [
655
+ 308,
656
+ 77
657
+ ],
658
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
659
+ "full_name": "pow_ofLex",
660
+ "start": [
661
+ 308,
662
+ 1
663
+ ],
664
+ "traced_tactics": [],
665
+ "url": "https://github.com/leanprover-community/mathlib4"
666
+ },
667
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
668
+ },
669
+ {
670
+ "error": "theorem has no selected tactic transitions",
671
+ "full_name": "pow_toDual",
672
+ "id": "pow_toDual",
673
+ "reason": "import_failure",
674
+ "selection": {
675
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
676
+ "end": [
677
+ 162,
678
+ 75
679
+ ],
680
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
681
+ "full_name": "pow_toDual",
682
+ "start": [
683
+ 162,
684
+ 1
685
+ ],
686
+ "traced_tactics": [],
687
+ "url": "https://github.com/leanprover-community/mathlib4"
688
+ },
689
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
690
+ },
691
+ {
692
+ "error": "theorem has no selected tactic transitions",
693
+ "full_name": "pow_toLex",
694
+ "id": "pow_toLex",
695
+ "reason": "import_failure",
696
+ "selection": {
697
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
698
+ "end": [
699
+ 302,
700
+ 73
701
+ ],
702
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
703
+ "full_name": "pow_toLex",
704
+ "start": [
705
+ 302,
706
+ 1
707
+ ],
708
+ "traced_tactics": [],
709
+ "url": "https://github.com/leanprover-community/mathlib4"
710
+ },
711
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
712
+ },
713
+ {
714
+ "error": "theorem has no selected tactic transitions",
715
+ "full_name": "toDual_div",
716
+ "id": "toDual_div",
717
+ "reason": "import_failure",
718
+ "selection": {
719
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
720
+ "end": [
721
+ 140,
722
+ 83
723
+ ],
724
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
725
+ "full_name": "toDual_div",
726
+ "start": [
727
+ 140,
728
+ 1
729
+ ],
730
+ "traced_tactics": [],
731
+ "url": "https://github.com/leanprover-community/mathlib4"
732
+ },
733
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
734
+ },
735
+ {
736
+ "error": "theorem has no selected tactic transitions",
737
+ "full_name": "toDual_inv",
738
+ "id": "toDual_inv",
739
+ "reason": "import_failure",
740
+ "selection": {
741
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
742
+ "end": [
743
+ 130,
744
+ 70
745
+ ],
746
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
747
+ "full_name": "toDual_inv",
748
+ "start": [
749
+ 130,
750
+ 1
751
+ ],
752
+ "traced_tactics": [],
753
+ "url": "https://github.com/leanprover-community/mathlib4"
754
+ },
755
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
756
+ },
757
+ {
758
+ "error": "theorem has no selected tactic transitions",
759
+ "full_name": "toDual_mul",
760
+ "id": "toDual_mul",
761
+ "reason": "import_failure",
762
+ "selection": {
763
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
764
+ "end": [
765
+ 120,
766
+ 83
767
+ ],
768
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
769
+ "full_name": "toDual_mul",
770
+ "start": [
771
+ 120,
772
+ 1
773
+ ],
774
+ "traced_tactics": [],
775
+ "url": "https://github.com/leanprover-community/mathlib4"
776
+ },
777
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
778
+ },
779
+ {
780
+ "error": "theorem has no selected tactic transitions",
781
+ "full_name": "toDual_one",
782
+ "id": "toDual_one",
783
+ "reason": "import_failure",
784
+ "selection": {
785
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
786
+ "end": [
787
+ 110,
788
+ 55
789
+ ],
790
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
791
+ "full_name": "toDual_one",
792
+ "start": [
793
+ 110,
794
+ 1
795
+ ],
796
+ "traced_tactics": [],
797
+ "url": "https://github.com/leanprover-community/mathlib4"
798
+ },
799
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
800
+ },
801
+ {
802
+ "error": "theorem has no selected tactic transitions",
803
+ "full_name": "toDual_pow",
804
+ "id": "toDual_pow",
805
+ "reason": "import_failure",
806
+ "selection": {
807
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
808
+ "end": [
809
+ 150,
810
+ 84
811
+ ],
812
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
813
+ "full_name": "toDual_pow",
814
+ "start": [
815
+ 150,
816
+ 1
817
+ ],
818
+ "traced_tactics": [],
819
+ "url": "https://github.com/leanprover-community/mathlib4"
820
+ },
821
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
822
+ },
823
+ {
824
+ "error": "theorem has no selected tactic transitions",
825
+ "full_name": "toLex_div",
826
+ "id": "toLex_div",
827
+ "reason": "import_failure",
828
+ "selection": {
829
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
830
+ "end": [
831
+ 280,
832
+ 79
833
+ ],
834
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
835
+ "full_name": "toLex_div",
836
+ "start": [
837
+ 280,
838
+ 1
839
+ ],
840
+ "traced_tactics": [],
841
+ "url": "https://github.com/leanprover-community/mathlib4"
842
+ },
843
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
844
+ },
845
+ {
846
+ "error": "theorem has no selected tactic transitions",
847
+ "full_name": "toLex_inv",
848
+ "id": "toLex_inv",
849
+ "reason": "import_failure",
850
+ "selection": {
851
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
852
+ "end": [
853
+ 270,
854
+ 67
855
+ ],
856
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
857
+ "full_name": "toLex_inv",
858
+ "start": [
859
+ 270,
860
+ 1
861
+ ],
862
+ "traced_tactics": [],
863
+ "url": "https://github.com/leanprover-community/mathlib4"
864
+ },
865
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
866
+ },
867
+ {
868
+ "error": "theorem has no selected tactic transitions",
869
+ "full_name": "toLex_mul",
870
+ "id": "toLex_mul",
871
+ "reason": "import_failure",
872
+ "selection": {
873
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
874
+ "end": [
875
+ 260,
876
+ 79
877
+ ],
878
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
879
+ "full_name": "toLex_mul",
880
+ "start": [
881
+ 260,
882
+ 1
883
+ ],
884
+ "traced_tactics": [],
885
+ "url": "https://github.com/leanprover-community/mathlib4"
886
+ },
887
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
888
+ },
889
+ {
890
+ "error": "theorem has no selected tactic transitions",
891
+ "full_name": "toLex_one",
892
+ "id": "toLex_one",
893
+ "reason": "import_failure",
894
+ "selection": {
895
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
896
+ "end": [
897
+ 250,
898
+ 53
899
+ ],
900
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
901
+ "full_name": "toLex_one",
902
+ "start": [
903
+ 250,
904
+ 1
905
+ ],
906
+ "traced_tactics": [],
907
+ "url": "https://github.com/leanprover-community/mathlib4"
908
+ },
909
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
910
+ },
911
+ {
912
+ "error": "theorem has no selected tactic transitions",
913
+ "full_name": "toLex_pow",
914
+ "id": "toLex_pow",
915
+ "reason": "import_failure",
916
+ "selection": {
917
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
918
+ "end": [
919
+ 290,
920
+ 81
921
+ ],
922
+ "file_path": "Mathlib/Algebra/Order/Group/Synonym.lean",
923
+ "full_name": "toLex_pow",
924
+ "start": [
925
+ 290,
926
+ 1
927
+ ],
928
+ "traced_tactics": [],
929
+ "url": "https://github.com/leanprover-community/mathlib4"
930
+ },
931
+ "source_file": "Mathlib/Algebra/Order/Group/Synonym.lean"
932
+ }
933
+ ],
934
+ "input_proofs": 67,
935
+ "input_units": 2,
936
+ "proofs": 25,
937
+ "published_proofs": 25,
938
+ "published_transitions": 35,
939
+ "replay_failures": [],
940
+ "transitions": 35,
941
+ "validation_failures": [],
942
+ "validation_rejected_proofs": 0,
943
+ "zero_transition_proofs": 0
944
+ },
945
+ "shards": [
946
+ {
947
+ "path": "data/train/mathlib-000258-0000-197fcab94098c222.parquet",
948
+ "sha256": "197fcab94098c22216bad9dab88137236da2b6536b273e525480bc9ca208b17d",
949
+ "bytes": 79549,
950
+ "rows": 27,
951
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
952
+ },
953
+ {
954
+ "path": "data/dev/mathlib-000258-0000-c7b69b059ca8afc3.parquet",
955
+ "sha256": "c7b69b059ca8afc3575ba8eb2ea9f3822886289fb9403463b0b1aaa8c924e54f",
956
+ "bytes": 37802,
957
+ "rows": 1,
958
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
959
+ },
960
+ {
961
+ "path": "data/internal_test/mathlib-000258-0000-49902e168d011e0c.parquet",
962
+ "sha256": "49902e168d011e0caa5d36b88c7746ffc8d4264329d26a069caad124602e6eb4",
963
+ "bytes": 45704,
964
+ "rows": 7,
965
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
966
+ }
967
+ ],
968
+ "proof_ids": [
969
+ "mathlib:div_mabs_eq_inv_leOnePart_sq",
970
+ "mathlib:inf_eq_div_oneLePart_div",
971
+ "mathlib:leOnePart_div_oneLePart",
972
+ "mathlib:leOnePart_eq_inv",
973
+ "mathlib:leOnePart_eq_inv_inf_one",
974
+ "mathlib:leOnePart_eq_ite",
975
+ "mathlib:leOnePart_eq_one",
976
+ "mathlib:leOnePart_inv",
977
+ "mathlib:leOnePart_le_one",
978
+ "mathlib:leOnePart_le_one'",
979
+ "mathlib:leOnePart_mul_oneLePart",
980
+ "mathlib:leOnePart_one",
981
+ "mathlib:le_iff_oneLePart_leOnePart",
982
+ "mathlib:mabs_div_eq_leOnePart_sq",
983
+ "mathlib:mabs_mul_eq_oneLePart_sq",
984
+ "mathlib:mul_mabs_eq_oneLePart_sq",
985
+ "mathlib:oneLePart_div_leOnePart",
986
+ "mathlib:oneLePart_eq_ite",
987
+ "mathlib:oneLePart_inf_leOnePart_eq_one",
988
+ "mathlib:oneLePart_le_one",
989
+ "mathlib:oneLePart_mul_leOnePart",
990
+ "mathlib:oneLePart_of_one_lt_oneLePart",
991
+ "mathlib:one_lt_ltOnePart",
992
+ "mathlib:one_lt_oneLePart",
993
+ "mathlib:sup_eq_mul_oneLePart_div"
994
+ ],
995
+ "proof_keys": [
996
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"div_mabs_eq_inv_leOnePart_sq\"]",
997
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"inf_eq_div_oneLePart_div\"]",
998
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"leOnePart_div_oneLePart\"]",
999
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"leOnePart_eq_inv\"]",
1000
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"leOnePart_eq_inv_inf_one\"]",
1001
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"leOnePart_eq_ite\"]",
1002
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"leOnePart_eq_one\"]",
1003
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"leOnePart_inv\"]",
1004
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"leOnePart_le_one\"]",
1005
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"leOnePart_le_one'\"]",
1006
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"leOnePart_mul_oneLePart\"]",
1007
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"leOnePart_one\"]",
1008
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"le_iff_oneLePart_leOnePart\"]",
1009
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"mabs_div_eq_leOnePart_sq\"]",
1010
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"mabs_mul_eq_oneLePart_sq\"]",
1011
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"mul_mabs_eq_oneLePart_sq\"]",
1012
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"oneLePart_div_leOnePart\"]",
1013
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"oneLePart_eq_ite\"]",
1014
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"oneLePart_inf_leOnePart_eq_one\"]",
1015
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"oneLePart_le_one\"]",
1016
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"oneLePart_mul_leOnePart\"]",
1017
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"oneLePart_of_one_lt_oneLePart\"]",
1018
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"one_lt_ltOnePart\"]",
1019
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"one_lt_oneLePart\"]",
1020
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/PosPart.lean\",null,null,\"sup_eq_mul_oneLePart_div\"]"
1021
+ ]
1022
+ }
manifests/batches/mathlib/000259.json ADDED
@@ -0,0 +1,1012 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000259",
4
+ "batch_fingerprint": "b2672d447ff038ccea2a87101f5451614f1290d8cef3f9e90694b575fbd97fb8",
5
+ "evidence": {
6
+ "batch_fingerprint": "b2672d447ff038ccea2a87101f5451614f1290d8cef3f9e90694b575fbd97fb8",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "WithTop.LinearOrderedAddCommGroup.coe_neg",
12
+ "id": "WithTop.LinearOrderedAddCommGroup.coe_neg",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 51,
18
+ 6
19
+ ],
20
+ "file_path": "Mathlib/Algebra/Order/Group/WithTop.lean",
21
+ "full_name": "WithTop.LinearOrderedAddCommGroup.coe_neg",
22
+ "start": [
23
+ 50,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/Algebra/Order/Group/WithTop.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "WithTop.LinearOrderedAddCommGroup.coe_sub",
34
+ "id": "WithTop.LinearOrderedAddCommGroup.coe_sub",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 58,
40
+ 68
41
+ ],
42
+ "file_path": "Mathlib/Algebra/Order/Group/WithTop.lean",
43
+ "full_name": "WithTop.LinearOrderedAddCommGroup.coe_sub",
44
+ "start": [
45
+ 58,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/Algebra/Order/Group/WithTop.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "WithTop.LinearOrderedAddCommGroup.neg_top",
56
+ "id": "WithTop.LinearOrderedAddCommGroup.neg_top",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 55,
62
+ 46
63
+ ],
64
+ "file_path": "Mathlib/Algebra/Order/Group/WithTop.lean",
65
+ "full_name": "WithTop.LinearOrderedAddCommGroup.neg_top",
66
+ "start": [
67
+ 55,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/Algebra/Order/Group/WithTop.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "Units.zero_lt",
78
+ "id": "Units.zero_lt",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 165,
84
+ 29
85
+ ],
86
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
87
+ "full_name": "Units.zero_lt",
88
+ "start": [
89
+ 164,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "WithZero.coe_le_coe",
100
+ "id": "WithZero.coe_le_coe",
101
+ "reason": "import_failure",
102
+ "selection": {
103
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
104
+ "end": [
105
+ 345,
106
+ 89
107
+ ],
108
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
109
+ "full_name": "WithZero.coe_le_coe",
110
+ "start": [
111
+ 345,
112
+ 1
113
+ ],
114
+ "traced_tactics": [],
115
+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
118
+ },
119
+ {
120
+ "error": "theorem has no selected tactic transitions",
121
+ "full_name": "WithZero.coe_le_iff",
122
+ "id": "WithZero.coe_le_iff",
123
+ "reason": "import_failure",
124
+ "selection": {
125
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
126
+ "end": [
127
+ 357,
128
+ 21
129
+ ],
130
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
131
+ "full_name": "WithZero.coe_le_iff",
132
+ "start": [
133
+ 356,
134
+ 1
135
+ ],
136
+ "traced_tactics": [],
137
+ "url": "https://github.com/leanprover-community/mathlib4"
138
+ },
139
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
140
+ },
141
+ {
142
+ "error": "theorem has no selected tactic transitions",
143
+ "full_name": "WithZero.coe_le_one",
144
+ "id": "WithZero.coe_le_one",
145
+ "reason": "import_failure",
146
+ "selection": {
147
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
148
+ "end": [
149
+ 354,
150
+ 89
151
+ ],
152
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
153
+ "full_name": "WithZero.coe_le_one",
154
+ "start": [
155
+ 354,
156
+ 1
157
+ ],
158
+ "traced_tactics": [],
159
+ "url": "https://github.com/leanprover-community/mathlib4"
160
+ },
161
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
162
+ },
163
+ {
164
+ "error": "theorem has no selected tactic transitions",
165
+ "full_name": "WithZero.coe_lt_coe",
166
+ "id": "WithZero.coe_lt_coe",
167
+ "reason": "import_failure",
168
+ "selection": {
169
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
170
+ "end": [
171
+ 342,
172
+ 89
173
+ ],
174
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
175
+ "full_name": "WithZero.coe_lt_coe",
176
+ "start": [
177
+ 342,
178
+ 1
179
+ ],
180
+ "traced_tactics": [],
181
+ "url": "https://github.com/leanprover-community/mathlib4"
182
+ },
183
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
184
+ },
185
+ {
186
+ "error": "theorem has no selected tactic transitions",
187
+ "full_name": "WithZero.coe_lt_one",
188
+ "id": "WithZero.coe_lt_one",
189
+ "reason": "import_failure",
190
+ "selection": {
191
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
192
+ "end": [
193
+ 352,
194
+ 89
195
+ ],
196
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
197
+ "full_name": "WithZero.coe_lt_one",
198
+ "start": [
199
+ 352,
200
+ 1
201
+ ],
202
+ "traced_tactics": [],
203
+ "url": "https://github.com/leanprover-community/mathlib4"
204
+ },
205
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
206
+ },
207
+ {
208
+ "error": "no internal trace for tactic 'rwa [zero_add, zero_add]'",
209
+ "full_name": "WithZero.covariantClass_add_le",
210
+ "id": "WithZero.covariantClass_add_le",
211
+ "reason": "import_failure",
212
+ "selection": {
213
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
214
+ "end": [
215
+ 384,
216
+ 33
217
+ ],
218
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
219
+ "full_name": "WithZero.covariantClass_add_le",
220
+ "start": [
221
+ 370,
222
+ 1
223
+ ],
224
+ "traced_tactics": [
225
+ {
226
+ "annotated_tactic": [
227
+ "\"refine \\u27e8fun a b c hbc => ?_\\u27e9\"",
228
+ "[]"
229
+ ],
230
+ "state_after": "\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na\u271d b\u271d : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\na b c : WithZero \u03b1\nhbc : b \u2264 c\n\u22a2 a + b \u2264 a + c",
231
+ "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\n\u22a2 CovariantClass (WithZero \u03b1) (WithZero \u03b1) (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1",
232
+ "tactic": "refine \u27e8fun a b c hbc => ?_\u27e9"
233
+ },
234
+ {
235
+ "annotated_tactic": [
236
+ "\"induction a\"",
237
+ "[]"
238
+ ],
239
+ "state_after": "case h\u2081\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b\u271d : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\nb c : WithZero \u03b1\nhbc : b \u2264 c\n\u22a2 0 + b \u2264 0 + c\n\ncase h\u2082\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b\u271d : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\nb c : WithZero \u03b1\nhbc : b \u2264 c\na\u271d : \u03b1\n\u22a2 \u2191a\u271d + b \u2264 \u2191a\u271d + c",
240
+ "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na\u271d b\u271d : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\na b c : WithZero \u03b1\nhbc : b \u2264 c\n\u22a2 a + b \u2264 a + c",
241
+ "tactic": "induction a"
242
+ },
243
+ {
244
+ "annotated_tactic": [
245
+ "\"induction b\"",
246
+ "[]"
247
+ ],
248
+ "state_after": "case h\u2082.h\u2081\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\nc : WithZero \u03b1\na\u271d : \u03b1\nhbc : 0 \u2264 c\n\u22a2 \u2191a\u271d + 0 \u2264 \u2191a\u271d + c\n\ncase h\u2082.h\u2082\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\nc : WithZero \u03b1\na\u271d\u00b9 a\u271d : \u03b1\nhbc : \u2191a\u271d \u2264 c\n\u22a2 \u2191a\u271d\u00b9 + \u2191a\u271d \u2264 \u2191a\u271d\u00b9 + c",
249
+ "state_before": "case h\u2082\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b\u271d : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\nb c : WithZero \u03b1\nhbc : b \u2264 c\na\u271d : \u03b1\n\u22a2 \u2191a\u271d + b \u2264 \u2191a\u271d + c",
250
+ "tactic": "induction b"
251
+ },
252
+ {
253
+ "annotated_tactic": [
254
+ "\"rwa [<a>zero_add<\\/a>, <a>zero_add<\\/a>]\"",
255
+ "[{\"full_name\":\"zero_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[476,3],\"def_end_pos\":[476,14]},{\"full_name\":\"zero_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[476,3],\"def_end_pos\":[476,14]}]"
256
+ ],
257
+ "state_after": "no goals",
258
+ "state_before": "case h\u2081\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b\u271d : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\nb c : WithZero \u03b1\nhbc : b \u2264 c\n\u22a2 0 + b \u2264 0 + c",
259
+ "tactic": "rwa [zero_add, zero_add]"
260
+ },
261
+ {
262
+ "annotated_tactic": [
263
+ "\"rw [<a>add_zero<\\/a>]\"",
264
+ "[{\"full_name\":\"add_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[482,3],\"def_end_pos\":[482,14]}]"
265
+ ],
266
+ "state_after": "case h\u2082.h\u2081\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\nc : WithZero \u03b1\na\u271d : \u03b1\nhbc : 0 \u2264 c\n\u22a2 \u2191a\u271d \u2264 \u2191a\u271d + c",
267
+ "state_before": "case h\u2082.h\u2081\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\nc : WithZero \u03b1\na\u271d : \u03b1\nhbc : 0 \u2264 c\n\u22a2 \u2191a\u271d + 0 \u2264 \u2191a\u271d + c",
268
+ "tactic": "rw [add_zero]"
269
+ },
270
+ {
271
+ "annotated_tactic": [
272
+ "\"induction c\"",
273
+ "[]"
274
+ ],
275
+ "state_after": "case h\u2082.h\u2081.h\u2081\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\na\u271d : \u03b1\nhbc : 0 \u2264 0\n\u22a2 \u2191a\u271d \u2264 \u2191a\u271d + 0\n\ncase h\u2082.h\u2081.h\u2082\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\na\u271d\u00b9 a\u271d : \u03b1\nhbc : 0 \u2264 \u2191a\u271d\n\u22a2 \u2191a\u271d\u00b9 \u2264 \u2191a\u271d\u00b9 + \u2191a\u271d",
276
+ "state_before": "case h\u2082.h\u2081\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\nc : WithZero \u03b1\na\u271d : \u03b1\nhbc : 0 \u2264 c\n\u22a2 \u2191a\u271d \u2264 \u2191a\u271d + c",
277
+ "tactic": "induction c"
278
+ },
279
+ {
280
+ "annotated_tactic": [
281
+ "\"rw [<a>add_zero<\\/a>]\"",
282
+ "[{\"full_name\":\"add_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[482,3],\"def_end_pos\":[482,14]}]"
283
+ ],
284
+ "state_after": "no goals",
285
+ "state_before": "case h\u2082.h\u2081.h\u2081\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\na\u271d : \u03b1\nhbc : 0 \u2264 0\n\u22a2 \u2191a\u271d \u2264 \u2191a\u271d + 0",
286
+ "tactic": "rw [add_zero]"
287
+ },
288
+ {
289
+ "annotated_tactic": [
290
+ "\"rw [\\u2190 <a>coe_add<\\/a>, <a>coe_le_coe<\\/a>]\"",
291
+ "[{\"full_name\":\"WithZero.coe_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/WithOne\\/Defs.lean\",\"def_pos\":[194,3],\"def_end_pos\":[194,14]},{\"full_name\":\"WithZero.coe_le_coe\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/GroupWithZero\\/Canonical.lean\",\"def_pos\":[345,26],\"def_end_pos\":[345,36]}]"
292
+ ],
293
+ "state_after": "case h\u2082.h\u2081.h\u2082\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\na\u271d\u00b9 a\u271d : \u03b1\nhbc : 0 \u2264 \u2191a\u271d\n\u22a2 a\u271d\u00b9 \u2264 a\u271d\u00b9 + a\u271d",
294
+ "state_before": "case h\u2082.h\u2081.h\u2082\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\na\u271d\u00b9 a\u271d : \u03b1\nhbc : 0 \u2264 \u2191a\u271d\n\u22a2 \u2191a\u271d\u00b9 \u2264 \u2191a\u271d\u00b9 + \u2191a\u271d",
295
+ "tactic": "rw [\u2190 coe_add, coe_le_coe]"
296
+ },
297
+ {
298
+ "annotated_tactic": [
299
+ "\"exact <a>le_add_of_nonneg_right<\\/a> (h _)\"",
300
+ "[{\"full_name\":\"le_add_of_nonneg_right\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Unbundled\\/Basic.lean\",\"def_pos\":[391,15],\"def_end_pos\":[391,37]}]"
301
+ ],
302
+ "state_after": "no goals",
303
+ "state_before": "case h\u2082.h\u2081.h\u2082\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\na\u271d\u00b9 a\u271d : \u03b1\nhbc : 0 \u2264 \u2191a\u271d\n\u22a2 a\u271d\u00b9 \u2264 a\u271d\u00b9 + a\u271d",
304
+ "tactic": "exact le_add_of_nonneg_right (h _)"
305
+ },
306
+ {
307
+ "annotated_tactic": [
308
+ "\"rcases <a>WithBot.coe_le_iff<\\/a>.1 hbc with \\u27e8c, rfl, hbc'\\u27e9\"",
309
+ "[{\"full_name\":\"WithBot.coe_le_iff\",\"def_path\":\"Mathlib\\/Order\\/WithBot.lean\",\"def_pos\":[257,9],\"def_end_pos\":[257,19]}]"
310
+ ],
311
+ "state_after": "case h\u2082.h\u2082.intro.intro\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\na\u271d\u00b9 a\u271d c : \u03b1\nhbc' : a\u271d \u2264 c\nhbc : \u2191a\u271d \u2264 \u2191c\n\u22a2 \u2191a\u271d\u00b9 + \u2191a\u271d \u2264 \u2191a\u271d\u00b9 + \u2191c",
312
+ "state_before": "case h\u2082.h\u2082\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\nc : WithZero \u03b1\na\u271d\u00b9 a\u271d : \u03b1\nhbc : \u2191a\u271d \u2264 c\n\u22a2 \u2191a\u271d\u00b9 + \u2191a\u271d \u2264 \u2191a\u271d\u00b9 + c",
313
+ "tactic": "rcases WithBot.coe_le_iff.1 hbc with \u27e8c, rfl, hbc'\u27e9"
314
+ },
315
+ {
316
+ "annotated_tactic": [
317
+ "\"refine <a>le_trans<\\/a> ?_ (<a>le_of_eq<\\/a> <| <a>coe_add<\\/a> _ _)\"",
318
+ "[{\"full_name\":\"le_trans\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[56,9],\"def_end_pos\":[56,17]},{\"full_name\":\"le_of_eq\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[72,9],\"def_end_pos\":[72,17]},{\"full_name\":\"WithZero.coe_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/WithOne\\/Defs.lean\",\"def_pos\":[194,3],\"def_end_pos\":[194,14]}]"
319
+ ],
320
+ "state_after": "case h\u2082.h\u2082.intro.intro\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\na\u271d\u00b9 a\u271d c : \u03b1\nhbc' : a\u271d \u2264 c\nhbc : \u2191a\u271d \u2264 \u2191c\n\u22a2 \u2191a\u271d\u00b9 + \u2191a\u271d \u2264 \u2191(a\u271d\u00b9 + c)",
321
+ "state_before": "case h\u2082.h\u2082.intro.intro\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\na\u271d\u00b9 a\u271d c : \u03b1\nhbc' : a\u271d \u2264 c\nhbc : \u2191a\u271d \u2264 \u2191c\n\u22a2 \u2191a\u271d\u00b9 + \u2191a\u271d \u2264 \u2191a\u271d\u00b9 + \u2191c",
322
+ "tactic": "refine le_trans ?_ (le_of_eq <| coe_add _ _)"
323
+ },
324
+ {
325
+ "annotated_tactic": [
326
+ "\"rw [\\u2190 <a>coe_add<\\/a>, <a>coe_le_coe<\\/a>]\"",
327
+ "[{\"full_name\":\"WithZero.coe_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/WithOne\\/Defs.lean\",\"def_pos\":[194,3],\"def_end_pos\":[194,14]},{\"full_name\":\"WithZero.coe_le_coe\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/GroupWithZero\\/Canonical.lean\",\"def_pos\":[345,26],\"def_end_pos\":[345,36]}]"
328
+ ],
329
+ "state_after": "case h\u2082.h\u2082.intro.intro\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\na\u271d\u00b9 a\u271d c : \u03b1\nhbc' : a\u271d \u2264 c\nhbc : \u2191a\u271d \u2264 \u2191c\n\u22a2 a\u271d\u00b9 + a\u271d \u2264 a\u271d\u00b9 + c",
330
+ "state_before": "case h\u2082.h\u2082.intro.intro\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\na\u271d\u00b9 a\u271d c : \u03b1\nhbc' : a\u271d \u2264 c\nhbc : \u2191a\u271d \u2264 \u2191c\n\u22a2 \u2191a\u271d\u00b9 + \u2191a\u271d \u2264 \u2191(a\u271d\u00b9 + c)",
331
+ "tactic": "rw [\u2190 coe_add, coe_le_coe]"
332
+ },
333
+ {
334
+ "annotated_tactic": [
335
+ "\"exact <a>add_le_add_left<\\/a> hbc' _\"",
336
+ "[{\"full_name\":\"add_le_add_left\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Unbundled\\/Basic.lean\",\"def_pos\":[49,32],\"def_end_pos\":[49,47]}]"
337
+ ],
338
+ "state_after": "no goals",
339
+ "state_before": "case h\u2082.h\u2082.intro.intro\n\u03b1 : Type u_1\ninst\u271d\u00b2 : Preorder \u03b1\na b : \u03b1\ninst\u271d\u00b9 : AddZeroClass \u03b1\ninst\u271d : CovariantClass \u03b1 \u03b1 (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nh : \u2200 (a : \u03b1), 0 \u2264 a\na\u271d\u00b9 a\u271d c : \u03b1\nhbc' : a\u271d \u2264 c\nhbc : \u2191a\u271d \u2264 \u2191c\n\u22a2 a\u271d\u00b9 + a\u271d \u2264 a\u271d\u00b9 + c",
340
+ "tactic": "exact add_le_add_left hbc' _"
341
+ }
342
+ ],
343
+ "url": "https://github.com/leanprover-community/mathlib4"
344
+ },
345
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
346
+ },
347
+ {
348
+ "error": "theorem has no selected tactic transitions",
349
+ "full_name": "WithZero.one_le_coe",
350
+ "id": "WithZero.one_le_coe",
351
+ "reason": "import_failure",
352
+ "selection": {
353
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
354
+ "end": [
355
+ 350,
356
+ 89
357
+ ],
358
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
359
+ "full_name": "WithZero.one_le_coe",
360
+ "start": [
361
+ 350,
362
+ 1
363
+ ],
364
+ "traced_tactics": [],
365
+ "url": "https://github.com/leanprover-community/mathlib4"
366
+ },
367
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
368
+ },
369
+ {
370
+ "error": "theorem has no selected tactic transitions",
371
+ "full_name": "WithZero.one_lt_coe",
372
+ "id": "WithZero.one_lt_coe",
373
+ "reason": "import_failure",
374
+ "selection": {
375
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
376
+ "end": [
377
+ 348,
378
+ 89
379
+ ],
380
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
381
+ "full_name": "WithZero.one_lt_coe",
382
+ "start": [
383
+ 348,
384
+ 1
385
+ ],
386
+ "traced_tactics": [],
387
+ "url": "https://github.com/leanprover-community/mathlib4"
388
+ },
389
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
390
+ },
391
+ {
392
+ "error": "theorem has no selected tactic transitions",
393
+ "full_name": "WithZero.zero_eq_bot",
394
+ "id": "WithZero.zero_eq_bot",
395
+ "reason": "import_failure",
396
+ "selection": {
397
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
398
+ "end": [
399
+ 339,
400
+ 48
401
+ ],
402
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
403
+ "full_name": "WithZero.zero_eq_bot",
404
+ "start": [
405
+ 339,
406
+ 1
407
+ ],
408
+ "traced_tactics": [],
409
+ "url": "https://github.com/leanprover-community/mathlib4"
410
+ },
411
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
412
+ },
413
+ {
414
+ "error": "theorem has no selected tactic transitions",
415
+ "full_name": "WithZero.zero_le",
416
+ "id": "WithZero.zero_le",
417
+ "reason": "import_failure",
418
+ "selection": {
419
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
420
+ "end": [
421
+ 333,
422
+ 49
423
+ ],
424
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
425
+ "full_name": "WithZero.zero_le",
426
+ "start": [
427
+ 333,
428
+ 1
429
+ ],
430
+ "traced_tactics": [],
431
+ "url": "https://github.com/leanprover-community/mathlib4"
432
+ },
433
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
434
+ },
435
+ {
436
+ "error": "theorem has no selected tactic transitions",
437
+ "full_name": "WithZero.zero_lt_coe",
438
+ "id": "WithZero.zero_lt_coe",
439
+ "reason": "import_failure",
440
+ "selection": {
441
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
442
+ "end": [
443
+ 336,
444
+ 73
445
+ ],
446
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
447
+ "full_name": "WithZero.zero_lt_coe",
448
+ "start": [
449
+ 336,
450
+ 1
451
+ ],
452
+ "traced_tactics": [],
453
+ "url": "https://github.com/leanprover-community/mathlib4"
454
+ },
455
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
456
+ },
457
+ {
458
+ "error": "theorem has no selected tactic transitions",
459
+ "full_name": "inv_le_inv\u2080",
460
+ "id": "inv_le_inv\u2080",
461
+ "reason": "import_failure",
462
+ "selection": {
463
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
464
+ "end": [
465
+ 216,
466
+ 19
467
+ ],
468
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
469
+ "full_name": "inv_le_inv\u2080",
470
+ "start": [
471
+ 214,
472
+ 1
473
+ ],
474
+ "traced_tactics": [],
475
+ "url": "https://github.com/leanprover-community/mathlib4"
476
+ },
477
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
478
+ },
479
+ {
480
+ "error": "theorem has no selected tactic transitions",
481
+ "full_name": "inv_le_one\u2080",
482
+ "id": "inv_le_one\u2080",
483
+ "reason": "import_failure",
484
+ "selection": {
485
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
486
+ "end": [
487
+ 143,
488
+ 41
489
+ ],
490
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
491
+ "full_name": "inv_le_one\u2080",
492
+ "start": [
493
+ 142,
494
+ 1
495
+ ],
496
+ "traced_tactics": [],
497
+ "url": "https://github.com/leanprover-community/mathlib4"
498
+ },
499
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
500
+ },
501
+ {
502
+ "error": "theorem has no selected tactic transitions",
503
+ "full_name": "inv_lt_inv\u2080",
504
+ "id": "inv_lt_inv\u2080",
505
+ "reason": "import_failure",
506
+ "selection": {
507
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
508
+ "end": [
509
+ 211,
510
+ 19
511
+ ],
512
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
513
+ "full_name": "inv_lt_inv\u2080",
514
+ "start": [
515
+ 207,
516
+ 1
517
+ ],
518
+ "traced_tactics": [],
519
+ "url": "https://github.com/leanprover-community/mathlib4"
520
+ },
521
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
522
+ },
523
+ {
524
+ "error": "theorem has no selected tactic transitions",
525
+ "full_name": "inv_lt_one\u2080",
526
+ "id": "inv_lt_one\u2080",
527
+ "reason": "import_failure",
528
+ "selection": {
529
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
530
+ "end": [
531
+ 202,
532
+ 41
533
+ ],
534
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
535
+ "full_name": "inv_lt_one\u2080",
536
+ "start": [
537
+ 201,
538
+ 1
539
+ ],
540
+ "traced_tactics": [],
541
+ "url": "https://github.com/leanprover-community/mathlib4"
542
+ },
543
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
544
+ },
545
+ {
546
+ "error": "theorem has no selected tactic transitions",
547
+ "full_name": "le_mul_inv_iff\u2080",
548
+ "id": "le_mul_inv_iff\u2080",
549
+ "reason": "import_failure",
550
+ "selection": {
551
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
552
+ "end": [
553
+ 151,
554
+ 72
555
+ ],
556
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
557
+ "full_name": "le_mul_inv_iff\u2080",
558
+ "start": [
559
+ 150,
560
+ 1
561
+ ],
562
+ "traced_tactics": [],
563
+ "url": "https://github.com/leanprover-community/mathlib4"
564
+ },
565
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
566
+ },
567
+ {
568
+ "error": "theorem has no selected tactic transitions",
569
+ "full_name": "le_zero_iff",
570
+ "id": "le_zero_iff",
571
+ "reason": "import_failure",
572
+ "selection": {
573
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
574
+ "end": [
575
+ 89,
576
+ 55
577
+ ],
578
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
579
+ "full_name": "le_zero_iff",
580
+ "start": [
581
+ 88,
582
+ 1
583
+ ],
584
+ "traced_tactics": [],
585
+ "url": "https://github.com/leanprover-community/mathlib4"
586
+ },
587
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
588
+ },
589
+ {
590
+ "error": "theorem has no selected tactic transitions",
591
+ "full_name": "mul_inv_le_iff\u2080",
592
+ "id": "mul_inv_le_iff\u2080",
593
+ "reason": "import_failure",
594
+ "selection": {
595
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
596
+ "end": [
597
+ 155,
598
+ 86
599
+ ],
600
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
601
+ "full_name": "mul_inv_le_iff\u2080",
602
+ "start": [
603
+ 154,
604
+ 1
605
+ ],
606
+ "traced_tactics": [],
607
+ "url": "https://github.com/leanprover-community/mathlib4"
608
+ },
609
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
610
+ },
611
+ {
612
+ "error": "no internal trace for tactic 'simpa [h] using hab'",
613
+ "full_name": "mul_inv_le_of_le_mul",
614
+ "id": "mul_inv_le_of_le_mul",
615
+ "reason": "import_failure",
616
+ "selection": {
617
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
618
+ "end": [
619
+ 139,
620
+ 56
621
+ ],
622
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
623
+ "full_name": "mul_inv_le_of_le_mul",
624
+ "start": [
625
+ 136,
626
+ 1
627
+ ],
628
+ "traced_tactics": [
629
+ {
630
+ "annotated_tactic": [
631
+ "\"by_cases h : c = 0\"",
632
+ "[]"
633
+ ],
634
+ "state_after": "case pos\n\u03b1 : Type u_1\ninst\u271d : LinearOrderedCommGroupWithZero \u03b1\na b c d : \u03b1\nm n : \u2115\nhab : a \u2264 b * c\nh : c = 0\n\u22a2 a * c\u207b\u00b9 \u2264 b\n\ncase neg\n\u03b1 : Type u_1\ninst\u271d : LinearOrderedCommGroupWithZero \u03b1\na b c d : \u03b1\nm n : \u2115\nhab : a \u2264 b * c\nh : \u00acc = 0\n\u22a2 a * c\u207b\u00b9 \u2264 b",
635
+ "state_before": "\u03b1 : Type u_1\ninst\u271d : LinearOrderedCommGroupWithZero \u03b1\na b c d : \u03b1\nm n : \u2115\nhab : a \u2264 b * c\n\u22a2 a * c\u207b\u00b9 \u2264 b",
636
+ "tactic": "by_cases h : c = 0"
637
+ },
638
+ {
639
+ "annotated_tactic": [
640
+ "\"simp [h]\"",
641
+ "[]"
642
+ ],
643
+ "state_after": "no goals",
644
+ "state_before": "case pos\n\u03b1 : Type u_1\ninst\u271d : LinearOrderedCommGroupWithZero \u03b1\na b c d : \u03b1\nm n : \u2115\nhab : a \u2264 b * c\nh : c = 0\n\u22a2 a * c\u207b\u00b9 \u2264 b",
645
+ "tactic": "simp [h]"
646
+ },
647
+ {
648
+ "annotated_tactic": [
649
+ "\"exact <a>le_of_le_mul_right<\\/a> h (by simpa [h] using hab)\"",
650
+ "[{\"full_name\":\"le_of_le_mul_right\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/GroupWithZero\\/Canonical.lean\",\"def_pos\":[128,9],\"def_end_pos\":[128,27]}]"
651
+ ],
652
+ "state_after": "no goals",
653
+ "state_before": "case neg\n\u03b1 : Type u_1\ninst\u271d : LinearOrderedCommGroupWithZero \u03b1\na b c d : \u03b1\nm n : \u2115\nhab : a \u2264 b * c\nh : \u00acc = 0\n\u22a2 a * c\u207b\u00b9 \u2264 b",
654
+ "tactic": "exact le_of_le_mul_right h (by simpa [h] using hab)"
655
+ },
656
+ {
657
+ "annotated_tactic": [
658
+ "\"simpa [h] using hab\"",
659
+ "[]"
660
+ ],
661
+ "state_after": "no goals",
662
+ "state_before": "\u03b1 : Type u_1\ninst\u271d : LinearOrderedCommGroupWithZero \u03b1\na b c d : \u03b1\nm n : \u2115\nhab : a \u2264 b * c\nh : \u00acc = 0\n\u22a2 a * c\u207b\u00b9 * c \u2264 b * c",
663
+ "tactic": "simpa [h] using hab"
664
+ }
665
+ ],
666
+ "url": "https://github.com/leanprover-community/mathlib4"
667
+ },
668
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
669
+ },
670
+ {
671
+ "error": "theorem has no selected tactic transitions",
672
+ "full_name": "mul_le_mul_right\u2080",
673
+ "id": "mul_le_mul_right\u2080",
674
+ "reason": "import_failure",
675
+ "selection": {
676
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
677
+ "end": [
678
+ 227,
679
+ 61
680
+ ],
681
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
682
+ "full_name": "mul_le_mul_right\u2080",
683
+ "start": [
684
+ 226,
685
+ 1
686
+ ],
687
+ "traced_tactics": [],
688
+ "url": "https://github.com/leanprover-community/mathlib4"
689
+ },
690
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
691
+ },
692
+ {
693
+ "error": "theorem has no selected tactic transitions",
694
+ "full_name": "mul_le_one\u2080",
695
+ "id": "mul_le_one\u2080",
696
+ "reason": "import_failure",
697
+ "selection": {
698
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
699
+ "end": [
700
+ 120,
701
+ 20
702
+ ],
703
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
704
+ "full_name": "mul_le_one\u2080",
705
+ "start": [
706
+ 119,
707
+ 1
708
+ ],
709
+ "traced_tactics": [],
710
+ "url": "https://github.com/leanprover-community/mathlib4"
711
+ },
712
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
713
+ },
714
+ {
715
+ "error": "no internal trace for tactic 'rw [hc, mul_zero, zero_lt_iff]'",
716
+ "full_name": "mul_lt_mul_of_lt_of_le\u2080",
717
+ "id": "mul_lt_mul_of_lt_of_le\u2080",
718
+ "reason": "import_failure",
719
+ "selection": {
720
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
721
+ "end": [
722
+ 179,
723
+ 39
724
+ ],
725
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
726
+ "full_name": "mul_lt_mul_of_lt_of_le\u2080",
727
+ "start": [
728
+ 168,
729
+ 1
730
+ ],
731
+ "traced_tactics": [
732
+ {
733
+ "annotated_tactic": [
734
+ "\"rw [ha, <a>zero_mul<\\/a>, <a>zero_lt_iff<\\/a>]\"",
735
+ "[{\"full_name\":\"MulZeroClass.zero_mul\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Defs.lean\",\"def_pos\":[37,3],\"def_end_pos\":[37,11]},{\"full_name\":\"zero_lt_iff\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/GroupWithZero\\/Canonical.lean\",\"def_pos\":[92,9],\"def_end_pos\":[92,20]}]"
736
+ ],
737
+ "state_after": "\u03b1 : Type u_1\ninst\u271d : LinearOrderedCommGroupWithZero \u03b1\na b c d : \u03b1\nm n : \u2115\nhab : a \u2264 b\nhb : b \u2260 0\nhcd : c < d\nhd : d \u2260 0\nha : a = 0\n\u22a2 b * d \u2260 0",
738
+ "state_before": "\u03b1 : Type u_1\ninst\u271d : LinearOrderedCommGroupWithZero \u03b1\na b c d : \u03b1\nm n : \u2115\nhab : a \u2264 b\nhb : b \u2260 0\nhcd : c < d\nhd : d \u2260 0\nha : a = 0\n\u22a2 a * c < b * d",
739
+ "tactic": "rw [ha, zero_mul, zero_lt_iff]"
740
+ },
741
+ {
742
+ "annotated_tactic": [
743
+ "\"exact <a>mul_ne_zero<\\/a> hb hd\"",
744
+ "[{\"full_name\":\"mul_ne_zero\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Basic.lean\",\"def_pos\":[89,9],\"def_end_pos\":[89,20]}]"
745
+ ],
746
+ "state_after": "no goals",
747
+ "state_before": "\u03b1 : Type u_1\ninst\u271d : LinearOrderedCommGroupWithZero \u03b1\na b c d : \u03b1\nm n : \u2115\nhab : a \u2264 b\nhb : b \u2260 0\nhcd : c < d\nhd : d \u2260 0\nha : a = 0\n\u22a2 b * d \u2260 0",
748
+ "tactic": "exact mul_ne_zero hb hd"
749
+ },
750
+ {
751
+ "annotated_tactic": [
752
+ "\"rw [hc, <a>mul_zero<\\/a>, <a>zero_lt_iff<\\/a>]\"",
753
+ "[{\"full_name\":\"MulZeroClass.mul_zero\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Defs.lean\",\"def_pos\":[39,3],\"def_end_pos\":[39,11]},{\"full_name\":\"zero_lt_iff\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/GroupWithZero\\/Canonical.lean\",\"def_pos\":[92,9],\"def_end_pos\":[92,20]}]"
754
+ ],
755
+ "state_after": "\u03b1 : Type u_1\ninst\u271d : LinearOrderedCommGroupWithZero \u03b1\na b c d : \u03b1\nm n : \u2115\nhab : a \u2264 b\nhb : b \u2260 0\nhcd : c < d\nhd : d \u2260 0\nha : \u00aca = 0\nhc : c = 0\n\u22a2 b * d \u2260 0",
756
+ "state_before": "\u03b1 : Type u_1\ninst\u271d : LinearOrderedCommGroupWithZero \u03b1\na b c d : \u03b1\nm n : \u2115\nhab : a \u2264 b\nhb : b \u2260 0\nhcd : c < d\nhd : d \u2260 0\nha : \u00aca = 0\nhc : c = 0\n\u22a2 a * c < b * d",
757
+ "tactic": "rw [hc, mul_zero, zero_lt_iff]"
758
+ },
759
+ {
760
+ "annotated_tactic": [
761
+ "\"exact <a>mul_ne_zero<\\/a> hb hd\"",
762
+ "[{\"full_name\":\"mul_ne_zero\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Basic.lean\",\"def_pos\":[89,9],\"def_end_pos\":[89,20]}]"
763
+ ],
764
+ "state_after": "no goals",
765
+ "state_before": "\u03b1 : Type u_1\ninst\u271d : LinearOrderedCommGroupWithZero \u03b1\na b c d : \u03b1\nm n : \u2115\nhab : a \u2264 b\nhb : b \u2260 0\nhcd : c < d\nhd : d \u2260 0\nha : \u00aca = 0\nhc : c = 0\n\u22a2 b * d \u2260 0",
766
+ "tactic": "exact mul_ne_zero hb hd"
767
+ }
768
+ ],
769
+ "url": "https://github.com/leanprover-community/mathlib4"
770
+ },
771
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
772
+ },
773
+ {
774
+ "error": "theorem has no selected tactic transitions",
775
+ "full_name": "mul_lt_mul\u2080",
776
+ "id": "mul_lt_mul\u2080",
777
+ "reason": "import_failure",
778
+ "selection": {
779
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
780
+ "end": [
781
+ 183,
782
+ 57
783
+ ],
784
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
785
+ "full_name": "mul_lt_mul\u2080",
786
+ "start": [
787
+ 182,
788
+ 1
789
+ ],
790
+ "traced_tactics": [],
791
+ "url": "https://github.com/leanprover-community/mathlib4"
792
+ },
793
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
794
+ },
795
+ {
796
+ "error": "theorem has no selected tactic transitions",
797
+ "full_name": "ne_zero_of_lt",
798
+ "id": "ne_zero_of_lt",
799
+ "reason": "import_failure",
800
+ "selection": {
801
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
802
+ "end": [
803
+ 96,
804
+ 93
805
+ ],
806
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
807
+ "full_name": "ne_zero_of_lt",
808
+ "start": [
809
+ 96,
810
+ 1
811
+ ],
812
+ "traced_tactics": [],
813
+ "url": "https://github.com/leanprover-community/mathlib4"
814
+ },
815
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
816
+ },
817
+ {
818
+ "error": "theorem has no selected tactic transitions",
819
+ "full_name": "not_lt_zero'",
820
+ "id": "not_lt_zero'",
821
+ "reason": "import_failure",
822
+ "selection": {
823
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
824
+ "end": [
825
+ 84,
826
+ 24
827
+ ],
828
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
829
+ "full_name": "not_lt_zero'",
830
+ "start": [
831
+ 83,
832
+ 1
833
+ ],
834
+ "traced_tactics": [],
835
+ "url": "https://github.com/leanprover-community/mathlib4"
836
+ },
837
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
838
+ },
839
+ {
840
+ "error": "theorem has no selected tactic transitions",
841
+ "full_name": "one_le_inv\u2080",
842
+ "id": "one_le_inv\u2080",
843
+ "reason": "import_failure",
844
+ "selection": {
845
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
846
+ "end": [
847
+ 147,
848
+ 41
849
+ ],
850
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
851
+ "full_name": "one_le_inv\u2080",
852
+ "start": [
853
+ 146,
854
+ 1
855
+ ],
856
+ "traced_tactics": [],
857
+ "url": "https://github.com/leanprover-community/mathlib4"
858
+ },
859
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
860
+ },
861
+ {
862
+ "error": "theorem has no selected tactic transitions",
863
+ "full_name": "one_le_mul\u2080",
864
+ "id": "one_le_mul\u2080",
865
+ "reason": "import_failure",
866
+ "selection": {
867
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
868
+ "end": [
869
+ 125,
870
+ 19
871
+ ],
872
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
873
+ "full_name": "one_le_mul\u2080",
874
+ "start": [
875
+ 124,
876
+ 1
877
+ ],
878
+ "traced_tactics": [],
879
+ "url": "https://github.com/leanprover-community/mathlib4"
880
+ },
881
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
882
+ },
883
+ {
884
+ "error": "theorem has no selected tactic transitions",
885
+ "full_name": "one_lt_inv\u2080",
886
+ "id": "one_lt_inv\u2080",
887
+ "reason": "import_failure",
888
+ "selection": {
889
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
890
+ "end": [
891
+ 205,
892
+ 41
893
+ ],
894
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
895
+ "full_name": "one_lt_inv\u2080",
896
+ "start": [
897
+ 204,
898
+ 1
899
+ ],
900
+ "traced_tactics": [],
901
+ "url": "https://github.com/leanprover-community/mathlib4"
902
+ },
903
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
904
+ },
905
+ {
906
+ "error": "theorem has no selected tactic transitions",
907
+ "full_name": "zero_lt_iff",
908
+ "id": "zero_lt_iff",
909
+ "reason": "import_failure",
910
+ "selection": {
911
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
912
+ "end": [
913
+ 93,
914
+ 53
915
+ ],
916
+ "file_path": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean",
917
+ "full_name": "zero_lt_iff",
918
+ "start": [
919
+ 92,
920
+ 1
921
+ ],
922
+ "traced_tactics": [],
923
+ "url": "https://github.com/leanprover-community/mathlib4"
924
+ },
925
+ "source_file": "Mathlib/Algebra/Order/GroupWithZero/Canonical.lean"
926
+ }
927
+ ],
928
+ "input_proofs": 56,
929
+ "input_units": 2,
930
+ "proofs": 23,
931
+ "published_proofs": 23,
932
+ "published_transitions": 34,
933
+ "replay_failures": [],
934
+ "transitions": 34,
935
+ "validation_failures": [],
936
+ "validation_rejected_proofs": 0,
937
+ "zero_transition_proofs": 0
938
+ },
939
+ "shards": [
940
+ {
941
+ "path": "data/train/mathlib-000259-0000-6901e101db8a498f.parquet",
942
+ "sha256": "6901e101db8a498fbc539671071771f90f7ed25f81e07e68365df05eb220655d",
943
+ "bytes": 92769,
944
+ "rows": 31,
945
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
946
+ },
947
+ {
948
+ "path": "data/dev/mathlib-000259-0000-3490924f3af0ce75.parquet",
949
+ "sha256": "3490924f3af0ce75eb67b5aa57da630e19f826ef05886a300fbd5c303ae74f67",
950
+ "bytes": 35260,
951
+ "rows": 1,
952
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
953
+ },
954
+ {
955
+ "path": "data/internal_test/mathlib-000259-0000-ebe01b49ba402049.parquet",
956
+ "sha256": "ebe01b49ba40204917f5c838f9f625b90500b65f59bbc7116100c315274fe1f0",
957
+ "bytes": 36195,
958
+ "rows": 2,
959
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
960
+ }
961
+ ],
962
+ "proof_ids": [
963
+ "mathlib:OrderIso.mulLeft\u2080'_symm",
964
+ "mathlib:OrderIso.mulRight\u2080'_symm",
965
+ "mathlib:WithTop.LinearOrderedAddCommGroup.sub_eq_top_iff",
966
+ "mathlib:WithTop.LinearOrderedAddCommGroup.sub_top",
967
+ "mathlib:WithTop.LinearOrderedAddCommGroup.top_sub",
968
+ "mathlib:WithZero.le_max_iff",
969
+ "mathlib:WithZero.min_le_iff",
970
+ "mathlib:div_le_div_left\u2080",
971
+ "mathlib:div_le_div_right\u2080",
972
+ "mathlib:div_le_div\u2080",
973
+ "mathlib:div_le_iff\u2080",
974
+ "mathlib:inv_mul_lt_of_lt_mul\u2080",
975
+ "mathlib:le_div_iff\u2080",
976
+ "mathlib:le_mul_inv_of_mul_le",
977
+ "mathlib:le_of_le_mul_right",
978
+ "mathlib:lt_of_mul_lt_mul_of_le\u2080",
979
+ "mathlib:mul_inv_lt_of_lt_mul\u2080",
980
+ "mathlib:mul_le_mul_left\u2080",
981
+ "mathlib:mul_lt_right\u2080",
982
+ "mathlib:pow_lt_pow_right\u2080",
983
+ "mathlib:pow_lt_pow_succ",
984
+ "mathlib:pow_pos_iff",
985
+ "mathlib:zero_le'"
986
+ ],
987
+ "proof_keys": [
988
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/WithTop.lean\",null,null,\"WithTop.LinearOrderedAddCommGroup.sub_eq_top_iff\"]",
989
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/WithTop.lean\",null,null,\"WithTop.LinearOrderedAddCommGroup.sub_top\"]",
990
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/Group/WithTop.lean\",null,null,\"WithTop.LinearOrderedAddCommGroup.top_sub\"]",
991
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"OrderIso.mulLeft\u2080'_symm\"]",
992
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"OrderIso.mulRight\u2080'_symm\"]",
993
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"WithZero.le_max_iff\"]",
994
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"WithZero.min_le_iff\"]",
995
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"div_le_div_left\u2080\"]",
996
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"div_le_div_right\u2080\"]",
997
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"div_le_div\u2080\"]",
998
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"div_le_iff\u2080\"]",
999
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"inv_mul_lt_of_lt_mul\u2080\"]",
1000
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"le_div_iff\u2080\"]",
1001
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"le_mul_inv_of_mul_le\"]",
1002
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"le_of_le_mul_right\"]",
1003
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"lt_of_mul_lt_mul_of_le\u2080\"]",
1004
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"mul_inv_lt_of_lt_mul\u2080\"]",
1005
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"mul_le_mul_left\u2080\"]",
1006
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"mul_lt_right\u2080\"]",
1007
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"pow_lt_pow_right\u2080\"]",
1008
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"pow_lt_pow_succ\"]",
1009
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"pow_pos_iff\"]",
1010
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Order/GroupWithZero/Canonical.lean\",null,null,\"zero_le'\"]"
1011
+ ]
1012
+ }
manifests/batches/numina/001012.json ADDED
@@ -0,0 +1,44 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "numina/001012",
4
+ "batch_fingerprint": "c1c0205c5a5d29468af1edeb2173742f7c505e4b2e60b58055e4f84a6d712525",
5
+ "evidence": {
6
+ "batch_fingerprint": "c1c0205c5a5d29468af1edeb2173742f7c505e4b2e60b58055e4f84a6d712525",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 5,
10
+ "input_units": 5,
11
+ "proofs": 5,
12
+ "published_proofs": 5,
13
+ "published_transitions": 12,
14
+ "replay_failures": [],
15
+ "trace_mode": "bundle",
16
+ "transitions": 12,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/numina-001012-0000-6391a56a86d1e2ce.parquet",
24
+ "sha256": "6391a56a86d1e2ce62313a651a1835536dbc80465e940e06daab30b477383098",
25
+ "bytes": 185149,
26
+ "rows": 12,
27
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
28
+ }
29
+ ],
30
+ "proof_ids": [
31
+ "numina:0104d9f5-62e1-5021-b259-53959e6351ad",
32
+ "numina:2459e99b-ffc8-5e0e-9643-56d5420c64ec",
33
+ "numina:25bf8799-b96a-5c32-9988-855fcbfd9b0f",
34
+ "numina:b3e65289-8690-594b-998e-7327d8502667",
35
+ "numina:dab6f3ec-2c13-56ee-9487-4182fff81d75"
36
+ ],
37
+ "proof_keys": [
38
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005060.lean\",\"0a910a95b3a3bed9b10fca2fc74430846857e82282e9625e48fe3254c8f1ce81\",0,\"algebra_9159\"]",
39
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005061.lean\",\"3238005f08fb384fda106e298617c79eed7b0632bef91537684393ff87a13a32\",0,\"algebra_9161\"]",
40
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005062.lean\",\"005fd95f5ea92b1ec7a397b3951910295debfa4f60bdc965774aa0a674d07966\",0,\"number_theory_16177\"]",
41
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005063.lean\",\"47252de41a9a33c722f3fa3a81f735e44ce71c9bb29beeab338d32235e23a204\",0,\"algebra_15690\"]",
42
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005064.lean\",\"856128ebc6535dbf430ac6419c5044ce7582eb941a32723840b054b3656bbaab\",0,\"algebra_11048\"]"
43
+ ]
44
+ }
manifests/batches/numina/001014.json ADDED
@@ -0,0 +1,44 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "numina/001014",
4
+ "batch_fingerprint": "3cd8052308ff96dbee104d52f302cda94aaabe1922571793940bbb76c00e6e4e",
5
+ "evidence": {
6
+ "batch_fingerprint": "3cd8052308ff96dbee104d52f302cda94aaabe1922571793940bbb76c00e6e4e",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 5,
10
+ "input_units": 5,
11
+ "proofs": 5,
12
+ "published_proofs": 5,
13
+ "published_transitions": 40,
14
+ "replay_failures": [],
15
+ "trace_mode": "bundle",
16
+ "transitions": 40,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/numina-001014-0000-6bddc65e1e45d006.parquet",
24
+ "sha256": "6bddc65e1e45d006c8f50995522bf168c2e84f4a6c18f76529ac6f26d25d7ce3",
25
+ "bytes": 361986,
26
+ "rows": 40,
27
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
28
+ }
29
+ ],
30
+ "proof_ids": [
31
+ "numina:06f4633b-fa3f-5939-b9b9-b2bb6c1e42fc",
32
+ "numina:333e9400-4658-5e1c-adcf-59cac5ba1254",
33
+ "numina:a5b0aee5-441d-568e-8b72-6cd3a4f68dff",
34
+ "numina:e0f3dada-9685-5c18-b9f3-ea49d0117228",
35
+ "numina:e5e0c75a-4cbf-5aaa-a10c-6dfc221df859"
36
+ ],
37
+ "proof_keys": [
38
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005070.lean\",\"c94af7be344670e10852c8b0bd2e7f63b3ba93dd10d6940b086ab2cf839c7098\",0,\"algebra_610954\"]",
39
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005071.lean\",\"c562c984c16be355c857b43b69692a5e2774169347e6f1aacb3b57d2e01a327f\",0,\"algebra_19630\"]",
40
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005072.lean\",\"f57478e4d6a8d18578c19046c38a7db1657f176e8c17a92b9c82eff7176f32e9\",0,\"algebra_97404\"]",
41
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005073.lean\",\"54eac057db95efbc97a0282036f9f84603eae0fc77a2772d1bf2518dcdbac86f\",0,\"algebra_21516\"]",
42
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005074.lean\",\"0d035be5e8f76e3ea1cb688f06d526eb2c21f22b62dbd884380c9f2cd11bb1ff\",0,\"number_theory_607565\"]"
43
+ ]
44
+ }
manifests/batches/numina/001015.json ADDED
@@ -0,0 +1,44 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "numina/001015",
4
+ "batch_fingerprint": "a5012b70319c67a6587210ba6b3f0d148159ba775d95df0b613c7547af3dfbe8",
5
+ "evidence": {
6
+ "batch_fingerprint": "a5012b70319c67a6587210ba6b3f0d148159ba775d95df0b613c7547af3dfbe8",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 5,
10
+ "input_units": 5,
11
+ "proofs": 5,
12
+ "published_proofs": 5,
13
+ "published_transitions": 20,
14
+ "replay_failures": [],
15
+ "trace_mode": "bundle",
16
+ "transitions": 20,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/numina-001015-0000-2a3a9494a551a955.parquet",
24
+ "sha256": "2a3a9494a551a955dfd119d9516527ab61d048f48144bec2b0848e5072db58f5",
25
+ "bytes": 98272,
26
+ "rows": 20,
27
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
28
+ }
29
+ ],
30
+ "proof_ids": [
31
+ "numina:3821ed1b-c97b-502d-81ae-b713a3617f7e",
32
+ "numina:6a622317-a6fa-5d9b-bd94-56ddeda10ae5",
33
+ "numina:6b58fac4-7dc8-533b-8c43-c98e9aa8ec01",
34
+ "numina:b5ae1979-2686-5c28-8052-88ca62b0681a",
35
+ "numina:fe43003d-8486-5d09-bc3a-259c207d7e62"
36
+ ],
37
+ "proof_keys": [
38
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005075.lean\",\"eee1ccfcf98c69318a7f1fe657d1550a8eab857bc82d5623e412b971fc4e9184\",0,\"number_theory_16187\"]",
39
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005076.lean\",\"26d74e15e0746a15870f8fcf78295d4af5fcffb7e696f0dd9e2e86ffcf2351d2\",0,\"algebra_21517\"]",
40
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005077.lean\",\"da4a5fc052c8612c598ecef01cea0041678f92e39137e6be35f9378685c1f447\",0,\"algebra_1118\"]",
41
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005078.lean\",\"95ec7d1f42404ebfd89add21b3b34f0956eeee8431f6dfca2831ff4f62829454\",0,\"algebra_14177\"]",
42
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005079.lean\",\"18188cf9077dcdb9762c0e278021531a1a1982248e1788360e2131395900f1fa\",0,\"algebra_609630\"]"
43
+ ]
44
+ }
manifests/batches/numina/001016.json ADDED
@@ -0,0 +1,51 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "numina/001016",
4
+ "batch_fingerprint": "174b07da6acbd5d2439e8e3ddb8c060414578805b969f3bd2d9e75ecf1b6da91",
5
+ "evidence": {
6
+ "batch_fingerprint": "174b07da6acbd5d2439e8e3ddb8c060414578805b969f3bd2d9e75ecf1b6da91",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 5,
10
+ "input_units": 5,
11
+ "proofs": 5,
12
+ "published_proofs": 5,
13
+ "published_transitions": 15,
14
+ "replay_failures": [],
15
+ "trace_mode": "bundle",
16
+ "transitions": 15,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/numina-001016-0000-b32fe679a4d1aa97.parquet",
24
+ "sha256": "b32fe679a4d1aa97e34db22881855b01d766712b66f338c32df588d6e68dbcc9",
25
+ "bytes": 70554,
26
+ "rows": 12,
27
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
28
+ },
29
+ {
30
+ "path": "data/dev/numina-001016-0000-681c581b0870306f.parquet",
31
+ "sha256": "681c581b0870306fe32e9bda69b0c026effc3a86fdd486b2ba4774bf9473ed3e",
32
+ "bytes": 32099,
33
+ "rows": 3,
34
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
35
+ }
36
+ ],
37
+ "proof_ids": [
38
+ "numina:16db4a45-a32c-5280-ab92-656c6d483665",
39
+ "numina:3b470502-ad4e-5335-b119-70e5e6d0240d",
40
+ "numina:4229868e-2951-53f5-bd17-84e78d4cb469",
41
+ "numina:6bbfa988-f3ce-54fd-b37a-e110ed8e60cd",
42
+ "numina:cb3b726a-1d5f-5e31-b0d5-91ca3fd1af4d"
43
+ ],
44
+ "proof_keys": [
45
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005080.lean\",\"e13f082b7d6058f400cbbe3b96ec610d9f8b5a2342dfc1ba7e1d6b1733f6931e\",0,\"algebra_19634\"]",
46
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005081.lean\",\"8ab093f5ad14ed3cd2cb5dcacc34a35c3e1170c5f0862f857b16dfd71344d8cc\",0,\"algebra_14180\"]",
47
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005082.lean\",\"67298b3f872e75cdb9269e99d848fdd0e52f45cbddfd46539e7c2c299c204e9b\",0,\"algebra_14173\"]",
48
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005083.lean\",\"485ea3a6fa636c4a05927cfd44f432962093dad41f88e793a82944be980eea68\",0,\"number_theory_14406\"]",
49
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005084.lean\",\"0f171c12762e9c8ef38c323a5015833242f8d9cc0a119f2666d7c5c9768f0893\",0,\"algebra_3728\"]"
50
+ ]
51
+ }
manifests/batches/numina/001017.json ADDED
@@ -0,0 +1,51 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "numina/001017",
4
+ "batch_fingerprint": "e419874584290c438856b8bc9a1b196e1dcf2076ac7f2288f5e41147cdb2ba6d",
5
+ "evidence": {
6
+ "batch_fingerprint": "e419874584290c438856b8bc9a1b196e1dcf2076ac7f2288f5e41147cdb2ba6d",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 5,
10
+ "input_units": 5,
11
+ "proofs": 5,
12
+ "published_proofs": 5,
13
+ "published_transitions": 73,
14
+ "replay_failures": [],
15
+ "trace_mode": "bundle",
16
+ "transitions": 73,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/numina-001017-0000-b219c36f2cdc507e.parquet",
24
+ "sha256": "b219c36f2cdc507e6100d888844e89488a8cbd98a9e50b4f533715190f021158",
25
+ "bytes": 342715,
26
+ "rows": 59,
27
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
28
+ },
29
+ {
30
+ "path": "data/internal_test/numina-001017-0000-31e27ed5961c3152.parquet",
31
+ "sha256": "31e27ed5961c31528eb5f94414c43b7a08c93e60a6db9ceb388d673643f1ccf5",
32
+ "bytes": 58124,
33
+ "rows": 14,
34
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
35
+ }
36
+ ],
37
+ "proof_ids": [
38
+ "numina:17f713f8-d058-53d6-a940-2cb1f232b9b6",
39
+ "numina:603774fd-1648-5781-b0b6-b2f5a4b1872a",
40
+ "numina:78f0551b-7969-5380-845e-6314f8a722cc",
41
+ "numina:e560492a-424e-5655-91a3-0af94c83b3a4",
42
+ "numina:f2aac9a8-4c53-5d02-865a-d173797712f5"
43
+ ],
44
+ "proof_keys": [
45
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005085.lean\",\"284786c3c8d984640b0f865216789c573a37965c420794f3f88a6ca830035b64\",0,\"algebra_21524\"]",
46
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005086.lean\",\"497b5595a8b6ab6818d3480c9c35b112044b27bef0c2b75b7bd38255375bf62d\",0,\"number_theory_162574\"]",
47
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005087.lean\",\"00a6fede3a518995cbaf7308d366ed9b31532dcea2f0576cc4f799e0bfffec96\",0,\"algebra_20048\"]",
48
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005088.lean\",\"9bcb34f805cd6e3065d5cf95bdbb7962f36456d85735985fd9f3f5c09229fba3\",0,\"algebra_18843\"]",
49
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005089.lean\",\"9fe0e28c3de6a521bba26c6b5bee8d94e68bf1c1e4c80461d0e512564b7f4460\",0,\"inequalities_604545\"]"
50
+ ]
51
+ }
manifests/batches/numina/001018.json ADDED
@@ -0,0 +1,51 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "numina/001018",
4
+ "batch_fingerprint": "178fef56efde813e506b831313d0fe7e83a9b5f959643f1ab745dda21a973877",
5
+ "evidence": {
6
+ "batch_fingerprint": "178fef56efde813e506b831313d0fe7e83a9b5f959643f1ab745dda21a973877",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 5,
10
+ "input_units": 5,
11
+ "proofs": 5,
12
+ "published_proofs": 5,
13
+ "published_transitions": 31,
14
+ "replay_failures": [],
15
+ "trace_mode": "bundle",
16
+ "transitions": 31,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/numina-001018-0000-527a37934e314120.parquet",
24
+ "sha256": "527a37934e314120770f086f055cfd282cca8c30db52f65e6bd5ef9a67653e36",
25
+ "bytes": 109004,
26
+ "rows": 21,
27
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
28
+ },
29
+ {
30
+ "path": "data/internal_test/numina-001018-0000-0d6e3d305fdb6732.parquet",
31
+ "sha256": "0d6e3d305fdb6732a038329432e572758558b44a8d8b53cbb1c5be57e2bd32d0",
32
+ "bytes": 57697,
33
+ "rows": 10,
34
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
35
+ }
36
+ ],
37
+ "proof_ids": [
38
+ "numina:17b9aa80-6839-5125-9ae4-fb48619b857b",
39
+ "numina:d2c009c2-4d70-54df-9e36-55c8ec1a574b",
40
+ "numina:e6a026be-4e8e-5897-a821-57470b7d551e",
41
+ "numina:e6cb680a-5768-58fb-b33e-5e6a961b9e64",
42
+ "numina:ff284757-4b24-5a26-900e-c9352f9b0713"
43
+ ],
44
+ "proof_keys": [
45
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005090.lean\",\"038c03f90a39f26d1ef9ebbcc92f21b02b06a4c14bcf4f42f235f55ef481a0df\",0,\"number_theory_11854\"]",
46
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005091.lean\",\"0d58fc46a87db223a02b921543e154e822b121f0f03833c888a9ed2bda45f288\",0,\"number_theory_17146\"]",
47
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005092.lean\",\"4664364129a1a417833c75b1955ca4c5ae346780649f7e8a91e6d47c10a1c4e8\",0,\"algebra_93930\"]",
48
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005093.lean\",\"16238f1a8ba52c094ea861b046dbca8caa447a7864facf69d7b5dc03dcad1099\",0,\"number_theory_275817\"]",
49
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005094.lean\",\"50faed388f4a4893c62a8257114e875f993d84a9ac11df9266ef74c0a886c9be\",0,\"algebra_20266\"]"
50
+ ]
51
+ }
manifests/batches/numina/001019.json ADDED
@@ -0,0 +1,51 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "numina/001019",
4
+ "batch_fingerprint": "d695bff3ae7893b6589b91087acfc6f39774dd275e3ce4fe83ba562e2d552e8d",
5
+ "evidence": {
6
+ "batch_fingerprint": "d695bff3ae7893b6589b91087acfc6f39774dd275e3ce4fe83ba562e2d552e8d",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 5,
10
+ "input_units": 5,
11
+ "proofs": 5,
12
+ "published_proofs": 5,
13
+ "published_transitions": 28,
14
+ "replay_failures": [],
15
+ "trace_mode": "bundle",
16
+ "transitions": 28,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/numina-001019-0000-b99665ba1665d7db.parquet",
24
+ "sha256": "b99665ba1665d7dbefb146d8edd092c5cc816be5bc3168566de8c918b69b85da",
25
+ "bytes": 184718,
26
+ "rows": 22,
27
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
28
+ },
29
+ {
30
+ "path": "data/internal_test/numina-001019-0000-d2f669e6badf817a.parquet",
31
+ "sha256": "d2f669e6badf817a4b51baa712e72962e63d1c7566ff5d4df3d79f04cc40cdef",
32
+ "bytes": 41301,
33
+ "rows": 6,
34
+ "revision": "9aefeacc54d041e099f52cde0715b5bc1f06aed9"
35
+ }
36
+ ],
37
+ "proof_ids": [
38
+ "numina:06976f82-7a90-55c4-aac2-4dcc41f17244",
39
+ "numina:1a0125f9-a959-5da9-9955-66acab7b590a",
40
+ "numina:5528b527-a1bf-576d-9f26-3339bbad05f5",
41
+ "numina:9006e4ed-ecda-5262-99b4-960f0d853c57",
42
+ "numina:e10b49c2-bf22-5025-bdc9-969d2fadb63f"
43
+ ],
44
+ "proof_keys": [
45
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005095.lean\",\"5feead8093cb796b2889a0b793a7e868459918654ff6d7911f2f7021ac131e14\",0,\"algebra_9037\"]",
46
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005096.lean\",\"dc09f37e45afc9792dd87b9d29a340e9acddeba498f077b30a01544c7c44ad2e\",0,\"AMC_Number_Theory_1188.lean\"]",
47
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005097.lean\",\"4cc1a56563a742bf485a439296597a0d4334b41c396e09b1f5ea6fe587a962cf\",0,\"algebra_13460\"]",
48
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005098.lean\",\"59f9d96667a721a6ed3fe89fa35cd06645b506fdbc774ff4d292be35da42c3b9\",0,\"inequalities_604938\"]",
49
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005099.lean\",\"680d0f4638794b4a8e5306263d2387c7b6f032d477e80070302f8372e1f1fe3b\",0,\"algebra_10732\"]"
50
+ ]
51
+ }