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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
b6476e0
·
verified ·
1 Parent(s): 4dbd977

Record 15 verified HPC batch manifests

Browse files
Files changed (15) hide show
  1. manifests/batches/deepseek/000416.json +148 -0
  2. manifests/batches/deepseek/000417.json +148 -0
  3. manifests/batches/mathlib/000340.json +470 -0
  4. manifests/batches/mathlib/000341.json +157 -0
  5. manifests/batches/mathlib/000342.json +948 -0
  6. manifests/batches/mathlib/000343.json +2098 -0
  7. manifests/batches/mathlib/000344.json +0 -0
  8. manifests/batches/mathlib/000345.json +0 -0
  9. manifests/batches/mathlib/000346.json +1702 -0
  10. manifests/batches/mathlib/000347.json +0 -0
  11. manifests/batches/numina/001101.json +44 -0
  12. manifests/batches/numina/001102.json +44 -0
  13. manifests/batches/numina/001104.json +51 -0
  14. manifests/batches/numina/001105.json +52 -0
  15. manifests/batches/numina/001106.json +44 -0
manifests/batches/deepseek/000416.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "deepseek/000416",
4
+ "batch_fingerprint": "96fc32e69aadc23872cd7ce6925d6a0a57c8a7c56c50ab3cb7a6684698f72630",
5
+ "evidence": {
6
+ "batch_fingerprint": "96fc32e69aadc23872cd7ce6925d6a0a57c8a7c56c50ab3cb7a6684698f72630",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 50,
10
+ "input_units": 50,
11
+ "proofs": 50,
12
+ "published_proofs": 50,
13
+ "published_transitions": 112,
14
+ "replay_failures": [],
15
+ "trace_mode": "individual",
16
+ "transitions": 112,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/deepseek-000416-0000-e45cbd668ca2f5c9.parquet",
24
+ "sha256": "e45cbd668ca2f5c9a06db9bffbf53dcb61df5e2b8e0c60fa667e00ebef2166e0",
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+ "bytes": 301466,
26
+ "rows": 95,
27
+ "revision": "4dbd9775daba0af0fd6fdd456fb509b76555ebbc"
28
+ },
29
+ {
30
+ "path": "data/dev/deepseek-000416-0000-2aa162f52ee59558.parquet",
31
+ "sha256": "2aa162f52ee59558c1a9e0497ae51350cc666c87c8d33ec25f5d6519b382de0e",
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+ "bytes": 36003,
33
+ "rows": 6,
34
+ "revision": "4dbd9775daba0af0fd6fdd456fb509b76555ebbc"
35
+ },
36
+ {
37
+ "path": "data/internal_test/deepseek-000416-0000-f5da1d1d89a96436.parquet",
38
+ "sha256": "f5da1d1d89a96436be106c74776caf3568cf65d5dae5659161891faa7921df1a",
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+ "bytes": 51906,
40
+ "rows": 11,
41
+ "revision": "4dbd9775daba0af0fd6fdd456fb509b76555ebbc"
42
+ }
43
+ ],
44
+ "proof_ids": [
45
+ "deepseek:thm_20845",
46
+ "deepseek:thm_20846",
47
+ "deepseek:thm_20847",
48
+ "deepseek:thm_20848",
49
+ "deepseek:thm_20849",
50
+ "deepseek:thm_20850",
51
+ "deepseek:thm_20851",
52
+ "deepseek:thm_20852",
53
+ "deepseek:thm_20853",
54
+ "deepseek:thm_20854",
55
+ "deepseek:thm_20855",
56
+ "deepseek:thm_20856",
57
+ "deepseek:thm_20857",
58
+ "deepseek:thm_20858",
59
+ "deepseek:thm_20859",
60
+ "deepseek:thm_20860",
61
+ "deepseek:thm_20861",
62
+ "deepseek:thm_20862",
63
+ "deepseek:thm_20863",
64
+ "deepseek:thm_20864",
65
+ "deepseek:thm_20865",
66
+ "deepseek:thm_20866",
67
+ "deepseek:thm_20867",
68
+ "deepseek:thm_20868",
69
+ "deepseek:thm_20869",
70
+ "deepseek:thm_20870",
71
+ "deepseek:thm_20871",
72
+ "deepseek:thm_20872",
73
+ "deepseek:thm_20873",
74
+ "deepseek:thm_20874",
75
+ "deepseek:thm_20875",
76
+ "deepseek:thm_20876",
77
+ "deepseek:thm_20877",
78
+ "deepseek:thm_20878",
79
+ "deepseek:thm_20879",
80
+ "deepseek:thm_20880",
81
+ "deepseek:thm_20881",
82
+ "deepseek:thm_20882",
83
+ "deepseek:thm_20883",
84
+ "deepseek:thm_20884",
85
+ "deepseek:thm_20885",
86
+ "deepseek:thm_20886",
87
+ "deepseek:thm_20887",
88
+ "deepseek:thm_20888",
89
+ "deepseek:thm_20889",
90
+ "deepseek:thm_20890",
91
+ "deepseek:thm_20891",
92
+ "deepseek:thm_20892",
93
+ "deepseek:thm_20893",
94
+ "deepseek:thm_20894"
95
+ ],
96
+ "proof_keys": [
97
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020800.lean\",\"fb9b3ba964426ffae8ede699de1189d9c7b1f36aa284a2a3610d9d85ba823b0c\",0,\"thm_20845\"]",
98
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020801.lean\",\"2787be7e67e0ba1fa23745d71a741b74984f3aa62911ae312b0a40f0d9d90eaa\",0,\"thm_20846\"]",
99
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020802.lean\",\"61ff8a624f57eb666fb44cfda52f24bb87a0d53d1f0ecd2a791680c76f4a77ad\",0,\"thm_20847\"]",
100
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020803.lean\",\"5efb69436cbb84aeaba32a06851c49bca9bf8c3ddf2cdda1e8acc545288c8449\",0,\"thm_20848\"]",
101
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020804.lean\",\"fbc74ac00f32399e353818a9eb06a403bb6adecd6e52f8cfef48f268aff7aa27\",0,\"thm_20849\"]",
102
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020805.lean\",\"e5840c5191000c04e6a9d5485e41a626fba8f67ff2de344e6e00c3b88cd30b53\",0,\"thm_20850\"]",
103
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020806.lean\",\"0f47789be9e12354014525f2af6c337300dbc0075fb516f1c42d198bf4611cb5\",0,\"thm_20851\"]",
104
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020807.lean\",\"9635ed9ac1ec381219f9d41d6dfb94783e4449ccc5d832bb59ac2a7f1c96fc8d\",0,\"thm_20852\"]",
105
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020808.lean\",\"49892f9ec1cb743bc1f8f5ff755a32101c34df5934827eaacc89579646f27ac5\",0,\"thm_20853\"]",
106
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020809.lean\",\"e44fcfe0edbd5c5e5062ccf8a89fdd04ff37edfdefdfbf8b1ef2d858851d91ca\",0,\"thm_20854\"]",
107
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020810.lean\",\"3e689305a78ff178fbc8ac4792cdd057199f88470bb46dc4d9580bcb27fb2661\",0,\"thm_20855\"]",
108
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020811.lean\",\"9a3677e1274b0456b76faf7f8a7ff5c9215bf4611de9ff3fc2d5e9cf7985190b\",0,\"thm_20856\"]",
109
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020812.lean\",\"0b3478e8d541ae6a6e7b9eacb140358172c7cd87b9fd27a259a7ad2fdaf35d2f\",0,\"thm_20857\"]",
110
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020813.lean\",\"7efc3bbcf66da7f7ed2482cb1d8f1f5a1ec12f6a4a6bc976b191e978e5c98359\",0,\"thm_20858\"]",
111
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020814.lean\",\"2d253f4af024c97ab3c890c0abbe4840a3a608369fb623296d51fee830531709\",0,\"thm_20859\"]",
112
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020815.lean\",\"134f734263275606c3958bf81a86287ec20146815c0061869363ebc96dc73aa8\",0,\"thm_20860\"]",
113
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020816.lean\",\"5e463e9c8bc126ddd9410ee10949e5d386249ea8d126c86d3f3b62794ac58e64\",0,\"thm_20861\"]",
114
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020817.lean\",\"d707243acf18e332e8533d3ae14ad681102bb64d886f6a57a742da307af28fbc\",0,\"thm_20862\"]",
115
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020818.lean\",\"cfa11513dd3681018e2d190ec829485e658be077ab465e9e1bb4a47d320de00f\",0,\"thm_20863\"]",
116
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020819.lean\",\"4884ce10d1bc2846edf5ca15e3653629366d4b94dcac84719655b1dd3ef74c87\",0,\"thm_20864\"]",
117
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020820.lean\",\"7c4780c249f20d25276102a7708a9a639a4ac50ee304c35f2cbd65e99fce1eb7\",0,\"thm_20865\"]",
118
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020821.lean\",\"cc434bb69edc621e80f8ff7523d2ba2fd919f6efdd19a1bb14aaec986477f60a\",0,\"thm_20866\"]",
119
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020822.lean\",\"b52cceceefb5399c309989452eb8a16b903af3d1c07034a8b51d498ef6b08365\",0,\"thm_20867\"]",
120
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020823.lean\",\"8cc9e6830a9ba21cd30d34e43b9a9d6863a365ae24198923a478bff279fa0fb5\",0,\"thm_20868\"]",
121
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020824.lean\",\"79e708582bd9e9223dff1acde4e5beb17a7280896be2506531f907dfe0d4aacc\",0,\"thm_20869\"]",
122
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020825.lean\",\"de929f27cb973f7690c602607f68076fcd0656ac167fe49d51d258bfbbd64b2f\",0,\"thm_20870\"]",
123
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020826.lean\",\"47e5597f4ef5e6faaabaae398cb4c5b4d70d1b9b6c644fdd7065c2921a9a2b12\",0,\"thm_20871\"]",
124
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020827.lean\",\"1d57677ac5617f2ecce133dfa192cfe6fc6b6e6ee45a1964a5e3c008a98a34cc\",0,\"thm_20872\"]",
125
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020828.lean\",\"3f2880996de0237b29cf694b457d1af49dae0329a571c72a096fb665dddaa318\",0,\"thm_20873\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020829.lean\",\"e6ac77006af337d13ecb4fecfe543e932233dc2b12c9d0378c097430d4c549d7\",0,\"thm_20874\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020830.lean\",\"1f2b744de38b487f712803ebe5d0f5986dc02c9e677b716c2d712159543190a8\",0,\"thm_20875\"]",
128
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020831.lean\",\"7cfcc086263362ca3578f2b8d07a670ae901e116ba50bf06371c2b7a79ebf360\",0,\"thm_20876\"]",
129
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020832.lean\",\"319fbcd82db880c2b3c855fa40dc1c77a3fe307eeb4015597e2cff9c16e2775e\",0,\"thm_20877\"]",
130
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020833.lean\",\"f9a8db89b7671719717731b84d3b5167c5c8b7ff5a96348eaf5c601166f3ac97\",0,\"thm_20878\"]",
131
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020834.lean\",\"6f7c63415eb1344d5a71942b6c1257bc9f3a3f635b95f3414f4a98949728bbbd\",0,\"thm_20879\"]",
132
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020835.lean\",\"6010d3d37fdde64925cea8e0a2bce37e79e4571c7bdfae7a2f7685ef0498fb0a\",0,\"thm_20880\"]",
133
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020836.lean\",\"f63a6f5db8b8e6fd54b46c7c470a01ecbbd5c7bbe34f9b38c23823cad8cc2c7c\",0,\"thm_20881\"]",
134
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020837.lean\",\"49e9cf0a3d3db55266432f57ea960f3f3acd7e677c6e57010e5062ad521b93e7\",0,\"thm_20882\"]",
135
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020838.lean\",\"3fa3bd9c09856428def65384bc6240ff072413ee1b81e6b81b4157f9e4ff11f8\",0,\"thm_20883\"]",
136
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020839.lean\",\"da4f2b755a124246db9682760c0e11f5303d450f97593e77c98ddc042db11bc3\",0,\"thm_20884\"]",
137
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020840.lean\",\"cb372cfd9cd0fce6a35279bca949dbcb80210833afd3e3a03646b8ae05e9b354\",0,\"thm_20885\"]",
138
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020841.lean\",\"981c24626f304e1db902d13f71eeb7adb5a6c11d00682959e9271fef22caaa3b\",0,\"thm_20886\"]",
139
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020842.lean\",\"6703047a2738ba351559cd64ba5d7aa9c5085f26ea0f367ef200ee73ea7bd414\",0,\"thm_20887\"]",
140
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020843.lean\",\"bc3235340a7757a97a5495088e865f0772b2d9a4fe2779e5fff418976754d681\",0,\"thm_20888\"]",
141
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020844.lean\",\"5d147b681bb69afbea2d674ed2f0eb40f445feeebf8ae5dde742a3a6dd3f382f\",0,\"thm_20889\"]",
142
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020845.lean\",\"59d0b9299678c0bc31945605f6a3c754207df52d3647555104494ce3ca76a2ed\",0,\"thm_20890\"]",
143
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020846.lean\",\"4cd1b3cdb906d1b8293f1ad83f45e138af030844c82eab6ffd369658cbafb79f\",0,\"thm_20891\"]",
144
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020847.lean\",\"be98acf44b735861da66ac1c2db3875b9ea696245b4dc460a53bc3dd93868fe5\",0,\"thm_20892\"]",
145
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020848.lean\",\"4a847f2709b63ab6fe066c338bd88dbf8ac134c0015a720358ddc1f902d2ce90\",0,\"thm_20893\"]",
146
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020849.lean\",\"d63d96320ef1e25596bad31ef85402b05b626bc0c26f7a0a69483eeb0c226324\",0,\"thm_20894\"]"
147
+ ]
148
+ }
manifests/batches/deepseek/000417.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
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+ "format": "leangpt-parquet-v2",
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+ "batch": "deepseek/000417",
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+ "batch_fingerprint": "e72aba83a6059682f74bd87466814197f0c5e536598566d3dc8d58dfb929ed81",
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+ "evidence": {
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+ "batch_fingerprint": "e72aba83a6059682f74bd87466814197f0c5e536598566d3dc8d58dfb929ed81",
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+ "contamination_matches": [],
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+ "failures": [],
9
+ "input_proofs": 50,
10
+ "input_units": 50,
11
+ "proofs": 50,
12
+ "published_proofs": 50,
13
+ "published_transitions": 116,
14
+ "replay_failures": [],
15
+ "trace_mode": "individual",
16
+ "transitions": 116,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/deepseek-000417-0000-b9662588b77bfc8f.parquet",
24
+ "sha256": "b9662588b77bfc8f71680ef86ce5f41eeeb6d3605a8dee5cf8cf1f0cb73a3f56",
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+ "bytes": 321454,
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+ "rows": 100,
27
+ "revision": "4dbd9775daba0af0fd6fdd456fb509b76555ebbc"
28
+ },
29
+ {
30
+ "path": "data/dev/deepseek-000417-0000-07900526c590545d.parquet",
31
+ "sha256": "07900526c590545dd040aad3ac96385a0aefbd2aa8974f2d0b96af0165455672",
32
+ "bytes": 31249,
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+ "rows": 3,
34
+ "revision": "4dbd9775daba0af0fd6fdd456fb509b76555ebbc"
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+ },
36
+ {
37
+ "path": "data/internal_test/deepseek-000417-0000-141e8c2a41480538.parquet",
38
+ "sha256": "141e8c2a414805385a7a216b849bc3ba628e0f2ec767c224970d272046089de5",
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+ "bytes": 51001,
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+ "rows": 13,
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+ "revision": "4dbd9775daba0af0fd6fdd456fb509b76555ebbc"
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+ }
43
+ ],
44
+ "proof_ids": [
45
+ "deepseek:thm_20895",
46
+ "deepseek:thm_20896",
47
+ "deepseek:thm_20897",
48
+ "deepseek:thm_20898",
49
+ "deepseek:thm_20899",
50
+ "deepseek:thm_20900",
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+ "deepseek:thm_20901",
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+ "deepseek:thm_20902",
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+ "deepseek:thm_20903",
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+ "deepseek:thm_20904",
55
+ "deepseek:thm_20905",
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+ "deepseek:thm_20906",
57
+ "deepseek:thm_20907",
58
+ "deepseek:thm_20908",
59
+ "deepseek:thm_20909",
60
+ "deepseek:thm_20910",
61
+ "deepseek:thm_20911",
62
+ "deepseek:thm_20912",
63
+ "deepseek:thm_20913",
64
+ "deepseek:thm_20914",
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+ "deepseek:thm_20915",
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+ "deepseek:thm_20916",
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+ "deepseek:thm_20917",
68
+ "deepseek:thm_20918",
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+ "deepseek:thm_20919",
70
+ "deepseek:thm_20920",
71
+ "deepseek:thm_20921",
72
+ "deepseek:thm_20922",
73
+ "deepseek:thm_20923",
74
+ "deepseek:thm_20924",
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+ "deepseek:thm_20925",
76
+ "deepseek:thm_20926",
77
+ "deepseek:thm_20927",
78
+ "deepseek:thm_20928",
79
+ "deepseek:thm_20929",
80
+ "deepseek:thm_20930",
81
+ "deepseek:thm_20931",
82
+ "deepseek:thm_20932",
83
+ "deepseek:thm_20933",
84
+ "deepseek:thm_20934",
85
+ "deepseek:thm_20935",
86
+ "deepseek:thm_20936",
87
+ "deepseek:thm_20937",
88
+ "deepseek:thm_20938",
89
+ "deepseek:thm_20939",
90
+ "deepseek:thm_20940",
91
+ "deepseek:thm_20941",
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+ "deepseek:thm_20942",
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+ "deepseek:thm_20943",
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+ "deepseek:thm_20944"
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+ ],
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+ "proof_keys": [
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020857.lean\",\"27bdb147d54a178f9e4af068fd8600d54558fe5e460705b2fe75be73e747346f\",0,\"thm_20902\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020858.lean\",\"f440f152978d77cf5d31c8a0c58cc5efd1d01849567b7cbbf2c13f4a073d1a96\",0,\"thm_20903\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020882.lean\",\"107e687add92e3a41eaf03994d788be6aa1d00e3fbf1162c9b78e6e6b1c9966f\",0,\"thm_20927\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020884.lean\",\"d572d28f047550f636b34cbeeb6b1e4914948aa4e311ad6345dbc965f610a363\",0,\"thm_20929\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020887.lean\",\"8e8b380460c26b472e3c2df36d8b94f829067682545ab5854a7b3295be4f51cb\",0,\"thm_20932\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020889.lean\",\"fe8dd15c07fc67ce7c87e9c782f20d7fce40263cf3517af68f08aaff28a2bba2\",0,\"thm_20934\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020890.lean\",\"c462639d175fc66007ee06c743baa26be836105d50039dbd51449297584f6d7f\",0,\"thm_20935\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020891.lean\",\"50a9bf6a9b6575daab2701a99b0a33da1002ee20f91248388412c9831a817f93\",0,\"thm_20936\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020892.lean\",\"c8a820573097c68e17c557772eddafdbaa0fee39fdb8a151b29e23ce25a67c52\",0,\"thm_20937\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020893.lean\",\"67cf2d7d60e38416ad431097ee229ac9a10dae4a78e234509f19be4688274397\",0,\"thm_20938\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020894.lean\",\"24a2477972a48bb82c335ab9ac261ff3178404b9d1fccb7f26cd98a4eeb99ba3\",0,\"thm_20939\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020895.lean\",\"b02dec8f99645d1af4bac43b94f4512c15e6a1afec264d62d235b986ca8f289b\",0,\"thm_20940\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_020897.lean\",\"7a7d4f1819929cd88362bfe1f5332b8f703239ed49c73d3826a66fd3eda46dd8\",0,\"thm_20942\"]",
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147
+ ]
148
+ }
manifests/batches/mathlib/000340.json ADDED
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+ 1
157
+ ],
158
+ "traced_tactics": [],
159
+ "url": "https://github.com/leanprover-community/mathlib4"
160
+ },
161
+ "source_file": "Mathlib/Algebra/Star/Pointwise.lean"
162
+ },
163
+ {
164
+ "error": "theorem has no selected tactic transitions",
165
+ "full_name": "Set.iInter_star",
166
+ "id": "Set.iInter_star",
167
+ "reason": "import_failure",
168
+ "selection": {
169
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
170
+ "end": [
171
+ 85,
172
+ 18
173
+ ],
174
+ "file_path": "Mathlib/Algebra/Star/Pointwise.lean",
175
+ "full_name": "Set.iInter_star",
176
+ "start": [
177
+ 84,
178
+ 1
179
+ ],
180
+ "traced_tactics": [],
181
+ "url": "https://github.com/leanprover-community/mathlib4"
182
+ },
183
+ "source_file": "Mathlib/Algebra/Star/Pointwise.lean"
184
+ },
185
+ {
186
+ "error": "theorem has no selected tactic transitions",
187
+ "full_name": "Set.iUnion_star",
188
+ "id": "Set.iUnion_star",
189
+ "reason": "import_failure",
190
+ "selection": {
191
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
192
+ "end": [
193
+ 90,
194
+ 18
195
+ ],
196
+ "file_path": "Mathlib/Algebra/Star/Pointwise.lean",
197
+ "full_name": "Set.iUnion_star",
198
+ "start": [
199
+ 89,
200
+ 1
201
+ ],
202
+ "traced_tactics": [],
203
+ "url": "https://github.com/leanprover-community/mathlib4"
204
+ },
205
+ "source_file": "Mathlib/Algebra/Star/Pointwise.lean"
206
+ },
207
+ {
208
+ "error": "theorem has no selected tactic transitions",
209
+ "full_name": "Set.mem_star",
210
+ "id": "Set.mem_star",
211
+ "reason": "import_failure",
212
+ "selection": {
213
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
214
+ "end": [
215
+ 59,
216
+ 55
217
+ ],
218
+ "file_path": "Mathlib/Algebra/Star/Pointwise.lean",
219
+ "full_name": "Set.mem_star",
220
+ "start": [
221
+ 59,
222
+ 1
223
+ ],
224
+ "traced_tactics": [],
225
+ "url": "https://github.com/leanprover-community/mathlib4"
226
+ },
227
+ "source_file": "Mathlib/Algebra/Star/Pointwise.lean"
228
+ },
229
+ {
230
+ "error": "theorem has no selected tactic transitions",
231
+ "full_name": "Set.nonempty_star",
232
+ "id": "Set.nonempty_star",
233
+ "reason": "import_failure",
234
+ "selection": {
235
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
236
+ "end": [
237
+ 51,
238
+ 47
239
+ ],
240
+ "file_path": "Mathlib/Algebra/Star/Pointwise.lean",
241
+ "full_name": "Set.nonempty_star",
242
+ "start": [
243
+ 50,
244
+ 1
245
+ ],
246
+ "traced_tactics": [],
247
+ "url": "https://github.com/leanprover-community/mathlib4"
248
+ },
249
+ "source_file": "Mathlib/Algebra/Star/Pointwise.lean"
250
+ },
251
+ {
252
+ "error": "theorem has no selected tactic transitions",
253
+ "full_name": "Set.star_empty",
254
+ "id": "Set.star_empty",
255
+ "reason": "import_failure",
256
+ "selection": {
257
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
258
+ "end": [
259
+ 42,
260
+ 54
261
+ ],
262
+ "file_path": "Mathlib/Algebra/Star/Pointwise.lean",
263
+ "full_name": "Set.star_empty",
264
+ "start": [
265
+ 42,
266
+ 1
267
+ ],
268
+ "traced_tactics": [],
269
+ "url": "https://github.com/leanprover-community/mathlib4"
270
+ },
271
+ "source_file": "Mathlib/Algebra/Star/Pointwise.lean"
272
+ },
273
+ {
274
+ "error": "theorem has no selected tactic transitions",
275
+ "full_name": "Set.star_preimage",
276
+ "id": "Set.star_preimage",
277
+ "reason": "import_failure",
278
+ "selection": {
279
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
280
+ "end": [
281
+ 66,
282
+ 61
283
+ ],
284
+ "file_path": "Mathlib/Algebra/Star/Pointwise.lean",
285
+ "full_name": "Set.star_preimage",
286
+ "start": [
287
+ 66,
288
+ 1
289
+ ],
290
+ "traced_tactics": [],
291
+ "url": "https://github.com/leanprover-community/mathlib4"
292
+ },
293
+ "source_file": "Mathlib/Algebra/Star/Pointwise.lean"
294
+ },
295
+ {
296
+ "error": "theorem has no selected tactic transitions",
297
+ "full_name": "Set.star_subset_star",
298
+ "id": "Set.star_subset_star",
299
+ "reason": "import_failure",
300
+ "selection": {
301
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
302
+ "end": [
303
+ 104,
304
+ 53
305
+ ],
306
+ "file_path": "Mathlib/Algebra/Star/Pointwise.lean",
307
+ "full_name": "Set.star_subset_star",
308
+ "start": [
309
+ 103,
310
+ 1
311
+ ],
312
+ "traced_tactics": [],
313
+ "url": "https://github.com/leanprover-community/mathlib4"
314
+ },
315
+ "source_file": "Mathlib/Algebra/Star/Pointwise.lean"
316
+ },
317
+ {
318
+ "error": "theorem has no selected tactic transitions",
319
+ "full_name": "Set.star_univ",
320
+ "id": "Set.star_univ",
321
+ "reason": "import_failure",
322
+ "selection": {
323
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
324
+ "end": [
325
+ 46,
326
+ 59
327
+ ],
328
+ "file_path": "Mathlib/Algebra/Star/Pointwise.lean",
329
+ "full_name": "Set.star_univ",
330
+ "start": [
331
+ 46,
332
+ 1
333
+ ],
334
+ "traced_tactics": [],
335
+ "url": "https://github.com/leanprover-community/mathlib4"
336
+ },
337
+ "source_file": "Mathlib/Algebra/Star/Pointwise.lean"
338
+ },
339
+ {
340
+ "error": "theorem has no selected tactic transitions",
341
+ "full_name": "Set.union_star",
342
+ "id": "Set.union_star",
343
+ "reason": "import_failure",
344
+ "selection": {
345
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
346
+ "end": [
347
+ 80,
348
+ 67
349
+ ],
350
+ "file_path": "Mathlib/Algebra/Star/Pointwise.lean",
351
+ "full_name": "Set.union_star",
352
+ "start": [
353
+ 80,
354
+ 1
355
+ ],
356
+ "traced_tactics": [],
357
+ "url": "https://github.com/leanprover-community/mathlib4"
358
+ },
359
+ "source_file": "Mathlib/Algebra/Star/Pointwise.lean"
360
+ },
361
+ {
362
+ "error": "no internal trace for tactic 'simpa only [star_star] using star_mem (s := s) (r := star x)'",
363
+ "full_name": "StarMemClass.star_coe_eq",
364
+ "id": "StarMemClass.star_coe_eq",
365
+ "reason": "import_failure",
366
+ "selection": {
367
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
368
+ "end": [
369
+ 154,
370
+ 84
371
+ ],
372
+ "file_path": "Mathlib/Algebra/Star/Pointwise.lean",
373
+ "full_name": "StarMemClass.star_coe_eq",
374
+ "start": [
375
+ 149,
376
+ 1
377
+ ],
378
+ "traced_tactics": [
379
+ {
380
+ "annotated_tactic": [
381
+ "\"ext x\"",
382
+ "[]"
383
+ ],
384
+ "state_after": "case h\nS : Type u_1\n\u03b1 : Type u_2\ninst\u271d\u00b2 : InvolutiveStar \u03b1\ninst\u271d\u00b9 : SetLike S \u03b1\ninst\u271d : StarMemClass S \u03b1\ns : S\nx : \u03b1\n\u22a2 x \u2208 star \u2191s \u2194 x \u2208 \u2191s",
385
+ "state_before": "S : Type u_1\n\u03b1 : Type u_2\ninst\u271d\u00b2 : InvolutiveStar \u03b1\ninst\u271d\u00b9 : SetLike S \u03b1\ninst\u271d : StarMemClass S \u03b1\ns : S\n\u22a2 star \u2191s = \u2191s",
386
+ "tactic": "ext x"
387
+ },
388
+ {
389
+ "annotated_tactic": [
390
+ "\"simp only [<a>Set.mem_star<\\/a>, <a>SetLike.mem_coe<\\/a>]\"",
391
+ "[{\"full_name\":\"Set.mem_star\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Pointwise.lean\",\"def_pos\":[59,9],\"def_end_pos\":[59,17]},{\"full_name\":\"SetLike.mem_coe\",\"def_path\":\"Mathlib\\/Data\\/SetLike\\/Basic.lean\",\"def_pos\":[180,9],\"def_end_pos\":[180,16]}]"
392
+ ],
393
+ "state_after": "case h\nS : Type u_1\n\u03b1 : Type u_2\ninst\u271d\u00b2 : InvolutiveStar \u03b1\ninst\u271d\u00b9 : SetLike S \u03b1\ninst\u271d : StarMemClass S \u03b1\ns : S\nx : \u03b1\n\u22a2 star x \u2208 s \u2194 x \u2208 s",
394
+ "state_before": "case h\nS : Type u_1\n\u03b1 : Type u_2\ninst\u271d\u00b2 : InvolutiveStar \u03b1\ninst\u271d\u00b9 : SetLike S \u03b1\ninst\u271d : StarMemClass S \u03b1\ns : S\nx : \u03b1\n\u22a2 x \u2208 star \u2191s \u2194 x \u2208 \u2191s",
395
+ "tactic": "simp only [Set.mem_star, SetLike.mem_coe]"
396
+ },
397
+ {
398
+ "annotated_tactic": [
399
+ "\"exact \\u27e8by simpa only [<a>star_star<\\/a>] using <a>star_mem<\\/a> (s := s) (r := <a>star<\\/a> x), <a>star_mem<\\/a>\\u27e9\"",
400
+ "[{\"full_name\":\"star_star\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[92,9],\"def_end_pos\":[92,18]},{\"full_name\":\"StarMemClass.star_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[64,3],\"def_end_pos\":[64,11]},{\"full_name\":\"Star.star\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[47,3],\"def_end_pos\":[47,7]},{\"full_name\":\"StarMemClass.star_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[64,3],\"def_end_pos\":[64,11]}]"
401
+ ],
402
+ "state_after": "no goals",
403
+ "state_before": "case h\nS : Type u_1\n\u03b1 : Type u_2\ninst\u271d\u00b2 : InvolutiveStar \u03b1\ninst\u271d\u00b9 : SetLike S \u03b1\ninst\u271d : StarMemClass S \u03b1\ns : S\nx : \u03b1\n\u22a2 star x \u2208 s \u2194 x \u2208 s",
404
+ "tactic": "exact \u27e8by simpa only [star_star] using star_mem (s := s) (r := star x), star_mem\u27e9"
405
+ },
406
+ {
407
+ "annotated_tactic": [
408
+ "\"simpa only [<a>star_star<\\/a>] using <a>star_mem<\\/a> (s := s) (r := <a>star<\\/a> x)\"",
409
+ "[{\"full_name\":\"star_star\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[92,9],\"def_end_pos\":[92,18]},{\"full_name\":\"StarMemClass.star_mem\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[64,3],\"def_end_pos\":[64,11]},{\"full_name\":\"Star.star\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[47,3],\"def_end_pos\":[47,7]}]"
410
+ ],
411
+ "state_after": "no goals",
412
+ "state_before": "S : Type u_1\n\u03b1 : Type u_2\ninst\u271d\u00b2 : InvolutiveStar \u03b1\ninst\u271d\u00b9 : SetLike S \u03b1\ninst\u271d : StarMemClass S \u03b1\ns : S\nx : \u03b1\n\u22a2 star x \u2208 s \u2192 x \u2208 s",
413
+ "tactic": "simpa only [star_star] using star_mem (s := s) (r := star x)"
414
+ }
415
+ ],
416
+ "url": "https://github.com/leanprover-community/mathlib4"
417
+ },
418
+ "source_file": "Mathlib/Algebra/Star/Pointwise.lean"
419
+ }
420
+ ],
421
+ "input_proofs": 26,
422
+ "input_units": 2,
423
+ "proofs": 9,
424
+ "published_proofs": 9,
425
+ "published_transitions": 14,
426
+ "replay_failures": [],
427
+ "transitions": 14,
428
+ "validation_failures": [],
429
+ "validation_rejected_proofs": 0,
430
+ "zero_transition_proofs": 0
431
+ },
432
+ "shards": [
433
+ {
434
+ "path": "data/train/mathlib-000340-0000-bee2466037256945.parquet",
435
+ "sha256": "bee24660372569457feb13582594fd3e6266225b2be75b1202f0d0f92ae1b7cb",
436
+ "bytes": 49227,
437
+ "rows": 12,
438
+ "revision": "4dbd9775daba0af0fd6fdd456fb509b76555ebbc"
439
+ },
440
+ {
441
+ "path": "data/internal_test/mathlib-000340-0000-a886d3bd7e3ad428.parquet",
442
+ "sha256": "a886d3bd7e3ad428b910193f0a55f24a6fcc64f0dcd812898c19d39e5fbad829",
443
+ "bytes": 47793,
444
+ "rows": 2,
445
+ "revision": "4dbd9775daba0af0fd6fdd456fb509b76555ebbc"
446
+ }
447
+ ],
448
+ "proof_ids": [
449
+ "mathlib:Function.star_sum_elim",
450
+ "mathlib:Set.image_star",
451
+ "mathlib:Set.star_add",
452
+ "mathlib:Set.star_inv",
453
+ "mathlib:Set.star_inv'",
454
+ "mathlib:Set.star_mem_star",
455
+ "mathlib:Set.star_mul",
456
+ "mathlib:Set.star_singleton",
457
+ "mathlib:Set.star_subset"
458
+ ],
459
+ "proof_keys": [
460
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/Pi.lean\",null,null,\"Function.star_sum_elim\"]",
461
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/Pointwise.lean\",null,null,\"Set.image_star\"]",
462
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/Pointwise.lean\",null,null,\"Set.star_add\"]",
463
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/Pointwise.lean\",null,null,\"Set.star_inv\"]",
464
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/Pointwise.lean\",null,null,\"Set.star_inv'\"]",
465
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/Pointwise.lean\",null,null,\"Set.star_mem_star\"]",
466
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/Pointwise.lean\",null,null,\"Set.star_mul\"]",
467
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/Pointwise.lean\",null,null,\"Set.star_singleton\"]",
468
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/Pointwise.lean\",null,null,\"Set.star_subset\"]"
469
+ ]
470
+ }
manifests/batches/mathlib/000341.json ADDED
@@ -0,0 +1,157 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000341",
4
+ "batch_fingerprint": "f2378249250f083ff8cb1ef484ae549d12cd9d540d72ed5e52a9f749db691139",
5
+ "evidence": {
6
+ "batch_fingerprint": "f2378249250f083ff8cb1ef484ae549d12cd9d540d72ed5e52a9f749db691139",
7
+ "batch_outcome": "all_inputs_failed_with_evidence",
8
+ "contamination_matches": [],
9
+ "failures": [
10
+ {
11
+ "error": "theorem has no selected tactic transitions",
12
+ "full_name": "Prod.fst_star",
13
+ "id": "Prod.fst_star",
14
+ "reason": "import_failure",
15
+ "selection": {
16
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
17
+ "end": [
18
+ 29,
19
+ 6
20
+ ],
21
+ "file_path": "Mathlib/Algebra/Star/Prod.lean",
22
+ "full_name": "Prod.fst_star",
23
+ "start": [
24
+ 28,
25
+ 1
26
+ ],
27
+ "traced_tactics": [],
28
+ "url": "https://github.com/leanprover-community/mathlib4"
29
+ },
30
+ "source_file": "Mathlib/Algebra/Star/Prod.lean"
31
+ },
32
+ {
33
+ "error": "theorem has no selected tactic transitions",
34
+ "full_name": "Prod.snd_star",
35
+ "id": "Prod.snd_star",
36
+ "reason": "import_failure",
37
+ "selection": {
38
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
39
+ "end": [
40
+ 34,
41
+ 6
42
+ ],
43
+ "file_path": "Mathlib/Algebra/Star/Prod.lean",
44
+ "full_name": "Prod.snd_star",
45
+ "start": [
46
+ 33,
47
+ 1
48
+ ],
49
+ "traced_tactics": [],
50
+ "url": "https://github.com/leanprover-community/mathlib4"
51
+ },
52
+ "source_file": "Mathlib/Algebra/Star/Prod.lean"
53
+ },
54
+ {
55
+ "error": "theorem has no selected tactic transitions",
56
+ "full_name": "Prod.star_def",
57
+ "id": "Prod.star_def",
58
+ "reason": "import_failure",
59
+ "selection": {
60
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
61
+ "end": [
62
+ 38,
63
+ 6
64
+ ],
65
+ "file_path": "Mathlib/Algebra/Star/Prod.lean",
66
+ "full_name": "Prod.star_def",
67
+ "start": [
68
+ 37,
69
+ 1
70
+ ],
71
+ "traced_tactics": [],
72
+ "url": "https://github.com/leanprover-community/mathlib4"
73
+ },
74
+ "source_file": "Mathlib/Algebra/Star/Prod.lean"
75
+ },
76
+ {
77
+ "error": "theorem has no selected tactic transitions",
78
+ "full_name": "Units.embed_product_star",
79
+ "id": "Units.embed_product_star",
80
+ "reason": "import_failure",
81
+ "selection": {
82
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
83
+ "end": [
84
+ 68,
85
+ 6
86
+ ],
87
+ "file_path": "Mathlib/Algebra/Star/Prod.lean",
88
+ "full_name": "Units.embed_product_star",
89
+ "start": [
90
+ 66,
91
+ 1
92
+ ],
93
+ "traced_tactics": [],
94
+ "url": "https://github.com/leanprover-community/mathlib4"
95
+ },
96
+ "source_file": "Mathlib/Algebra/Star/Prod.lean"
97
+ },
98
+ {
99
+ "error": "theorem has no selected tactic transitions",
100
+ "full_name": "star_nnratCast",
101
+ "id": "star_nnratCast",
102
+ "reason": "import_failure",
103
+ "selection": {
104
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
105
+ "end": [
106
+ 26,
107
+ 92
108
+ ],
109
+ "file_path": "Mathlib/Algebra/Star/Rat.lean",
110
+ "full_name": "star_nnratCast",
111
+ "start": [
112
+ 24,
113
+ 1
114
+ ],
115
+ "traced_tactics": [],
116
+ "url": "https://github.com/leanprover-community/mathlib4"
117
+ },
118
+ "source_file": "Mathlib/Algebra/Star/Rat.lean"
119
+ },
120
+ {
121
+ "error": "theorem has no selected tactic transitions",
122
+ "full_name": "star_ratCast",
123
+ "id": "star_ratCast",
124
+ "reason": "import_failure",
125
+ "selection": {
126
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
127
+ "end": [
128
+ 30,
129
+ 88
130
+ ],
131
+ "file_path": "Mathlib/Algebra/Star/Rat.lean",
132
+ "full_name": "star_ratCast",
133
+ "start": [
134
+ 29,
135
+ 1
136
+ ],
137
+ "traced_tactics": [],
138
+ "url": "https://github.com/leanprover-community/mathlib4"
139
+ },
140
+ "source_file": "Mathlib/Algebra/Star/Rat.lean"
141
+ }
142
+ ],
143
+ "input_proofs": 6,
144
+ "input_units": 2,
145
+ "proofs": 0,
146
+ "published_proofs": 0,
147
+ "published_transitions": 0,
148
+ "replay_failures": [],
149
+ "transitions": 0,
150
+ "validation_failures": [],
151
+ "validation_rejected_proofs": 0,
152
+ "zero_transition_proofs": 0
153
+ },
154
+ "shards": [],
155
+ "proof_ids": [],
156
+ "proof_keys": []
157
+ }
manifests/batches/mathlib/000342.json ADDED
@@ -0,0 +1,948 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000342",
4
+ "batch_fingerprint": "c6d71225f1264ed3d977bdfba2e7400b81a116ba2671683d323c9ccfe635311b",
5
+ "evidence": {
6
+ "batch_fingerprint": "c6d71225f1264ed3d977bdfba2e7400b81a116ba2671683d323c9ccfe635311b",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "no internal trace for tactic 'exact Rel.of (hr _ _ h)'",
11
+ "full_name": "RingQuot.Rel.star",
12
+ "id": "RingQuot.Rel.star",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 31,
18
+ 42
19
+ ],
20
+ "file_path": "Mathlib/Algebra/Star/RingQuot.lean",
21
+ "full_name": "RingQuot.Rel.star",
22
+ "start": [
23
+ 23,
24
+ 1
25
+ ],
26
+ "traced_tactics": [
27
+ {
28
+ "annotated_tactic": [
29
+ "\"induction h with\\n | <a>of<\\/a> h => exact <a>Rel.of<\\/a> (hr _ _ h)\\n | <a>add_left<\\/a> _ h => rw [<a>star_add<\\/a>, <a>star_add<\\/a>]\\n exact <a>Rel.add_left<\\/a> h\\n | <a>mul_left<\\/a> _ h => rw [<a>star_mul<\\/a>, <a>star_mul<\\/a>]\\n exact <a>Rel.mul_right<\\/a> h\\n | <a>mul_right<\\/a> _ h => rw [<a>star_mul<\\/a>, <a>star_mul<\\/a>]\\n exact <a>Rel.mul_left<\\/a> h\"",
30
+ "[{\"full_name\":\"RingQuot.Rel.of\",\"def_path\":\"Mathlib\\/Algebra\\/RingQuot.lean\",\"def_pos\":[58,5],\"def_end_pos\":[58,7]},{\"full_name\":\"RingQuot.Rel.of\",\"def_path\":\"Mathlib\\/Algebra\\/RingQuot.lean\",\"def_pos\":[58,5],\"def_end_pos\":[58,7]},{\"full_name\":\"RingQuot.Rel.add_left\",\"def_path\":\"Mathlib\\/Algebra\\/RingQuot.lean\",\"def_pos\":[59,5],\"def_end_pos\":[59,13]},{\"full_name\":\"StarAddMonoid.star_add\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[259,3],\"def_end_pos\":[259,11]},{\"full_name\":\"StarAddMonoid.star_add\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[259,3],\"def_end_pos\":[259,11]},{\"full_name\":\"RingQuot.Rel.add_left\",\"def_path\":\"Mathlib\\/Algebra\\/RingQuot.lean\",\"def_pos\":[59,5],\"def_end_pos\":[59,13]},{\"full_name\":\"RingQuot.Rel.mul_left\",\"def_path\":\"Mathlib\\/Algebra\\/RingQuot.lean\",\"def_pos\":[60,5],\"def_end_pos\":[60,13]},{\"full_name\":\"StarMul.star_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[138,3],\"def_end_pos\":[138,11]},{\"full_name\":\"StarMul.star_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[138,3],\"def_end_pos\":[138,11]},{\"full_name\":\"RingQuot.Rel.mul_right\",\"def_path\":\"Mathlib\\/Algebra\\/RingQuot.lean\",\"def_pos\":[61,5],\"def_end_pos\":[61,14]},{\"full_name\":\"RingQuot.Rel.mul_right\",\"def_path\":\"Mathlib\\/Algebra\\/RingQuot.lean\",\"def_pos\":[61,5],\"def_end_pos\":[61,14]},{\"full_name\":\"StarMul.star_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[138,3],\"def_end_pos\":[138,11]},{\"full_name\":\"StarMul.star_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[138,3],\"def_end_pos\":[138,11]},{\"full_name\":\"RingQuot.Rel.mul_left\",\"def_path\":\"Mathlib\\/Algebra\\/RingQuot.lean\",\"def_pos\":[60,5],\"def_end_pos\":[60,13]}]"
31
+ ],
32
+ "state_after": "no goals",
33
+ "state_before": "R : Type u\ninst\u271d\u00b9 : Semiring R\nr : R \u2192 R \u2192 Prop\ninst\u271d : StarRing R\nhr : \u2200 (a b : R), r a b \u2192 r (Star.star a) (Star.star b)\na b : R\nh : Rel r a b\n\u22a2 Rel r (Star.star a) (Star.star b)",
34
+ "tactic": "induction h with\n| of h => exact Rel.of (hr _ _ h)\n| add_left _ h => rw [star_add, star_add]\n exact Rel.add_left h\n| mul_left _ h => rw [star_mul, star_mul]\n exact Rel.mul_right h\n| mul_right _ h => rw [star_mul, star_mul]\n exact Rel.mul_left h"
35
+ },
36
+ {
37
+ "annotated_tactic": [
38
+ "\"exact <a>Rel.of<\\/a> (hr _ _ h)\"",
39
+ "[{\"full_name\":\"RingQuot.Rel.of\",\"def_path\":\"Mathlib\\/Algebra\\/RingQuot.lean\",\"def_pos\":[58,5],\"def_end_pos\":[58,7]}]"
40
+ ],
41
+ "state_after": "no goals",
42
+ "state_before": "case of\nR : Type u\ninst\u271d\u00b9 : Semiring R\nr : R \u2192 R \u2192 Prop\ninst\u271d : StarRing R\nhr : \u2200 (a b : R), r a b \u2192 r (Star.star a) (Star.star b)\na b x\u271d y\u271d : R\nh : r x\u271d y\u271d\n\u22a2 Rel r (Star.star x\u271d) (Star.star y\u271d)",
43
+ "tactic": "exact Rel.of (hr _ _ h)"
44
+ },
45
+ {
46
+ "annotated_tactic": [
47
+ "\"rw [<a>star_add<\\/a>, <a>star_add<\\/a>]\"",
48
+ "[{\"full_name\":\"StarAddMonoid.star_add\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[259,3],\"def_end_pos\":[259,11]},{\"full_name\":\"StarAddMonoid.star_add\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[259,3],\"def_end_pos\":[259,11]}]"
49
+ ],
50
+ "state_after": "case add_left\nR : Type u\ninst\u271d\u00b9 : Semiring R\nr : R \u2192 R \u2192 Prop\ninst\u271d : StarRing R\nhr : \u2200 (a b : R), r a b \u2192 r (Star.star a) (Star.star b)\na b a\u271d\u00b9 b\u271d c\u271d : R\na\u271d : Rel r a\u271d\u00b9 b\u271d\nh : Rel r (Star.star a\u271d\u00b9) (Star.star b\u271d)\n\u22a2 Rel r (Star.star a\u271d\u00b9 + Star.star c\u271d) (Star.star b\u271d + Star.star c\u271d)",
51
+ "state_before": "case add_left\nR : Type u\ninst\u271d\u00b9 : Semiring R\nr : R \u2192 R \u2192 Prop\ninst\u271d : StarRing R\nhr : \u2200 (a b : R), r a b \u2192 r (Star.star a) (Star.star b)\na b a\u271d\u00b9 b\u271d c\u271d : R\na\u271d : Rel r a\u271d\u00b9 b\u271d\nh : Rel r (Star.star a\u271d\u00b9) (Star.star b\u271d)\n\u22a2 Rel r (Star.star (a\u271d\u00b9 + c\u271d)) (Star.star (b\u271d + c\u271d))",
52
+ "tactic": "rw [star_add, star_add]"
53
+ },
54
+ {
55
+ "annotated_tactic": [
56
+ "\"exact <a>Rel.add_left<\\/a> h\"",
57
+ "[{\"full_name\":\"RingQuot.Rel.add_left\",\"def_path\":\"Mathlib\\/Algebra\\/RingQuot.lean\",\"def_pos\":[59,5],\"def_end_pos\":[59,13]}]"
58
+ ],
59
+ "state_after": "no goals",
60
+ "state_before": "case add_left\nR : Type u\ninst\u271d\u00b9 : Semiring R\nr : R \u2192 R \u2192 Prop\ninst\u271d : StarRing R\nhr : \u2200 (a b : R), r a b \u2192 r (Star.star a) (Star.star b)\na b a\u271d\u00b9 b\u271d c\u271d : R\na\u271d : Rel r a\u271d\u00b9 b\u271d\nh : Rel r (Star.star a\u271d\u00b9) (Star.star b\u271d)\n\u22a2 Rel r (Star.star a\u271d\u00b9 + Star.star c\u271d) (Star.star b\u271d + Star.star c\u271d)",
61
+ "tactic": "exact Rel.add_left h"
62
+ },
63
+ {
64
+ "annotated_tactic": [
65
+ "\"rw [<a>star_mul<\\/a>, <a>star_mul<\\/a>]\"",
66
+ "[{\"full_name\":\"StarMul.star_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[138,3],\"def_end_pos\":[138,11]},{\"full_name\":\"StarMul.star_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[138,3],\"def_end_pos\":[138,11]}]"
67
+ ],
68
+ "state_after": "case mul_left\nR : Type u\ninst\u271d\u00b9 : Semiring R\nr : R \u2192 R \u2192 Prop\ninst\u271d : StarRing R\nhr : \u2200 (a b : R), r a b \u2192 r (Star.star a) (Star.star b)\na b a\u271d\u00b9 b\u271d c\u271d : R\na\u271d : Rel r a\u271d\u00b9 b\u271d\nh : Rel r (Star.star a\u271d\u00b9) (Star.star b\u271d)\n\u22a2 Rel r (Star.star c\u271d * Star.star a\u271d\u00b9) (Star.star c\u271d * Star.star b\u271d)",
69
+ "state_before": "case mul_left\nR : Type u\ninst\u271d\u00b9 : Semiring R\nr : R \u2192 R \u2192 Prop\ninst\u271d : StarRing R\nhr : \u2200 (a b : R), r a b \u2192 r (Star.star a) (Star.star b)\na b a\u271d\u00b9 b\u271d c\u271d : R\na\u271d : Rel r a\u271d\u00b9 b\u271d\nh : Rel r (Star.star a\u271d\u00b9) (Star.star b\u271d)\n\u22a2 Rel r (Star.star (a\u271d\u00b9 * c\u271d)) (Star.star (b\u271d * c\u271d))",
70
+ "tactic": "rw [star_mul, star_mul]"
71
+ },
72
+ {
73
+ "annotated_tactic": [
74
+ "\"exact <a>Rel.mul_right<\\/a> h\"",
75
+ "[{\"full_name\":\"RingQuot.Rel.mul_right\",\"def_path\":\"Mathlib\\/Algebra\\/RingQuot.lean\",\"def_pos\":[61,5],\"def_end_pos\":[61,14]}]"
76
+ ],
77
+ "state_after": "no goals",
78
+ "state_before": "case mul_left\nR : Type u\ninst\u271d\u00b9 : Semiring R\nr : R \u2192 R \u2192 Prop\ninst\u271d : StarRing R\nhr : \u2200 (a b : R), r a b \u2192 r (Star.star a) (Star.star b)\na b a\u271d\u00b9 b\u271d c\u271d : R\na\u271d : Rel r a\u271d\u00b9 b\u271d\nh : Rel r (Star.star a\u271d\u00b9) (Star.star b\u271d)\n\u22a2 Rel r (Star.star c\u271d * Star.star a\u271d\u00b9) (Star.star c\u271d * Star.star b\u271d)",
79
+ "tactic": "exact Rel.mul_right h"
80
+ },
81
+ {
82
+ "annotated_tactic": [
83
+ "\"rw [<a>star_mul<\\/a>, <a>star_mul<\\/a>]\"",
84
+ "[{\"full_name\":\"StarMul.star_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[138,3],\"def_end_pos\":[138,11]},{\"full_name\":\"StarMul.star_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Star\\/Basic.lean\",\"def_pos\":[138,3],\"def_end_pos\":[138,11]}]"
85
+ ],
86
+ "state_after": "case mul_right\nR : Type u\ninst\u271d\u00b9 : Semiring R\nr : R \u2192 R \u2192 Prop\ninst\u271d : StarRing R\nhr : \u2200 (a b : R), r a b \u2192 r (Star.star a) (Star.star b)\na b a\u271d\u00b9 b\u271d c\u271d : R\na\u271d : Rel r b\u271d c\u271d\nh : Rel r (Star.star b\u271d) (Star.star c\u271d)\n\u22a2 Rel r (Star.star b\u271d * Star.star a\u271d\u00b9) (Star.star c\u271d * Star.star a\u271d\u00b9)",
87
+ "state_before": "case mul_right\nR : Type u\ninst\u271d\u00b9 : Semiring R\nr : R \u2192 R \u2192 Prop\ninst\u271d : StarRing R\nhr : \u2200 (a b : R), r a b \u2192 r (Star.star a) (Star.star b)\na b a\u271d\u00b9 b\u271d c\u271d : R\na\u271d : Rel r b\u271d c\u271d\nh : Rel r (Star.star b\u271d) (Star.star c\u271d)\n\u22a2 Rel r (Star.star (a\u271d\u00b9 * b\u271d)) (Star.star (a\u271d\u00b9 * c\u271d))",
88
+ "tactic": "rw [star_mul, star_mul]"
89
+ },
90
+ {
91
+ "annotated_tactic": [
92
+ "\"exact <a>Rel.mul_left<\\/a> h\"",
93
+ "[{\"full_name\":\"RingQuot.Rel.mul_left\",\"def_path\":\"Mathlib\\/Algebra\\/RingQuot.lean\",\"def_pos\":[60,5],\"def_end_pos\":[60,13]}]"
94
+ ],
95
+ "state_after": "no goals",
96
+ "state_before": "case mul_right\nR : Type u\ninst\u271d\u00b9 : Semiring R\nr : R \u2192 R \u2192 Prop\ninst\u271d : StarRing R\nhr : \u2200 (a b : R), r a b \u2192 r (Star.star a) (Star.star b)\na b a\u271d\u00b9 b\u271d c\u271d : R\na\u271d : Rel r b\u271d c\u271d\nh : Rel r (Star.star b\u271d) (Star.star c\u271d)\n\u22a2 Rel r (Star.star b\u271d * Star.star a\u271d\u00b9) (Star.star c\u271d * Star.star a\u271d\u00b9)",
97
+ "tactic": "exact Rel.mul_left h"
98
+ }
99
+ ],
100
+ "url": "https://github.com/leanprover-community/mathlib4"
101
+ },
102
+ "source_file": "Mathlib/Algebra/Star/RingQuot.lean"
103
+ },
104
+ {
105
+ "error": "theorem has no selected tactic transitions",
106
+ "full_name": "RingQuot.star'_quot",
107
+ "id": "RingQuot.star'_quot",
108
+ "reason": "import_failure",
109
+ "selection": {
110
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
111
+ "end": [
112
+ 38,
113
+ 86
114
+ ],
115
+ "file_path": "Mathlib/Algebra/Star/RingQuot.lean",
116
+ "full_name": "RingQuot.star'_quot",
117
+ "start": [
118
+ 37,
119
+ 1
120
+ ],
121
+ "traced_tactics": [],
122
+ "url": "https://github.com/leanprover-community/mathlib4"
123
+ },
124
+ "source_file": "Mathlib/Algebra/Star/RingQuot.lean"
125
+ },
126
+ {
127
+ "error": "theorem has no selected tactic transitions",
128
+ "full_name": "IsSelfAdjoint.all",
129
+ "id": "IsSelfAdjoint.all",
130
+ "reason": "import_failure",
131
+ "selection": {
132
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
133
+ "end": [
134
+ 71,
135
+ 17
136
+ ],
137
+ "file_path": "Mathlib/Algebra/Star/SelfAdjoint.lean",
138
+ "full_name": "IsSelfAdjoint.all",
139
+ "start": [
140
+ 70,
141
+ 1
142
+ ],
143
+ "traced_tactics": [],
144
+ "url": "https://github.com/leanprover-community/mathlib4"
145
+ },
146
+ "source_file": "Mathlib/Algebra/Star/SelfAdjoint.lean"
147
+ },
148
+ {
149
+ "error": "theorem has no selected tactic transitions",
150
+ "full_name": "IsSelfAdjoint.conj_eq",
151
+ "id": "IsSelfAdjoint.conj_eq",
152
+ "reason": "import_failure",
153
+ "selection": {
154
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
155
+ "end": [
156
+ 244,
157
+ 64
158
+ ],
159
+ "file_path": "Mathlib/Algebra/Star/SelfAdjoint.lean",
160
+ "full_name": "IsSelfAdjoint.conj_eq",
161
+ "start": [
162
+ 244,
163
+ 1
164
+ ],
165
+ "traced_tactics": [],
166
+ "url": "https://github.com/leanprover-community/mathlib4"
167
+ },
168
+ "source_file": "Mathlib/Algebra/Star/SelfAdjoint.lean"
169
+ },
170
+ {
171
+ "error": "theorem has no selected tactic transitions",
172
+ "full_name": "IsSelfAdjoint.intCast",
173
+ "id": "IsSelfAdjoint.intCast",
174
+ "reason": "import_failure",
175
+ "selection": {
176
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
177
+ "end": [
178
+ 254,
179
+ 17
180
+ ],
181
+ "file_path": "Mathlib/Algebra/Star/SelfAdjoint.lean",
182
+ "full_name": "IsSelfAdjoint.intCast",
183
+ "start": [
184
+ 253,
185
+ 11
186
+ ],
187
+ "traced_tactics": [],
188
+ "url": "https://github.com/leanprover-community/mathlib4"
189
+ },
190
+ "source_file": "Mathlib/Algebra/Star/SelfAdjoint.lean"
191
+ },
192
+ {
193
+ "error": "theorem has no selected tactic transitions",
194
+ "full_name": "IsSelfAdjoint.natCast",
195
+ "id": "IsSelfAdjoint.natCast",
196
+ "reason": "import_failure",
197
+ "selection": {
198
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
199
+ "end": [
200
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+ {
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+ },
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+ {
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851
+ ],
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853
+ "state_before": "case refine_1\nR\u271d : Type u_1\nA : Type u_2\nR : Type u_3\ninst\u271d\u00b9 : Mul R\ninst\u271d : StarMul R\nx y : R\nhx : IsSelfAdjoint x\nhy : IsSelfAdjoint y\nh : Commute x y\n\u22a2 IsSelfAdjoint (x * y)",
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856
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857
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+ "\"simpa only [<a>star_mul<\\/a>, hx.star_eq, hy.star_eq] using h.symm\"",
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860
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861
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862
+ "state_before": "case refine_2\nR\u271d : Type u_1\nA : Type u_2\nR : Type u_3\ninst\u271d\u00b9 : Mul R\ninst\u271d : StarMul R\nx y : R\nhx : IsSelfAdjoint x\nhy : IsSelfAdjoint y\nh : IsSelfAdjoint (x * y)\n\u22a2 Commute x y",
863
+ "tactic": "simpa only [star_mul, hx.star_eq, hy.star_eq] using h.symm"
864
+ }
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+ "url": "https://github.com/leanprover-community/mathlib4"
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+ }
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+ },
869
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870
+ }
871
+ ],
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+ "mathlib:IsSelfAdjoint.add_star_self",
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+ "mathlib:IsSelfAdjoint.conjugate",
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+ "mathlib:IsSelfAdjoint.sub",
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920
+ "mathlib:skewAdjoint.mem_iff",
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+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/SelfAdjoint.lean\",null,null,\"IsSelfAdjoint.neg\"]",
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+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/SelfAdjoint.lean\",null,null,\"IsSelfAdjoint.star_iff\"]",
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946
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/SelfAdjoint.lean\",null,null,\"skewAdjoint.smul_mem\"]"
947
+ ]
948
+ }
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1
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7
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9
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10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "NonUnitalStarAlgHom.coe_coe",
12
+ "id": "NonUnitalStarAlgHom.coe_coe",
13
+ "reason": "import_failure",
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25
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26
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27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/Algebra/Star/StarAlgHom.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "NonUnitalStarAlgHom.coe_comp",
34
+ "id": "NonUnitalStarAlgHom.coe_comp",
35
+ "reason": "import_failure",
36
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50
+ },
51
+ "source_file": "Mathlib/Algebra/Star/StarAlgHom.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "NonUnitalStarAlgHom.coe_copy",
56
+ "id": "NonUnitalStarAlgHom.coe_copy",
57
+ "reason": "import_failure",
58
+ "selection": {
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66
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+ ],
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+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/Algebra/Star/StarAlgHom.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
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+ "reason": "import_failure",
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1899
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1968
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2030
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+ "error": "theorem has no selected tactic transitions",
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2052
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+ {
2069
+ "path": "data/train/mathlib-000343-0000-42bff448f7e59230.parquet",
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+ "sha256": "42bff448f7e59230599470657a36cd6919e124d0e1bb043160dd29493f0fff32",
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+ "bytes": 115761,
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+ "revision": "4dbd9775daba0af0fd6fdd456fb509b76555ebbc"
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+ }
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+ ],
2076
+ "proof_ids": [
2077
+ "mathlib:NonUnitalStarAlgHom.fst_prod",
2078
+ "mathlib:NonUnitalStarAlgHom.mk_coe",
2079
+ "mathlib:NonUnitalStarAlgHom.snd_prod",
2080
+ "mathlib:NonUnitalStarRingHom.mk_coe",
2081
+ "mathlib:StarAlgEquiv.symm_symm",
2082
+ "mathlib:StarAlgHom.fst_prod",
2083
+ "mathlib:StarAlgHom.mk_coe",
2084
+ "mathlib:StarAlgHom.snd_prod",
2085
+ "mathlib:StarRingEquiv.symm_symm"
2086
+ ],
2087
+ "proof_keys": [
2088
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/StarAlgHom.lean\",null,null,\"NonUnitalStarAlgHom.fst_prod\"]",
2089
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/StarAlgHom.lean\",null,null,\"NonUnitalStarAlgHom.mk_coe\"]",
2090
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/StarAlgHom.lean\",null,null,\"NonUnitalStarAlgHom.snd_prod\"]",
2091
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/StarAlgHom.lean\",null,null,\"StarAlgEquiv.symm_symm\"]",
2092
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/StarAlgHom.lean\",null,null,\"StarAlgHom.fst_prod\"]",
2093
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/StarAlgHom.lean\",null,null,\"StarAlgHom.mk_coe\"]",
2094
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/StarAlgHom.lean\",null,null,\"StarAlgHom.snd_prod\"]",
2095
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/StarRingHom.lean\",null,null,\"NonUnitalStarRingHom.mk_coe\"]",
2096
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Star/StarRingHom.lean\",null,null,\"StarRingEquiv.symm_symm\"]"
2097
+ ]
2098
+ }
manifests/batches/mathlib/000344.json ADDED
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manifests/batches/mathlib/000345.json ADDED
The diff for this file is too large to render. See raw diff
 
manifests/batches/mathlib/000346.json ADDED
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1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000346",
4
+ "batch_fingerprint": "6fb3c3451104b27db80643cc0bd68e8378e7f767ee2212c68d2bab460724ac0f",
5
+ "evidence": {
6
+ "batch_fingerprint": "6fb3c3451104b27db80643cc0bd68e8378e7f767ee2212c68d2bab460724ac0f",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "Tropical.add_self",
12
+ "id": "Tropical.add_self",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 347,
18
+ 41
19
+ ],
20
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
21
+ "full_name": "Tropical.add_self",
22
+ "start": [
23
+ 346,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "Tropical.bit0",
34
+ "id": "Tropical.bit0",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 353,
40
+ 13
41
+ ],
42
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
43
+ "full_name": "Tropical.bit0",
44
+ "start": [
45
+ 352,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "Tropical.injective_trop",
56
+ "id": "Tropical.injective_trop",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 141,
62
+ 22
63
+ ],
64
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
65
+ "full_name": "Tropical.injective_trop",
66
+ "start": [
67
+ 140,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "Tropical.injective_untrop",
78
+ "id": "Tropical.injective_untrop",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 145,
84
+ 27
85
+ ],
86
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
87
+ "full_name": "Tropical.injective_untrop",
88
+ "start": [
89
+ 144,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "Tropical.le_zero",
100
+ "id": "Tropical.le_zero",
101
+ "reason": "import_failure",
102
+ "selection": {
103
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
104
+ "end": [
105
+ 252,
106
+ 18
107
+ ],
108
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
109
+ "full_name": "Tropical.le_zero",
110
+ "start": [
111
+ 251,
112
+ 1
113
+ ],
114
+ "traced_tactics": [],
115
+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
118
+ },
119
+ {
120
+ "error": "theorem has no selected tactic transitions",
121
+ "full_name": "Tropical.leftInverse_trop",
122
+ "id": "Tropical.leftInverse_trop",
123
+ "reason": "import_failure",
124
+ "selection": {
125
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
126
+ "end": [
127
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128
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129
+ ],
130
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
131
+ "full_name": "Tropical.leftInverse_trop",
132
+ "start": [
133
+ 105,
134
+ 1
135
+ ],
136
+ "traced_tactics": [],
137
+ "url": "https://github.com/leanprover-community/mathlib4"
138
+ },
139
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
140
+ },
141
+ {
142
+ "error": "theorem has no selected tactic transitions",
143
+ "full_name": "Tropical.min_eq_add",
144
+ "id": "Tropical.min_eq_add",
145
+ "reason": "import_failure",
146
+ "selection": {
147
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
148
+ "end": [
149
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150
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151
+ ],
152
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
153
+ "full_name": "Tropical.min_eq_add",
154
+ "start": [
155
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156
+ 1
157
+ ],
158
+ "traced_tactics": [],
159
+ "url": "https://github.com/leanprover-community/mathlib4"
160
+ },
161
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
162
+ },
163
+ {
164
+ "error": "theorem has no selected tactic transitions",
165
+ "full_name": "Tropical.surjective_trop",
166
+ "id": "Tropical.surjective_trop",
167
+ "reason": "import_failure",
168
+ "selection": {
169
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
170
+ "end": [
171
+ 149,
172
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173
+ ],
174
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
175
+ "full_name": "Tropical.surjective_trop",
176
+ "start": [
177
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178
+ 1
179
+ ],
180
+ "traced_tactics": [],
181
+ "url": "https://github.com/leanprover-community/mathlib4"
182
+ },
183
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
184
+ },
185
+ {
186
+ "error": "theorem has no selected tactic transitions",
187
+ "full_name": "Tropical.surjective_untrop",
188
+ "id": "Tropical.surjective_untrop",
189
+ "reason": "import_failure",
190
+ "selection": {
191
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
192
+ "end": [
193
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194
+ 28
195
+ ],
196
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
197
+ "full_name": "Tropical.surjective_untrop",
198
+ "start": [
199
+ 152,
200
+ 1
201
+ ],
202
+ "traced_tactics": [],
203
+ "url": "https://github.com/leanprover-community/mathlib4"
204
+ },
205
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
206
+ },
207
+ {
208
+ "error": "theorem has no selected tactic transitions",
209
+ "full_name": "Tropical.tropEquiv_coe_fn",
210
+ "id": "Tropical.tropEquiv_coe_fn",
211
+ "reason": "import_failure",
212
+ "selection": {
213
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
214
+ "end": [
215
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216
+ 6
217
+ ],
218
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
219
+ "full_name": "Tropical.tropEquiv_coe_fn",
220
+ "start": [
221
+ 123,
222
+ 1
223
+ ],
224
+ "traced_tactics": [],
225
+ "url": "https://github.com/leanprover-community/mathlib4"
226
+ },
227
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
228
+ },
229
+ {
230
+ "error": "theorem has no selected tactic transitions",
231
+ "full_name": "Tropical.tropEquiv_symm_coe_fn",
232
+ "id": "Tropical.tropEquiv_symm_coe_fn",
233
+ "reason": "import_failure",
234
+ "selection": {
235
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
236
+ "end": [
237
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238
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239
+ ],
240
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
241
+ "full_name": "Tropical.tropEquiv_symm_coe_fn",
242
+ "start": [
243
+ 128,
244
+ 1
245
+ ],
246
+ "traced_tactics": [],
247
+ "url": "https://github.com/leanprover-community/mathlib4"
248
+ },
249
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
250
+ },
251
+ {
252
+ "error": "theorem has no selected tactic transitions",
253
+ "full_name": "Tropical.tropOrderIso_coe_fn",
254
+ "id": "Tropical.tropOrderIso_coe_fn",
255
+ "reason": "import_failure",
256
+ "selection": {
257
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
258
+ "end": [
259
+ 207,
260
+ 6
261
+ ],
262
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
263
+ "full_name": "Tropical.tropOrderIso_coe_fn",
264
+ "start": [
265
+ 206,
266
+ 1
267
+ ],
268
+ "traced_tactics": [],
269
+ "url": "https://github.com/leanprover-community/mathlib4"
270
+ },
271
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
272
+ },
273
+ {
274
+ "error": "theorem has no selected tactic transitions",
275
+ "full_name": "Tropical.tropOrderIso_symm_coe_fn",
276
+ "id": "Tropical.tropOrderIso_symm_coe_fn",
277
+ "reason": "import_failure",
278
+ "selection": {
279
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
280
+ "end": [
281
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282
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283
+ ],
284
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
285
+ "full_name": "Tropical.tropOrderIso_symm_coe_fn",
286
+ "start": [
287
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288
+ 1
289
+ ],
290
+ "traced_tactics": [],
291
+ "url": "https://github.com/leanprover-community/mathlib4"
292
+ },
293
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
294
+ },
295
+ {
296
+ "error": "theorem has no selected tactic transitions",
297
+ "full_name": "Tropical.trop_add",
298
+ "id": "Tropical.trop_add",
299
+ "reason": "import_failure",
300
+ "selection": {
301
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
302
+ "end": [
303
+ 388,
304
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305
+ ],
306
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
307
+ "full_name": "Tropical.trop_add",
308
+ "start": [
309
+ 387,
310
+ 1
311
+ ],
312
+ "traced_tactics": [],
313
+ "url": "https://github.com/leanprover-community/mathlib4"
314
+ },
315
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
316
+ },
317
+ {
318
+ "error": "theorem has no selected tactic transitions",
319
+ "full_name": "Tropical.trop_add_def",
320
+ "id": "Tropical.trop_add_def",
321
+ "reason": "import_failure",
322
+ "selection": {
323
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
324
+ "end": [
325
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326
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327
+ ],
328
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
329
+ "full_name": "Tropical.trop_add_def",
330
+ "start": [
331
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332
+ 1
333
+ ],
334
+ "traced_tactics": [],
335
+ "url": "https://github.com/leanprover-community/mathlib4"
336
+ },
337
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
338
+ },
339
+ {
340
+ "error": "theorem has no selected tactic transitions",
341
+ "full_name": "Tropical.trop_coe_ne_zero",
342
+ "id": "Tropical.trop_coe_ne_zero",
343
+ "reason": "import_failure",
344
+ "selection": {
345
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
346
+ "end": [
347
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348
+ 8
349
+ ],
350
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
351
+ "full_name": "Tropical.trop_coe_ne_zero",
352
+ "start": [
353
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354
+ 1
355
+ ],
356
+ "traced_tactics": [],
357
+ "url": "https://github.com/leanprover-community/mathlib4"
358
+ },
359
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
360
+ },
361
+ {
362
+ "error": "theorem has no selected tactic transitions",
363
+ "full_name": "Tropical.trop_eq_iff_eq_untrop",
364
+ "id": "Tropical.trop_eq_iff_eq_untrop",
365
+ "reason": "import_failure",
366
+ "selection": {
367
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
368
+ "end": [
369
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370
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371
+ ],
372
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
373
+ "full_name": "Tropical.trop_eq_iff_eq_untrop",
374
+ "start": [
375
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376
+ 1
377
+ ],
378
+ "traced_tactics": [],
379
+ "url": "https://github.com/leanprover-community/mathlib4"
380
+ },
381
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
382
+ },
383
+ {
384
+ "error": "theorem has no selected tactic transitions",
385
+ "full_name": "Tropical.trop_inf",
386
+ "id": "Tropical.trop_inf",
387
+ "reason": "import_failure",
388
+ "selection": {
389
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
390
+ "end": [
391
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392
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393
+ ],
394
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
395
+ "full_name": "Tropical.trop_inf",
396
+ "start": [
397
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398
+ 1
399
+ ],
400
+ "traced_tactics": [],
401
+ "url": "https://github.com/leanprover-community/mathlib4"
402
+ },
403
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
404
+ },
405
+ {
406
+ "error": "theorem has no selected tactic transitions",
407
+ "full_name": "Tropical.trop_inj_iff",
408
+ "id": "Tropical.trop_inj_iff",
409
+ "reason": "import_failure",
410
+ "selection": {
411
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
412
+ "end": [
413
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414
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415
+ ],
416
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
417
+ "full_name": "Tropical.trop_inj_iff",
418
+ "start": [
419
+ 83,
420
+ 1
421
+ ],
422
+ "traced_tactics": [],
423
+ "url": "https://github.com/leanprover-community/mathlib4"
424
+ },
425
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
426
+ },
427
+ {
428
+ "error": "theorem has no selected tactic transitions",
429
+ "full_name": "Tropical.trop_injective",
430
+ "id": "Tropical.trop_injective",
431
+ "reason": "import_failure",
432
+ "selection": {
433
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
434
+ "end": [
435
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436
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437
+ ],
438
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
439
+ "full_name": "Tropical.trop_injective",
440
+ "start": [
441
+ 76,
442
+ 1
443
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1008
+ 6
1009
+ ],
1010
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
1011
+ "full_name": "Tropical.untrop_zero",
1012
+ "start": [
1013
+ 231,
1014
+ 1
1015
+ ],
1016
+ "traced_tactics": [],
1017
+ "url": "https://github.com/leanprover-community/mathlib4"
1018
+ },
1019
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
1020
+ },
1021
+ {
1022
+ "error": "theorem has no selected tactic transitions",
1023
+ "full_name": "Tropical.untrop_zpow",
1024
+ "id": "Tropical.untrop_zpow",
1025
+ "reason": "import_failure",
1026
+ "selection": {
1027
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1028
+ "end": [
1029
+ 494,
1030
+ 6
1031
+ ],
1032
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
1033
+ "full_name": "Tropical.untrop_zpow",
1034
+ "start": [
1035
+ 493,
1036
+ 1
1037
+ ],
1038
+ "traced_tactics": [],
1039
+ "url": "https://github.com/leanprover-community/mathlib4"
1040
+ },
1041
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
1042
+ },
1043
+ {
1044
+ "error": "theorem has no selected tactic transitions",
1045
+ "full_name": "Tropical.zero_ne_trop_coe",
1046
+ "id": "Tropical.zero_ne_trop_coe",
1047
+ "reason": "import_failure",
1048
+ "selection": {
1049
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1050
+ "end": [
1051
+ 247,
1052
+ 8
1053
+ ],
1054
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
1055
+ "full_name": "Tropical.zero_ne_trop_coe",
1056
+ "start": [
1057
+ 246,
1058
+ 1
1059
+ ],
1060
+ "traced_tactics": [],
1061
+ "url": "https://github.com/leanprover-community/mathlib4"
1062
+ },
1063
+ "source_file": "Mathlib/Algebra/Tropical/Basic.lean"
1064
+ },
1065
+ {
1066
+ "error": "no internal trace for tactic 'simp only [Set.image_empty, coe_empty, sum_empty, WithTop.sInf_empty, trop_top]'",
1067
+ "full_name": "trop_sInf_image",
1068
+ "id": "trop_sInf_image",
1069
+ "reason": "import_failure",
1070
+ "selection": {
1071
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1072
+ "end": [
1073
+ 103,
1074
+ 58
1075
+ ],
1076
+ "file_path": "Mathlib/Algebra/Tropical/BigOperators.lean",
1077
+ "full_name": "trop_sInf_image",
1078
+ "start": [
1079
+ 99,
1080
+ 1
1081
+ ],
1082
+ "traced_tactics": [
1083
+ {
1084
+ "annotated_tactic": [
1085
+ "\"rcases s.eq_empty_or_nonempty with (rfl | h)\"",
1086
+ "[]"
1087
+ ],
1088
+ "state_after": "case inl\nR : Type u_1\nS : Type u_2\ninst\u271d : ConditionallyCompleteLinearOrder R\nf : S \u2192 WithTop R\n\u22a2 trop (sInf (f '' \u2191\u2205)) = \u2211 i \u2208 \u2205, trop (f i)\n\ncase inr\nR : Type u_1\nS : Type u_2\ninst\u271d : ConditionallyCompleteLinearOrder R\ns : Finset S\nf : S \u2192 WithTop R\nh : s.Nonempty\n\u22a2 trop (sInf (f '' \u2191s)) = \u2211 i \u2208 s, trop (f i)",
1089
+ "state_before": "R : Type u_1\nS : Type u_2\ninst\u271d : ConditionallyCompleteLinearOrder R\ns : Finset S\nf : S \u2192 WithTop R\n\u22a2 trop (sInf (f '' \u2191s)) = \u2211 i \u2208 s, trop (f i)",
1090
+ "tactic": "rcases s.eq_empty_or_nonempty with (rfl | h)"
1091
+ },
1092
+ {
1093
+ "annotated_tactic": [
1094
+ "\"rw [\\u2190 <a>inf'_eq_csInf_image<\\/a> _ h, <a>inf'_eq_inf<\\/a>, s.trop_inf]\"",
1095
+ "[{\"full_name\":\"Finset.inf'_eq_csInf_image\",\"def_path\":\"Mathlib\\/Order\\/ConditionallyCompleteLattice\\/Finset.lean\",\"def_pos\":[80,9],\"def_end_pos\":[80,28]},{\"full_name\":\"Finset.inf'_eq_inf\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Lattice.lean\",\"def_pos\":[1198,9],\"def_end_pos\":[1198,20]}]"
1096
+ ],
1097
+ "state_after": "no goals",
1098
+ "state_before": "case inr\nR : Type u_1\nS : Type u_2\ninst\u271d : ConditionallyCompleteLinearOrder R\ns : Finset S\nf : S \u2192 WithTop R\nh : s.Nonempty\n\u22a2 trop (sInf (f '' \u2191s)) = \u2211 i \u2208 s, trop (f i)",
1099
+ "tactic": "rw [\u2190 inf'_eq_csInf_image _ h, inf'_eq_inf, s.trop_inf]"
1100
+ },
1101
+ {
1102
+ "annotated_tactic": [
1103
+ "\"simp only [<a>Set.image_empty<\\/a>, <a>coe_empty<\\/a>, <a>sum_empty<\\/a>, <a>WithTop.sInf_empty<\\/a>, <a>trop_top<\\/a>]\"",
1104
+ "[{\"full_name\":\"Set.image_empty\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Image.lean\",\"def_pos\":[309,9],\"def_end_pos\":[309,20]},{\"full_name\":\"Finset.coe_empty\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[620,9],\"def_end_pos\":[620,18]},{\"full_name\":\"Finset.sum_empty\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Finset.lean\",\"def_pos\":[329,3],\"def_end_pos\":[329,14]},{\"full_name\":\"WithTop.sInf_empty\",\"def_path\":\"Mathlib\\/Order\\/ConditionallyCompleteLattice\\/Basic.lean\",\"def_pos\":[86,9],\"def_end_pos\":[86,27]},{\"full_name\":\"Tropical.trop_top\",\"def_path\":\"Mathlib\\/Algebra\\/Tropical\\/Basic.lean\",\"def_pos\":[236,9],\"def_end_pos\":[236,17]}]"
1105
+ ],
1106
+ "state_after": "no goals",
1107
+ "state_before": "case inl\nR : Type u_1\nS : Type u_2\ninst\u271d : ConditionallyCompleteLinearOrder R\nf : S \u2192 WithTop R\n\u22a2 trop (sInf (f '' \u2191\u2205)) = \u2211 i \u2208 \u2205, trop (f i)",
1108
+ "tactic": "simp only [Set.image_empty, coe_empty, sum_empty, WithTop.sInf_empty, trop_top]"
1109
+ }
1110
+ ],
1111
+ "url": "https://github.com/leanprover-community/mathlib4"
1112
+ },
1113
+ "source_file": "Mathlib/Algebra/Tropical/BigOperators.lean"
1114
+ }
1115
+ ],
1116
+ "input_proofs": 72,
1117
+ "input_units": 2,
1118
+ "proofs": 23,
1119
+ "published_proofs": 14,
1120
+ "published_transitions": 23,
1121
+ "replay_failures": [],
1122
+ "transitions": 55,
1123
+ "validation_failures": [
1124
+ {
1125
+ "errors": [
1126
+ "internal transition boundary mismatch",
1127
+ "internal transition boundary mismatch",
1128
+ "internal transition boundary mismatch",
1129
+ "internal transition boundary mismatch"
1130
+ ],
1131
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
1132
+ "proof_id": "mathlib:Tropical.add_eq_zero_iff",
1133
+ "provenance": {
1134
+ "selection": {
1135
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1136
+ "end": [
1137
+ 369,
1138
+ 9
1139
+ ],
1140
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
1141
+ "full_name": "Tropical.add_eq_zero_iff",
1142
+ "start": [
1143
+ 362,
1144
+ 1
1145
+ ],
1146
+ "traced_tactics": [
1147
+ {
1148
+ "annotated_tactic": [
1149
+ "\"rw [<a>add_eq_iff<\\/a>]\"",
1150
+ "[{\"full_name\":\"Tropical.add_eq_iff\",\"def_path\":\"Mathlib\\/Algebra\\/Tropical\\/Basic.lean\",\"def_pos\":[356,9],\"def_end_pos\":[356,19]}]"
1151
+ ],
1152
+ "state_after": "R : Type u\ninst\u271d : LinearOrder R\na b : Tropical (WithTop R)\n\u22a2 a = 0 \u2227 a \u2264 b \u2228 b = 0 \u2227 b \u2264 a \u2194 a = 0 \u2227 b = 0",
1153
+ "state_before": "R : Type u\ninst\u271d : LinearOrder R\na b : Tropical (WithTop R)\n\u22a2 a + b = 0 \u2194 a = 0 \u2227 b = 0",
1154
+ "tactic": "rw [add_eq_iff]"
1155
+ },
1156
+ {
1157
+ "annotated_tactic": [
1158
+ "\"constructor\"",
1159
+ "[]"
1160
+ ],
1161
+ "state_after": "case mp\nR : Type u\ninst\u271d : LinearOrder R\na b : Tropical (WithTop R)\n\u22a2 a = 0 \u2227 a \u2264 b \u2228 b = 0 \u2227 b \u2264 a \u2192 a = 0 \u2227 b = 0\n\ncase mpr\nR : Type u\ninst\u271d : LinearOrder R\na b : Tropical (WithTop R)\n\u22a2 a = 0 \u2227 b = 0 \u2192 a = 0 \u2227 a \u2264 b \u2228 b = 0 \u2227 b \u2264 a",
1162
+ "state_before": "R : Type u\ninst\u271d : LinearOrder R\na b : Tropical (WithTop R)\n\u22a2 a = 0 \u2227 a \u2264 b \u2228 b = 0 \u2227 b \u2264 a \u2194 a = 0 \u2227 b = 0",
1163
+ "tactic": "constructor"
1164
+ },
1165
+ {
1166
+ "annotated_tactic": [
1167
+ "\"rintro (\\u27e8rfl, h\\u27e9 | \\u27e8rfl, h\\u27e9)\"",
1168
+ "[]"
1169
+ ],
1170
+ "state_after": "case mp.inl.intro\nR : Type u\ninst\u271d : LinearOrder R\nb : Tropical (WithTop R)\nh : 0 \u2264 b\n\u22a2 0 = 0 \u2227 b = 0\n\ncase mp.inr.intro\nR : Type u\ninst\u271d : LinearOrder R\na : Tropical (WithTop R)\nh : 0 \u2264 a\n\u22a2 a = 0 \u2227 0 = 0",
1171
+ "state_before": "case mp\nR : Type u\ninst\u271d : LinearOrder R\na b : Tropical (WithTop R)\n\u22a2 a = 0 \u2227 a \u2264 b \u2228 b = 0 \u2227 b \u2264 a \u2192 a = 0 \u2227 b = 0",
1172
+ "tactic": "rintro (\u27e8rfl, h\u27e9 | \u27e8rfl, h\u27e9)"
1173
+ },
1174
+ {
1175
+ "annotated_tactic": [
1176
+ "\"exact \\u27e8<a>rfl<\\/a>, <a>le_antisymm<\\/a> (<a>le_zero<\\/a> _) h\\u27e9\"",
1177
+ "[{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]},{\"full_name\":\"le_antisymm\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[188,9],\"def_end_pos\":[188,20]},{\"full_name\":\"Tropical.le_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Tropical\\/Basic.lean\",\"def_pos\":[251,9],\"def_end_pos\":[251,16]}]"
1178
+ ],
1179
+ "state_after": "no goals",
1180
+ "state_before": "case mp.inl.intro\nR : Type u\ninst\u271d : LinearOrder R\nb : Tropical (WithTop R)\nh : 0 \u2264 b\n\u22a2 0 = 0 \u2227 b = 0",
1181
+ "tactic": "exact \u27e8rfl, le_antisymm (le_zero _) h\u27e9"
1182
+ },
1183
+ {
1184
+ "annotated_tactic": [
1185
+ "\"exact \\u27e8<a>le_antisymm<\\/a> (<a>le_zero<\\/a> _) h, <a>rfl<\\/a>\\u27e9\"",
1186
+ "[{\"full_name\":\"le_antisymm\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[188,9],\"def_end_pos\":[188,20]},{\"full_name\":\"Tropical.le_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Tropical\\/Basic.lean\",\"def_pos\":[251,9],\"def_end_pos\":[251,16]},{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]}]"
1187
+ ],
1188
+ "state_after": "no goals",
1189
+ "state_before": "case mp.inr.intro\nR : Type u\ninst\u271d : LinearOrder R\na : Tropical (WithTop R)\nh : 0 \u2264 a\n\u22a2 a = 0 \u2227 0 = 0",
1190
+ "tactic": "exact \u27e8le_antisymm (le_zero _) h, rfl\u27e9"
1191
+ },
1192
+ {
1193
+ "annotated_tactic": [
1194
+ "\"rintro \\u27e8rfl, rfl\\u27e9\"",
1195
+ "[]"
1196
+ ],
1197
+ "state_after": "case mpr.intro\nR : Type u\ninst\u271d : LinearOrder R\n\u22a2 0 = 0 \u2227 0 \u2264 0 \u2228 0 = 0 \u2227 0 \u2264 0",
1198
+ "state_before": "case mpr\nR : Type u\ninst\u271d : LinearOrder R\na b : Tropical (WithTop R)\n\u22a2 a = 0 \u2227 b = 0 \u2192 a = 0 \u2227 a \u2264 b \u2228 b = 0 \u2227 b \u2264 a",
1199
+ "tactic": "rintro \u27e8rfl, rfl\u27e9"
1200
+ },
1201
+ {
1202
+ "annotated_tactic": [
1203
+ "\"simp\"",
1204
+ "[]"
1205
+ ],
1206
+ "state_after": "no goals",
1207
+ "state_before": "case mpr.intro\nR : Type u\ninst\u271d : LinearOrder R\n\u22a2 0 = 0 \u2227 0 \u2264 0 \u2228 0 = 0 \u2227 0 \u2264 0",
1208
+ "tactic": "simp"
1209
+ }
1210
+ ],
1211
+ "url": "https://github.com/leanprover-community/mathlib4"
1212
+ }
1213
+ },
1214
+ "theorem_name": "Tropical.add_eq_zero_iff"
1215
+ },
1216
+ {
1217
+ "errors": [
1218
+ "internal transition boundary mismatch",
1219
+ "internal transition boundary mismatch"
1220
+ ],
1221
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
1222
+ "proof_id": "mathlib:Tropical.add_pow",
1223
+ "provenance": {
1224
+ "selection": {
1225
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1226
+ "end": [
1227
+ 551,
1228
+ 61
1229
+ ],
1230
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
1231
+ "full_name": "Tropical.add_pow",
1232
+ "start": [
1233
+ 546,
1234
+ 1
1235
+ ],
1236
+ "traced_tactics": [
1237
+ {
1238
+ "annotated_tactic": [
1239
+ "\"rcases <a>le_total<\\/a> x y with h | h\"",
1240
+ "[{\"full_name\":\"le_total\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[297,9],\"def_end_pos\":[297,17]}]"
1241
+ ],
1242
+ "state_after": "case inl\nR : Type u\ninst\u271d\u00b3 : LinearOrder R\ninst\u271d\u00b2 : AddMonoid R\ninst\u271d\u00b9 : CovariantClass R R (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\ninst\u271d : CovariantClass R R (Function.swap fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nx y : Tropical R\nn : \u2115\nh : x \u2264 y\n\u22a2 (x + y) ^ n = x ^ n + y ^ n\n\ncase inr\nR : Type u\ninst\u271d\u00b3 : LinearOrder R\ninst\u271d\u00b2 : AddMonoid R\ninst\u271d\u00b9 : CovariantClass R R (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\ninst\u271d : CovariantClass R R (Function.swap fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nx y : Tropical R\nn : \u2115\nh : y \u2264 x\n\u22a2 (x + y) ^ n = x ^ n + y ^ n",
1243
+ "state_before": "R : Type u\ninst\u271d\u00b3 : LinearOrder R\ninst\u271d\u00b2 : AddMonoid R\ninst\u271d\u00b9 : CovariantClass R R (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\ninst\u271d : CovariantClass R R (Function.swap fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nx y : Tropical R\nn : \u2115\n\u22a2 (x + y) ^ n = x ^ n + y ^ n",
1244
+ "tactic": "rcases le_total x y with h | h"
1245
+ },
1246
+ {
1247
+ "annotated_tactic": [
1248
+ "\"rw [<a>add_eq_left<\\/a> h, <a>add_eq_left<\\/a> (<a>pow_le_pow_left'<\\/a> h _)]\"",
1249
+ "[{\"full_name\":\"Tropical.add_eq_left\",\"def_path\":\"Mathlib\\/Algebra\\/Tropical\\/Basic.lean\",\"def_pos\":[328,9],\"def_end_pos\":[328,20]},{\"full_name\":\"Tropical.add_eq_left\",\"def_path\":\"Mathlib\\/Algebra\\/Tropical\\/Basic.lean\",\"def_pos\":[328,9],\"def_end_pos\":[328,20]},{\"full_name\":\"pow_le_pow_left'\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Unbundled\\/Pow.lean\",\"def_pos\":[31,9],\"def_end_pos\":[31,25]}]"
1250
+ ],
1251
+ "state_after": "no goals",
1252
+ "state_before": "case inl\nR : Type u\ninst\u271d\u00b3 : LinearOrder R\ninst\u271d\u00b2 : AddMonoid R\ninst\u271d\u00b9 : CovariantClass R R (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\ninst\u271d : CovariantClass R R (Function.swap fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nx y : Tropical R\nn : \u2115\nh : x \u2264 y\n\u22a2 (x + y) ^ n = x ^ n + y ^ n",
1253
+ "tactic": "rw [add_eq_left h, add_eq_left (pow_le_pow_left' h _)]"
1254
+ },
1255
+ {
1256
+ "annotated_tactic": [
1257
+ "\"rw [<a>add_eq_right<\\/a> h, <a>add_eq_right<\\/a> (<a>pow_le_pow_left'<\\/a> h _)]\"",
1258
+ "[{\"full_name\":\"Tropical.add_eq_right\",\"def_path\":\"Mathlib\\/Algebra\\/Tropical\\/Basic.lean\",\"def_pos\":[333,9],\"def_end_pos\":[333,21]},{\"full_name\":\"Tropical.add_eq_right\",\"def_path\":\"Mathlib\\/Algebra\\/Tropical\\/Basic.lean\",\"def_pos\":[333,9],\"def_end_pos\":[333,21]},{\"full_name\":\"pow_le_pow_left'\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Monoid\\/Unbundled\\/Pow.lean\",\"def_pos\":[31,9],\"def_end_pos\":[31,25]}]"
1259
+ ],
1260
+ "state_after": "no goals",
1261
+ "state_before": "case inr\nR : Type u\ninst\u271d\u00b3 : LinearOrder R\ninst\u271d\u00b2 : AddMonoid R\ninst\u271d\u00b9 : CovariantClass R R (fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\ninst\u271d : CovariantClass R R (Function.swap fun x x_1 => x + x_1) fun x x_1 => x \u2264 x_1\nx y : Tropical R\nn : \u2115\nh : y \u2264 x\n\u22a2 (x + y) ^ n = x ^ n + y ^ n",
1262
+ "tactic": "rw [add_eq_right h, add_eq_right (pow_le_pow_left' h _)]"
1263
+ }
1264
+ ],
1265
+ "url": "https://github.com/leanprover-community/mathlib4"
1266
+ }
1267
+ },
1268
+ "theorem_name": "Tropical.add_pow"
1269
+ },
1270
+ {
1271
+ "errors": [
1272
+ "internal transition boundary mismatch",
1273
+ "internal transition boundary mismatch"
1274
+ ],
1275
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
1276
+ "proof_id": "mathlib:Tropical.succ_nsmul",
1277
+ "provenance": {
1278
+ "selection": {
1279
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1280
+ "end": [
1281
+ 572,
1282
+ 44
1283
+ ],
1284
+ "file_path": "Mathlib/Algebra/Tropical/Basic.lean",
1285
+ "full_name": "Tropical.succ_nsmul",
1286
+ "start": [
1287
+ 569,
1288
+ 1
1289
+ ],
1290
+ "traced_tactics": [
1291
+ {
1292
+ "annotated_tactic": [
1293
+ "\"induction' n with n IH\"",
1294
+ "[]"
1295
+ ],
1296
+ "state_after": "case zero\nR\u271d : Type u\ninst\u271d\u00b2 : LinearOrderedAddCommMonoidWithTop R\u271d\nR : Type u_1\ninst\u271d\u00b9 : LinearOrder R\ninst\u271d : OrderTop R\nx : Tropical R\n\u22a2 (0 + 1) \u2022 x = x\n\ncase succ\nR\u271d : Type u\ninst\u271d\u00b2 : LinearOrderedAddCommMonoidWithTop R\u271d\nR : Type u_1\ninst\u271d\u00b9 : LinearOrder R\ninst\u271d : OrderTop R\nx : Tropical R\nn : \u2115\nIH : (n + 1) \u2022 x = x\n\u22a2 (n + 1 + 1) \u2022 x = x",
1297
+ "state_before": "R\u271d : Type u\ninst\u271d\u00b2 : LinearOrderedAddCommMonoidWithTop R\u271d\nR : Type u_1\ninst\u271d\u00b9 : LinearOrder R\ninst\u271d : OrderTop R\nx : Tropical R\nn : \u2115\n\u22a2 (n + 1) \u2022 x = x",
1298
+ "tactic": "induction' n with n IH"
1299
+ },
1300
+ {
1301
+ "annotated_tactic": [
1302
+ "\"simp\"",
1303
+ "[]"
1304
+ ],
1305
+ "state_after": "no goals",
1306
+ "state_before": "case zero\nR\u271d : Type u\ninst\u271d\u00b2 : LinearOrderedAddCommMonoidWithTop R\u271d\nR : Type u_1\ninst\u271d\u00b9 : LinearOrder R\ninst\u271d : OrderTop R\nx : Tropical R\n\u22a2 (0 + 1) \u2022 x = x",
1307
+ "tactic": "simp"
1308
+ },
1309
+ {
1310
+ "annotated_tactic": [
1311
+ "\"rw [<a>add_nsmul<\\/a>, IH, <a>one_nsmul<\\/a>, <a>add_self<\\/a>]\"",
1312
+ "[{\"full_name\":\"add_nsmul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[702,15],\"def_end_pos\":[702,24]},{\"full_name\":\"one_nsmul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[662,30],\"def_end_pos\":[662,39]},{\"full_name\":\"Tropical.add_self\",\"def_path\":\"Mathlib\\/Algebra\\/Tropical\\/Basic.lean\",\"def_pos\":[346,9],\"def_end_pos\":[346,17]}]"
1313
+ ],
1314
+ "state_after": "no goals",
1315
+ "state_before": "case succ\nR\u271d : Type u\ninst\u271d\u00b2 : LinearOrderedAddCommMonoidWithTop R\u271d\nR : Type u_1\ninst\u271d\u00b9 : LinearOrder R\ninst\u271d : OrderTop R\nx : Tropical R\nn : \u2115\nIH : (n + 1) \u2022 x = x\n\u22a2 (n + 1 + 1) \u2022 x = x",
1316
+ "tactic": "rw [add_nsmul, IH, one_nsmul, add_self]"
1317
+ }
1318
+ ],
1319
+ "url": "https://github.com/leanprover-community/mathlib4"
1320
+ }
1321
+ },
1322
+ "theorem_name": "Tropical.succ_nsmul"
1323
+ },
1324
+ {
1325
+ "errors": [
1326
+ "internal transition boundary mismatch",
1327
+ "internal transition boundary mismatch"
1328
+ ],
1329
+ "file_path": "Mathlib/Algebra/Tropical/BigOperators.lean",
1330
+ "proof_id": "mathlib:List.trop_minimum",
1331
+ "provenance": {
1332
+ "selection": {
1333
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1334
+ "end": [
1335
+ 82,
1336
+ 35
1337
+ ],
1338
+ "file_path": "Mathlib/Algebra/Tropical/BigOperators.lean",
1339
+ "full_name": "List.trop_minimum",
1340
+ "start": [
1341
+ 78,
1342
+ 1
1343
+ ],
1344
+ "traced_tactics": [
1345
+ {
1346
+ "annotated_tactic": [
1347
+ "\"induction' l with hd tl IH\"",
1348
+ "[]"
1349
+ ],
1350
+ "state_after": "case nil\nR : Type u_1\nS : Type u_2\ninst\u271d : LinearOrder R\n\u22a2 trop [].minimum = (map (trop \u2218 WithTop.some) []).sum\n\ncase cons\nR : Type u_1\nS : Type u_2\ninst\u271d : LinearOrder R\nhd : R\ntl : List R\nIH : trop tl.minimum = (map (trop \u2218 WithTop.some) tl).sum\n\u22a2 trop (hd :: tl).minimum = (map (trop \u2218 WithTop.some) (hd :: tl)).sum",
1351
+ "state_before": "R : Type u_1\nS : Type u_2\ninst\u271d : LinearOrder R\nl : List R\n\u22a2 trop l.minimum = (map (trop \u2218 WithTop.some) l).sum",
1352
+ "tactic": "induction' l with hd tl IH"
1353
+ },
1354
+ {
1355
+ "annotated_tactic": [
1356
+ "\"simp\"",
1357
+ "[]"
1358
+ ],
1359
+ "state_after": "no goals",
1360
+ "state_before": "case nil\nR : Type u_1\nS : Type u_2\ninst\u271d : LinearOrder R\n\u22a2 trop [].minimum = (map (trop \u2218 WithTop.some) []).sum",
1361
+ "tactic": "simp"
1362
+ },
1363
+ {
1364
+ "annotated_tactic": [
1365
+ "\"simp [<a>List.minimum_cons<\\/a>, \\u2190 IH]\"",
1366
+ "[{\"full_name\":\"List.minimum_cons\",\"def_path\":\"Mathlib\\/Data\\/List\\/MinMax.lean\",\"def_pos\":[385,9],\"def_end_pos\":[385,21]}]"
1367
+ ],
1368
+ "state_after": "no goals",
1369
+ "state_before": "case cons\nR : Type u_1\nS : Type u_2\ninst\u271d : LinearOrder R\nhd : R\ntl : List R\nIH : trop tl.minimum = (map (trop \u2218 WithTop.some) tl).sum\n\u22a2 trop (hd :: tl).minimum = (map (trop \u2218 WithTop.some) (hd :: tl)).sum",
1370
+ "tactic": "simp [List.minimum_cons, \u2190 IH]"
1371
+ }
1372
+ ],
1373
+ "url": "https://github.com/leanprover-community/mathlib4"
1374
+ }
1375
+ },
1376
+ "theorem_name": "List.trop_minimum"
1377
+ },
1378
+ {
1379
+ "errors": [
1380
+ "internal transition boundary mismatch",
1381
+ "internal transition boundary mismatch"
1382
+ ],
1383
+ "file_path": "Mathlib/Algebra/Tropical/BigOperators.lean",
1384
+ "proof_id": "mathlib:List.trop_sum",
1385
+ "provenance": {
1386
+ "selection": {
1387
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1388
+ "end": [
1389
+ 43,
1390
+ 16
1391
+ ],
1392
+ "file_path": "Mathlib/Algebra/Tropical/BigOperators.lean",
1393
+ "full_name": "List.trop_sum",
1394
+ "start": [
1395
+ 40,
1396
+ 1
1397
+ ],
1398
+ "traced_tactics": [
1399
+ {
1400
+ "annotated_tactic": [
1401
+ "\"induction' l with hd tl IH\"",
1402
+ "[]"
1403
+ ],
1404
+ "state_after": "case nil\nR : Type u_1\nS : Type u_2\ninst\u271d : AddMonoid R\n\u22a2 trop [].sum = (map trop []).prod\n\ncase cons\nR : Type u_1\nS : Type u_2\ninst\u271d : AddMonoid R\nhd : R\ntl : List R\nIH : trop tl.sum = (map trop tl).prod\n\u22a2 trop (hd :: tl).sum = (map trop (hd :: tl)).prod",
1405
+ "state_before": "R : Type u_1\nS : Type u_2\ninst\u271d : AddMonoid R\nl : List R\n\u22a2 trop l.sum = (map trop l).prod",
1406
+ "tactic": "induction' l with hd tl IH"
1407
+ },
1408
+ {
1409
+ "annotated_tactic": [
1410
+ "\"simp\"",
1411
+ "[]"
1412
+ ],
1413
+ "state_after": "no goals",
1414
+ "state_before": "case nil\nR : Type u_1\nS : Type u_2\ninst\u271d : AddMonoid R\n\u22a2 trop [].sum = (map trop []).prod",
1415
+ "tactic": "simp"
1416
+ },
1417
+ {
1418
+ "annotated_tactic": [
1419
+ "\"simp [\\u2190 IH]\"",
1420
+ "[]"
1421
+ ],
1422
+ "state_after": "no goals",
1423
+ "state_before": "case cons\nR : Type u_1\nS : Type u_2\ninst\u271d : AddMonoid R\nhd : R\ntl : List R\nIH : trop tl.sum = (map trop tl).prod\n\u22a2 trop (hd :: tl).sum = (map trop (hd :: tl)).prod",
1424
+ "tactic": "simp [\u2190 IH]"
1425
+ }
1426
+ ],
1427
+ "url": "https://github.com/leanprover-community/mathlib4"
1428
+ }
1429
+ },
1430
+ "theorem_name": "List.trop_sum"
1431
+ },
1432
+ {
1433
+ "errors": [
1434
+ "internal transition boundary mismatch",
1435
+ "internal transition boundary mismatch"
1436
+ ],
1437
+ "file_path": "Mathlib/Algebra/Tropical/BigOperators.lean",
1438
+ "proof_id": "mathlib:List.untrop_prod",
1439
+ "provenance": {
1440
+ "selection": {
1441
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1442
+ "end": [
1443
+ 62,
1444
+ 16
1445
+ ],
1446
+ "file_path": "Mathlib/Algebra/Tropical/BigOperators.lean",
1447
+ "full_name": "List.untrop_prod",
1448
+ "start": [
1449
+ 58,
1450
+ 1
1451
+ ],
1452
+ "traced_tactics": [
1453
+ {
1454
+ "annotated_tactic": [
1455
+ "\"induction' l with hd tl IH\"",
1456
+ "[]"
1457
+ ],
1458
+ "state_after": "case nil\nR : Type u_1\nS : Type u_2\ninst\u271d : AddMonoid R\n\u22a2 untrop [].prod = (map untrop []).sum\n\ncase cons\nR : Type u_1\nS : Type u_2\ninst\u271d : AddMonoid R\nhd : Tropical R\ntl : List (Tropical R)\nIH : untrop tl.prod = (map untrop tl).sum\n\u22a2 untrop (hd :: tl).prod = (map untrop (hd :: tl)).sum",
1459
+ "state_before": "R : Type u_1\nS : Type u_2\ninst\u271d : AddMonoid R\nl : List (Tropical R)\n\u22a2 untrop l.prod = (map untrop l).sum",
1460
+ "tactic": "induction' l with hd tl IH"
1461
+ },
1462
+ {
1463
+ "annotated_tactic": [
1464
+ "\"simp\"",
1465
+ "[]"
1466
+ ],
1467
+ "state_after": "no goals",
1468
+ "state_before": "case nil\nR : Type u_1\nS : Type u_2\ninst\u271d : AddMonoid R\n\u22a2 untrop [].prod = (map untrop []).sum",
1469
+ "tactic": "simp"
1470
+ },
1471
+ {
1472
+ "annotated_tactic": [
1473
+ "\"simp [\\u2190 IH]\"",
1474
+ "[]"
1475
+ ],
1476
+ "state_after": "no goals",
1477
+ "state_before": "case cons\nR : Type u_1\nS : Type u_2\ninst\u271d : AddMonoid R\nhd : Tropical R\ntl : List (Tropical R)\nIH : untrop tl.prod = (map untrop tl).sum\n\u22a2 untrop (hd :: tl).prod = (map untrop (hd :: tl)).sum",
1478
+ "tactic": "simp [\u2190 IH]"
1479
+ }
1480
+ ],
1481
+ "url": "https://github.com/leanprover-community/mathlib4"
1482
+ }
1483
+ },
1484
+ "theorem_name": "List.untrop_prod"
1485
+ },
1486
+ {
1487
+ "errors": [
1488
+ "internal transition boundary mismatch",
1489
+ "internal transition boundary mismatch"
1490
+ ],
1491
+ "file_path": "Mathlib/Algebra/Tropical/BigOperators.lean",
1492
+ "proof_id": "mathlib:Multiset.trop_inf",
1493
+ "provenance": {
1494
+ "selection": {
1495
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1496
+ "end": [
1497
+ 89,
1498
+ 16
1499
+ ],
1500
+ "file_path": "Mathlib/Algebra/Tropical/BigOperators.lean",
1501
+ "full_name": "Multiset.trop_inf",
1502
+ "start": [
1503
+ 85,
1504
+ 1
1505
+ ],
1506
+ "traced_tactics": [
1507
+ {
1508
+ "annotated_tactic": [
1509
+ "\"induction' s using <a>Multiset.induction<\\/a> with s x IH\"",
1510
+ "[{\"full_name\":\"Multiset.induction\",\"def_path\":\"Mathlib\\/Data\\/Multiset\\/Basic.lean\",\"def_pos\":[168,19],\"def_end_pos\":[168,28]}]"
1511
+ ],
1512
+ "state_after": "case empty\nR : Type u_1\nS : Type u_2\ninst\u271d\u00b9 : LinearOrder R\ninst\u271d : OrderTop R\n\u22a2 trop (inf 0) = (map trop 0).sum\n\ncase cons\nR : Type u_1\nS : Type u_2\ninst\u271d\u00b9 : LinearOrder R\ninst\u271d : OrderTop R\ns : R\nx : Multiset R\nIH : trop x.inf = (map trop x).sum\n\u22a2 trop (s ::\u2098 x).inf = (map trop (s ::\u2098 x)).sum",
1513
+ "state_before": "R : Type u_1\nS : Type u_2\ninst\u271d\u00b9 : LinearOrder R\ninst\u271d : OrderTop R\ns : Multiset R\n\u22a2 trop s.inf = (map trop s).sum",
1514
+ "tactic": "induction' s using Multiset.induction with s x IH"
1515
+ },
1516
+ {
1517
+ "annotated_tactic": [
1518
+ "\"simp\"",
1519
+ "[]"
1520
+ ],
1521
+ "state_after": "no goals",
1522
+ "state_before": "case empty\nR : Type u_1\nS : Type u_2\ninst\u271d\u00b9 : LinearOrder R\ninst\u271d : OrderTop R\n\u22a2 trop (inf 0) = (map trop 0).sum",
1523
+ "tactic": "simp"
1524
+ },
1525
+ {
1526
+ "annotated_tactic": [
1527
+ "\"simp [\\u2190 IH]\"",
1528
+ "[]"
1529
+ ],
1530
+ "state_after": "no goals",
1531
+ "state_before": "case cons\nR : Type u_1\nS : Type u_2\ninst\u271d\u00b9 : LinearOrder R\ninst\u271d : OrderTop R\ns : R\nx : Multiset R\nIH : trop x.inf = (map trop x).sum\n\u22a2 trop (s ::\u2098 x).inf = (map trop (s ::\u2098 x)).sum",
1532
+ "tactic": "simp [\u2190 IH]"
1533
+ }
1534
+ ],
1535
+ "url": "https://github.com/leanprover-community/mathlib4"
1536
+ }
1537
+ },
1538
+ "theorem_name": "Multiset.trop_inf"
1539
+ },
1540
+ {
1541
+ "errors": [
1542
+ "internal transition boundary mismatch",
1543
+ "internal transition boundary mismatch"
1544
+ ],
1545
+ "file_path": "Mathlib/Algebra/Tropical/BigOperators.lean",
1546
+ "proof_id": "mathlib:Multiset.untrop_sum",
1547
+ "provenance": {
1548
+ "selection": {
1549
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1550
+ "end": [
1551
+ 116,
1552
+ 8
1553
+ ],
1554
+ "file_path": "Mathlib/Algebra/Tropical/BigOperators.lean",
1555
+ "full_name": "Multiset.untrop_sum",
1556
+ "start": [
1557
+ 111,
1558
+ 1
1559
+ ],
1560
+ "traced_tactics": [
1561
+ {
1562
+ "annotated_tactic": [
1563
+ "\"induction' s using <a>Multiset.induction<\\/a> with s x IH\"",
1564
+ "[{\"full_name\":\"Multiset.induction\",\"def_path\":\"Mathlib\\/Data\\/Multiset\\/Basic.lean\",\"def_pos\":[168,19],\"def_end_pos\":[168,28]}]"
1565
+ ],
1566
+ "state_after": "case empty\nR : Type u_1\nS : Type u_2\ninst\u271d\u00b9 : LinearOrder R\ninst\u271d : OrderTop R\n\u22a2 untrop (sum 0) = (map untrop 0).inf\n\ncase cons\nR : Type u_1\nS : Type u_2\ninst\u271d\u00b9 : LinearOrder R\ninst\u271d : OrderTop R\ns : Tropical R\nx : Multiset (Tropical R)\nIH : untrop x.sum = (map untrop x).inf\n\u22a2 untrop (s ::\u2098 x).sum = (map untrop (s ::\u2098 x)).inf",
1567
+ "state_before": "R : Type u_1\nS : Type u_2\ninst\u271d\u00b9 : LinearOrder R\ninst\u271d : OrderTop R\ns : Multiset (Tropical R)\n\u22a2 untrop s.sum = (map untrop s).inf",
1568
+ "tactic": "induction' s using Multiset.induction with s x IH"
1569
+ },
1570
+ {
1571
+ "annotated_tactic": [
1572
+ "\"simp\"",
1573
+ "[]"
1574
+ ],
1575
+ "state_after": "no goals",
1576
+ "state_before": "case empty\nR : Type u_1\nS : Type u_2\ninst\u271d\u00b9 : LinearOrder R\ninst\u271d : OrderTop R\n\u22a2 untrop (sum 0) = (map untrop 0).inf",
1577
+ "tactic": "simp"
1578
+ },
1579
+ {
1580
+ "annotated_tactic": [
1581
+ "\"simp only [<a>sum_cons<\\/a>, <a>ge_iff_le<\\/a>, <a>untrop_add<\\/a>, <a>untrop_le_iff<\\/a>, <a>map_cons<\\/a>, <a>inf_cons<\\/a>, \\u2190 IH]\"",
1582
+ "[{\"full_name\":\"Multiset.sum_cons\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Multiset.lean\",\"def_pos\":[78,3],\"def_end_pos\":[78,14]},{\"full_name\":\"ge_iff_le\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[1947,17],\"def_end_pos\":[1947,26]},{\"full_name\":\"Tropical.untrop_add\",\"def_path\":\"Mathlib\\/Algebra\\/Tropical\\/Basic.lean\",\"def_pos\":[270,9],\"def_end_pos\":[270,19]},{\"full_name\":\"Tropical.untrop_le_iff\",\"def_path\":\"Mathlib\\/Algebra\\/Tropical\\/Basic.lean\",\"def_pos\":[173,9],\"def_end_pos\":[173,22]},{\"full_name\":\"Multiset.map_cons\",\"def_path\":\"Mathlib\\/Data\\/Multiset\\/Basic.lean\",\"def_pos\":[1225,9],\"def_end_pos\":[1225,17]},{\"full_name\":\"Multiset.inf_cons\",\"def_path\":\"Mathlib\\/Data\\/Multiset\\/Lattice.lean\",\"def_pos\":[128,9],\"def_end_pos\":[128,17]}]"
1583
+ ],
1584
+ "state_after": "case cons\nR : Type u_1\nS : Type u_2\ninst\u271d\u00b9 : LinearOrder R\ninst\u271d : OrderTop R\ns : Tropical R\nx : Multiset (Tropical R)\nIH : untrop x.sum = (map untrop x).inf\n\u22a2 min (untrop s) (untrop x.sum) = untrop s \u2293 untrop x.sum",
1585
+ "state_before": "case cons\nR : Type u_1\nS : Type u_2\ninst\u271d\u00b9 : LinearOrder R\ninst\u271d : OrderTop R\ns : Tropical R\nx : Multiset (Tropical R)\nIH : untrop x.sum = (map untrop x).inf\n\u22a2 untrop (s ::\u2098 x).sum = (map untrop (s ::\u2098 x)).inf",
1586
+ "tactic": "simp only [sum_cons, ge_iff_le, untrop_add, untrop_le_iff, map_cons, inf_cons, \u2190 IH]"
1587
+ },
1588
+ {
1589
+ "annotated_tactic": [
1590
+ "\"rfl\"",
1591
+ "[]"
1592
+ ],
1593
+ "state_after": "no goals",
1594
+ "state_before": "case cons\nR : Type u_1\nS : Type u_2\ninst\u271d\u00b9 : LinearOrder R\ninst\u271d : OrderTop R\ns : Tropical R\nx : Multiset (Tropical R)\nIH : untrop x.sum = (map untrop x).inf\n\u22a2 min (untrop s) (untrop x.sum) = untrop s \u2293 untrop x.sum",
1595
+ "tactic": "rfl"
1596
+ }
1597
+ ],
1598
+ "url": "https://github.com/leanprover-community/mathlib4"
1599
+ }
1600
+ },
1601
+ "theorem_name": "Multiset.untrop_sum"
1602
+ },
1603
+ {
1604
+ "errors": [
1605
+ "internal transition boundary mismatch",
1606
+ "internal transition boundary mismatch"
1607
+ ],
1608
+ "file_path": "Mathlib/Algebra/Tropical/BigOperators.lean",
1609
+ "proof_id": "mathlib:untrop_sum_eq_sInf_image",
1610
+ "provenance": {
1611
+ "selection": {
1612
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1613
+ "end": [
1614
+ 130,
1615
+ 68
1616
+ ],
1617
+ "file_path": "Mathlib/Algebra/Tropical/BigOperators.lean",
1618
+ "full_name": "untrop_sum_eq_sInf_image",
1619
+ "start": [
1620
+ 126,
1621
+ 1
1622
+ ],
1623
+ "traced_tactics": [
1624
+ {
1625
+ "annotated_tactic": [
1626
+ "\"rcases s.eq_empty_or_nonempty with (rfl | h)\"",
1627
+ "[]"
1628
+ ],
1629
+ "state_after": "case inl\nR : Type u_1\nS : Type u_2\ninst\u271d : ConditionallyCompleteLinearOrder R\nf : S \u2192 Tropical (WithTop R)\n\u22a2 untrop (\u2211 i \u2208 \u2205, f i) = sInf (untrop \u2218 f '' \u2191\u2205)\n\ncase inr\nR : Type u_1\nS : Type u_2\ninst\u271d : ConditionallyCompleteLinearOrder R\ns : Finset S\nf : S \u2192 Tropical (WithTop R)\nh : s.Nonempty\n\u22a2 untrop (\u2211 i \u2208 s, f i) = sInf (untrop \u2218 f '' \u2191s)",
1630
+ "state_before": "R : Type u_1\nS : Type u_2\ninst\u271d : ConditionallyCompleteLinearOrder R\ns : Finset S\nf : S \u2192 Tropical (WithTop R)\n\u22a2 untrop (\u2211 i \u2208 s, f i) = sInf (untrop \u2218 f '' \u2191s)",
1631
+ "tactic": "rcases s.eq_empty_or_nonempty with (rfl | h)"
1632
+ },
1633
+ {
1634
+ "annotated_tactic": [
1635
+ "\"simp only [<a>Set.image_empty<\\/a>, <a>coe_empty<\\/a>, <a>sum_empty<\\/a>, <a>WithTop.sInf_empty<\\/a>, <a>untrop_zero<\\/a>]\"",
1636
+ "[{\"full_name\":\"Set.image_empty\",\"def_path\":\"Mathlib\\/Data\\/Set\\/Image.lean\",\"def_pos\":[309,9],\"def_end_pos\":[309,20]},{\"full_name\":\"Finset.coe_empty\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[620,9],\"def_end_pos\":[620,18]},{\"full_name\":\"Finset.sum_empty\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Finset.lean\",\"def_pos\":[329,3],\"def_end_pos\":[329,14]},{\"full_name\":\"WithTop.sInf_empty\",\"def_path\":\"Mathlib\\/Order\\/ConditionallyCompleteLattice\\/Basic.lean\",\"def_pos\":[86,9],\"def_end_pos\":[86,27]},{\"full_name\":\"Tropical.untrop_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Tropical\\/Basic.lean\",\"def_pos\":[231,9],\"def_end_pos\":[231,20]}]"
1637
+ ],
1638
+ "state_after": "no goals",
1639
+ "state_before": "case inl\nR : Type u_1\nS : Type u_2\ninst\u271d : ConditionallyCompleteLinearOrder R\nf : S \u2192 Tropical (WithTop R)\n\u22a2 untrop (\u2211 i \u2208 \u2205, f i) = sInf (untrop \u2218 f '' \u2191\u2205)",
1640
+ "tactic": "simp only [Set.image_empty, coe_empty, sum_empty, WithTop.sInf_empty, untrop_zero]"
1641
+ },
1642
+ {
1643
+ "annotated_tactic": [
1644
+ "\"rw [\\u2190 <a>inf'_eq_csInf_image<\\/a> _ h, <a>inf'_eq_inf<\\/a>, <a>Finset.untrop_sum'<\\/a>]\"",
1645
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1646
+ ],
1647
+ "state_after": "no goals",
1648
+ "state_before": "case inr\nR : Type u_1\nS : Type u_2\ninst\u271d : ConditionallyCompleteLinearOrder R\ns : Finset S\nf : S \u2192 Tropical (WithTop R)\nh : s.Nonempty\n\u22a2 untrop (\u2211 i \u2208 s, f i) = sInf (untrop \u2218 f '' \u2191s)",
1649
+ "tactic": "rw [\u2190 inf'_eq_csInf_image _ h, inf'_eq_inf, Finset.untrop_sum']"
1650
+ }
1651
+ ],
1652
+ "url": "https://github.com/leanprover-community/mathlib4"
1653
+ }
1654
+ },
1655
+ "theorem_name": "untrop_sum_eq_sInf_image"
1656
+ }
1657
+ ],
1658
+ "validation_rejected_proofs": 9,
1659
+ "zero_transition_proofs": 0
1660
+ },
1661
+ "shards": [
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+ {
1663
+ "path": "data/train/mathlib-000346-0000-96168f005e65be87.parquet",
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+ "sha256": "96168f005e65be871184cb67a21e4980be963d7b627215f2cb9020de4087cdee",
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+ "revision": "4dbd9775daba0af0fd6fdd456fb509b76555ebbc"
1668
+ }
1669
+ ],
1670
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1671
+ "mathlib:Finset.trop_inf",
1672
+ "mathlib:Finset.untrop_sum",
1673
+ "mathlib:Finset.untrop_sum'",
1674
+ "mathlib:Multiset.trop_sum",
1675
+ "mathlib:Multiset.untrop_prod",
1676
+ "mathlib:Tropical.add_eq_left",
1677
+ "mathlib:Tropical.add_eq_left_iff",
1678
+ "mathlib:Tropical.add_eq_right",
1679
+ "mathlib:Tropical.add_eq_right_iff",
1680
+ "mathlib:Tropical.mul_eq_zero_iff",
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1682
+ "mathlib:trop_sum",
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+ "mathlib:untrop_prod",
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+ "mathlib:untrop_sum"
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+ ],
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+ "proof_keys": [
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+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Tropical/Basic.lean\",null,null,\"Tropical.add_eq_left\"]",
1688
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1689
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1690
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1691
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1692
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1693
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1694
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1695
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1696
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1697
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1698
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1699
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1700
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Algebra/Tropical/BigOperators.lean\",null,null,\"untrop_sum\"]"
1701
+ ]
1702
+ }
manifests/batches/mathlib/000347.json ADDED
The diff for this file is too large to render. See raw diff
 
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manifests/batches/numina/001106.json ADDED
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