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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
fb40e6f
·
verified ·
1 Parent(s): 160f1cc

Record 16 verified HPC batch manifests

Browse files
Files changed (16) hide show
  1. manifests/batches/deepseek/000483.json +148 -0
  2. manifests/batches/deepseek/000486.json +148 -0
  3. manifests/batches/deepseek/000487.json +148 -0
  4. manifests/batches/deepseek/000488.json +148 -0
  5. manifests/batches/mathlib/000412.json +681 -0
  6. manifests/batches/mathlib/000413.json +967 -0
  7. manifests/batches/mathlib/000414.json +0 -0
  8. manifests/batches/mathlib/000415.json +0 -0
  9. manifests/batches/mathlib/000416.json +0 -0
  10. manifests/batches/mathlib/000417.json +0 -0
  11. manifests/batches/mathlib/000419.json +0 -0
  12. manifests/batches/numina/001172.json +44 -0
  13. manifests/batches/numina/001173.json +44 -0
  14. manifests/batches/numina/001174.json +58 -0
  15. manifests/batches/numina/001175.json +52 -0
  16. manifests/batches/numina/001176.json +73 -0
manifests/batches/deepseek/000483.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "deepseek/000483",
4
+ "batch_fingerprint": "73a1fe65999e8d8688bea655c1cfa75a5b7f287b2d152634a8d72d208da4a250",
5
+ "evidence": {
6
+ "batch_fingerprint": "73a1fe65999e8d8688bea655c1cfa75a5b7f287b2d152634a8d72d208da4a250",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 50,
10
+ "input_units": 50,
11
+ "proofs": 50,
12
+ "published_proofs": 50,
13
+ "published_transitions": 121,
14
+ "replay_failures": [],
15
+ "trace_mode": "individual",
16
+ "transitions": 121,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/deepseek-000483-0000-82ed193f4a403736.parquet",
24
+ "sha256": "82ed193f4a4037361c96007dcbc75bcc49ed881d9482a7936e7f9e4261f5d4cf",
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+ "bytes": 330439,
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+ "rows": 105,
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+ "revision": "160f1cc216c96ed97eed787dd32318f0ea6b31a0"
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+ },
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+ {
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+ "path": "data/dev/deepseek-000483-0000-06c2fb8199e01416.parquet",
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+ "sha256": "06c2fb8199e0141676d0c533cda9eb2dede6c0b6f0cdd9c6dfaa60368214dd93",
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+ "bytes": 49400,
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+ "rows": 9,
34
+ "revision": "160f1cc216c96ed97eed787dd32318f0ea6b31a0"
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+ },
36
+ {
37
+ "path": "data/internal_test/deepseek-000483-0000-462119a81b9dd57d.parquet",
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+ "sha256": "462119a81b9dd57d17ac5a99fabde53d263f8661e136fb8eee11d74a0e1a83b7",
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+ "bytes": 39564,
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+ "rows": 7,
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+ "revision": "160f1cc216c96ed97eed787dd32318f0ea6b31a0"
42
+ }
43
+ ],
44
+ "proof_ids": [
45
+ "deepseek:thm_24197",
46
+ "deepseek:thm_24198",
47
+ "deepseek:thm_24199",
48
+ "deepseek:thm_24200",
49
+ "deepseek:thm_24201",
50
+ "deepseek:thm_24202",
51
+ "deepseek:thm_24203",
52
+ "deepseek:thm_24204",
53
+ "deepseek:thm_24205",
54
+ "deepseek:thm_24206",
55
+ "deepseek:thm_24207",
56
+ "deepseek:thm_24208",
57
+ "deepseek:thm_24209",
58
+ "deepseek:thm_24210",
59
+ "deepseek:thm_24211",
60
+ "deepseek:thm_24212",
61
+ "deepseek:thm_24213",
62
+ "deepseek:thm_24214",
63
+ "deepseek:thm_24215",
64
+ "deepseek:thm_24216",
65
+ "deepseek:thm_24217",
66
+ "deepseek:thm_24218",
67
+ "deepseek:thm_24219",
68
+ "deepseek:thm_24220",
69
+ "deepseek:thm_24221",
70
+ "deepseek:thm_24222",
71
+ "deepseek:thm_24223",
72
+ "deepseek:thm_24224",
73
+ "deepseek:thm_24225",
74
+ "deepseek:thm_24226",
75
+ "deepseek:thm_24227",
76
+ "deepseek:thm_24228",
77
+ "deepseek:thm_24229",
78
+ "deepseek:thm_24230",
79
+ "deepseek:thm_24231",
80
+ "deepseek:thm_24232",
81
+ "deepseek:thm_24233",
82
+ "deepseek:thm_24234",
83
+ "deepseek:thm_24235",
84
+ "deepseek:thm_24236",
85
+ "deepseek:thm_24237",
86
+ "deepseek:thm_24238",
87
+ "deepseek:thm_24239",
88
+ "deepseek:thm_24240",
89
+ "deepseek:thm_24241",
90
+ "deepseek:thm_24242",
91
+ "deepseek:thm_24243",
92
+ "deepseek:thm_24244",
93
+ "deepseek:thm_24245",
94
+ "deepseek:thm_24246"
95
+ ],
96
+ "proof_keys": [
97
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024150.lean\",\"cf8ea33af0660fe2929223d7276a67fbf3ddcb2d3eb0ee8dc0857c9e856b03b0\",0,\"thm_24197\"]",
98
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024151.lean\",\"71d6c9891dcee38f436b5ad399e50e5e9e17705d648e321aee34b28d71669bb8\",0,\"thm_24198\"]",
99
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024152.lean\",\"b2892dd91db6e1ff95007f731e1babcf977ceaaec5a998cc105dddb6062bb998\",0,\"thm_24199\"]",
100
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024153.lean\",\"938e053fa9fa0b905ae8207515a3eb1b4b6d19cb0bf8390abc450b32102cbc09\",0,\"thm_24200\"]",
101
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024154.lean\",\"8035c794873b99270361a811956a596dfe127cbb7bb623946522ed1eb2109994\",0,\"thm_24201\"]",
102
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024155.lean\",\"049f3363862e577ff1f7c4b531dfc65310f807eebb5384e3d6241a4386251e64\",0,\"thm_24202\"]",
103
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024156.lean\",\"7312055f80bbd8284353fb1368f71022462043a735e3695438fb744d70d07bb2\",0,\"thm_24203\"]",
104
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024157.lean\",\"d14f7d203c3052b76aa0b8d2cb5bc58ce69a15f95a8ff1ad466a7dac3c7111e7\",0,\"thm_24204\"]",
105
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024158.lean\",\"619c4e04401cd6c07adb4d3ef95d91326b697f499cf85aedefb702cea0266c28\",0,\"thm_24205\"]",
106
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024159.lean\",\"11d71606d6810eba68de5c15ea2d357c6ab01743a8fdbe5c465a4454ef012715\",0,\"thm_24206\"]",
107
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024160.lean\",\"9db372f352805e7808f005ab727927ae3ef3729edd810cc7c09afb9efa6d1b39\",0,\"thm_24207\"]",
108
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024161.lean\",\"833819bf5e134ebd01f12550fcad0eaf06267c63480f749320fce9b4c5e838e4\",0,\"thm_24208\"]",
109
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024162.lean\",\"28037f997adabacbe3bd3aefc16e1cdf860d88777f2acbdb52495bb1c4747bd3\",0,\"thm_24209\"]",
110
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024163.lean\",\"4b867f9ea5ef8873938fcd01a81042ca9638ef86e70b9eb276a4f5d0a7096119\",0,\"thm_24210\"]",
111
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024164.lean\",\"b540d029561dcdfef1de1fde0c53938208c780552a8d645151056f644e3a743d\",0,\"thm_24211\"]",
112
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024165.lean\",\"5eeeee7adfb7aeba0e1d0e3b4c97c0bb1be5a76fe3bc957c290c42800ca4dea9\",0,\"thm_24212\"]",
113
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024166.lean\",\"2370126ea9cc21a23da85e8899829af5ad92e1091767b9d1d7d3aa9ab31b4412\",0,\"thm_24213\"]",
114
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024167.lean\",\"03aa861f72c7f34ac5ac2028394e58807693c16adf5203e452cd2a56940dc73e\",0,\"thm_24214\"]",
115
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024168.lean\",\"12178e2c1ef17c4c79e0c2ae30764ef20a9b9e3874cdac125c99699d49a646ca\",0,\"thm_24215\"]",
116
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024169.lean\",\"10e43a512d9a40e92665a3e472aeb140702ae6e9e3383dc7106bccbe12813705\",0,\"thm_24216\"]",
117
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024170.lean\",\"783065e27d24f0f4e126ecb2d4cef4cc29464497c316f977864f4121d0933c49\",0,\"thm_24217\"]",
118
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024171.lean\",\"fd7a60cc4fa3a59b11d304fec55ae0f203c87b9cd4c79114a66740881d166afc\",0,\"thm_24218\"]",
119
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024172.lean\",\"8daf6dc6b1a3161a5fb929f1d3ef2423ad4eae643872b0c8c7602e8a4f7fa196\",0,\"thm_24219\"]",
120
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024173.lean\",\"de04481bb1c55080e8421c002a255e5b1179f524d013db8af9b6a8250dced046\",0,\"thm_24220\"]",
121
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024174.lean\",\"baf05c324b935ea4da6a29b9900b1da4be932162577bf12e479a8ec21296a503\",0,\"thm_24221\"]",
122
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024175.lean\",\"78a278ea1025b184f58234635cd769f37b70f2019ef1ea710cf522b7b4ba3b2a\",0,\"thm_24222\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024176.lean\",\"a233dde6c3b849f0e76b7c7d8850b7f20519956314f24791e9b202e4ff7b63c7\",0,\"thm_24223\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024177.lean\",\"8459d6d98cfc2a466495ee2575b8d32e3e8f27a27438ffdf5efa89f01ebcf6b8\",0,\"thm_24224\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024178.lean\",\"0d6e441040c109d5a1f766502835581a02bf1847976dd731c9889cf444f9db47\",0,\"thm_24225\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024179.lean\",\"bdb9d6fc3abfcbc9f28646c2d296b3070b57aaf1fe1838b8117c8dd754a46fd3\",0,\"thm_24226\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024180.lean\",\"b7a897643970e99ced307982dad1cee2702b8f16d1a7c0591db8732e66b0cc9d\",0,\"thm_24227\"]",
128
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024181.lean\",\"e6c77b25dbe7ff26bf7c862ccc06965b176d0cc6b44bab060e987e415789c953\",0,\"thm_24228\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024182.lean\",\"1127d96860a86007645f110c3e8e3a298fd3753f192b694c19af32b63ffdc6e6\",0,\"thm_24229\"]",
130
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024183.lean\",\"7e7abb8024b2f2560f14c27f077ba974cf16b8235aa6263e982d399b9a9f7f5a\",0,\"thm_24230\"]",
131
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024184.lean\",\"ea876793460963913a578369be4a8aa98da7173d5e45abfe32c5eec4d95f4cdf\",0,\"thm_24231\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024185.lean\",\"c8bc54752bfe43f92593c210d19a99738ea15f092584f2fe900f79057b696f4a\",0,\"thm_24232\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024186.lean\",\"483fceb2c65e9d7ec321fcc8bbf41594c3ad6def422accb1104264449275a271\",0,\"thm_24233\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024187.lean\",\"44aae2521f3a6802a5bfd92aacff7f5d19eba52195cca76a0143971ea9cceb68\",0,\"thm_24234\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024188.lean\",\"a7d5bb069e307ac2e8e48e7955f93784031b5ce1ffd0e49ca5658c6dd97d3ac3\",0,\"thm_24235\"]",
136
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024189.lean\",\"2711af63976542101af1464daeb6d66a5cb46d84e52a03ea0f9b63c68724a98e\",0,\"thm_24236\"]",
137
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024190.lean\",\"c6ff67f73f91ff441003e0d774f71960b9e2a382762c9867c207af01ea0810c6\",0,\"thm_24237\"]",
138
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024191.lean\",\"7197873a1d93fed8d3dcaa2e8a382a2502a5c74590f8b60d37148c4e0aa11af5\",0,\"thm_24238\"]",
139
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024192.lean\",\"3f5e7ecbb2356df2d0f7340662c2c47cf25832c8fe355117bd7d85b7de595828\",0,\"thm_24239\"]",
140
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024193.lean\",\"99405df81011d88618d0bd1322c6898dfd5a1f4c18ff54cdf24963031e60bf51\",0,\"thm_24240\"]",
141
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024194.lean\",\"a118214fc4da4e6d709f1a1e22e22d737bda7abc0a3640b93e39621d9fc20bc2\",0,\"thm_24241\"]",
142
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024195.lean\",\"e32aadc151e1c9aa05b5e93912d8b618ca3d710a96de628a2e877c25e15eed7e\",0,\"thm_24242\"]",
143
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024196.lean\",\"f8c300b4dfac4738ede922bcc7ac29fc143e4cef3006bf257654f33da9a8700a\",0,\"thm_24243\"]",
144
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024197.lean\",\"05db7df2f0a9cd2ae2087cac67620423cd3ca1837a485402ade3d62e2cc97a74\",0,\"thm_24244\"]",
145
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024198.lean\",\"9fe562b7a8604ea086bf005a1876514ab5c79de255c854d5fae660691eb77c8e\",0,\"thm_24245\"]",
146
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024199.lean\",\"dfa381b487a2746a23c86c5f63f01deebf78b8ebfbb7838b6112bdac14f6b7b3\",0,\"thm_24246\"]"
147
+ ]
148
+ }
manifests/batches/deepseek/000486.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
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+ "format": "leangpt-parquet-v2",
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+ "batch": "deepseek/000486",
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+ "batch_fingerprint": "662ce68be4f8be97cd2a26c8a0055bd6a3fe8e41b3a80b714736ae808d01e0aa",
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+ "evidence": {
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+ "batch_fingerprint": "662ce68be4f8be97cd2a26c8a0055bd6a3fe8e41b3a80b714736ae808d01e0aa",
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+ "contamination_matches": [],
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+ "failures": [],
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+ "input_proofs": 50,
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+ "input_units": 50,
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+ "proofs": 50,
12
+ "published_proofs": 50,
13
+ "published_transitions": 113,
14
+ "replay_failures": [],
15
+ "trace_mode": "individual",
16
+ "transitions": 113,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
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+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/deepseek-000486-0000-f82fcd1055bb7c68.parquet",
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+ "sha256": "f82fcd1055bb7c684615ca180c62c65681a73fdb52669f148dfbb2268f912c34",
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+ "bytes": 321306,
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+ "rows": 103,
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+ "revision": "160f1cc216c96ed97eed787dd32318f0ea6b31a0"
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+ },
29
+ {
30
+ "path": "data/dev/deepseek-000486-0000-b1a4329736eb080f.parquet",
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+ "sha256": "b1a4329736eb080ff98bc1021ef002269ed62914b11fa80d80f7b477eb2e4312",
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+ "bytes": 32120,
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+ "rows": 4,
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+ "revision": "160f1cc216c96ed97eed787dd32318f0ea6b31a0"
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+ },
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+ {
37
+ "path": "data/internal_test/deepseek-000486-0000-ea6f45e6f2f85ef9.parquet",
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+ "sha256": "ea6f45e6f2f85ef91617ec21ff074db458425c3c9793473e51f13cdcec04cf54",
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+ "bytes": 41437,
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+ "rows": 6,
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+ "revision": "160f1cc216c96ed97eed787dd32318f0ea6b31a0"
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+ }
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+ ],
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+ "proof_ids": [
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+ "deepseek:thm_24347",
46
+ "deepseek:thm_24348",
47
+ "deepseek:thm_24349",
48
+ "deepseek:thm_24350",
49
+ "deepseek:thm_24351",
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+ "deepseek:thm_24372",
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+ "deepseek:thm_24373",
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+ "deepseek:thm_24374",
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+ "deepseek:thm_24375",
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+ "deepseek:thm_24378",
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+ "deepseek:thm_24379",
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+ "deepseek:thm_24380",
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+ "deepseek:thm_24381",
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+ "deepseek:thm_24382",
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+ "deepseek:thm_24383",
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+ "deepseek:thm_24384",
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+ "deepseek:thm_24385",
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+ "deepseek:thm_24388",
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+ "deepseek:thm_24389",
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+ "deepseek:thm_24390",
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+ "deepseek:thm_24391",
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+ "deepseek:thm_24394",
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+ "deepseek:thm_24395",
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+ "deepseek:thm_24396"
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+ ],
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024340.lean\",\"7719f4551b80215171ac6c05c447550ed6a37869e2b813a13c636976414660c0\",0,\"thm_24387\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024343.lean\",\"5c1de449945daa411d9f18602056add56dd7cfbc843094721bdfe7d7fbfe4cb3\",0,\"thm_24390\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024345.lean\",\"bdee37d6c03052215dbfae803d16e1ed2f90d16dd9a2ac5b64b3f199ce9f1805\",0,\"thm_24392\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024347.lean\",\"eaf85860bdb76a1f963ca86a1c6f8af7b85df68a94e7d718412ac7ba459a622b\",0,\"thm_24394\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024348.lean\",\"fbdaf53e87e934c9c54d2a3be54be91c58e4cc3f7c782dfbe9968ef33a0dd19a\",0,\"thm_24395\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024349.lean\",\"ebca81d65de215bb00f861308067f60b611db6abe43084b1ffac62bc6942e7e7\",0,\"thm_24396\"]"
147
+ ]
148
+ }
manifests/batches/deepseek/000487.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ {
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+ "format": "leangpt-parquet-v2",
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+ "batch": "deepseek/000487",
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+ "batch_fingerprint": "40551fc1b63c3b8e076f0d30beede3e5e2caac5123c62a601dc9d27ce11c3ae8",
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+ "evidence": {
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+ "contamination_matches": [],
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+ "failures": [],
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+ "input_proofs": 50,
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+ "proofs": 50,
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+ "published_proofs": 50,
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+ "published_transitions": 112,
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+ "replay_failures": [],
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+ "trace_mode": "individual",
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+ "transitions": 112,
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+ "validation_failures": [],
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+ "validation_rejected_proofs": 0,
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+ "zero_transition_proofs": 0
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+ "shards": [
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+ {
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+ "path": "data/train/deepseek-000487-0000-590326ed733fa1f7.parquet",
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+ "path": "data/dev/deepseek-000487-0000-5bb2aeb45bb29096.parquet",
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+ "path": "data/internal_test/deepseek-000487-0000-fe5c50567b60d1ad.parquet",
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+ "proof_ids": [
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+ "deepseek:thm_24397",
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+ "deepseek:thm_24398",
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+ "deepseek:thm_24399",
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+ "deepseek:thm_24400",
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+ "deepseek:thm_24402",
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+ "deepseek:thm_24403",
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+ "deepseek:thm_24404",
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+ "deepseek:thm_24405",
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+ "deepseek:thm_24435",
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+ "deepseek:thm_24444",
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+ "deepseek:thm_24445",
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+ ],
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+ "proof_keys": [
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+ ]
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+ }
manifests/batches/deepseek/000488.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ {
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+ "trace_mode": "individual",
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123
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124
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125
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126
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127
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128
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129
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130
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024433.lean\",\"8336b13b86ca488b7659f19a54cf39bc6af2edfecb0f50ee582676c1bd7becf2\",0,\"thm_24480\"]",
131
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024434.lean\",\"0a013eb952368ba1402e7a954b82f0b4091e3a486a2d6ec9eea0ef258d98c847\",0,\"thm_24481\"]",
132
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024435.lean\",\"f78ae7bc94e88e5ebe279c5408063378fbe257303444bf3330e18b82f38e83d3\",0,\"thm_24482\"]",
133
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134
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024437.lean\",\"7d3680b3ea6c2e8e1bb4d0afa36478245fd296c0a6a7b66b591ede0bbf20e4e8\",0,\"thm_24484\"]",
135
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024438.lean\",\"c66a8a8121cf117dac7a1d4c42245b83b249722fa0278bd9850d1a393ffbca56\",0,\"thm_24485\"]",
136
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024439.lean\",\"8ca0f05a7d89f550c365f16110ade2ae9826b05a290c34dbe17755cc2ff250a7\",0,\"thm_24486\"]",
137
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024440.lean\",\"c0f95f447a110b316e506cba5c7cf806f6ebaf3877aabce1c215aa9778dabb6f\",0,\"thm_24487\"]",
138
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024441.lean\",\"30f6d5cd9786f9e6e14ef3a12d6ad655ee0a5b644d3afd6aafb4ced4986e2c31\",0,\"thm_24488\"]",
139
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024442.lean\",\"0b46b452de201cf0208a9c295ec0bb886b85cf55c2c1ed99867087bfba7fd04c\",0,\"thm_24489\"]",
140
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024443.lean\",\"529324bc23b6b3e7192133ff18382fa2ee657f2ac581304447a1ebfe01ac5dd2\",0,\"thm_24490\"]",
141
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024444.lean\",\"7f7751f066aa825f463ae83373cce639020003da8299de9cfb189444f3d83468\",0,\"thm_24491\"]",
142
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024445.lean\",\"19a39b301a82e5a1cec083d775b20375462de45d70bec2bb280ebe8d9e0bfdd3\",0,\"thm_24492\"]",
143
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024446.lean\",\"5d697a5440f713167eff71dbad380d1901ebebd940b7d9e93dc3c3343ad30c69\",0,\"thm_24493\"]",
144
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024447.lean\",\"421bad8ed61c2c7f4a5cefed981a7da28139b7c3840131ac39432683a9262d08\",0,\"thm_24494\"]",
145
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024448.lean\",\"a5f4544796f34c422a381f5b7aceeb416181c08c865c5cdb57832a43ed754e29\",0,\"thm_24495\"]",
146
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_024449.lean\",\"f2f98a73de063a4294689306af6fd4e6db2718ebc83274054ed982590235709b\",0,\"thm_24496\"]"
147
+ ]
148
+ }
manifests/batches/mathlib/000412.json ADDED
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+ {
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+ "batch": "mathlib/000412",
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+ "batch_fingerprint": "f2b997330dd80987eb2961574ff355eb1f79d591bc31e3c8ea5380aa6a845cc8",
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+ "evidence": {
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+ "batch_fingerprint": "f2b997330dd80987eb2961574ff355eb1f79d591bc31e3c8ea5380aa6a845cc8",
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+ "contamination_matches": [],
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+ "error": "theorem has no selected tactic transitions",
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+ "id": "HasCompactSupport.deriv",
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+ "reason": "import_failure",
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+ "url": "https://github.com/leanprover-community/mathlib4"
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+ },
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+ "source_file": "Mathlib/Analysis/Calculus/Deriv/Support.lean"
30
+ },
31
+ {
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+ "error": "theorem has no selected tactic transitions",
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+ "full_name": "Differentiable.zpow",
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+ "id": "Differentiable.zpow",
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+ },
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+ "source_file": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean"
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+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
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73
+ "source_file": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
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78
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+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "DifferentiableWithinAt.zpow",
100
+ "id": "DifferentiableWithinAt.zpow",
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+ "reason": "import_failure",
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+ "selection": {
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+ "full_name": "DifferentiableWithinAt.zpow",
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+ "start": [
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+ ],
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+ "traced_tactics": [],
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+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
+ "source_file": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean"
118
+ },
119
+ {
120
+ "error": "theorem has no selected tactic transitions",
121
+ "full_name": "derivWithin_zpow",
122
+ "id": "derivWithin_zpow",
123
+ "reason": "import_failure",
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+ "selection": {
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+ "full_name": "derivWithin_zpow",
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+ "start": [
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+ 1
135
+ ],
136
+ "traced_tactics": [],
137
+ "url": "https://github.com/leanprover-community/mathlib4"
138
+ },
139
+ "source_file": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean"
140
+ },
141
+ {
142
+ "error": "theorem has no selected tactic transitions",
143
+ "full_name": "differentiableAt_zpow",
144
+ "id": "differentiableAt_zpow",
145
+ "reason": "import_failure",
146
+ "selection": {
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+ "end": [
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151
+ ],
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+ "file_path": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean",
153
+ "full_name": "differentiableAt_zpow",
154
+ "start": [
155
+ 71,
156
+ 1
157
+ ],
158
+ "traced_tactics": [],
159
+ "url": "https://github.com/leanprover-community/mathlib4"
160
+ },
161
+ "source_file": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean"
162
+ },
163
+ {
164
+ "error": "theorem has no selected tactic transitions",
165
+ "full_name": "differentiableOn_zpow",
166
+ "id": "differentiableOn_zpow",
167
+ "reason": "import_failure",
168
+ "selection": {
169
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
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+ "end": [
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+ 83,
172
+ 76
173
+ ],
174
+ "file_path": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean",
175
+ "full_name": "differentiableOn_zpow",
176
+ "start": [
177
+ 81,
178
+ 1
179
+ ],
180
+ "traced_tactics": [],
181
+ "url": "https://github.com/leanprover-community/mathlib4"
182
+ },
183
+ "source_file": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean"
184
+ },
185
+ {
186
+ "error": "theorem has no selected tactic transitions",
187
+ "full_name": "hasDerivAt_zpow",
188
+ "id": "hasDerivAt_zpow",
189
+ "reason": "import_failure",
190
+ "selection": {
191
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
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+ "end": [
193
+ 63,
194
+ 43
195
+ ],
196
+ "file_path": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean",
197
+ "full_name": "hasDerivAt_zpow",
198
+ "start": [
199
+ 61,
200
+ 1
201
+ ],
202
+ "traced_tactics": [],
203
+ "url": "https://github.com/leanprover-community/mathlib4"
204
+ },
205
+ "source_file": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean"
206
+ },
207
+ {
208
+ "error": "theorem has no selected tactic transitions",
209
+ "full_name": "hasDerivWithinAt_zpow",
210
+ "id": "hasDerivWithinAt_zpow",
211
+ "reason": "import_failure",
212
+ "selection": {
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+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
214
+ "end": [
215
+ 68,
216
+ 43
217
+ ],
218
+ "file_path": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean",
219
+ "full_name": "hasDerivWithinAt_zpow",
220
+ "start": [
221
+ 66,
222
+ 1
223
+ ],
224
+ "traced_tactics": [],
225
+ "url": "https://github.com/leanprover-community/mathlib4"
226
+ },
227
+ "source_file": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean"
228
+ },
229
+ {
230
+ "error": "no internal trace for tactic 'lift m to \u2115 using hm.le'",
231
+ "full_name": "hasStrictDerivAt_zpow",
232
+ "id": "hasStrictDerivAt_zpow",
233
+ "reason": "import_failure",
234
+ "selection": {
235
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
236
+ "end": [
237
+ 58,
238
+ 20
239
+ ],
240
+ "file_path": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean",
241
+ "full_name": "hasStrictDerivAt_zpow",
242
+ "start": [
243
+ 39,
244
+ 1
245
+ ],
246
+ "traced_tactics": [
247
+ {
248
+ "annotated_tactic": [
249
+ "\"rcases <a>lt_trichotomy<\\/a> m 0 with (hm | hm | hm)\"",
250
+ "[{\"full_name\":\"lt_trichotomy\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[313,9],\"def_end_pos\":[313,22]}]"
251
+ ],
252
+ "state_after": "case inl\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\nthis : \u2200 (m : \u2124), 0 < m \u2192 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\nhm : m < 0\n\u22a2 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\n\ncase inr.inl\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\nthis : \u2200 (m : \u2124), 0 < m \u2192 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\nhm : m = 0\n\u22a2 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\n\ncase inr.inr\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\nthis : \u2200 (m : \u2124), 0 < m \u2192 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\nhm : 0 < m\n\u22a2 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x",
253
+ "state_before": "\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\nthis : \u2200 (m : \u2124), 0 < m \u2192 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\n\u22a2 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x",
254
+ "tactic": "rcases lt_trichotomy m 0 with (hm | hm | hm)"
255
+ },
256
+ {
257
+ "annotated_tactic": [
258
+ "\"lift m to \\u2115 using hm.le\"",
259
+ "[]"
260
+ ],
261
+ "state_after": "case intro\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d\u00b9 m\u271d : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\u271d\nm : \u2115\nhm : 0 < \u2191m\n\u22a2 HasStrictDerivAt (fun x => x ^ \u2191m) (\u2191\u2191m * x ^ (\u2191m - 1)) x",
262
+ "state_before": "\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d\u00b9 m\u271d : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\u271d\nm : \u2124\nhm : 0 < m\n\u22a2 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x",
263
+ "tactic": "lift m to \u2115 using hm.le"
264
+ },
265
+ {
266
+ "annotated_tactic": [
267
+ "\"simp only [<a>zpow_natCast<\\/a>, <a>Int.cast_natCast<\\/a>]\"",
268
+ "[{\"full_name\":\"zpow_natCast\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1021,9],\"def_end_pos\":[1021,21]},{\"full_name\":\"Int.cast_natCast\",\"def_path\":\"Mathlib\\/Data\\/Int\\/Cast\\/Basic.lean\",\"def_pos\":[66,9],\"def_end_pos\":[66,21]}]"
269
+ ],
270
+ "state_after": "case intro\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d\u00b9 m\u271d : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\u271d\nm : \u2115\nhm : 0 < \u2191m\n\u22a2 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (\u2191m - 1)) x",
271
+ "state_before": "case intro\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d\u00b9 m\u271d : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\u271d\nm : \u2115\nhm : 0 < \u2191m\n\u22a2 HasStrictDerivAt (fun x => x ^ \u2191m) (\u2191\u2191m * x ^ (\u2191m - 1)) x",
272
+ "tactic": "simp only [zpow_natCast, Int.cast_natCast]"
273
+ },
274
+ {
275
+ "annotated_tactic": [
276
+ "\"convert <a>hasStrictDerivAt_pow<\\/a> m x using 2\"",
277
+ "[{\"full_name\":\"hasStrictDerivAt_pow\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Deriv\\/Pow.lean\",\"def_pos\":[45,9],\"def_end_pos\":[45,29]}]"
278
+ ],
279
+ "state_after": "case h.e'_7.h.e'_6\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d\u00b9 m\u271d : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\u271d\nm : \u2115\nhm : 0 < \u2191m\n\u22a2 x ^ (\u2191m - 1) = x ^ (m - 1)",
280
+ "state_before": "case intro\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d\u00b9 m\u271d : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\u271d\nm : \u2115\nhm : 0 < \u2191m\n\u22a2 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (\u2191m - 1)) x",
281
+ "tactic": "convert hasStrictDerivAt_pow m x using 2"
282
+ },
283
+ {
284
+ "annotated_tactic": [
285
+ "\"rw [\\u2190 <a>Int.ofNat_one<\\/a>, \\u2190 <a>Int.ofNat_sub<\\/a>, <a>zpow_natCast<\\/a>]\"",
286
+ "[{\"full_name\":\"Int.ofNat_one\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Basic.lean\",\"def_pos\":[75,17],\"def_end_pos\":[75,26]},{\"full_name\":\"Int.ofNat_sub\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Lemmas.lean\",\"def_pos\":[302,22],\"def_end_pos\":[302,31]},{\"full_name\":\"zpow_natCast\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1021,9],\"def_end_pos\":[1021,21]}]"
287
+ ],
288
+ "state_after": "case h.e'_7.h.e'_6\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d\u00b9 m\u271d : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\u271d\nm : \u2115\nhm : 0 < \u2191m\n\u22a2 1 \u2264 m",
289
+ "state_before": "case h.e'_7.h.e'_6\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d\u00b9 m\u271d : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\u271d\nm : \u2115\nhm : 0 < \u2191m\n\u22a2 x ^ (\u2191m - 1) = x ^ (m - 1)",
290
+ "tactic": "rw [\u2190 Int.ofNat_one, \u2190 Int.ofNat_sub, zpow_natCast]"
291
+ },
292
+ {
293
+ "annotated_tactic": [
294
+ "\"norm_cast at hm\"",
295
+ "[]"
296
+ ],
297
+ "state_after": "no goals",
298
+ "state_before": "case h.e'_7.h.e'_6\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d\u00b9 m\u271d : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\u271d\nm : \u2115\nhm : 0 < \u2191m\n\u22a2 1 \u2264 m",
299
+ "tactic": "norm_cast at hm"
300
+ },
301
+ {
302
+ "annotated_tactic": [
303
+ "\"have hx : x \\u2260 0 := h.resolve_right hm.not_le\"",
304
+ "[]"
305
+ ],
306
+ "state_after": "case inl\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\nthis : \u2200 (m : \u2124), 0 < m \u2192 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\nhm : m < 0\nhx : x \u2260 0\n\u22a2 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x",
307
+ "state_before": "case inl\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\nthis : \u2200 (m : \u2124), 0 < m \u2192 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\nhm : m < 0\n\u22a2 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x",
308
+ "tactic": "have hx : x \u2260 0 := h.resolve_right hm.not_le"
309
+ },
310
+ {
311
+ "annotated_tactic": [
312
+ "\"have := (<a>hasStrictDerivAt_inv<\\/a> ?_).<a>scomp<\\/a> _ (this (-m) (<a>neg_pos<\\/a>.2 hm)) <;>\\n [skip; exact <a>zpow_ne_zero<\\/a> _ hx]\"",
313
+ "[{\"full_name\":\"hasStrictDerivAt_inv\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Deriv\\/Inv.lean\",\"def_pos\":[48,9],\"def_end_pos\":[48,29]},{\"full_name\":\"HasStrictDerivAt.scomp\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Deriv\\/Comp.lean\",\"def_pos\":[118,9],\"def_end_pos\":[118,31]},{\"full_name\":\"neg_pos\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Defs.lean\",\"def_pos\":[677,24],\"def_end_pos\":[677,31]},{\"full_name\":\"zpow_ne_zero\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Units\\/Basic.lean\",\"def_pos\":[435,7],\"def_end_pos\":[435,19]}]"
314
+ ],
315
+ "state_after": "case inl.refine_2\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\nthis\u271d : \u2200 (m : \u2124), 0 < m \u2192 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\nhm : m < 0\nhx : x \u2260 0\nthis : HasStrictDerivAt (Inv.inv \u2218 fun x => x ^ (-m)) ((\u2191(-m) * x ^ (-m - 1)) \u2022 -((x ^ (-m)) ^ 2)\u207b\u00b9) x\n\u22a2 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x",
316
+ "state_before": "case inl\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\nthis : \u2200 (m : \u2124), 0 < m \u2192 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\nhm : m < 0\nhx : x \u2260 0\n\u22a2 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x",
317
+ "tactic": "have := (hasStrictDerivAt_inv ?_).scomp _ (this (-m) (neg_pos.2 hm)) <;>\n [skip; exact zpow_ne_zero _ hx]"
318
+ },
319
+ {
320
+ "annotated_tactic": [
321
+ "\"convert this using 1\"",
322
+ "[]"
323
+ ],
324
+ "state_after": "case h.e'_7\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\nthis\u271d : \u2200 (m : \u2124), 0 < m \u2192 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\nhm : m < 0\nhx : x \u2260 0\nthis : HasStrictDerivAt (fun x => x ^ m) (\u2191(-m) * x ^ (-m - 1) * -((x ^ m)\u207b\u00b9 ^ 2)\u207b\u00b9) x\n\u22a2 \u2191m * x ^ (m - 1) = \u2191(-m) * x ^ (-m - 1) * -((x ^ m)\u207b\u00b9 ^ 2)\u207b\u00b9",
325
+ "state_before": "case inl.refine_2\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\nthis\u271d : \u2200 (m : \u2124), 0 < m \u2192 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\nhm : m < 0\nhx : x \u2260 0\nthis : HasStrictDerivAt (fun x => x ^ m) (\u2191(-m) * x ^ (-m - 1) * -((x ^ m)\u207b\u00b9 ^ 2)\u207b\u00b9) x\n\u22a2 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x",
326
+ "tactic": "convert this using 1"
327
+ },
328
+ {
329
+ "annotated_tactic": [
330
+ "\"rw [<a>sq<\\/a>, <a>mul_inv<\\/a>, <a>inv_inv<\\/a>, <a>Int.cast_neg<\\/a>, <a>neg_mul<\\/a>, <a>neg_mul_neg<\\/a>, \\u2190 <a>zpow_add\\u2080<\\/a> hx, <a>mul_assoc<\\/a>, \\u2190\\n <a>zpow_add\\u2080<\\/a> hx]\"",
331
+ "[{\"full_name\":\"sq\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[684,41],\"def_end_pos\":[684,43]},{\"full_name\":\"mul_inv\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[726,9],\"def_end_pos\":[726,16]},{\"full_name\":\"inv_inv\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[870,9],\"def_end_pos\":[870,16]},{\"full_name\":\"Int.cast_neg\",\"def_path\":\"Mathlib\\/Data\\/Int\\/Cast\\/Basic.lean\",\"def_pos\":[85,9],\"def_end_pos\":[85,17]},{\"full_name\":\"neg_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[318,9],\"def_end_pos\":[318,16]},{\"full_name\":\"neg_mul_neg\",\"def_path\":\"Mathlib\\/Algebra\\/Ring\\/Defs.lean\",\"def_pos\":[327,9],\"def_end_pos\":[327,20]},{\"full_name\":\"zpow_add\\u2080\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Basic.lean\",\"def_pos\":[470,7],\"def_end_pos\":[470,16]},{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]},{\"full_name\":\"zpow_add\\u2080\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Basic.lean\",\"def_pos\":[470,7],\"def_end_pos\":[470,16]}]"
332
+ ],
333
+ "state_after": "case h.e'_7\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\nthis\u271d : \u2200 (m : \u2124), 0 < m \u2192 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\nhm : m < 0\nhx : x \u2260 0\nthis : HasStrictDerivAt (fun x => x ^ m) (\u2191(-m) * x ^ (-m - 1) * -((x ^ m)\u207b\u00b9 ^ 2)\u207b\u00b9) x\n\u22a2 \u2191m * x ^ (m - 1) = \u2191m * x ^ (-m - 1 + (m + m))",
334
+ "state_before": "case h.e'_7\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\nthis\u271d : \u2200 (m : \u2124), 0 < m \u2192 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\nhm : m < 0\nhx : x \u2260 0\nthis : HasStrictDerivAt (fun x => x ^ m) (\u2191(-m) * x ^ (-m - 1) * -((x ^ m)\u207b\u00b9 ^ 2)\u207b\u00b9) x\n\u22a2 \u2191m * x ^ (m - 1) = \u2191(-m) * x ^ (-m - 1) * -((x ^ m)\u207b\u00b9 ^ 2)\u207b\u00b9",
335
+ "tactic": "rw [sq, mul_inv, inv_inv, Int.cast_neg, neg_mul, neg_mul_neg, \u2190 zpow_add\u2080 hx, mul_assoc, \u2190\n zpow_add\u2080 hx]"
336
+ },
337
+ {
338
+ "annotated_tactic": [
339
+ "\"congr\"",
340
+ "[]"
341
+ ],
342
+ "state_after": "case h.e'_7.e_a.e_a\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\nthis\u271d : \u2200 (m : \u2124), 0 < m \u2192 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\nhm : m < 0\nhx : x \u2260 0\nthis : HasStrictDerivAt (fun x => x ^ m) (\u2191(-m) * x ^ (-m - 1) * -((x ^ m)\u207b\u00b9 ^ 2)\u207b\u00b9) x\n\u22a2 m - 1 = -m - 1 + (m + m)",
343
+ "state_before": "case h.e'_7\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\nthis\u271d : \u2200 (m : \u2124), 0 < m \u2192 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\nhm : m < 0\nhx : x \u2260 0\nthis : HasStrictDerivAt (fun x => x ^ m) (\u2191(-m) * x ^ (-m - 1) * -((x ^ m)\u207b\u00b9 ^ 2)\u207b\u00b9) x\n\u22a2 \u2191m * x ^ (m - 1) = \u2191m * x ^ (-m - 1 + (m + m))",
344
+ "tactic": "congr"
345
+ },
346
+ {
347
+ "annotated_tactic": [
348
+ "\"abel\"",
349
+ "[]"
350
+ ],
351
+ "state_after": "no goals",
352
+ "state_before": "case h.e'_7.e_a.e_a\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\nthis\u271d : \u2200 (m : \u2124), 0 < m \u2192 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\nhm : m < 0\nhx : x \u2260 0\nthis : HasStrictDerivAt (fun x => x ^ m) (\u2191(-m) * x ^ (-m - 1) * -((x ^ m)\u207b\u00b9 ^ 2)\u207b\u00b9) x\n\u22a2 m - 1 = -m - 1 + (m + m)",
353
+ "tactic": "abel"
354
+ },
355
+ {
356
+ "annotated_tactic": [
357
+ "\"simp only [hm, <a>zpow_zero<\\/a>, <a>Int.cast_zero<\\/a>, <a>zero_mul<\\/a>, <a>hasStrictDerivAt_const<\\/a>]\"",
358
+ "[{\"full_name\":\"zpow_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1015,50],\"def_end_pos\":[1015,59]},{\"full_name\":\"Int.cast_zero\",\"def_path\":\"Mathlib\\/Data\\/Int\\/Cast\\/Basic.lean\",\"def_pos\":[59,9],\"def_end_pos\":[59,18]},{\"full_name\":\"MulZeroClass.zero_mul\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Defs.lean\",\"def_pos\":[37,3],\"def_end_pos\":[37,11]},{\"full_name\":\"hasStrictDerivAt_const\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Deriv\\/Basic.lean\",\"def_pos\":[718,9],\"def_end_pos\":[718,31]}]"
359
+ ],
360
+ "state_after": "no goals",
361
+ "state_before": "case inr.inl\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\nthis : \u2200 (m : \u2124), 0 < m \u2192 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\nhm : m = 0\n\u22a2 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x",
362
+ "tactic": "simp only [hm, zpow_zero, Int.cast_zero, zero_mul, hasStrictDerivAt_const]"
363
+ },
364
+ {
365
+ "annotated_tactic": [
366
+ "\"exact this m hm\"",
367
+ "[]"
368
+ ],
369
+ "state_after": "no goals",
370
+ "state_before": "case inr.inr\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nh : x \u2260 0 \u2228 0 \u2264 m\nthis : \u2200 (m : \u2124), 0 < m \u2192 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x\nhm : 0 < m\n\u22a2 HasStrictDerivAt (fun x => x ^ m) (\u2191m * x ^ (m - 1)) x",
371
+ "tactic": "exact this m hm"
372
+ }
373
+ ],
374
+ "url": "https://github.com/leanprover-community/mathlib4"
375
+ },
376
+ "source_file": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean"
377
+ },
378
+ {
379
+ "error": "theorem has no selected tactic transitions",
380
+ "full_name": "iter_deriv_inv'",
381
+ "id": "iter_deriv_inv'",
382
+ "reason": "import_failure",
383
+ "selection": {
384
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
385
+ "end": [
386
+ 146,
387
+ 28
388
+ ],
389
+ "file_path": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean",
390
+ "full_name": "iter_deriv_inv'",
391
+ "start": [
392
+ 144,
393
+ 1
394
+ ],
395
+ "traced_tactics": [],
396
+ "url": "https://github.com/leanprover-community/mathlib4"
397
+ },
398
+ "source_file": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean"
399
+ },
400
+ {
401
+ "error": "theorem has no selected tactic transitions",
402
+ "full_name": "iter_deriv_pow'",
403
+ "id": "iter_deriv_pow'",
404
+ "reason": "import_failure",
405
+ "selection": {
406
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
407
+ "end": [
408
+ 135,
409
+ 39
410
+ ],
411
+ "file_path": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean",
412
+ "full_name": "iter_deriv_pow'",
413
+ "start": [
414
+ 132,
415
+ 1
416
+ ],
417
+ "traced_tactics": [],
418
+ "url": "https://github.com/leanprover-community/mathlib4"
419
+ },
420
+ "source_file": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean"
421
+ },
422
+ {
423
+ "error": "theorem has no selected tactic transitions",
424
+ "full_name": "iter_deriv_zpow",
425
+ "id": "iter_deriv_zpow",
426
+ "reason": "import_failure",
427
+ "selection": {
428
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
429
+ "end": [
430
+ 118,
431
+ 37
432
+ ],
433
+ "file_path": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean",
434
+ "full_name": "iter_deriv_zpow",
435
+ "start": [
436
+ 116,
437
+ 1
438
+ ],
439
+ "traced_tactics": [],
440
+ "url": "https://github.com/leanprover-community/mathlib4"
441
+ },
442
+ "source_file": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean"
443
+ }
444
+ ],
445
+ "input_proofs": 19,
446
+ "input_units": 2,
447
+ "proofs": 5,
448
+ "published_proofs": 2,
449
+ "published_transitions": 6,
450
+ "replay_failures": [],
451
+ "transitions": 20,
452
+ "validation_failures": [
453
+ {
454
+ "errors": [
455
+ "internal transition boundary mismatch",
456
+ "internal transition boundary mismatch"
457
+ ],
458
+ "file_path": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean",
459
+ "proof_id": "mathlib:deriv_zpow",
460
+ "provenance": {
461
+ "selection": {
462
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
463
+ "end": [
464
+ 92,
465
+ 60
466
+ ],
467
+ "file_path": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean",
468
+ "full_name": "deriv_zpow",
469
+ "start": [
470
+ 86,
471
+ 1
472
+ ],
473
+ "traced_tactics": [
474
+ {
475
+ "annotated_tactic": [
476
+ "\"by_cases H : x \\u2260 0 \\u2228 0 \\u2264 m\"",
477
+ "[]"
478
+ ],
479
+ "state_after": "case pos\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nH : x \u2260 0 \u2228 0 \u2264 m\n\u22a2 deriv (fun x => x ^ m) x = \u2191m * x ^ (m - 1)\n\ncase neg\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nH : \u00ac(x \u2260 0 \u2228 0 \u2264 m)\n\u22a2 deriv (fun x => x ^ m) x = \u2191m * x ^ (m - 1)",
480
+ "state_before": "\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\n\u22a2 deriv (fun x => x ^ m) x = \u2191m * x ^ (m - 1)",
481
+ "tactic": "by_cases H : x \u2260 0 \u2228 0 \u2264 m"
482
+ },
483
+ {
484
+ "annotated_tactic": [
485
+ "\"exact (<a>hasDerivAt_zpow<\\/a> m x H).<a>deriv<\\/a>\"",
486
+ "[{\"full_name\":\"hasDerivAt_zpow\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Deriv\\/ZPow.lean\",\"def_pos\":[61,9],\"def_end_pos\":[61,24]},{\"full_name\":\"HasDerivAt.deriv\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Deriv\\/Basic.lean\",\"def_pos\":[453,9],\"def_end_pos\":[453,25]}]"
487
+ ],
488
+ "state_after": "no goals",
489
+ "state_before": "case pos\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nH : x \u2260 0 \u2228 0 \u2264 m\n\u22a2 deriv (fun x => x ^ m) x = \u2191m * x ^ (m - 1)",
490
+ "tactic": "exact (hasDerivAt_zpow m x H).deriv"
491
+ },
492
+ {
493
+ "annotated_tactic": [
494
+ "\"rw [<a>deriv_zero_of_not_differentiableAt<\\/a> (<a>mt<\\/a> <a>differentiableAt_zpow<\\/a>.1 H)]\"",
495
+ "[{\"full_name\":\"deriv_zero_of_not_differentiableAt\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Deriv\\/Basic.lean\",\"def_pos\":[246,9],\"def_end_pos\":[246,43]},{\"full_name\":\"mt\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[647,9],\"def_end_pos\":[647,11]},{\"full_name\":\"differentiableAt_zpow\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Deriv\\/ZPow.lean\",\"def_pos\":[71,9],\"def_end_pos\":[71,30]}]"
496
+ ],
497
+ "state_after": "case neg\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nH : \u00ac(x \u2260 0 \u2228 0 \u2264 m)\n\u22a2 0 = \u2191m * x ^ (m - 1)",
498
+ "state_before": "case neg\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nH : \u00ac(x \u2260 0 \u2228 0 \u2264 m)\n\u22a2 deriv (fun x => x ^ m) x = \u2191m * x ^ (m - 1)",
499
+ "tactic": "rw [deriv_zero_of_not_differentiableAt (mt differentiableAt_zpow.1 H)]"
500
+ },
501
+ {
502
+ "annotated_tactic": [
503
+ "\"push_neg at H\"",
504
+ "[]"
505
+ ],
506
+ "state_after": "case neg\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nH : x = 0 \u2227 m < 0\n\u22a2 0 = \u2191m * x ^ (m - 1)",
507
+ "state_before": "case neg\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nH : \u00ac(x \u2260 0 \u2228 0 \u2264 m)\n\u22a2 0 = \u2191m * x ^ (m - 1)",
508
+ "tactic": "push_neg at H"
509
+ },
510
+ {
511
+ "annotated_tactic": [
512
+ "\"rcases H with \\u27e8rfl, hm\\u27e9\"",
513
+ "[]"
514
+ ],
515
+ "state_after": "case neg.intro\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nhm : m < 0\n\u22a2 0 = \u2191m * 0 ^ (m - 1)",
516
+ "state_before": "case neg\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nx : \ud835\udd5c\nH : x = 0 \u2227 m < 0\n\u22a2 0 = \u2191m * x ^ (m - 1)",
517
+ "tactic": "rcases H with \u27e8rfl, hm\u27e9"
518
+ },
519
+ {
520
+ "annotated_tactic": [
521
+ "\"rw [<a>zero_zpow<\\/a> _ ((<a>sub_one_lt<\\/a> _).<a>trans<\\/a> hm).<a>ne<\\/a>, <a>mul_zero<\\/a>]\"",
522
+ "[{\"full_name\":\"zero_zpow\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Basic.lean\",\"def_pos\":[444,7],\"def_end_pos\":[444,16]},{\"full_name\":\"sub_one_lt\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Ring\\/Defs.lean\",\"def_pos\":[1261,7],\"def_end_pos\":[1261,17]},{\"full_name\":\"LT.lt.trans\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[139,7],\"def_end_pos\":[139,18]},{\"full_name\":\"LT.lt.ne\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[147,7],\"def_end_pos\":[147,15]},{\"full_name\":\"MulZeroClass.mul_zero\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Defs.lean\",\"def_pos\":[39,3],\"def_end_pos\":[39,11]}]"
523
+ ],
524
+ "state_after": "no goals",
525
+ "state_before": "case neg.intro\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nhm : m < 0\n\u22a2 0 = \u2191m * 0 ^ (m - 1)",
526
+ "tactic": "rw [zero_zpow _ ((sub_one_lt _).trans hm).ne, mul_zero]"
527
+ }
528
+ ],
529
+ "url": "https://github.com/leanprover-community/mathlib4"
530
+ }
531
+ },
532
+ "theorem_name": "deriv_zpow"
533
+ },
534
+ {
535
+ "errors": [
536
+ "internal transition boundary mismatch",
537
+ "internal transition boundary mismatch"
538
+ ],
539
+ "file_path": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean",
540
+ "proof_id": "mathlib:iter_deriv_pow",
541
+ "provenance": {
542
+ "selection": {
543
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
544
+ "end": [
545
+ 128,
546
+ 31
547
+ ],
548
+ "file_path": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean",
549
+ "full_name": "iter_deriv_pow",
550
+ "start": [
551
+ 121,
552
+ 1
553
+ ],
554
+ "traced_tactics": [
555
+ {
556
+ "annotated_tactic": [
557
+ "\"simp only [\\u2190 <a>zpow_natCast<\\/a>, <a>iter_deriv_zpow<\\/a>, <a>Int.cast_natCast<\\/a>]\"",
558
+ "[{\"full_name\":\"zpow_natCast\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[1021,9],\"def_end_pos\":[1021,21]},{\"full_name\":\"iter_deriv_zpow\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Deriv\\/ZPow.lean\",\"def_pos\":[116,9],\"def_end_pos\":[116,24]},{\"full_name\":\"Int.cast_natCast\",\"def_path\":\"Mathlib\\/Data\\/Int\\/Cast\\/Basic.lean\",\"def_pos\":[66,9],\"def_end_pos\":[66,21]}]"
559
+ ],
560
+ "state_after": "\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm : \u2124\nn : \u2115\nx : \ud835\udd5c\nk : \u2115\n\u22a2 (\u220f x \u2208 Finset.range k, (\u2191n - \u2191x)) * x ^ (\u2191n - \u2191k) = (\u220f i \u2208 Finset.range k, (\u2191n - \u2191i)) * x ^ \u2191(n - k)",
561
+ "state_before": "\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm : \u2124\nn : \u2115\nx : \ud835\udd5c\nk : \u2115\n\u22a2 deriv^[k] (fun x => x ^ n) x = (\u220f i \u2208 Finset.range k, (\u2191n - \u2191i)) * x ^ (n - k)",
562
+ "tactic": "simp only [\u2190 zpow_natCast, iter_deriv_zpow, Int.cast_natCast]"
563
+ },
564
+ {
565
+ "annotated_tactic": [
566
+ "\"rcases <a>le_or_lt<\\/a> k n with hkn | hnk\"",
567
+ "[{\"full_name\":\"le_or_lt\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[342,9],\"def_end_pos\":[342,17]}]"
568
+ ],
569
+ "state_after": "case inl\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm : \u2124\nn : \u2115\nx : \ud835\udd5c\nk : \u2115\nhkn : k \u2264 n\n\u22a2 (\u220f x \u2208 Finset.range k, (\u2191n - \u2191x)) * x ^ (\u2191n - \u2191k) = (\u220f i \u2208 Finset.range k, (\u2191n - \u2191i)) * x ^ \u2191(n - k)\n\ncase inr\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm : \u2124\nn : \u2115\nx : \ud835\udd5c\nk : \u2115\nhnk : n < k\n\u22a2 (\u220f x \u2208 Finset.range k, (\u2191n - \u2191x)) * x ^ (\u2191n - \u2191k) = (\u220f i \u2208 Finset.range k, (\u2191n - \u2191i)) * x ^ \u2191(n - k)",
570
+ "state_before": "\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm : \u2124\nn : \u2115\nx : \ud835\udd5c\nk : \u2115\n\u22a2 (\u220f x \u2208 Finset.range k, (\u2191n - \u2191x)) * x ^ (\u2191n - \u2191k) = (\u220f i \u2208 Finset.range k, (\u2191n - \u2191i)) * x ^ \u2191(n - k)",
571
+ "tactic": "rcases le_or_lt k n with hkn | hnk"
572
+ },
573
+ {
574
+ "annotated_tactic": [
575
+ "\"rw [<a>Int.ofNat_sub<\\/a> hkn]\"",
576
+ "[{\"full_name\":\"Int.ofNat_sub\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Lemmas.lean\",\"def_pos\":[302,22],\"def_end_pos\":[302,31]}]"
577
+ ],
578
+ "state_after": "no goals",
579
+ "state_before": "case inl\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm : \u2124\nn : \u2115\nx : \ud835\udd5c\nk : \u2115\nhkn : k \u2264 n\n\u22a2 (\u220f x \u2208 Finset.range k, (\u2191n - \u2191x)) * x ^ (\u2191n - \u2191k) = (\u220f i \u2208 Finset.range k, (\u2191n - \u2191i)) * x ^ \u2191(n - k)",
580
+ "tactic": "rw [Int.ofNat_sub hkn]"
581
+ },
582
+ {
583
+ "annotated_tactic": [
584
+ "\"have : (\\u220f i \\u2208 <a>Finset.range<\\/a> k, (n - i : \\ud835\\udd5c)) = 0 :=\\n <a>Finset.prod_eq_zero<\\/a> (<a>Finset.mem_range<\\/a>.2 hnk) (<a>sub_self<\\/a> _)\"",
585
+ "[{\"full_name\":\"Finset.range\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[2925,5],\"def_end_pos\":[2925,10]},{\"full_name\":\"Finset.prod_eq_zero\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/GroupWithZero\\/Finset.lean\",\"def_pos\":[25,7],\"def_end_pos\":[25,19]},{\"full_name\":\"Finset.mem_range\",\"def_path\":\"Mathlib\\/Data\\/Finset\\/Basic.lean\",\"def_pos\":[2935,9],\"def_end_pos\":[2935,18]},{\"full_name\":\"sub_self\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[1003,30],\"def_end_pos\":[1003,38]}]"
586
+ ],
587
+ "state_after": "case inr\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm : \u2124\nn : \u2115\nx : \ud835\udd5c\nk : \u2115\nhnk : n < k\nthis : \u220f i \u2208 Finset.range k, (\u2191n - \u2191i) = 0\n\u22a2 (\u220f x \u2208 Finset.range k, (\u2191n - \u2191x)) * x ^ (\u2191n - \u2191k) = (\u220f i \u2208 Finset.range k, (\u2191n - \u2191i)) * x ^ \u2191(n - k)",
588
+ "state_before": "case inr\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm : \u2124\nn : \u2115\nx : \ud835\udd5c\nk : \u2115\nhnk : n < k\n\u22a2 (\u220f x \u2208 Finset.range k, (\u2191n - \u2191x)) * x ^ (\u2191n - \u2191k) = (\u220f i \u2208 Finset.range k, (\u2191n - \u2191i)) * x ^ \u2191(n - k)",
589
+ "tactic": "have : (\u220f i \u2208 Finset.range k, (n - i : \ud835\udd5c)) = 0 :=\n Finset.prod_eq_zero (Finset.mem_range.2 hnk) (sub_self _)"
590
+ },
591
+ {
592
+ "annotated_tactic": [
593
+ "\"simp only [this, <a>zero_mul<\\/a>]\"",
594
+ "[{\"full_name\":\"MulZeroClass.zero_mul\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Defs.lean\",\"def_pos\":[37,3],\"def_end_pos\":[37,11]}]"
595
+ ],
596
+ "state_after": "no goals",
597
+ "state_before": "case inr\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nm : \u2124\nn : \u2115\nx : \ud835\udd5c\nk : \u2115\nhnk : n < k\nthis : \u220f i \u2208 Finset.range k, (\u2191n - \u2191i) = 0\n\u22a2 (\u220f x \u2208 Finset.range k, (\u2191n - \u2191x)) * x ^ (\u2191n - \u2191k) = (\u220f i \u2208 Finset.range k, (\u2191n - \u2191i)) * x ^ \u2191(n - k)",
598
+ "tactic": "simp only [this, zero_mul]"
599
+ }
600
+ ],
601
+ "url": "https://github.com/leanprover-community/mathlib4"
602
+ }
603
+ },
604
+ "theorem_name": "iter_deriv_pow"
605
+ },
606
+ {
607
+ "errors": [
608
+ "internal transition boundary mismatch",
609
+ "internal transition boundary mismatch"
610
+ ],
611
+ "file_path": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean",
612
+ "proof_id": "mathlib:iter_deriv_zpow'",
613
+ "provenance": {
614
+ "selection": {
615
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
616
+ "end": [
617
+ 113,
618
+ 100
619
+ ],
620
+ "file_path": "Mathlib/Analysis/Calculus/Deriv/ZPow.lean",
621
+ "full_name": "iter_deriv_zpow'",
622
+ "start": [
623
+ 106,
624
+ 1
625
+ ],
626
+ "traced_tactics": [
627
+ {
628
+ "annotated_tactic": [
629
+ "\"induction' k with k ihk\"",
630
+ "[]"
631
+ ],
632
+ "state_after": "case zero\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\n\u22a2 (deriv^[0] fun x => x ^ m) = fun x => (\u220f i \u2208 Finset.range 0, (\u2191m - \u2191i)) * x ^ (m - \u21910)\n\ncase succ\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nk : \u2115\nihk : (deriv^[k] fun x => x ^ m) = fun x => (\u220f i \u2208 Finset.range k, (\u2191m - \u2191i)) * x ^ (m - \u2191k)\n\u22a2 (deriv^[k + 1] fun x => x ^ m) = fun x => (\u220f i \u2208 Finset.range (k + 1), (\u2191m - \u2191i)) * x ^ (m - \u2191(k + 1))",
633
+ "state_before": "\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nk : \u2115\n\u22a2 (deriv^[k] fun x => x ^ m) = fun x => (\u220f i \u2208 Finset.range k, (\u2191m - \u2191i)) * x ^ (m - \u2191k)",
634
+ "tactic": "induction' k with k ihk"
635
+ },
636
+ {
637
+ "annotated_tactic": [
638
+ "\"simp only [<a>Nat.zero_eq<\\/a>, <a>one_mul<\\/a>, <a>Int.ofNat_zero<\\/a>, <a>id<\\/a>, <a>sub_zero<\\/a>, <a>Finset.prod_range_zero<\\/a>,\\n <a>Function.iterate_zero<\\/a>]\"",
639
+ "[{\"full_name\":\"Nat.zero_eq\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Nat\\/Basic.lean\",\"def_pos\":[106,17],\"def_end_pos\":[106,24]},{\"full_name\":\"one_mul\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[477,9],\"def_end_pos\":[477,16]},{\"full_name\":\"Int.ofNat_zero\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Basic.lean\",\"def_pos\":[73,17],\"def_end_pos\":[73,27]},{\"full_name\":\"id\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[33,15],\"def_end_pos\":[33,17]},{\"full_name\":\"sub_zero\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[489,3],\"def_end_pos\":[489,14]},{\"full_name\":\"Finset.prod_range_zero\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Finset.lean\",\"def_pos\":[1562,9],\"def_end_pos\":[1562,24]},{\"full_name\":\"Function.iterate_zero\",\"def_path\":\"Mathlib\\/Logic\\/Function\\/Iterate.lean\",\"def_pos\":[53,9],\"def_end_pos\":[53,21]}]"
640
+ ],
641
+ "state_after": "no goals",
642
+ "state_before": "case zero\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\n\u22a2 (deriv^[0] fun x => x ^ m) = fun x => (\u220f i \u2208 Finset.range 0, (\u2191m - \u2191i)) * x ^ (m - \u21910)",
643
+ "tactic": "simp only [Nat.zero_eq, one_mul, Int.ofNat_zero, id, sub_zero, Finset.prod_range_zero,\n Function.iterate_zero]"
644
+ },
645
+ {
646
+ "annotated_tactic": [
647
+ "\"simp only [<a>Function.iterate_succ_apply'<\\/a>, ihk, <a>deriv_const_mul_field'<\\/a>, <a>deriv_zpow'<\\/a>,\\n <a>Finset.prod_range_succ<\\/a>, <a>Int.ofNat_succ<\\/a>, \\u2190 <a>sub_sub<\\/a>, <a>Int.cast_sub<\\/a>, <a>Int.cast_natCast<\\/a>, <a>mul_assoc<\\/a>]\"",
648
+ "[{\"full_name\":\"Function.iterate_succ_apply'\",\"def_path\":\"Mathlib\\/Logic\\/Function\\/Iterate.lean\",\"def_pos\":[191,9],\"def_end_pos\":[191,28]},{\"full_name\":\"deriv_const_mul_field'\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Deriv\\/Mul.lean\",\"def_pos\":[323,9],\"def_end_pos\":[323,31]},{\"full_name\":\"deriv_zpow'\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Deriv\\/ZPow.lean\",\"def_pos\":[96,9],\"def_end_pos\":[96,20]},{\"full_name\":\"Finset.prod_range_succ\",\"def_path\":\"Mathlib\\/Algebra\\/BigOperators\\/Group\\/Finset.lean\",\"def_pos\":[1520,9],\"def_end_pos\":[1520,24]},{\"full_name\":\"Int.ofNat_succ\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Data\\/Int\\/Lemmas.lean\",\"def_pos\":[27,9],\"def_end_pos\":[27,19]},{\"full_name\":\"sub_sub\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Basic.lean\",\"def_pos\":[770,3],\"def_end_pos\":[770,14]},{\"full_name\":\"Int.cast_sub\",\"def_path\":\"Mathlib\\/Data\\/Int\\/Cast\\/Basic.lean\",\"def_pos\":[123,9],\"def_end_pos\":[123,17]},{\"full_name\":\"Int.cast_natCast\",\"def_path\":\"Mathlib\\/Data\\/Int\\/Cast\\/Basic.lean\",\"def_pos\":[66,9],\"def_end_pos\":[66,21]},{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]}]"
649
+ ],
650
+ "state_after": "no goals",
651
+ "state_before": "case succ\n\ud835\udd5c : Type u\ninst\u271d\u00b2 : NontriviallyNormedField \ud835\udd5c\nE : Type v\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : NormedSpace \ud835\udd5c E\nx : \ud835\udd5c\ns : Set \ud835\udd5c\nm\u271d m : \u2124\nk : \u2115\nihk : (deriv^[k] fun x => x ^ m) = fun x => (\u220f i \u2208 Finset.range k, (\u2191m - \u2191i)) * x ^ (m - \u2191k)\n\u22a2 (deriv^[k + 1] fun x => x ^ m) = fun x => (\u220f i \u2208 Finset.range (k + 1), (\u2191m - \u2191i)) * x ^ (m - \u2191(k + 1))",
652
+ "tactic": "simp only [Function.iterate_succ_apply', ihk, deriv_const_mul_field', deriv_zpow',\n Finset.prod_range_succ, Int.ofNat_succ, \u2190 sub_sub, Int.cast_sub, Int.cast_natCast, mul_assoc]"
653
+ }
654
+ ],
655
+ "url": "https://github.com/leanprover-community/mathlib4"
656
+ }
657
+ },
658
+ "theorem_name": "iter_deriv_zpow'"
659
+ }
660
+ ],
661
+ "validation_rejected_proofs": 3,
662
+ "zero_transition_proofs": 0
663
+ },
664
+ "shards": [
665
+ {
666
+ "path": "data/train/mathlib-000412-0000-a3e0e1e23758c26d.parquet",
667
+ "sha256": "a3e0e1e23758c26d82329b4dbc50179227b0462bb4789b98a9f6b535e7d7b1b3",
668
+ "bytes": 61849,
669
+ "rows": 6,
670
+ "revision": "160f1cc216c96ed97eed787dd32318f0ea6b31a0"
671
+ }
672
+ ],
673
+ "proof_ids": [
674
+ "mathlib:iter_deriv_inv",
675
+ "mathlib:support_deriv_subset"
676
+ ],
677
+ "proof_keys": [
678
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Deriv/Support.lean\",null,null,\"support_deriv_subset\"]",
679
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/Calculus/Deriv/ZPow.lean\",null,null,\"iter_deriv_inv\"]"
680
+ ]
681
+ }
manifests/batches/mathlib/000413.json ADDED
@@ -0,0 +1,967 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000413",
4
+ "batch_fingerprint": "3989df5a389827b3b7c3af3247a4cdb26066dd3ac6452147b9862c5aa7f6df30",
5
+ "evidence": {
6
+ "batch_fingerprint": "3989df5a389827b3b7c3af3247a4cdb26066dd3ac6452147b9862c5aa7f6df30",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "DiffContOnCl.add",
12
+ "id": "DiffContOnCl.add",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 92,
18
+ 33
19
+ ],
20
+ "file_path": "Mathlib/Analysis/Calculus/DiffContOnCl.lean",
21
+ "full_name": "DiffContOnCl.add",
22
+ "start": [
23
+ 91,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/Analysis/Calculus/DiffContOnCl.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "DiffContOnCl.add_const",
34
+ "id": "DiffContOnCl.add_const",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 96,
40
+ 28
41
+ ],
42
+ "file_path": "Mathlib/Analysis/Calculus/DiffContOnCl.lean",
43
+ "full_name": "DiffContOnCl.add_const",
44
+ "start": [
45
+ 95,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/Analysis/Calculus/DiffContOnCl.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "DiffContOnCl.comp",
56
+ "id": "DiffContOnCl.comp",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 61,
62
+ 71
63
+ ],
64
+ "file_path": "Mathlib/Analysis/Calculus/DiffContOnCl.lean",
65
+ "full_name": "DiffContOnCl.comp",
66
+ "start": [
67
+ 59,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/Analysis/Calculus/DiffContOnCl.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "DiffContOnCl.const_add",
78
+ "id": "DiffContOnCl.const_add",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 100,
84
+ 28
85
+ ],
86
+ "file_path": "Mathlib/Analysis/Calculus/DiffContOnCl.lean",
87
+ "full_name": "DiffContOnCl.const_add",
88
+ "start": [
89
+ 99,
90
+ 1
91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/Analysis/Calculus/DiffContOnCl.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "DiffContOnCl.const_smul",
100
+ "id": "DiffContOnCl.const_smul",
101
+ "reason": "import_failure",
102
+ "selection": {
103
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
104
+ "end": [
105
+ 121,
106
+ 41
107
+ ],
108
+ "file_path": "Mathlib/Analysis/Calculus/DiffContOnCl.lean",
109
+ "full_name": "DiffContOnCl.const_smul",
110
+ "start": [
111
+ 119,
112
+ 1
113
+ ],
114
+ "traced_tactics": [],
115
+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
+ "source_file": "Mathlib/Analysis/Calculus/DiffContOnCl.lean"
118
+ },
119
+ {
120
+ "error": "theorem has no selected tactic transitions",
121
+ "full_name": "DiffContOnCl.const_sub",
122
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687
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688
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689
+ "source_file": "Mathlib/Analysis/Calculus/Dslope.lean"
690
+ },
691
+ {
692
+ "error": "theorem has no selected tactic transitions",
693
+ "full_name": "dslope_same",
694
+ "id": "dslope_same",
695
+ "reason": "import_failure",
696
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697
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699
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701
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702
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703
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704
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705
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706
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707
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708
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709
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710
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711
+ "source_file": "Mathlib/Analysis/Calculus/Dslope.lean"
712
+ },
713
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714
+ "error": "theorem has no selected tactic transitions",
715
+ "full_name": "dslope_sub_smul",
716
+ "id": "dslope_sub_smul",
717
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718
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719
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720
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721
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722
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723
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724
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725
+ "full_name": "dslope_sub_smul",
726
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727
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728
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729
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730
+ "traced_tactics": [],
731
+ "url": "https://github.com/leanprover-community/mathlib4"
732
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733
+ "source_file": "Mathlib/Analysis/Calculus/Dslope.lean"
734
+ },
735
+ {
736
+ "error": "theorem has no selected tactic transitions",
737
+ "full_name": "eqOn_dslope_slope",
738
+ "id": "eqOn_dslope_slope",
739
+ "reason": "import_failure",
740
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741
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
742
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743
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744
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745
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746
+ "file_path": "Mathlib/Analysis/Calculus/Dslope.lean",
747
+ "full_name": "eqOn_dslope_slope",
748
+ "start": [
749
+ 55,
750
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751
+ ],
752
+ "traced_tactics": [],
753
+ "url": "https://github.com/leanprover-community/mathlib4"
754
+ },
755
+ "source_file": "Mathlib/Analysis/Calculus/Dslope.lean"
756
+ },
757
+ {
758
+ "error": "theorem has no selected tactic transitions",
759
+ "full_name": "eqOn_dslope_sub_smul",
760
+ "id": "eqOn_dslope_sub_smul",
761
+ "reason": "import_failure",
762
+ "selection": {
763
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
764
+ "end": [
765
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766
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767
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768
+ "file_path": "Mathlib/Analysis/Calculus/Dslope.lean",
769
+ "full_name": "eqOn_dslope_sub_smul",
770
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771
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772
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773
+ ],
774
+ "traced_tactics": [],
775
+ "url": "https://github.com/leanprover-community/mathlib4"
776
+ },
777
+ "source_file": "Mathlib/Analysis/Calculus/Dslope.lean"
778
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779
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780
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781
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782
+ "proofs": 12,
783
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784
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785
+ "replay_failures": [],
786
+ "transitions": 28,
787
+ "validation_failures": [
788
+ {
789
+ "errors": [
790
+ "internal transition boundary mismatch",
791
+ "internal transition boundary mismatch"
792
+ ],
793
+ "file_path": "Mathlib/Analysis/Calculus/DiffContOnCl.lean",
794
+ "proof_id": "mathlib:DiffContOnCl.continuousOn_ball",
795
+ "provenance": {
796
+ "selection": {
797
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
798
+ "end": [
799
+ 70,
800
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801
+ ],
802
+ "file_path": "Mathlib/Analysis/Calculus/DiffContOnCl.lean",
803
+ "full_name": "DiffContOnCl.continuousOn_ball",
804
+ "start": [
805
+ 64,
806
+ 1
807
+ ],
808
+ "traced_tactics": [
809
+ {
810
+ "annotated_tactic": [
811
+ "\"rcases <a>eq_or_ne<\\/a> r 0 with (rfl | hr)\"",
812
+ "[{\"full_name\":\"eq_or_ne\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[212,9],\"def_end_pos\":[212,17]}]"
813
+ ],
814
+ "state_after": "case inl\n\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst\u271d\u2077 : NontriviallyNormedField \ud835\udd5c\ninst\u271d\u2076 : NormedAddCommGroup E\ninst\u271d\u2075 : NormedAddCommGroup F\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : NormedSpace \ud835\udd5c F\ninst\u271d\u00b2 : NormedAddCommGroup G\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c G\nf g : E \u2192 F\ns t : Set E\nx\u271d : E\ninst\u271d : NormedSpace \u211d E\nx : E\nh : DiffContOnCl \ud835\udd5c f (ball x 0)\n\u22a2 ContinuousOn f (closedBall x 0)\n\ncase inr\n\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst\u271d\u2077 : NontriviallyNormedField \ud835\udd5c\ninst\u271d\u2076 : NormedAddCommGroup E\ninst\u271d\u2075 : NormedAddCommGroup F\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : NormedSpace \ud835\udd5c F\ninst\u271d\u00b2 : NormedAddCommGroup G\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c G\nf g : E \u2192 F\ns t : Set E\nx\u271d : E\ninst\u271d : NormedSpace \u211d E\nx : E\nr : \u211d\nh : DiffContOnCl \ud835\udd5c f (ball x r)\nhr : r \u2260 0\n\u22a2 ContinuousOn f (closedBall x r)",
815
+ "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst\u271d\u2077 : NontriviallyNormedField \ud835\udd5c\ninst\u271d\u2076 : NormedAddCommGroup E\ninst\u271d\u2075 : NormedAddCommGroup F\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : NormedSpace \ud835\udd5c F\ninst\u271d\u00b2 : NormedAddCommGroup G\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c G\nf g : E \u2192 F\ns t : Set E\nx\u271d : E\ninst\u271d : NormedSpace \u211d E\nx : E\nr : \u211d\nh : DiffContOnCl \ud835\udd5c f (ball x r)\n\u22a2 ContinuousOn f (closedBall x r)",
816
+ "tactic": "rcases eq_or_ne r 0 with (rfl | hr)"
817
+ },
818
+ {
819
+ "annotated_tactic": [
820
+ "\"rw [<a>closedBall_zero<\\/a>]\"",
821
+ "[{\"full_name\":\"Metric.closedBall_zero\",\"def_path\":\"Mathlib\\/Topology\\/MetricSpace\\/Basic.lean\",\"def_pos\":[115,17],\"def_end_pos\":[115,32]}]"
822
+ ],
823
+ "state_after": "case inl\n\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst\u271d\u2077 : NontriviallyNormedField \ud835\udd5c\ninst\u271d\u2076 : NormedAddCommGroup E\ninst\u271d\u2075 : NormedAddCommGroup F\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : NormedSpace \ud835\udd5c F\ninst\u271d\u00b2 : NormedAddCommGroup G\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c G\nf g : E \u2192 F\ns t : Set E\nx\u271d : E\ninst\u271d : NormedSpace \u211d E\nx : E\nh : DiffContOnCl \ud835\udd5c f (ball x 0)\n\u22a2 ContinuousOn f {x}",
824
+ "state_before": "case inl\n\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst\u271d\u2077 : NontriviallyNormedField \ud835\udd5c\ninst\u271d\u2076 : NormedAddCommGroup E\ninst\u271d\u2075 : NormedAddCommGroup F\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : NormedSpace \ud835\udd5c F\ninst\u271d\u00b2 : NormedAddCommGroup G\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c G\nf g : E \u2192 F\ns t : Set E\nx\u271d : E\ninst\u271d : NormedSpace \u211d E\nx : E\nh : DiffContOnCl \ud835\udd5c f (ball x 0)\n\u22a2 ContinuousOn f (closedBall x 0)",
825
+ "tactic": "rw [closedBall_zero]"
826
+ },
827
+ {
828
+ "annotated_tactic": [
829
+ "\"exact <a>continuousOn_singleton<\\/a> f x\"",
830
+ "[{\"full_name\":\"continuousOn_singleton\",\"def_path\":\"Mathlib\\/Topology\\/ContinuousOn.lean\",\"def_pos\":[726,9],\"def_end_pos\":[726,31]}]"
831
+ ],
832
+ "state_after": "no goals",
833
+ "state_before": "case inl\n\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst\u271d\u2077 : NontriviallyNormedField \ud835\udd5c\ninst\u271d\u2076 : NormedAddCommGroup E\ninst\u271d\u2075 : NormedAddCommGroup F\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : NormedSpace \ud835\udd5c F\ninst\u271d\u00b2 : NormedAddCommGroup G\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c G\nf g : E \u2192 F\ns t : Set E\nx\u271d : E\ninst\u271d : NormedSpace \u211d E\nx : E\nh : DiffContOnCl \ud835\udd5c f (ball x 0)\n\u22a2 ContinuousOn f {x}",
834
+ "tactic": "exact continuousOn_singleton f x"
835
+ },
836
+ {
837
+ "annotated_tactic": [
838
+ "\"rw [\\u2190 <a>closure_ball<\\/a> x hr]\"",
839
+ "[{\"full_name\":\"closure_ball\",\"def_path\":\"Mathlib\\/Analysis\\/NormedSpace\\/Real.lean\",\"def_pos\":[61,9],\"def_end_pos\":[61,21]}]"
840
+ ],
841
+ "state_after": "case inr\n\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst\u271d\u2077 : NontriviallyNormedField \ud835\udd5c\ninst\u271d\u2076 : NormedAddCommGroup E\ninst\u271d\u2075 : NormedAddCommGroup F\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : NormedSpace \ud835\udd5c F\ninst\u271d\u00b2 : NormedAddCommGroup G\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c G\nf g : E \u2192 F\ns t : Set E\nx\u271d : E\ninst\u271d : NormedSpace \u211d E\nx : E\nr : \u211d\nh : DiffContOnCl \ud835\udd5c f (ball x r)\nhr : r \u2260 0\n\u22a2 ContinuousOn f (closure (ball x r))",
842
+ "state_before": "case inr\n\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst\u271d\u2077 : NontriviallyNormedField \ud835\udd5c\ninst\u271d\u2076 : NormedAddCommGroup E\ninst\u271d\u2075 : NormedAddCommGroup F\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : NormedSpace \ud835\udd5c F\ninst\u271d\u00b2 : NormedAddCommGroup G\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c G\nf g : E \u2192 F\ns t : Set E\nx\u271d : E\ninst\u271d : NormedSpace \u211d E\nx : E\nr : \u211d\nh : DiffContOnCl \ud835\udd5c f (ball x r)\nhr : r \u2260 0\n\u22a2 ContinuousOn f (closedBall x r)",
843
+ "tactic": "rw [\u2190 closure_ball x hr]"
844
+ },
845
+ {
846
+ "annotated_tactic": [
847
+ "\"exact h.continuousOn\"",
848
+ "[]"
849
+ ],
850
+ "state_after": "no goals",
851
+ "state_before": "case inr\n\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst\u271d\u2077 : NontriviallyNormedField \ud835\udd5c\ninst\u271d\u2076 : NormedAddCommGroup E\ninst\u271d\u2075 : NormedAddCommGroup F\ninst\u271d\u2074 : NormedSpace \ud835\udd5c E\ninst\u271d\u00b3 : NormedSpace \ud835\udd5c F\ninst\u271d\u00b2 : NormedAddCommGroup G\ninst\u271d\u00b9 : NormedSpace \ud835\udd5c G\nf g : E \u2192 F\ns t : Set E\nx\u271d : E\ninst\u271d : NormedSpace \u211d E\nx : E\nr : \u211d\nh : DiffContOnCl \ud835\udd5c f (ball x r)\nhr : r \u2260 0\n\u22a2 ContinuousOn f (closure (ball x r))",
852
+ "tactic": "exact h.continuousOn"
853
+ }
854
+ ],
855
+ "url": "https://github.com/leanprover-community/mathlib4"
856
+ }
857
+ },
858
+ "theorem_name": "DiffContOnCl.continuousOn_ball"
859
+ },
860
+ {
861
+ "errors": [
862
+ "internal transition boundary mismatch",
863
+ "internal transition boundary mismatch"
864
+ ],
865
+ "file_path": "Mathlib/Analysis/Calculus/Dslope.lean",
866
+ "proof_id": "mathlib:ContinuousLinearMap.dslope_comp",
867
+ "provenance": {
868
+ "selection": {
869
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
870
+ "end": [
871
+ 52,
872
+ 73
873
+ ],
874
+ "file_path": "Mathlib/Analysis/Calculus/Dslope.lean",
875
+ "full_name": "ContinuousLinearMap.dslope_comp",
876
+ "start": [
877
+ 46,
878
+ 1
879
+ ],
880
+ "traced_tactics": [
881
+ {
882
+ "annotated_tactic": [
883
+ "\"rcases <a>eq_or_ne<\\/a> b a with (rfl | hne)\"",
884
+ "[{\"full_name\":\"eq_or_ne\",\"def_path\":\"Mathlib\\/Logic\\/Basic.lean\",\"def_pos\":[212,9],\"def_end_pos\":[212,17]}]"
885
+ ],
886
+ "state_after": "case inl\n\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u2074 : NontriviallyNormedField \ud835\udd5c\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c E\nf\u271d : \ud835\udd5c \u2192 E\na b\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nF : Type u_3\ninst\u271d\u00b9 : NormedAddCommGroup F\ninst\u271d : NormedSpace \ud835\udd5c F\nf : E \u2192L[\ud835\udd5c] F\ng : \ud835\udd5c \u2192 E\nb : \ud835\udd5c\nH : b = b \u2192 DifferentiableAt \ud835\udd5c g b\n\u22a2 dslope (\u21d1f \u2218 g) b b = f (dslope g b b)\n\ncase inr\n\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u2074 : NontriviallyNormedField \ud835\udd5c\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c E\nf\u271d : \ud835\udd5c \u2192 E\na\u271d b\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nF : Type u_3\ninst\u271d\u00b9 : NormedAddCommGroup F\ninst\u271d : NormedSpace \ud835\udd5c F\nf : E \u2192L[\ud835\udd5c] F\ng : \ud835\udd5c \u2192 E\na b : \ud835\udd5c\nH : a = b \u2192 DifferentiableAt \ud835\udd5c g a\nhne : b \u2260 a\n\u22a2 dslope (\u21d1f \u2218 g) a b = f (dslope g a b)",
887
+ "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u2074 : NontriviallyNormedField \ud835\udd5c\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c E\nf\u271d : \ud835\udd5c \u2192 E\na\u271d b\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nF : Type u_3\ninst\u271d\u00b9 : NormedAddCommGroup F\ninst\u271d : NormedSpace \ud835\udd5c F\nf : E \u2192L[\ud835\udd5c] F\ng : \ud835\udd5c \u2192 E\na b : \ud835\udd5c\nH : a = b \u2192 DifferentiableAt \ud835\udd5c g a\n\u22a2 dslope (\u21d1f \u2218 g) a b = f (dslope g a b)",
888
+ "tactic": "rcases eq_or_ne b a with (rfl | hne)"
889
+ },
890
+ {
891
+ "annotated_tactic": [
892
+ "\"simp only [<a>dslope_same<\\/a>]\"",
893
+ "[{\"full_name\":\"dslope_same\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Dslope.lean\",\"def_pos\":[36,9],\"def_end_pos\":[36,20]}]"
894
+ ],
895
+ "state_after": "case inl\n\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u2074 : NontriviallyNormedField \ud835\udd5c\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c E\nf\u271d : \ud835\udd5c \u2192 E\na b\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nF : Type u_3\ninst\u271d\u00b9 : NormedAddCommGroup F\ninst\u271d : NormedSpace \ud835\udd5c F\nf : E \u2192L[\ud835\udd5c] F\ng : \ud835\udd5c \u2192 E\nb : \ud835\udd5c\nH : b = b \u2192 DifferentiableAt \ud835\udd5c g b\n\u22a2 deriv (\u21d1f \u2218 g) b = f (deriv g b)",
896
+ "state_before": "case inl\n\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u2074 : NontriviallyNormedField \ud835\udd5c\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c E\nf\u271d : \ud835\udd5c \u2192 E\na b\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nF : Type u_3\ninst\u271d\u00b9 : NormedAddCommGroup F\ninst\u271d : NormedSpace \ud835\udd5c F\nf : E \u2192L[\ud835\udd5c] F\ng : \ud835\udd5c \u2192 E\nb : \ud835\udd5c\nH : b = b \u2192 DifferentiableAt \ud835\udd5c g b\n\u22a2 dslope (\u21d1f \u2218 g) b b = f (dslope g b b)",
897
+ "tactic": "simp only [dslope_same]"
898
+ },
899
+ {
900
+ "annotated_tactic": [
901
+ "\"exact (f.hasFDerivAt.comp_hasDerivAt b (H <a>rfl<\\/a>).<a>hasDerivAt<\\/a>).<a>deriv<\\/a>\"",
902
+ "[{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]},{\"full_name\":\"DifferentiableAt.hasDerivAt\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Deriv\\/Basic.lean\",\"def_pos\":[433,9],\"def_end_pos\":[433,36]},{\"full_name\":\"HasDerivAt.deriv\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Deriv\\/Basic.lean\",\"def_pos\":[453,9],\"def_end_pos\":[453,25]}]"
903
+ ],
904
+ "state_after": "no goals",
905
+ "state_before": "case inl\n\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u2074 : NontriviallyNormedField \ud835\udd5c\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedSpace \ud835\udd5c E\nf\u271d : \ud835\udd5c \u2192 E\na b\u271d : \ud835\udd5c\ns : Set \ud835\udd5c\nF : Type u_3\ninst\u271d\u00b9 : NormedAddCommGroup F\ninst\u271d : NormedSpace \ud835\udd5c F\nf : E \u2192L[\ud835\udd5c] F\ng : \ud835\udd5c \u2192 E\nb : \ud835\udd5c\nH : b = b \u2192 DifferentiableAt \ud835\udd5c g b\n\u22a2 deriv (\u21d1f \u2218 g) b = f (deriv g b)",
906
+ "tactic": "exact (f.hasFDerivAt.comp_hasDerivAt b (H rfl).hasDerivAt).deriv"
907
+ },
908
+ {
909
+ "annotated_tactic": [
910
+ "\"simpa only [<a>dslope_of_ne<\\/a> _ hne] using f.toLinearMap.slope_comp g a b\"",
911
+ "[{\"full_name\":\"dslope_of_ne\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/Dslope.lean\",\"def_pos\":[42,9],\"def_end_pos\":[42,21]}]"
912
+ ],
913
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