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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
3aa359b
·
verified ·
1 Parent(s): 2724ca8

Record 20 verified HPC batch manifests

Browse files
Files changed (20) hide show
  1. manifests/batches/deepseek/000186.json +148 -0
  2. manifests/batches/deepseek/000187.json +148 -0
  3. manifests/batches/deepseek/000189.json +148 -0
  4. manifests/batches/deepseek/000191.json +141 -0
  5. manifests/batches/deepseek/000192.json +148 -0
  6. manifests/batches/mathlib/000116.json +1639 -0
  7. manifests/batches/mathlib/000117.json +1408 -0
  8. manifests/batches/mathlib/000118.json +794 -0
  9. manifests/batches/mathlib/000119.json +307 -0
  10. manifests/batches/mathlib/000120.json +369 -0
  11. manifests/batches/mathlib/000121.json +1827 -0
  12. manifests/batches/mathlib/000122.json +1422 -0
  13. manifests/batches/mathlib/000123.json +860 -0
  14. manifests/batches/numina/000877.json +44 -0
  15. manifests/batches/numina/000878.json +51 -0
  16. manifests/batches/numina/000879.json +44 -0
  17. manifests/batches/numina/000880.json +58 -0
  18. manifests/batches/numina/000881.json +44 -0
  19. manifests/batches/numina/000882.json +44 -0
  20. manifests/batches/numina/000883.json +51 -0
manifests/batches/deepseek/000186.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "deepseek/000186",
4
+ "batch_fingerprint": "ea021c1a042faba19fea12b93718df41295b0ecc83c72a91ecfb91bb27c3a07e",
5
+ "evidence": {
6
+ "batch_fingerprint": "ea021c1a042faba19fea12b93718df41295b0ecc83c72a91ecfb91bb27c3a07e",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 50,
10
+ "input_units": 50,
11
+ "proofs": 50,
12
+ "published_proofs": 50,
13
+ "published_transitions": 118,
14
+ "replay_failures": [],
15
+ "trace_mode": "individual",
16
+ "transitions": 118,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/deepseek-000186-0000-bcc50feb8ae49b66.parquet",
24
+ "sha256": "bcc50feb8ae49b667811b6a2064d0eeae6e6d7685f7d0d189b1e46b787758129",
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+ "bytes": 308222,
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+ "rows": 98,
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+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
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+ },
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+ {
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+ "path": "data/dev/deepseek-000186-0000-86053a25d81288e4.parquet",
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+ "sha256": "86053a25d81288e4797a60c3e49c866b729be455bcc91277240441141089a1be",
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+ "bytes": 55331,
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+ "rows": 9,
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+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
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+ },
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+ {
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+ "path": "data/internal_test/deepseek-000186-0000-cfc7d899bc004652.parquet",
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+ "sha256": "cfc7d899bc004652526bd25ac576bc63fc8462b137e0973e97573e8511ab1ef5",
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+ "bytes": 57449,
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+ "rows": 11,
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+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
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+ }
43
+ ],
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+ "proof_ids": [
45
+ "deepseek:thm_9335",
46
+ "deepseek:thm_9336",
47
+ "deepseek:thm_9337",
48
+ "deepseek:thm_9338",
49
+ "deepseek:thm_9339",
50
+ "deepseek:thm_9340",
51
+ "deepseek:thm_9341",
52
+ "deepseek:thm_9342",
53
+ "deepseek:thm_9343",
54
+ "deepseek:thm_9344",
55
+ "deepseek:thm_9345",
56
+ "deepseek:thm_9346",
57
+ "deepseek:thm_9347",
58
+ "deepseek:thm_9348",
59
+ "deepseek:thm_9349",
60
+ "deepseek:thm_9350",
61
+ "deepseek:thm_9351",
62
+ "deepseek:thm_9352",
63
+ "deepseek:thm_9353",
64
+ "deepseek:thm_9354",
65
+ "deepseek:thm_9355",
66
+ "deepseek:thm_9356",
67
+ "deepseek:thm_9357",
68
+ "deepseek:thm_9358",
69
+ "deepseek:thm_9359",
70
+ "deepseek:thm_9360",
71
+ "deepseek:thm_9361",
72
+ "deepseek:thm_9362",
73
+ "deepseek:thm_9363",
74
+ "deepseek:thm_9364",
75
+ "deepseek:thm_9365",
76
+ "deepseek:thm_9366",
77
+ "deepseek:thm_9367",
78
+ "deepseek:thm_9368",
79
+ "deepseek:thm_9369",
80
+ "deepseek:thm_9370",
81
+ "deepseek:thm_9371",
82
+ "deepseek:thm_9372",
83
+ "deepseek:thm_9373",
84
+ "deepseek:thm_9374",
85
+ "deepseek:thm_9375",
86
+ "deepseek:thm_9376",
87
+ "deepseek:thm_9377",
88
+ "deepseek:thm_9378",
89
+ "deepseek:thm_9379",
90
+ "deepseek:thm_9380",
91
+ "deepseek:thm_9382",
92
+ "deepseek:thm_9383",
93
+ "deepseek:thm_9384",
94
+ "deepseek:thm_9385"
95
+ ],
96
+ "proof_keys": [
97
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009300.lean\",\"2181ef5a09d439bbea00dd8516ffcb922160bb4b5e1485979831e6fa71ca8b5f\",0,\"thm_9335\"]",
98
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009301.lean\",\"67fd677e6845ad4731227efc5075a72174d6bd376bdc877b073b7fbb3acf9ab7\",0,\"thm_9336\"]",
99
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009302.lean\",\"40cea22acdd275f2207ab0565ad6b42d31157a9ac64df1f657f179797a65d245\",0,\"thm_9337\"]",
100
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009303.lean\",\"9a8aadb22e7a57a1728a1331513235d1ad2c1c069cd9deb59062b7252c6fc707\",0,\"thm_9338\"]",
101
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009304.lean\",\"2da41bf2b71c25e665967af780d46e07a0efcc6d0e5575514eec1cb6391efffd\",0,\"thm_9339\"]",
102
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009305.lean\",\"04a5be45ef361a68245888643f053baab236d59af155c02fab1995245abc136a\",0,\"thm_9340\"]",
103
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009306.lean\",\"aef3fae2f919bc9cc72aaa2e42f37787dacd3de4de162b54e2d796a26c2ba20e\",0,\"thm_9341\"]",
104
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009307.lean\",\"3828ee5ec5073dfdf24a0f68b9281bb3ec5bfdd98ac0a218be2def815cbf3e5c\",0,\"thm_9342\"]",
105
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009308.lean\",\"bad12c192c86e119ee2a271f682078443c736b85e69a281355ad373bf4a89d26\",0,\"thm_9343\"]",
106
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009309.lean\",\"45587deebb6b891f654dd71900b560f5bbc4139ecd542362be0bf6a7e63fa02d\",0,\"thm_9344\"]",
107
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009310.lean\",\"760da0d71f9430c8efd5f61b7f6ae19465b8357f9cb948036c5b2d5bb6f1175e\",0,\"thm_9345\"]",
108
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009311.lean\",\"ad90be60bd7465ca6d271f8b94ee7f601709fb1f99a3343a22f0fab661c0abc3\",0,\"thm_9346\"]",
109
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009312.lean\",\"a7958508ab5e2186ef39724cf61ac773f1e0cedbf203c3230d5b7bb68f1fb060\",0,\"thm_9347\"]",
110
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009313.lean\",\"97cf714dc692abe072101049c1b53908c7066ac4faa06e4d8bb63e62b78e9702\",0,\"thm_9348\"]",
111
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009314.lean\",\"5b4b3917617355af40596753e175c11ce65089bd96ee5cdac998237fcd662352\",0,\"thm_9349\"]",
112
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009315.lean\",\"dfe6a1a1f49eb4a5427570d341199940e384b4e5055e15ff0f4db3469befcdb8\",0,\"thm_9350\"]",
113
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009316.lean\",\"9aefd3d0c6e2cae7f9defce6405449bffd00a170ae7990f426271932afe0abf0\",0,\"thm_9351\"]",
114
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009317.lean\",\"884eb97b4ebbfcfbda8b86a1e539b7e74526c00577e20c7d886d69f79fb0e0af\",0,\"thm_9352\"]",
115
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009318.lean\",\"35aa93320569be03449fd9b899eb0a5619a6c139d762e1ddb60b8775aabe7113\",0,\"thm_9353\"]",
116
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009319.lean\",\"91c1cebf767167e5922cbe6efef51d35d6ed73716ce6cbf65fe9f5a790c2e852\",0,\"thm_9354\"]",
117
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009320.lean\",\"642c77ec23c4634086059ddbcd8a6afeeba9086fcf0e9a9202d713644350fbf7\",0,\"thm_9355\"]",
118
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009321.lean\",\"912907557d71e660a7a9e1686bce95746d9961a637960a742fdbc5c301915724\",0,\"thm_9356\"]",
119
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009322.lean\",\"ab243c39d16c1e03aee775487edc0338931fd5aaf1042ee54f54eb36ec73ddfe\",0,\"thm_9357\"]",
120
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009323.lean\",\"9898494a84f3584129dce98908093eb9fbc33bf8bdac53a9ce1e7c161fdb2011\",0,\"thm_9358\"]",
121
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009324.lean\",\"116669728611dbacc5ed37c538022d3e7008d1487b61965dee55d8ba86c2c713\",0,\"thm_9359\"]",
122
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009325.lean\",\"19fbbb80b387213f0b891f2866b77090c99efd955397849841d9d7d5c78767ee\",0,\"thm_9360\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009326.lean\",\"51d69ac89402e0561a4455b9c716c9442a3c54530f368ec701709286b39130b8\",0,\"thm_9361\"]",
124
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009327.lean\",\"bf1677cf08fbc127f5f5966157fd13688032b03cab18b054f1cdb6aaf843d2f5\",0,\"thm_9362\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009328.lean\",\"64da155f0a802fa37207215a4d5bb477ffbfe732b80cf19829655b2299765ce1\",0,\"thm_9363\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009329.lean\",\"4f5efeecde64112e0e0570b41ac999347bde80fdb3223978f9de0d950accba06\",0,\"thm_9364\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009330.lean\",\"26d56903c14799a9675f03dec6e0ed6a0cd92f7a85262b7a673c70e66bdcd2b5\",0,\"thm_9365\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009331.lean\",\"5c4ca2c6582ef1c14d792bad65d79377ac3ae818ab7bb16aad986d769424fee3\",0,\"thm_9366\"]",
129
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009332.lean\",\"0294bf5096ec11ca33b73011c0e85f216d94cfad1bab2d67edd2a3c6b6c5da68\",0,\"thm_9367\"]",
130
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009333.lean\",\"32b8b1ee8dd30c4996c190d11e441bde2fd68278c74893aa800c9336cf534ddc\",0,\"thm_9368\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009334.lean\",\"3f2533d5b785dcd26529cbd9cf725f4546956ae2f5e35550482d9909a98b1a99\",0,\"thm_9369\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009335.lean\",\"bfc3c5a85e947f5bf269235ab12fb3896d796e192d99cc6748183bb8a0500964\",0,\"thm_9370\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009336.lean\",\"c0e1f3b91c1cdee33aca6ba63c2dfcf2c1cf84024af22d291925124f84c48137\",0,\"thm_9371\"]",
134
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009337.lean\",\"0d3d9c3b18ec5163a0564f6b74ef804043403bf18b0dea28abed52678c70afd6\",0,\"thm_9372\"]",
135
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009338.lean\",\"128c3f3613ba3f12cb254782fd5399b9df1732940d109c9fcdffe124a26ce5b5\",0,\"thm_9373\"]",
136
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009339.lean\",\"7749ca7cb8700862001e48e9f8f45c93f2a6b57548ccec44ae78c695aa035374\",0,\"thm_9374\"]",
137
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009340.lean\",\"56fa91c0ff7660c688bc72f2f5a6a82fb32fd1634b2d15a7c02bd09544ecc011\",0,\"thm_9375\"]",
138
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009341.lean\",\"b53563cc78e5ea637391c6485d2bd01ef317b88f9e67bd01bfde82a9bd59636b\",0,\"thm_9376\"]",
139
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009342.lean\",\"a2e54aaab044a00b1745478ff44ff39a7dbcab870cf8711241cd31c3084ab36d\",0,\"thm_9377\"]",
140
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009343.lean\",\"d0bf0b79ae459ea93bbf03a4c7564cf9c2ded6edc277b5b47ca1638f4c46e7b2\",0,\"thm_9378\"]",
141
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009344.lean\",\"47951f2eb538e1cbb53e2fd8fe5dfc521cba82abe37f66eab08c313e366b35d8\",0,\"thm_9379\"]",
142
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009345.lean\",\"b7223699b98e85b1c4e1febee43cad4f0da574348d28a7daee98228684b63616\",0,\"thm_9380\"]",
143
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009346.lean\",\"e710bdd8f522c1edfafb8a50bdcad634651ceeaf42f146c6ac9c7763cef8f321\",0,\"thm_9382\"]",
144
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009347.lean\",\"8ff9ac432f47912be78b7d537a9f940396aff482b64bfcb85a7452dd340c0e7c\",0,\"thm_9383\"]",
145
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009348.lean\",\"fd99e59c03314c5e9259c525ebc7590a0babda78f23a35694bf3831e3fb03add\",0,\"thm_9384\"]",
146
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_009349.lean\",\"52d43589db0c848ff2a739f53b7ab0a026db2e461e273c2b6cf3104216996990\",0,\"thm_9385\"]"
147
+ ]
148
+ }
manifests/batches/deepseek/000187.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
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+ "format": "leangpt-parquet-v2",
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+ "batch": "deepseek/000187",
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+ "batch_fingerprint": "f55664f79152066013c73edd7eb5086137a250eced925d103744cb751bddc3b4",
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+ "evidence": {
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+ "batch_fingerprint": "f55664f79152066013c73edd7eb5086137a250eced925d103744cb751bddc3b4",
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+ "contamination_matches": [],
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+ "failures": [],
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+ "input_proofs": 50,
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+ "input_units": 50,
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+ "proofs": 50,
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+ "published_proofs": 50,
13
+ "published_transitions": 122,
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+ "replay_failures": [],
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+ "trace_mode": "individual",
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+ "transitions": 122,
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+ "validation_failures": [],
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+ "validation_rejected_proofs": 0,
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+ "zero_transition_proofs": 0
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+ },
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+ "shards": [
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+ {
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+ "path": "data/train/deepseek-000187-0000-dd2116fbe8e02630.parquet",
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+ "sha256": "dd2116fbe8e0263022e6f64d54bc02d1b6c29a3eb5bbf1d9e4007603f20d2434",
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+ "bytes": 365387,
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+ "rows": 109,
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+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
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+ },
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+ {
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+ "path": "data/dev/deepseek-000187-0000-c8c22c01924e7b79.parquet",
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+ "sha256": "c8c22c01924e7b792c752d65a9e166141c570a9b6f92f448182eda785d1c37ac",
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+ "bytes": 42512,
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+ "rows": 6,
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+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
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+ },
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+ {
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+ "path": "data/internal_test/deepseek-000187-0000-365a9b2206b54844.parquet",
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+ "sha256": "365a9b2206b5484433d80eb9e1b1d4bc8e3a7f2c3561fd098c7047633d06bff0",
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+ "bytes": 53969,
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+ "rows": 7,
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+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
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+ }
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+ ],
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+ "proof_ids": [
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+ "deepseek:thm_9386",
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+ "deepseek:thm_9387",
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+ "deepseek:thm_9388",
48
+ "deepseek:thm_9389",
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+ "deepseek:thm_9390",
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+ "deepseek:thm_9415",
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+ "deepseek:thm_9418",
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+ "deepseek:thm_9420",
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+ "deepseek:thm_9421",
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+ "deepseek:thm_9422",
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+ "deepseek:thm_9423",
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+ "deepseek:thm_9424",
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+ "deepseek:thm_9426",
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+ "deepseek:thm_9429",
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+ "deepseek:thm_9430",
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+ "deepseek:thm_9434",
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147
+ ]
148
+ }
manifests/batches/deepseek/000189.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ {
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+ "format": "leangpt-parquet-v2",
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+ "batch": "deepseek/000189",
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+ "batch_fingerprint": "c090ededc2c0942e58532d55da266c45c15c8c71a827b21bf3de044f36e8bcb9",
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+ "evidence": {
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+ "contamination_matches": [],
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+ "failures": [],
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+ "input_proofs": 50,
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+ "input_units": 50,
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+ "proofs": 50,
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+ "published_proofs": 50,
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+ "published_transitions": 119,
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+ "replay_failures": [],
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+ "trace_mode": "individual",
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+ "transitions": 119,
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+ "validation_failures": [],
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+ "validation_rejected_proofs": 0,
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+ "zero_transition_proofs": 0
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+ "shards": [
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+ {
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+ "path": "data/train/deepseek-000189-0000-58fcba5b9c285da7.parquet",
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+ "path": "data/dev/deepseek-000189-0000-80a178729a2b11f0.parquet",
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+ "proof_ids": [
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+ "deepseek:thm_9486",
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+ "deepseek:thm_9488",
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+ "deepseek:thm_9533",
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+ "deepseek:thm_9534",
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+ ],
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+ "proof_keys": [
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+ ]
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+ }
manifests/batches/deepseek/000191.json ADDED
@@ -0,0 +1,141 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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manifests/batches/deepseek/000192.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ ]
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manifests/batches/mathlib/000116.json ADDED
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1
+ {
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+ "format": "leangpt-parquet-v2",
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+ "batch": "mathlib/000116",
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+ "batch_fingerprint": "9ca4dcc4ce53629792eadb5ec1e7f5298ce14ef577fa986f7e94ffff368dc0d8",
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+ "contamination_matches": [],
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+ {
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+ "error": "theorem has no selected tactic transitions",
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+ "full_name": "ConjClasses.carrier_eq_preimage_mk",
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+ "id": "ConjClasses.carrier_eq_preimage_mk",
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+ "reason": "import_failure",
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+ },
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+ "source_file": "Mathlib/Algebra/Group/Conj.lean"
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+ },
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+ {
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+ "error": "theorem has no selected tactic transitions",
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+ "full_name": "ConjClasses.exists_rep",
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+ "id": "ConjClasses.exists_rep",
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+ "reason": "import_failure",
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+ "selection": {
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+ },
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+ "source_file": "Mathlib/Algebra/Group/Conj.lean"
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+ },
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+ {
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55
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+ "id": "ConjClasses.forall_isConj",
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+ "reason": "import_failure",
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+ "selection": {
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+ "end": [
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+ ],
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+ "full_name": "ConjClasses.forall_isConj",
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+ ],
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+ "traced_tactics": [],
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+ "url": "https://github.com/leanprover-community/mathlib4"
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+ },
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+ "source_file": "Mathlib/Algebra/Group/Conj.lean"
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+ },
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+ {
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+ "error": "theorem has no selected tactic transitions",
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+ "full_name": "ConjClasses.mem_carrier_mk",
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+ "id": "ConjClasses.mem_carrier_mk",
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+ "reason": "import_failure",
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+ "selection": {
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+ "end": [
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+ ],
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+ ],
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+ },
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+ "source_file": "Mathlib/Algebra/Group/Conj.lean"
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+ },
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+ {
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+ "error": "theorem has no selected tactic transitions",
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+ "full_name": "ConjClasses.mk_bijective",
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+ "id": "ConjClasses.mk_bijective",
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+ "reason": "import_failure",
102
+ "selection": {
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+ ],
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+ },
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+ "source_file": "Mathlib/Algebra/Group/Conj.lean"
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+ },
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+ {
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+ "error": "theorem has no selected tactic transitions",
121
+ "full_name": "ConjClasses.mk_eq_mk_iff_isConj",
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+ "id": "ConjClasses.mk_eq_mk_iff_isConj",
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+ "reason": "import_failure",
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+ },
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+ },
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+ {
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+ "error": "theorem has no selected tactic transitions",
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+ "full_name": "ConjClasses.mk_injective",
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+ "id": "ConjClasses.mk_injective",
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+ },
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+ "source_file": "Mathlib/Algebra/Group/Conj.lean"
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+ },
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+ {
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+ "error": "theorem has no selected tactic transitions",
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+ "id": "ConjClasses.mk_surjective",
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+ },
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+ "source_file": "Mathlib/Algebra/Group/Conj.lean"
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+ },
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+ {
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+ "error": "theorem has no selected tactic transitions",
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+ "full_name": "ConjClasses.one_eq_mk_one",
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+ "id": "ConjClasses.one_eq_mk_one",
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+ "reason": "import_failure",
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+ ],
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+ },
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+ "source_file": "Mathlib/Algebra/Group/Conj.lean"
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+ },
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+ {
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+ "error": "theorem has no selected tactic transitions",
209
+ "full_name": "ConjClasses.quot_mk_eq_mk",
210
+ "id": "ConjClasses.quot_mk_eq_mk",
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+ "reason": "import_failure",
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+ ],
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+ ],
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+ },
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+ "source_file": "Mathlib/Algebra/Group/Conj.lean"
228
+ },
229
+ {
230
+ "error": "theorem has no selected tactic transitions",
231
+ "full_name": "ConjClasses.quotient_mk_eq_mk",
232
+ "id": "ConjClasses.quotient_mk_eq_mk",
233
+ "reason": "import_failure",
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+ "selection": {
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+ },
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+ },
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+ {
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253
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254
+ "id": "IsConj.conjugatesOf_eq",
255
+ "reason": "import_failure",
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+ "selection": {
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+ },
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276
+ "id": "IsConj.refl",
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+ "reason": "import_failure",
278
+ "selection": {
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+ },
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+ },
295
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+ "error": "theorem has no selected tactic transitions",
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+ "full_name": "IsConj.symm",
298
+ "id": "IsConj.symm",
299
+ "reason": "import_failure",
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+ "selection": {
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+ },
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+ "source_file": "Mathlib/Algebra/Group/Conj.lean"
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+ },
317
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+ "error": "theorem has no selected tactic transitions",
319
+ "full_name": "IsConj.trans",
320
+ "id": "IsConj.trans",
321
+ "reason": "import_failure",
322
+ "selection": {
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+ },
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341
+ "full_name": "conj_injective",
342
+ "id": "conj_injective",
343
+ "reason": "import_failure",
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+ "selection": {
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+ },
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+ "source_file": "Mathlib/Algebra/Group/Conj.lean"
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+ },
361
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362
+ "error": "theorem has no selected tactic transitions",
363
+ "full_name": "conj_inv",
364
+ "id": "conj_inv",
365
+ "reason": "import_failure",
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+ "selection": {
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+ },
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+ "source_file": "Mathlib/Algebra/Group/Conj.lean"
382
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383
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+ "error": "theorem has no selected tactic transitions",
385
+ "full_name": "conj_mul",
386
+ "id": "conj_mul",
387
+ "reason": "import_failure",
388
+ "selection": {
389
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
390
+ "end": [
391
+ 106,
392
+ 37
393
+ ],
394
+ "file_path": "Mathlib/Algebra/Group/Conj.lean",
395
+ "full_name": "conj_mul",
396
+ "start": [
397
+ 105,
398
+ 1
399
+ ],
400
+ "traced_tactics": [],
401
+ "url": "https://github.com/leanprover-community/mathlib4"
402
+ },
403
+ "source_file": "Mathlib/Algebra/Group/Conj.lean"
404
+ },
405
+ {
406
+ "error": "theorem has no selected tactic transitions",
407
+ "full_name": "isConj_comm",
408
+ "id": "isConj_comm",
409
+ "reason": "import_failure",
410
+ "selection": {
411
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
412
+ "end": [
413
+ 45,
414
+ 29
415
+ ],
416
+ "file_path": "Mathlib/Algebra/Group/Conj.lean",
417
+ "full_name": "isConj_comm",
418
+ "start": [
419
+ 44,
420
+ 1
421
+ ],
422
+ "traced_tactics": [],
423
+ "url": "https://github.com/leanprover-community/mathlib4"
424
+ },
425
+ "source_file": "Mathlib/Algebra/Group/Conj.lean"
426
+ },
427
+ {
428
+ "error": "theorem has no selected tactic transitions",
429
+ "full_name": "isConj_iff",
430
+ "id": "isConj_iff",
431
+ "reason": "import_failure",
432
+ "selection": {
433
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
434
+ "end": [
435
+ 95,
436
+ 76
437
+ ],
438
+ "file_path": "Mathlib/Algebra/Group/Conj.lean",
439
+ "full_name": "isConj_iff",
440
+ "start": [
441
+ 93,
442
+ 1
443
+ ],
444
+ "traced_tactics": [],
445
+ "url": "https://github.com/leanprover-community/mathlib4"
446
+ },
447
+ "source_file": "Mathlib/Algebra/Group/Conj.lean"
448
+ },
449
+ {
450
+ "error": "theorem has no selected tactic transitions",
451
+ "full_name": "isConj_one_left",
452
+ "id": "isConj_one_left",
453
+ "reason": "import_failure",
454
+ "selection": {
455
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
456
+ "end": [
457
+ 83,
458
+ 34
459
+ ],
460
+ "file_path": "Mathlib/Algebra/Group/Conj.lean",
461
+ "full_name": "isConj_one_left",
462
+ "start": [
463
+ 80,
464
+ 1
465
+ ],
466
+ "traced_tactics": [],
467
+ "url": "https://github.com/leanprover-community/mathlib4"
468
+ },
469
+ "source_file": "Mathlib/Algebra/Group/Conj.lean"
470
+ },
471
+ {
472
+ "error": "theorem has no selected tactic transitions",
473
+ "full_name": "mem_conjugatesOf_self",
474
+ "id": "mem_conjugatesOf_self",
475
+ "reason": "import_failure",
476
+ "selection": {
477
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
478
+ "end": [
479
+ 277,
480
+ 16
481
+ ],
482
+ "file_path": "Mathlib/Algebra/Group/Conj.lean",
483
+ "full_name": "mem_conjugatesOf_self",
484
+ "start": [
485
+ 276,
486
+ 1
487
+ ],
488
+ "traced_tactics": [],
489
+ "url": "https://github.com/leanprover-community/mathlib4"
490
+ },
491
+ "source_file": "Mathlib/Algebra/Group/Conj.lean"
492
+ },
493
+ {
494
+ "error": "theorem has no selected tactic transitions",
495
+ "full_name": "CommMagma.IsLeftCancelMul.toIsCancelMul",
496
+ "id": "CommMagma.IsLeftCancelMul.toIsCancelMul",
497
+ "reason": "import_failure",
498
+ "selection": {
499
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
500
+ "end": [
501
+ 358,
502
+ 77
503
+ ],
504
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
505
+ "full_name": "CommMagma.IsLeftCancelMul.toIsCancelMul",
506
+ "start": [
507
+ 354,
508
+ 1
509
+ ],
510
+ "traced_tactics": [],
511
+ "url": "https://github.com/leanprover-community/mathlib4"
512
+ },
513
+ "source_file": "Mathlib/Algebra/Group/Defs.lean"
514
+ },
515
+ {
516
+ "error": "theorem has no selected tactic transitions",
517
+ "full_name": "CommMagma.IsLeftCancelMul.toIsRightCancelMul",
518
+ "id": "CommMagma.IsLeftCancelMul.toIsRightCancelMul",
519
+ "reason": "import_failure",
520
+ "selection": {
521
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
522
+ "end": [
523
+ 350,
524
+ 84
525
+ ],
526
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
527
+ "full_name": "CommMagma.IsLeftCancelMul.toIsRightCancelMul",
528
+ "start": [
529
+ 345,
530
+ 1
531
+ ],
532
+ "traced_tactics": [],
533
+ "url": "https://github.com/leanprover-community/mathlib4"
534
+ },
535
+ "source_file": "Mathlib/Algebra/Group/Defs.lean"
536
+ },
537
+ {
538
+ "error": "theorem has no selected tactic transitions",
539
+ "full_name": "CommMagma.IsRightCancelMul.toIsCancelMul",
540
+ "id": "CommMagma.IsRightCancelMul.toIsCancelMul",
541
+ "reason": "import_failure",
542
+ "selection": {
543
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
544
+ "end": [
545
+ 366,
546
+ 77
547
+ ],
548
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
549
+ "full_name": "CommMagma.IsRightCancelMul.toIsCancelMul",
550
+ "start": [
551
+ 362,
552
+ 1
553
+ ],
554
+ "traced_tactics": [],
555
+ "url": "https://github.com/leanprover-community/mathlib4"
556
+ },
557
+ "source_file": "Mathlib/Algebra/Group/Defs.lean"
558
+ },
559
+ {
560
+ "error": "theorem has no selected tactic transitions",
561
+ "full_name": "CommMagma.IsRightCancelMul.toIsLeftCancelMul",
562
+ "id": "CommMagma.IsRightCancelMul.toIsLeftCancelMul",
563
+ "reason": "import_failure",
564
+ "selection": {
565
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
566
+ "end": [
567
+ 341,
568
+ 85
569
+ ],
570
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
571
+ "full_name": "CommMagma.IsRightCancelMul.toIsLeftCancelMul",
572
+ "start": [
573
+ 336,
574
+ 1
575
+ ],
576
+ "traced_tactics": [],
577
+ "url": "https://github.com/leanprover-community/mathlib4"
578
+ },
579
+ "source_file": "Mathlib/Algebra/Group/Defs.lean"
580
+ },
581
+ {
582
+ "error": "no internal trace for tactic 'cases this'",
583
+ "full_name": "MulOneClass.ext",
584
+ "id": "MulOneClass.ext",
585
+ "reason": "import_failure",
586
+ "selection": {
587
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
588
+ "end": [
589
+ 468,
590
+ 51
591
+ ],
592
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
593
+ "full_name": "MulOneClass.ext",
594
+ "start": [
595
+ 463,
596
+ 1
597
+ ],
598
+ "traced_tactics": [
599
+ {
600
+ "annotated_tactic": [
601
+ "\"rintro @\\u27e8\\u27e8one\\u2081\\u27e9, \\u27e8mul\\u2081\\u27e9, one_mul\\u2081, mul_one\\u2081\\u27e9 @\\u27e8\\u27e8one\\u2082\\u27e9, \\u27e8mul\\u2082\\u27e9, one_mul\\u2082, mul_one\\u2082\\u27e9 \\u27e8rfl\\u27e9\"",
602
+ "[]"
603
+ ],
604
+ "state_after": "case mk.mk.mk.mk.mk.mk.refl\nG : Type u_1\nM : Type u\none\u2081 : M\nmul\u2081 : M \u2192 M \u2192 M\none_mul\u2081 : \u2200 (a : M), 1 * a = a\nmul_one\u2081 : \u2200 (a : M), a * 1 = a\none\u2082 : M\none_mul\u2082 : \u2200 (a : M), 1 * a = a\nmul_one\u2082 : \u2200 (a : M), a * 1 = a\n\u22a2 mk one_mul\u2081 mul_one\u2081 = mk one_mul\u2082 mul_one\u2082",
605
+ "state_before": "G : Type u_1\nM : Type u\n\u22a2 \u2200 \u2983m\u2081 m\u2082 : MulOneClass M\u2984, Mul.mul = Mul.mul \u2192 m\u2081 = m\u2082",
606
+ "tactic": "rintro @\u27e8\u27e8one\u2081\u27e9, \u27e8mul\u2081\u27e9, one_mul\u2081, mul_one\u2081\u27e9 @\u27e8\u27e8one\u2082\u27e9, \u27e8mul\u2082\u27e9, one_mul\u2082, mul_one\u2082\u27e9 \u27e8rfl\u27e9"
607
+ },
608
+ {
609
+ "annotated_tactic": [
610
+ "\"suffices one\\u2081 = one\\u2082 by cases this; rfl\"",
611
+ "[]"
612
+ ],
613
+ "state_after": "case mk.mk.mk.mk.mk.mk.refl\nG : Type u_1\nM : Type u\none\u2081 : M\nmul\u2081 : M \u2192 M \u2192 M\none_mul\u2081 : \u2200 (a : M), 1 * a = a\nmul_one\u2081 : \u2200 (a : M), a * 1 = a\none\u2082 : M\none_mul\u2082 : \u2200 (a : M), 1 * a = a\nmul_one\u2082 : \u2200 (a : M), a * 1 = a\n\u22a2 one\u2081 = one\u2082",
614
+ "state_before": "case mk.mk.mk.mk.mk.mk.refl\nG : Type u_1\nM : Type u\none\u2081 : M\nmul\u2081 : M \u2192 M \u2192 M\none_mul\u2081 : \u2200 (a : M), 1 * a = a\nmul_one\u2081 : \u2200 (a : M), a * 1 = a\none\u2082 : M\none_mul\u2082 : \u2200 (a : M), 1 * a = a\nmul_one\u2082 : \u2200 (a : M), a * 1 = a\n\u22a2 mk one_mul\u2081 mul_one\u2081 = mk one_mul\u2082 mul_one\u2082",
615
+ "tactic": "suffices one\u2081 = one\u2082 by cases this; rfl"
616
+ },
617
+ {
618
+ "annotated_tactic": [
619
+ "\"exact (one_mul\\u2082 one\\u2081).symm.trans (mul_one\\u2081 one\\u2082)\"",
620
+ "[]"
621
+ ],
622
+ "state_after": "no goals",
623
+ "state_before": "case mk.mk.mk.mk.mk.mk.refl\nG : Type u_1\nM : Type u\none\u2081 : M\nmul\u2081 : M \u2192 M \u2192 M\none_mul\u2081 : \u2200 (a : M), 1 * a = a\nmul_one\u2081 : \u2200 (a : M), a * 1 = a\none\u2082 : M\none_mul\u2082 : \u2200 (a : M), 1 * a = a\nmul_one\u2082 : \u2200 (a : M), a * 1 = a\n\u22a2 one\u2081 = one\u2082",
624
+ "tactic": "exact (one_mul\u2082 one\u2081).symm.trans (mul_one\u2081 one\u2082)"
625
+ },
626
+ {
627
+ "annotated_tactic": [
628
+ "\"cases this\"",
629
+ "[]"
630
+ ],
631
+ "state_after": "case refl\nG : Type u_1\nM : Type u\none\u2081 : M\nmul\u2081 : M \u2192 M \u2192 M\none_mul\u2081 : \u2200 (a : M), 1 * a = a\nmul_one\u2081 : \u2200 (a : M), a * 1 = a\none_mul\u2082 : \u2200 (a : M), 1 * a = a\nmul_one\u2082 : \u2200 (a : M), a * 1 = a\n\u22a2 mk one_mul\u2081 mul_one\u2081 = mk one_mul\u2082 mul_one\u2082",
632
+ "state_before": "G : Type u_1\nM : Type u\none\u2081 : M\nmul\u2081 : M \u2192 M \u2192 M\none_mul\u2081 : \u2200 (a : M), 1 * a = a\nmul_one\u2081 : \u2200 (a : M), a * 1 = a\none\u2082 : M\none_mul\u2082 : \u2200 (a : M), 1 * a = a\nmul_one\u2082 : \u2200 (a : M), a * 1 = a\nthis : one\u2081 = one\u2082\n\u22a2 mk one_mul\u2081 mul_one\u2081 = mk one_mul\u2082 mul_one\u2082",
633
+ "tactic": "cases this"
634
+ },
635
+ {
636
+ "annotated_tactic": [
637
+ "\"rfl\"",
638
+ "[]"
639
+ ],
640
+ "state_after": "no goals",
641
+ "state_before": "case refl\nG : Type u_1\nM : Type u\none\u2081 : M\nmul\u2081 : M \u2192 M \u2192 M\none_mul\u2081 : \u2200 (a : M), 1 * a = a\nmul_one\u2081 : \u2200 (a : M), a * 1 = a\none_mul\u2082 : \u2200 (a : M), 1 * a = a\nmul_one\u2082 : \u2200 (a : M), a * 1 = a\n\u22a2 mk one_mul\u2081 mul_one\u2081 = mk one_mul\u2082 mul_one\u2082",
642
+ "tactic": "rfl"
643
+ }
644
+ ],
645
+ "url": "https://github.com/leanprover-community/mathlib4"
646
+ },
647
+ "source_file": "Mathlib/Algebra/Group/Defs.lean"
648
+ },
649
+ {
650
+ "error": "theorem has no selected tactic transitions",
651
+ "full_name": "SMul.smul_eq_hSMul",
652
+ "id": "SMul.smul_eq_hSMul",
653
+ "reason": "import_failure",
654
+ "selection": {
655
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
656
+ "end": [
657
+ 158,
658
+ 91
659
+ ],
660
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
661
+ "full_name": "SMul.smul_eq_hSMul",
662
+ "start": [
663
+ 158,
664
+ 1
665
+ ],
666
+ "traced_tactics": [],
667
+ "url": "https://github.com/leanprover-community/mathlib4"
668
+ },
669
+ "source_file": "Mathlib/Algebra/Group/Defs.lean"
670
+ },
671
+ {
672
+ "error": "theorem has no selected tactic transitions",
673
+ "full_name": "div_eq_mul_inv",
674
+ "id": "div_eq_mul_inv",
675
+ "reason": "import_failure",
676
+ "selection": {
677
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
678
+ "end": [
679
+ 1060,
680
+ 34
681
+ ],
682
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
683
+ "full_name": "div_eq_mul_inv",
684
+ "start": [
685
+ 1059,
686
+ 1
687
+ ],
688
+ "traced_tactics": [],
689
+ "url": "https://github.com/leanprover-community/mathlib4"
690
+ },
691
+ "source_file": "Mathlib/Algebra/Group/Defs.lean"
692
+ },
693
+ {
694
+ "error": "theorem has no selected tactic transitions",
695
+ "full_name": "eq_inv_of_mul_eq_one_left",
696
+ "id": "eq_inv_of_mul_eq_one_left",
697
+ "reason": "import_failure",
698
+ "selection": {
699
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
700
+ "end": [
701
+ 1172,
702
+ 37
703
+ ],
704
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
705
+ "full_name": "eq_inv_of_mul_eq_one_left",
706
+ "start": [
707
+ 1171,
708
+ 1
709
+ ],
710
+ "traced_tactics": [],
711
+ "url": "https://github.com/leanprover-community/mathlib4"
712
+ },
713
+ "source_file": "Mathlib/Algebra/Group/Defs.lean"
714
+ },
715
+ {
716
+ "error": "theorem has no selected tactic transitions",
717
+ "full_name": "inv_eq_of_mul",
718
+ "id": "inv_eq_of_mul",
719
+ "reason": "import_failure",
720
+ "selection": {
721
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
722
+ "end": [
723
+ 1235,
724
+ 43
725
+ ],
726
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
727
+ "full_name": "inv_eq_of_mul",
728
+ "start": [
729
+ 1234,
730
+ 9
731
+ ],
732
+ "traced_tactics": [],
733
+ "url": "https://github.com/leanprover-community/mathlib4"
734
+ },
735
+ "source_file": "Mathlib/Algebra/Group/Defs.lean"
736
+ },
737
+ {
738
+ "error": "theorem has no selected tactic transitions",
739
+ "full_name": "inv_eq_of_mul_eq_one_right",
740
+ "id": "inv_eq_of_mul_eq_one_right",
741
+ "reason": "import_failure",
742
+ "selection": {
743
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
744
+ "end": [
745
+ 1160,
746
+ 35
747
+ ],
748
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
749
+ "full_name": "inv_eq_of_mul_eq_one_right",
750
+ "start": [
751
+ 1159,
752
+ 1
753
+ ],
754
+ "traced_tactics": [],
755
+ "url": "https://github.com/leanprover-community/mathlib4"
756
+ },
757
+ "source_file": "Mathlib/Algebra/Group/Defs.lean"
758
+ },
759
+ {
760
+ "error": "theorem has no selected tactic transitions",
761
+ "full_name": "inv_inv",
762
+ "id": "inv_inv",
763
+ "reason": "import_failure",
764
+ "selection": {
765
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
766
+ "end": [
767
+ 871,
768
+ 26
769
+ ],
770
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
771
+ "full_name": "inv_inv",
772
+ "start": [
773
+ 870,
774
+ 1
775
+ ],
776
+ "traced_tactics": [],
777
+ "url": "https://github.com/leanprover-community/mathlib4"
778
+ },
779
+ "source_file": "Mathlib/Algebra/Group/Defs.lean"
780
+ },
781
+ {
782
+ "error": "theorem has no selected tactic transitions",
783
+ "full_name": "inv_mul_self",
784
+ "id": "inv_mul_self",
785
+ "reason": "import_failure",
786
+ "selection": {
787
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
788
+ "end": [
789
+ 1229,
790
+ 17
791
+ ],
792
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
793
+ "full_name": "inv_mul_self",
794
+ "start": [
795
+ 1228,
796
+ 1
797
+ ],
798
+ "traced_tactics": [],
799
+ "url": "https://github.com/leanprover-community/mathlib4"
800
+ },
801
+ "source_file": "Mathlib/Algebra/Group/Defs.lean"
802
+ },
803
+ {
804
+ "error": "theorem has no selected tactic transitions",
805
+ "full_name": "inv_one",
806
+ "id": "inv_one",
807
+ "reason": "import_failure",
808
+ "selection": {
809
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
810
+ "end": [
811
+ 1119,
812
+ 22
813
+ ],
814
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
815
+ "full_name": "inv_one",
816
+ "start": [
817
+ 1118,
818
+ 1
819
+ ],
820
+ "traced_tactics": [],
821
+ "url": "https://github.com/leanprover-community/mathlib4"
822
+ },
823
+ "source_file": "Mathlib/Algebra/Group/Defs.lean"
824
+ },
825
+ {
826
+ "error": "theorem has no selected tactic transitions",
827
+ "full_name": "mul_assoc",
828
+ "id": "mul_assoc",
829
+ "reason": "import_failure",
830
+ "selection": {
831
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
832
+ "end": [
833
+ 290,
834
+ 22
835
+ ],
836
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
837
+ "full_name": "mul_assoc",
838
+ "start": [
839
+ 289,
840
+ 1
841
+ ],
842
+ "traced_tactics": [],
843
+ "url": "https://github.com/leanprover-community/mathlib4"
844
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870
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891
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892
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893
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937
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956
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957
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958
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959
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978
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979
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980
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981
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997
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998
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999
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1000
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1001
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1002
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1003
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1004
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1005
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1006
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1014
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1018
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1019
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1020
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1021
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1022
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1023
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1024
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1025
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1026
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1027
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1028
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1035
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1036
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1040
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1041
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1042
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1043
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1044
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1045
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1046
+ "error": "theorem has no selected tactic transitions",
1047
+ "full_name": "one_mul",
1048
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1049
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1050
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1056
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1058
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1062
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1063
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1064
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1065
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1066
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1067
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1068
+ "error": "theorem has no selected tactic transitions",
1069
+ "full_name": "pow_succ",
1070
+ "id": "pow_succ",
1071
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1072
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1078
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1079
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1080
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1084
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1085
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1086
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1087
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1088
+ },
1089
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1090
+ "error": "theorem has no selected tactic transitions",
1091
+ "full_name": "pow_zero",
1092
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1093
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1094
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1100
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1101
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1102
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1103
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1106
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1107
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1108
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1109
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1110
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1111
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1112
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1113
+ "full_name": "zpow_eq_pow",
1114
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1115
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1116
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1117
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1121
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1122
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1123
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1124
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1125
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1127
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1128
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1129
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1130
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1131
+ "source_file": "Mathlib/Algebra/Group/Defs.lean"
1132
+ },
1133
+ {
1134
+ "error": "theorem has no selected tactic transitions",
1135
+ "full_name": "zpow_natCast",
1136
+ "id": "zpow_natCast",
1137
+ "reason": "import_failure",
1138
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1139
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1143
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1144
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1145
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1150
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1151
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1152
+ },
1153
+ "source_file": "Mathlib/Algebra/Group/Defs.lean"
1154
+ },
1155
+ {
1156
+ "error": "theorem has no selected tactic transitions",
1157
+ "full_name": "zpow_neg_coe_of_pos",
1158
+ "id": "zpow_neg_coe_of_pos",
1159
+ "reason": "import_failure",
1160
+ "selection": {
1161
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1166
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1167
+ "full_name": "zpow_neg_coe_of_pos",
1168
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1169
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1172
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1173
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1174
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1175
+ "source_file": "Mathlib/Algebra/Group/Defs.lean"
1176
+ },
1177
+ {
1178
+ "error": "theorem has no selected tactic transitions",
1179
+ "full_name": "zpow_neg_one",
1180
+ "id": "zpow_neg_one",
1181
+ "reason": "import_failure",
1182
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1183
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1187
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1188
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1189
+ "full_name": "zpow_neg_one",
1190
+ "start": [
1191
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1192
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1193
+ ],
1194
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1195
+ "url": "https://github.com/leanprover-community/mathlib4"
1196
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1197
+ "source_file": "Mathlib/Algebra/Group/Defs.lean"
1198
+ },
1199
+ {
1200
+ "error": "theorem has no selected tactic transitions",
1201
+ "full_name": "zpow_ofNat",
1202
+ "id": "zpow_ofNat",
1203
+ "reason": "import_failure",
1204
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1205
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1206
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1207
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1209
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1210
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
1211
+ "full_name": "zpow_ofNat",
1212
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1213
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1214
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1215
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1216
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1217
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1218
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1219
+ "source_file": "Mathlib/Algebra/Group/Defs.lean"
1220
+ },
1221
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1222
+ "error": "theorem has no selected tactic transitions",
1223
+ "full_name": "zpow_zero",
1224
+ "id": "zpow_zero",
1225
+ "reason": "import_failure",
1226
+ "selection": {
1227
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1228
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1229
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1231
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1232
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
1233
+ "full_name": "zpow_zero",
1234
+ "start": [
1235
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1236
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1237
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1238
+ "traced_tactics": [],
1239
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1240
+ },
1241
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1242
+ }
1243
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1244
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1245
+ "input_units": 2,
1246
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1247
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1248
+ "published_transitions": 36,
1249
+ "replay_failures": [],
1250
+ "transitions": 52,
1251
+ "validation_failures": [
1252
+ {
1253
+ "errors": [
1254
+ "internal transition boundary mismatch",
1255
+ "internal transition boundary mismatch"
1256
+ ],
1257
+ "file_path": "Mathlib/Algebra/Group/Conj.lean",
1258
+ "proof_id": "mathlib:conj_pow",
1259
+ "provenance": {
1260
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1261
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1262
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1263
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1265
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1266
+ "file_path": "Mathlib/Algebra/Group/Conj.lean",
1267
+ "full_name": "conj_pow",
1268
+ "start": [
1269
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1270
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1271
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1272
+ "traced_tactics": [
1273
+ {
1274
+ "annotated_tactic": [
1275
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1276
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1277
+ ],
1278
+ "state_after": "case zero\n\u03b1 : Type u\n\u03b2 : Type v\ninst\u271d : Group \u03b1\na b : \u03b1\n\u22a2 (a * b * a\u207b\u00b9) ^ 0 = a * b ^ 0 * a\u207b\u00b9\n\ncase succ\n\u03b1 : Type u\n\u03b2 : Type v\ninst\u271d : Group \u03b1\na b : \u03b1\ni : \u2115\nhi : (a * b * a\u207b\u00b9) ^ i = a * b ^ i * a\u207b\u00b9\n\u22a2 (a * b * a\u207b\u00b9) ^ (i + 1) = a * b ^ (i + 1) * a\u207b\u00b9",
1279
+ "state_before": "\u03b1 : Type u\n\u03b2 : Type v\ninst\u271d : Group \u03b1\ni : \u2115\na b : \u03b1\n\u22a2 (a * b * a\u207b\u00b9) ^ i = a * b ^ i * a\u207b\u00b9",
1280
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1281
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1282
+ {
1283
+ "annotated_tactic": [
1284
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1285
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1286
+ ],
1287
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1288
+ "state_before": "case zero\n\u03b1 : Type u\n\u03b2 : Type v\ninst\u271d : Group \u03b1\na b : \u03b1\n\u22a2 (a * b * a\u207b\u00b9) ^ 0 = a * b ^ 0 * a\u207b\u00b9",
1289
+ "tactic": "simp"
1290
+ },
1291
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1292
+ "annotated_tactic": [
1293
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1294
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1295
+ ],
1296
+ "state_after": "no goals",
1297
+ "state_before": "case succ\n\u03b1 : Type u\n\u03b2 : Type v\ninst\u271d : Group \u03b1\na b : \u03b1\ni : \u2115\nhi : (a * b * a\u207b\u00b9) ^ i = a * b ^ i * a\u207b\u00b9\n\u22a2 (a * b * a\u207b\u00b9) ^ (i + 1) = a * b ^ (i + 1) * a\u207b\u00b9",
1298
+ "tactic": "simp [pow_succ, hi]"
1299
+ }
1300
+ ],
1301
+ "url": "https://github.com/leanprover-community/mathlib4"
1302
+ }
1303
+ },
1304
+ "theorem_name": "conj_pow"
1305
+ },
1306
+ {
1307
+ "errors": [
1308
+ "internal transition boundary mismatch",
1309
+ "internal transition boundary mismatch"
1310
+ ],
1311
+ "file_path": "Mathlib/Algebra/Group/Conj.lean",
1312
+ "proof_id": "mathlib:conj_zpow",
1313
+ "provenance": {
1314
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1315
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1316
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1317
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1318
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1319
+ ],
1320
+ "file_path": "Mathlib/Algebra/Group/Conj.lean",
1321
+ "full_name": "conj_zpow",
1322
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1323
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1324
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1325
+ ],
1326
+ "traced_tactics": [
1327
+ {
1328
+ "annotated_tactic": [
1329
+ "\"induction' i\"",
1330
+ "[]"
1331
+ ],
1332
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1333
+ "state_before": "\u03b1 : Type u\n\u03b2 : Type v\ninst\u271d : Group \u03b1\ni : \u2124\na b : \u03b1\n\u22a2 (a * b * a\u207b\u00b9) ^ i = a * b ^ i * a\u207b\u00b9",
1334
+ "tactic": "induction' i"
1335
+ },
1336
+ {
1337
+ "annotated_tactic": [
1338
+ "\"simp [<a>zpow_natCast<\\/a>]\"",
1339
+ "[{\"full_name\":\"zpow_natCast\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1021,9],\"def_end_pos\":[1021,21]}]"
1340
+ ],
1341
+ "state_after": "no goals",
1342
+ "state_before": "case ofNat\n\u03b1 : Type u\n\u03b2 : Type v\ninst\u271d : Group \u03b1\na b : \u03b1\na\u271d : \u2115\n\u22a2 (a * b * a\u207b\u00b9) ^ Int.ofNat a\u271d = a * b ^ Int.ofNat a\u271d * a\u207b\u00b9",
1343
+ "tactic": "simp [zpow_natCast]"
1344
+ },
1345
+ {
1346
+ "annotated_tactic": [
1347
+ "\"simp only [<a>zpow_negSucc<\\/a>, <a>conj_pow<\\/a>, <a>mul_inv_rev<\\/a>, <a>inv_inv<\\/a>]\"",
1348
+ "[{\"full_name\":\"zpow_negSucc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1040,9],\"def_end_pos\":[1040,21]},{\"full_name\":\"conj_pow\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Conj.lean\",\"def_pos\":[110,9],\"def_end_pos\":[110,17]},{\"full_name\":\"mul_inv_rev\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1153,9],\"def_end_pos\":[1153,20]},{\"full_name\":\"inv_inv\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[870,9],\"def_end_pos\":[870,16]}]"
1349
+ ],
1350
+ "state_after": "case negSucc\n\u03b1 : Type u\n\u03b2 : Type v\ninst\u271d : Group \u03b1\na b : \u03b1\na\u271d : \u2115\n\u22a2 a * ((b ^ (a\u271d + 1))\u207b\u00b9 * a\u207b\u00b9) = a * (b ^ (a\u271d + 1))\u207b\u00b9 * a\u207b\u00b9",
1351
+ "state_before": "case negSucc\n\u03b1 : Type u\n\u03b2 : Type v\ninst\u271d : Group \u03b1\na b : \u03b1\na\u271d : \u2115\n\u22a2 (a * b * a\u207b\u00b9) ^ Int.negSucc a\u271d = a * b ^ Int.negSucc a\u271d * a\u207b\u00b9",
1352
+ "tactic": "simp only [zpow_negSucc, conj_pow, mul_inv_rev, inv_inv]"
1353
+ },
1354
+ {
1355
+ "annotated_tactic": [
1356
+ "\"rw [<a>mul_assoc<\\/a>]\"",
1357
+ "[{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]}]"
1358
+ ],
1359
+ "state_after": "no goals",
1360
+ "state_before": "case negSucc\n\u03b1 : Type u\n\u03b2 : Type v\ninst\u271d : Group \u03b1\na b : \u03b1\na\u271d : \u2115\n\u22a2 a * ((b ^ (a\u271d + 1))\u207b\u00b9 * a\u207b\u00b9) = a * (b ^ (a\u271d + 1))\u207b\u00b9 * a\u207b\u00b9",
1361
+ "tactic": "rw [mul_assoc]"
1362
+ }
1363
+ ],
1364
+ "url": "https://github.com/leanprover-community/mathlib4"
1365
+ }
1366
+ },
1367
+ "theorem_name": "conj_zpow"
1368
+ },
1369
+ {
1370
+ "errors": [
1371
+ "internal transition boundary mismatch"
1372
+ ],
1373
+ "file_path": "Mathlib/Algebra/Group/Conj.lean",
1374
+ "proof_id": "mathlib:isConj_iff_eq",
1375
+ "provenance": {
1376
+ "selection": {
1377
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1378
+ "end": [
1379
+ 57,
1380
+ 34
1381
+ ],
1382
+ "file_path": "Mathlib/Algebra/Group/Conj.lean",
1383
+ "full_name": "isConj_iff_eq",
1384
+ "start": [
1385
+ 54,
1386
+ 1
1387
+ ],
1388
+ "traced_tactics": [
1389
+ {
1390
+ "annotated_tactic": [
1391
+ "\"rw [<a>SemiconjBy<\\/a>, <a>mul_comm<\\/a>, \\u2190 <a>Units.mul_inv_eq_iff_eq_mul<\\/a>, <a>mul_assoc<\\/a>, c.mul_inv, <a>mul_one<\\/a>] at hc\"",
1392
+ "[{\"full_name\":\"SemiconjBy\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Semiconj\\/Defs.lean\",\"def_pos\":[40,5],\"def_end_pos\":[40,15]},{\"full_name\":\"mul_comm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[332,9],\"def_end_pos\":[332,17]},{\"full_name\":\"Units.mul_inv_eq_iff_eq_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Units.lean\",\"def_pos\":[342,9],\"def_end_pos\":[342,30]},{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]}]"
1393
+ ],
1394
+ "state_after": "\u03b1\u271d : Type u\n\u03b2 : Type v\ninst\u271d\u00b2 : Monoid \u03b1\u271d\ninst\u271d\u00b9 : Monoid \u03b2\n\u03b1 : Type u_1\ninst\u271d : CommMonoid \u03b1\na b : \u03b1\nx\u271d : IsConj a b\nc : \u03b1\u02e3\nhc : a = b\n\u22a2 a = b",
1395
+ "state_before": "\u03b1\u271d : Type u\n\u03b2 : Type v\ninst\u271d\u00b2 : Monoid \u03b1\u271d\ninst\u271d\u00b9 : Monoid \u03b2\n\u03b1 : Type u_1\ninst\u271d : CommMonoid \u03b1\na b : \u03b1\nx\u271d : IsConj a b\nc : \u03b1\u02e3\nhc : SemiconjBy (\u2191c) a b\n\u22a2 a = b",
1396
+ "tactic": "rw [SemiconjBy, mul_comm, \u2190 Units.mul_inv_eq_iff_eq_mul, mul_assoc, c.mul_inv, mul_one] at hc"
1397
+ },
1398
+ {
1399
+ "annotated_tactic": [
1400
+ "\"exact hc\"",
1401
+ "[]"
1402
+ ],
1403
+ "state_after": "no goals",
1404
+ "state_before": "\u03b1\u271d : Type u\n\u03b2 : Type v\ninst\u271d\u00b2 : Monoid \u03b1\u271d\ninst\u271d\u00b9 : Monoid \u03b2\n\u03b1 : Type u_1\ninst\u271d : CommMonoid \u03b1\na b : \u03b1\nx\u271d : IsConj a b\nc : \u03b1\u02e3\nhc : a = b\n\u22a2 a = b",
1405
+ "tactic": "exact hc"
1406
+ },
1407
+ {
1408
+ "annotated_tactic": [
1409
+ "\"rw [h]\"",
1410
+ "[]"
1411
+ ],
1412
+ "state_after": "no goals",
1413
+ "state_before": "\u03b1\u271d : Type u\n\u03b2 : Type v\ninst\u271d\u00b2 : Monoid \u03b1\u271d\ninst\u271d\u00b9 : Monoid \u03b2\n\u03b1 : Type u_1\ninst\u271d : CommMonoid \u03b1\na b : \u03b1\nh : a = b\n\u22a2 IsConj a b",
1414
+ "tactic": "rw [h]"
1415
+ }
1416
+ ],
1417
+ "url": "https://github.com/leanprover-community/mathlib4"
1418
+ }
1419
+ },
1420
+ "theorem_name": "isConj_iff_eq"
1421
+ },
1422
+ {
1423
+ "errors": [
1424
+ "internal transition boundary mismatch"
1425
+ ],
1426
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
1427
+ "proof_id": "mathlib:pow_add",
1428
+ "provenance": {
1429
+ "selection": {
1430
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1431
+ "end": [
1432
+ 705,
1433
+ 81
1434
+ ],
1435
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
1436
+ "full_name": "pow_add",
1437
+ "start": [
1438
+ 702,
1439
+ 1
1440
+ ],
1441
+ "traced_tactics": [
1442
+ {
1443
+ "annotated_tactic": [
1444
+ "\"rw [<a>Nat.add_zero<\\/a>, <a>pow_zero<\\/a>, <a>mul_one<\\/a>]\"",
1445
+ "[{\"full_name\":\"Nat.add_zero\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[588,27],\"def_end_pos\":[588,39]},{\"full_name\":\"pow_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[651,9],\"def_end_pos\":[651,17]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]}]"
1446
+ ],
1447
+ "state_after": "no goals",
1448
+ "state_before": "G : Type u_1\nM : Type u_2\ninst\u271d : Monoid M\na\u271d b c : M\nm\u271d n : \u2115\na : M\nm : \u2115\n\u22a2 a ^ (m + 0) = a ^ m * a ^ 0",
1449
+ "tactic": "rw [Nat.add_zero, pow_zero, mul_one]"
1450
+ },
1451
+ {
1452
+ "annotated_tactic": [
1453
+ "\"rw [<a>pow_succ<\\/a>, \\u2190 <a>mul_assoc<\\/a>, \\u2190 pow_add, \\u2190 <a>pow_succ<\\/a>, <a>Nat.add_assoc<\\/a>]\"",
1454
+ "[{\"full_name\":\"pow_succ\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[657,9],\"def_end_pos\":[657,17]},{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]},{\"full_name\":\"pow_succ\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[657,9],\"def_end_pos\":[657,17]},{\"full_name\":\"Nat.add_assoc\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[168,19],\"def_end_pos\":[168,28]}]"
1455
+ ],
1456
+ "state_after": "no goals",
1457
+ "state_before": "G : Type u_1\nM : Type u_2\ninst\u271d : Monoid M\na\u271d b c : M\nm\u271d n\u271d : \u2115\na : M\nm n : \u2115\n\u22a2 a ^ (m + (n + 1)) = a ^ m * a ^ (n + 1)",
1458
+ "tactic": "rw [pow_succ, \u2190 mul_assoc, \u2190 pow_add, \u2190 pow_succ, Nat.add_assoc]"
1459
+ }
1460
+ ],
1461
+ "url": "https://github.com/leanprover-community/mathlib4"
1462
+ }
1463
+ },
1464
+ "theorem_name": "pow_add"
1465
+ },
1466
+ {
1467
+ "errors": [
1468
+ "internal transition boundary mismatch"
1469
+ ],
1470
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
1471
+ "proof_id": "mathlib:pow_mul",
1472
+ "provenance": {
1473
+ "selection": {
1474
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1475
+ "end": [
1476
+ 715,
1477
+ 62
1478
+ ],
1479
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
1480
+ "full_name": "pow_mul",
1481
+ "start": [
1482
+ 713,
1483
+ 1
1484
+ ],
1485
+ "traced_tactics": [
1486
+ {
1487
+ "annotated_tactic": [
1488
+ "\"rw [<a>Nat.mul_zero<\\/a>, <a>pow_zero<\\/a>, <a>pow_zero<\\/a>]\"",
1489
+ "[{\"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\":\"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]}]"
1490
+ ],
1491
+ "state_after": "no goals",
1492
+ "state_before": "G : Type u_1\nM : Type u_2\ninst\u271d : Monoid M\na\u271d b c : M\nm\u271d n : \u2115\na : M\nm : \u2115\n\u22a2 a ^ (m * 0) = (a ^ m) ^ 0",
1493
+ "tactic": "rw [Nat.mul_zero, pow_zero, pow_zero]"
1494
+ },
1495
+ {
1496
+ "annotated_tactic": [
1497
+ "\"rw [<a>Nat.mul_succ<\\/a>, <a>pow_add<\\/a>, <a>pow_succ<\\/a>, pow_mul]\"",
1498
+ "[{\"full_name\":\"Nat.mul_succ\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[200,9],\"def_end_pos\":[200,17]},{\"full_name\":\"pow_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[703,7],\"def_end_pos\":[703,14]},{\"full_name\":\"pow_succ\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[657,9],\"def_end_pos\":[657,17]}]"
1499
+ ],
1500
+ "state_after": "no goals",
1501
+ "state_before": "G : Type u_1\nM : Type u_2\ninst\u271d : Monoid M\na\u271d b c : M\nm\u271d n\u271d : \u2115\na : M\nm n : \u2115\n\u22a2 a ^ (m * (n + 1)) = (a ^ m) ^ (n + 1)",
1502
+ "tactic": "rw [Nat.mul_succ, pow_add, pow_succ, pow_mul]"
1503
+ }
1504
+ ],
1505
+ "url": "https://github.com/leanprover-community/mathlib4"
1506
+ }
1507
+ },
1508
+ "theorem_name": "pow_mul"
1509
+ },
1510
+ {
1511
+ "errors": [
1512
+ "internal transition boundary mismatch"
1513
+ ],
1514
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
1515
+ "proof_id": "mathlib:pow_succ'",
1516
+ "provenance": {
1517
+ "selection": {
1518
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1519
+ "end": [
1520
+ 669,
1521
+ 66
1522
+ ],
1523
+ "file_path": "Mathlib/Algebra/Group/Defs.lean",
1524
+ "full_name": "pow_succ'",
1525
+ "start": [
1526
+ 667,
1527
+ 1
1528
+ ],
1529
+ "traced_tactics": [
1530
+ {
1531
+ "annotated_tactic": [
1532
+ "\"simp\"",
1533
+ "[]"
1534
+ ],
1535
+ "state_after": "no goals",
1536
+ "state_before": "G : Type u_1\nM : Type u_2\ninst\u271d : Monoid M\na\u271d b c : M\nm n : \u2115\na : M\n\u22a2 a ^ (0 + 1) = a * a ^ 0",
1537
+ "tactic": "simp"
1538
+ },
1539
+ {
1540
+ "annotated_tactic": [
1541
+ "\"rw [<a>pow_succ<\\/a> _ n, <a>pow_succ<\\/a>, pow_succ', <a>mul_assoc<\\/a>]\"",
1542
+ "[{\"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]},{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]}]"
1543
+ ],
1544
+ "state_after": "no goals",
1545
+ "state_before": "G : Type u_1\nM : Type u_2\ninst\u271d : Monoid M\na\u271d b c : M\nm n\u271d : \u2115\na : M\nn : \u2115\n\u22a2 a ^ (n + 1 + 1) = a * a ^ (n + 1)",
1546
+ "tactic": "rw [pow_succ _ n, pow_succ, pow_succ', mul_assoc]"
1547
+ }
1548
+ ],
1549
+ "url": "https://github.com/leanprover-community/mathlib4"
1550
+ }
1551
+ },
1552
+ "theorem_name": "pow_succ'"
1553
+ }
1554
+ ],
1555
+ "validation_rejected_proofs": 6,
1556
+ "zero_transition_proofs": 0
1557
+ },
1558
+ "shards": [
1559
+ {
1560
+ "path": "data/train/mathlib-000116-0000-b802391611e91bd9.parquet",
1561
+ "sha256": "b802391611e91bd9e1cba1b0b43b7202e7aefe3051646ce1b9c4501f4ad222de",
1562
+ "bytes": 97981,
1563
+ "rows": 34,
1564
+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
1565
+ },
1566
+ {
1567
+ "path": "data/dev/mathlib-000116-0000-642c8252a3676d09.parquet",
1568
+ "sha256": "642c8252a3676d098a90bd286f1144fae3e6765f6cc1a38c91c4a44a56ac20d0",
1569
+ "bytes": 34633,
1570
+ "rows": 1,
1571
+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
1572
+ },
1573
+ {
1574
+ "path": "data/internal_test/mathlib-000116-0000-24f272a9435c0c22.parquet",
1575
+ "sha256": "24f272a9435c0c22587e26099c9c963aeb22dbb6e48c296b588bfa44d92c6059",
1576
+ "bytes": 33677,
1577
+ "rows": 1,
1578
+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
1579
+ }
1580
+ ],
1581
+ "proof_ids": [
1582
+ "mathlib:ConjClasses.map_surjective",
1583
+ "mathlib:ConjClasses.mem_carrier_iff_mk_eq",
1584
+ "mathlib:MonoidHom.map_isConj",
1585
+ "mathlib:inv_eq_of_mul_eq_one_left",
1586
+ "mathlib:inv_mul_cancel_comm",
1587
+ "mathlib:inv_mul_cancel_comm_assoc",
1588
+ "mathlib:inv_mul_cancel_left",
1589
+ "mathlib:inv_mul_cancel_right",
1590
+ "mathlib:isConj_iff_conjugatesOf_eq",
1591
+ "mathlib:isConj_one_right",
1592
+ "mathlib:left_inv_eq_right_inv",
1593
+ "mathlib:mul_inv_cancel_comm",
1594
+ "mathlib:mul_inv_cancel_comm_assoc",
1595
+ "mathlib:mul_inv_cancel_left",
1596
+ "mathlib:mul_inv_cancel_right",
1597
+ "mathlib:mul_right_inv",
1598
+ "mathlib:one_pow",
1599
+ "mathlib:pow_mul'",
1600
+ "mathlib:pow_mul_comm",
1601
+ "mathlib:pow_mul_comm'",
1602
+ "mathlib:pow_one",
1603
+ "mathlib:pow_right_comm",
1604
+ "mathlib:pow_three",
1605
+ "mathlib:pow_three'",
1606
+ "mathlib:zpow_negSucc",
1607
+ "mathlib:zpow_one",
1608
+ "mathlib:zpow_two"
1609
+ ],
1610
+ "proof_keys": [
1611
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Conj.lean\",null,null,\"ConjClasses.map_surjective\"]",
1612
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Conj.lean\",null,null,\"ConjClasses.mem_carrier_iff_mk_eq\"]",
1613
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Conj.lean\",null,null,\"MonoidHom.map_isConj\"]",
1614
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Conj.lean\",null,null,\"isConj_iff_conjugatesOf_eq\"]",
1615
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Conj.lean\",null,null,\"isConj_one_right\"]",
1616
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Defs.lean\",null,null,\"inv_eq_of_mul_eq_one_left\"]",
1617
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Defs.lean\",null,null,\"inv_mul_cancel_comm\"]",
1618
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Defs.lean\",null,null,\"inv_mul_cancel_comm_assoc\"]",
1619
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Defs.lean\",null,null,\"inv_mul_cancel_left\"]",
1620
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Defs.lean\",null,null,\"inv_mul_cancel_right\"]",
1621
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1218
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1238
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1242
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1282
+ },
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+ "source_file": "Mathlib/Algebra/Group/Equiv/Basic.lean"
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1304
+ },
1305
+ "source_file": "Mathlib/Algebra/Group/Equiv/Basic.lean"
1306
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1307
+ {
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+ "full_name": "MulEquivClass.toMulEquiv_injective",
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1326
+ },
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1329
+ {
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+ "error": "theorem has no selected tactic transitions",
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+ "full_name": "MulHom.toMulEquiv_apply",
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+ "reason": "import_failure",
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+ "url": "https://github.com/leanprover-community/mathlib4"
1348
+ },
1349
+ "source_file": "Mathlib/Algebra/Group/Equiv/Basic.lean"
1350
+ },
1351
+ {
1352
+ "error": "theorem has no selected tactic transitions",
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+ "full_name": "MulHom.toMulEquiv_symm_apply",
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+ "id": "MulHom.toMulEquiv_symm_apply",
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+ "reason": "import_failure",
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1368
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1370
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1372
+ }
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+ "input_proofs": 67,
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+ "input_units": 2,
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+ "proofs": 5,
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+ "published_proofs": 5,
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+ "published_transitions": 8,
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+ "replay_failures": [],
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+ "validation_failures": [],
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+ "shards": [
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+ {
1387
+ "path": "data/train/mathlib-000117-0000-d78ac41c1efbce6b.parquet",
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+ "sha256": "d78ac41c1efbce6b9ca43574afd07cde59b092e09a164ecf017b3a036ae98d45",
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+ "rows": 8,
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+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
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+ }
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+ ],
1394
+ "proof_ids": [
1395
+ "mathlib:MulEquiv.coe_monoidHom_comp_coe_monoidHom_symm",
1396
+ "mathlib:MulEquiv.coe_monoidHom_symm_comp_coe_monoidHom",
1397
+ "mathlib:MulEquiv.comp_left_injective",
1398
+ "mathlib:MulEquiv.comp_right_injective",
1399
+ "mathlib:mulLeftEmbedding_eq_mulRightEmbedding"
1400
+ ],
1401
+ "proof_keys": [
1402
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Embedding.lean\",null,null,\"mulLeftEmbedding_eq_mulRightEmbedding\"]",
1403
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Equiv/Basic.lean\",null,null,\"MulEquiv.coe_monoidHom_comp_coe_monoidHom_symm\"]",
1404
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Equiv/Basic.lean\",null,null,\"MulEquiv.coe_monoidHom_symm_comp_coe_monoidHom\"]",
1405
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Equiv/Basic.lean\",null,null,\"MulEquiv.comp_left_injective\"]",
1406
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Equiv/Basic.lean\",null,null,\"MulEquiv.comp_right_injective\"]"
1407
+ ]
1408
+ }
manifests/batches/mathlib/000118.json ADDED
@@ -0,0 +1,794 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000118",
4
+ "batch_fingerprint": "0118656487cdb6a6240517f46e813f9591f65d35342a8df440ab4fc66b28f1d0",
5
+ "evidence": {
6
+ "batch_fingerprint": "0118656487cdb6a6240517f46e813f9591f65d35342a8df440ab4fc66b28f1d0",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "no internal trace for tactic 'simp'",
11
+ "full_name": "IsSquare.map",
12
+ "id": "IsSquare.map",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 105,
18
+ 23
19
+ ],
20
+ "file_path": "Mathlib/Algebra/Group/Even.lean",
21
+ "full_name": "IsSquare.map",
22
+ "start": [
23
+ 100,
24
+ 1
25
+ ],
26
+ "traced_tactics": [
27
+ {
28
+ "annotated_tactic": [
29
+ "\"rintro \\u27e8m, rfl\\u27e9\"",
30
+ "[]"
31
+ ],
32
+ "state_after": "case intro\nF : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nR : Type u_4\ninst\u271d\u00b3 : MulOneClass \u03b1\ninst\u271d\u00b2 : MulOneClass \u03b2\ninst\u271d\u00b9 : FunLike F \u03b1 \u03b2\ninst\u271d : MonoidHomClass F \u03b1 \u03b2\nf : F\nm : \u03b1\n\u22a2 IsSquare (f (m * m))",
33
+ "state_before": "F : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nR : Type u_4\ninst\u271d\u00b3 : MulOneClass \u03b1\ninst\u271d\u00b2 : MulOneClass \u03b2\ninst\u271d\u00b9 : FunLike F \u03b1 \u03b2\ninst\u271d : MonoidHomClass F \u03b1 \u03b2\nm : \u03b1\nf : F\n\u22a2 IsSquare m \u2192 IsSquare (f m)",
34
+ "tactic": "rintro \u27e8m, rfl\u27e9"
35
+ },
36
+ {
37
+ "annotated_tactic": [
38
+ "\"exact \\u27e8f m, by simp\\u27e9\"",
39
+ "[]"
40
+ ],
41
+ "state_after": "no goals",
42
+ "state_before": "case intro\nF : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nR : Type u_4\ninst\u271d\u00b3 : MulOneClass \u03b1\ninst\u271d\u00b2 : MulOneClass \u03b2\ninst\u271d\u00b9 : FunLike F \u03b1 \u03b2\ninst\u271d : MonoidHomClass F \u03b1 \u03b2\nf : F\nm : \u03b1\n\u22a2 IsSquare (f (m * m))",
43
+ "tactic": "exact \u27e8f m, by simp\u27e9"
44
+ },
45
+ {
46
+ "annotated_tactic": [
47
+ "\"simp\"",
48
+ "[]"
49
+ ],
50
+ "state_after": "no goals",
51
+ "state_before": "F : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nR : Type u_4\ninst\u271d\u00b3 : MulOneClass \u03b1\ninst\u271d\u00b2 : MulOneClass \u03b2\ninst\u271d\u00b9 : FunLike F \u03b1 \u03b2\ninst\u271d : MonoidHomClass F \u03b1 \u03b2\nf : F\nm : \u03b1\n\u22a2 f (m * m) = f m * f m",
52
+ "tactic": "simp"
53
+ }
54
+ ],
55
+ "url": "https://github.com/leanprover-community/mathlib4"
56
+ },
57
+ "source_file": "Mathlib/Algebra/Group/Even.lean"
58
+ },
59
+ {
60
+ "error": "theorem has no selected tactic transitions",
61
+ "full_name": "IsSquare_sq",
62
+ "id": "IsSquare_sq",
63
+ "reason": "import_failure",
64
+ "selection": {
65
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
66
+ "end": [
67
+ 135,
68
+ 93
69
+ ],
70
+ "file_path": "Mathlib/Algebra/Group/Even.lean",
71
+ "full_name": "IsSquare_sq",
72
+ "start": [
73
+ 135,
74
+ 1
75
+ ],
76
+ "traced_tactics": [],
77
+ "url": "https://github.com/leanprover-community/mathlib4"
78
+ },
79
+ "source_file": "Mathlib/Algebra/Group/Even.lean"
80
+ },
81
+ {
82
+ "error": "theorem has no selected tactic transitions",
83
+ "full_name": "even_ofMul_iff",
84
+ "id": "even_ofMul_iff",
85
+ "reason": "import_failure",
86
+ "selection": {
87
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
88
+ "end": [
89
+ 70,
90
+ 79
91
+ ],
92
+ "file_path": "Mathlib/Algebra/Group/Even.lean",
93
+ "full_name": "even_ofMul_iff",
94
+ "start": [
95
+ 69,
96
+ 1
97
+ ],
98
+ "traced_tactics": [],
99
+ "url": "https://github.com/leanprover-community/mathlib4"
100
+ },
101
+ "source_file": "Mathlib/Algebra/Group/Even.lean"
102
+ },
103
+ {
104
+ "error": "theorem has no selected tactic transitions",
105
+ "full_name": "even_toAdd_iff",
106
+ "id": "even_toAdd_iff",
107
+ "reason": "import_failure",
108
+ "selection": {
109
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
110
+ "end": [
111
+ 87,
112
+ 100
113
+ ],
114
+ "file_path": "Mathlib/Algebra/Group/Even.lean",
115
+ "full_name": "even_toAdd_iff",
116
+ "start": [
117
+ 86,
118
+ 1
119
+ ],
120
+ "traced_tactics": [],
121
+ "url": "https://github.com/leanprover-community/mathlib4"
122
+ },
123
+ "source_file": "Mathlib/Algebra/Group/Even.lean"
124
+ },
125
+ {
126
+ "error": "theorem has no selected tactic transitions",
127
+ "full_name": "isSquare_mul_self",
128
+ "id": "isSquare_mul_self",
129
+ "reason": "import_failure",
130
+ "selection": {
131
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
132
+ "end": [
133
+ 52,
134
+ 93
135
+ ],
136
+ "file_path": "Mathlib/Algebra/Group/Even.lean",
137
+ "full_name": "isSquare_mul_self",
138
+ "start": [
139
+ 52,
140
+ 1
141
+ ],
142
+ "traced_tactics": [],
143
+ "url": "https://github.com/leanprover-community/mathlib4"
144
+ },
145
+ "source_file": "Mathlib/Algebra/Group/Even.lean"
146
+ },
147
+ {
148
+ "error": "theorem has no selected tactic transitions",
149
+ "full_name": "isSquare_ofAdd_iff",
150
+ "id": "isSquare_ofAdd_iff",
151
+ "reason": "import_failure",
152
+ "selection": {
153
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
154
+ "end": [
155
+ 84,
156
+ 97
157
+ ],
158
+ "file_path": "Mathlib/Algebra/Group/Even.lean",
159
+ "full_name": "isSquare_ofAdd_iff",
160
+ "start": [
161
+ 84,
162
+ 1
163
+ ],
164
+ "traced_tactics": [],
165
+ "url": "https://github.com/leanprover-community/mathlib4"
166
+ },
167
+ "source_file": "Mathlib/Algebra/Group/Even.lean"
168
+ },
169
+ {
170
+ "error": "theorem has no selected tactic transitions",
171
+ "full_name": "isSquare_one",
172
+ "id": "isSquare_one",
173
+ "reason": "import_failure",
174
+ "selection": {
175
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
176
+ "end": [
177
+ 96,
178
+ 79
179
+ ],
180
+ "file_path": "Mathlib/Algebra/Group/Even.lean",
181
+ "full_name": "isSquare_one",
182
+ "start": [
183
+ 95,
184
+ 1
185
+ ],
186
+ "traced_tactics": [],
187
+ "url": "https://github.com/leanprover-community/mathlib4"
188
+ },
189
+ "source_file": "Mathlib/Algebra/Group/Even.lean"
190
+ },
191
+ {
192
+ "error": "theorem has no selected tactic transitions",
193
+ "full_name": "isSquare_op_iff",
194
+ "id": "isSquare_op_iff",
195
+ "reason": "import_failure",
196
+ "selection": {
197
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
198
+ "end": [
199
+ 58,
200
+ 85
201
+ ],
202
+ "file_path": "Mathlib/Algebra/Group/Even.lean",
203
+ "full_name": "isSquare_op_iff",
204
+ "start": [
205
+ 56,
206
+ 1
207
+ ],
208
+ "traced_tactics": [],
209
+ "url": "https://github.com/leanprover-community/mathlib4"
210
+ },
211
+ "source_file": "Mathlib/Algebra/Group/Even.lean"
212
+ },
213
+ {
214
+ "error": "theorem has no selected tactic transitions",
215
+ "full_name": "isSquare_toMul_iff",
216
+ "id": "isSquare_toMul_iff",
217
+ "reason": "import_failure",
218
+ "selection": {
219
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
220
+ "end": [
221
+ 73,
222
+ 92
223
+ ],
224
+ "file_path": "Mathlib/Algebra/Group/Even.lean",
225
+ "full_name": "isSquare_toMul_iff",
226
+ "start": [
227
+ 72,
228
+ 1
229
+ ],
230
+ "traced_tactics": [],
231
+ "url": "https://github.com/leanprover-community/mathlib4"
232
+ },
233
+ "source_file": "Mathlib/Algebra/Group/Even.lean"
234
+ },
235
+ {
236
+ "error": "theorem has no selected tactic transitions",
237
+ "full_name": "isSquare_unop_iff",
238
+ "id": "isSquare_unop_iff",
239
+ "reason": "import_failure",
240
+ "selection": {
241
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
242
+ "end": [
243
+ 63,
244
+ 92
245
+ ],
246
+ "file_path": "Mathlib/Algebra/Group/Even.lean",
247
+ "full_name": "isSquare_unop_iff",
248
+ "start": [
249
+ 62,
250
+ 1
251
+ ],
252
+ "traced_tactics": [],
253
+ "url": "https://github.com/leanprover-community/mathlib4"
254
+ },
255
+ "source_file": "Mathlib/Algebra/Group/Even.lean"
256
+ },
257
+ {
258
+ "error": "theorem has no selected tactic transitions",
259
+ "full_name": "CancelCommMonoid.ext",
260
+ "id": "CancelCommMonoid.ext",
261
+ "reason": "import_failure",
262
+ "selection": {
263
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
264
+ "end": [
265
+ 132,
266
+ 66
267
+ ],
268
+ "file_path": "Mathlib/Algebra/Group/Ext.lean",
269
+ "full_name": "CancelCommMonoid.ext",
270
+ "start": [
271
+ 129,
272
+ 1
273
+ ],
274
+ "traced_tactics": [],
275
+ "url": "https://github.com/leanprover-community/mathlib4"
276
+ },
277
+ "source_file": "Mathlib/Algebra/Group/Ext.lean"
278
+ },
279
+ {
280
+ "error": "no internal trace for tactic \"injection h with h'\"",
281
+ "full_name": "CancelCommMonoid.toCommMonoid_injective",
282
+ "id": "CancelCommMonoid.toCommMonoid_injective",
283
+ "reason": "import_failure",
284
+ "selection": {
285
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
286
+ "end": [
287
+ 124,
288
+ 19
289
+ ],
290
+ "file_path": "Mathlib/Algebra/Group/Ext.lean",
291
+ "full_name": "CancelCommMonoid.toCommMonoid_injective",
292
+ "start": [
293
+ 119,
294
+ 1
295
+ ],
296
+ "traced_tactics": [
297
+ {
298
+ "annotated_tactic": [
299
+ "\"rintro @\\u27e8@\\u27e8@\\u27e8\\u27e9\\u27e9\\u27e9 @\\u27e8@\\u27e8@\\u27e8\\u27e9\\u27e9\\u27e9 h\"",
300
+ "[]"
301
+ ],
302
+ "state_after": "case mk.mk.mk.mk.mk.mk\nM : Type u\ntoOne\u271d\u00b9 : One M\nnpow\u271d\u00b9 : \u2115 \u2192 M \u2192 M\nnpow_zero\u271d\u00b9 : \u2200 (x : M), npow\u271d\u00b9 0 x = 1\ntoSemigroup\u271d\u00b9 : Semigroup M\nmul_left_cancel\u271d\u00b9 : \u2200 (a b c : M), a * b = a * c \u2192 b = c\none_mul\u271d\u00b9 : \u2200 (a : M), 1 * a = a\nmul_one\u271d\u00b9 : \u2200 (a : M), a * 1 = a\nnpow_succ\u271d\u00b9 : \u2200 (n : \u2115) (x : M), npow\u271d\u00b9 (n + 1) x = npow\u271d\u00b9 n x * x\nmul_comm\u271d\u00b9 : \u2200 (a b : M), a * b = b * a\ntoOne\u271d : One M\nnpow\u271d : \u2115 \u2192 M \u2192 M\nnpow_zero\u271d : \u2200 (x : M), npow\u271d 0 x = 1\ntoSemigroup\u271d : Semigroup M\nmul_left_cancel\u271d : \u2200 (a b c : M), a * b = a * c \u2192 b = c\none_mul\u271d : \u2200 (a : M), 1 * a = a\nmul_one\u271d : \u2200 (a : M), a * 1 = a\nnpow_succ\u271d : \u2200 (n : \u2115) (x : M), npow\u271d (n + 1) x = npow\u271d n x * x\nmul_comm\u271d : \u2200 (a b : M), a * b = b * a\nh : toCommMonoid = toCommMonoid\n\u22a2 mk mul_comm\u271d\u00b9 = mk mul_comm\u271d",
303
+ "state_before": "M : Type u\n\u22a2 Injective (@toCommMonoid M)",
304
+ "tactic": "rintro @\u27e8@\u27e8@\u27e8\u27e9\u27e9\u27e9 @\u27e8@\u27e8@\u27e8\u27e9\u27e9\u27e9 h"
305
+ },
306
+ {
307
+ "annotated_tactic": [
308
+ "\"congr <;> {\\n injection h with h'\\n injection h' }\"",
309
+ "[]"
310
+ ],
311
+ "state_after": "no goals",
312
+ "state_before": "case mk.mk.mk.mk.mk.mk\nM : Type u\ntoOne\u271d\u00b9 : One M\nnpow\u271d\u00b9 : \u2115 \u2192 M \u2192 M\nnpow_zero\u271d\u00b9 : \u2200 (x : M), npow\u271d\u00b9 0 x = 1\ntoSemigroup\u271d\u00b9 : Semigroup M\nmul_left_cancel\u271d\u00b9 : \u2200 (a b c : M), a * b = a * c \u2192 b = c\none_mul\u271d\u00b9 : \u2200 (a : M), 1 * a = a\nmul_one\u271d\u00b9 : \u2200 (a : M), a * 1 = a\nnpow_succ\u271d\u00b9 : \u2200 (n : \u2115) (x : M), npow\u271d\u00b9 (n + 1) x = npow\u271d\u00b9 n x * x\nmul_comm\u271d\u00b9 : \u2200 (a b : M), a * b = b * a\ntoOne\u271d : One M\nnpow\u271d : \u2115 \u2192 M \u2192 M\nnpow_zero\u271d : \u2200 (x : M), npow\u271d 0 x = 1\ntoSemigroup\u271d : Semigroup M\nmul_left_cancel\u271d : \u2200 (a b c : M), a * b = a * c \u2192 b = c\none_mul\u271d : \u2200 (a : M), 1 * a = a\nmul_one\u271d : \u2200 (a : M), a * 1 = a\nnpow_succ\u271d : \u2200 (n : \u2115) (x : M), npow\u271d (n + 1) x = npow\u271d n x * x\nmul_comm\u271d : \u2200 (a b : M), a * b = b * a\nh : toCommMonoid = toCommMonoid\n\u22a2 mk mul_comm\u271d\u00b9 = mk mul_comm\u271d",
313
+ "tactic": "congr <;> {\n injection h with h'\n injection h' }"
314
+ },
315
+ {
316
+ "annotated_tactic": [
317
+ "\"injection h with h'\"",
318
+ "[]"
319
+ ],
320
+ "state_after": "case mk.mk.mk.mk.mk.mk.e_toLeftCancelMonoid.e_npow\nM : Type u\ntoOne\u271d\u00b9 : One M\nnpow\u271d\u00b9 : \u2115 \u2192 M \u2192 M\nnpow_zero\u271d\u00b9 : \u2200 (x : M), npow\u271d\u00b9 0 x = 1\ntoSemigroup\u271d\u00b9 : Semigroup M\nmul_left_cancel\u271d\u00b9 : \u2200 (a b c : M), a * b = a * c \u2192 b = c\none_mul\u271d\u00b9 : \u2200 (a : M), 1 * a = a\nmul_one\u271d\u00b9 : \u2200 (a : M), a * 1 = a\nnpow_succ\u271d\u00b9 : \u2200 (n : \u2115) (x : M), npow\u271d\u00b9 (n + 1) x = npow\u271d\u00b9 n x * x\nmul_comm\u271d\u00b9 : \u2200 (a b : M), a * b = b * a\ntoOne\u271d : One M\nnpow\u271d : \u2115 \u2192 M \u2192 M\nnpow_zero\u271d : \u2200 (x : M), npow\u271d 0 x = 1\ntoSemigroup\u271d : Semigroup M\nmul_left_cancel\u271d : \u2200 (a b c : M), a * b = a * c \u2192 b = c\none_mul\u271d : \u2200 (a : M), 1 * a = a\nmul_one\u271d : \u2200 (a : M), a * 1 = a\nnpow_succ\u271d : \u2200 (n : \u2115) (x : M), npow\u271d (n + 1) x = npow\u271d n x * x\nmul_comm\u271d : \u2200 (a b : M), a * b = b * a\nh' : Monoid.mk \u22ef \u22ef LeftCancelMonoid.npow \u22ef \u22ef = Monoid.mk \u22ef \u22ef LeftCancelMonoid.npow \u22ef \u22ef\n\u22a2 npow\u271d\u00b9 = npow\u271d",
321
+ "state_before": "case mk.mk.mk.mk.mk.mk.e_toLeftCancelMonoid.e_npow\nM : Type u\ntoOne\u271d\u00b9 : One M\nnpow\u271d\u00b9 : \u2115 \u2192 M \u2192 M\nnpow_zero\u271d\u00b9 : \u2200 (x : M), npow\u271d\u00b9 0 x = 1\ntoSemigroup\u271d\u00b9 : Semigroup M\nmul_left_cancel\u271d\u00b9 : \u2200 (a b c : M), a * b = a * c \u2192 b = c\none_mul\u271d\u00b9 : \u2200 (a : M), 1 * a = a\nmul_one\u271d\u00b9 : \u2200 (a : M), a * 1 = a\nnpow_succ\u271d\u00b9 : \u2200 (n : \u2115) (x : M), npow\u271d\u00b9 (n + 1) x = npow\u271d\u00b9 n x * x\nmul_comm\u271d\u00b9 : \u2200 (a b : M), a * b = b * a\ntoOne\u271d : One M\nnpow\u271d : \u2115 \u2192 M \u2192 M\nnpow_zero\u271d : \u2200 (x : M), npow\u271d 0 x = 1\ntoSemigroup\u271d : Semigroup M\nmul_left_cancel\u271d : \u2200 (a b c : M), a * b = a * c \u2192 b = c\none_mul\u271d : \u2200 (a : M), 1 * a = a\nmul_one\u271d : \u2200 (a : M), a * 1 = a\nnpow_succ\u271d : \u2200 (n : \u2115) (x : M), npow\u271d (n + 1) x = npow\u271d n x * x\nmul_comm\u271d : \u2200 (a b : M), a * b = b * a\nh : toCommMonoid = toCommMonoid\n\u22a2 npow\u271d\u00b9 = npow\u271d",
322
+ "tactic": "injection h with h'"
323
+ },
324
+ {
325
+ "annotated_tactic": [
326
+ "\"injection h'\"",
327
+ "[]"
328
+ ],
329
+ "state_after": "no goals",
330
+ "state_before": "case mk.mk.mk.mk.mk.mk.e_toLeftCancelMonoid.e_npow\nM : Type u\ntoOne\u271d\u00b9 : One M\nnpow\u271d\u00b9 : \u2115 \u2192 M \u2192 M\nnpow_zero\u271d\u00b9 : \u2200 (x : M), npow\u271d\u00b9 0 x = 1\ntoSemigroup\u271d\u00b9 : Semigroup M\nmul_left_cancel\u271d\u00b9 : \u2200 (a b c : M), a * b = a * c \u2192 b = c\none_mul\u271d\u00b9 : \u2200 (a : M), 1 * a = a\nmul_one\u271d\u00b9 : \u2200 (a : M), a * 1 = a\nnpow_succ\u271d\u00b9 : \u2200 (n : \u2115) (x : M), npow\u271d\u00b9 (n + 1) x = npow\u271d\u00b9 n x * x\nmul_comm\u271d\u00b9 : \u2200 (a b : M), a * b = b * a\ntoOne\u271d : One M\nnpow\u271d : \u2115 \u2192 M \u2192 M\nnpow_zero\u271d : \u2200 (x : M), npow\u271d 0 x = 1\ntoSemigroup\u271d : Semigroup M\nmul_left_cancel\u271d : \u2200 (a b c : M), a * b = a * c \u2192 b = c\none_mul\u271d : \u2200 (a : M), 1 * a = a\nmul_one\u271d : \u2200 (a : M), a * 1 = a\nnpow_succ\u271d : \u2200 (n : \u2115) (x : M), npow\u271d (n + 1) x = npow\u271d n x * x\nmul_comm\u271d : \u2200 (a b : M), a * b = b * a\nh' : Monoid.mk \u22ef \u22ef LeftCancelMonoid.npow \u22ef \u22ef = Monoid.mk \u22ef \u22ef LeftCancelMonoid.npow \u22ef \u22ef\n\u22a2 npow\u271d\u00b9 = npow\u271d",
331
+ "tactic": "injection h'"
332
+ }
333
+ ],
334
+ "url": "https://github.com/leanprover-community/mathlib4"
335
+ },
336
+ "source_file": "Mathlib/Algebra/Group/Ext.lean"
337
+ },
338
+ {
339
+ "error": "theorem has no selected tactic transitions",
340
+ "full_name": "CancelMonoid.ext",
341
+ "id": "CancelMonoid.ext",
342
+ "reason": "import_failure",
343
+ "selection": {
344
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
345
+ "end": [
346
+ 114,
347
+ 74
348
+ ],
349
+ "file_path": "Mathlib/Algebra/Group/Ext.lean",
350
+ "full_name": "CancelMonoid.ext",
351
+ "start": [
352
+ 111,
353
+ 1
354
+ ],
355
+ "traced_tactics": [],
356
+ "url": "https://github.com/leanprover-community/mathlib4"
357
+ },
358
+ "source_file": "Mathlib/Algebra/Group/Ext.lean"
359
+ },
360
+ {
361
+ "error": "theorem has no selected tactic transitions",
362
+ "full_name": "CommGroup.ext",
363
+ "id": "CommGroup.ext",
364
+ "reason": "import_failure",
365
+ "selection": {
366
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
367
+ "end": [
368
+ 187,
369
+ 49
370
+ ],
371
+ "file_path": "Mathlib/Algebra/Group/Ext.lean",
372
+ "full_name": "CommGroup.ext",
373
+ "start": [
374
+ 186,
375
+ 1
376
+ ],
377
+ "traced_tactics": [],
378
+ "url": "https://github.com/leanprover-community/mathlib4"
379
+ },
380
+ "source_file": "Mathlib/Algebra/Group/Ext.lean"
381
+ },
382
+ {
383
+ "error": "theorem has no selected tactic transitions",
384
+ "full_name": "CommMonoid.ext",
385
+ "id": "CommMonoid.ext",
386
+ "reason": "import_failure",
387
+ "selection": {
388
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
389
+ "end": [
390
+ 66,
391
+ 52
392
+ ],
393
+ "file_path": "Mathlib/Algebra/Group/Ext.lean",
394
+ "full_name": "CommMonoid.ext",
395
+ "start": [
396
+ 64,
397
+ 1
398
+ ],
399
+ "traced_tactics": [],
400
+ "url": "https://github.com/leanprover-community/mathlib4"
401
+ },
402
+ "source_file": "Mathlib/Algebra/Group/Ext.lean"
403
+ },
404
+ {
405
+ "error": "no internal trace for tactic 'ext m x'",
406
+ "full_name": "DivInvMonoid.ext",
407
+ "id": "DivInvMonoid.ext",
408
+ "reason": "import_failure",
409
+ "selection": {
410
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
411
+ "end": [
412
+ 156,
413
+ 8
414
+ ],
415
+ "file_path": "Mathlib/Algebra/Group/Ext.lean",
416
+ "full_name": "DivInvMonoid.ext",
417
+ "start": [
418
+ 137,
419
+ 1
420
+ ],
421
+ "traced_tactics": [
422
+ {
423
+ "annotated_tactic": [
424
+ "\"have h_mon := <a>Monoid.ext<\\/a> h_mul\"",
425
+ "[{\"full_name\":\"Monoid.ext\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Ext.lean\",\"def_pos\":[38,9],\"def_end_pos\":[38,19]}]"
426
+ ],
427
+ "state_after": "M : Type u_1\nm\u2081 m\u2082 : DivInvMonoid M\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\n\u22a2 m\u2081 = m\u2082",
428
+ "state_before": "M : Type u_1\nm\u2081 m\u2082 : DivInvMonoid M\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\n\u22a2 m\u2081 = m\u2082",
429
+ "tactic": "have h_mon := Monoid.ext h_mul"
430
+ },
431
+ {
432
+ "annotated_tactic": [
433
+ "\"let f : @<a>MonoidHom<\\/a> M M m\\u2081.toMulOneClass m\\u2082.toMulOneClass :=\\n @<a>MonoidHom.mk<\\/a> _ _ (_) _ (@<a>OneHom.mk<\\/a> _ _ (_) _ <a>id<\\/a> h\\u2081)\\n (fun x y => <a>congr_fun<\\/a> (<a>congr_fun<\\/a> h_mul x) y)\"",
434
+ "[{\"full_name\":\"MonoidHom\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[353,11],\"def_end_pos\":[353,20]},{\"full_name\":\"MonoidHom.mk\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[353,11],\"def_end_pos\":[353,20]},{\"full_name\":\"OneHom.mk\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[174,11],\"def_end_pos\":[174,17]},{\"full_name\":\"id\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[33,15],\"def_end_pos\":[33,17]},{\"full_name\":\"congr_fun\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Logic.lean\",\"def_pos\":[78,7],\"def_end_pos\":[78,16]},{\"full_name\":\"congr_fun\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Logic.lean\",\"def_pos\":[78,7],\"def_end_pos\":[78,16]}]"
435
+ ],
436
+ "state_after": "M : Type u_1\nm\u2081 m\u2082 : DivInvMonoid M\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\n\u22a2 m\u2081 = m\u2082",
437
+ "state_before": "M : Type u_1\nm\u2081 m\u2082 : DivInvMonoid M\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\nh\u2081 : One.one = One.one\n\u22a2 m\u2081 = m\u2082",
438
+ "tactic": "let f : @MonoidHom M M m\u2081.toMulOneClass m\u2082.toMulOneClass :=\n @MonoidHom.mk _ _ (_) _ (@OneHom.mk _ _ (_) _ id h\u2081)\n (fun x y => congr_fun (congr_fun h_mul x) y)"
439
+ },
440
+ {
441
+ "annotated_tactic": [
442
+ "\"have : m\\u2081.zpow = m\\u2082.zpow := by\\n ext m x\\n exact @<a>MonoidHom.map_zpow'<\\/a> M M m\\u2081 m\\u2082 f (<a>congr_fun<\\/a> h_inv) x m\"",
443
+ "[{\"full_name\":\"MonoidHom.map_zpow'\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[1026,19],\"def_end_pos\":[1026,38]},{\"full_name\":\"congr_fun\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Logic.lean\",\"def_pos\":[78,7],\"def_end_pos\":[78,16]}]"
444
+ ],
445
+ "state_after": "M : Type u_1\nm\u2081 m\u2082 : DivInvMonoid M\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis\u271d : Monoid.npow = Monoid.npow\nthis : DivInvMonoid.zpow = DivInvMonoid.zpow\n\u22a2 m\u2081 = m\u2082",
446
+ "state_before": "M : Type u_1\nm\u2081 m\u2082 : DivInvMonoid M\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis : Monoid.npow = Monoid.npow\n\u22a2 m\u2081 = m\u2082",
447
+ "tactic": "have : m\u2081.zpow = m\u2082.zpow := by\n ext m x\n exact @MonoidHom.map_zpow' M M m\u2081 m\u2082 f (congr_fun h_inv) x m"
448
+ },
449
+ {
450
+ "annotated_tactic": [
451
+ "\"have : m\\u2081.div = m\\u2082.div := by\\n ext a b\\n exact @<a>map_div'<\\/a> _ _\\n (F := @<a>MonoidHom<\\/a> _ _ (_) _) _ (<a>id<\\/a> _) _\\n (@<a>MonoidHom.instMonoidHomClass<\\/a> _ _ (_) _) f (<a>congr_fun<\\/a> h_inv) a b\"",
452
+ "[{\"full_name\":\"map_div'\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[425,9],\"def_end_pos\":[425,17]},{\"full_name\":\"MonoidHom\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[353,11],\"def_end_pos\":[353,20]},{\"full_name\":\"id\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[33,15],\"def_end_pos\":[33,17]},{\"full_name\":\"MonoidHom.instMonoidHomClass\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[385,10],\"def_end_pos\":[385,38]},{\"full_name\":\"congr_fun\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Logic.lean\",\"def_pos\":[78,7],\"def_end_pos\":[78,16]}]"
453
+ ],
454
+ "state_after": "M : Type u_1\nm\u2081 m\u2082 : DivInvMonoid M\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis\u271d\u00b9 : Monoid.npow = Monoid.npow\nthis\u271d : DivInvMonoid.zpow = DivInvMonoid.zpow\nthis : Div.div = Div.div\n\u22a2 m\u2081 = m\u2082",
455
+ "state_before": "M : Type u_1\nm\u2081 m\u2082 : DivInvMonoid M\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis\u271d : Monoid.npow = Monoid.npow\nthis : DivInvMonoid.zpow = DivInvMonoid.zpow\n\u22a2 m\u2081 = m\u2082",
456
+ "tactic": "have : m\u2081.div = m\u2082.div := by\n ext a b\n exact @map_div' _ _\n (F := @MonoidHom _ _ (_) _) _ (id _) _\n (@MonoidHom.instMonoidHomClass _ _ (_) _) f (congr_fun h_inv) a b"
457
+ },
458
+ {
459
+ "annotated_tactic": [
460
+ "\"rcases m\\u2081 with @\\u27e8_, \\u27e8_\\u27e9, \\u27e8_\\u27e9\\u27e9\"",
461
+ "[]"
462
+ ],
463
+ "state_after": "case mk.mk.mk\nM : Type u_1\nm\u2082 : DivInvMonoid M\ntoMonoid\u271d : Monoid M\nzpow\u271d : \u2124 \u2192 M \u2192 M\nzpow_zero'\u271d : \u2200 (a : M), zpow\u271d 0 a = 1\nzpow_succ'\u271d : \u2200 (n : \u2115) (a : M), zpow\u271d (Int.ofNat n.succ) a = zpow\u271d (Int.ofNat n) a * a\ninv\u271d : M \u2192 M\nzpow_neg'\u271d : \u2200 (n : \u2115) (a : M), zpow\u271d (Int.negSucc n) a = (zpow\u271d (\u2191n.succ) a)\u207b\u00b9\ndiv\u271d : M \u2192 M \u2192 M\ndiv_eq_mul_inv\u271d : \u2200 (a b : M), a / b = a * b\u207b\u00b9\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis\u271d\u00b9 : Monoid.npow = Monoid.npow\nthis\u271d : DivInvMonoid.zpow = DivInvMonoid.zpow\nthis : Div.div = Div.div\n\u22a2 mk div_eq_mul_inv\u271d zpow\u271d zpow_zero'\u271d zpow_succ'\u271d zpow_neg'\u271d = m\u2082",
464
+ "state_before": "M : Type u_1\nm\u2081 m\u2082 : DivInvMonoid M\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis\u271d\u00b9 : Monoid.npow = Monoid.npow\nthis\u271d : DivInvMonoid.zpow = DivInvMonoid.zpow\nthis : Div.div = Div.div\n\u22a2 m\u2081 = m\u2082",
465
+ "tactic": "rcases m\u2081 with @\u27e8_, \u27e8_\u27e9, \u27e8_\u27e9\u27e9"
466
+ },
467
+ {
468
+ "annotated_tactic": [
469
+ "\"rcases m\\u2082 with @\\u27e8_, \\u27e8_\\u27e9, \\u27e8_\\u27e9\\u27e9\"",
470
+ "[]"
471
+ ],
472
+ "state_after": "case mk.mk.mk.mk.mk.mk\nM : Type u_1\ntoMonoid\u271d\u00b9 : Monoid M\nzpow\u271d\u00b9 : \u2124 \u2192 M \u2192 M\nzpow_zero'\u271d\u00b9 : \u2200 (a : M), zpow\u271d\u00b9 0 a = 1\nzpow_succ'\u271d\u00b9 : \u2200 (n : \u2115) (a : M), zpow\u271d\u00b9 (Int.ofNat n.succ) a = zpow\u271d\u00b9 (Int.ofNat n) a * a\ninv\u271d\u00b9 : M \u2192 M\nzpow_neg'\u271d\u00b9 : \u2200 (n : \u2115) (a : M), zpow\u271d\u00b9 (Int.negSucc n) a = (zpow\u271d\u00b9 (\u2191n.succ) a)\u207b\u00b9\ndiv\u271d\u00b9 : M \u2192 M \u2192 M\ndiv_eq_mul_inv\u271d\u00b9 : \u2200 (a b : M), a / b = a * b\u207b\u00b9\ntoMonoid\u271d : Monoid M\nzpow\u271d : \u2124 \u2192 M \u2192 M\nzpow_zero'\u271d : \u2200 (a : M), zpow\u271d 0 a = 1\nzpow_succ'\u271d : \u2200 (n : \u2115) (a : M), zpow\u271d (Int.ofNat n.succ) a = zpow\u271d (Int.ofNat n) a * a\ninv\u271d : M \u2192 M\nzpow_neg'\u271d : \u2200 (n : \u2115) (a : M), zpow\u271d (Int.negSucc n) a = (zpow\u271d (\u2191n.succ) a)\u207b\u00b9\ndiv\u271d : M \u2192 M \u2192 M\ndiv_eq_mul_inv\u271d : \u2200 (a b : M), a / b = a * b\u207b\u00b9\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis\u271d\u00b9 : Monoid.npow = Monoid.npow\nthis\u271d : DivInvMonoid.zpow = DivInvMonoid.zpow\nthis : Div.div = Div.div\n\u22a2 mk div_eq_mul_inv\u271d\u00b9 zpow\u271d\u00b9 zpow_zero'\u271d\u00b9 zpow_succ'\u271d\u00b9 zpow_neg'\u271d\u00b9 =\n mk div_eq_mul_inv\u271d zpow\u271d zpow_zero'\u271d zpow_succ'\u271d zpow_neg'\u271d",
473
+ "state_before": "case mk.mk.mk\nM : Type u_1\nm\u2082 : DivInvMonoid M\ntoMonoid\u271d : Monoid M\nzpow\u271d : \u2124 \u2192 M \u2192 M\nzpow_zero'\u271d : \u2200 (a : M), zpow\u271d 0 a = 1\nzpow_succ'\u271d : \u2200 (n : \u2115) (a : M), zpow\u271d (Int.ofNat n.succ) a = zpow\u271d (Int.ofNat n) a * a\ninv\u271d : M \u2192 M\nzpow_neg'\u271d : \u2200 (n : \u2115) (a : M), zpow\u271d (Int.negSucc n) a = (zpow\u271d (\u2191n.succ) a)\u207b\u00b9\ndiv\u271d : M \u2192 M \u2192 M\ndiv_eq_mul_inv\u271d : \u2200 (a b : M), a / b = a * b\u207b\u00b9\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis\u271d\u00b9 : Monoid.npow = Monoid.npow\nthis\u271d : DivInvMonoid.zpow = DivInvMonoid.zpow\nthis : Div.div = Div.div\n\u22a2 mk div_eq_mul_inv\u271d zpow\u271d zpow_zero'\u271d zpow_succ'\u271d zpow_neg'\u271d = m\u2082",
474
+ "tactic": "rcases m\u2082 with @\u27e8_, \u27e8_\u27e9, \u27e8_\u27e9\u27e9"
475
+ },
476
+ {
477
+ "annotated_tactic": [
478
+ "\"congr\"",
479
+ "[]"
480
+ ],
481
+ "state_after": "no goals",
482
+ "state_before": "case mk.mk.mk.mk.mk.mk\nM : Type u_1\ntoMonoid\u271d\u00b9 : Monoid M\nzpow\u271d\u00b9 : \u2124 \u2192 M \u2192 M\nzpow_zero'\u271d\u00b9 : \u2200 (a : M), zpow\u271d\u00b9 0 a = 1\nzpow_succ'\u271d\u00b9 : \u2200 (n : \u2115) (a : M), zpow\u271d\u00b9 (Int.ofNat n.succ) a = zpow\u271d\u00b9 (Int.ofNat n) a * a\ninv\u271d\u00b9 : M \u2192 M\nzpow_neg'\u271d\u00b9 : \u2200 (n : \u2115) (a : M), zpow\u271d\u00b9 (Int.negSucc n) a = (zpow\u271d\u00b9 (\u2191n.succ) a)\u207b\u00b9\ndiv\u271d\u00b9 : M \u2192 M \u2192 M\ndiv_eq_mul_inv\u271d\u00b9 : \u2200 (a b : M), a / b = a * b\u207b\u00b9\ntoMonoid\u271d : Monoid M\nzpow\u271d : \u2124 \u2192 M \u2192 M\nzpow_zero'\u271d : \u2200 (a : M), zpow\u271d 0 a = 1\nzpow_succ'\u271d : \u2200 (n : \u2115) (a : M), zpow\u271d (Int.ofNat n.succ) a = zpow\u271d (Int.ofNat n) a * a\ninv\u271d : M \u2192 M\nzpow_neg'\u271d : \u2200 (n : \u2115) (a : M), zpow\u271d (Int.negSucc n) a = (zpow\u271d (\u2191n.succ) a)\u207b\u00b9\ndiv\u271d : M \u2192 M \u2192 M\ndiv_eq_mul_inv\u271d : \u2200 (a b : M), a / b = a * b\u207b\u00b9\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis\u271d\u00b9 : Monoid.npow = Monoid.npow\nthis\u271d : DivInvMonoid.zpow = DivInvMonoid.zpow\nthis : Div.div = Div.div\n\u22a2 mk div_eq_mul_inv\u271d\u00b9 zpow\u271d\u00b9 zpow_zero'\u271d\u00b9 zpow_succ'\u271d\u00b9 zpow_neg'\u271d\u00b9 =\n mk div_eq_mul_inv\u271d zpow\u271d zpow_zero'\u271d zpow_succ'\u271d zpow_neg'\u271d",
483
+ "tactic": "congr"
484
+ },
485
+ {
486
+ "annotated_tactic": [
487
+ "\"ext m x\"",
488
+ "[]"
489
+ ],
490
+ "state_after": "case h.h\nM : Type u_1\nm\u2081 m\u2082 : DivInvMonoid M\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis : Monoid.npow = Monoid.npow\nm : \u2124\nx : M\n\u22a2 DivInvMonoid.zpow m x = DivInvMonoid.zpow m x",
491
+ "state_before": "M : Type u_1\nm\u2081 m\u2082 : DivInvMonoid M\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis : Monoid.npow = Monoid.npow\n\u22a2 DivInvMonoid.zpow = DivInvMonoid.zpow",
492
+ "tactic": "ext m x"
493
+ },
494
+ {
495
+ "annotated_tactic": [
496
+ "\"exact @<a>MonoidHom.map_zpow'<\\/a> M M m\\u2081 m\\u2082 f (<a>congr_fun<\\/a> h_inv) x m\"",
497
+ "[{\"full_name\":\"MonoidHom.map_zpow'\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[1026,19],\"def_end_pos\":[1026,38]},{\"full_name\":\"congr_fun\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Logic.lean\",\"def_pos\":[78,7],\"def_end_pos\":[78,16]}]"
498
+ ],
499
+ "state_after": "no goals",
500
+ "state_before": "case h.h\nM : Type u_1\nm\u2081 m\u2082 : DivInvMonoid M\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis : Monoid.npow = Monoid.npow\nm : \u2124\nx : M\n\u22a2 DivInvMonoid.zpow m x = DivInvMonoid.zpow m x",
501
+ "tactic": "exact @MonoidHom.map_zpow' M M m\u2081 m\u2082 f (congr_fun h_inv) x m"
502
+ },
503
+ {
504
+ "annotated_tactic": [
505
+ "\"ext a b\"",
506
+ "[]"
507
+ ],
508
+ "state_after": "case h.h\nM : Type u_1\nm\u2081 m\u2082 : DivInvMonoid M\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis\u271d : Monoid.npow = Monoid.npow\nthis : DivInvMonoid.zpow = DivInvMonoid.zpow\na b : M\n\u22a2 Div.div a b = Div.div a b",
509
+ "state_before": "M : Type u_1\nm\u2081 m\u2082 : DivInvMonoid M\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis\u271d : Monoid.npow = Monoid.npow\nthis : DivInvMonoid.zpow = DivInvMonoid.zpow\n\u22a2 Div.div = Div.div",
510
+ "tactic": "ext a b"
511
+ },
512
+ {
513
+ "annotated_tactic": [
514
+ "\"exact @<a>map_div'<\\/a> _ _\\n (F := @<a>MonoidHom<\\/a> _ _ (_) _) _ (<a>id<\\/a> _) _\\n (@<a>MonoidHom.instMonoidHomClass<\\/a> _ _ (_) _) f (<a>congr_fun<\\/a> h_inv) a b\"",
515
+ "[{\"full_name\":\"map_div'\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[425,9],\"def_end_pos\":[425,17]},{\"full_name\":\"MonoidHom\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[353,11],\"def_end_pos\":[353,20]},{\"full_name\":\"id\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[33,15],\"def_end_pos\":[33,17]},{\"full_name\":\"MonoidHom.instMonoidHomClass\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[385,10],\"def_end_pos\":[385,38]},{\"full_name\":\"congr_fun\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Logic.lean\",\"def_pos\":[78,7],\"def_end_pos\":[78,16]}]"
516
+ ],
517
+ "state_after": "no goals",
518
+ "state_before": "case h.h\nM : Type u_1\nm\u2081 m\u2082 : DivInvMonoid M\nh_mul : HMul.hMul = HMul.hMul\nh_inv : Inv.inv = Inv.inv\nh_mon : toMonoid = toMonoid\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis\u271d : Monoid.npow = Monoid.npow\nthis : DivInvMonoid.zpow = DivInvMonoid.zpow\na b : M\n\u22a2 Div.div a b = Div.div a b",
519
+ "tactic": "exact @map_div' _ _\n (F := @MonoidHom _ _ (_) _) _ (id _) _\n (@MonoidHom.instMonoidHomClass _ _ (_) _) f (congr_fun h_inv) a b"
520
+ }
521
+ ],
522
+ "url": "https://github.com/leanprover-community/mathlib4"
523
+ },
524
+ "source_file": "Mathlib/Algebra/Group/Ext.lean"
525
+ },
526
+ {
527
+ "error": "theorem has no selected tactic transitions",
528
+ "full_name": "LeftCancelMonoid.ext",
529
+ "id": "LeftCancelMonoid.ext",
530
+ "reason": "import_failure",
531
+ "selection": {
532
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
533
+ "end": [
534
+ 82,
535
+ 58
536
+ ],
537
+ "file_path": "Mathlib/Algebra/Group/Ext.lean",
538
+ "full_name": "LeftCancelMonoid.ext",
539
+ "start": [
540
+ 79,
541
+ 1
542
+ ],
543
+ "traced_tactics": [],
544
+ "url": "https://github.com/leanprover-community/mathlib4"
545
+ },
546
+ "source_file": "Mathlib/Algebra/Group/Ext.lean"
547
+ },
548
+ {
549
+ "error": "no internal trace for tactic 'ext n x'",
550
+ "full_name": "Monoid.ext",
551
+ "id": "Monoid.ext",
552
+ "reason": "import_failure",
553
+ "selection": {
554
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
555
+ "end": [
556
+ 51,
557
+ 8
558
+ ],
559
+ "file_path": "Mathlib/Algebra/Group/Ext.lean",
560
+ "full_name": "Monoid.ext",
561
+ "start": [
562
+ 38,
563
+ 1
564
+ ],
565
+ "traced_tactics": [
566
+ {
567
+ "annotated_tactic": [
568
+ "\"have : m\\u2081.toMulOneClass = m\\u2082.toMulOneClass := <a>MulOneClass.ext<\\/a> h_mul\"",
569
+ "[{\"full_name\":\"MulOneClass.ext\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[463,9],\"def_end_pos\":[463,24]}]"
570
+ ],
571
+ "state_after": "M : Type u\nm\u2081 m\u2082 : Monoid M\nh_mul : HMul.hMul = HMul.hMul\nthis : toMulOneClass = toMulOneClass\n\u22a2 m\u2081 = m\u2082",
572
+ "state_before": "M : Type u\nm\u2081 m\u2082 : Monoid M\nh_mul : HMul.hMul = HMul.hMul\n\u22a2 m\u2081 = m\u2082",
573
+ "tactic": "have : m\u2081.toMulOneClass = m\u2082.toMulOneClass := MulOneClass.ext h_mul"
574
+ },
575
+ {
576
+ "annotated_tactic": [
577
+ "\"let f : @<a>MonoidHom<\\/a> M M m\\u2081.toMulOneClass m\\u2082.toMulOneClass :=\\n @<a>MonoidHom.mk<\\/a> _ _ (_) _ (@<a>OneHom.mk<\\/a> _ _ (_) _ <a>id<\\/a> h\\u2081)\\n (fun x y => <a>congr_fun<\\/a> (<a>congr_fun<\\/a> h_mul x) y)\"",
578
+ "[{\"full_name\":\"MonoidHom\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[353,11],\"def_end_pos\":[353,20]},{\"full_name\":\"MonoidHom.mk\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[353,11],\"def_end_pos\":[353,20]},{\"full_name\":\"OneHom.mk\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[174,11],\"def_end_pos\":[174,17]},{\"full_name\":\"id\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[33,15],\"def_end_pos\":[33,17]},{\"full_name\":\"congr_fun\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Logic.lean\",\"def_pos\":[78,7],\"def_end_pos\":[78,16]},{\"full_name\":\"congr_fun\",\"def_path\":\".lake\\/packages\\/batteries\\/Batteries\\/Logic.lean\",\"def_pos\":[78,7],\"def_end_pos\":[78,16]}]"
579
+ ],
580
+ "state_after": "M : Type u\nm\u2081 m\u2082 : Monoid M\nh_mul : HMul.hMul = HMul.hMul\nthis : toMulOneClass = toMulOneClass\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\n\u22a2 m\u2081 = m\u2082",
581
+ "state_before": "M : Type u\nm\u2081 m\u2082 : Monoid M\nh_mul : HMul.hMul = HMul.hMul\nthis : toMulOneClass = toMulOneClass\nh\u2081 : One.one = One.one\n\u22a2 m\u2081 = m\u2082",
582
+ "tactic": "let f : @MonoidHom M M m\u2081.toMulOneClass m\u2082.toMulOneClass :=\n @MonoidHom.mk _ _ (_) _ (@OneHom.mk _ _ (_) _ id h\u2081)\n (fun x y => congr_fun (congr_fun h_mul x) y)"
583
+ },
584
+ {
585
+ "annotated_tactic": [
586
+ "\"have : m\\u2081.npow = m\\u2082.npow := by\\n ext n x\\n exact @<a>MonoidHom.map_pow<\\/a> M M m\\u2081 m\\u2082 f x n\"",
587
+ "[{\"full_name\":\"MonoidHom.map_pow\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[1020,19],\"def_end_pos\":[1020,36]}]"
588
+ ],
589
+ "state_after": "M : Type u\nm\u2081 m\u2082 : Monoid M\nh_mul : HMul.hMul = HMul.hMul\nthis\u271d : toMulOneClass = toMulOneClass\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis : Monoid.npow = Monoid.npow\n\u22a2 m\u2081 = m\u2082",
590
+ "state_before": "M : Type u\nm\u2081 m\u2082 : Monoid M\nh_mul : HMul.hMul = HMul.hMul\nthis : toMulOneClass = toMulOneClass\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\n\u22a2 m\u2081 = m\u2082",
591
+ "tactic": "have : m\u2081.npow = m\u2082.npow := by\n ext n x\n exact @MonoidHom.map_pow M M m\u2081 m\u2082 f x n"
592
+ },
593
+ {
594
+ "annotated_tactic": [
595
+ "\"rcases m\\u2081 with @\\u27e8@\\u27e8\\u27e8_\\u27e9\\u27e9, \\u27e8_\\u27e9\\u27e9\"",
596
+ "[]"
597
+ ],
598
+ "state_after": "case mk.mk.mk.mk\nM : Type u\nm\u2082 : Monoid M\nnpow\u271d : \u2115 \u2192 M \u2192 M\nmul\u271d : M \u2192 M \u2192 M\nmul_assoc\u271d : \u2200 (a b c : M), a * b * c = a * (b * c)\nnpow_succ\u271d : \u2200 (n : \u2115) (x : M), npow\u271d (n + 1) x = npow\u271d n x * x\none\u271d : M\nnpow_zero\u271d : \u2200 (x : M), npow\u271d 0 x = 1\none_mul\u271d : \u2200 (a : M), 1 * a = a\nmul_one\u271d : \u2200 (a : M), a * 1 = a\nh_mul : HMul.hMul = HMul.hMul\nthis\u271d : toMulOneClass = toMulOneClass\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis : Monoid.npow = Monoid.npow\n\u22a2 mk one_mul\u271d mul_one\u271d npow\u271d npow_zero\u271d npow_succ\u271d = m\u2082",
599
+ "state_before": "M : Type u\nm\u2081 m\u2082 : Monoid M\nh_mul : HMul.hMul = HMul.hMul\nthis\u271d : toMulOneClass = toMulOneClass\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis : Monoid.npow = Monoid.npow\n\u22a2 m\u2081 = m\u2082",
600
+ "tactic": "rcases m\u2081 with @\u27e8@\u27e8\u27e8_\u27e9\u27e9, \u27e8_\u27e9\u27e9"
601
+ },
602
+ {
603
+ "annotated_tactic": [
604
+ "\"rcases m\\u2082 with @\\u27e8@\\u27e8\\u27e8_\\u27e9\\u27e9, \\u27e8_\\u27e9\\u27e9\"",
605
+ "[]"
606
+ ],
607
+ "state_after": "case mk.mk.mk.mk.mk.mk.mk.mk\nM : Type u\nnpow\u271d\u00b9 : \u2115 \u2192 M \u2192 M\nmul\u271d\u00b9 : M \u2192 M \u2192 M\nmul_assoc\u271d\u00b9 : \u2200 (a b c : M), a * b * c = a * (b * c)\nnpow_succ\u271d\u00b9 : \u2200 (n : \u2115) (x : M), npow\u271d\u00b9 (n + 1) x = npow\u271d\u00b9 n x * x\none\u271d\u00b9 : M\nnpow_zero\u271d\u00b9 : \u2200 (x : M), npow\u271d\u00b9 0 x = 1\none_mul\u271d\u00b9 : \u2200 (a : M), 1 * a = a\nmul_one\u271d\u00b9 : \u2200 (a : M), a * 1 = a\nnpow\u271d : \u2115 \u2192 M \u2192 M\nmul\u271d : M \u2192 M \u2192 M\nmul_assoc\u271d : \u2200 (a b c : M), a * b * c = a * (b * c)\nnpow_succ\u271d : \u2200 (n : \u2115) (x : M), npow\u271d (n + 1) x = npow\u271d n x * x\none\u271d : M\nnpow_zero\u271d : \u2200 (x : M), npow\u271d 0 x = 1\none_mul\u271d : \u2200 (a : M), 1 * a = a\nmul_one\u271d : \u2200 (a : M), a * 1 = a\nh_mul : HMul.hMul = HMul.hMul\nthis\u271d : toMulOneClass = toMulOneClass\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis : Monoid.npow = Monoid.npow\n\u22a2 mk one_mul\u271d\u00b9 mul_one\u271d\u00b9 npow\u271d\u00b9 npow_zero\u271d\u00b9 npow_succ\u271d\u00b9 = mk one_mul\u271d mul_one\u271d npow\u271d npow_zero\u271d npow_succ\u271d",
608
+ "state_before": "case mk.mk.mk.mk\nM : Type u\nm\u2082 : Monoid M\nnpow\u271d : \u2115 \u2192 M \u2192 M\nmul\u271d : M \u2192 M \u2192 M\nmul_assoc\u271d : \u2200 (a b c : M), a * b * c = a * (b * c)\nnpow_succ\u271d : \u2200 (n : \u2115) (x : M), npow\u271d (n + 1) x = npow\u271d n x * x\none\u271d : M\nnpow_zero\u271d : \u2200 (x : M), npow\u271d 0 x = 1\none_mul\u271d : \u2200 (a : M), 1 * a = a\nmul_one\u271d : \u2200 (a : M), a * 1 = a\nh_mul : HMul.hMul = HMul.hMul\nthis\u271d : toMulOneClass = toMulOneClass\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis : Monoid.npow = Monoid.npow\n\u22a2 mk one_mul\u271d mul_one\u271d npow\u271d npow_zero\u271d npow_succ\u271d = m\u2082",
609
+ "tactic": "rcases m\u2082 with @\u27e8@\u27e8\u27e8_\u27e9\u27e9, \u27e8_\u27e9\u27e9"
610
+ },
611
+ {
612
+ "annotated_tactic": [
613
+ "\"congr\"",
614
+ "[]"
615
+ ],
616
+ "state_after": "no goals",
617
+ "state_before": "case mk.mk.mk.mk.mk.mk.mk.mk\nM : Type u\nnpow\u271d\u00b9 : \u2115 \u2192 M \u2192 M\nmul\u271d\u00b9 : M \u2192 M \u2192 M\nmul_assoc\u271d\u00b9 : \u2200 (a b c : M), a * b * c = a * (b * c)\nnpow_succ\u271d\u00b9 : \u2200 (n : \u2115) (x : M), npow\u271d\u00b9 (n + 1) x = npow\u271d\u00b9 n x * x\none\u271d\u00b9 : M\nnpow_zero\u271d\u00b9 : \u2200 (x : M), npow\u271d\u00b9 0 x = 1\none_mul\u271d\u00b9 : \u2200 (a : M), 1 * a = a\nmul_one\u271d\u00b9 : \u2200 (a : M), a * 1 = a\nnpow\u271d : \u2115 \u2192 M \u2192 M\nmul\u271d : M \u2192 M \u2192 M\nmul_assoc\u271d : \u2200 (a b c : M), a * b * c = a * (b * c)\nnpow_succ\u271d : \u2200 (n : \u2115) (x : M), npow\u271d (n + 1) x = npow\u271d n x * x\none\u271d : M\nnpow_zero\u271d : \u2200 (x : M), npow\u271d 0 x = 1\none_mul\u271d : \u2200 (a : M), 1 * a = a\nmul_one\u271d : \u2200 (a : M), a * 1 = a\nh_mul : HMul.hMul = HMul.hMul\nthis\u271d : toMulOneClass = toMulOneClass\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nthis : Monoid.npow = Monoid.npow\n\u22a2 mk one_mul\u271d\u00b9 mul_one\u271d\u00b9 npow\u271d\u00b9 npow_zero\u271d\u00b9 npow_succ\u271d\u00b9 = mk one_mul\u271d mul_one\u271d npow\u271d npow_zero\u271d npow_succ\u271d",
618
+ "tactic": "congr"
619
+ },
620
+ {
621
+ "annotated_tactic": [
622
+ "\"ext n x\"",
623
+ "[]"
624
+ ],
625
+ "state_after": "case h.h\nM : Type u\nm\u2081 m\u2082 : Monoid M\nh_mul : HMul.hMul = HMul.hMul\nthis : toMulOneClass = toMulOneClass\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nn : \u2115\nx : M\n\u22a2 Monoid.npow n x = Monoid.npow n x",
626
+ "state_before": "M : Type u\nm\u2081 m\u2082 : Monoid M\nh_mul : HMul.hMul = HMul.hMul\nthis : toMulOneClass = toMulOneClass\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\n\u22a2 Monoid.npow = Monoid.npow",
627
+ "tactic": "ext n x"
628
+ },
629
+ {
630
+ "annotated_tactic": [
631
+ "\"exact @<a>MonoidHom.map_pow<\\/a> M M m\\u2081 m\\u2082 f x n\"",
632
+ "[{\"full_name\":\"MonoidHom.map_pow\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[1020,19],\"def_end_pos\":[1020,36]}]"
633
+ ],
634
+ "state_after": "no goals",
635
+ "state_before": "case h.h\nM : Type u\nm\u2081 m\u2082 : Monoid M\nh_mul : HMul.hMul = HMul.hMul\nthis : toMulOneClass = toMulOneClass\nh\u2081 : One.one = One.one\nf : M \u2192* M := { toFun := id, map_one' := h\u2081, map_mul' := \u22ef }\nn : \u2115\nx : M\n\u22a2 Monoid.npow n x = Monoid.npow n x",
636
+ "tactic": "exact @MonoidHom.map_pow M M m\u2081 m\u2082 f x n"
637
+ }
638
+ ],
639
+ "url": "https://github.com/leanprover-community/mathlib4"
640
+ },
641
+ "source_file": "Mathlib/Algebra/Group/Ext.lean"
642
+ },
643
+ {
644
+ "error": "theorem has no selected tactic transitions",
645
+ "full_name": "RightCancelMonoid.ext",
646
+ "id": "RightCancelMonoid.ext",
647
+ "reason": "import_failure",
648
+ "selection": {
649
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
650
+ "end": [
651
+ 98,
652
+ 59
653
+ ],
654
+ "file_path": "Mathlib/Algebra/Group/Ext.lean",
655
+ "full_name": "RightCancelMonoid.ext",
656
+ "start": [
657
+ 95,
658
+ 1
659
+ ],
660
+ "traced_tactics": [],
661
+ "url": "https://github.com/leanprover-community/mathlib4"
662
+ },
663
+ "source_file": "Mathlib/Algebra/Group/Ext.lean"
664
+ }
665
+ ],
666
+ "input_proofs": 33,
667
+ "input_units": 2,
668
+ "proofs": 14,
669
+ "published_proofs": 13,
670
+ "published_transitions": 25,
671
+ "replay_failures": [],
672
+ "transitions": 29,
673
+ "validation_failures": [
674
+ {
675
+ "errors": [
676
+ "internal transition boundary mismatch",
677
+ "internal transition boundary mismatch"
678
+ ],
679
+ "file_path": "Mathlib/Algebra/Group/Even.lean",
680
+ "proof_id": "mathlib:isSquare_inv",
681
+ "provenance": {
682
+ "selection": {
683
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
684
+ "end": [
685
+ 154,
686
+ 61
687
+ ],
688
+ "file_path": "Mathlib/Algebra/Group/Even.lean",
689
+ "full_name": "isSquare_inv",
690
+ "start": [
691
+ 150,
692
+ 1
693
+ ],
694
+ "traced_tactics": [
695
+ {
696
+ "annotated_tactic": [
697
+ "\"constructor <;> intro h\"",
698
+ "[]"
699
+ ],
700
+ "state_after": "case mp\nF : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nR : Type u_4\ninst\u271d : DivisionMonoid \u03b1\na : \u03b1\nh : IsSquare a\u207b\u00b9\n\u22a2 IsSquare a\n\ncase mpr\nF : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nR : Type u_4\ninst\u271d : DivisionMonoid \u03b1\na : \u03b1\nh : IsSquare a\n\u22a2 IsSquare a\u207b\u00b9",
701
+ "state_before": "F : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nR : Type u_4\ninst\u271d : DivisionMonoid \u03b1\na : \u03b1\n\u22a2 IsSquare a\u207b\u00b9 \u2194 IsSquare a",
702
+ "tactic": "constructor <;> intro h"
703
+ },
704
+ {
705
+ "annotated_tactic": [
706
+ "\"rw [\\u2190 <a>isSquare_op_iff<\\/a>, \\u2190 <a>inv_inv<\\/a> a]\"",
707
+ "[{\"full_name\":\"isSquare_op_iff\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Even.lean\",\"def_pos\":[57,7],\"def_end_pos\":[57,22]},{\"full_name\":\"inv_inv\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[870,9],\"def_end_pos\":[870,16]}]"
708
+ ],
709
+ "state_after": "case mp\nF : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nR : Type u_4\ninst\u271d : DivisionMonoid \u03b1\na : \u03b1\nh : IsSquare a\u207b\u00b9\n\u22a2 IsSquare (op a\u207b\u00b9\u207b\u00b9)",
710
+ "state_before": "case mp\nF : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nR : Type u_4\ninst\u271d : DivisionMonoid \u03b1\na : \u03b1\nh : IsSquare a\u207b\u00b9\n\u22a2 IsSquare a",
711
+ "tactic": "rw [\u2190 isSquare_op_iff, \u2190 inv_inv a]"
712
+ },
713
+ {
714
+ "annotated_tactic": [
715
+ "\"exact h.map (<a>MulEquiv.inv'<\\/a> \\u03b1)\"",
716
+ "[{\"full_name\":\"MulEquiv.inv'\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Opposite.lean\",\"def_pos\":[418,5],\"def_end_pos\":[418,18]}]"
717
+ ],
718
+ "state_after": "no goals",
719
+ "state_before": "case mp\nF : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nR : Type u_4\ninst\u271d : DivisionMonoid \u03b1\na : \u03b1\nh : IsSquare a\u207b\u00b9\n\u22a2 IsSquare (op a\u207b\u00b9\u207b\u00b9)",
720
+ "tactic": "exact h.map (MulEquiv.inv' \u03b1)"
721
+ },
722
+ {
723
+ "annotated_tactic": [
724
+ "\"exact (isSquare_op_iff.mpr h).<a>map<\\/a> (<a>MulEquiv.inv'<\\/a> \\u03b1).<a>symm<\\/a>\"",
725
+ "[{\"full_name\":\"IsSquare.map\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Even.lean\",\"def_pos\":[101,7],\"def_end_pos\":[101,19]},{\"full_name\":\"MulEquiv.inv'\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Opposite.lean\",\"def_pos\":[418,5],\"def_end_pos\":[418,18]},{\"full_name\":\"MulEquiv.symm\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Equiv\\/Basic.lean\",\"def_pos\":[292,5],\"def_end_pos\":[292,9]}]"
726
+ ],
727
+ "state_after": "no goals",
728
+ "state_before": "case mpr\nF : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nR : Type u_4\ninst\u271d : DivisionMonoid \u03b1\na : \u03b1\nh : IsSquare a\n\u22a2 IsSquare a\u207b\u00b9",
729
+ "tactic": "exact (isSquare_op_iff.mpr h).map (MulEquiv.inv' \u03b1).symm"
730
+ }
731
+ ],
732
+ "url": "https://github.com/leanprover-community/mathlib4"
733
+ }
734
+ },
735
+ "theorem_name": "isSquare_inv"
736
+ }
737
+ ],
738
+ "validation_rejected_proofs": 1,
739
+ "zero_transition_proofs": 0
740
+ },
741
+ "shards": [
742
+ {
743
+ "path": "data/train/mathlib-000118-0000-cff045d350ac6010.parquet",
744
+ "sha256": "cff045d350ac60107d6e3151bb7dabe871a0f0182d6f027bf24ee4325c05e00d",
745
+ "bytes": 70909,
746
+ "rows": 21,
747
+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
748
+ },
749
+ {
750
+ "path": "data/dev/mathlib-000118-0000-4bf5121d814a0906.parquet",
751
+ "sha256": "4bf5121d814a0906d1be2d0c108b27c6f47478163655a7d02d4a588f8728809c",
752
+ "bytes": 52848,
753
+ "rows": 2,
754
+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
755
+ },
756
+ {
757
+ "path": "data/internal_test/mathlib-000118-0000-68051980e99a7f6b.parquet",
758
+ "sha256": "68051980e99a7f6b501d3aacbd32dedb86d5cf8df1e13b6291de0ebfb0956fdd",
759
+ "bytes": 42822,
760
+ "rows": 2,
761
+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
762
+ }
763
+ ],
764
+ "proof_ids": [
765
+ "mathlib:CancelMonoid.toLeftCancelMonoid_injective",
766
+ "mathlib:CommGroup.toGroup_injective",
767
+ "mathlib:CommMonoid.toMonoid_injective",
768
+ "mathlib:Even.isSquare_pow",
769
+ "mathlib:Even.isSquare_zpow",
770
+ "mathlib:Group.ext",
771
+ "mathlib:Group.toDivInvMonoid_injective",
772
+ "mathlib:IsSquare.div",
773
+ "mathlib:IsSquare.mul",
774
+ "mathlib:IsSquare.zpow",
775
+ "mathlib:LeftCancelMonoid.toMonoid_injective",
776
+ "mathlib:RightCancelMonoid.toMonoid_injective",
777
+ "mathlib:isSquare_iff_exists_sq"
778
+ ],
779
+ "proof_keys": [
780
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Even.lean\",null,null,\"Even.isSquare_pow\"]",
781
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Even.lean\",null,null,\"Even.isSquare_zpow\"]",
782
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Even.lean\",null,null,\"IsSquare.div\"]",
783
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Even.lean\",null,null,\"IsSquare.mul\"]",
784
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Even.lean\",null,null,\"IsSquare.zpow\"]",
785
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Even.lean\",null,null,\"isSquare_iff_exists_sq\"]",
786
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Ext.lean\",null,null,\"CancelMonoid.toLeftCancelMonoid_injective\"]",
787
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Ext.lean\",null,null,\"CommGroup.toGroup_injective\"]",
788
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Ext.lean\",null,null,\"CommMonoid.toMonoid_injective\"]",
789
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Ext.lean\",null,null,\"Group.ext\"]",
790
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Ext.lean\",null,null,\"Group.toDivInvMonoid_injective\"]",
791
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Ext.lean\",null,null,\"LeftCancelMonoid.toMonoid_injective\"]",
792
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Ext.lean\",null,null,\"RightCancelMonoid.toMonoid_injective\"]"
793
+ ]
794
+ }
manifests/batches/mathlib/000119.json ADDED
@@ -0,0 +1,307 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000119",
4
+ "batch_fingerprint": "044d1d5801159be539b5617effddfacd50df48ed56b4ac8be71105b9e13bea2f",
5
+ "evidence": {
6
+ "batch_fingerprint": "044d1d5801159be539b5617effddfacd50df48ed56b4ac8be71105b9e13bea2f",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "no internal trace for tactic 'simp'",
11
+ "full_name": "Fin.coe_sub_one",
12
+ "id": "Fin.coe_sub_one",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 98,
18
+ 25
19
+ ],
20
+ "file_path": "Mathlib/Algebra/Group/Fin.lean",
21
+ "full_name": "Fin.coe_sub_one",
22
+ "start": [
23
+ 90,
24
+ 1
25
+ ],
26
+ "traced_tactics": [
27
+ {
28
+ "annotated_tactic": [
29
+ "\"cases n\"",
30
+ "[]"
31
+ ],
32
+ "state_after": "case zero\nm : \u2115\na : Fin (0 + 1)\n\u22a2 \u2191(a - 1) = if a = 0 then 0 else \u2191a - 1\n\ncase succ\nm n\u271d : \u2115\na : Fin (n\u271d + 1 + 1)\n\u22a2 \u2191(a - 1) = if a = 0 then n\u271d + 1 else \u2191a - 1",
33
+ "state_before": "m n : \u2115\na : Fin (n + 1)\n\u22a2 \u2191(a - 1) = if a = 0 then n else \u2191a - 1",
34
+ "tactic": "cases n"
35
+ },
36
+ {
37
+ "annotated_tactic": [
38
+ "\"split_ifs with h\"",
39
+ "[]"
40
+ ],
41
+ "state_after": "case pos\nm n\u271d : \u2115\na : Fin (n\u271d + 1 + 1)\nh : a = 0\n\u22a2 \u2191(a - 1) = n\u271d + 1\n\ncase neg\nm n\u271d : \u2115\na : Fin (n\u271d + 1 + 1)\nh : \u00aca = 0\n\u22a2 \u2191(a - 1) = \u2191a - 1",
42
+ "state_before": "case succ\nm n\u271d : \u2115\na : Fin (n\u271d + 1 + 1)\n\u22a2 \u2191(a - 1) = if a = 0 then n\u271d + 1 else \u2191a - 1",
43
+ "tactic": "split_ifs with h"
44
+ },
45
+ {
46
+ "annotated_tactic": [
47
+ "\"rw [<a>sub_eq_add_neg<\\/a>, <a>val_add_eq_ite<\\/a>, <a>coe_neg_one<\\/a>, <a>if_pos<\\/a>, <a>Nat.add_comm<\\/a>, <a>Nat.add_sub_add_left<\\/a>]\"",
48
+ "[{\"full_name\":\"sub_eq_add_neg\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1057,3],\"def_end_pos\":[1057,14]},{\"full_name\":\"Fin.val_add_eq_ite\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Basic.lean\",\"def_pos\":[494,9],\"def_end_pos\":[494,23]},{\"full_name\":\"Fin.coe_neg_one\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Basic.lean\",\"def_pos\":[1876,9],\"def_end_pos\":[1876,20]},{\"full_name\":\"if_pos\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[932,9],\"def_end_pos\":[932,15]},{\"full_name\":\"Nat.add_comm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[160,19],\"def_end_pos\":[160,27]},{\"full_name\":\"Nat.add_sub_add_left\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[901,19],\"def_end_pos\":[901,35]}]"
49
+ ],
50
+ "state_after": "case neg.hc\nm n\u271d : \u2115\na : Fin (n\u271d + 1 + 1)\nh : \u00aca = 0\n\u22a2 n\u271d + 1 + 1 \u2264 \u2191a + (n\u271d + 1)",
51
+ "state_before": "case neg\nm n\u271d : \u2115\na : Fin (n\u271d + 1 + 1)\nh : \u00aca = 0\n\u22a2 \u2191(a - 1) = \u2191a - 1",
52
+ "tactic": "rw [sub_eq_add_neg, val_add_eq_ite, coe_neg_one, if_pos, Nat.add_comm, Nat.add_sub_add_left]"
53
+ },
54
+ {
55
+ "annotated_tactic": [
56
+ "\"conv_rhs => rw [<a>Nat.add_comm<\\/a>]\"",
57
+ "[{\"full_name\":\"Nat.add_comm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[160,19],\"def_end_pos\":[160,27]}]"
58
+ ],
59
+ "state_after": "case neg.hc\nm n\u271d : \u2115\na : Fin (n\u271d + 1 + 1)\nh : \u00aca = 0\n\u22a2 n\u271d + 1 + 1 \u2264 n\u271d + 1 + \u2191a",
60
+ "state_before": "case neg.hc\nm n\u271d : \u2115\na : Fin (n\u271d + 1 + 1)\nh : \u00aca = 0\n\u22a2 n\u271d + 1 + 1 \u2264 \u2191a + (n\u271d + 1)",
61
+ "tactic": "conv_rhs => rw [Nat.add_comm]"
62
+ },
63
+ {
64
+ "annotated_tactic": [
65
+ "\"rw [<a>Nat.add_le_add_iff_left<\\/a>, <a>Nat.one_le_iff_ne_zero<\\/a>]\"",
66
+ "[{\"full_name\":\"Nat.add_le_add_iff_left\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Lemmas.lean\",\"def_pos\":[45,19],\"def_end_pos\":[45,38]},{\"full_name\":\"Nat.one_le_iff_ne_zero\",\"def_path\":\"Mathlib\\/Data\\/Nat\\/Defs.lean\",\"def_pos\":[166,7],\"def_end_pos\":[166,25]}]"
67
+ ],
68
+ "state_after": "case neg.hc\nm n\u271d : \u2115\na : Fin (n\u271d + 1 + 1)\nh : \u00aca = 0\n\u22a2 \u2191a \u2260 0",
69
+ "state_before": "case neg.hc\nm n\u271d : \u2115\na : Fin (n\u271d + 1 + 1)\nh : \u00aca = 0\n\u22a2 n\u271d + 1 + 1 \u2264 n\u271d + 1 + \u2191a",
70
+ "tactic": "rw [Nat.add_le_add_iff_left, Nat.one_le_iff_ne_zero]"
71
+ },
72
+ {
73
+ "annotated_tactic": [
74
+ "\"rwa [<a>Fin.ext_iff<\\/a>] at h\"",
75
+ "[{\"full_name\":\"Fin.ext_iff\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[42,9],\"def_end_pos\":[42,16]}]"
76
+ ],
77
+ "state_after": "no goals",
78
+ "state_before": "case neg.hc\nm n\u271d : \u2115\na : Fin (n\u271d + 1 + 1)\nh : \u00aca = 0\n\u22a2 \u2191a \u2260 0",
79
+ "tactic": "rwa [Fin.ext_iff] at h"
80
+ },
81
+ {
82
+ "annotated_tactic": [
83
+ "\"simp\"",
84
+ "[]"
85
+ ],
86
+ "state_after": "no goals",
87
+ "state_before": "case zero\nm : \u2115\na : Fin (0 + 1)\n\u22a2 \u2191(a - 1) = if a = 0 then 0 else \u2191a - 1",
88
+ "tactic": "simp"
89
+ },
90
+ {
91
+ "annotated_tactic": [
92
+ "\"simp [h]\"",
93
+ "[]"
94
+ ],
95
+ "state_after": "no goals",
96
+ "state_before": "case pos\nm n\u271d : \u2115\na : Fin (n\u271d + 1 + 1)\nh : a = 0\n\u22a2 \u2191(a - 1) = n\u271d + 1",
97
+ "tactic": "simp [h]"
98
+ }
99
+ ],
100
+ "url": "https://github.com/leanprover-community/mathlib4"
101
+ },
102
+ "source_file": "Mathlib/Algebra/Group/Fin.lean"
103
+ },
104
+ {
105
+ "error": "no internal trace for tactic 'simp [fin_one_eq_zero k]'",
106
+ "full_name": "Fin.le_sub_one_iff",
107
+ "id": "Fin.le_sub_one_iff",
108
+ "reason": "import_failure",
109
+ "selection": {
110
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
111
+ "end": [
112
+ 119,
113
+ 7
114
+ ],
115
+ "file_path": "Mathlib/Algebra/Group/Fin.lean",
116
+ "full_name": "Fin.le_sub_one_iff",
117
+ "start": [
118
+ 113,
119
+ 1
120
+ ],
121
+ "traced_tactics": [
122
+ {
123
+ "annotated_tactic": [
124
+ "\"cases n\"",
125
+ "[]"
126
+ ],
127
+ "state_after": "case zero\nm : \u2115\nk : Fin (0 + 1)\n\u22a2 k \u2264 k - 1 \u2194 k = 0\n\ncase succ\nm n\u271d : \u2115\nk : Fin (n\u271d + 1 + 1)\n\u22a2 k \u2264 k - 1 \u2194 k = 0",
128
+ "state_before": "m n : \u2115\nk : Fin (n + 1)\n\u22a2 k \u2264 k - 1 \u2194 k = 0",
129
+ "tactic": "cases n"
130
+ },
131
+ {
132
+ "annotated_tactic": [
133
+ "\"simp [-<a>val_fin_le<\\/a>, <a>le_def<\\/a>]\"",
134
+ "[{\"full_name\":\"Fin.val_fin_le\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Basic.lean\",\"def_pos\":[250,9],\"def_end_pos\":[250,19]},{\"full_name\":\"Fin.le_def\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[84,9],\"def_end_pos\":[84,15]}]"
135
+ ],
136
+ "state_after": "case succ\nm n\u271d : \u2115\nk : Fin (n\u271d + 1 + 1)\n\u22a2 \u2191k \u2264 \u2191(k - 1) \u2194 k = 0",
137
+ "state_before": "case succ\nm n\u271d : \u2115\nk : Fin (n\u271d + 1 + 1)\n\u22a2 k \u2264 k - 1 \u2194 k = 0",
138
+ "tactic": "simp [-val_fin_le, le_def]"
139
+ },
140
+ {
141
+ "annotated_tactic": [
142
+ "\"rw [\\u2190 <a>lt_sub_one_iff<\\/a>, <a>le_iff_lt_or_eq<\\/a>, <a>val_fin_lt<\\/a>, <a>val_inj<\\/a>, <a>lt_sub_one_iff<\\/a>, <a>or_iff_left_iff_imp<\\/a>,\\n <a>eq_comm<\\/a>, <a>sub_eq_iff_eq_add<\\/a>]\"",
143
+ "[{\"full_name\":\"Fin.lt_sub_one_iff\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Fin.lean\",\"def_pos\":[104,7],\"def_end_pos\":[104,21]},{\"full_name\":\"le_iff_lt_or_eq\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[234,9],\"def_end_pos\":[234,24]},{\"full_name\":\"Fin.val_fin_lt\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Basic.lean\",\"def_pos\":[244,9],\"def_end_pos\":[244,19]},{\"full_name\":\"Fin.val_inj\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Basic.lean\",\"def_pos\":[200,9],\"def_end_pos\":[200,16]},{\"full_name\":\"Fin.lt_sub_one_iff\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Fin.lean\",\"def_pos\":[104,7],\"def_end_pos\":[104,21]},{\"full_name\":\"or_iff_left_iff_imp\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[187,17],\"def_end_pos\":[187,36]},{\"full_name\":\"eq_comm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[811,9],\"def_end_pos\":[811,16]},{\"full_name\":\"sub_eq_iff_eq_add\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[1098,3],\"def_end_pos\":[1098,14]}]"
144
+ ],
145
+ "state_after": "case succ\nm n\u271d : \u2115\nk : Fin (n\u271d + 1 + 1)\n\u22a2 k = k + 1 \u2192 k = 0",
146
+ "state_before": "case succ\nm n\u271d : \u2115\nk : Fin (n\u271d + 1 + 1)\n\u22a2 \u2191k \u2264 \u2191(k - 1) \u2194 k = 0",
147
+ "tactic": "rw [\u2190 lt_sub_one_iff, le_iff_lt_or_eq, val_fin_lt, val_inj, lt_sub_one_iff, or_iff_left_iff_imp,\n eq_comm, sub_eq_iff_eq_add]"
148
+ },
149
+ {
150
+ "annotated_tactic": [
151
+ "\"simp\"",
152
+ "[]"
153
+ ],
154
+ "state_after": "no goals",
155
+ "state_before": "case succ\nm n\u271d : \u2115\nk : Fin (n\u271d + 1 + 1)\n\u22a2 k = k + 1 \u2192 k = 0",
156
+ "tactic": "simp"
157
+ },
158
+ {
159
+ "annotated_tactic": [
160
+ "\"simp [<a>fin_one_eq_zero<\\/a> k]\"",
161
+ "[{\"full_name\":\"Fin.fin_one_eq_zero\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[200,9],\"def_end_pos\":[200,24]}]"
162
+ ],
163
+ "state_after": "no goals",
164
+ "state_before": "case zero\nm : \u2115\nk : Fin (0 + 1)\n\u22a2 k \u2264 k - 1 \u2194 k = 0",
165
+ "tactic": "simp [fin_one_eq_zero k]"
166
+ }
167
+ ],
168
+ "url": "https://github.com/leanprover-community/mathlib4"
169
+ },
170
+ "source_file": "Mathlib/Algebra/Group/Fin.lean"
171
+ },
172
+ {
173
+ "error": "no internal trace for tactic 'simp only [zero_eta, zero_sub, lt_iff_val_lt_val, val_zero, coe_neg_one, zero_lt_succ]'",
174
+ "full_name": "Fin.lt_sub_one_iff",
175
+ "id": "Fin.lt_sub_one_iff",
176
+ "reason": "import_failure",
177
+ "selection": {
178
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
179
+ "end": [
180
+ 110,
181
+ 46
182
+ ],
183
+ "file_path": "Mathlib/Algebra/Group/Fin.lean",
184
+ "full_name": "Fin.lt_sub_one_iff",
185
+ "start": [
186
+ 103,
187
+ 1
188
+ ],
189
+ "traced_tactics": [
190
+ {
191
+ "annotated_tactic": [
192
+ "\"rcases k with \\u27e8_ | k, hk\\u27e9\"",
193
+ "[]"
194
+ ],
195
+ "state_after": "case mk.zero\nm n : \u2115\nhk : 0 < n + 2\n\u22a2 \u27e80, hk\u27e9 < \u27e80, hk\u27e9 - 1 \u2194 \u27e80, hk\u27e9 = 0\n\ncase mk.succ\nm n k : \u2115\nhk : k + 1 < n + 2\n\u22a2 \u27e8k + 1, hk\u27e9 < \u27e8k + 1, hk\u27e9 - 1 \u2194 \u27e8k + 1, hk\u27e9 = 0",
196
+ "state_before": "m n : \u2115\nk : Fin (n + 2)\n\u22a2 k < k - 1 \u2194 k = 0",
197
+ "tactic": "rcases k with \u27e8_ | k, hk\u27e9"
198
+ },
199
+ {
200
+ "annotated_tactic": [
201
+ "\"have : (n + 1 + (k + 1)) % (n + 2) = k % (n + 2) := by\\n rw [<a>Nat.add_comm<\\/a>, <a>Nat.add_right_comm<\\/a>, <a>Nat.add_assoc<\\/a>, <a>Nat.add_assoc<\\/a>, <a>add_mod_right<\\/a>]\"",
202
+ "[{\"full_name\":\"Nat.add_comm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[160,19],\"def_end_pos\":[160,27]},{\"full_name\":\"Nat.add_right_comm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[176,19],\"def_end_pos\":[176,33]},{\"full_name\":\"Nat.add_assoc\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[168,19],\"def_end_pos\":[168,28]},{\"full_name\":\"Nat.add_assoc\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[168,19],\"def_end_pos\":[168,28]},{\"full_name\":\"Nat.add_mod_right\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Div.lean\",\"def_pos\":[268,17],\"def_end_pos\":[268,30]}]"
203
+ ],
204
+ "state_after": "case mk.succ\nm n k : \u2115\nhk : k + 1 < n + 2\nthis : (n + 1 + (k + 1)) % (n + 2) = k % (n + 2)\n\u22a2 \u27e8k + 1, hk\u27e9 < \u27e8k + 1, hk\u27e9 - 1 \u2194 \u27e8k + 1, hk\u27e9 = 0",
205
+ "state_before": "case mk.succ\nm n k : \u2115\nhk : k + 1 < n + 2\n\u22a2 \u27e8k + 1, hk\u27e9 < \u27e8k + 1, hk\u27e9 - 1 \u2194 \u27e8k + 1, hk\u27e9 = 0",
206
+ "tactic": "have : (n + 1 + (k + 1)) % (n + 2) = k % (n + 2) := by\n rw [Nat.add_comm, Nat.add_right_comm, Nat.add_assoc, Nat.add_assoc, add_mod_right]"
207
+ },
208
+ {
209
+ "annotated_tactic": [
210
+ "\"simp [<a>lt_iff_val_lt_val<\\/a>, <a>ext_iff<\\/a>, <a>Fin.coe_sub<\\/a>, this,\\n <a>mod_eq_of_lt<\\/a> ((<a>lt_succ_self<\\/a> _).<a>trans<\\/a> hk)]\"",
211
+ "[{\"full_name\":\"Fin.lt_iff_val_lt_val\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[88,9],\"def_end_pos\":[88,26]},{\"full_name\":\"Fin.ext_iff\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[42,9],\"def_end_pos\":[42,16]},{\"full_name\":\"Fin.coe_sub\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[762,19],\"def_end_pos\":[762,26]},{\"full_name\":\"Nat.mod_eq_of_lt\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Div.lean\",\"def_pos\":[131,9],\"def_end_pos\":[131,21]},{\"full_name\":\"Nat.lt_succ_self\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[358,17],\"def_end_pos\":[358,29]},{\"full_name\":\"LT.lt.trans\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[139,7],\"def_end_pos\":[139,18]}]"
212
+ ],
213
+ "state_after": "no goals",
214
+ "state_before": "case mk.succ\nm n k : \u2115\nhk : k + 1 < n + 2\nthis : (n + 1 + (k + 1)) % (n + 2) = k % (n + 2)\n\u22a2 \u27e8k + 1, hk\u27e9 < \u27e8k + 1, hk\u27e9 - 1 \u2194 \u27e8k + 1, hk\u27e9 = 0",
215
+ "tactic": "simp [lt_iff_val_lt_val, ext_iff, Fin.coe_sub, this,\n mod_eq_of_lt ((lt_succ_self _).trans hk)]"
216
+ },
217
+ {
218
+ "annotated_tactic": [
219
+ "\"simp only [<a>zero_eta<\\/a>, <a>zero_sub<\\/a>, <a>lt_iff_val_lt_val<\\/a>, <a>val_zero<\\/a>, <a>coe_neg_one<\\/a>, <a>zero_lt_succ<\\/a>]\"",
220
+ "[{\"full_name\":\"Fin.zero_eta\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Basic.lean\",\"def_pos\":[150,17],\"def_end_pos\":[150,25]},{\"full_name\":\"zero_sub\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[467,3],\"def_end_pos\":[467,14]},{\"full_name\":\"Fin.lt_iff_val_lt_val\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[88,9],\"def_end_pos\":[88,26]},{\"full_name\":\"Fin.val_zero\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Fin\\/Lemmas.lean\",\"def_pos\":[126,17],\"def_end_pos\":[126,25]},{\"full_name\":\"Fin.coe_neg_one\",\"def_path\":\"Mathlib\\/Data\\/Fin\\/Basic.lean\",\"def_pos\":[1876,9],\"def_end_pos\":[1876,20]},{\"full_name\":\"Nat.zero_lt_succ\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[1671,9],\"def_end_pos\":[1671,25]}]"
221
+ ],
222
+ "state_after": "no goals",
223
+ "state_before": "case mk.zero\nm n : \u2115\nhk : 0 < n + 2\n\u22a2 \u27e80, hk\u27e9 < \u27e80, hk\u27e9 - 1 \u2194 \u27e80, hk\u27e9 = 0",
224
+ "tactic": "simp only [zero_eta, zero_sub, lt_iff_val_lt_val, val_zero, coe_neg_one, zero_lt_succ]"
225
+ },
226
+ {
227
+ "annotated_tactic": [
228
+ "\"rw [<a>Nat.add_comm<\\/a>, <a>Nat.add_right_comm<\\/a>, <a>Nat.add_assoc<\\/a>, <a>Nat.add_assoc<\\/a>, <a>add_mod_right<\\/a>]\"",
229
+ "[{\"full_name\":\"Nat.add_comm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[160,19],\"def_end_pos\":[160,27]},{\"full_name\":\"Nat.add_right_comm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[176,19],\"def_end_pos\":[176,33]},{\"full_name\":\"Nat.add_assoc\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[168,19],\"def_end_pos\":[168,28]},{\"full_name\":\"Nat.add_assoc\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[168,19],\"def_end_pos\":[168,28]},{\"full_name\":\"Nat.add_mod_right\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Div.lean\",\"def_pos\":[268,17],\"def_end_pos\":[268,30]}]"
230
+ ],
231
+ "state_after": "no goals",
232
+ "state_before": "m n k : \u2115\nhk : k + 1 < n + 2\n\u22a2 (n + 1 + (k + 1)) % (n + 2) = k % (n + 2)",
233
+ "tactic": "rw [Nat.add_comm, Nat.add_right_comm, Nat.add_assoc, Nat.add_assoc, add_mod_right]"
234
+ }
235
+ ],
236
+ "url": "https://github.com/leanprover-community/mathlib4"
237
+ },
238
+ "source_file": "Mathlib/Algebra/Group/Fin.lean"
239
+ },
240
+ {
241
+ "error": "theorem has no selected tactic transitions",
242
+ "full_name": "Function.mulSupport_along_fiber_finite_of_finite",
243
+ "id": "Function.mulSupport_along_fiber_finite_of_finite",
244
+ "reason": "import_failure",
245
+ "selection": {
246
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
247
+ "end": [
248
+ 19,
249
+ 64
250
+ ],
251
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306
+ ]
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+ },
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+ },
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+ {
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+ "id": "MonoidHom.CompTriple.comp",
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+ "reason": "import_failure",
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+ "full_name": "MonoidHom.CompTriple.comp",
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+ ],
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+ "traced_tactics": [],
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+ "url": "https://github.com/leanprover-community/mathlib4"
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+ },
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+ "source_file": "Mathlib/Algebra/Group/Hom/CompTypeclasses.lean"
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+ },
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+ {
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+ "error": "no internal trace for tactic \"simp only [\u2190 \u03ba.comp_eq, \u2190 h, \u2190 \u03ba'.comp_eq, MonoidHom.comp_assoc]\"",
275
+ "full_name": "MonoidHom.CompTriple.comp_assoc",
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+ "id": "MonoidHom.CompTriple.comp_assoc",
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+ "reason": "import_failure",
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+ "selection": {
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+ "end": [
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+ "file_path": "Mathlib/Algebra/Group/Hom/CompTypeclasses.lean",
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+ "full_name": "MonoidHom.CompTriple.comp_assoc",
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+ "start": [
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+ 98,
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+ 1
289
+ ],
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+ "traced_tactics": [
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+ {
292
+ "annotated_tactic": [
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+ "\"rintro \\u27e8h\\u27e9\"",
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+ "[]"
295
+ ],
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+ "state_after": "case mpr.mk\nM' : Type u_1\ninst\u271d\u2074 : Monoid M'\nM : Type u_2\nN : Type u_3\nP : Type u_4\ninst\u271d\u00b3 : Monoid M\ninst\u271d\u00b2 : Monoid N\ninst\u271d\u00b9 : Monoid P\nQ : Type u_5\ninst\u271d : Monoid Q\n\u03c6\u2081 : M \u2192* N\n\u03c6\u2082 : N \u2192* P\n\u03c6\u2081\u2082 : M \u2192* P\n\u03ba : \u03c6\u2081.CompTriple \u03c6\u2082 \u03c6\u2081\u2082\n\u03c6\u2083 : P \u2192* Q\n\u03c6\u2082\u2083 : N \u2192* Q\n\u03ba' : \u03c6\u2082.CompTriple \u03c6\u2083 \u03c6\u2082\u2083\n\u03c6\u2081\u2082\u2083 : M \u2192* Q\nh : \u03c6\u2083.comp \u03c6\u2081\u2082 = \u03c6\u2081\u2082\u2083\n\u22a2 \u03c6\u2081.CompTriple \u03c6\u2082\u2083 \u03c6\u2081\u2082\u2083",
297
+ "state_before": "case mpr\nM' : Type u_1\ninst\u271d\u2074 : Monoid M'\nM : Type u_2\nN : Type u_3\nP : Type u_4\ninst\u271d\u00b3 : Monoid M\ninst\u271d\u00b2 : Monoid N\ninst\u271d\u00b9 : Monoid P\nQ : Type u_5\ninst\u271d : Monoid Q\n\u03c6\u2081 : M \u2192* N\n\u03c6\u2082 : N \u2192* P\n\u03c6\u2081\u2082 : M \u2192* P\n\u03ba : \u03c6\u2081.CompTriple \u03c6\u2082 \u03c6\u2081\u2082\n\u03c6\u2083 : P \u2192* Q\n\u03c6\u2082\u2083 : N \u2192* Q\n\u03ba' : \u03c6\u2082.CompTriple \u03c6\u2083 \u03c6\u2082\u2083\n\u03c6\u2081\u2082\u2083 : M \u2192* Q\n\u22a2 \u03c6\u2081\u2082.CompTriple \u03c6\u2083 \u03c6\u2081\u2082\u2083 \u2192 \u03c6\u2081.CompTriple \u03c6\u2082\u2083 \u03c6\u2081\u2082\u2083",
298
+ "tactic": "rintro \u27e8h\u27e9"
299
+ },
300
+ {
301
+ "annotated_tactic": [
302
+ "\"exact \\u27e8by simp only [\\u2190 \\u03ba.comp_eq, \\u2190 h, \\u2190 \\u03ba'.comp_eq, <a>MonoidHom.comp_assoc<\\/a>]\\u27e9\"",
303
+ "[{\"full_name\":\"MonoidHom.comp_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[913,9],\"def_end_pos\":[913,29]}]"
304
+ ],
305
+ "state_after": "no goals",
306
+ "state_before": "case mpr.mk\nM' : Type u_1\ninst\u271d\u2074 : Monoid M'\nM : Type u_2\nN : Type u_3\nP : Type u_4\ninst\u271d\u00b3 : Monoid M\ninst\u271d\u00b2 : Monoid N\ninst\u271d\u00b9 : Monoid P\nQ : Type u_5\ninst\u271d : Monoid Q\n\u03c6\u2081 : M \u2192* N\n\u03c6\u2082 : N \u2192* P\n\u03c6\u2081\u2082 : M \u2192* P\n\u03ba : \u03c6\u2081.CompTriple \u03c6\u2082 \u03c6\u2081\u2082\n\u03c6\u2083 : P \u2192* Q\n\u03c6\u2082\u2083 : N \u2192* Q\n\u03ba' : \u03c6\u2082.CompTriple \u03c6\u2083 \u03c6\u2082\u2083\n\u03c6\u2081\u2082\u2083 : M \u2192* Q\nh : \u03c6\u2083.comp \u03c6\u2081\u2082 = \u03c6\u2081\u2082\u2083\n\u22a2 \u03c6\u2081.CompTriple \u03c6\u2082\u2083 \u03c6\u2081\u2082\u2083",
307
+ "tactic": "exact \u27e8by simp only [\u2190 \u03ba.comp_eq, \u2190 h, \u2190 \u03ba'.comp_eq, MonoidHom.comp_assoc]\u27e9"
308
+ },
309
+ {
310
+ "annotated_tactic": [
311
+ "\"simp only [\\u2190 \\u03ba.comp_eq, \\u2190 h, \\u2190 \\u03ba'.comp_eq, <a>MonoidHom.comp_assoc<\\/a>]\"",
312
+ "[{\"full_name\":\"MonoidHom.comp_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[913,9],\"def_end_pos\":[913,29]}]"
313
+ ],
314
+ "state_after": "no goals",
315
+ "state_before": "M' : Type u_1\ninst\u271d\u2074 : Monoid M'\nM : Type u_2\nN : Type u_3\nP : Type u_4\ninst\u271d\u00b3 : Monoid M\ninst\u271d\u00b2 : Monoid N\ninst\u271d\u00b9 : Monoid P\nQ : Type u_5\ninst\u271d : Monoid Q\n\u03c6\u2081 : M \u2192* N\n\u03c6\u2082 : N \u2192* P\n\u03c6\u2081\u2082 : M \u2192* P\n\u03ba : \u03c6\u2081.CompTriple \u03c6\u2082 \u03c6\u2081\u2082\n\u03c6\u2083 : P \u2192* Q\n\u03c6\u2082\u2083 : N \u2192* Q\n\u03ba' : \u03c6\u2082.CompTriple \u03c6\u2083 \u03c6\u2082\u2083\n\u03c6\u2081\u2082\u2083 : M \u2192* Q\nh : \u03c6\u2083.comp \u03c6\u2081\u2082 = \u03c6\u2081\u2082\u2083\n\u22a2 \u03c6\u2082\u2083.comp \u03c6\u2081 = \u03c6\u2081\u2082\u2083",
316
+ "tactic": "simp only [\u2190 \u03ba.comp_eq, \u2190 h, \u2190 \u03ba'.comp_eq, MonoidHom.comp_assoc]"
317
+ }
318
+ ],
319
+ "url": "https://github.com/leanprover-community/mathlib4"
320
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1458
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1459
+ "source_file": "Mathlib/Algebra/Group/Hom/Defs.lean"
1460
+ },
1461
+ {
1462
+ "error": "theorem has no selected tactic transitions",
1463
+ "full_name": "AddMonoid.End.mulRight_eq_mulLeft",
1464
+ "id": "AddMonoid.End.mulRight_eq_mulLeft",
1465
+ "reason": "import_failure",
1466
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1471
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1472
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1473
+ "full_name": "AddMonoid.End.mulRight_eq_mulLeft",
1474
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1477
+ ],
1478
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1479
+ "url": "https://github.com/leanprover-community/mathlib4"
1480
+ },
1481
+ "source_file": "Mathlib/Algebra/Group/Hom/End.lean"
1482
+ },
1483
+ {
1484
+ "error": "theorem has no selected tactic transitions",
1485
+ "full_name": "AddMonoid.End.natCast_apply",
1486
+ "id": "AddMonoid.End.natCast_apply",
1487
+ "reason": "import_failure",
1488
+ "selection": {
1489
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1494
+ "file_path": "Mathlib/Algebra/Group/Hom/End.lean",
1495
+ "full_name": "AddMonoid.End.natCast_apply",
1496
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1499
+ ],
1500
+ "traced_tactics": [],
1501
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1502
+ },
1503
+ "source_file": "Mathlib/Algebra/Group/Hom/End.lean"
1504
+ },
1505
+ {
1506
+ "error": "theorem has no selected tactic transitions",
1507
+ "full_name": "AddMonoid.End.ofNat_apply",
1508
+ "id": "AddMonoid.End.ofNat_apply",
1509
+ "reason": "import_failure",
1510
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1511
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1515
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1516
+ "file_path": "Mathlib/Algebra/Group/Hom/End.lean",
1517
+ "full_name": "AddMonoid.End.ofNat_apply",
1518
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1519
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1520
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1521
+ ],
1522
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1523
+ "url": "https://github.com/leanprover-community/mathlib4"
1524
+ },
1525
+ "source_file": "Mathlib/Algebra/Group/Hom/End.lean"
1526
+ },
1527
+ {
1528
+ "error": "theorem has no selected tactic transitions",
1529
+ "full_name": "AddMonoidHom.coe_flip_mul",
1530
+ "id": "AddMonoidHom.coe_flip_mul",
1531
+ "reason": "import_failure",
1532
+ "selection": {
1533
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1534
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1535
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1537
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1538
+ "file_path": "Mathlib/Algebra/Group/Hom/End.lean",
1539
+ "full_name": "AddMonoidHom.coe_flip_mul",
1540
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1541
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1542
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1543
+ ],
1544
+ "traced_tactics": [],
1545
+ "url": "https://github.com/leanprover-community/mathlib4"
1546
+ },
1547
+ "source_file": "Mathlib/Algebra/Group/Hom/End.lean"
1548
+ },
1549
+ {
1550
+ "error": "theorem has no selected tactic transitions",
1551
+ "full_name": "AddMonoidHom.coe_mul",
1552
+ "id": "AddMonoidHom.coe_mul",
1553
+ "reason": "import_failure",
1554
+ "selection": {
1555
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1556
+ "end": [
1557
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1559
+ ],
1560
+ "file_path": "Mathlib/Algebra/Group/Hom/End.lean",
1561
+ "full_name": "AddMonoidHom.coe_mul",
1562
+ "start": [
1563
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1564
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1565
+ ],
1566
+ "traced_tactics": [],
1567
+ "url": "https://github.com/leanprover-community/mathlib4"
1568
+ },
1569
+ "source_file": "Mathlib/Algebra/Group/Hom/End.lean"
1570
+ },
1571
+ {
1572
+ "error": "theorem has no selected tactic transitions",
1573
+ "full_name": "AddMonoidHom.map_mul_iff",
1574
+ "id": "AddMonoidHom.map_mul_iff",
1575
+ "reason": "import_failure",
1576
+ "selection": {
1577
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1578
+ "end": [
1579
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1581
+ ],
1582
+ "file_path": "Mathlib/Algebra/Group/Hom/End.lean",
1583
+ "full_name": "AddMonoidHom.map_mul_iff",
1584
+ "start": [
1585
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1586
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1587
+ ],
1588
+ "traced_tactics": [],
1589
+ "url": "https://github.com/leanprover-community/mathlib4"
1590
+ },
1591
+ "source_file": "Mathlib/Algebra/Group/Hom/End.lean"
1592
+ },
1593
+ {
1594
+ "error": "theorem has no selected tactic transitions",
1595
+ "full_name": "AddMonoidHom.mulLeft_eq_mulRight_iff_forall_commute",
1596
+ "id": "AddMonoidHom.mulLeft_eq_mulRight_iff_forall_commute",
1597
+ "reason": "import_failure",
1598
+ "selection": {
1599
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1600
+ "end": [
1601
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1602
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1603
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1604
+ "file_path": "Mathlib/Algebra/Group/Hom/End.lean",
1605
+ "full_name": "AddMonoidHom.mulLeft_eq_mulRight_iff_forall_commute",
1606
+ "start": [
1607
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1608
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1609
+ ],
1610
+ "traced_tactics": [],
1611
+ "url": "https://github.com/leanprover-community/mathlib4"
1612
+ },
1613
+ "source_file": "Mathlib/Algebra/Group/Hom/End.lean"
1614
+ },
1615
+ {
1616
+ "error": "theorem has no selected tactic transitions",
1617
+ "full_name": "AddMonoidHom.mulRight_eq_mulLeft_iff_forall_commute",
1618
+ "id": "AddMonoidHom.mulRight_eq_mulLeft_iff_forall_commute",
1619
+ "reason": "import_failure",
1620
+ "selection": {
1621
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1622
+ "end": [
1623
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1624
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1625
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1626
+ "file_path": "Mathlib/Algebra/Group/Hom/End.lean",
1627
+ "full_name": "AddMonoidHom.mulRight_eq_mulLeft_iff_forall_commute",
1628
+ "start": [
1629
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1630
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1631
+ ],
1632
+ "traced_tactics": [],
1633
+ "url": "https://github.com/leanprover-community/mathlib4"
1634
+ },
1635
+ "source_file": "Mathlib/Algebra/Group/Hom/End.lean"
1636
+ },
1637
+ {
1638
+ "error": "theorem has no selected tactic transitions",
1639
+ "full_name": "AddMonoidHom.mul_apply",
1640
+ "id": "AddMonoidHom.mul_apply",
1641
+ "reason": "import_failure",
1642
+ "selection": {
1643
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1644
+ "end": [
1645
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1646
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1647
+ ],
1648
+ "file_path": "Mathlib/Algebra/Group/Hom/End.lean",
1649
+ "full_name": "AddMonoidHom.mul_apply",
1650
+ "start": [
1651
+ 85,
1652
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1653
+ ],
1654
+ "traced_tactics": [],
1655
+ "url": "https://github.com/leanprover-community/mathlib4"
1656
+ },
1657
+ "source_file": "Mathlib/Algebra/Group/Hom/End.lean"
1658
+ }
1659
+ ],
1660
+ "input_proofs": 97,
1661
+ "input_units": 2,
1662
+ "proofs": 22,
1663
+ "published_proofs": 20,
1664
+ "published_transitions": 28,
1665
+ "replay_failures": [],
1666
+ "transitions": 32,
1667
+ "validation_failures": [
1668
+ {
1669
+ "errors": [
1670
+ "internal transition boundary mismatch"
1671
+ ],
1672
+ "file_path": "Mathlib/Algebra/Group/Hom/Defs.lean",
1673
+ "proof_id": "mathlib:map_pow",
1674
+ "provenance": {
1675
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1676
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1677
+ "end": [
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1680
+ ],
1681
+ "file_path": "Mathlib/Algebra/Group/Hom/Defs.lean",
1682
+ "full_name": "map_pow",
1683
+ "start": [
1684
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1685
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1686
+ ],
1687
+ "traced_tactics": [
1688
+ {
1689
+ "annotated_tactic": [
1690
+ "\"rw [<a>pow_zero<\\/a>, <a>pow_zero<\\/a>, <a>map_one<\\/a>]\"",
1691
+ "[{\"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]},{\"full_name\":\"map_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[204,9],\"def_end_pos\":[204,16]}]"
1692
+ ],
1693
+ "state_after": "no goals",
1694
+ "state_before": "\u03b9 : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\nN : Type u_5\nP : Type u_6\nG : Type u_7\nH : Type u_8\nF : Type u_9\ninst\u271d\u2076 : MulOneClass M\ninst\u271d\u2075 : MulOneClass N\ninst\u271d\u2074 : FunLike F M N\ninst\u271d\u00b3 : FunLike F G H\ninst\u271d\u00b2 : Monoid G\ninst\u271d\u00b9 : Monoid H\ninst\u271d : MonoidHomClass F G H\nf : F\na : G\n\u22a2 f (a ^ 0) = f a ^ 0",
1695
+ "tactic": "rw [pow_zero, pow_zero, map_one]"
1696
+ },
1697
+ {
1698
+ "annotated_tactic": [
1699
+ "\"rw [<a>pow_succ<\\/a>, <a>pow_succ<\\/a>, <a>map_mul<\\/a>, map_pow f a n]\"",
1700
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1701
+ ],
1702
+ "state_after": "no goals",
1703
+ "state_before": "\u03b9 : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\nN : Type u_5\nP : Type u_6\nG : Type u_7\nH : Type u_8\nF : Type u_9\ninst\u271d\u2076 : MulOneClass M\ninst\u271d\u2075 : MulOneClass N\ninst\u271d\u2074 : FunLike F M N\ninst\u271d\u00b3 : FunLike F G H\ninst\u271d\u00b2 : Monoid G\ninst\u271d\u00b9 : Monoid H\ninst\u271d : MonoidHomClass F G H\nf : F\na : G\nn : \u2115\n\u22a2 f (a ^ (n + 1)) = f a ^ (n + 1)",
1704
+ "tactic": "rw [pow_succ, pow_succ, map_mul, map_pow f a n]"
1705
+ }
1706
+ ],
1707
+ "url": "https://github.com/leanprover-community/mathlib4"
1708
+ }
1709
+ },
1710
+ "theorem_name": "map_pow"
1711
+ },
1712
+ {
1713
+ "errors": [
1714
+ "internal transition boundary mismatch"
1715
+ ],
1716
+ "file_path": "Mathlib/Algebra/Group/Hom/Defs.lean",
1717
+ "proof_id": "mathlib:map_zpow'",
1718
+ "provenance": {
1719
+ "selection": {
1720
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1721
+ "end": [
1722
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1724
+ ],
1725
+ "file_path": "Mathlib/Algebra/Group/Hom/Defs.lean",
1726
+ "full_name": "map_zpow'",
1727
+ "start": [
1728
+ 485,
1729
+ 1
1730
+ ],
1731
+ "traced_tactics": [
1732
+ {
1733
+ "annotated_tactic": [
1734
+ "\"rw [<a>zpow_natCast<\\/a>, <a>map_pow<\\/a>, <a>zpow_natCast<\\/a>]\"",
1735
+ "[{\"full_name\":\"zpow_natCast\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1021,9],\"def_end_pos\":[1021,21]},{\"full_name\":\"map_pow\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[473,9],\"def_end_pos\":[473,16]},{\"full_name\":\"zpow_natCast\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1021,9],\"def_end_pos\":[1021,21]}]"
1736
+ ],
1737
+ "state_after": "no goals",
1738
+ "state_before": "\u03b9 : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\nN : Type u_5\nP : Type u_6\nG : Type u_7\nH : Type u_8\nF : Type u_9\ninst\u271d\u2076 : MulOneClass M\ninst\u271d\u2075 : MulOneClass N\ninst\u271d\u2074 : FunLike F M N\ninst\u271d\u00b3 : FunLike F G H\ninst\u271d\u00b2 : DivInvMonoid G\ninst\u271d\u00b9 : DivInvMonoid H\ninst\u271d : MonoidHomClass F G H\nf : F\nhf : \u2200 (x : G), f x\u207b\u00b9 = (f x)\u207b\u00b9\na : G\nn : \u2115\n\u22a2 f (a ^ \u2191n) = f a ^ \u2191n",
1739
+ "tactic": "rw [zpow_natCast, map_pow, zpow_natCast]"
1740
+ },
1741
+ {
1742
+ "annotated_tactic": [
1743
+ "\"rw [<a>zpow_negSucc<\\/a>, hf, <a>map_pow<\\/a>, \\u2190 <a>zpow_negSucc<\\/a>]\"",
1744
+ "[{\"full_name\":\"zpow_negSucc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1040,9],\"def_end_pos\":[1040,21]},{\"full_name\":\"map_pow\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Hom\\/Defs.lean\",\"def_pos\":[473,9],\"def_end_pos\":[473,16]},{\"full_name\":\"zpow_negSucc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1040,9],\"def_end_pos\":[1040,21]}]"
1745
+ ],
1746
+ "state_after": "no goals",
1747
+ "state_before": "\u03b9 : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nM : Type u_4\nN : Type u_5\nP : Type u_6\nG : Type u_7\nH : Type u_8\nF : Type u_9\ninst\u271d\u2076 : MulOneClass M\ninst\u271d\u2075 : MulOneClass N\ninst\u271d\u2074 : FunLike F M N\ninst\u271d\u00b3 : FunLike F G H\ninst\u271d\u00b2 : DivInvMonoid G\ninst\u271d\u00b9 : DivInvMonoid H\ninst\u271d : MonoidHomClass F G H\nf : F\nhf : \u2200 (x : G), f x\u207b\u00b9 = (f x)\u207b\u00b9\na : G\nn : \u2115\n\u22a2 f (a ^ Int.negSucc n) = f a ^ Int.negSucc n",
1748
+ "tactic": "rw [zpow_negSucc, hf, map_pow, \u2190 zpow_negSucc]"
1749
+ }
1750
+ ],
1751
+ "url": "https://github.com/leanprover-community/mathlib4"
1752
+ }
1753
+ },
1754
+ "theorem_name": "map_zpow'"
1755
+ }
1756
+ ],
1757
+ "validation_rejected_proofs": 2,
1758
+ "zero_transition_proofs": 0
1759
+ },
1760
+ "shards": [
1761
+ {
1762
+ "path": "data/train/mathlib-000121-0000-e2af47b7f06e660c.parquet",
1763
+ "sha256": "e2af47b7f06e660c88515259bb9f87d66048146ca4c0b953f7abbca5a7503529",
1764
+ "bytes": 83909,
1765
+ "rows": 19,
1766
+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
1767
+ },
1768
+ {
1769
+ "path": "data/dev/mathlib-000121-0000-13434d6f9d730d13.parquet",
1770
+ "sha256": "13434d6f9d730d13a940552009f1e545ed61d5e4cae9ead278543b5c96aeabd0",
1771
+ "bytes": 39885,
1772
+ "rows": 1,
1773
+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
1774
+ },
1775
+ {
1776
+ "path": "data/internal_test/mathlib-000121-0000-f6dad0cd9445a557.parquet",
1777
+ "sha256": "f6dad0cd9445a557aad58da459c3d248da8564606fe737e0661a39d83a513350",
1778
+ "bytes": 64866,
1779
+ "rows": 8,
1780
+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
1781
+ }
1782
+ ],
1783
+ "proof_ids": [
1784
+ "mathlib:MonoidHom.cancel_left",
1785
+ "mathlib:MonoidHom.comp_one",
1786
+ "mathlib:MonoidHom.map_mul_inv",
1787
+ "mathlib:MulHom.cancel_left",
1788
+ "mathlib:OneHom.cancel_left",
1789
+ "mathlib:OneHom.comp_one",
1790
+ "mathlib:Subsingleton.of_oneHomClass",
1791
+ "mathlib:map_comp_div",
1792
+ "mathlib:map_comp_div'",
1793
+ "mathlib:map_comp_inv",
1794
+ "mathlib:map_comp_mul",
1795
+ "mathlib:map_comp_mul_inv",
1796
+ "mathlib:map_comp_one",
1797
+ "mathlib:map_comp_pow",
1798
+ "mathlib:map_comp_zpow",
1799
+ "mathlib:map_comp_zpow'",
1800
+ "mathlib:map_div'",
1801
+ "mathlib:map_mul_eq_one",
1802
+ "mathlib:map_mul_inv",
1803
+ "mathlib:ne_one_of_map"
1804
+ ],
1805
+ "proof_keys": [
1806
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"MonoidHom.cancel_left\"]",
1807
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"MonoidHom.comp_one\"]",
1808
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"MonoidHom.map_mul_inv\"]",
1809
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"MulHom.cancel_left\"]",
1810
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"OneHom.cancel_left\"]",
1811
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"OneHom.comp_one\"]",
1812
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"Subsingleton.of_oneHomClass\"]",
1813
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"map_comp_div\"]",
1814
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"map_comp_div'\"]",
1815
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"map_comp_inv\"]",
1816
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"map_comp_mul\"]",
1817
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"map_comp_mul_inv\"]",
1818
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"map_comp_one\"]",
1819
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"map_comp_pow\"]",
1820
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"map_comp_zpow\"]",
1821
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"map_comp_zpow'\"]",
1822
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"map_div'\"]",
1823
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"map_mul_eq_one\"]",
1824
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"map_mul_inv\"]",
1825
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Group/Hom/Defs.lean\",null,null,\"ne_one_of_map\"]"
1826
+ ]
1827
+ }
manifests/batches/mathlib/000122.json ADDED
@@ -0,0 +1,1422 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000122",
4
+ "batch_fingerprint": "83938558eabbeb7685b21ec869253abaa5432ef65f5331f650f491d6f94951a4",
5
+ "evidence": {
6
+ "batch_fingerprint": "83938558eabbeb7685b21ec869253abaa5432ef65f5331f650f491d6f94951a4",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "AddMonoid.End.intCast_apply",
12
+ "id": "AddMonoid.End.intCast_apply",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 96,
18
+ 6
19
+ ],
20
+ "file_path": "Mathlib/Algebra/Group/Hom/Instances.lean",
21
+ "full_name": "AddMonoid.End.intCast_apply",
22
+ "start": [
23
+ 94,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/Algebra/Group/Hom/Instances.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "AddMonoid.End.one_apply",
34
+ "id": "AddMonoid.End.one_apply",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 84,
40
+ 6
41
+ ],
42
+ "file_path": "Mathlib/Algebra/Group/Hom/Instances.lean",
43
+ "full_name": "AddMonoid.End.one_apply",
44
+ "start": [
45
+ 83,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/Algebra/Group/Hom/Instances.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "AddMonoid.End.zero_apply",
56
+ "id": "AddMonoid.End.zero_apply",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 80,
62
+ 6
63
+ ],
64
+ "file_path": "Mathlib/Algebra/Group/Hom/Instances.lean",
65
+ "full_name": "AddMonoid.End.zero_apply",
66
+ "start": [
67
+ 79,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/Algebra/Group/Hom/Instances.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "MonoidHom.compl\u2082_apply",
78
+ "id": "MonoidHom.compl\u2082_apply",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 254,
84
+ 6
85
+ ],
86
+ "file_path": "Mathlib/Algebra/Group/Hom/Instances.lean",
87
+ "full_name": "MonoidHom.compl\u2082_apply",
88
+ "start": [
89
+ 252,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/Algebra/Group/Hom/Instances.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "MonoidHom.compr\u2082_apply",
100
+ "id": "MonoidHom.compr\u2082_apply",
101
+ "reason": "import_failure",
102
+ "selection": {
103
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
104
+ "end": [
105
+ 272,
106
+ 6
107
+ ],
108
+ "file_path": "Mathlib/Algebra/Group/Hom/Instances.lean",
109
+ "full_name": "MonoidHom.compr\u2082_apply",
110
+ "start": [
111
+ 270,
112
+ 1
113
+ ],
114
+ "traced_tactics": [],
115
+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
+ "source_file": "Mathlib/Algebra/Group/Hom/Instances.lean"
118
+ },
119
+ {
120
+ "error": "theorem has no selected tactic transitions",
121
+ "full_name": "MonoidHom.ext_iff\u2082",
122
+ "id": "MonoidHom.ext_iff\u2082",
123
+ "reason": "import_failure",
124
+ "selection": {
125
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
126
+ "end": [
127
+ 120,
128
+ 68
129
+ ],
130
+ "file_path": "Mathlib/Algebra/Group/Hom/Instances.lean",
131
+ "full_name": "MonoidHom.ext_iff\u2082",
132
+ "start": [
133
+ 118,
134
+ 1
135
+ ],
136
+ "traced_tactics": [],
137
+ "url": "https://github.com/leanprover-community/mathlib4"
138
+ },
139
+ "source_file": "Mathlib/Algebra/Group/Hom/Instances.lean"
140
+ },
141
+ {
142
+ "error": "theorem has no selected tactic transitions",
143
+ "full_name": "MonoidHom.flip_apply",
144
+ "id": "MonoidHom.flip_apply",
145
+ "reason": "import_failure",
146
+ "selection": {
147
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
148
+ "end": [
149
+ 140,
150
+ 6
151
+ ],
152
+ "file_path": "Mathlib/Algebra/Group/Hom/Instances.lean",
153
+ "full_name": "MonoidHom.flip_apply",
154
+ "start": [
155
+ 138,
156
+ 1
157
+ ],
158
+ "traced_tactics": [],
159
+ "url": "https://github.com/leanprover-community/mathlib4"
160
+ },
161
+ "source_file": "Mathlib/Algebra/Group/Hom/Instances.lean"
162
+ },
163
+ {
164
+ "error": "theorem has no selected tactic transitions",
165
+ "full_name": "MonoidHom.map_div\u2082",
166
+ "id": "MonoidHom.map_div\u2082",
167
+ "reason": "import_failure",
168
+ "selection": {
169
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
170
+ "end": [
171
+ 168,
172
+ 25
173
+ ],
174
+ "file_path": "Mathlib/Algebra/Group/Hom/Instances.lean",
175
+ "full_name": "MonoidHom.map_div\u2082",
176
+ "start": [
177
+ 166,
178
+ 1
179
+ ],
180
+ "traced_tactics": [],
181
+ "url": "https://github.com/leanprover-community/mathlib4"
182
+ },
183
+ "source_file": "Mathlib/Algebra/Group/Hom/Instances.lean"
184
+ },
185
+ {
186
+ "error": "theorem has no selected tactic transitions",
187
+ "full_name": "MonoidHom.map_inv\u2082",
188
+ "id": "MonoidHom.map_inv\u2082",
189
+ "reason": "import_failure",
190
+ "selection": {
191
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
192
+ "end": [
193
+ 161,
194
+ 23
195
+ ],
196
+ "file_path": "Mathlib/Algebra/Group/Hom/Instances.lean",
197
+ "full_name": "MonoidHom.map_inv\u2082",
198
+ "start": [
199
+ 159,
200
+ 1
201
+ ],
202
+ "traced_tactics": [],
203
+ "url": "https://github.com/leanprover-community/mathlib4"
204
+ },
205
+ "source_file": "Mathlib/Algebra/Group/Hom/Instances.lean"
206
+ },
207
+ {
208
+ "error": "theorem has no selected tactic transitions",
209
+ "full_name": "MonoidHom.map_mul\u2082",
210
+ "id": "MonoidHom.map_mul\u2082",
211
+ "reason": "import_failure",
212
+ "selection": {
213
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
214
+ "end": [
215
+ 154,
216
+ 25
217
+ ],
218
+ "file_path": "Mathlib/Algebra/Group/Hom/Instances.lean",
219
+ "full_name": "MonoidHom.map_mul\u2082",
220
+ "start": [
221
+ 152,
222
+ 1
223
+ ],
224
+ "traced_tactics": [],
225
+ "url": "https://github.com/leanprover-community/mathlib4"
226
+ },
227
+ "source_file": "Mathlib/Algebra/Group/Hom/Instances.lean"
228
+ },
229
+ {
230
+ "error": "theorem has no selected tactic transitions",
231
+ "full_name": "MonoidHom.map_one\u2082",
232
+ "id": "MonoidHom.map_one\u2082",
233
+ "reason": "import_failure",
234
+ "selection": {
235
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
236
+ "end": [
237
+ 147,
238
+ 21
239
+ ],
240
+ "file_path": "Mathlib/Algebra/Group/Hom/Instances.lean",
241
+ "full_name": "MonoidHom.map_one\u2082",
242
+ "start": [
243
+ 145,
244
+ 1
245
+ ],
246
+ "traced_tactics": [],
247
+ "url": "https://github.com/leanprover-community/mathlib4"
248
+ },
249
+ "source_file": "Mathlib/Algebra/Group/Hom/Instances.lean"
250
+ },
251
+ {
252
+ "error": "theorem has no selected tactic transitions",
253
+ "full_name": "Set.comp_mulIndicator_const",
254
+ "id": "Set.comp_mulIndicator_const",
255
+ "reason": "import_failure",
256
+ "selection": {
257
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
258
+ "end": [
259
+ 273,
260
+ 37
261
+ ],
262
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
263
+ "full_name": "Set.comp_mulIndicator_const",
264
+ "start": [
265
+ 271,
266
+ 1
267
+ ],
268
+ "traced_tactics": [],
269
+ "url": "https://github.com/leanprover-community/mathlib4"
270
+ },
271
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
272
+ },
273
+ {
274
+ "error": "theorem has no selected tactic transitions",
275
+ "full_name": "Set.eqOn_mulIndicator",
276
+ "id": "Set.eqOn_mulIndicator",
277
+ "reason": "import_failure",
278
+ "selection": {
279
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
280
+ "end": [
281
+ 154,
282
+ 96
283
+ ],
284
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
285
+ "full_name": "Set.eqOn_mulIndicator",
286
+ "start": [
287
+ 154,
288
+ 1
289
+ ],
290
+ "traced_tactics": [],
291
+ "url": "https://github.com/leanprover-community/mathlib4"
292
+ },
293
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
294
+ },
295
+ {
296
+ "error": "theorem has no selected tactic transitions",
297
+ "full_name": "Set.indicator_one_preimage",
298
+ "id": "Set.indicator_one_preimage",
299
+ "reason": "import_failure",
300
+ "selection": {
301
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
302
+ "end": [
303
+ 314,
304
+ 33
305
+ ],
306
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
307
+ "full_name": "Set.indicator_one_preimage",
308
+ "start": [
309
+ 312,
310
+ 1
311
+ ],
312
+ "traced_tactics": [],
313
+ "url": "https://github.com/leanprover-community/mathlib4"
314
+ },
315
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
316
+ },
317
+ {
318
+ "error": "theorem has no selected tactic transitions",
319
+ "full_name": "Set.mem_of_mulIndicator_ne_one",
320
+ "id": "Set.mem_of_mulIndicator_ne_one",
321
+ "reason": "import_failure",
322
+ "selection": {
323
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
324
+ "end": [
325
+ 149,
326
+ 60
327
+ ],
328
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
329
+ "full_name": "Set.mem_of_mulIndicator_ne_one",
330
+ "start": [
331
+ 148,
332
+ 1
333
+ ],
334
+ "traced_tactics": [],
335
+ "url": "https://github.com/leanprover-community/mathlib4"
336
+ },
337
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
338
+ },
339
+ {
340
+ "error": "theorem has no selected tactic transitions",
341
+ "full_name": "Set.mulIndicator_apply_eq_one",
342
+ "id": "Set.mulIndicator_apply_eq_one",
343
+ "reason": "import_failure",
344
+ "selection": {
345
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
346
+ "end": [
347
+ 113,
348
+ 19
349
+ ],
350
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
351
+ "full_name": "Set.mulIndicator_apply_eq_one",
352
+ "start": [
353
+ 111,
354
+ 1
355
+ ],
356
+ "traced_tactics": [],
357
+ "url": "https://github.com/leanprover-community/mathlib4"
358
+ },
359
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
360
+ },
361
+ {
362
+ "error": "no internal trace for tactic 'rfl'",
363
+ "full_name": "Set.mulIndicator_comp_right",
364
+ "id": "Set.mulIndicator_comp_right",
365
+ "reason": "import_failure",
366
+ "selection": {
367
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
368
+ "end": [
369
+ 250,
370
+ 58
371
+ ],
372
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
373
+ "full_name": "Set.mulIndicator_comp_right",
374
+ "start": [
375
+ 247,
376
+ 1
377
+ ],
378
+ "traced_tactics": [
379
+ {
380
+ "annotated_tactic": [
381
+ "\"simp only [<a>mulIndicator<\\/a>, <a>Function.comp<\\/a>]\"",
382
+ "[{\"full_name\":\"Set.mulIndicator\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[48,19],\"def_end_pos\":[48,31]},{\"full_name\":\"Function.comp\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[52,15],\"def_end_pos\":[52,28]}]"
383
+ ],
384
+ "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns\u271d t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ns : Set \u03b1\nf : \u03b2 \u2192 \u03b1\ng : \u03b1 \u2192 M\nx : \u03b2\n\u22a2 (if x \u2208 f \u207b\u00b9' s then g (f x) else 1) = if f x \u2208 s then g (f x) else 1",
385
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns\u271d t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ns : Set \u03b1\nf : \u03b2 \u2192 \u03b1\ng : \u03b1 \u2192 M\nx : \u03b2\n\u22a2 (f \u207b\u00b9' s).mulIndicator (g \u2218 f) x = s.mulIndicator g (f x)",
386
+ "tactic": "simp only [mulIndicator, Function.comp]"
387
+ },
388
+ {
389
+ "annotated_tactic": [
390
+ "\"split_ifs with h h' h'' <;> first | rfl | contradiction\"",
391
+ "[]"
392
+ ],
393
+ "state_after": "no goals",
394
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns\u271d t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ns : Set \u03b1\nf : \u03b2 \u2192 \u03b1\ng : \u03b1 \u2192 M\nx : \u03b2\n\u22a2 (if x \u2208 f \u207b\u00b9' s then g (f x) else 1) = if f x \u2208 s then g (f x) else 1",
395
+ "tactic": "split_ifs with h h' h'' <;> first | rfl | contradiction"
396
+ },
397
+ {
398
+ "annotated_tactic": [
399
+ "\"rfl\"",
400
+ "[]"
401
+ ],
402
+ "state_after": "no goals",
403
+ "state_before": "case neg\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns\u271d t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ns : Set \u03b1\nf : \u03b2 \u2192 \u03b1\ng : \u03b1 \u2192 M\nx : \u03b2\nh : x \u2209 f \u207b\u00b9' s\nh'' : f x \u2209 s\n\u22a2 1 = 1",
404
+ "tactic": "rfl"
405
+ },
406
+ {
407
+ "annotated_tactic": [
408
+ "\"contradiction\"",
409
+ "[]"
410
+ ],
411
+ "state_after": "no goals",
412
+ "state_before": "case pos\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns\u271d t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ns : Set \u03b1\nf : \u03b2 \u2192 \u03b1\ng : \u03b1 \u2192 M\nx : \u03b2\nh : x \u2209 f \u207b\u00b9' s\nh'' : f x \u2208 s\n\u22a2 1 = g (f x)",
413
+ "tactic": "contradiction"
414
+ }
415
+ ],
416
+ "url": "https://github.com/leanprover-community/mathlib4"
417
+ },
418
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
419
+ },
420
+ {
421
+ "error": "theorem has no selected tactic transitions",
422
+ "full_name": "Set.mulIndicator_compl",
423
+ "id": "Set.mulIndicator_compl",
424
+ "reason": "import_failure",
425
+ "selection": {
426
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
427
+ "end": [
428
+ 503,
429
+ 58
430
+ ],
431
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
432
+ "full_name": "Set.mulIndicator_compl",
433
+ "start": [
434
+ 501,
435
+ 1
436
+ ],
437
+ "traced_tactics": [],
438
+ "url": "https://github.com/leanprover-community/mathlib4"
439
+ },
440
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
441
+ },
442
+ {
443
+ "error": "theorem has no selected tactic transitions",
444
+ "full_name": "Set.mulIndicator_compl_mul_self",
445
+ "id": "Set.mulIndicator_compl_mul_self",
446
+ "reason": "import_failure",
447
+ "selection": {
448
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
449
+ "end": [
450
+ 410,
451
+ 50
452
+ ],
453
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
454
+ "full_name": "Set.mulIndicator_compl_mul_self",
455
+ "start": [
456
+ 408,
457
+ 1
458
+ ],
459
+ "traced_tactics": [],
460
+ "url": "https://github.com/leanprover-community/mathlib4"
461
+ },
462
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
463
+ },
464
+ {
465
+ "error": "no internal trace for tactic 'simp [ha]'",
466
+ "full_name": "Set.mulIndicator_compl_mul_self_apply",
467
+ "id": "Set.mulIndicator_compl_mul_self_apply",
468
+ "reason": "import_failure",
469
+ "selection": {
470
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
471
+ "end": [
472
+ 403,
473
+ 67
474
+ ],
475
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
476
+ "full_name": "Set.mulIndicator_compl_mul_self_apply",
477
+ "start": [
478
+ 401,
479
+ 1
480
+ ],
481
+ "traced_tactics": [
482
+ {
483
+ "annotated_tactic": [
484
+ "\"simp [ha]\"",
485
+ "[]"
486
+ ],
487
+ "state_after": "no goals",
488
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d : MulOneClass M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na\u271d : \u03b1\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\nha : a \u2208 s\n\u22a2 s\u1d9c.mulIndicator f a * s.mulIndicator f a = f a",
489
+ "tactic": "simp [ha]"
490
+ },
491
+ {
492
+ "annotated_tactic": [
493
+ "\"simp [ha]\"",
494
+ "[]"
495
+ ],
496
+ "state_after": "no goals",
497
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d : MulOneClass M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na\u271d : \u03b1\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\nha : a \u2209 s\n\u22a2 s\u1d9c.mulIndicator f a * s.mulIndicator f a = f a",
498
+ "tactic": "simp [ha]"
499
+ }
500
+ ],
501
+ "url": "https://github.com/leanprover-community/mathlib4"
502
+ },
503
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
504
+ },
505
+ {
506
+ "error": "no internal trace for tactic 'exact h h_1'",
507
+ "full_name": "Set.mulIndicator_congr",
508
+ "id": "Set.mulIndicator_congr",
509
+ "reason": "import_failure",
510
+ "selection": {
511
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
512
+ "end": [
513
+ 184,
514
+ 8
515
+ ],
516
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
517
+ "full_name": "Set.mulIndicator_congr",
518
+ "start": [
519
+ 179,
520
+ 1
521
+ ],
522
+ "traced_tactics": [
523
+ {
524
+ "annotated_tactic": [
525
+ "\"simp only [<a>mulIndicator<\\/a>]\"",
526
+ "[{\"full_name\":\"Set.mulIndicator\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[48,19],\"def_end_pos\":[48,31]}]"
527
+ ],
528
+ "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns t : Set \u03b1\nf g : \u03b1 \u2192 M\na : \u03b1\nh : EqOn f g s\nx : \u03b1\n\u22a2 (if x \u2208 s then f x else 1) = if x \u2208 s then g x else 1",
529
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns t : Set \u03b1\nf g : \u03b1 \u2192 M\na : \u03b1\nh : EqOn f g s\nx : \u03b1\n\u22a2 s.mulIndicator f x = s.mulIndicator g x",
530
+ "tactic": "simp only [mulIndicator]"
531
+ },
532
+ {
533
+ "annotated_tactic": [
534
+ "\"split_ifs with h_1\"",
535
+ "[]"
536
+ ],
537
+ "state_after": "case pos\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns t : Set \u03b1\nf g : \u03b1 \u2192 M\na : \u03b1\nh : EqOn f g s\nx : \u03b1\nh_1 : x \u2208 s\n\u22a2 f x = g x\n\ncase neg\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns t : Set \u03b1\nf g : \u03b1 \u2192 M\na : \u03b1\nh : EqOn f g s\nx : \u03b1\nh_1 : x \u2209 s\n\u22a2 1 = 1",
538
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns t : Set \u03b1\nf g : \u03b1 \u2192 M\na : \u03b1\nh : EqOn f g s\nx : \u03b1\n\u22a2 (if x \u2208 s then f x else 1) = if x \u2208 s then g x else 1",
539
+ "tactic": "split_ifs with h_1"
540
+ },
541
+ {
542
+ "annotated_tactic": [
543
+ "\"rfl\"",
544
+ "[]"
545
+ ],
546
+ "state_after": "no goals",
547
+ "state_before": "case neg\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns t : Set \u03b1\nf g : \u03b1 \u2192 M\na : \u03b1\nh : EqOn f g s\nx : \u03b1\nh_1 : x \u2209 s\n\u22a2 1 = 1",
548
+ "tactic": "rfl"
549
+ },
550
+ {
551
+ "annotated_tactic": [
552
+ "\"exact h h_1\"",
553
+ "[]"
554
+ ],
555
+ "state_after": "no goals",
556
+ "state_before": "case pos\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns t : Set \u03b1\nf g : \u03b1 \u2192 M\na : \u03b1\nh : EqOn f g s\nx : \u03b1\nh_1 : x \u2208 s\n\u22a2 f x = g x",
557
+ "tactic": "exact h h_1"
558
+ }
559
+ ],
560
+ "url": "https://github.com/leanprover-community/mathlib4"
561
+ },
562
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
563
+ },
564
+ {
565
+ "error": "no internal trace for tactic 'rw [mulIndicator_const_preimage_eq_union]'",
566
+ "full_name": "Set.mulIndicator_const_preimage",
567
+ "id": "Set.mulIndicator_const_preimage",
568
+ "reason": "import_failure",
569
+ "selection": {
570
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
571
+ "end": [
572
+ 308,
573
+ 23
574
+ ],
575
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
576
+ "full_name": "Set.mulIndicator_const_preimage",
577
+ "start": [
578
+ 304,
579
+ 1
580
+ ],
581
+ "traced_tactics": [
582
+ {
583
+ "annotated_tactic": [
584
+ "\"classical\\n rw [<a>mulIndicator_const_preimage_eq_union<\\/a>]\\n split_ifs <;> simp\"",
585
+ "[{\"full_name\":\"Set.mulIndicator_const_preimage_eq_union\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[295,9],\"def_end_pos\":[295,45]}]"
586
+ ],
587
+ "state_after": "no goals",
588
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns\u271d t : Set \u03b1\nf g : \u03b1 \u2192 M\na\u271d : \u03b1\nU : Set \u03b1\ns : Set M\na : M\n\u22a2 (U.mulIndicator fun x => a) \u207b\u00b9' s \u2208 {univ, U, U\u1d9c, \u2205}",
589
+ "tactic": "classical\n rw [mulIndicator_const_preimage_eq_union]\n split_ifs <;> simp"
590
+ },
591
+ {
592
+ "annotated_tactic": [
593
+ "\"rw [<a>mulIndicator_const_preimage_eq_union<\\/a>]\"",
594
+ "[{\"full_name\":\"Set.mulIndicator_const_preimage_eq_union\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[295,9],\"def_end_pos\":[295,45]}]"
595
+ ],
596
+ "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns\u271d t : Set \u03b1\nf g : \u03b1 \u2192 M\na\u271d : \u03b1\nU : Set \u03b1\ns : Set M\na : M\n\u22a2 ((if a \u2208 s then U else \u2205) \u222a if 1 \u2208 s then U\u1d9c else \u2205) \u2208 {univ, U, U\u1d9c, \u2205}",
597
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns\u271d t : Set \u03b1\nf g : \u03b1 \u2192 M\na\u271d : \u03b1\nU : Set \u03b1\ns : Set M\na : M\n\u22a2 (U.mulIndicator fun x => a) \u207b\u00b9' s \u2208 {univ, U, U\u1d9c, \u2205}",
598
+ "tactic": "rw [mulIndicator_const_preimage_eq_union]"
599
+ },
600
+ {
601
+ "annotated_tactic": [
602
+ "\"split_ifs <;> simp\"",
603
+ "[]"
604
+ ],
605
+ "state_after": "no goals",
606
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns\u271d t : Set \u03b1\nf g : \u03b1 \u2192 M\na\u271d : \u03b1\nU : Set \u03b1\ns : Set M\na : M\n\u22a2 ((if a \u2208 s then U else \u2205) \u222a if 1 \u2208 s then U\u1d9c else \u2205) \u2208 {univ, U, U\u1d9c, \u2205}",
607
+ "tactic": "split_ifs <;> simp"
608
+ }
609
+ ],
610
+ "url": "https://github.com/leanprover-community/mathlib4"
611
+ },
612
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
613
+ },
614
+ {
615
+ "error": "theorem has no selected tactic transitions",
616
+ "full_name": "Set.mulIndicator_div",
617
+ "id": "Set.mulIndicator_div",
618
+ "reason": "import_failure",
619
+ "selection": {
620
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
621
+ "end": [
622
+ 489,
623
+ 36
624
+ ],
625
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
626
+ "full_name": "Set.mulIndicator_div",
627
+ "start": [
628
+ 487,
629
+ 1
630
+ ],
631
+ "traced_tactics": [],
632
+ "url": "https://github.com/leanprover-community/mathlib4"
633
+ },
634
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
635
+ },
636
+ {
637
+ "error": "theorem has no selected tactic transitions",
638
+ "full_name": "Set.mulIndicator_div'",
639
+ "id": "Set.mulIndicator_div'",
640
+ "reason": "import_failure",
641
+ "selection": {
642
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
643
+ "end": [
644
+ 496,
645
+ 25
646
+ ],
647
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
648
+ "full_name": "Set.mulIndicator_div'",
649
+ "start": [
650
+ 494,
651
+ 1
652
+ ],
653
+ "traced_tactics": [],
654
+ "url": "https://github.com/leanprover-community/mathlib4"
655
+ },
656
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
657
+ },
658
+ {
659
+ "error": "theorem has no selected tactic transitions",
660
+ "full_name": "Set.mulIndicator_empty",
661
+ "id": "Set.mulIndicator_empty",
662
+ "reason": "import_failure",
663
+ "selection": {
664
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
665
+ "end": [
666
+ 196,
667
+ 44
668
+ ],
669
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
670
+ "full_name": "Set.mulIndicator_empty",
671
+ "start": [
672
+ 195,
673
+ 1
674
+ ],
675
+ "traced_tactics": [],
676
+ "url": "https://github.com/leanprover-community/mathlib4"
677
+ },
678
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
679
+ },
680
+ {
681
+ "error": "theorem has no selected tactic transitions",
682
+ "full_name": "Set.mulIndicator_eq_one'",
683
+ "id": "Set.mulIndicator_eq_one'",
684
+ "reason": "import_failure",
685
+ "selection": {
686
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
687
+ "end": [
688
+ 126,
689
+ 22
690
+ ],
691
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
692
+ "full_name": "Set.mulIndicator_eq_one'",
693
+ "start": [
694
+ 125,
695
+ 1
696
+ ],
697
+ "traced_tactics": [],
698
+ "url": "https://github.com/leanprover-community/mathlib4"
699
+ },
700
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
701
+ },
702
+ {
703
+ "error": "theorem has no selected tactic transitions",
704
+ "full_name": "Set.mulIndicator_inv",
705
+ "id": "Set.mulIndicator_inv",
706
+ "reason": "import_failure",
707
+ "selection": {
708
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
709
+ "end": [
710
+ 482,
711
+ 24
712
+ ],
713
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
714
+ "full_name": "Set.mulIndicator_inv",
715
+ "start": [
716
+ 480,
717
+ 1
718
+ ],
719
+ "traced_tactics": [],
720
+ "url": "https://github.com/leanprover-community/mathlib4"
721
+ },
722
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
723
+ },
724
+ {
725
+ "error": "theorem has no selected tactic transitions",
726
+ "full_name": "Set.mulIndicator_inv'",
727
+ "id": "Set.mulIndicator_inv'",
728
+ "reason": "import_failure",
729
+ "selection": {
730
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
731
+ "end": [
732
+ 475,
733
+ 34
734
+ ],
735
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
736
+ "full_name": "Set.mulIndicator_inv'",
737
+ "start": [
738
+ 474,
739
+ 1
740
+ ],
741
+ "traced_tactics": [],
742
+ "url": "https://github.com/leanprover-community/mathlib4"
743
+ },
744
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
745
+ },
746
+ {
747
+ "error": "no internal trace for tactic 'rfl'",
748
+ "full_name": "Set.mulIndicator_mul",
749
+ "id": "Set.mulIndicator_mul",
750
+ "reason": "import_failure",
751
+ "selection": {
752
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
753
+ "end": [
754
+ 389,
755
+ 15
756
+ ],
757
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
758
+ "full_name": "Set.mulIndicator_mul",
759
+ "start": [
760
+ 383,
761
+ 1
762
+ ],
763
+ "traced_tactics": [
764
+ {
765
+ "annotated_tactic": [
766
+ "\"funext\"",
767
+ "[]"
768
+ ],
769
+ "state_after": "case h\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d : MulOneClass M\ns\u271d t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ns : Set \u03b1\nf g : \u03b1 \u2192 M\nx\u271d : \u03b1\n\u22a2 s.mulIndicator (fun a => f a * g a) x\u271d = s.mulIndicator f x\u271d * s.mulIndicator g x\u271d",
770
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d : MulOneClass M\ns\u271d t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ns : Set \u03b1\nf g : \u03b1 \u2192 M\n\u22a2 (s.mulIndicator fun a => f a * g a) = fun a => s.mulIndicator f a * s.mulIndicator g a",
771
+ "tactic": "funext"
772
+ },
773
+ {
774
+ "annotated_tactic": [
775
+ "\"simp only [<a>mulIndicator<\\/a>]\"",
776
+ "[{\"full_name\":\"Set.mulIndicator\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[48,19],\"def_end_pos\":[48,31]}]"
777
+ ],
778
+ "state_after": "case h\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d : MulOneClass M\ns\u271d t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ns : Set \u03b1\nf g : \u03b1 \u2192 M\nx\u271d : \u03b1\n\u22a2 (if x\u271d \u2208 s then f x\u271d * g x\u271d else 1) = (if x\u271d \u2208 s then f x\u271d else 1) * if x\u271d \u2208 s then g x\u271d else 1",
779
+ "state_before": "case h\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d : MulOneClass M\ns\u271d t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ns : Set \u03b1\nf g : \u03b1 \u2192 M\nx\u271d : \u03b1\n\u22a2 s.mulIndicator (fun a => f a * g a) x\u271d = s.mulIndicator f x\u271d * s.mulIndicator g x\u271d",
780
+ "tactic": "simp only [mulIndicator]"
781
+ },
782
+ {
783
+ "annotated_tactic": [
784
+ "\"split_ifs\"",
785
+ "[]"
786
+ ],
787
+ "state_after": "case pos\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d : MulOneClass M\ns\u271d t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ns : Set \u03b1\nf g : \u03b1 \u2192 M\nx\u271d : \u03b1\nh\u271d : x\u271d \u2208 s\n\u22a2 f x\u271d * g x\u271d = f x\u271d * g x\u271d\n\ncase neg\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d : MulOneClass M\ns\u271d t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ns : Set \u03b1\nf g : \u03b1 \u2192 M\nx\u271d : \u03b1\nh\u271d : x\u271d \u2209 s\n\u22a2 1 = 1 * 1",
788
+ "state_before": "case h\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d : MulOneClass M\ns\u271d t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ns : Set \u03b1\nf g : \u03b1 \u2192 M\nx\u271d : \u03b1\n\u22a2 (if x\u271d \u2208 s then f x\u271d * g x\u271d else 1) = (if x\u271d \u2208 s then f x\u271d else 1) * if x\u271d \u2208 s then g x\u271d else 1",
789
+ "tactic": "split_ifs"
790
+ },
791
+ {
792
+ "annotated_tactic": [
793
+ "\"rw [<a>mul_one<\\/a>]\"",
794
+ "[{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]}]"
795
+ ],
796
+ "state_after": "no goals",
797
+ "state_before": "case neg\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d : MulOneClass M\ns\u271d t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ns : Set \u03b1\nf g : \u03b1 \u2192 M\nx\u271d : \u03b1\nh\u271d : x\u271d \u2209 s\n\u22a2 1 = 1 * 1",
798
+ "tactic": "rw [mul_one]"
799
+ },
800
+ {
801
+ "annotated_tactic": [
802
+ "\"rfl\"",
803
+ "[]"
804
+ ],
805
+ "state_after": "no goals",
806
+ "state_before": "case pos\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d : MulOneClass M\ns\u271d t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ns : Set \u03b1\nf g : \u03b1 \u2192 M\nx\u271d : \u03b1\nh\u271d : x\u271d \u2208 s\n\u22a2 f x\u271d * g x\u271d = f x\u271d * g x\u271d",
807
+ "tactic": "rfl"
808
+ }
809
+ ],
810
+ "url": "https://github.com/leanprover-community/mathlib4"
811
+ },
812
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
813
+ },
814
+ {
815
+ "error": "theorem has no selected tactic transitions",
816
+ "full_name": "Set.mulIndicator_mul'",
817
+ "id": "Set.mulIndicator_mul'",
818
+ "reason": "import_failure",
819
+ "selection": {
820
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
821
+ "end": [
822
+ 396,
823
+ 25
824
+ ],
825
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
826
+ "full_name": "Set.mulIndicator_mul'",
827
+ "start": [
828
+ 394,
829
+ 1
830
+ ],
831
+ "traced_tactics": [],
832
+ "url": "https://github.com/leanprover-community/mathlib4"
833
+ },
834
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
835
+ },
836
+ {
837
+ "error": "theorem has no selected tactic transitions",
838
+ "full_name": "Set.mulIndicator_mulSupport",
839
+ "id": "Set.mulIndicator_mulSupport",
840
+ "reason": "import_failure",
841
+ "selection": {
842
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
843
+ "end": [
844
+ 166,
845
+ 36
846
+ ],
847
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
848
+ "full_name": "Set.mulIndicator_mulSupport",
849
+ "start": [
850
+ 165,
851
+ 1
852
+ ],
853
+ "traced_tactics": [],
854
+ "url": "https://github.com/leanprover-community/mathlib4"
855
+ },
856
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
857
+ },
858
+ {
859
+ "error": "theorem has no selected tactic transitions",
860
+ "full_name": "Set.mulIndicator_of_mem",
861
+ "id": "Set.mulIndicator_of_mem",
862
+ "reason": "import_failure",
863
+ "selection": {
864
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
865
+ "end": [
866
+ 70,
867
+ 11
868
+ ],
869
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
870
+ "full_name": "Set.mulIndicator_of_mem",
871
+ "start": [
872
+ 69,
873
+ 1
874
+ ],
875
+ "traced_tactics": [],
876
+ "url": "https://github.com/leanprover-community/mathlib4"
877
+ },
878
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
879
+ },
880
+ {
881
+ "error": "theorem has no selected tactic transitions",
882
+ "full_name": "Set.mulIndicator_of_not_mem",
883
+ "id": "Set.mulIndicator_of_not_mem",
884
+ "reason": "import_failure",
885
+ "selection": {
886
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
887
+ "end": [
888
+ 76,
889
+ 11
890
+ ],
891
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
892
+ "full_name": "Set.mulIndicator_of_not_mem",
893
+ "start": [
894
+ 75,
895
+ 1
896
+ ],
897
+ "traced_tactics": [],
898
+ "url": "https://github.com/leanprover-community/mathlib4"
899
+ },
900
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
901
+ },
902
+ {
903
+ "error": "theorem has no selected tactic transitions",
904
+ "full_name": "Set.mulIndicator_one'",
905
+ "id": "Set.mulIndicator_one'",
906
+ "reason": "import_failure",
907
+ "selection": {
908
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
909
+ "end": [
910
+ 216,
911
+ 23
912
+ ],
913
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
914
+ "full_name": "Set.mulIndicator_one'",
915
+ "start": [
916
+ 215,
917
+ 1
918
+ ],
919
+ "traced_tactics": [],
920
+ "url": "https://github.com/leanprover-community/mathlib4"
921
+ },
922
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
923
+ },
924
+ {
925
+ "error": "no internal trace for tactic \"rw [mulIndicator_one', preimage_one]\"",
926
+ "full_name": "Set.mulIndicator_one_preimage",
927
+ "id": "Set.mulIndicator_one_preimage",
928
+ "reason": "import_failure",
929
+ "selection": {
930
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
931
+ "end": [
932
+ 290,
933
+ 23
934
+ ],
935
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
936
+ "full_name": "Set.mulIndicator_one_preimage",
937
+ "start": [
938
+ 286,
939
+ 1
940
+ ],
941
+ "traced_tactics": [
942
+ {
943
+ "annotated_tactic": [
944
+ "\"classical\\n rw [<a>mulIndicator_one'<\\/a>, <a>preimage_one<\\/a>]\\n split_ifs <;> simp\"",
945
+ "[{\"full_name\":\"Set.mulIndicator_one'\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[215,9],\"def_end_pos\":[215,26]},{\"full_name\":\"Set.preimage_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Lemmas.lean\",\"def_pos\":[39,9],\"def_end_pos\":[39,25]}]"
946
+ ],
947
+ "state_after": "no goals",
948
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns\u271d t : Set \u03b1\nf g : \u03b1 \u2192 M\na : \u03b1\ns : Set M\n\u22a2 t.mulIndicator 1 \u207b\u00b9' s \u2208 {univ, \u2205}",
949
+ "tactic": "classical\n rw [mulIndicator_one', preimage_one]\n split_ifs <;> simp"
950
+ },
951
+ {
952
+ "annotated_tactic": [
953
+ "\"rw [<a>mulIndicator_one'<\\/a>, <a>preimage_one<\\/a>]\"",
954
+ "[{\"full_name\":\"Set.mulIndicator_one'\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[215,9],\"def_end_pos\":[215,26]},{\"full_name\":\"Set.preimage_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Lemmas.lean\",\"def_pos\":[39,9],\"def_end_pos\":[39,25]}]"
955
+ ],
956
+ "state_after": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns\u271d t : Set \u03b1\nf g : \u03b1 \u2192 M\na : \u03b1\ns : Set M\n\u22a2 (if 1 \u2208 s then univ else \u2205) \u2208 {univ, \u2205}",
957
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns\u271d t : Set \u03b1\nf g : \u03b1 \u2192 M\na : \u03b1\ns : Set M\n\u22a2 t.mulIndicator 1 \u207b\u00b9' s \u2208 {univ, \u2205}",
958
+ "tactic": "rw [mulIndicator_one', preimage_one]"
959
+ },
960
+ {
961
+ "annotated_tactic": [
962
+ "\"split_ifs <;> simp\"",
963
+ "[]"
964
+ ],
965
+ "state_after": "no goals",
966
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns\u271d t : Set \u03b1\nf g : \u03b1 \u2192 M\na : \u03b1\ns : Set M\n\u22a2 (if 1 \u2208 s then univ else \u2205) \u2208 {univ, \u2205}",
967
+ "tactic": "split_ifs <;> simp"
968
+ }
969
+ ],
970
+ "url": "https://github.com/leanprover-community/mathlib4"
971
+ },
972
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
973
+ },
974
+ {
975
+ "error": "theorem has no selected tactic transitions",
976
+ "full_name": "Set.mulIndicator_preimage",
977
+ "id": "Set.mulIndicator_preimage",
978
+ "reason": "import_failure",
979
+ "selection": {
980
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
981
+ "end": [
982
+ 281,
983
+ 29
984
+ ],
985
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
986
+ "full_name": "Set.mulIndicator_preimage",
987
+ "start": [
988
+ 278,
989
+ 1
990
+ ],
991
+ "traced_tactics": [],
992
+ "url": "https://github.com/leanprover-community/mathlib4"
993
+ },
994
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
995
+ },
996
+ {
997
+ "error": "theorem has no selected tactic transitions",
998
+ "full_name": "Set.mulIndicator_range_comp",
999
+ "id": "Set.mulIndicator_range_comp",
1000
+ "reason": "import_failure",
1001
+ "selection": {
1002
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1003
+ "end": [
1004
+ 174,
1005
+ 29
1006
+ ],
1007
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
1008
+ "full_name": "Set.mulIndicator_range_comp",
1009
+ "start": [
1010
+ 171,
1011
+ 1
1012
+ ],
1013
+ "traced_tactics": [],
1014
+ "url": "https://github.com/leanprover-community/mathlib4"
1015
+ },
1016
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
1017
+ },
1018
+ {
1019
+ "error": "theorem has no selected tactic transitions",
1020
+ "full_name": "Set.mulIndicator_self_mul_compl",
1021
+ "id": "Set.mulIndicator_self_mul_compl",
1022
+ "reason": "import_failure",
1023
+ "selection": {
1024
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1025
+ "end": [
1026
+ 424,
1027
+ 50
1028
+ ],
1029
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
1030
+ "full_name": "Set.mulIndicator_self_mul_compl",
1031
+ "start": [
1032
+ 422,
1033
+ 1
1034
+ ],
1035
+ "traced_tactics": [],
1036
+ "url": "https://github.com/leanprover-community/mathlib4"
1037
+ },
1038
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
1039
+ },
1040
+ {
1041
+ "error": "no internal trace for tactic 'simp [ha]'",
1042
+ "full_name": "Set.mulIndicator_self_mul_compl_apply",
1043
+ "id": "Set.mulIndicator_self_mul_compl_apply",
1044
+ "reason": "import_failure",
1045
+ "selection": {
1046
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1047
+ "end": [
1048
+ 417,
1049
+ 67
1050
+ ],
1051
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
1052
+ "full_name": "Set.mulIndicator_self_mul_compl_apply",
1053
+ "start": [
1054
+ 415,
1055
+ 1
1056
+ ],
1057
+ "traced_tactics": [
1058
+ {
1059
+ "annotated_tactic": [
1060
+ "\"simp [ha]\"",
1061
+ "[]"
1062
+ ],
1063
+ "state_after": "no goals",
1064
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d : MulOneClass M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na\u271d : \u03b1\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\nha : a \u2208 s\n\u22a2 s.mulIndicator f a * s\u1d9c.mulIndicator f a = f a",
1065
+ "tactic": "simp [ha]"
1066
+ },
1067
+ {
1068
+ "annotated_tactic": [
1069
+ "\"simp [ha]\"",
1070
+ "[]"
1071
+ ],
1072
+ "state_after": "no goals",
1073
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d : MulOneClass M\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na\u271d : \u03b1\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\nha : a \u2209 s\n\u22a2 s.mulIndicator f a * s\u1d9c.mulIndicator f a = f a",
1074
+ "tactic": "simp [ha]"
1075
+ }
1076
+ ],
1077
+ "url": "https://github.com/leanprover-community/mathlib4"
1078
+ },
1079
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
1080
+ },
1081
+ {
1082
+ "error": "theorem has no selected tactic transitions",
1083
+ "full_name": "Set.mulIndicator_symmDiff",
1084
+ "id": "Set.mulIndicator_symmDiff",
1085
+ "reason": "import_failure",
1086
+ "selection": {
1087
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1088
+ "end": [
1089
+ 380,
1090
+ 82
1091
+ ],
1092
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
1093
+ "full_name": "Set.mulIndicator_symmDiff",
1094
+ "start": [
1095
+ 378,
1096
+ 1
1097
+ ],
1098
+ "traced_tactics": [],
1099
+ "url": "https://github.com/leanprover-community/mathlib4"
1100
+ },
1101
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
1102
+ },
1103
+ {
1104
+ "error": "theorem has no selected tactic transitions",
1105
+ "full_name": "Set.mulIndicator_union_mul_inter",
1106
+ "id": "Set.mulIndicator_union_mul_inter",
1107
+ "reason": "import_failure",
1108
+ "selection": {
1109
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1110
+ "end": [
1111
+ 358,
1112
+ 53
1113
+ ],
1114
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
1115
+ "full_name": "Set.mulIndicator_union_mul_inter",
1116
+ "start": [
1117
+ 356,
1118
+ 1
1119
+ ],
1120
+ "traced_tactics": [],
1121
+ "url": "https://github.com/leanprover-community/mathlib4"
1122
+ },
1123
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
1124
+ },
1125
+ {
1126
+ "error": "theorem has no selected tactic transitions",
1127
+ "full_name": "Set.mulIndicator_union_of_disjoint",
1128
+ "id": "Set.mulIndicator_union_of_disjoint",
1129
+ "reason": "import_failure",
1130
+ "selection": {
1131
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1132
+ "end": [
1133
+ 372,
1134
+ 80
1135
+ ],
1136
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
1137
+ "full_name": "Set.mulIndicator_union_of_disjoint",
1138
+ "start": [
1139
+ 370,
1140
+ 1
1141
+ ],
1142
+ "traced_tactics": [],
1143
+ "url": "https://github.com/leanprover-community/mathlib4"
1144
+ },
1145
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
1146
+ },
1147
+ {
1148
+ "error": "theorem has no selected tactic transitions",
1149
+ "full_name": "Set.mulIndicator_univ",
1150
+ "id": "Set.mulIndicator_univ",
1151
+ "reason": "import_failure",
1152
+ "selection": {
1153
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1154
+ "end": [
1155
+ 190,
1156
+ 42
1157
+ ],
1158
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
1159
+ "full_name": "Set.mulIndicator_univ",
1160
+ "start": [
1161
+ 189,
1162
+ 1
1163
+ ],
1164
+ "traced_tactics": [],
1165
+ "url": "https://github.com/leanprover-community/mathlib4"
1166
+ },
1167
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
1168
+ },
1169
+ {
1170
+ "error": "theorem has no selected tactic transitions",
1171
+ "full_name": "Set.mulSupport_mulIndicator_subset",
1172
+ "id": "Set.mulSupport_mulIndicator_subset",
1173
+ "reason": "import_failure",
1174
+ "selection": {
1175
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1176
+ "end": [
1177
+ 160,
1178
+ 51
1179
+ ],
1180
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
1181
+ "full_name": "Set.mulSupport_mulIndicator_subset",
1182
+ "start": [
1183
+ 159,
1184
+ 1
1185
+ ],
1186
+ "traced_tactics": [],
1187
+ "url": "https://github.com/leanprover-community/mathlib4"
1188
+ },
1189
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
1190
+ },
1191
+ {
1192
+ "error": "theorem has no selected tactic transitions",
1193
+ "full_name": "Set.piecewise_eq_mulIndicator",
1194
+ "id": "Set.piecewise_eq_mulIndicator",
1195
+ "reason": "import_failure",
1196
+ "selection": {
1197
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1198
+ "end": [
1199
+ 55,
1200
+ 67
1201
+ ],
1202
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
1203
+ "full_name": "Set.piecewise_eq_mulIndicator",
1204
+ "start": [
1205
+ 54,
1206
+ 1
1207
+ ],
1208
+ "traced_tactics": [],
1209
+ "url": "https://github.com/leanprover-community/mathlib4"
1210
+ },
1211
+ "source_file": "Mathlib/Algebra/Group/Indicator.lean"
1212
+ }
1213
+ ],
1214
+ "input_proofs": 73,
1215
+ "input_units": 2,
1216
+ "proofs": 28,
1217
+ "published_proofs": 26,
1218
+ "published_transitions": 39,
1219
+ "replay_failures": [],
1220
+ "transitions": 46,
1221
+ "validation_failures": [
1222
+ {
1223
+ "errors": [
1224
+ "internal transition boundary mismatch",
1225
+ "internal transition boundary mismatch"
1226
+ ],
1227
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
1228
+ "proof_id": "mathlib:Set.mulIndicator_eq_one_or_self",
1229
+ "provenance": {
1230
+ "selection": {
1231
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1232
+ "end": [
1233
+ 85,
1234
+ 47
1235
+ ],
1236
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
1237
+ "full_name": "Set.mulIndicator_eq_one_or_self",
1238
+ "start": [
1239
+ 81,
1240
+ 1
1241
+ ],
1242
+ "traced_tactics": [
1243
+ {
1244
+ "annotated_tactic": [
1245
+ "\"by_cases h : a \\u2208 s\"",
1246
+ "[]"
1247
+ ],
1248
+ "state_after": "case pos\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na\u271d : \u03b1\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\nh : a \u2208 s\n\u22a2 s.mulIndicator f a = 1 \u2228 s.mulIndicator f a = f a\n\ncase neg\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na\u271d : \u03b1\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\nh : a \u2209 s\n\u22a2 s.mulIndicator f a = 1 \u2228 s.mulIndicator f a = f a",
1249
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na\u271d : \u03b1\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\n\u22a2 s.mulIndicator f a = 1 \u2228 s.mulIndicator f a = f a",
1250
+ "tactic": "by_cases h : a \u2208 s"
1251
+ },
1252
+ {
1253
+ "annotated_tactic": [
1254
+ "\"exact <a>Or.inr<\\/a> (<a>mulIndicator_of_mem<\\/a> h f)\"",
1255
+ "[{\"full_name\":\"Or.inr\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[536,5],\"def_end_pos\":[536,8]},{\"full_name\":\"Set.mulIndicator_of_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,28]}]"
1256
+ ],
1257
+ "state_after": "no goals",
1258
+ "state_before": "case pos\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na\u271d : \u03b1\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\nh : a \u2208 s\n\u22a2 s.mulIndicator f a = 1 \u2228 s.mulIndicator f a = f a",
1259
+ "tactic": "exact Or.inr (mulIndicator_of_mem h f)"
1260
+ },
1261
+ {
1262
+ "annotated_tactic": [
1263
+ "\"exact <a>Or.inl<\\/a> (<a>mulIndicator_of_not_mem<\\/a> h f)\"",
1264
+ "[{\"full_name\":\"Or.inl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[534,5],\"def_end_pos\":[534,8]},{\"full_name\":\"Set.mulIndicator_of_not_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[75,9],\"def_end_pos\":[75,32]}]"
1265
+ ],
1266
+ "state_after": "no goals",
1267
+ "state_before": "case neg\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : One M\ninst\u271d : One N\ns\u271d t : Set \u03b1\nf\u271d g : \u03b1 \u2192 M\na\u271d : \u03b1\ns : Set \u03b1\nf : \u03b1 \u2192 M\na : \u03b1\nh : a \u2209 s\n\u22a2 s.mulIndicator f a = 1 \u2228 s.mulIndicator f a = f a",
1268
+ "tactic": "exact Or.inl (mulIndicator_of_not_mem h f)"
1269
+ }
1270
+ ],
1271
+ "url": "https://github.com/leanprover-community/mathlib4"
1272
+ }
1273
+ },
1274
+ "theorem_name": "Set.mulIndicator_eq_one_or_self"
1275
+ },
1276
+ {
1277
+ "errors": [
1278
+ "internal transition boundary mismatch",
1279
+ "internal transition boundary mismatch"
1280
+ ],
1281
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
1282
+ "proof_id": "mathlib:Set.mulIndicator_mul_compl_eq_piecewise",
1283
+ "provenance": {
1284
+ "selection": {
1285
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1286
+ "end": [
1287
+ 454,
1288
+ 58
1289
+ ],
1290
+ "file_path": "Mathlib/Algebra/Group/Indicator.lean",
1291
+ "full_name": "Set.mulIndicator_mul_compl_eq_piecewise",
1292
+ "start": [
1293
+ 447,
1294
+ 1
1295
+ ],
1296
+ "traced_tactics": [
1297
+ {
1298
+ "annotated_tactic": [
1299
+ "\"ext x\"",
1300
+ "[]"
1301
+ ],
1302
+ "state_after": "case h\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : MulOneClass M\ns t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ninst\u271d : DecidablePred fun x => x \u2208 s\nf g : \u03b1 \u2192 M\nx : \u03b1\n\u22a2 (s.mulIndicator f * s\u1d9c.mulIndicator g) x = s.piecewise f g x",
1303
+ "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : MulOneClass M\ns t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ninst\u271d : DecidablePred fun x => x \u2208 s\nf g : \u03b1 \u2192 M\n\u22a2 s.mulIndicator f * s\u1d9c.mulIndicator g = s.piecewise f g",
1304
+ "tactic": "ext x"
1305
+ },
1306
+ {
1307
+ "annotated_tactic": [
1308
+ "\"by_cases h : x \\u2208 s\"",
1309
+ "[]"
1310
+ ],
1311
+ "state_after": "case pos\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : MulOneClass M\ns t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ninst\u271d : DecidablePred fun x => x \u2208 s\nf g : \u03b1 \u2192 M\nx : \u03b1\nh : x \u2208 s\n\u22a2 (s.mulIndicator f * s\u1d9c.mulIndicator g) x = s.piecewise f g x\n\ncase neg\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : MulOneClass M\ns t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ninst\u271d : DecidablePred fun x => x \u2208 s\nf g : \u03b1 \u2192 M\nx : \u03b1\nh : x \u2209 s\n\u22a2 (s.mulIndicator f * s\u1d9c.mulIndicator g) x = s.piecewise f g x",
1312
+ "state_before": "case h\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : MulOneClass M\ns t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ninst\u271d : DecidablePred fun x => x \u2208 s\nf g : \u03b1 \u2192 M\nx : \u03b1\n\u22a2 (s.mulIndicator f * s\u1d9c.mulIndicator g) x = s.piecewise f g x",
1313
+ "tactic": "by_cases h : x \u2208 s"
1314
+ },
1315
+ {
1316
+ "annotated_tactic": [
1317
+ "\"rw [<a>piecewise_eq_of_mem<\\/a> _ _ _ h, <a>Pi.mul_apply<\\/a>, <a>Set.mulIndicator_of_mem<\\/a> h,\\n <a>Set.mulIndicator_of_not_mem<\\/a> (<a>Set.not_mem_compl_iff<\\/a>.2 h), <a>mul_one<\\/a>]\"",
1318
+ "[{\"full_name\":\"Set.piecewise_eq_of_mem\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Function.lean\",\"def_pos\":[1596,9],\"def_end_pos\":[1596,28]},{\"full_name\":\"Pi.mul_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[97,9],\"def_end_pos\":[97,18]},{\"full_name\":\"Set.mulIndicator_of_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,28]},{\"full_name\":\"Set.mulIndicator_of_not_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[75,9],\"def_end_pos\":[75,32]},{\"full_name\":\"Set.not_mem_compl_iff\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[1613,9],\"def_end_pos\":[1613,26]},{\"full_name\":\"mul_one\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[483,9],\"def_end_pos\":[483,16]}]"
1319
+ ],
1320
+ "state_after": "no goals",
1321
+ "state_before": "case pos\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : MulOneClass M\ns t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ninst\u271d : DecidablePred fun x => x \u2208 s\nf g : \u03b1 \u2192 M\nx : \u03b1\nh : x \u2208 s\n\u22a2 (s.mulIndicator f * s\u1d9c.mulIndicator g) x = s.piecewise f g x",
1322
+ "tactic": "rw [piecewise_eq_of_mem _ _ _ h, Pi.mul_apply, Set.mulIndicator_of_mem h,\n Set.mulIndicator_of_not_mem (Set.not_mem_compl_iff.2 h), mul_one]"
1323
+ },
1324
+ {
1325
+ "annotated_tactic": [
1326
+ "\"rw [<a>piecewise_eq_of_not_mem<\\/a> _ _ _ h, <a>Pi.mul_apply<\\/a>, <a>Set.mulIndicator_of_not_mem<\\/a> h,\\n <a>Set.mulIndicator_of_mem<\\/a> (<a>Set.mem_compl<\\/a> h), <a>one_mul<\\/a>]\"",
1327
+ "[{\"full_name\":\"Set.piecewise_eq_of_not_mem\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Function.lean\",\"def_pos\":[1601,9],\"def_end_pos\":[1601,32]},{\"full_name\":\"Pi.mul_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[97,9],\"def_end_pos\":[97,18]},{\"full_name\":\"Set.mulIndicator_of_not_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[75,9],\"def_end_pos\":[75,32]},{\"full_name\":\"Set.mulIndicator_of_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Indicator.lean\",\"def_pos\":[69,9],\"def_end_pos\":[69,28]},{\"full_name\":\"Set.mem_compl\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Basic.lean\",\"def_pos\":[1601,9],\"def_end_pos\":[1601,18]},{\"full_name\":\"one_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[477,9],\"def_end_pos\":[477,16]}]"
1328
+ ],
1329
+ "state_after": "no goals",
1330
+ "state_before": "case neg\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b9 : Type u_3\nM : Type u_4\nN : Type u_5\ninst\u271d\u00b9 : MulOneClass M\ns t : Set \u03b1\nf\u271d g\u271d : \u03b1 \u2192 M\na : \u03b1\ninst\u271d : DecidablePred fun x => x \u2208 s\nf g : \u03b1 \u2192 M\nx : \u03b1\nh : x \u2209 s\n\u22a2 (s.mulIndicator f * s\u1d9c.mulIndicator g) x = s.piecewise f g x",
1331
+ "tactic": "rw [piecewise_eq_of_not_mem _ _ _ h, Pi.mul_apply, Set.mulIndicator_of_not_mem h,\n Set.mulIndicator_of_mem (Set.mem_compl h), one_mul]"
1332
+ }
1333
+ ],
1334
+ "url": "https://github.com/leanprover-community/mathlib4"
1335
+ }
1336
+ },
1337
+ "theorem_name": "Set.mulIndicator_mul_compl_eq_piecewise"
1338
+ }
1339
+ ],
1340
+ "validation_rejected_proofs": 2,
1341
+ "zero_transition_proofs": 0
1342
+ },
1343
+ "shards": [
1344
+ {
1345
+ "path": "data/train/mathlib-000122-0000-8601404e53c8bc28.parquet",
1346
+ "sha256": "8601404e53c8bc289fa4a01f10bafce7db51f166896eb5a6ed4f6b6d86ed0faa",
1347
+ "bytes": 145758,
1348
+ "rows": 33,
1349
+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
1350
+ },
1351
+ {
1352
+ "path": "data/dev/mathlib-000122-0000-7255672ce98eb8df.parquet",
1353
+ "sha256": "7255672ce98eb8dfe7df3a7a56a5a76ae2dfd45c6c7600e9be5a0a99444a48be",
1354
+ "bytes": 61575,
1355
+ "rows": 4,
1356
+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
1357
+ },
1358
+ {
1359
+ "path": "data/internal_test/mathlib-000122-0000-785ba3f255f159ce.parquet",
1360
+ "sha256": "785ba3f255f159cebbd58c5a454c7a88577b54c37ccb0941d863ab11a776c7f2",
1361
+ "bytes": 48196,
1362
+ "rows": 2,
1363
+ "revision": "2724ca87965eb93b92ebc27360ea585252124c49"
1364
+ }
1365
+ ],
1366
+ "proof_ids": [
1367
+ "mathlib:MonoidHom.map_mulIndicator",
1368
+ "mathlib:Set.apply_mulIndicator_symmDiff",
1369
+ "mathlib:Set.comp_mulIndicator",
1370
+ "mathlib:Set.mem_range_mulIndicator",
1371
+ "mathlib:Set.mulIndicator_apply",
1372
+ "mathlib:Set.mulIndicator_apply_eq_self",
1373
+ "mathlib:Set.mulIndicator_apply_ne_one",
1374
+ "mathlib:Set.mulIndicator_comp_of_one",
1375
+ "mathlib:Set.mulIndicator_compl'",
1376
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1377
+ "mathlib:Set.mulIndicator_diff",
1378
+ "mathlib:Set.mulIndicator_diff'",
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+ "mathlib:Set.mulIndicator_eq_one",
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+ "mathlib:Set.mulIndicator_eq_self",
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+ "mathlib:Set.mulIndicator_image",
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+ "mathlib:Set.mulIndicator_inter_mulSupport",
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+ "mathlib:Set.mulIndicator_mulIndicator",
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+ "mathlib:Set.mulIndicator_mul_eq_left",
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+ "mathlib:Set.mulIndicator_mul_eq_right",
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+ "mathlib:Set.mulIndicator_one",
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+ "mathlib:Set.mulIndicator_preimage_of_not_mem",
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+ "mathlib:Set.mulIndicator_union_of_not_mem_inter",
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+ "mathlib:Set.mulSupport_mulIndicator"
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+ ],
1394
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1421
+ ]
1422
+ }
manifests/batches/mathlib/000123.json ADDED
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167
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181
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182
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184
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186
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187
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190
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191
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193
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195
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196
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198
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200
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201
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202
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203
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204
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205
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206
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207
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209
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210
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211
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228
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229
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232
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+ "source_file": "Mathlib/Algebra/Group/Int.lean"
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+ },
319
+ {
320
+ "error": "theorem has no selected tactic transitions",
321
+ "full_name": "Int.toAdd_zpow",
322
+ "id": "Int.toAdd_zpow",
323
+ "reason": "import_failure",
324
+ "selection": {
325
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
326
+ "end": [
327
+ 84,
328
+ 94
329
+ ],
330
+ "file_path": "Mathlib/Algebra/Group/Int.lean",
331
+ "full_name": "Int.toAdd_zpow",
332
+ "start": [
333
+ 84,
334
+ 1
335
+ ],
336
+ "traced_tactics": [],
337
+ "url": "https://github.com/leanprover-community/mathlib4"
338
+ },
339
+ "source_file": "Mathlib/Algebra/Group/Int.lean"
340
+ },
341
+ {
342
+ "error": "theorem has no selected tactic transitions",
343
+ "full_name": "Int.two_mul_ediv_two_of_even",
344
+ "id": "Int.two_mul_ediv_two_of_even",
345
+ "reason": "import_failure",
346
+ "selection": {
347
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
348
+ "end": [
349
+ 256,
350
+ 68
351
+ ],
352
+ "file_path": "Mathlib/Algebra/Group/Int.lean",
353
+ "full_name": "Int.two_mul_ediv_two_of_even",
354
+ "start": [
355
+ 255,
356
+ 1
357
+ ],
358
+ "traced_tactics": [],
359
+ "url": "https://github.com/leanprover-community/mathlib4"
360
+ },
361
+ "source_file": "Mathlib/Algebra/Group/Int.lean"
362
+ },
363
+ {
364
+ "error": "no internal trace for tactic 'rw [\u2190 natAbs_mul, Units.inv_mul]'",
365
+ "full_name": "Int.units_natAbs",
366
+ "id": "Int.units_natAbs",
367
+ "reason": "import_failure",
368
+ "selection": {
369
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
370
+ "end": [
371
+ 100,
372
+ 47
373
+ ],
374
+ "file_path": "Mathlib/Algebra/Group/Int.lean",
375
+ "full_name": "Int.units_natAbs",
376
+ "start": [
377
+ 96,
378
+ 1
379
+ ],
380
+ "traced_tactics": [
381
+ {
382
+ "annotated_tactic": [
383
+ "\"rw [\\u2190 <a>natAbs_mul<\\/a>, <a>Units.mul_inv<\\/a>]\"",
384
+ "[{\"full_name\":\"Int.natAbs_mul\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Order.lean\",\"def_pos\":[438,9],\"def_end_pos\":[438,19]},{\"full_name\":\"Units.mul_inv\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Units.lean\",\"def_pos\":[265,9],\"def_end_pos\":[265,16]}]"
385
+ ],
386
+ "state_after": "u\u271d v : \u2124\nu : \u2124\u02e3\n\u22a2 natAbs 1 = 1",
387
+ "state_before": "u\u271d v : \u2124\nu : \u2124\u02e3\n\u22a2 (\u2191u).natAbs * (\u2191u\u207b\u00b9).natAbs = 1",
388
+ "tactic": "rw [\u2190 natAbs_mul, Units.mul_inv]"
389
+ },
390
+ {
391
+ "annotated_tactic": [
392
+ "\"rfl\"",
393
+ "[]"
394
+ ],
395
+ "state_after": "no goals",
396
+ "state_before": "u\u271d v : \u2124\nu : \u2124\u02e3\n\u22a2 natAbs 1 = 1",
397
+ "tactic": "rfl"
398
+ },
399
+ {
400
+ "annotated_tactic": [
401
+ "\"rw [\\u2190 <a>natAbs_mul<\\/a>, <a>Units.inv_mul<\\/a>]\"",
402
+ "[{\"full_name\":\"Int.natAbs_mul\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Order.lean\",\"def_pos\":[438,9],\"def_end_pos\":[438,19]},{\"full_name\":\"Units.inv_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Units.lean\",\"def_pos\":[259,9],\"def_end_pos\":[259,16]}]"
403
+ ],
404
+ "state_after": "u\u271d v : \u2124\nu : \u2124\u02e3\n\u22a2 natAbs 1 = 1",
405
+ "state_before": "u\u271d v : \u2124\nu : \u2124\u02e3\n\u22a2 (\u2191u\u207b\u00b9).natAbs * (\u2191u).natAbs = 1",
406
+ "tactic": "rw [\u2190 natAbs_mul, Units.inv_mul]"
407
+ }
408
+ ],
409
+ "url": "https://github.com/leanprover-community/mathlib4"
410
+ },
411
+ "source_file": "Mathlib/Algebra/Group/Int.lean"
412
+ },
413
+ {
414
+ "error": "theorem has no selected tactic transitions",
415
+ "full_name": "zsmul_int_int",
416
+ "id": "zsmul_int_int",
417
+ "reason": "import_failure",
418
+ "selection": {
419
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
420
+ "end": [
421
+ 272,
422
+ 53
423
+ ],
424
+ "file_path": "Mathlib/Algebra/Group/Int.lean",
425
+ "full_name": "zsmul_int_int",
426
+ "start": [
427
+ 272,
428
+ 1
429
+ ],
430
+ "traced_tactics": [],
431
+ "url": "https://github.com/leanprover-community/mathlib4"
432
+ },
433
+ "source_file": "Mathlib/Algebra/Group/Int.lean"
434
+ },
435
+ {
436
+ "error": "theorem has no selected tactic transitions",
437
+ "full_name": "zsmul_int_one",
438
+ "id": "zsmul_int_one",
439
+ "reason": "import_failure",
440
+ "selection": {
441
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
442
+ "end": [
443
+ 275,
444
+ 59
445
+ ],
446
+ "file_path": "Mathlib/Algebra/Group/Int.lean",
447
+ "full_name": "zsmul_int_one",
448
+ "start": [
449
+ 275,
450
+ 1
451
+ ],
452
+ "traced_tactics": [],
453
+ "url": "https://github.com/leanprover-community/mathlib4"
454
+ },
455
+ "source_file": "Mathlib/Algebra/Group/Int.lean"
456
+ },
457
+ {
458
+ "error": "no internal trace for tactic 'rw [h.eq]'",
459
+ "full_name": "Commute.invOf_left",
460
+ "id": "Commute.invOf_left",
461
+ "reason": "import_failure",
462
+ "selection": {
463
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
464
+ "end": [
465
+ 82,
466
+ 39
467
+ ],
468
+ "file_path": "Mathlib/Algebra/Group/Invertible/Basic.lean",
469
+ "full_name": "Commute.invOf_left",
470
+ "start": [
471
+ 77,
472
+ 1
473
+ ],
474
+ "traced_tactics": [
475
+ {
476
+ "annotated_tactic": [
477
+ "\"simp [<a>mul_assoc<\\/a>]\"",
478
+ "[{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]}]"
479
+ ],
480
+ "state_after": "no goals",
481
+ "state_before": "\u03b1 : Type u\ninst\u271d\u00b9 : Monoid \u03b1\na b : \u03b1\ninst\u271d : Invertible b\nh : Commute b a\n\u22a2 \u215fb * a = \u215fb * (a * b * \u215fb)",
482
+ "tactic": "simp [mul_assoc]"
483
+ },
484
+ {
485
+ "annotated_tactic": [
486
+ "\"rw [h.eq]\"",
487
+ "[]"
488
+ ],
489
+ "state_after": "no goals",
490
+ "state_before": "\u03b1 : Type u\ninst\u271d\u00b9 : Monoid \u03b1\na b : \u03b1\ninst\u271d : Invertible b\nh : Commute b a\n\u22a2 \u215fb * (a * b * \u215fb) = \u215fb * (b * a * \u215fb)",
491
+ "tactic": "rw [h.eq]"
492
+ },
493
+ {
494
+ "annotated_tactic": [
495
+ "\"simp [<a>mul_assoc<\\/a>]\"",
496
+ "[{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]}]"
497
+ ],
498
+ "state_after": "no goals",
499
+ "state_before": "\u03b1 : Type u\ninst\u271d\u00b9 : Monoid \u03b1\na b : \u03b1\ninst\u271d : Invertible b\nh : Commute b a\n\u22a2 \u215fb * (b * a * \u215fb) = a * \u215fb",
500
+ "tactic": "simp [mul_assoc]"
501
+ }
502
+ ],
503
+ "url": "https://github.com/leanprover-community/mathlib4"
504
+ },
505
+ "source_file": "Mathlib/Algebra/Group/Invertible/Basic.lean"
506
+ },
507
+ {
508
+ "error": "no internal trace for tactic 'rw [h.eq]'",
509
+ "full_name": "Commute.invOf_right",
510
+ "id": "Commute.invOf_right",
511
+ "reason": "import_failure",
512
+ "selection": {
513
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
514
+ "end": [
515
+ 74,
516
+ 39
517
+ ],
518
+ "file_path": "Mathlib/Algebra/Group/Invertible/Basic.lean",
519
+ "full_name": "Commute.invOf_right",
520
+ "start": [
521
+ 69,
522
+ 1
523
+ ],
524
+ "traced_tactics": [
525
+ {
526
+ "annotated_tactic": [
527
+ "\"simp [<a>mul_assoc<\\/a>]\"",
528
+ "[{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]}]"
529
+ ],
530
+ "state_after": "no goals",
531
+ "state_before": "\u03b1 : Type u\ninst\u271d\u00b9 : Monoid \u03b1\na b : \u03b1\ninst\u271d : Invertible b\nh : Commute a b\n\u22a2 a * \u215fb = \u215fb * (b * a * \u215fb)",
532
+ "tactic": "simp [mul_assoc]"
533
+ },
534
+ {
535
+ "annotated_tactic": [
536
+ "\"rw [h.eq]\"",
537
+ "[]"
538
+ ],
539
+ "state_after": "no goals",
540
+ "state_before": "\u03b1 : Type u\ninst\u271d\u00b9 : Monoid \u03b1\na b : \u03b1\ninst\u271d : Invertible b\nh : Commute a b\n\u22a2 \u215fb * (b * a * \u215fb) = \u215fb * (a * b * \u215fb)",
541
+ "tactic": "rw [h.eq]"
542
+ },
543
+ {
544
+ "annotated_tactic": [
545
+ "\"simp [<a>mul_assoc<\\/a>]\"",
546
+ "[{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]}]"
547
+ ],
548
+ "state_after": "no goals",
549
+ "state_before": "\u03b1 : Type u\ninst\u271d\u00b9 : Monoid \u03b1\na b : \u03b1\ninst\u271d : Invertible b\nh : Commute a b\n\u22a2 \u215fb * (a * b * \u215fb) = \u215fb * a",
550
+ "tactic": "simp [mul_assoc]"
551
+ }
552
+ ],
553
+ "url": "https://github.com/leanprover-community/mathlib4"
554
+ },
555
+ "source_file": "Mathlib/Algebra/Group/Invertible/Basic.lean"
556
+ },
557
+ {
558
+ "error": "theorem has no selected tactic transitions",
559
+ "full_name": "IsUnit.nonempty_invertible",
560
+ "id": "IsUnit.nonempty_invertible",
561
+ "reason": "import_failure",
562
+ "selection": {
563
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
564
+ "end": [
565
+ 54,
566
+ 32
567
+ ],
568
+ "file_path": "Mathlib/Algebra/Group/Invertible/Basic.lean",
569
+ "full_name": "IsUnit.nonempty_invertible",
570
+ "start": [
571
+ 52,
572
+ 1
573
+ ],
574
+ "traced_tactics": [],
575
+ "url": "https://github.com/leanprover-community/mathlib4"
576
+ },
577
+ "source_file": "Mathlib/Algebra/Group/Invertible/Basic.lean"
578
+ },
579
+ {
580
+ "error": "theorem has no selected tactic transitions",
581
+ "full_name": "commute_invOf",
582
+ "id": "commute_invOf",
583
+ "reason": "import_failure",
584
+ "selection": {
585
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
586
+ "end": [
587
+ 88,
588
+ 43
589
+ ],
590
+ "file_path": "Mathlib/Algebra/Group/Invertible/Basic.lean",
591
+ "full_name": "commute_invOf",
592
+ "start": [
593
+ 85,
594
+ 1
595
+ ],
596
+ "traced_tactics": [],
597
+ "url": "https://github.com/leanprover-community/mathlib4"
598
+ },
599
+ "source_file": "Mathlib/Algebra/Group/Invertible/Basic.lean"
600
+ },
601
+ {
602
+ "error": "theorem has no selected tactic transitions",
603
+ "full_name": "invOf_pow",
604
+ "id": "invOf_pow",
605
+ "reason": "import_failure",
606
+ "selection": {
607
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
608
+ "end": [
609
+ 142,
610
+ 55
611
+ ],
612
+ "file_path": "Mathlib/Algebra/Group/Invertible/Basic.lean",
613
+ "full_name": "invOf_pow",
614
+ "start": [
615
+ 141,
616
+ 1
617
+ ],
618
+ "traced_tactics": [],
619
+ "url": "https://github.com/leanprover-community/mathlib4"
620
+ },
621
+ "source_file": "Mathlib/Algebra/Group/Invertible/Basic.lean"
622
+ },
623
+ {
624
+ "error": "theorem has no selected tactic transitions",
625
+ "full_name": "invOf_units",
626
+ "id": "invOf_units",
627
+ "reason": "import_failure",
628
+ "selection": {
629
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
630
+ "end": [
631
+ 49,
632
+ 31
633
+ ],
634
+ "file_path": "Mathlib/Algebra/Group/Invertible/Basic.lean",
635
+ "full_name": "invOf_units",
636
+ "start": [
637
+ 48,
638
+ 1
639
+ ],
640
+ "traced_tactics": [],
641
+ "url": "https://github.com/leanprover-community/mathlib4"
642
+ },
643
+ "source_file": "Mathlib/Algebra/Group/Invertible/Basic.lean"
644
+ },
645
+ {
646
+ "error": "theorem has no selected tactic transitions",
647
+ "full_name": "isUnit_of_invertible",
648
+ "id": "isUnit_of_invertible",
649
+ "reason": "import_failure",
650
+ "selection": {
651
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
652
+ "end": [
653
+ 36,
654
+ 28
655
+ ],
656
+ "file_path": "Mathlib/Algebra/Group/Invertible/Basic.lean",
657
+ "full_name": "isUnit_of_invertible",
658
+ "start": [
659
+ 35,
660
+ 1
661
+ ],
662
+ "traced_tactics": [],
663
+ "url": "https://github.com/leanprover-community/mathlib4"
664
+ },
665
+ "source_file": "Mathlib/Algebra/Group/Invertible/Basic.lean"
666
+ },
667
+ {
668
+ "error": "theorem has no selected tactic transitions",
669
+ "full_name": "nonempty_invertible_iff_isUnit",
670
+ "id": "nonempty_invertible_iff_isUnit",
671
+ "reason": "import_failure",
672
+ "selection": {
673
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
674
+ "end": [
675
+ 66,
676
+ 76
677
+ ],
678
+ "file_path": "Mathlib/Algebra/Group/Invertible/Basic.lean",
679
+ "full_name": "nonempty_invertible_iff_isUnit",
680
+ "start": [
681
+ 65,
682
+ 1
683
+ ],
684
+ "traced_tactics": [],
685
+ "url": "https://github.com/leanprover-community/mathlib4"
686
+ },
687
+ "source_file": "Mathlib/Algebra/Group/Invertible/Basic.lean"
688
+ }
689
+ ],
690
+ "input_proofs": 47,
691
+ "input_units": 2,
692
+ "proofs": 22,
693
+ "published_proofs": 20,
694
+ "published_transitions": 23,
695
+ "replay_failures": [],
696
+ "transitions": 28,
697
+ "validation_failures": [
698
+ {
699
+ "errors": [
700
+ "internal transition boundary mismatch",
701
+ "internal transition boundary mismatch"
702
+ ],
703
+ "file_path": "Mathlib/Algebra/Group/Int.lean",
704
+ "proof_id": "mathlib:Int.eq_one_or_neg_one_of_mul_eq_neg_one'",
705
+ "provenance": {
706
+ "selection": {
707
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
708
+ "end": [
709
+ 146,
710
+ 32
711
+ ],
712
+ "file_path": "Mathlib/Algebra/Group/Int.lean",
713
+ "full_name": "Int.eq_one_or_neg_one_of_mul_eq_neg_one'",
714
+ "start": [
715
+ 143,
716
+ 1
717
+ ],
718
+ "traced_tactics": [
719
+ {
720
+ "annotated_tactic": [
721
+ "\"obtain rfl | rfl := <a>isUnit_eq_one_or<\\/a> (IsUnit.mul_iff.mp (Int.isUnit_iff.mpr (<a>Or.inr<\\/a> h))).1\"",
722
+ "[{\"full_name\":\"Int.isUnit_eq_one_or\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Int.lean\",\"def_pos\":[105,7],\"def_end_pos\":[105,23]},{\"full_name\":\"Or.inr\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[536,5],\"def_end_pos\":[536,8]}]"
723
+ ],
724
+ "state_after": "case inl\nv : \u2124\nh : 1 * v = -1\n\u22a2 1 = 1 \u2227 v = -1 \u2228 1 = -1 \u2227 v = 1\n\ncase inr\nv : \u2124\nh : -1 * v = -1\n\u22a2 -1 = 1 \u2227 v = -1 \u2228 -1 = -1 \u2227 v = 1",
725
+ "state_before": "u v : \u2124\nh : u * v = -1\n\u22a2 u = 1 \u2227 v = -1 \u2228 u = -1 \u2227 v = 1",
726
+ "tactic": "obtain rfl | rfl := isUnit_eq_one_or (IsUnit.mul_iff.mp (Int.isUnit_iff.mpr (Or.inr h))).1"
727
+ },
728
+ {
729
+ "annotated_tactic": [
730
+ "\"exact <a>Or.inl<\\/a> \\u27e8<a>rfl<\\/a>, <a>one_mul<\\/a> v \\u25b8 h\\u27e9\"",
731
+ "[{\"full_name\":\"Or.inl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[534,5],\"def_end_pos\":[534,8]},{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]},{\"full_name\":\"one_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[477,9],\"def_end_pos\":[477,16]}]"
732
+ ],
733
+ "state_after": "no goals",
734
+ "state_before": "case inl\nv : \u2124\nh : 1 * v = -1\n\u22a2 1 = 1 \u2227 v = -1 \u2228 1 = -1 \u2227 v = 1",
735
+ "tactic": "exact Or.inl \u27e8rfl, one_mul v \u25b8 h\u27e9"
736
+ },
737
+ {
738
+ "annotated_tactic": [
739
+ "\"simpa [<a>Int.neg_mul<\\/a>] using h\"",
740
+ "[{\"full_name\":\"Int.neg_mul\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Lemmas.lean\",\"def_pos\":[447,33],\"def_end_pos\":[447,40]}]"
741
+ ],
742
+ "state_after": "no goals",
743
+ "state_before": "case inr\nv : \u2124\nh : -1 * v = -1\n\u22a2 -1 = 1 \u2227 v = -1 \u2228 -1 = -1 \u2227 v = 1",
744
+ "tactic": "simpa [Int.neg_mul] using h"
745
+ }
746
+ ],
747
+ "url": "https://github.com/leanprover-community/mathlib4"
748
+ }
749
+ },
750
+ "theorem_name": "Int.eq_one_or_neg_one_of_mul_eq_neg_one'"
751
+ },
752
+ {
753
+ "errors": [
754
+ "internal transition boundary mismatch"
755
+ ],
756
+ "file_path": "Mathlib/Algebra/Group/Int.lean",
757
+ "proof_id": "mathlib:Int.even_iff",
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