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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
8b25d5b
·
verified ·
1 Parent(s): af86e21

Record 21 verified HPC batch manifests

Browse files
Files changed (21) hide show
  1. manifests/batches/deepseek/000195.json +148 -0
  2. manifests/batches/deepseek/000197.json +148 -0
  3. manifests/batches/deepseek/000198.json +148 -0
  4. manifests/batches/deepseek/000199.json +148 -0
  5. manifests/batches/deepseek/000201.json +141 -0
  6. manifests/batches/mathlib/000124.json +651 -0
  7. manifests/batches/mathlib/000125.json +921 -0
  8. manifests/batches/mathlib/000126.json +1241 -0
  9. manifests/batches/mathlib/000127.json +0 -0
  10. manifests/batches/mathlib/000128.json +332 -0
  11. manifests/batches/mathlib/000129.json +367 -0
  12. manifests/batches/mathlib/000130.json +0 -0
  13. manifests/batches/mathlib/000131.json +0 -0
  14. manifests/batches/numina/000884.json +44 -0
  15. manifests/batches/numina/000885.json +51 -0
  16. manifests/batches/numina/000886.json +51 -0
  17. manifests/batches/numina/000887.json +58 -0
  18. manifests/batches/numina/000888.json +58 -0
  19. manifests/batches/numina/000889.json +44 -0
  20. manifests/batches/numina/000890.json +44 -0
  21. manifests/batches/numina/000891.json +44 -0
manifests/batches/deepseek/000195.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "deepseek/000195",
4
+ "batch_fingerprint": "16b4c207142c1dac76a7a7d7d94d52a154081a51541c3e6e6b012c2dc7df786f",
5
+ "evidence": {
6
+ "batch_fingerprint": "16b4c207142c1dac76a7a7d7d94d52a154081a51541c3e6e6b012c2dc7df786f",
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-000195-0000-865a13164d5beb06.parquet",
24
+ "sha256": "865a13164d5beb06fe4dd0fe87404e26b1125625f7fcbd458ffb51d4a01a4c0a",
25
+ "bytes": 356015,
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+ "rows": 99,
27
+ "revision": "af86e21b60c160a59e94c440a8a9eafd00a59b94"
28
+ },
29
+ {
30
+ "path": "data/dev/deepseek-000195-0000-536f49fcecba7b59.parquet",
31
+ "sha256": "536f49fcecba7b596cd547636fa88cc2a24da2550c07569b7c7881ae3ee77c3b",
32
+ "bytes": 42400,
33
+ "rows": 5,
34
+ "revision": "af86e21b60c160a59e94c440a8a9eafd00a59b94"
35
+ },
36
+ {
37
+ "path": "data/internal_test/deepseek-000195-0000-31e49a64e6df1b8c.parquet",
38
+ "sha256": "31e49a64e6df1b8c21332a6895aeea466cbefa15ad0cef7be3b3a104abb0715f",
39
+ "bytes": 62773,
40
+ "rows": 13,
41
+ "revision": "af86e21b60c160a59e94c440a8a9eafd00a59b94"
42
+ }
43
+ ],
44
+ "proof_ids": [
45
+ "deepseek:thm_9787",
46
+ "deepseek:thm_9788",
47
+ "deepseek:thm_9789",
48
+ "deepseek:thm_9790",
49
+ "deepseek:thm_9791",
50
+ "deepseek:thm_9792",
51
+ "deepseek:thm_9793",
52
+ "deepseek:thm_9794",
53
+ "deepseek:thm_9795",
54
+ "deepseek:thm_9796",
55
+ "deepseek:thm_9797",
56
+ "deepseek:thm_9798",
57
+ "deepseek:thm_9799",
58
+ "deepseek:thm_9800",
59
+ "deepseek:thm_9801",
60
+ "deepseek:thm_9802",
61
+ "deepseek:thm_9803",
62
+ "deepseek:thm_9804",
63
+ "deepseek:thm_9805",
64
+ "deepseek:thm_9806",
65
+ "deepseek:thm_9807",
66
+ "deepseek:thm_9808",
67
+ "deepseek:thm_9809",
68
+ "deepseek:thm_9810",
69
+ "deepseek:thm_9811",
70
+ "deepseek:thm_9812",
71
+ "deepseek:thm_9813",
72
+ "deepseek:thm_9814",
73
+ "deepseek:thm_9815",
74
+ "deepseek:thm_9816",
75
+ "deepseek:thm_9817",
76
+ "deepseek:thm_9818",
77
+ "deepseek:thm_9819",
78
+ "deepseek:thm_9820",
79
+ "deepseek:thm_9821",
80
+ "deepseek:thm_9822",
81
+ "deepseek:thm_9823",
82
+ "deepseek:thm_9824",
83
+ "deepseek:thm_9825",
84
+ "deepseek:thm_9826",
85
+ "deepseek:thm_9827",
86
+ "deepseek:thm_9828",
87
+ "deepseek:thm_9829",
88
+ "deepseek:thm_9830",
89
+ "deepseek:thm_9831",
90
+ "deepseek:thm_9832",
91
+ "deepseek:thm_9833",
92
+ "deepseek:thm_9834",
93
+ "deepseek:thm_9835",
94
+ "deepseek:thm_9836"
95
+ ],
96
+ "proof_keys": [
97
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009750.lean\",\"6fbc5a7e6577608aca6c45327e492766f8ead5d90d0b4102ecc6e22a97bb8eeb\",0,\"thm_9787\"]",
98
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009751.lean\",\"dfd9d1179754d1dca512be0fb76620dfec4ca23cec0dc1d9da447dfc3581582a\",0,\"thm_9788\"]",
99
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009752.lean\",\"094701e4cbfa188ac4c1264c08ac09b9b1edda184e219cbeb612d6285d19e50c\",0,\"thm_9789\"]",
100
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009753.lean\",\"e7300413c3007020bb80f0dc1386bda924370c58a5d7d1f69f98ef991e6b8565\",0,\"thm_9790\"]",
101
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009754.lean\",\"668990f163e0e6fc5e6d8685a4841c32e0d5d194cdc57809ad9d53bad310276f\",0,\"thm_9791\"]",
102
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009755.lean\",\"b6d68a04addb1f59412654da92edddf26ad18d0279c9c120bea59adaef2af281\",0,\"thm_9792\"]",
103
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009756.lean\",\"1963414c97d3b60f858dafe5bfc49f5e205388ce8fdefd3d594f795c9a71d35c\",0,\"thm_9793\"]",
104
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009757.lean\",\"dc5a330c2225fc56f39c5034445a158cbaac808d1d6586cfb8565d862a6b91a8\",0,\"thm_9794\"]",
105
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009758.lean\",\"9404ec399b2d41c167c5fdc9b0f67db8f6f4e2ea33bb5d9c39a343283496f980\",0,\"thm_9795\"]",
106
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009759.lean\",\"82eafc3b851f010ef56b4d40e90e4676726fee3866dae988ea72d5a47c5a093b\",0,\"thm_9796\"]",
107
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009760.lean\",\"e08b8e6a1092017252f3f926b0cdb2443a24ee985a2f076294a5eed2d07a8c4d\",0,\"thm_9797\"]",
108
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009761.lean\",\"c797ebe53e9b36342617196156d721fd34c15f14f511360bfb1037c1c3aac853\",0,\"thm_9798\"]",
109
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009762.lean\",\"672ce1dc30dd79ad79d8495a8f0663b97358c0a3166f5125a92dd34bd5ff6c8b\",0,\"thm_9799\"]",
110
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009763.lean\",\"a668c6bf701bd823ac98c676b94ec78208f39188107156bac581600dd796dfc8\",0,\"thm_9800\"]",
111
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009764.lean\",\"3bbb63d35733bb22e8a748bb19ba4536467bce21aa358518b2c993e8f071568e\",0,\"thm_9801\"]",
112
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009765.lean\",\"96d13e5c2a6d9e63619ea314e4b3cac8ea01fd00941e420c3c8cdc4212da72c0\",0,\"thm_9802\"]",
113
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009766.lean\",\"7119f3a1d69bab89a9282ddf5a13ec2e6c885089c1548740b8d22bb143e34f9e\",0,\"thm_9803\"]",
114
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009767.lean\",\"4c695d0ca396a5d872ed468eef0334d84d47bcddf5e10137fce7b32e6c94d43d\",0,\"thm_9804\"]",
115
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009768.lean\",\"21b5e2f6d106c83320f612c06b000615879148e34544df23b4f4c1ee5ca904a3\",0,\"thm_9805\"]",
116
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009769.lean\",\"6883bc59028e0fdbeaa5c4f1fd5c239f020ce9f43f0d9f66d9f194663eaa6263\",0,\"thm_9806\"]",
117
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009770.lean\",\"029a4bfb6dc3ba55f2a8a4be52c9347ee1e8d6c050e3007d83cf05a5269b354e\",0,\"thm_9807\"]",
118
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009771.lean\",\"4deb1d7f523489c4efb78b0ab334f604d88c41c56d8f4fdbda15cf7406288063\",0,\"thm_9808\"]",
119
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009772.lean\",\"ec4f90e586389b993eb679dcbadb1f3be42d2a33bd0f94bcb7671039f37a60db\",0,\"thm_9809\"]",
120
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009773.lean\",\"3112f486c2308663fa6467e3b89461bc925a29ada3e16de8c0cf8d3e97951f21\",0,\"thm_9810\"]",
121
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009774.lean\",\"cc43a6853c7e30bcf5e428ae1a5b1ef91f65834028d76804527504fc70a7924a\",0,\"thm_9811\"]",
122
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009775.lean\",\"083c6658b3e5c75155bf58b843a50a094f0a12a8fc23adc92493b126c67297ef\",0,\"thm_9812\"]",
123
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009776.lean\",\"5da73730d7aa746bcb8565313fe4c055d492ee35ce67099f604f0435d1d701c4\",0,\"thm_9813\"]",
124
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009777.lean\",\"b3275a0b590a36fd25b1d5c38c9a0ab94563f35b39c6f10b976c15a5467c7296\",0,\"thm_9814\"]",
125
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009778.lean\",\"3137609c62bacb2e978f18df7ebedb7771df27cff5f3f4fd3d6f00fde4d66fa0\",0,\"thm_9815\"]",
126
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009779.lean\",\"12b8b4f458301a8a663be1d764593281b2d50197fdffabbc97feafec6d049af4\",0,\"thm_9816\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009780.lean\",\"940f561a9b9aef5be5dcba4fa2338620d182de86edee2c8c1d8abc9607bff5f8\",0,\"thm_9817\"]",
128
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009781.lean\",\"405ab2c8548d45d67e07db2ea372131bd4770ec15eb4f87e0dc3d161d8e6b4ae\",0,\"thm_9818\"]",
129
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009782.lean\",\"f080365c7806557a33de4e698a15cadd27c0f76d73f784cde7f51485c8182783\",0,\"thm_9819\"]",
130
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009783.lean\",\"908fee7274b252e451cc1da0b1de0092a68e142312afc0ae3b761f0df03541da\",0,\"thm_9820\"]",
131
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009784.lean\",\"7565e0f66fc3f9ea8f16bbe647feb2be2ccccd0afd93c5142c3b19ece039ec07\",0,\"thm_9821\"]",
132
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009785.lean\",\"4549309d3c44499eda2583e3b23359da37d21a630f56d5d0cd8b0c99f78c33bd\",0,\"thm_9822\"]",
133
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009786.lean\",\"b8b443d3c1689357c56d03d075dcdd295d863d30b43d6114f6619d24d79a4282\",0,\"thm_9823\"]",
134
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009787.lean\",\"befaf93246022b35a6862bf58f6954bd7cbeb6a965673a114ec97de45879f61c\",0,\"thm_9824\"]",
135
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009788.lean\",\"4ce20dfdd2f268493ee875fa67afc5c54c8137e4ff70643c5af412c6f7a3c45e\",0,\"thm_9825\"]",
136
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009789.lean\",\"ad1bbc2fde2344bcff9f0b73ab3be00dbfb160b2c61c1137be2dbc44b316bb8e\",0,\"thm_9826\"]",
137
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009790.lean\",\"e971bc140b4b281530e105d8885fa7a8ffb979e18dd19682a73d90db20ae2f00\",0,\"thm_9827\"]",
138
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009791.lean\",\"38db08e78ac6aa51df1ff62bd12cfd6395ef8e8f9238155e227b086fadddac46\",0,\"thm_9828\"]",
139
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009792.lean\",\"b18dd44a74788002358c2a11956920ecfb75d47c91bca4ab9dccbe4868bc6348\",0,\"thm_9829\"]",
140
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009793.lean\",\"c1957c66bc20f972dac11d475afe79952a38a2b0ff19edba28abf67f2ed6db9c\",0,\"thm_9830\"]",
141
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009794.lean\",\"00982135e3bc1478fb2aac99ca030ffb1225101eeb2108c10b03ceab5af22c2b\",0,\"thm_9831\"]",
142
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009795.lean\",\"af7f56d94f3621670c5fb64d5a9a4bbed4d5ab54ab187c26636bfb316413ec11\",0,\"thm_9832\"]",
143
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009796.lean\",\"7c69e23d04d8ad89c4093eb1957ec48202358c48b673d80efd3c3745af27757d\",0,\"thm_9833\"]",
144
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009797.lean\",\"d20c636fbc5c355693e87e510205e4dbbb740fe1d40a52b357998e5a2afb08e2\",0,\"thm_9834\"]",
145
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009798.lean\",\"603aa8055a4d3c01c304473c8a337400ab6af577deb38d17df32b84ae80492f5\",0,\"thm_9835\"]",
146
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009799.lean\",\"6ddcae9f758d3db3e88fd2b3d6d3b571ff2870a3eb8d52f724828b222fccc474\",0,\"thm_9836\"]"
147
+ ]
148
+ }
manifests/batches/deepseek/000197.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "deepseek/000197",
4
+ "batch_fingerprint": "3b2e1bef660f6fa6e70dd69a71f14c1133828eefdbfc2e98d88e28ebf5a05118",
5
+ "evidence": {
6
+ "batch_fingerprint": "3b2e1bef660f6fa6e70dd69a71f14c1133828eefdbfc2e98d88e28ebf5a05118",
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-000197-0000-96e320f228210fdb.parquet",
24
+ "sha256": "96e320f228210fdb9d9f86c8ad0ad9b544e2d98eb5f18f79fdf97196fe6eaeb2",
25
+ "bytes": 344969,
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+ "rows": 98,
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+ "revision": "af86e21b60c160a59e94c440a8a9eafd00a59b94"
28
+ },
29
+ {
30
+ "path": "data/dev/deepseek-000197-0000-739f9f623b1bde1f.parquet",
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+ "sha256": "739f9f623b1bde1f5c50e9e1108691a4af0c19af2ec6d31cd037a2c811667f6f",
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+ "bytes": 42248,
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+ "rows": 6,
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+ "revision": "af86e21b60c160a59e94c440a8a9eafd00a59b94"
35
+ },
36
+ {
37
+ "path": "data/internal_test/deepseek-000197-0000-31842effbb8ded45.parquet",
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manifests/batches/deepseek/000198.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ ]
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+ }
manifests/batches/deepseek/000199.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ {
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147
+ ]
148
+ }
manifests/batches/deepseek/000201.json ADDED
@@ -0,0 +1,141 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ {
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+ "batch_fingerprint": "33da969d8bf0904a49da3f049b3fb5afe6ae245c2f93d9b7d357a68d4b8ce411",
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+ "contamination_matches": [],
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+ "replay_failures": [],
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+ "validation_failures": [],
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431
+ "reason": "import_failure",
432
+ "selection": {
433
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
434
+ "end": [
435
+ 102,
436
+ 60
437
+ ],
438
+ "file_path": "Mathlib/Algebra/Group/Nat.lean",
439
+ "full_name": "Nat.two_dvd_ne_zero",
440
+ "start": [
441
+ 101,
442
+ 1
443
+ ],
444
+ "traced_tactics": [],
445
+ "url": "https://github.com/leanprover-community/mathlib4"
446
+ },
447
+ "source_file": "Mathlib/Algebra/Group/Nat.lean"
448
+ },
449
+ {
450
+ "error": "theorem has no selected tactic transitions",
451
+ "full_name": "Nat.two_mul_div_two_of_even",
452
+ "id": "Nat.two_mul_div_two_of_even",
453
+ "reason": "import_failure",
454
+ "selection": {
455
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
456
+ "end": [
457
+ 159,
458
+ 63
459
+ ],
460
+ "file_path": "Mathlib/Algebra/Group/Nat.lean",
461
+ "full_name": "Nat.two_mul_div_two_of_even",
462
+ "start": [
463
+ 158,
464
+ 1
465
+ ],
466
+ "traced_tactics": [],
467
+ "url": "https://github.com/leanprover-community/mathlib4"
468
+ },
469
+ "source_file": "Mathlib/Algebra/Group/Nat.lean"
470
+ },
471
+ {
472
+ "error": "theorem has no selected tactic transitions",
473
+ "full_name": "Nat.two_not_dvd_two_mul_sub_one",
474
+ "id": "Nat.two_not_dvd_two_mul_sub_one",
475
+ "reason": "import_failure",
476
+ "selection": {
477
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
478
+ "end": [
479
+ 126,
480
+ 46
481
+ ],
482
+ "file_path": "Mathlib/Algebra/Group/Nat.lean",
483
+ "full_name": "Nat.two_not_dvd_two_mul_sub_one",
484
+ "start": [
485
+ 125,
486
+ 1
487
+ ],
488
+ "traced_tactics": [],
489
+ "url": "https://github.com/leanprover-community/mathlib4"
490
+ },
491
+ "source_file": "Mathlib/Algebra/Group/Nat.lean"
492
+ },
493
+ {
494
+ "error": "theorem has no selected tactic transitions",
495
+ "full_name": "Nat.units_eq_one",
496
+ "id": "Nat.units_eq_one",
497
+ "reason": "import_failure",
498
+ "selection": {
499
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
500
+ "end": [
501
+ 174,
502
+ 98
503
+ ],
504
+ "file_path": "Mathlib/Algebra/Group/Nat.lean",
505
+ "full_name": "Nat.units_eq_one",
506
+ "start": [
507
+ 174,
508
+ 1
509
+ ],
510
+ "traced_tactics": [],
511
+ "url": "https://github.com/leanprover-community/mathlib4"
512
+ },
513
+ "source_file": "Mathlib/Algebra/Group/Nat.lean"
514
+ }
515
+ ],
516
+ "input_proofs": 50,
517
+ "input_units": 2,
518
+ "proofs": 27,
519
+ "published_proofs": 26,
520
+ "published_transitions": 33,
521
+ "replay_failures": [],
522
+ "transitions": 35,
523
+ "validation_failures": [
524
+ {
525
+ "errors": [
526
+ "internal transition boundary mismatch"
527
+ ],
528
+ "file_path": "Mathlib/Algebra/Group/Nat.lean",
529
+ "proof_id": "mathlib:Nat.even_iff",
530
+ "provenance": {
531
+ "selection": {
532
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
533
+ "end": [
534
+ 88,
535
+ 78
536
+ ],
537
+ "file_path": "Mathlib/Algebra/Group/Nat.lean",
538
+ "full_name": "Nat.even_iff",
539
+ "start": [
540
+ 86,
541
+ 1
542
+ ],
543
+ "traced_tactics": [
544
+ {
545
+ "annotated_tactic": [
546
+ "\"simp [\\u2190 <a>Nat.two_mul<\\/a>, hm]\"",
547
+ "[{\"full_name\":\"Nat.two_mul\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[254,19],\"def_end_pos\":[254,26]}]"
548
+ ],
549
+ "state_after": "no goals",
550
+ "state_before": "m\u271d n : \u2115\nx\u271d : Even n\nm : \u2115\nhm : n = m + m\n\u22a2 n % 2 = 0",
551
+ "tactic": "simp [\u2190 Nat.two_mul, hm]"
552
+ },
553
+ {
554
+ "annotated_tactic": [
555
+ "\"simp [\\u2190 <a>Nat.two_mul<\\/a>, h]\"",
556
+ "[{\"full_name\":\"Nat.two_mul\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[254,19],\"def_end_pos\":[254,26]}]"
557
+ ],
558
+ "state_after": "no goals",
559
+ "state_before": "m n : \u2115\nh : n % 2 = 0\n\u22a2 n % 2 + 2 * (n / 2) = n / 2 + n / 2",
560
+ "tactic": "simp [\u2190 Nat.two_mul, h]"
561
+ }
562
+ ],
563
+ "url": "https://github.com/leanprover-community/mathlib4"
564
+ }
565
+ },
566
+ "theorem_name": "Nat.even_iff"
567
+ }
568
+ ],
569
+ "validation_rejected_proofs": 1,
570
+ "zero_transition_proofs": 0
571
+ },
572
+ "shards": [
573
+ {
574
+ "path": "data/train/mathlib-000124-0000-b1996e3042510c47.parquet",
575
+ "sha256": "b1996e3042510c47fc2fd02eea64040569194e3c403e48b3fefa79f56a3bfdd9",
576
+ "bytes": 65581,
577
+ "rows": 26,
578
+ "revision": "af86e21b60c160a59e94c440a8a9eafd00a59b94"
579
+ },
580
+ {
581
+ "path": "data/dev/mathlib-000124-0000-cdb32930c88bb4bf.parquet",
582
+ "sha256": "cdb32930c88bb4bf1672a843ac827d13336003bee160044133157183b391cdac",
583
+ "bytes": 27330,
584
+ "rows": 1,
585
+ "revision": "af86e21b60c160a59e94c440a8a9eafd00a59b94"
586
+ },
587
+ {
588
+ "path": "data/internal_test/mathlib-000124-0000-64df095db45c9601.parquet",
589
+ "sha256": "64df095db45c9601b72bdb5436a20deab4c4a7c8ae15a81179b4544010dbf903",
590
+ "bytes": 36589,
591
+ "rows": 6,
592
+ "revision": "af86e21b60c160a59e94c440a8a9eafd00a59b94"
593
+ }
594
+ ],
595
+ "proof_ids": [
596
+ "mathlib:Invertible.congr",
597
+ "mathlib:Nat.even_add",
598
+ "mathlib:Nat.even_add_one",
599
+ "mathlib:Nat.even_mul",
600
+ "mathlib:Nat.even_mul_succ_self",
601
+ "mathlib:Nat.even_pow",
602
+ "mathlib:Nat.even_sub",
603
+ "mathlib:Nat.isUnit_iff",
604
+ "mathlib:Nat.not_even_iff",
605
+ "mathlib:Nat.not_even_one",
606
+ "mathlib:Nat.succ_mod_two_eq_one_iff",
607
+ "mathlib:Nat.succ_mod_two_eq_zero_iff",
608
+ "mathlib:Nat.two_not_dvd_two_mul_add_one",
609
+ "mathlib:invOf_mul",
610
+ "mathlib:invOf_mul_eq_iff_eq_mul_left",
611
+ "mathlib:invOf_mul_self_assoc",
612
+ "mathlib:invOf_mul_self_assoc'",
613
+ "mathlib:invertible_unique",
614
+ "mathlib:mul_invOf_eq_iff_eq_mul_right",
615
+ "mathlib:mul_invOf_mul_self_cancel'",
616
+ "mathlib:mul_invOf_self_assoc",
617
+ "mathlib:mul_invOf_self_assoc'",
618
+ "mathlib:mul_left_eq_iff_eq_invOf_mul",
619
+ "mathlib:mul_mul_invOf_self_cancel",
620
+ "mathlib:mul_mul_invOf_self_cancel'",
621
+ "mathlib:mul_right_eq_iff_eq_mul_invOf"
622
+ ],
623
+ "proof_keys": [
624
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Invertible/Defs.lean\",null,null,\"Invertible.congr\"]",
625
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Invertible/Defs.lean\",null,null,\"invOf_mul\"]",
626
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Invertible/Defs.lean\",null,null,\"invOf_mul_eq_iff_eq_mul_left\"]",
627
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Invertible/Defs.lean\",null,null,\"invOf_mul_self_assoc\"]",
628
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Invertible/Defs.lean\",null,null,\"invOf_mul_self_assoc'\"]",
629
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Invertible/Defs.lean\",null,null,\"invertible_unique\"]",
630
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Invertible/Defs.lean\",null,null,\"mul_invOf_eq_iff_eq_mul_right\"]",
631
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Invertible/Defs.lean\",null,null,\"mul_invOf_mul_self_cancel'\"]",
632
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Invertible/Defs.lean\",null,null,\"mul_invOf_self_assoc\"]",
633
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Invertible/Defs.lean\",null,null,\"mul_invOf_self_assoc'\"]",
634
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Invertible/Defs.lean\",null,null,\"mul_left_eq_iff_eq_invOf_mul\"]",
635
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Invertible/Defs.lean\",null,null,\"mul_mul_invOf_self_cancel\"]",
636
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Invertible/Defs.lean\",null,null,\"mul_mul_invOf_self_cancel'\"]",
637
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Invertible/Defs.lean\",null,null,\"mul_right_eq_iff_eq_mul_invOf\"]",
638
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Nat.lean\",null,null,\"Nat.even_add\"]",
639
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Nat.lean\",null,null,\"Nat.even_add_one\"]",
640
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Nat.lean\",null,null,\"Nat.even_mul\"]",
641
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Nat.lean\",null,null,\"Nat.even_mul_succ_self\"]",
642
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Nat.lean\",null,null,\"Nat.even_pow\"]",
643
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Nat.lean\",null,null,\"Nat.even_sub\"]",
644
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Nat.lean\",null,null,\"Nat.isUnit_iff\"]",
645
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Nat.lean\",null,null,\"Nat.not_even_iff\"]",
646
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Nat.lean\",null,null,\"Nat.not_even_one\"]",
647
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Nat.lean\",null,null,\"Nat.succ_mod_two_eq_one_iff\"]",
648
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Nat.lean\",null,null,\"Nat.succ_mod_two_eq_zero_iff\"]",
649
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Nat.lean\",null,null,\"Nat.two_not_dvd_two_mul_add_one\"]"
650
+ ]
651
+ }
manifests/batches/mathlib/000125.json ADDED
@@ -0,0 +1,921 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000125",
4
+ "batch_fingerprint": "a74797aac0088730a3173f5618dc89ff72a0b455ef7a91ad0821633fa22aa558",
5
+ "evidence": {
6
+ "batch_fingerprint": "a74797aac0088730a3173f5618dc89ff72a0b455ef7a91ad0821633fa22aa558",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "no internal trace for tactic 'simp only [npow_zero, one_mul]'",
11
+ "full_name": "neg_npow_assoc",
12
+ "id": "neg_npow_assoc",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 91,
18
+ 28
19
+ ],
20
+ "file_path": "Mathlib/Algebra/Group/NatPowAssoc.lean",
21
+ "full_name": "neg_npow_assoc",
22
+ "start": [
23
+ 85,
24
+ 1
25
+ ],
26
+ "traced_tactics": [
27
+ {
28
+ "annotated_tactic": [
29
+ "\"induction k with\\n | zero => simp only [<a>npow_zero<\\/a>, <a>one_mul<\\/a>]\\n | succ k ih =>\\n rw [<a>npow_add<\\/a>, <a>npow_one<\\/a>, \\u2190 <a>neg_mul_comm<\\/a>, <a>mul_one<\\/a>]\\n simp only [<a>neg_mul<\\/a>, ih]\"",
30
+ "[{\"full_name\":\"npow_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/NatPowAssoc.lean\",\"def_pos\":[58,9],\"def_end_pos\":[58,18]},{\"full_name\":\"one_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[477,9],\"def_end_pos\":[477,16]},{\"full_name\":\"npow_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/NatPowAssoc.lean\",\"def_pos\":[54,9],\"def_end_pos\":[54,17]},{\"full_name\":\"npow_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/NatPowAssoc.lean\",\"def_pos\":[62,9],\"def_end_pos\":[62,17]},{\"full_name\":\"neg_mul_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[338,9],\"def_end_pos\":[338,21]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"neg_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[318,9],\"def_end_pos\":[318,16]}]"
31
+ ],
32
+ "state_after": "no goals",
33
+ "state_before": "M : Type u_1\nR : Type u_2\ninst\u271d\u00b2 : NonAssocRing R\ninst\u271d\u00b9 : Pow R \u2115\ninst\u271d : NatPowAssoc R\na b : R\nk : \u2115\n\u22a2 (-1) ^ k * a * b = (-1) ^ k * (a * b)",
34
+ "tactic": "induction k with\n| zero => simp only [npow_zero, one_mul]\n| succ k ih =>\n rw [npow_add, npow_one, \u2190 neg_mul_comm, mul_one]\n simp only [neg_mul, ih]"
35
+ },
36
+ {
37
+ "annotated_tactic": [
38
+ "\"simp only [<a>npow_zero<\\/a>, <a>one_mul<\\/a>]\"",
39
+ "[{\"full_name\":\"npow_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/NatPowAssoc.lean\",\"def_pos\":[58,9],\"def_end_pos\":[58,18]},{\"full_name\":\"one_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[477,9],\"def_end_pos\":[477,16]}]"
40
+ ],
41
+ "state_after": "no goals",
42
+ "state_before": "case zero\nM : Type u_1\nR : Type u_2\ninst\u271d\u00b2 : NonAssocRing R\ninst\u271d\u00b9 : Pow R \u2115\ninst\u271d : NatPowAssoc R\na b : R\n\u22a2 (-1) ^ 0 * a * b = (-1) ^ 0 * (a * b)",
43
+ "tactic": "simp only [npow_zero, one_mul]"
44
+ },
45
+ {
46
+ "annotated_tactic": [
47
+ "\"rw [<a>npow_add<\\/a>, <a>npow_one<\\/a>, \\u2190 <a>neg_mul_comm<\\/a>, <a>mul_one<\\/a>]\"",
48
+ "[{\"full_name\":\"npow_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/NatPowAssoc.lean\",\"def_pos\":[54,9],\"def_end_pos\":[54,17]},{\"full_name\":\"npow_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/NatPowAssoc.lean\",\"def_pos\":[62,9],\"def_end_pos\":[62,17]},{\"full_name\":\"neg_mul_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[338,9],\"def_end_pos\":[338,21]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]}]"
49
+ ],
50
+ "state_after": "case succ\nM : Type u_1\nR : Type u_2\ninst\u271d\u00b2 : NonAssocRing R\ninst\u271d\u00b9 : Pow R \u2115\ninst\u271d : NatPowAssoc R\na b : R\nk : \u2115\nih : (-1) ^ k * a * b = (-1) ^ k * (a * b)\n\u22a2 -(-1) ^ k * a * b = -(-1) ^ k * (a * b)",
51
+ "state_before": "case succ\nM : Type u_1\nR : Type u_2\ninst\u271d\u00b2 : NonAssocRing R\ninst\u271d\u00b9 : Pow R \u2115\ninst\u271d : NatPowAssoc R\na b : R\nk : \u2115\nih : (-1) ^ k * a * b = (-1) ^ k * (a * b)\n\u22a2 (-1) ^ (k + 1) * a * b = (-1) ^ (k + 1) * (a * b)",
52
+ "tactic": "rw [npow_add, npow_one, \u2190 neg_mul_comm, mul_one]"
53
+ },
54
+ {
55
+ "annotated_tactic": [
56
+ "\"simp only [<a>neg_mul<\\/a>, ih]\"",
57
+ "[{\"full_name\":\"neg_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[318,9],\"def_end_pos\":[318,16]}]"
58
+ ],
59
+ "state_after": "no goals",
60
+ "state_before": "case succ\nM : Type u_1\nR : Type u_2\ninst\u271d\u00b2 : NonAssocRing R\ninst\u271d\u00b9 : Pow R \u2115\ninst\u271d : NatPowAssoc R\na b : R\nk : \u2115\nih : (-1) ^ k * a * b = (-1) ^ k * (a * b)\n\u22a2 -(-1) ^ k * a * b = -(-1) ^ k * (a * b)",
61
+ "tactic": "simp only [neg_mul, ih]"
62
+ }
63
+ ],
64
+ "url": "https://github.com/leanprover-community/mathlib4"
65
+ },
66
+ "source_file": "Mathlib/Algebra/Group/NatPowAssoc.lean"
67
+ },
68
+ {
69
+ "error": "theorem has no selected tactic transitions",
70
+ "full_name": "npow_add",
71
+ "id": "npow_add",
72
+ "reason": "import_failure",
73
+ "selection": {
74
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
75
+ "end": [
76
+ 55,
77
+ 29
78
+ ],
79
+ "file_path": "Mathlib/Algebra/Group/NatPowAssoc.lean",
80
+ "full_name": "npow_add",
81
+ "start": [
82
+ 54,
83
+ 1
84
+ ],
85
+ "traced_tactics": [],
86
+ "url": "https://github.com/leanprover-community/mathlib4"
87
+ },
88
+ "source_file": "Mathlib/Algebra/Group/NatPowAssoc.lean"
89
+ },
90
+ {
91
+ "error": "no internal trace for tactic 'rw [npow_zero, Nat.mul_zero, npow_zero]'",
92
+ "full_name": "npow_mul",
93
+ "id": "npow_mul",
94
+ "reason": "import_failure",
95
+ "selection": {
96
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
97
+ "end": [
98
+ 75,
99
+ 73
100
+ ],
101
+ "file_path": "Mathlib/Algebra/Group/NatPowAssoc.lean",
102
+ "full_name": "npow_mul",
103
+ "start": [
104
+ 72,
105
+ 1
106
+ ],
107
+ "traced_tactics": [
108
+ {
109
+ "annotated_tactic": [
110
+ "\"induction n with\\n | zero => rw [<a>npow_zero<\\/a>, <a>Nat.mul_zero<\\/a>, <a>npow_zero<\\/a>]\\n | succ n ih => rw [<a>mul_add<\\/a>, <a>npow_add<\\/a>, ih, <a>mul_one<\\/a>, <a>npow_add<\\/a>, <a>npow_one<\\/a>]\"",
111
+ "[{\"full_name\":\"npow_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/NatPowAssoc.lean\",\"def_pos\":[58,9],\"def_end_pos\":[58,18]},{\"full_name\":\"Nat.mul_zero\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[197,27],\"def_end_pos\":[197,35]},{\"full_name\":\"npow_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/NatPowAssoc.lean\",\"def_pos\":[58,9],\"def_end_pos\":[58,18]},{\"full_name\":\"mul_add\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[83,7],\"def_end_pos\":[83,14]},{\"full_name\":\"npow_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/NatPowAssoc.lean\",\"def_pos\":[54,9],\"def_end_pos\":[54,17]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"npow_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/NatPowAssoc.lean\",\"def_pos\":[54,9],\"def_end_pos\":[54,17]},{\"full_name\":\"npow_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/NatPowAssoc.lean\",\"def_pos\":[62,9],\"def_end_pos\":[62,17]}]"
112
+ ],
113
+ "state_after": "no goals",
114
+ "state_before": "M : Type u_1\ninst\u271d\u00b2 : MulOneClass M\ninst\u271d\u00b9 : Pow M \u2115\ninst\u271d : NatPowAssoc M\nx : M\nm n : \u2115\n\u22a2 x ^ (m * n) = (x ^ m) ^ n",
115
+ "tactic": "induction n with\n| zero => rw [npow_zero, Nat.mul_zero, npow_zero]\n| succ n ih => rw [mul_add, npow_add, ih, mul_one, npow_add, npow_one]"
116
+ },
117
+ {
118
+ "annotated_tactic": [
119
+ "\"rw [<a>npow_zero<\\/a>, <a>Nat.mul_zero<\\/a>, <a>npow_zero<\\/a>]\"",
120
+ "[{\"full_name\":\"npow_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/NatPowAssoc.lean\",\"def_pos\":[58,9],\"def_end_pos\":[58,18]},{\"full_name\":\"Nat.mul_zero\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[197,27],\"def_end_pos\":[197,35]},{\"full_name\":\"npow_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/NatPowAssoc.lean\",\"def_pos\":[58,9],\"def_end_pos\":[58,18]}]"
121
+ ],
122
+ "state_after": "no goals",
123
+ "state_before": "case zero\nM : Type u_1\ninst\u271d\u00b2 : MulOneClass M\ninst\u271d\u00b9 : Pow M \u2115\ninst\u271d : NatPowAssoc M\nx : M\nm : \u2115\n\u22a2 x ^ (m * 0) = (x ^ m) ^ 0",
124
+ "tactic": "rw [npow_zero, Nat.mul_zero, npow_zero]"
125
+ },
126
+ {
127
+ "annotated_tactic": [
128
+ "\"rw [<a>mul_add<\\/a>, <a>npow_add<\\/a>, ih, <a>mul_one<\\/a>, <a>npow_add<\\/a>, <a>npow_one<\\/a>]\"",
129
+ "[{\"full_name\":\"mul_add\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[83,7],\"def_end_pos\":[83,14]},{\"full_name\":\"npow_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/NatPowAssoc.lean\",\"def_pos\":[54,9],\"def_end_pos\":[54,17]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]},{\"full_name\":\"npow_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/NatPowAssoc.lean\",\"def_pos\":[54,9],\"def_end_pos\":[54,17]},{\"full_name\":\"npow_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/NatPowAssoc.lean\",\"def_pos\":[62,9],\"def_end_pos\":[62,17]}]"
130
+ ],
131
+ "state_after": "no goals",
132
+ "state_before": "case succ\nM : Type u_1\ninst\u271d\u00b2 : MulOneClass M\ninst\u271d\u00b9 : Pow M \u2115\ninst\u271d : NatPowAssoc M\nx : M\nm n : \u2115\nih : x ^ (m * n) = (x ^ m) ^ n\n\u22a2 x ^ (m * (n + 1)) = (x ^ m) ^ (n + 1)",
133
+ "tactic": "rw [mul_add, npow_add, ih, mul_one, npow_add, npow_one]"
134
+ }
135
+ ],
136
+ "url": "https://github.com/leanprover-community/mathlib4"
137
+ },
138
+ "source_file": "Mathlib/Algebra/Group/NatPowAssoc.lean"
139
+ },
140
+ {
141
+ "error": "theorem has no selected tactic transitions",
142
+ "full_name": "npow_one",
143
+ "id": "npow_one",
144
+ "reason": "import_failure",
145
+ "selection": {
146
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
147
+ "end": [
148
+ 63,
149
+ 25
150
+ ],
151
+ "file_path": "Mathlib/Algebra/Group/NatPowAssoc.lean",
152
+ "full_name": "npow_one",
153
+ "start": [
154
+ 62,
155
+ 1
156
+ ],
157
+ "traced_tactics": [],
158
+ "url": "https://github.com/leanprover-community/mathlib4"
159
+ },
160
+ "source_file": "Mathlib/Algebra/Group/NatPowAssoc.lean"
161
+ },
162
+ {
163
+ "error": "theorem has no selected tactic transitions",
164
+ "full_name": "npow_zero",
165
+ "id": "npow_zero",
166
+ "reason": "import_failure",
167
+ "selection": {
168
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
169
+ "end": [
170
+ 59,
171
+ 26
172
+ ],
173
+ "file_path": "Mathlib/Algebra/Group/NatPowAssoc.lean",
174
+ "full_name": "npow_zero",
175
+ "start": [
176
+ 58,
177
+ 1
178
+ ],
179
+ "traced_tactics": [],
180
+ "url": "https://github.com/leanprover-community/mathlib4"
181
+ },
182
+ "source_file": "Mathlib/Algebra/Group/NatPowAssoc.lean"
183
+ },
184
+ {
185
+ "error": "theorem has no selected tactic transitions",
186
+ "full_name": "AddMonoidHom.mul_op_ext",
187
+ "id": "AddMonoidHom.mul_op_ext",
188
+ "reason": "import_failure",
189
+ "selection": {
190
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
191
+ "end": [
192
+ 718,
193
+ 77
194
+ ],
195
+ "file_path": "Mathlib/Algebra/Group/Opposite.lean",
196
+ "full_name": "AddMonoidHom.mul_op_ext",
197
+ "start": [
198
+ 713,
199
+ 1
200
+ ],
201
+ "traced_tactics": [],
202
+ "url": "https://github.com/leanprover-community/mathlib4"
203
+ },
204
+ "source_file": "Mathlib/Algebra/Group/Opposite.lean"
205
+ },
206
+ {
207
+ "error": "theorem has no selected tactic transitions",
208
+ "full_name": "AddOpposite.opMulEquiv_toEquiv",
209
+ "id": "AddOpposite.opMulEquiv_toEquiv",
210
+ "reason": "import_failure",
211
+ "selection": {
212
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
213
+ "end": [
214
+ 406,
215
+ 6
216
+ ],
217
+ "file_path": "Mathlib/Algebra/Group/Opposite.lean",
218
+ "full_name": "AddOpposite.opMulEquiv_toEquiv",
219
+ "start": [
220
+ 405,
221
+ 1
222
+ ],
223
+ "traced_tactics": [],
224
+ "url": "https://github.com/leanprover-community/mathlib4"
225
+ },
226
+ "source_file": "Mathlib/Algebra/Group/Opposite.lean"
227
+ },
228
+ {
229
+ "error": "theorem has no selected tactic transitions",
230
+ "full_name": "AddOpposite.op_pow",
231
+ "id": "AddOpposite.op_pow",
232
+ "reason": "import_failure",
233
+ "selection": {
234
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
235
+ "end": [
236
+ 356,
237
+ 6
238
+ ],
239
+ "file_path": "Mathlib/Algebra/Group/Opposite.lean",
240
+ "full_name": "AddOpposite.op_pow",
241
+ "start": [
242
+ 355,
243
+ 1
244
+ ],
245
+ "traced_tactics": [],
246
+ "url": "https://github.com/leanprover-community/mathlib4"
247
+ },
248
+ "source_file": "Mathlib/Algebra/Group/Opposite.lean"
249
+ },
250
+ {
251
+ "error": "theorem has no selected tactic transitions",
252
+ "full_name": "AddOpposite.unop_pow",
253
+ "id": "AddOpposite.unop_pow",
254
+ "reason": "import_failure",
255
+ "selection": {
256
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
257
+ "end": [
258
+ 361,
259
+ 6
260
+ ],
261
+ "file_path": "Mathlib/Algebra/Group/Opposite.lean",
262
+ "full_name": "AddOpposite.unop_pow",
263
+ "start": [
264
+ 360,
265
+ 1
266
+ ],
267
+ "traced_tactics": [],
268
+ "url": "https://github.com/leanprover-community/mathlib4"
269
+ },
270
+ "source_file": "Mathlib/Algebra/Group/Opposite.lean"
271
+ },
272
+ {
273
+ "error": "theorem has no selected tactic transitions",
274
+ "full_name": "Commute.op",
275
+ "id": "Commute.op",
276
+ "reason": "import_failure",
277
+ "selection": {
278
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
279
+ "end": [
280
+ 292,
281
+ 18
282
+ ],
283
+ "file_path": "Mathlib/Algebra/Group/Opposite.lean",
284
+ "full_name": "Commute.op",
285
+ "start": [
286
+ 291,
287
+ 1
288
+ ],
289
+ "traced_tactics": [],
290
+ "url": "https://github.com/leanprover-community/mathlib4"
291
+ },
292
+ "source_file": "Mathlib/Algebra/Group/Opposite.lean"
293
+ },
294
+ {
295
+ "error": "theorem has no selected tactic transitions",
296
+ "full_name": "Commute.unop",
297
+ "id": "Commute.unop",
298
+ "reason": "import_failure",
299
+ "selection": {
300
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
301
+ "end": [
302
+ 299,
303
+ 9
304
+ ],
305
+ "file_path": "Mathlib/Algebra/Group/Opposite.lean",
306
+ "full_name": "Commute.unop",
307
+ "start": [
308
+ 297,
309
+ 8
310
+ ],
311
+ "traced_tactics": [],
312
+ "url": "https://github.com/leanprover-community/mathlib4"
313
+ },
314
+ "source_file": "Mathlib/Algebra/Group/Opposite.lean"
315
+ },
316
+ {
317
+ "error": "theorem has no selected tactic transitions",
318
+ "full_name": "IsUnit.op",
319
+ "id": "IsUnit.op",
320
+ "reason": "import_failure",
321
+ "selection": {
322
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
323
+ "end": [
324
+ 513,
325
+ 40
326
+ ],
327
+ "file_path": "Mathlib/Algebra/Group/Opposite.lean",
328
+ "full_name": "IsUnit.op",
329
+ "start": [
330
+ 511,
331
+ 8
332
+ ],
333
+ "traced_tactics": [],
334
+ "url": "https://github.com/leanprover-community/mathlib4"
335
+ },
336
+ "source_file": "Mathlib/Algebra/Group/Opposite.lean"
337
+ },
338
+ {
339
+ "error": "theorem has no selected tactic transitions",
340
+ "full_name": "IsUnit.unop",
341
+ "id": "IsUnit.unop",
342
+ "reason": "import_failure",
343
+ "selection": {
344
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
345
+ "end": [
346
+ 520,
347
+ 37
348
+ ],
349
+ "file_path": "Mathlib/Algebra/Group/Opposite.lean",
350
+ "full_name": "IsUnit.unop",
351
+ "start": [
352
+ 518,
353
+ 8
354
+ ],
355
+ "traced_tactics": [],
356
+ "url": "https://github.com/leanprover-community/mathlib4"
357
+ },
358
+ "source_file": "Mathlib/Algebra/Group/Opposite.lean"
359
+ },
360
+ {
361
+ "error": "theorem has no selected tactic transitions",
362
+ "full_name": "MulOpposite.commute_unop",
363
+ "id": "MulOpposite.commute_unop",
364
+ "reason": "import_failure",
365
+ "selection": {
366
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
367
+ "end": [
368
+ 311,
369
+ 18
370
+ ],
371
+ "file_path": "Mathlib/Algebra/Group/Opposite.lean",
372
+ "full_name": "MulOpposite.commute_unop",
373
+ "start": [
374
+ 310,
375
+ 1
376
+ ],
377
+ "traced_tactics": [],
378
+ "url": "https://github.com/leanprover-community/mathlib4"
379
+ },
380
+ "source_file": "Mathlib/Algebra/Group/Opposite.lean"
381
+ },
382
+ {
383
+ "error": "theorem has no selected tactic transitions",
384
+ "full_name": "MulOpposite.opAddEquiv_toEquiv",
385
+ "id": "MulOpposite.opAddEquiv_toEquiv",
386
+ "reason": "import_failure",
387
+ "selection": {
388
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
389
+ "end": [
390
+ 326,
391
+ 92
392
+ ],
393
+ "file_path": "Mathlib/Algebra/Group/Opposite.lean",
394
+ "full_name": "MulOpposite.opAddEquiv_toEquiv",
395
+ "start": [
396
+ 326,
397
+ 1
398
+ ],
399
+ "traced_tactics": [],
400
+ "url": "https://github.com/leanprover-community/mathlib4"
401
+ },
402
+ "source_file": "Mathlib/Algebra/Group/Opposite.lean"
403
+ },
404
+ {
405
+ "error": "theorem has no selected tactic transitions",
406
+ "full_name": "MulOpposite.op_intCast",
407
+ "id": "MulOpposite.op_intCast",
408
+ "reason": "import_failure",
409
+ "selection": {
410
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
411
+ "end": [
412
+ 228,
413
+ 6
414
+ ],
415
+ "file_path": "Mathlib/Algebra/Group/Opposite.lean",
416
+ "full_name": "MulOpposite.op_intCast",
417
+ "start": [
418
+ 227,
419
+ 1
420
+ ],
421
+ "traced_tactics": [],
422
+ "url": "https://github.com/leanprover-community/mathlib4"
423
+ },
424
+ "source_file": "Mathlib/Algebra/Group/Opposite.lean"
425
+ },
426
+ {
427
+ "error": "theorem has no selected tactic transitions",
428
+ "full_name": "MulOpposite.op_natCast",
429
+ "id": "MulOpposite.op_natCast",
430
+ "reason": "import_failure",
431
+ "selection": {
432
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
433
+ "end": [
434
+ 216,
435
+ 6
436
+ ],
437
+ "file_path": "Mathlib/Algebra/Group/Opposite.lean",
438
+ "full_name": "MulOpposite.op_natCast",
439
+ "start": [
440
+ 215,
441
+ 1
442
+ ],
443
+ "traced_tactics": [],
444
+ "url": "https://github.com/leanprover-community/mathlib4"
445
+ },
446
+ "source_file": "Mathlib/Algebra/Group/Opposite.lean"
447
+ },
448
+ {
449
+ "error": "theorem has no selected tactic transitions",
450
+ "full_name": "MulOpposite.op_ofNat",
451
+ "id": "MulOpposite.op_ofNat",
452
+ "reason": "import_failure",
453
+ "selection": {
454
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
455
+ "end": [
456
+ 224,
457
+ 6
458
+ ],
459
+ "file_path": "Mathlib/Algebra/Group/Opposite.lean",
460
+ "full_name": "MulOpposite.op_ofNat",
461
+ "start": [
462
+ 222,
463
+ 1
464
+ ],
465
+ "traced_tactics": [],
466
+ "url": "https://github.com/leanprover-community/mathlib4"
467
+ },
468
+ "source_file": "Mathlib/Algebra/Group/Opposite.lean"
469
+ },
470
+ {
471
+ "error": "theorem has no selected tactic transitions",
472
+ "full_name": "MulOpposite.op_pow",
473
+ "id": "MulOpposite.op_pow",
474
+ "reason": "import_failure",
475
+ "selection": {
476
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
477
+ "end": [
478
+ 195,
479
+ 68
480
+ ],
481
+ "file_path": "Mathlib/Algebra/Group/Opposite.lean",
482
+ "full_name": "MulOpposite.op_pow",
483
+ "start": [
484
+ 195,
485
+ 1
486
+ ],
487
+ "traced_tactics": [],
488
+ "url": "https://github.com/leanprover-community/mathlib4"
489
+ },
490
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515
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535
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536
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537
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558
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559
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560
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562
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578
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580
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581
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582
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599
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600
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601
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602
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603
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604
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605
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606
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607
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613
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620
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621
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622
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623
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624
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625
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626
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627
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628
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629
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643
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644
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645
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646
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647
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648
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649
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650
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651
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663
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664
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665
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666
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667
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668
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669
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670
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671
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672
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673
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682
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684
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685
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686
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687
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688
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689
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690
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691
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692
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693
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694
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695
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696
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701
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702
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703
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707
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708
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709
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710
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711
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712
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713
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714
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715
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716
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729
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730
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732
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733
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734
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735
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736
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737
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738
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753
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754
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755
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756
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757
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758
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760
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761
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768
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773
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774
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775
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776
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777
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778
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779
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788
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789
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790
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791
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792
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793
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794
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803
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807
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809
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814
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815
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816
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817
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818
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820
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821
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822
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823
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824
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825
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826
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827
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828
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829
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830
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831
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832
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833
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834
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835
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836
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837
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838
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839
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840
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846
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847
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852
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853
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854
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855
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856
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857
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858
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859
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860
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861
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862
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863
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864
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865
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866
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867
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868
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869
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870
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871
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872
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873
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874
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875
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876
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877
+ "tactic": "rw [npow_add, npow_add, Nat.cast_mul, ih, npow_one, npow_one]"
878
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879
+ ],
880
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881
+ }
882
+ },
883
+ "theorem_name": "Nat.cast_npow"
884
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885
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886
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906
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909
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910
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+ "mathlib:npow_mul_comm"
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913
+ "proof_keys": [
914
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/NatPowAssoc.lean\",null,null,\"npow_mul'\"]",
915
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/NatPowAssoc.lean\",null,null,\"npow_mul_assoc\"]",
916
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/NatPowAssoc.lean\",null,null,\"npow_mul_comm\"]",
917
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Opposite.lean\",null,null,\"MulOpposite.op_div\"]",
918
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Opposite.lean\",null,null,\"MulOpposite.semiconjBy_op\"]",
919
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Opposite.lean\",null,null,\"MulOpposite.semiconjBy_unop\"]"
920
+ ]
921
+ }
manifests/batches/mathlib/000126.json ADDED
@@ -0,0 +1,1241 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000126",
4
+ "batch_fingerprint": "c7df772f042ccede31693c9b91040af5e6d11b1b36781ae8abf8ef75f63f60d3",
5
+ "evidence": {
6
+ "batch_fingerprint": "c7df772f042ccede31693c9b91040af5e6d11b1b36781ae8abf8ef75f63f60d3",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "ppow_add",
12
+ "id": "ppow_add",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 54,
18
+ 30
19
+ ],
20
+ "file_path": "Mathlib/Algebra/Group/PNatPowAssoc.lean",
21
+ "full_name": "ppow_add",
22
+ "start": [
23
+ 53,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/Algebra/Group/PNatPowAssoc.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "ppow_one",
34
+ "id": "ppow_one",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 58,
40
+ 26
41
+ ],
42
+ "file_path": "Mathlib/Algebra/Group/PNatPowAssoc.lean",
43
+ "full_name": "ppow_one",
44
+ "start": [
45
+ 57,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/Algebra/Group/PNatPowAssoc.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "Function.bijective_pi_map",
56
+ "id": "Function.bijective_pi_map",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 537,
62
+ 93
63
+ ],
64
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
65
+ "full_name": "Function.bijective_pi_map",
66
+ "start": [
67
+ 535,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "Function.comp_eq_const_iff",
78
+ "id": "Function.comp_eq_const_iff",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 542,
84
+ 27
85
+ ],
86
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
87
+ "full_name": "Function.comp_eq_const_iff",
88
+ "start": [
89
+ 540,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "Function.comp_ne_one_iff",
100
+ "id": "Function.comp_ne_one_iff",
101
+ "reason": "import_failure",
102
+ "selection": {
103
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
104
+ "end": [
105
+ 552,
106
+ 32
107
+ ],
108
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
109
+ "full_name": "Function.comp_ne_one_iff",
110
+ "start": [
111
+ 549,
112
+ 1
113
+ ],
114
+ "traced_tactics": [],
115
+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
118
+ },
119
+ {
120
+ "error": "theorem has no selected tactic transitions",
121
+ "full_name": "Function.const_div",
122
+ "id": "Function.const_div",
123
+ "reason": "import_failure",
124
+ "selection": {
125
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
126
+ "end": [
127
+ 214,
128
+ 99
129
+ ],
130
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
131
+ "full_name": "Function.const_div",
132
+ "start": [
133
+ 213,
134
+ 1
135
+ ],
136
+ "traced_tactics": [],
137
+ "url": "https://github.com/leanprover-community/mathlib4"
138
+ },
139
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
140
+ },
141
+ {
142
+ "error": "theorem has no selected tactic transitions",
143
+ "full_name": "Function.const_inv",
144
+ "id": "Function.const_inv",
145
+ "reason": "import_failure",
146
+ "selection": {
147
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
148
+ "end": [
149
+ 179,
150
+ 85
151
+ ],
152
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
153
+ "full_name": "Function.const_inv",
154
+ "start": [
155
+ 178,
156
+ 1
157
+ ],
158
+ "traced_tactics": [],
159
+ "url": "https://github.com/leanprover-community/mathlib4"
160
+ },
161
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
162
+ },
163
+ {
164
+ "error": "theorem has no selected tactic transitions",
165
+ "full_name": "Function.const_mul",
166
+ "id": "Function.const_mul",
167
+ "reason": "import_failure",
168
+ "selection": {
169
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
170
+ "end": [
171
+ 109,
172
+ 99
173
+ ],
174
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
175
+ "full_name": "Function.const_mul",
176
+ "start": [
177
+ 108,
178
+ 1
179
+ ],
180
+ "traced_tactics": [],
181
+ "url": "https://github.com/leanprover-community/mathlib4"
182
+ },
183
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
184
+ },
185
+ {
186
+ "error": "theorem has no selected tactic transitions",
187
+ "full_name": "Function.const_one",
188
+ "id": "Function.const_one",
189
+ "reason": "import_failure",
190
+ "selection": {
191
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
192
+ "end": [
193
+ 74,
194
+ 99
195
+ ],
196
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
197
+ "full_name": "Function.const_one",
198
+ "start": [
199
+ 74,
200
+ 1
201
+ ],
202
+ "traced_tactics": [],
203
+ "url": "https://github.com/leanprover-community/mathlib4"
204
+ },
205
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
206
+ },
207
+ {
208
+ "error": "theorem has no selected tactic transitions",
209
+ "full_name": "Function.const_pow",
210
+ "id": "Function.const_pow",
211
+ "reason": "import_failure",
212
+ "selection": {
213
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
214
+ "end": [
215
+ 144,
216
+ 99
217
+ ],
218
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
219
+ "full_name": "Function.const_pow",
220
+ "start": [
221
+ 143,
222
+ 1
223
+ ],
224
+ "traced_tactics": [],
225
+ "url": "https://github.com/leanprover-community/mathlib4"
226
+ },
227
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
228
+ },
229
+ {
230
+ "error": "no internal trace for tactic 'funext x'",
231
+ "full_name": "Function.extend_div",
232
+ "id": "Function.extend_div",
233
+ "reason": "import_failure",
234
+ "selection": {
235
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
236
+ "end": [
237
+ 514,
238
+ 42
239
+ ],
240
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
241
+ "full_name": "Function.extend_div",
242
+ "start": [
243
+ 510,
244
+ 1
245
+ ],
246
+ "traced_tactics": [
247
+ {
248
+ "annotated_tactic": [
249
+ "\"classical\\n funext x\\n simp [<a>Function.extend_def<\\/a>, <a>apply_dite\\u2082<\\/a>]\"",
250
+ "[{\"full_name\":\"Function.extend_def\",\"def_path\":\"Mathlib\\/Logic\\/Function\\/Basic.lean\",\"def_pos\":[726,9],\"def_end_pos\":[726,19]},{\"full_name\":\"apply_dite\\u2082\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[1266,9],\"def_end_pos\":[1266,20]}]"
251
+ ],
252
+ "state_after": "no goals",
253
+ "state_before": "I : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf\u271d : I \u2192 Type v\u2081\ng : I \u2192 Type v\u2082\nh : I \u2192 Type v\u2083\nx y : (i : I) \u2192 f\u271d i\ni : I\ninst\u271d : Div \u03b3\nf : \u03b1 \u2192 \u03b2\ng\u2081 g\u2082 : \u03b1 \u2192 \u03b3\ne\u2081 e\u2082 : \u03b2 \u2192 \u03b3\n\u22a2 extend f (g\u2081 / g\u2082) (e\u2081 / e\u2082) = extend f g\u2081 e\u2081 / extend f g\u2082 e\u2082",
254
+ "tactic": "classical\nfunext x\nsimp [Function.extend_def, apply_dite\u2082]"
255
+ },
256
+ {
257
+ "annotated_tactic": [
258
+ "\"funext x\"",
259
+ "[]"
260
+ ],
261
+ "state_after": "case h\nI : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf\u271d : I \u2192 Type v\u2081\ng : I \u2192 Type v\u2082\nh : I \u2192 Type v\u2083\nx\u271d y : (i : I) \u2192 f\u271d i\ni : I\ninst\u271d : Div \u03b3\nf : \u03b1 \u2192 \u03b2\ng\u2081 g\u2082 : \u03b1 \u2192 \u03b3\ne\u2081 e\u2082 : \u03b2 \u2192 \u03b3\nx : \u03b2\n\u22a2 extend f (g\u2081 / g\u2082) (e\u2081 / e\u2082) x = (extend f g\u2081 e\u2081 / extend f g\u2082 e\u2082) x",
262
+ "state_before": "I : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf\u271d : I \u2192 Type v\u2081\ng : I \u2192 Type v\u2082\nh : I \u2192 Type v\u2083\nx y : (i : I) \u2192 f\u271d i\ni : I\ninst\u271d : Div \u03b3\nf : \u03b1 \u2192 \u03b2\ng\u2081 g\u2082 : \u03b1 \u2192 \u03b3\ne\u2081 e\u2082 : \u03b2 \u2192 \u03b3\n\u22a2 extend f (g\u2081 / g\u2082) (e\u2081 / e\u2082) = extend f g\u2081 e\u2081 / extend f g\u2082 e\u2082",
263
+ "tactic": "funext x"
264
+ },
265
+ {
266
+ "annotated_tactic": [
267
+ "\"simp [<a>Function.extend_def<\\/a>, <a>apply_dite\\u2082<\\/a>]\"",
268
+ "[{\"full_name\":\"Function.extend_def\",\"def_path\":\"Mathlib\\/Logic\\/Function\\/Basic.lean\",\"def_pos\":[726,9],\"def_end_pos\":[726,19]},{\"full_name\":\"apply_dite\\u2082\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[1266,9],\"def_end_pos\":[1266,20]}]"
269
+ ],
270
+ "state_after": "no goals",
271
+ "state_before": "case h\nI : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf\u271d : I \u2192 Type v\u2081\ng : I \u2192 Type v\u2082\nh : I \u2192 Type v\u2083\nx\u271d y : (i : I) \u2192 f\u271d i\ni : I\ninst\u271d : Div \u03b3\nf : \u03b1 \u2192 \u03b2\ng\u2081 g\u2082 : \u03b1 \u2192 \u03b3\ne\u2081 e\u2082 : \u03b2 \u2192 \u03b3\nx : \u03b2\n\u22a2 extend f (g\u2081 / g\u2082) (e\u2081 / e\u2082) x = (extend f g\u2081 e\u2081 / extend f g\u2082 e\u2082) x",
272
+ "tactic": "simp [Function.extend_def, apply_dite\u2082]"
273
+ }
274
+ ],
275
+ "url": "https://github.com/leanprover-community/mathlib4"
276
+ },
277
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
278
+ },
279
+ {
280
+ "error": "no internal trace for tactic 'funext x'",
281
+ "full_name": "Function.extend_inv",
282
+ "id": "Function.extend_inv",
283
+ "reason": "import_failure",
284
+ "selection": {
285
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
286
+ "end": [
287
+ 500,
288
+ 71
289
+ ],
290
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
291
+ "full_name": "Function.extend_inv",
292
+ "start": [
293
+ 496,
294
+ 1
295
+ ],
296
+ "traced_tactics": [
297
+ {
298
+ "annotated_tactic": [
299
+ "\"classical\\n funext x\\n simp only [<a>not_exists<\\/a>, <a>extend_def<\\/a>, <a>Pi.inv_apply<\\/a>, <a>apply_dite<\\/a> <a>Inv.inv<\\/a>]\"",
300
+ "[{\"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\":\"Function.extend_def\",\"def_path\":\"Mathlib\\/Logic\\/Function\\/Basic.lean\",\"def_pos\":[726,9],\"def_end_pos\":[726,19]},{\"full_name\":\"Pi.inv_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[167,9],\"def_end_pos\":[167,18]},{\"full_name\":\"apply_dite\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/ByCases.lean\",\"def_pos\":[31,9],\"def_end_pos\":[31,19]},{\"full_name\":\"Inv.inv\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[168,3],\"def_end_pos\":[168,6]}]"
301
+ ],
302
+ "state_after": "no goals",
303
+ "state_before": "I : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf\u271d : I \u2192 Type v\u2081\ng\u271d : I \u2192 Type v\u2082\nh : I \u2192 Type v\u2083\nx y : (i : I) \u2192 f\u271d i\ni : I\ninst\u271d : Inv \u03b3\nf : \u03b1 \u2192 \u03b2\ng : \u03b1 \u2192 \u03b3\ne : \u03b2 \u2192 \u03b3\n\u22a2 extend f g\u207b\u00b9 e\u207b\u00b9 = (extend f g e)\u207b\u00b9",
304
+ "tactic": "classical\nfunext x\nsimp only [not_exists, extend_def, Pi.inv_apply, apply_dite Inv.inv]"
305
+ },
306
+ {
307
+ "annotated_tactic": [
308
+ "\"funext x\"",
309
+ "[]"
310
+ ],
311
+ "state_after": "case h\nI : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf\u271d : I \u2192 Type v\u2081\ng\u271d : I \u2192 Type v\u2082\nh : I \u2192 Type v\u2083\nx\u271d y : (i : I) \u2192 f\u271d i\ni : I\ninst\u271d : Inv \u03b3\nf : \u03b1 \u2192 \u03b2\ng : \u03b1 \u2192 \u03b3\ne : \u03b2 \u2192 \u03b3\nx : \u03b2\n\u22a2 extend f g\u207b\u00b9 e\u207b\u00b9 x = (extend f g e)\u207b\u00b9 x",
312
+ "state_before": "I : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf\u271d : I \u2192 Type v\u2081\ng\u271d : I \u2192 Type v\u2082\nh : I \u2192 Type v\u2083\nx y : (i : I) \u2192 f\u271d i\ni : I\ninst\u271d : Inv \u03b3\nf : \u03b1 \u2192 \u03b2\ng : \u03b1 \u2192 \u03b3\ne : \u03b2 \u2192 \u03b3\n\u22a2 extend f g\u207b\u00b9 e\u207b\u00b9 = (extend f g e)\u207b\u00b9",
313
+ "tactic": "funext x"
314
+ },
315
+ {
316
+ "annotated_tactic": [
317
+ "\"simp only [<a>not_exists<\\/a>, <a>extend_def<\\/a>, <a>Pi.inv_apply<\\/a>, <a>apply_dite<\\/a> <a>Inv.inv<\\/a>]\"",
318
+ "[{\"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\":\"Function.extend_def\",\"def_path\":\"Mathlib\\/Logic\\/Function\\/Basic.lean\",\"def_pos\":[726,9],\"def_end_pos\":[726,19]},{\"full_name\":\"Pi.inv_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[167,9],\"def_end_pos\":[167,18]},{\"full_name\":\"apply_dite\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/ByCases.lean\",\"def_pos\":[31,9],\"def_end_pos\":[31,19]},{\"full_name\":\"Inv.inv\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[168,3],\"def_end_pos\":[168,6]}]"
319
+ ],
320
+ "state_after": "no goals",
321
+ "state_before": "case h\nI : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf\u271d : I \u2192 Type v\u2081\ng\u271d : I \u2192 Type v\u2082\nh : I \u2192 Type v\u2083\nx\u271d y : (i : I) \u2192 f\u271d i\ni : I\ninst\u271d : Inv \u03b3\nf : \u03b1 \u2192 \u03b2\ng : \u03b1 \u2192 \u03b3\ne : \u03b2 \u2192 \u03b3\nx : \u03b2\n\u22a2 extend f g\u207b\u00b9 e\u207b\u00b9 x = (extend f g e)\u207b\u00b9 x",
322
+ "tactic": "simp only [not_exists, extend_def, Pi.inv_apply, apply_dite Inv.inv]"
323
+ }
324
+ ],
325
+ "url": "https://github.com/leanprover-community/mathlib4"
326
+ },
327
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
328
+ },
329
+ {
330
+ "error": "no internal trace for tactic 'funext x'",
331
+ "full_name": "Function.extend_mul",
332
+ "id": "Function.extend_mul",
333
+ "reason": "import_failure",
334
+ "selection": {
335
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
336
+ "end": [
337
+ 486,
338
+ 87
339
+ ],
340
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
341
+ "full_name": "Function.extend_mul",
342
+ "start": [
343
+ 482,
344
+ 1
345
+ ],
346
+ "traced_tactics": [
347
+ {
348
+ "annotated_tactic": [
349
+ "\"classical\\n funext x\\n simp only [<a>not_exists<\\/a>, <a>extend_def<\\/a>, <a>Pi.mul_apply<\\/a>, <a>apply_dite\\u2082<\\/a>, <a>dite_eq_ite<\\/a>, <a>ite_self<\\/a>]\"",
350
+ "[{\"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\":\"Function.extend_def\",\"def_path\":\"Mathlib\\/Logic\\/Function\\/Basic.lean\",\"def_pos\":[726,9],\"def_end_pos\":[726,19]},{\"full_name\":\"Pi.mul_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[97,9],\"def_end_pos\":[97,18]},{\"full_name\":\"apply_dite\\u2082\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[1266,9],\"def_end_pos\":[1266,20]},{\"full_name\":\"dite_eq_ite\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/ByCases.lean\",\"def_pos\":[55,17],\"def_end_pos\":[55,28]},{\"full_name\":\"ite_self\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[102,17],\"def_end_pos\":[102,25]}]"
351
+ ],
352
+ "state_after": "no goals",
353
+ "state_before": "I : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf\u271d : I \u2192 Type v\u2081\ng : I \u2192 Type v\u2082\nh : I \u2192 Type v\u2083\nx y : (i : I) \u2192 f\u271d i\ni : I\ninst\u271d : Mul \u03b3\nf : \u03b1 \u2192 \u03b2\ng\u2081 g\u2082 : \u03b1 \u2192 \u03b3\ne\u2081 e\u2082 : \u03b2 \u2192 \u03b3\n\u22a2 extend f (g\u2081 * g\u2082) (e\u2081 * e\u2082) = extend f g\u2081 e\u2081 * extend f g\u2082 e\u2082",
354
+ "tactic": "classical\nfunext x\nsimp only [not_exists, extend_def, Pi.mul_apply, apply_dite\u2082, dite_eq_ite, ite_self]"
355
+ },
356
+ {
357
+ "annotated_tactic": [
358
+ "\"funext x\"",
359
+ "[]"
360
+ ],
361
+ "state_after": "case h\nI : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf\u271d : I \u2192 Type v\u2081\ng : I \u2192 Type v\u2082\nh : I \u2192 Type v\u2083\nx\u271d y : (i : I) \u2192 f\u271d i\ni : I\ninst\u271d : Mul \u03b3\nf : \u03b1 \u2192 \u03b2\ng\u2081 g\u2082 : \u03b1 \u2192 \u03b3\ne\u2081 e\u2082 : \u03b2 \u2192 \u03b3\nx : \u03b2\n\u22a2 extend f (g\u2081 * g\u2082) (e\u2081 * e\u2082) x = (extend f g\u2081 e\u2081 * extend f g\u2082 e\u2082) x",
362
+ "state_before": "I : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf\u271d : I \u2192 Type v\u2081\ng : I \u2192 Type v\u2082\nh : I \u2192 Type v\u2083\nx y : (i : I) \u2192 f\u271d i\ni : I\ninst\u271d : Mul \u03b3\nf : \u03b1 \u2192 \u03b2\ng\u2081 g\u2082 : \u03b1 \u2192 \u03b3\ne\u2081 e\u2082 : \u03b2 \u2192 \u03b3\n\u22a2 extend f (g\u2081 * g\u2082) (e\u2081 * e\u2082) = extend f g\u2081 e\u2081 * extend f g\u2082 e\u2082",
363
+ "tactic": "funext x"
364
+ },
365
+ {
366
+ "annotated_tactic": [
367
+ "\"simp only [<a>not_exists<\\/a>, <a>extend_def<\\/a>, <a>Pi.mul_apply<\\/a>, <a>apply_dite\\u2082<\\/a>, <a>dite_eq_ite<\\/a>, <a>ite_self<\\/a>]\"",
368
+ "[{\"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\":\"Function.extend_def\",\"def_path\":\"Mathlib\\/Logic\\/Function\\/Basic.lean\",\"def_pos\":[726,9],\"def_end_pos\":[726,19]},{\"full_name\":\"Pi.mul_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[97,9],\"def_end_pos\":[97,18]},{\"full_name\":\"apply_dite\\u2082\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[1266,9],\"def_end_pos\":[1266,20]},{\"full_name\":\"dite_eq_ite\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/ByCases.lean\",\"def_pos\":[55,17],\"def_end_pos\":[55,28]},{\"full_name\":\"ite_self\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[102,17],\"def_end_pos\":[102,25]}]"
369
+ ],
370
+ "state_after": "no goals",
371
+ "state_before": "case h\nI : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf\u271d : I \u2192 Type v\u2081\ng : I \u2192 Type v\u2082\nh : I \u2192 Type v\u2083\nx\u271d y : (i : I) \u2192 f\u271d i\ni : I\ninst\u271d : Mul \u03b3\nf : \u03b1 \u2192 \u03b2\ng\u2081 g\u2082 : \u03b1 \u2192 \u03b3\ne\u2081 e\u2082 : \u03b2 \u2192 \u03b3\nx : \u03b2\n\u22a2 extend f (g\u2081 * g\u2082) (e\u2081 * e\u2082) x = (extend f g\u2081 e\u2081 * extend f g\u2082 e\u2082) x",
372
+ "tactic": "simp only [not_exists, extend_def, Pi.mul_apply, apply_dite\u2082, dite_eq_ite, ite_self]"
373
+ }
374
+ ],
375
+ "url": "https://github.com/leanprover-community/mathlib4"
376
+ },
377
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
378
+ },
379
+ {
380
+ "error": "theorem has no selected tactic transitions",
381
+ "full_name": "Function.injective_pi_map",
382
+ "id": "Function.injective_pi_map",
383
+ "reason": "import_failure",
384
+ "selection": {
385
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
386
+ "end": [
387
+ 532,
388
+ 59
389
+ ],
390
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
391
+ "full_name": "Function.injective_pi_map",
392
+ "start": [
393
+ 530,
394
+ 1
395
+ ],
396
+ "traced_tactics": [],
397
+ "url": "https://github.com/leanprover-community/mathlib4"
398
+ },
399
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
400
+ },
401
+ {
402
+ "error": "theorem has no selected tactic transitions",
403
+ "full_name": "Pi.comp_one",
404
+ "id": "Pi.comp_one",
405
+ "reason": "import_failure",
406
+ "selection": {
407
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
408
+ "end": [
409
+ 86,
410
+ 6
411
+ ],
412
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
413
+ "full_name": "Pi.comp_one",
414
+ "start": [
415
+ 85,
416
+ 1
417
+ ],
418
+ "traced_tactics": [],
419
+ "url": "https://github.com/leanprover-community/mathlib4"
420
+ },
421
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
422
+ },
423
+ {
424
+ "error": "theorem has no selected tactic transitions",
425
+ "full_name": "Pi.div_apply",
426
+ "id": "Pi.div_apply",
427
+ "reason": "import_failure",
428
+ "selection": {
429
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
430
+ "end": [
431
+ 197,
432
+ 6
433
+ ],
434
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
435
+ "full_name": "Pi.div_apply",
436
+ "start": [
437
+ 196,
438
+ 1
439
+ ],
440
+ "traced_tactics": [],
441
+ "url": "https://github.com/leanprover-community/mathlib4"
442
+ },
443
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
444
+ },
445
+ {
446
+ "error": "theorem has no selected tactic transitions",
447
+ "full_name": "Pi.div_comp",
448
+ "id": "Pi.div_comp",
449
+ "reason": "import_failure",
450
+ "selection": {
451
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
452
+ "end": [
453
+ 209,
454
+ 6
455
+ ],
456
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
457
+ "full_name": "Pi.div_comp",
458
+ "start": [
459
+ 208,
460
+ 1
461
+ ],
462
+ "traced_tactics": [],
463
+ "url": "https://github.com/leanprover-community/mathlib4"
464
+ },
465
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
466
+ },
467
+ {
468
+ "error": "theorem has no selected tactic transitions",
469
+ "full_name": "Pi.div_def",
470
+ "id": "Pi.div_def",
471
+ "reason": "import_failure",
472
+ "selection": {
473
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
474
+ "end": [
475
+ 203,
476
+ 6
477
+ ],
478
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
479
+ "full_name": "Pi.div_def",
480
+ "start": [
481
+ 202,
482
+ 1
483
+ ],
484
+ "traced_tactics": [],
485
+ "url": "https://github.com/leanprover-community/mathlib4"
486
+ },
487
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
488
+ },
489
+ {
490
+ "error": "theorem has no selected tactic transitions",
491
+ "full_name": "Pi.inv_apply",
492
+ "id": "Pi.inv_apply",
493
+ "reason": "import_failure",
494
+ "selection": {
495
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
496
+ "end": [
497
+ 168,
498
+ 6
499
+ ],
500
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
501
+ "full_name": "Pi.inv_apply",
502
+ "start": [
503
+ 167,
504
+ 1
505
+ ],
506
+ "traced_tactics": [],
507
+ "url": "https://github.com/leanprover-community/mathlib4"
508
+ },
509
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
510
+ },
511
+ {
512
+ "error": "theorem has no selected tactic transitions",
513
+ "full_name": "Pi.inv_comp",
514
+ "id": "Pi.inv_comp",
515
+ "reason": "import_failure",
516
+ "selection": {
517
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
518
+ "end": [
519
+ 185,
520
+ 6
521
+ ],
522
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
523
+ "full_name": "Pi.inv_comp",
524
+ "start": [
525
+ 184,
526
+ 1
527
+ ],
528
+ "traced_tactics": [],
529
+ "url": "https://github.com/leanprover-community/mathlib4"
530
+ },
531
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
532
+ },
533
+ {
534
+ "error": "theorem has no selected tactic transitions",
535
+ "full_name": "Pi.inv_def",
536
+ "id": "Pi.inv_def",
537
+ "reason": "import_failure",
538
+ "selection": {
539
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
540
+ "end": [
541
+ 174,
542
+ 6
543
+ ],
544
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
545
+ "full_name": "Pi.inv_def",
546
+ "start": [
547
+ 173,
548
+ 1
549
+ ],
550
+ "traced_tactics": [],
551
+ "url": "https://github.com/leanprover-community/mathlib4"
552
+ },
553
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
554
+ },
555
+ {
556
+ "error": "theorem has no selected tactic transitions",
557
+ "full_name": "Pi.mulSingle_apply",
558
+ "id": "Pi.mulSingle_apply",
559
+ "reason": "import_failure",
560
+ "selection": {
561
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
562
+ "end": [
563
+ 388,
564
+ 43
565
+ ],
566
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
567
+ "full_name": "Pi.mulSingle_apply",
568
+ "start": [
569
+ 386,
570
+ 1
571
+ ],
572
+ "traced_tactics": [],
573
+ "url": "https://github.com/leanprover-community/mathlib4"
574
+ },
575
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
576
+ },
577
+ {
578
+ "error": "theorem has no selected tactic transitions",
579
+ "full_name": "Pi.mulSingle_eq_of_ne",
580
+ "id": "Pi.mulSingle_eq_of_ne",
581
+ "reason": "import_failure",
582
+ "selection": {
583
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
584
+ "end": [
585
+ 362,
586
+ 30
587
+ ],
588
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
589
+ "full_name": "Pi.mulSingle_eq_of_ne",
590
+ "start": [
591
+ 361,
592
+ 1
593
+ ],
594
+ "traced_tactics": [],
595
+ "url": "https://github.com/leanprover-community/mathlib4"
596
+ },
597
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
598
+ },
599
+ {
600
+ "error": "theorem has no selected tactic transitions",
601
+ "full_name": "Pi.mulSingle_eq_of_ne'",
602
+ "id": "Pi.mulSingle_eq_of_ne'",
603
+ "reason": "import_failure",
604
+ "selection": {
605
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
606
+ "end": [
607
+ 370,
608
+ 30
609
+ ],
610
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
611
+ "full_name": "Pi.mulSingle_eq_of_ne'",
612
+ "start": [
613
+ 369,
614
+ 1
615
+ ],
616
+ "traced_tactics": [],
617
+ "url": "https://github.com/leanprover-community/mathlib4"
618
+ },
619
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
620
+ },
621
+ {
622
+ "error": "theorem has no selected tactic transitions",
623
+ "full_name": "Pi.mulSingle_eq_same",
624
+ "id": "Pi.mulSingle_eq_same",
625
+ "reason": "import_failure",
626
+ "selection": {
627
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
628
+ "end": [
629
+ 356,
630
+ 29
631
+ ],
632
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
633
+ "full_name": "Pi.mulSingle_eq_same",
634
+ "start": [
635
+ 355,
636
+ 1
637
+ ],
638
+ "traced_tactics": [],
639
+ "url": "https://github.com/leanprover-community/mathlib4"
640
+ },
641
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
642
+ },
643
+ {
644
+ "error": "theorem has no selected tactic transitions",
645
+ "full_name": "Pi.mulSingle_inj",
646
+ "id": "Pi.mulSingle_inj",
647
+ "reason": "import_failure",
648
+ "selection": {
649
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
650
+ "end": [
651
+ 445,
652
+ 38
653
+ ],
654
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
655
+ "full_name": "Pi.mulSingle_inj",
656
+ "start": [
657
+ 444,
658
+ 1
659
+ ],
660
+ "traced_tactics": [],
661
+ "url": "https://github.com/leanprover-community/mathlib4"
662
+ },
663
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
664
+ },
665
+ {
666
+ "error": "theorem has no selected tactic transitions",
667
+ "full_name": "Pi.mulSingle_injective",
668
+ "id": "Pi.mulSingle_injective",
669
+ "reason": "import_failure",
670
+ "selection": {
671
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
672
+ "end": [
673
+ 439,
674
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675
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676
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677
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678
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679
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682
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684
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685
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686
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687
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688
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689
+ "full_name": "Pi.mulSingle_one",
690
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691
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692
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693
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706
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707
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708
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709
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710
+ "error": "theorem has no selected tactic transitions",
711
+ "full_name": "Pi.mulSingle_op\u2082",
712
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713
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714
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715
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716
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720
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722
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726
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727
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728
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729
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730
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731
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732
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733
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734
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735
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736
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737
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744
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748
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749
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750
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751
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752
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753
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754
+ "error": "theorem has no selected tactic transitions",
755
+ "full_name": "Pi.mul_comp",
756
+ "id": "Pi.mul_comp",
757
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758
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759
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760
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761
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764
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765
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766
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767
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770
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771
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772
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773
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
774
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775
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776
+ "error": "theorem has no selected tactic transitions",
777
+ "full_name": "Pi.mul_def",
778
+ "id": "Pi.mul_def",
779
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780
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781
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782
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783
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785
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786
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787
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788
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789
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790
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791
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792
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793
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794
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795
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
796
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797
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798
+ "error": "theorem has no selected tactic transitions",
799
+ "full_name": "Pi.one_apply",
800
+ "id": "Pi.one_apply",
801
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802
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803
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804
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805
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806
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807
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808
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809
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810
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811
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812
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813
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814
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815
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816
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817
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
818
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819
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820
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821
+ "full_name": "Pi.one_comp",
822
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823
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824
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825
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826
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827
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828
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829
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830
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831
+ "full_name": "Pi.one_comp",
832
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833
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834
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835
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836
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837
+ "url": "https://github.com/leanprover-community/mathlib4"
838
+ },
839
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
840
+ },
841
+ {
842
+ "error": "theorem has no selected tactic transitions",
843
+ "full_name": "Pi.one_def",
844
+ "id": "Pi.one_def",
845
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846
+ "selection": {
847
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848
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849
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850
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851
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852
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
853
+ "full_name": "Pi.one_def",
854
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855
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856
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857
+ ],
858
+ "traced_tactics": [],
859
+ "url": "https://github.com/leanprover-community/mathlib4"
860
+ },
861
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
862
+ },
863
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864
+ "error": "theorem has no selected tactic transitions",
865
+ "full_name": "Pi.pow_apply",
866
+ "id": "Pi.pow_apply",
867
+ "reason": "import_failure",
868
+ "selection": {
869
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870
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871
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872
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873
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874
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
875
+ "full_name": "Pi.pow_apply",
876
+ "start": [
877
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878
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879
+ ],
880
+ "traced_tactics": [],
881
+ "url": "https://github.com/leanprover-community/mathlib4"
882
+ },
883
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
884
+ },
885
+ {
886
+ "error": "theorem has no selected tactic transitions",
887
+ "full_name": "Pi.pow_comp",
888
+ "id": "Pi.pow_comp",
889
+ "reason": "import_failure",
890
+ "selection": {
891
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892
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893
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894
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895
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896
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
897
+ "full_name": "Pi.pow_comp",
898
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899
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900
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901
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902
+ "traced_tactics": [],
903
+ "url": "https://github.com/leanprover-community/mathlib4"
904
+ },
905
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
906
+ },
907
+ {
908
+ "error": "theorem has no selected tactic transitions",
909
+ "full_name": "Pi.pow_def",
910
+ "id": "Pi.pow_def",
911
+ "reason": "import_failure",
912
+ "selection": {
913
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
914
+ "end": [
915
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916
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917
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918
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
919
+ "full_name": "Pi.pow_def",
920
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921
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922
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923
+ ],
924
+ "traced_tactics": [],
925
+ "url": "https://github.com/leanprover-community/mathlib4"
926
+ },
927
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
928
+ },
929
+ {
930
+ "error": "theorem has no selected tactic transitions",
931
+ "full_name": "Pi.prod_fst_snd",
932
+ "id": "Pi.prod_fst_snd",
933
+ "reason": "import_failure",
934
+ "selection": {
935
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
936
+ "end": [
937
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938
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939
+ ],
940
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
941
+ "full_name": "Pi.prod_fst_snd",
942
+ "start": [
943
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944
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945
+ ],
946
+ "traced_tactics": [],
947
+ "url": "https://github.com/leanprover-community/mathlib4"
948
+ },
949
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
950
+ },
951
+ {
952
+ "error": "theorem has no selected tactic transitions",
953
+ "full_name": "Pi.prod_snd_fst",
954
+ "id": "Pi.prod_snd_fst",
955
+ "reason": "import_failure",
956
+ "selection": {
957
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
958
+ "end": [
959
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960
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961
+ ],
962
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
963
+ "full_name": "Pi.prod_snd_fst",
964
+ "start": [
965
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966
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967
+ ],
968
+ "traced_tactics": [],
969
+ "url": "https://github.com/leanprover-community/mathlib4"
970
+ },
971
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
972
+ },
973
+ {
974
+ "error": "theorem has no selected tactic transitions",
975
+ "full_name": "Sum.elim_inv_inv",
976
+ "id": "Sum.elim_inv_inv",
977
+ "reason": "import_failure",
978
+ "selection": {
979
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
980
+ "end": [
981
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982
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983
+ ],
984
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
985
+ "full_name": "Sum.elim_inv_inv",
986
+ "start": [
987
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988
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989
+ ],
990
+ "traced_tactics": [],
991
+ "url": "https://github.com/leanprover-community/mathlib4"
992
+ },
993
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
994
+ },
995
+ {
996
+ "error": "theorem has no selected tactic transitions",
997
+ "full_name": "Sum.elim_one_one",
998
+ "id": "Sum.elim_one_one",
999
+ "reason": "import_failure",
1000
+ "selection": {
1001
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1002
+ "end": [
1003
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1004
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1005
+ ],
1006
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
1007
+ "full_name": "Sum.elim_one_one",
1008
+ "start": [
1009
+ 576,
1010
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1011
+ ],
1012
+ "traced_tactics": [],
1013
+ "url": "https://github.com/leanprover-community/mathlib4"
1014
+ },
1015
+ "source_file": "Mathlib/Algebra/Group/Pi/Basic.lean"
1016
+ }
1017
+ ],
1018
+ "input_proofs": 55,
1019
+ "input_units": 2,
1020
+ "proofs": 13,
1021
+ "published_proofs": 10,
1022
+ "published_transitions": 13,
1023
+ "replay_failures": [],
1024
+ "transitions": 23,
1025
+ "validation_failures": [
1026
+ {
1027
+ "errors": [
1028
+ "internal transition boundary mismatch",
1029
+ "internal transition boundary mismatch"
1030
+ ],
1031
+ "file_path": "Mathlib/Algebra/Group/PNatPowAssoc.lean",
1032
+ "proof_id": "mathlib:ppow_eq_pow",
1033
+ "provenance": {
1034
+ "selection": {
1035
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1036
+ "end": [
1037
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1038
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1039
+ ],
1040
+ "file_path": "Mathlib/Algebra/Group/PNatPowAssoc.lean",
1041
+ "full_name": "ppow_eq_pow",
1042
+ "start": [
1043
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1044
+ 1
1045
+ ],
1046
+ "traced_tactics": [
1047
+ {
1048
+ "annotated_tactic": [
1049
+ "\"refine <a>PNat.recOn<\\/a> n ?_ fun k hk \\u21a6 ?_\"",
1050
+ "[{\"full_name\":\"PNat.recOn\",\"def_path\":\"Mathlib\\/Data\\/PNat\\/Basic.lean\",\"def_pos\":[194,5],\"def_end_pos\":[194,10]}]"
1051
+ ],
1052
+ "state_after": "case refine_1\nM : Type u_1\ninst\u271d\u00b2 : Monoid M\ninst\u271d\u00b9 : Pow M \u2115+\ninst\u271d : PNatPowAssoc M\nx : M\nn : \u2115+\n\u22a2 x ^ 1 = x ^ \u21911\n\ncase refine_2\nM : Type u_1\ninst\u271d\u00b2 : Monoid M\ninst\u271d\u00b9 : Pow M \u2115+\ninst\u271d : PNatPowAssoc M\nx : M\nn k : \u2115+\nhk : x ^ k = x ^ \u2191k\n\u22a2 x ^ (k + 1) = x ^ \u2191(k + 1)",
1053
+ "state_before": "M : Type u_1\ninst\u271d\u00b2 : Monoid M\ninst\u271d\u00b9 : Pow M \u2115+\ninst\u271d : PNatPowAssoc M\nx : M\nn : \u2115+\n\u22a2 x ^ n = x ^ \u2191n",
1054
+ "tactic": "refine PNat.recOn n ?_ fun k hk \u21a6 ?_"
1055
+ },
1056
+ {
1057
+ "annotated_tactic": [
1058
+ "\"rw [<a>ppow_one<\\/a>, <a>PNat.one_coe<\\/a>, <a>pow_one<\\/a>]\"",
1059
+ "[{\"full_name\":\"ppow_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/PNatPowAssoc.lean\",\"def_pos\":[57,9],\"def_end_pos\":[57,17]},{\"full_name\":\"PNat.one_coe\",\"def_path\":\"Mathlib\\/Data\\/PNat\\/Defs.lean\",\"def_pos\":[197,9],\"def_end_pos\":[197,16]},{\"full_name\":\"pow_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[663,7],\"def_end_pos\":[663,14]}]"
1060
+ ],
1061
+ "state_after": "no goals",
1062
+ "state_before": "case refine_1\nM : Type u_1\ninst\u271d\u00b2 : Monoid M\ninst\u271d\u00b9 : Pow M \u2115+\ninst\u271d : PNatPowAssoc M\nx : M\nn : \u2115+\n\u22a2 x ^ 1 = x ^ \u21911",
1063
+ "tactic": "rw [ppow_one, PNat.one_coe, pow_one]"
1064
+ },
1065
+ {
1066
+ "annotated_tactic": [
1067
+ "\"rw [<a>ppow_add<\\/a>, <a>ppow_one<\\/a>, <a>PNat.add_coe<\\/a>, <a>pow_add<\\/a>, <a>PNat.one_coe<\\/a>, <a>pow_one<\\/a>, \\u2190 hk]\"",
1068
+ "[{\"full_name\":\"ppow_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/PNatPowAssoc.lean\",\"def_pos\":[53,9],\"def_end_pos\":[53,17]},{\"full_name\":\"ppow_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/PNatPowAssoc.lean\",\"def_pos\":[57,9],\"def_end_pos\":[57,17]},{\"full_name\":\"PNat.add_coe\",\"def_path\":\"Mathlib\\/Data\\/PNat\\/Basic.lean\",\"def_pos\":[129,9],\"def_end_pos\":[129,16]},{\"full_name\":\"pow_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[703,7],\"def_end_pos\":[703,14]},{\"full_name\":\"PNat.one_coe\",\"def_path\":\"Mathlib\\/Data\\/PNat\\/Defs.lean\",\"def_pos\":[197,9],\"def_end_pos\":[197,16]},{\"full_name\":\"pow_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[663,7],\"def_end_pos\":[663,14]}]"
1069
+ ],
1070
+ "state_after": "no goals",
1071
+ "state_before": "case refine_2\nM : Type u_1\ninst\u271d\u00b2 : Monoid M\ninst\u271d\u00b9 : Pow M \u2115+\ninst\u271d : PNatPowAssoc M\nx : M\nn k : \u2115+\nhk : x ^ k = x ^ \u2191k\n\u22a2 x ^ (k + 1) = x ^ \u2191(k + 1)",
1072
+ "tactic": "rw [ppow_add, ppow_one, PNat.add_coe, pow_add, PNat.one_coe, pow_one, \u2190 hk]"
1073
+ }
1074
+ ],
1075
+ "url": "https://github.com/leanprover-community/mathlib4"
1076
+ }
1077
+ },
1078
+ "theorem_name": "ppow_eq_pow"
1079
+ },
1080
+ {
1081
+ "errors": [
1082
+ "internal transition boundary mismatch",
1083
+ "internal transition boundary mismatch"
1084
+ ],
1085
+ "file_path": "Mathlib/Algebra/Group/PNatPowAssoc.lean",
1086
+ "proof_id": "mathlib:ppow_mul",
1087
+ "provenance": {
1088
+ "selection": {
1089
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1090
+ "end": [
1091
+ 70,
1092
+ 60
1093
+ ],
1094
+ "file_path": "Mathlib/Algebra/Group/PNatPowAssoc.lean",
1095
+ "full_name": "ppow_mul",
1096
+ "start": [
1097
+ 67,
1098
+ 1
1099
+ ],
1100
+ "traced_tactics": [
1101
+ {
1102
+ "annotated_tactic": [
1103
+ "\"refine <a>PNat.recOn<\\/a> n ?_ fun k hk \\u21a6 ?_\"",
1104
+ "[{\"full_name\":\"PNat.recOn\",\"def_path\":\"Mathlib\\/Data\\/PNat\\/Basic.lean\",\"def_pos\":[194,5],\"def_end_pos\":[194,10]}]"
1105
+ ],
1106
+ "state_after": "case refine_1\nM : Type u_1\ninst\u271d\u00b2 : Mul M\ninst\u271d\u00b9 : Pow M \u2115+\ninst\u271d : PNatPowAssoc M\nx : M\nm n : \u2115+\n\u22a2 x ^ (m * 1) = (x ^ m) ^ 1\n\ncase refine_2\nM : Type u_1\ninst\u271d\u00b2 : Mul M\ninst\u271d\u00b9 : Pow M \u2115+\ninst\u271d : PNatPowAssoc M\nx : M\nm n k : \u2115+\nhk : x ^ (m * k) = (x ^ m) ^ k\n\u22a2 x ^ (m * (k + 1)) = (x ^ m) ^ (k + 1)",
1107
+ "state_before": "M : Type u_1\ninst\u271d\u00b2 : Mul M\ninst\u271d\u00b9 : Pow M \u2115+\ninst\u271d : PNatPowAssoc M\nx : M\nm n : \u2115+\n\u22a2 x ^ (m * n) = (x ^ m) ^ n",
1108
+ "tactic": "refine PNat.recOn n ?_ fun k hk \u21a6 ?_"
1109
+ },
1110
+ {
1111
+ "annotated_tactic": [
1112
+ "\"rw [<a>ppow_one<\\/a>, <a>mul_one<\\/a>]\"",
1113
+ "[{\"full_name\":\"ppow_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/PNatPowAssoc.lean\",\"def_pos\":[57,9],\"def_end_pos\":[57,17]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]}]"
1114
+ ],
1115
+ "state_after": "no goals",
1116
+ "state_before": "case refine_1\nM : Type u_1\ninst\u271d\u00b2 : Mul M\ninst\u271d\u00b9 : Pow M \u2115+\ninst\u271d : PNatPowAssoc M\nx : M\nm n : \u2115+\n\u22a2 x ^ (m * 1) = (x ^ m) ^ 1",
1117
+ "tactic": "rw [ppow_one, mul_one]"
1118
+ },
1119
+ {
1120
+ "annotated_tactic": [
1121
+ "\"rw [<a>ppow_add<\\/a>, <a>ppow_one<\\/a>, <a>mul_add<\\/a>, <a>ppow_add<\\/a>, <a>mul_one<\\/a>, hk]\"",
1122
+ "[{\"full_name\":\"ppow_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/PNatPowAssoc.lean\",\"def_pos\":[53,9],\"def_end_pos\":[53,17]},{\"full_name\":\"ppow_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/PNatPowAssoc.lean\",\"def_pos\":[57,9],\"def_end_pos\":[57,17]},{\"full_name\":\"mul_add\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[83,7],\"def_end_pos\":[83,14]},{\"full_name\":\"ppow_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/PNatPowAssoc.lean\",\"def_pos\":[53,9],\"def_end_pos\":[53,17]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]}]"
1123
+ ],
1124
+ "state_after": "no goals",
1125
+ "state_before": "case refine_2\nM : Type u_1\ninst\u271d\u00b2 : Mul M\ninst\u271d\u00b9 : Pow M \u2115+\ninst\u271d : PNatPowAssoc M\nx : M\nm n k : \u2115+\nhk : x ^ (m * k) = (x ^ m) ^ k\n\u22a2 x ^ (m * (k + 1)) = (x ^ m) ^ (k + 1)",
1126
+ "tactic": "rw [ppow_add, ppow_one, mul_add, ppow_add, mul_one, hk]"
1127
+ }
1128
+ ],
1129
+ "url": "https://github.com/leanprover-community/mathlib4"
1130
+ }
1131
+ },
1132
+ "theorem_name": "ppow_mul"
1133
+ },
1134
+ {
1135
+ "errors": [
1136
+ "internal transition boundary mismatch",
1137
+ "internal transition boundary mismatch"
1138
+ ],
1139
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
1140
+ "proof_id": "mathlib:Pi.apply_mulSingle\u2082",
1141
+ "provenance": {
1142
+ "selection": {
1143
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1144
+ "end": [
1145
+ 415,
1146
+ 42
1147
+ ],
1148
+ "file_path": "Mathlib/Algebra/Group/Pi/Basic.lean",
1149
+ "full_name": "Pi.apply_mulSingle\u2082",
1150
+ "start": [
1151
+ 409,
1152
+ 1
1153
+ ],
1154
+ "traced_tactics": [
1155
+ {
1156
+ "annotated_tactic": [
1157
+ "\"by_cases h : j = i\"",
1158
+ "[]"
1159
+ ],
1160
+ "state_after": "case pos\nI : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf : I \u2192 Type v\u2081\ng : I \u2192 Type v\u2082\nh\u271d : I \u2192 Type v\u2083\nx\u271d y\u271d : (i : I) \u2192 f i\ni\u271d : I\ninst\u271d\u00b3 : DecidableEq I\ninst\u271d\u00b2 : (i : I) \u2192 One (f i)\ninst\u271d\u00b9 : (i : I) \u2192 One (g i)\ninst\u271d : (i : I) \u2192 One (h\u271d i)\nf' : (i : I) \u2192 f i \u2192 g i \u2192 h\u271d i\nhf' : \u2200 (i : I), f' i 1 1 = 1\ni : I\nx : f i\ny : g i\nj : I\nh : j = i\n\u22a2 f' j (mulSingle i x j) (mulSingle i y j) = mulSingle i (f' i x y) j\n\ncase neg\nI : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf : I \u2192 Type v\u2081\ng : I \u2192 Type v\u2082\nh\u271d : I \u2192 Type v\u2083\nx\u271d y\u271d : (i : I) \u2192 f i\ni\u271d : I\ninst\u271d\u00b3 : DecidableEq I\ninst\u271d\u00b2 : (i : I) \u2192 One (f i)\ninst\u271d\u00b9 : (i : I) \u2192 One (g i)\ninst\u271d : (i : I) \u2192 One (h\u271d i)\nf' : (i : I) \u2192 f i \u2192 g i \u2192 h\u271d i\nhf' : \u2200 (i : I), f' i 1 1 = 1\ni : I\nx : f i\ny : g i\nj : I\nh : \u00acj = i\n\u22a2 f' j (mulSingle i x j) (mulSingle i y j) = mulSingle i (f' i x y) j",
1161
+ "state_before": "I : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf : I \u2192 Type v\u2081\ng : I \u2192 Type v\u2082\nh : I \u2192 Type v\u2083\nx\u271d y\u271d : (i : I) \u2192 f i\ni\u271d : I\ninst\u271d\u00b3 : DecidableEq I\ninst\u271d\u00b2 : (i : I) \u2192 One (f i)\ninst\u271d\u00b9 : (i : I) \u2192 One (g i)\ninst\u271d : (i : I) \u2192 One (h i)\nf' : (i : I) \u2192 f i \u2192 g i \u2192 h i\nhf' : \u2200 (i : I), f' i 1 1 = 1\ni : I\nx : f i\ny : g i\nj : I\n\u22a2 f' j (mulSingle i x j) (mulSingle i y j) = mulSingle i (f' i x y) j",
1162
+ "tactic": "by_cases h : j = i"
1163
+ },
1164
+ {
1165
+ "annotated_tactic": [
1166
+ "\"subst h\"",
1167
+ "[]"
1168
+ ],
1169
+ "state_after": "case pos\nI : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf : I \u2192 Type v\u2081\ng : I \u2192 Type v\u2082\nh : I \u2192 Type v\u2083\nx\u271d y\u271d : (i : I) \u2192 f i\ni : I\ninst\u271d\u00b3 : DecidableEq I\ninst\u271d\u00b2 : (i : I) \u2192 One (f i)\ninst\u271d\u00b9 : (i : I) \u2192 One (g i)\ninst\u271d : (i : I) \u2192 One (h i)\nf' : (i : I) \u2192 f i \u2192 g i \u2192 h i\nhf' : \u2200 (i : I), f' i 1 1 = 1\nj : I\nx : f j\ny : g j\n\u22a2 f' j (mulSingle j x j) (mulSingle j y j) = mulSingle j (f' j x y) j",
1170
+ "state_before": "case pos\nI : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf : I \u2192 Type v\u2081\ng : I \u2192 Type v\u2082\nh\u271d : I \u2192 Type v\u2083\nx\u271d y\u271d : (i : I) \u2192 f i\ni\u271d : I\ninst\u271d\u00b3 : DecidableEq I\ninst\u271d\u00b2 : (i : I) \u2192 One (f i)\ninst\u271d\u00b9 : (i : I) \u2192 One (g i)\ninst\u271d : (i : I) \u2192 One (h\u271d i)\nf' : (i : I) \u2192 f i \u2192 g i \u2192 h\u271d i\nhf' : \u2200 (i : I), f' i 1 1 = 1\ni : I\nx : f i\ny : g i\nj : I\nh : j = i\n\u22a2 f' j (mulSingle i x j) (mulSingle i y j) = mulSingle i (f' i x y) j",
1171
+ "tactic": "subst h"
1172
+ },
1173
+ {
1174
+ "annotated_tactic": [
1175
+ "\"simp only [<a>mulSingle_eq_same<\\/a>]\"",
1176
+ "[{\"full_name\":\"Pi.mulSingle_eq_same\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[355,9],\"def_end_pos\":[355,26]}]"
1177
+ ],
1178
+ "state_after": "no goals",
1179
+ "state_before": "case pos\nI : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf : I \u2192 Type v\u2081\ng : I \u2192 Type v\u2082\nh : I \u2192 Type v\u2083\nx\u271d y\u271d : (i : I) \u2192 f i\ni : I\ninst\u271d\u00b3 : DecidableEq I\ninst\u271d\u00b2 : (i : I) \u2192 One (f i)\ninst\u271d\u00b9 : (i : I) \u2192 One (g i)\ninst\u271d : (i : I) \u2192 One (h i)\nf' : (i : I) \u2192 f i \u2192 g i \u2192 h i\nhf' : \u2200 (i : I), f' i 1 1 = 1\nj : I\nx : f j\ny : g j\n\u22a2 f' j (mulSingle j x j) (mulSingle j y j) = mulSingle j (f' j x y) j",
1180
+ "tactic": "simp only [mulSingle_eq_same]"
1181
+ },
1182
+ {
1183
+ "annotated_tactic": [
1184
+ "\"simp only [<a>mulSingle_eq_of_ne<\\/a> h, hf']\"",
1185
+ "[{\"full_name\":\"Pi.mulSingle_eq_of_ne\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[361,9],\"def_end_pos\":[361,27]}]"
1186
+ ],
1187
+ "state_after": "no goals",
1188
+ "state_before": "case neg\nI : Type u\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nf : I \u2192 Type v\u2081\ng : I \u2192 Type v\u2082\nh\u271d : I \u2192 Type v\u2083\nx\u271d y\u271d : (i : I) \u2192 f i\ni\u271d : I\ninst\u271d\u00b3 : DecidableEq I\ninst\u271d\u00b2 : (i : I) \u2192 One (f i)\ninst\u271d\u00b9 : (i : I) \u2192 One (g i)\ninst\u271d : (i : I) \u2192 One (h\u271d i)\nf' : (i : I) \u2192 f i \u2192 g i \u2192 h\u271d i\nhf' : \u2200 (i : I), f' i 1 1 = 1\ni : I\nx : f i\ny : g i\nj : I\nh : \u00acj = i\n\u22a2 f' j (mulSingle i x j) (mulSingle i y j) = mulSingle i (f' i x y) j",
1189
+ "tactic": "simp only [mulSingle_eq_of_ne h, hf']"
1190
+ }
1191
+ ],
1192
+ "url": "https://github.com/leanprover-community/mathlib4"
1193
+ }
1194
+ },
1195
+ "theorem_name": "Pi.apply_mulSingle\u2082"
1196
+ }
1197
+ ],
1198
+ "validation_rejected_proofs": 3,
1199
+ "zero_transition_proofs": 0
1200
+ },
1201
+ "shards": [
1202
+ {
1203
+ "path": "data/train/mathlib-000126-0000-379bbb6e80f96e69.parquet",
1204
+ "sha256": "379bbb6e80f96e69707b3623d49d1ab4505fef3257838cbb0527b85e49b6148c",
1205
+ "bytes": 61442,
1206
+ "rows": 11,
1207
+ "revision": "af86e21b60c160a59e94c440a8a9eafd00a59b94"
1208
+ },
1209
+ {
1210
+ "path": "data/internal_test/mathlib-000126-0000-557f3ab4cd01fa5f.parquet",
1211
+ "sha256": "557f3ab4cd01fa5f612f6344081f692b24c518df0d9d1f3b040d152b04e6fd7d",
1212
+ "bytes": 45529,
1213
+ "rows": 2,
1214
+ "revision": "af86e21b60c160a59e94c440a8a9eafd00a59b94"
1215
+ }
1216
+ ],
1217
+ "proof_ids": [
1218
+ "mathlib:Function.comp_eq_one_iff",
1219
+ "mathlib:Function.extend_one",
1220
+ "mathlib:Subsingleton.pi_mulSingle_eq",
1221
+ "mathlib:Sum.elim_div_div",
1222
+ "mathlib:Sum.elim_mulSingle_one",
1223
+ "mathlib:Sum.elim_mul_mul",
1224
+ "mathlib:Sum.elim_one_mulSingle",
1225
+ "mathlib:ppow_mul'",
1226
+ "mathlib:ppow_mul_assoc",
1227
+ "mathlib:ppow_mul_comm"
1228
+ ],
1229
+ "proof_keys": [
1230
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/PNatPowAssoc.lean\",null,null,\"ppow_mul'\"]",
1231
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/PNatPowAssoc.lean\",null,null,\"ppow_mul_assoc\"]",
1232
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/PNatPowAssoc.lean\",null,null,\"ppow_mul_comm\"]",
1233
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Pi/Basic.lean\",null,null,\"Function.comp_eq_one_iff\"]",
1234
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Pi/Basic.lean\",null,null,\"Function.extend_one\"]",
1235
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Pi/Basic.lean\",null,null,\"Subsingleton.pi_mulSingle_eq\"]",
1236
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Pi/Basic.lean\",null,null,\"Sum.elim_div_div\"]",
1237
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Pi/Basic.lean\",null,null,\"Sum.elim_mulSingle_one\"]",
1238
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Pi/Basic.lean\",null,null,\"Sum.elim_mul_mul\"]",
1239
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Pi/Basic.lean\",null,null,\"Sum.elim_one_mulSingle\"]"
1240
+ ]
1241
+ }
manifests/batches/mathlib/000127.json ADDED
The diff for this file is too large to render. See raw diff
 
manifests/batches/mathlib/000128.json ADDED
@@ -0,0 +1,332 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000128",
4
+ "batch_fingerprint": "6fbb34d7d224fa1080eab189733229505bb215db26b29c2716cafe94c107fd24",
5
+ "evidence": {
6
+ "batch_fingerprint": "6fbb34d7d224fa1080eab189733229505bb215db26b29c2716cafe94c107fd24",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "no internal trace for tactic 'rw [mul_assoc]'",
11
+ "full_name": "SemiconjBy.conj_iff",
12
+ "id": "SemiconjBy.conj_iff",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 152,
18
+ 75
19
+ ],
20
+ "file_path": "Mathlib/Algebra/Group/Semiconj/Defs.lean",
21
+ "full_name": "SemiconjBy.conj_iff",
22
+ "start": [
23
+ 147,
24
+ 1
25
+ ],
26
+ "traced_tactics": [
27
+ {
28
+ "annotated_tactic": [
29
+ "\"unfold <a>SemiconjBy<\\/a>\"",
30
+ "[{\"full_name\":\"SemiconjBy\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Semiconj\\/Defs.lean\",\"def_pos\":[40,5],\"def_end_pos\":[40,15]}]"
31
+ ],
32
+ "state_after": "S : Type u_1\nM : Type u_2\nG : Type u_3\ninst\u271d : Group G\na\u271d x\u271d y\u271d a x y b : G\n\u22a2 b * a * b\u207b\u00b9 * (b * x * b\u207b\u00b9) = b * y * b\u207b\u00b9 * (b * a * b\u207b\u00b9) \u2194 a * x = y * a",
33
+ "state_before": "S : Type u_1\nM : Type u_2\nG : Type u_3\ninst\u271d : Group G\na\u271d x\u271d y\u271d a x y b : G\n\u22a2 SemiconjBy (b * a * b\u207b\u00b9) (b * x * b\u207b\u00b9) (b * y * b\u207b\u00b9) \u2194 SemiconjBy a x y",
34
+ "tactic": "unfold SemiconjBy"
35
+ },
36
+ {
37
+ "annotated_tactic": [
38
+ "\"simp only [\\u2190 <a>mul_assoc<\\/a>, <a>inv_mul_cancel_right<\\/a>]\"",
39
+ "[{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]},{\"full_name\":\"inv_mul_cancel_right\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1268,9],\"def_end_pos\":[1268,29]}]"
40
+ ],
41
+ "state_after": "S : Type u_1\nM : Type u_2\nG : Type u_3\ninst\u271d : Group G\na\u271d x\u271d y\u271d a x y b : G\n\u22a2 b * a * x * b\u207b\u00b9 = b * y * a * b\u207b\u00b9 \u2194 a * x = y * a",
42
+ "state_before": "S : Type u_1\nM : Type u_2\nG : Type u_3\ninst\u271d : Group G\na\u271d x\u271d y\u271d a x y b : G\n\u22a2 b * a * b\u207b\u00b9 * (b * x * b\u207b\u00b9) = b * y * b\u207b\u00b9 * (b * a * b\u207b\u00b9) \u2194 a * x = y * a",
43
+ "tactic": "simp only [\u2190 mul_assoc, inv_mul_cancel_right]"
44
+ },
45
+ {
46
+ "annotated_tactic": [
47
+ "\"repeat rw [<a>mul_assoc<\\/a>]\"",
48
+ "[{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]}]"
49
+ ],
50
+ "state_after": "S : Type u_1\nM : Type u_2\nG : Type u_3\ninst\u271d : Group G\na\u271d x\u271d y\u271d a x y b : G\n\u22a2 b * (a * (x * b\u207b\u00b9)) = b * (y * (a * b\u207b\u00b9)) \u2194 a * x = y * a",
51
+ "state_before": "S : Type u_1\nM : Type u_2\nG : Type u_3\ninst\u271d : Group G\na\u271d x\u271d y\u271d a x y b : G\n\u22a2 b * a * x * b\u207b\u00b9 = b * y * a * b\u207b\u00b9 \u2194 a * x = y * a",
52
+ "tactic": "repeat rw [mul_assoc]"
53
+ },
54
+ {
55
+ "annotated_tactic": [
56
+ "\"rw [<a>mul_left_cancel_iff<\\/a>, \\u2190 <a>mul_assoc<\\/a>, \\u2190 <a>mul_assoc<\\/a>, <a>mul_right_cancel_iff<\\/a>]\"",
57
+ "[{\"full_name\":\"mul_left_cancel_iff\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[237,9],\"def_end_pos\":[237,28]},{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]},{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]},{\"full_name\":\"mul_right_cancel_iff\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[255,9],\"def_end_pos\":[255,29]}]"
58
+ ],
59
+ "state_after": "no goals",
60
+ "state_before": "S : Type u_1\nM : Type u_2\nG : Type u_3\ninst\u271d : Group G\na\u271d x\u271d y\u271d a x y b : G\n\u22a2 b * (a * (x * b\u207b\u00b9)) = b * (y * (a * b\u207b\u00b9)) \u2194 a * x = y * a",
61
+ "tactic": "rw [mul_left_cancel_iff, \u2190 mul_assoc, \u2190 mul_assoc, mul_right_cancel_iff]"
62
+ },
63
+ {
64
+ "annotated_tactic": [
65
+ "\"rw [<a>mul_assoc<\\/a>]\"",
66
+ "[{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]}]"
67
+ ],
68
+ "state_after": "S : Type u_1\nM : Type u_2\nG : Type u_3\ninst\u271d : Group G\na\u271d x\u271d y\u271d a x y b : G\n\u22a2 b * (a * (x * b\u207b\u00b9)) = b * (y * (a * b\u207b\u00b9)) \u2194 a * x = y * a",
69
+ "state_before": "S : Type u_1\nM : Type u_2\nG : Type u_3\ninst\u271d : Group G\na\u271d x\u271d y\u271d a x y b : G\n\u22a2 b * (a * (x * b\u207b\u00b9)) = b * y * (a * b\u207b\u00b9) \u2194 a * x = y * a",
70
+ "tactic": "rw [mul_assoc]"
71
+ }
72
+ ],
73
+ "url": "https://github.com/leanprover-community/mathlib4"
74
+ },
75
+ "source_file": "Mathlib/Algebra/Group/Semiconj/Defs.lean"
76
+ },
77
+ {
78
+ "error": "theorem has no selected tactic transitions",
79
+ "full_name": "SemiconjBy.eq",
80
+ "id": "SemiconjBy.eq",
81
+ "reason": "import_failure",
82
+ "selection": {
83
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
84
+ "end": [
85
+ 50,
86
+ 4
87
+ ],
88
+ "file_path": "Mathlib/Algebra/Group/Semiconj/Defs.lean",
89
+ "full_name": "SemiconjBy.eq",
90
+ "start": [
91
+ 49,
92
+ 11
93
+ ],
94
+ "traced_tactics": [],
95
+ "url": "https://github.com/leanprover-community/mathlib4"
96
+ },
97
+ "source_file": "Mathlib/Algebra/Group/Semiconj/Defs.lean"
98
+ },
99
+ {
100
+ "error": "theorem has no selected tactic transitions",
101
+ "full_name": "SemiconjBy.one_left",
102
+ "id": "SemiconjBy.one_left",
103
+ "reason": "import_failure",
104
+ "selection": {
105
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
106
+ "end": [
107
+ 104,
108
+ 25
109
+ ],
110
+ "file_path": "Mathlib/Algebra/Group/Semiconj/Defs.lean",
111
+ "full_name": "SemiconjBy.one_left",
112
+ "start": [
113
+ 103,
114
+ 1
115
+ ],
116
+ "traced_tactics": [],
117
+ "url": "https://github.com/leanprover-community/mathlib4"
118
+ },
119
+ "source_file": "Mathlib/Algebra/Group/Semiconj/Defs.lean"
120
+ },
121
+ {
122
+ "error": "theorem has no selected tactic transitions",
123
+ "full_name": "SemiconjBy.reflexive",
124
+ "id": "SemiconjBy.reflexive",
125
+ "reason": "import_failure",
126
+ "selection": {
127
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
128
+ "end": [
129
+ 113,
130
+ 25
131
+ ],
132
+ "file_path": "Mathlib/Algebra/Group/Semiconj/Defs.lean",
133
+ "full_name": "SemiconjBy.reflexive",
134
+ "start": [
135
+ 112,
136
+ 11
137
+ ],
138
+ "traced_tactics": [],
139
+ "url": "https://github.com/leanprover-community/mathlib4"
140
+ },
141
+ "source_file": "Mathlib/Algebra/Group/Semiconj/Defs.lean"
142
+ },
143
+ {
144
+ "error": "theorem has no selected tactic transitions",
145
+ "full_name": "SemiconjBy.transitive",
146
+ "id": "SemiconjBy.transitive",
147
+ "reason": "import_failure",
148
+ "selection": {
149
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
150
+ "end": [
151
+ 85,
152
+ 57
153
+ ],
154
+ "file_path": "Mathlib/Algebra/Group/Semiconj/Defs.lean",
155
+ "full_name": "SemiconjBy.transitive",
156
+ "start": [
157
+ 84,
158
+ 11
159
+ ],
160
+ "traced_tactics": [],
161
+ "url": "https://github.com/leanprover-community/mathlib4"
162
+ },
163
+ "source_file": "Mathlib/Algebra/Group/Semiconj/Defs.lean"
164
+ }
165
+ ],
166
+ "input_proofs": 15,
167
+ "input_units": 2,
168
+ "proofs": 10,
169
+ "published_proofs": 8,
170
+ "published_transitions": 11,
171
+ "replay_failures": [],
172
+ "transitions": 19,
173
+ "validation_failures": [
174
+ {
175
+ "errors": [
176
+ "internal transition boundary mismatch"
177
+ ],
178
+ "file_path": "Mathlib/Algebra/Group/Semiconj/Basic.lean",
179
+ "proof_id": "mathlib:SemiconjBy.zpow_right",
180
+ "provenance": {
181
+ "selection": {
182
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
183
+ "end": [
184
+ 62,
185
+ 22
186
+ ],
187
+ "file_path": "Mathlib/Algebra/Group/Semiconj/Basic.lean",
188
+ "full_name": "SemiconjBy.zpow_right",
189
+ "start": [
190
+ 57,
191
+ 1
192
+ ],
193
+ "traced_tactics": [
194
+ {
195
+ "annotated_tactic": [
196
+ "\"simp [<a>zpow_natCast<\\/a>, h.pow_right n]\"",
197
+ "[{\"full_name\":\"zpow_natCast\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1021,9],\"def_end_pos\":[1021,21]}]"
198
+ ],
199
+ "state_after": "no goals",
200
+ "state_before": "G : Type u_1\ninst\u271d : Group G\na x y : G\nh : SemiconjBy a x y\nn : \u2115\n\u22a2 SemiconjBy a (x ^ \u2191n) (y ^ \u2191n)",
201
+ "tactic": "simp [zpow_natCast, h.pow_right n]"
202
+ },
203
+ {
204
+ "annotated_tactic": [
205
+ "\"simp only [<a>zpow_negSucc<\\/a>, <a>inv_right_iff<\\/a>]\"",
206
+ "[{\"full_name\":\"zpow_negSucc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1040,9],\"def_end_pos\":[1040,21]},{\"full_name\":\"SemiconjBy.inv_right_iff\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Semiconj\\/Basic.lean\",\"def_pos\":[49,37],\"def_end_pos\":[49,50]}]"
207
+ ],
208
+ "state_after": "G : Type u_1\ninst\u271d : Group G\na x y : G\nh : SemiconjBy a x y\nn : \u2115\n\u22a2 SemiconjBy a (x ^ (n + 1)) (y ^ (n + 1))",
209
+ "state_before": "G : Type u_1\ninst\u271d : Group G\na x y : G\nh : SemiconjBy a x y\nn : \u2115\n\u22a2 SemiconjBy a (x ^ Int.negSucc n) (y ^ Int.negSucc n)",
210
+ "tactic": "simp only [zpow_negSucc, inv_right_iff]"
211
+ },
212
+ {
213
+ "annotated_tactic": [
214
+ "\"apply <a>pow_right<\\/a> h\"",
215
+ "[{\"full_name\":\"SemiconjBy.pow_right\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Semiconj\\/Defs.lean\",\"def_pos\":[124,9],\"def_end_pos\":[124,18]}]"
216
+ ],
217
+ "state_after": "no goals",
218
+ "state_before": "G : Type u_1\ninst\u271d : Group G\na x y : G\nh : SemiconjBy a x y\nn : \u2115\n\u22a2 SemiconjBy a (x ^ (n + 1)) (y ^ (n + 1))",
219
+ "tactic": "apply pow_right h"
220
+ }
221
+ ],
222
+ "url": "https://github.com/leanprover-community/mathlib4"
223
+ }
224
+ },
225
+ "theorem_name": "SemiconjBy.zpow_right"
226
+ },
227
+ {
228
+ "errors": [
229
+ "internal transition boundary mismatch",
230
+ "internal transition boundary mismatch"
231
+ ],
232
+ "file_path": "Mathlib/Algebra/Group/Semiconj/Defs.lean",
233
+ "proof_id": "mathlib:SemiconjBy.pow_right",
234
+ "provenance": {
235
+ "selection": {
236
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
237
+ "end": [
238
+ 129,
239
+ 25
240
+ ],
241
+ "file_path": "Mathlib/Algebra/Group/Semiconj/Defs.lean",
242
+ "full_name": "SemiconjBy.pow_right",
243
+ "start": [
244
+ 124,
245
+ 1
246
+ ],
247
+ "traced_tactics": [
248
+ {
249
+ "annotated_tactic": [
250
+ "\"induction' n with n ih\"",
251
+ "[]"
252
+ ],
253
+ "state_after": "case zero\nS : Type u_1\nM : Type u_2\nG : Type u_3\ninst\u271d : Monoid M\na x y : M\nh : SemiconjBy a x y\n\u22a2 SemiconjBy a (x ^ 0) (y ^ 0)\n\ncase succ\nS : Type u_1\nM : Type u_2\nG : Type u_3\ninst\u271d : Monoid M\na x y : M\nh : SemiconjBy a x y\nn : \u2115\nih : SemiconjBy a (x ^ n) (y ^ n)\n\u22a2 SemiconjBy a (x ^ (n + 1)) (y ^ (n + 1))",
254
+ "state_before": "S : Type u_1\nM : Type u_2\nG : Type u_3\ninst\u271d : Monoid M\na x y : M\nh : SemiconjBy a x y\nn : \u2115\n\u22a2 SemiconjBy a (x ^ n) (y ^ n)",
255
+ "tactic": "induction' n with n ih"
256
+ },
257
+ {
258
+ "annotated_tactic": [
259
+ "\"rw [<a>pow_zero<\\/a>, <a>pow_zero<\\/a>]\"",
260
+ "[{\"full_name\":\"pow_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[651,9],\"def_end_pos\":[651,17]},{\"full_name\":\"pow_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[651,9],\"def_end_pos\":[651,17]}]"
261
+ ],
262
+ "state_after": "case zero\nS : Type u_1\nM : Type u_2\nG : Type u_3\ninst\u271d : Monoid M\na x y : M\nh : SemiconjBy a x y\n\u22a2 SemiconjBy a 1 1",
263
+ "state_before": "case zero\nS : Type u_1\nM : Type u_2\nG : Type u_3\ninst\u271d : Monoid M\na x y : M\nh : SemiconjBy a x y\n\u22a2 SemiconjBy a (x ^ 0) (y ^ 0)",
264
+ "tactic": "rw [pow_zero, pow_zero]"
265
+ },
266
+ {
267
+ "annotated_tactic": [
268
+ "\"exact <a>SemiconjBy.one_right<\\/a> _\"",
269
+ "[{\"full_name\":\"SemiconjBy.one_right\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Semiconj\\/Defs.lean\",\"def_pos\":[97,9],\"def_end_pos\":[97,18]}]"
270
+ ],
271
+ "state_after": "no goals",
272
+ "state_before": "case zero\nS : Type u_1\nM : Type u_2\nG : Type u_3\ninst\u271d : Monoid M\na x y : M\nh : SemiconjBy a x y\n\u22a2 SemiconjBy a 1 1",
273
+ "tactic": "exact SemiconjBy.one_right _"
274
+ },
275
+ {
276
+ "annotated_tactic": [
277
+ "\"rw [<a>pow_succ<\\/a>, <a>pow_succ<\\/a>]\"",
278
+ "[{\"full_name\":\"pow_succ\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[657,9],\"def_end_pos\":[657,17]},{\"full_name\":\"pow_succ\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[657,9],\"def_end_pos\":[657,17]}]"
279
+ ],
280
+ "state_after": "case succ\nS : Type u_1\nM : Type u_2\nG : Type u_3\ninst\u271d : Monoid M\na x y : M\nh : SemiconjBy a x y\nn : \u2115\nih : SemiconjBy a (x ^ n) (y ^ n)\n\u22a2 SemiconjBy a (x ^ n * x) (y ^ n * y)",
281
+ "state_before": "case succ\nS : Type u_1\nM : Type u_2\nG : Type u_3\ninst\u271d : Monoid M\na x y : M\nh : SemiconjBy a x y\nn : \u2115\nih : SemiconjBy a (x ^ n) (y ^ n)\n\u22a2 SemiconjBy a (x ^ (n + 1)) (y ^ (n + 1))",
282
+ "tactic": "rw [pow_succ, pow_succ]"
283
+ },
284
+ {
285
+ "annotated_tactic": [
286
+ "\"exact ih.mul_right h\"",
287
+ "[]"
288
+ ],
289
+ "state_after": "no goals",
290
+ "state_before": "case succ\nS : Type u_1\nM : Type u_2\nG : Type u_3\ninst\u271d : Monoid M\na x y : M\nh : SemiconjBy a x y\nn : \u2115\nih : SemiconjBy a (x ^ n) (y ^ n)\n\u22a2 SemiconjBy a (x ^ n * x) (y ^ n * y)",
291
+ "tactic": "exact ih.mul_right h"
292
+ }
293
+ ],
294
+ "url": "https://github.com/leanprover-community/mathlib4"
295
+ }
296
+ },
297
+ "theorem_name": "SemiconjBy.pow_right"
298
+ }
299
+ ],
300
+ "validation_rejected_proofs": 2,
301
+ "zero_transition_proofs": 0
302
+ },
303
+ "shards": [
304
+ {
305
+ "path": "data/train/mathlib-000128-0000-3202b1edbb039a72.parquet",
306
+ "sha256": "3202b1edbb039a728fc537c86da8a821d82872e87edbcf196b8de34d59f323bc",
307
+ "bytes": 50345,
308
+ "rows": 11,
309
+ "revision": "af86e21b60c160a59e94c440a8a9eafd00a59b94"
310
+ }
311
+ ],
312
+ "proof_ids": [
313
+ "mathlib:SemiconjBy.conj_mk",
314
+ "mathlib:SemiconjBy.inv_inv_symm_iff",
315
+ "mathlib:SemiconjBy.inv_right_iff",
316
+ "mathlib:SemiconjBy.inv_symm_left_iff",
317
+ "mathlib:SemiconjBy.mul_left",
318
+ "mathlib:SemiconjBy.mul_right",
319
+ "mathlib:SemiconjBy.one_right",
320
+ "mathlib:semiconjBy_iff_eq"
321
+ ],
322
+ "proof_keys": [
323
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Semiconj/Basic.lean\",null,null,\"SemiconjBy.inv_inv_symm_iff\"]",
324
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Semiconj/Basic.lean\",null,null,\"SemiconjBy.inv_right_iff\"]",
325
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Semiconj/Basic.lean\",null,null,\"SemiconjBy.inv_symm_left_iff\"]",
326
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Semiconj/Defs.lean\",null,null,\"SemiconjBy.conj_mk\"]",
327
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Semiconj/Defs.lean\",null,null,\"SemiconjBy.mul_left\"]",
328
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Semiconj/Defs.lean\",null,null,\"SemiconjBy.mul_right\"]",
329
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Semiconj/Defs.lean\",null,null,\"SemiconjBy.one_right\"]",
330
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Semiconj/Defs.lean\",null,null,\"semiconjBy_iff_eq\"]"
331
+ ]
332
+ }
manifests/batches/mathlib/000129.json ADDED
@@ -0,0 +1,367 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000129",
4
+ "batch_fingerprint": "5cb9c219487af463a77a4e50386aafa6ef16d60b2a0d21ac066e0e249b98fb3b",
5
+ "evidence": {
6
+ "batch_fingerprint": "5cb9c219487af463a77a4e50386aafa6ef16d60b2a0d21ac066e0e249b98fb3b",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "SemiconjBy.units_inv_right_iff",
12
+ "id": "SemiconjBy.units_inv_right_iff",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
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18
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19
+ ],
20
+ "file_path": "Mathlib/Algebra/Group/Semiconj/Units.lean",
21
+ "full_name": "SemiconjBy.units_inv_right_iff",
22
+ "start": [
23
+ 56,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/Algebra/Group/Semiconj/Units.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "SemiconjBy.units_inv_symm_left_iff",
34
+ "id": "SemiconjBy.units_inv_symm_left_iff",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 73,
40
+ 45
41
+ ],
42
+ "file_path": "Mathlib/Algebra/Group/Semiconj/Units.lean",
43
+ "full_name": "SemiconjBy.units_inv_symm_left_iff",
44
+ "start": [
45
+ 72,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/Algebra/Group/Semiconj/Units.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "SemiconjBy.units_of_val",
56
+ "id": "SemiconjBy.units_of_val",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 85,
62
+ 14
63
+ ],
64
+ "file_path": "Mathlib/Algebra/Group/Semiconj/Units.lean",
65
+ "full_name": "SemiconjBy.units_of_val",
66
+ "start": [
67
+ 84,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/Algebra/Group/Semiconj/Units.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "SemiconjBy.units_val",
78
+ "id": "SemiconjBy.units_val",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 79,
84
+ 24
85
+ ],
86
+ "file_path": "Mathlib/Algebra/Group/Semiconj/Units.lean",
87
+ "full_name": "SemiconjBy.units_val",
88
+ "start": [
89
+ 78,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/Algebra/Group/Semiconj/Units.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "SemiconjBy.units_val_iff",
100
+ "id": "SemiconjBy.units_val_iff",
101
+ "reason": "import_failure",
102
+ "selection": {
103
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
104
+ "end": [
105
+ 91,
106
+ 28
107
+ ],
108
+ "file_path": "Mathlib/Algebra/Group/Semiconj/Units.lean",
109
+ "full_name": "SemiconjBy.units_val_iff",
110
+ "start": [
111
+ 90,
112
+ 1
113
+ ],
114
+ "traced_tactics": [],
115
+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
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142
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+ }
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+ },
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34
+ "numina:1edfe1b1-8113-5afb-8cd2-98b297640891",
35
+ "numina:ac694573-06db-5da0-b91b-d7f1b091fa6c"
36
+ ],
37
+ "proof_keys": [
38
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_004455.lean\",\"1ee525579f4160a1e17392d22fce6430f54c96a9a10746d67569e8416cd0743b\",0,\"algebra_1112\"]",
39
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_004456.lean\",\"05a335d1f3392c386be75f7a79824004dc4ad4cfea89835fe8d42e65217797e2\",0,\"number_theory_608236\"]",
40
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_004457.lean\",\"e024de4f56c9821feb91a3bdd76217952c73013498861c09f2567cf4a6ab09ac\",0,\"algebra_605156\"]",
41
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_004458.lean\",\"a822347b04460817c584a0e1337083b69970c1e0cd9952f08511a12084f81eaa\",0,\"algebra_605157\"]",
42
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_004459.lean\",\"7521ae778b18fabfadacd91448404626d2196126be1e82ecea44a7c5f970609d\",0,\"algebra_14205\"]"
43
+ ]
44
+ }