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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
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1
HyperCactus0 commited on
Commit
cf40ea1
·
verified ·
1 Parent(s): 03bde7f

Record 9 verified HPC batch manifests

Browse files
Files changed (9) hide show
  1. manifests/batches/deepseek/000548.json +148 -0
  2. manifests/batches/deepseek/000549.json +148 -0
  3. manifests/batches/deepseek/000550.json +54 -0
  4. manifests/batches/mathlib/000477.json +0 -0
  5. manifests/batches/mathlib/000480.json +0 -0
  6. manifests/batches/mathlib/000481.json +0 -0
  7. manifests/batches/mathlib/000483.json +1401 -0
  8. manifests/batches/mathlib/000484.json +457 -0
  9. manifests/batches/numina/001238.json +52 -0
manifests/batches/deepseek/000548.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "deepseek/000548",
4
+ "batch_fingerprint": "7e04979c5023a522f080446a5d1e0af71a7e018003b0733993548660bba7dea0",
5
+ "evidence": {
6
+ "batch_fingerprint": "7e04979c5023a522f080446a5d1e0af71a7e018003b0733993548660bba7dea0",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 50,
10
+ "input_units": 50,
11
+ "proofs": 50,
12
+ "published_proofs": 50,
13
+ "published_transitions": 122,
14
+ "replay_failures": [],
15
+ "trace_mode": "individual",
16
+ "transitions": 122,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/deepseek-000548-0000-7024a154f07a8e3a.parquet",
24
+ "sha256": "7024a154f07a8e3a0513598d85464531740524c17db6b09c5cc75abecaa07993",
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+ "bytes": 311167,
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+ "rows": 101,
27
+ "revision": "03bde7f2d1ad989476e75d92008e2f729cf4919a"
28
+ },
29
+ {
30
+ "path": "data/dev/deepseek-000548-0000-79be2c14a25a38ff.parquet",
31
+ "sha256": "79be2c14a25a38ff2b6cf687143422e3090eec007cdc6fefa0f599fb452ca53d",
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+ "bytes": 46694,
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+ "rows": 9,
34
+ "revision": "03bde7f2d1ad989476e75d92008e2f729cf4919a"
35
+ },
36
+ {
37
+ "path": "data/internal_test/deepseek-000548-0000-779407c0ccd93023.parquet",
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+ "sha256": "779407c0ccd93023e9ef1bf6f8a64049c1c2a1c4508c04e9d14639083fc11ff2",
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+ "bytes": 52765,
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+ "rows": 12,
41
+ "revision": "03bde7f2d1ad989476e75d92008e2f729cf4919a"
42
+ }
43
+ ],
44
+ "proof_ids": [
45
+ "deepseek:thm_27448",
46
+ "deepseek:thm_27449",
47
+ "deepseek:thm_27450",
48
+ "deepseek:thm_27451",
49
+ "deepseek:thm_27452",
50
+ "deepseek:thm_27453",
51
+ "deepseek:thm_27454",
52
+ "deepseek:thm_27455",
53
+ "deepseek:thm_27456",
54
+ "deepseek:thm_27457",
55
+ "deepseek:thm_27458",
56
+ "deepseek:thm_27459",
57
+ "deepseek:thm_27460",
58
+ "deepseek:thm_27461",
59
+ "deepseek:thm_27462",
60
+ "deepseek:thm_27463",
61
+ "deepseek:thm_27464",
62
+ "deepseek:thm_27465",
63
+ "deepseek:thm_27466",
64
+ "deepseek:thm_27467",
65
+ "deepseek:thm_27468",
66
+ "deepseek:thm_27469",
67
+ "deepseek:thm_27470",
68
+ "deepseek:thm_27471",
69
+ "deepseek:thm_27472",
70
+ "deepseek:thm_27473",
71
+ "deepseek:thm_27474",
72
+ "deepseek:thm_27475",
73
+ "deepseek:thm_27476",
74
+ "deepseek:thm_27477",
75
+ "deepseek:thm_27478",
76
+ "deepseek:thm_27479",
77
+ "deepseek:thm_27480",
78
+ "deepseek:thm_27481",
79
+ "deepseek:thm_27482",
80
+ "deepseek:thm_27483",
81
+ "deepseek:thm_27484",
82
+ "deepseek:thm_27485",
83
+ "deepseek:thm_27486",
84
+ "deepseek:thm_27487",
85
+ "deepseek:thm_27488",
86
+ "deepseek:thm_27489",
87
+ "deepseek:thm_27490",
88
+ "deepseek:thm_27491",
89
+ "deepseek:thm_27492",
90
+ "deepseek:thm_27493",
91
+ "deepseek:thm_27494",
92
+ "deepseek:thm_27495",
93
+ "deepseek:thm_27496",
94
+ "deepseek:thm_27497"
95
+ ],
96
+ "proof_keys": [
97
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027400.lean\",\"87fd8cd159bd7b48fcd66f2d1795141ff0dab050cfacf12c8be2556c238e4d53\",0,\"thm_27448\"]",
98
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027401.lean\",\"9992e0ee84cbd6b95f89eaba4af215af896fedce6a91d81d285e07dfc6c75d43\",0,\"thm_27449\"]",
99
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027402.lean\",\"e94545f75883ba3b4b4c93513ac0d859c8a1c8e3651c4232aa8f4f61081f1fc8\",0,\"thm_27450\"]",
100
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027403.lean\",\"ce9e4873f00ba2add59dea85c6dee7eff80a3268f44ef0e45685d5ff756b898a\",0,\"thm_27451\"]",
101
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027404.lean\",\"6ea1b0942dcf076b9e9323b50d09d2764832f83c17326fde66a6a1009c297e15\",0,\"thm_27452\"]",
102
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027405.lean\",\"c1005971e4885f8097b07bb3c273e5a8a1e853d9e4b7e5bfabe16a3ec7f853b0\",0,\"thm_27453\"]",
103
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027406.lean\",\"1e7e55728e14dc047ffd4d9afb7549dae8774542c508d559971c8ab6c260c710\",0,\"thm_27454\"]",
104
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027407.lean\",\"d839c6b97da14c0bb979f5cc67bc235dcc54a4d89f996de19984e4579b0e3955\",0,\"thm_27455\"]",
105
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027408.lean\",\"84dda96ef8f3fb74f4018bb999b0c2d1680358819aa14dc7f4b2202a42c1bf8b\",0,\"thm_27456\"]",
106
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027409.lean\",\"46e5c21be2f4b1c78a0b1511ecce20df444d4f0578723927bbe6f076d0c60372\",0,\"thm_27457\"]",
107
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027410.lean\",\"d1142ffabcfb4af3263dae10897fc6c4c4ef8cd350f25ca833901e6838d9d5f7\",0,\"thm_27458\"]",
108
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027411.lean\",\"54bed0bd6cab0d05a3c0d814c34927e2304588d899aa51b930078f22a84b4527\",0,\"thm_27459\"]",
109
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027412.lean\",\"04ca9354b73f7e521f4cffc7524948d577f83a9ed8ed4a858e3d2c6025912cda\",0,\"thm_27460\"]",
110
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027413.lean\",\"09db6c7c1a7229af056aa53eb8830dd6f744520453f8ab67d2fbeff0a7dcd020\",0,\"thm_27461\"]",
111
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027414.lean\",\"48cd1bc683c254b222801e1c86a5e8dade6f5ea19b2449cba841d0d85fb42adc\",0,\"thm_27462\"]",
112
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027415.lean\",\"778d5133da97eb07b5333582db8964794c99fb27a6fb90577bdef30624f62e6f\",0,\"thm_27463\"]",
113
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027416.lean\",\"ff72602b792c5b30ab84cd254662ebbce31d3040b654acf5720ac8531b589dfe\",0,\"thm_27464\"]",
114
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027417.lean\",\"5cabaf0dfb84faa2839f4187166ecd948289d9f12430b0899e22d1d0f5d7e53e\",0,\"thm_27465\"]",
115
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027418.lean\",\"08a281ed8bb4d4e462de1b91cfeffe2ce1ddb17f6b164b1ce8d4d0b023bac67a\",0,\"thm_27466\"]",
116
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027419.lean\",\"5cb2fc122cd0bfbbcb6419d8d030b68a10f6fa1b8cb15c9b127fd4ef3bd83431\",0,\"thm_27467\"]",
117
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027420.lean\",\"185cc0424225d6dc2a982fd2b1cf993a6bcc1ceb64f7e8fd66e05f90d02fbdf4\",0,\"thm_27468\"]",
118
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027421.lean\",\"53f91e51ae96d726d6d92e36afbfa5eec078059be22609c14093c0ec88ed6cb7\",0,\"thm_27469\"]",
119
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027422.lean\",\"4e4d23de1d4ef68600606ba0b3184a7a11029ab686b4fb2b3a661fd2bfc9b5e0\",0,\"thm_27470\"]",
120
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027423.lean\",\"c0a7e9109f8f3ee61d8eaf7010f98ed10ef32f35d2e0e1ef36b44e8391db2a36\",0,\"thm_27471\"]",
121
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027424.lean\",\"a92dc68223c9df2badc48e698025b5842bb5527b6a296fe93ecb7f271a81365c\",0,\"thm_27472\"]",
122
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027425.lean\",\"d231886bfa2b5c18a643334d22d47ea2952710ca0da9585768e09b9375f42e46\",0,\"thm_27473\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027426.lean\",\"7b573206340a9ead620e02bc009373eb52f0c9aec9838bdc779f9689b9f1d225\",0,\"thm_27474\"]",
124
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027427.lean\",\"e59428bfd39f17c94511ea09f13b8105d3ec5a39ce2c7217bf5bb1d6a6702781\",0,\"thm_27475\"]",
125
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027428.lean\",\"5413c269f800def90e81abe55507ef437c7a3ee847f02a9eb0c951879c27c157\",0,\"thm_27476\"]",
126
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027429.lean\",\"2a35e690dbf5ed4c431312b005c481dfcd4806af5d2ef99e5005948daf8a2133\",0,\"thm_27477\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027430.lean\",\"238032108699352bc968ed263737029cdd1e3c2126c21651fb7cd350992cb6c4\",0,\"thm_27478\"]",
128
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027431.lean\",\"025655970dbeb606cb104340b611498aa3f24127b971cd34bdb59e9df68c2f59\",0,\"thm_27479\"]",
129
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027432.lean\",\"5ed6c9ab85deec1411c0d019a084bfabab2af98d391ef913cd6390a71c92f09b\",0,\"thm_27480\"]",
130
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027433.lean\",\"344fbcb03d60c0694cb03c64a32439bd525badb9351dd32c2645c6d661d67b6f\",0,\"thm_27481\"]",
131
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027434.lean\",\"cb870dd7747a48bb2c8db929a50a6958e7721c9d3afe2425ce24908183180307\",0,\"thm_27482\"]",
132
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027435.lean\",\"91f508ac421304a5355e44b415f72aca64e5d4d5cdb891da29663820c84f55f7\",0,\"thm_27483\"]",
133
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027436.lean\",\"3a90fda1a1be86cc306945a59d8bbb4c63fd711c3e5e9cf53cc748c55cb52189\",0,\"thm_27484\"]",
134
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027437.lean\",\"b4e74d16e39305663e763a484ef47c66e3a67b52b54a6195c9a95ba77d8b1ad7\",0,\"thm_27485\"]",
135
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027438.lean\",\"ddab4420117b05db56ca18cbe14f33051b0ae43e55a54dc1302728cedc6c2019\",0,\"thm_27486\"]",
136
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027439.lean\",\"6b9726ec58e5276304fb5b08e8cd1d0572466b0e7b5326ce0ec02bb5408744a5\",0,\"thm_27487\"]",
137
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027440.lean\",\"e9dbb3b5f0031b1a214cf4481bccbdf742f6b7076fabae2b6ed3c497188b0f9e\",0,\"thm_27488\"]",
138
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027441.lean\",\"2721a2628a9839567301b772acbc296b8c67cbd012177a3f5a691fcedd084ddd\",0,\"thm_27489\"]",
139
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027442.lean\",\"5bec22157aa32e626d75791bc4f2854d68d46cb5c92726470c0930586e9e3199\",0,\"thm_27490\"]",
140
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027443.lean\",\"ecb90f57be002ef63f39faeac83742e418af81a05e8e13d2a9b5ae26ba96d52d\",0,\"thm_27491\"]",
141
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027444.lean\",\"25ac1e6d2d362b199a34e30fb0a5091ec407383b4d92735288f04e4536692df7\",0,\"thm_27492\"]",
142
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027445.lean\",\"016c2cae58826a65da1fe2fbf3f337a528e9c462a160f946d142b8568c24a8e7\",0,\"thm_27493\"]",
143
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027446.lean\",\"4750d0c43f4c26db57bb470d5b0de052e51949b8c4955a45482da74e6765c797\",0,\"thm_27494\"]",
144
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027447.lean\",\"f1255b2ab5fe03dd2b1b0870e0ed5b00afc69734e5952d0abc9c0dc6f4d303f4\",0,\"thm_27495\"]",
145
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027448.lean\",\"68a03904a454fb5c65295614d239ffc98aa3945b5e7a855156ffc05e16ede26f\",0,\"thm_27496\"]",
146
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027449.lean\",\"67b93cd68fd55d116ad7fb8c85174c95603aea9ca1f8bf7d72eae93eb56ec555\",0,\"thm_27497\"]"
147
+ ]
148
+ }
manifests/batches/deepseek/000549.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
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+ "format": "leangpt-parquet-v2",
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+ "batch": "deepseek/000549",
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+ "batch_fingerprint": "af04327d9336ccd3adcbab71bc71ff624f22efc257f933e605b974e8fd32b6be",
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+ "evidence": {
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+ "batch_fingerprint": "af04327d9336ccd3adcbab71bc71ff624f22efc257f933e605b974e8fd32b6be",
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+ "contamination_matches": [],
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+ "failures": [],
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+ "input_proofs": 50,
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+ "input_units": 50,
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+ "proofs": 50,
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+ "published_proofs": 50,
13
+ "published_transitions": 126,
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+ "replay_failures": [],
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+ "trace_mode": "individual",
16
+ "transitions": 126,
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+ "validation_failures": [],
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+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
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+ },
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+ "shards": [
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+ {
23
+ "path": "data/train/deepseek-000549-0000-2b499203f5574810.parquet",
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+ "sha256": "2b499203f5574810354e9bcbd1aaea7a23dcf4dc0da912315dc6833a7c8e341b",
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+ "bytes": 358488,
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+ "rows": 107,
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+ "revision": "03bde7f2d1ad989476e75d92008e2f729cf4919a"
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+ },
29
+ {
30
+ "path": "data/dev/deepseek-000549-0000-660685847ca2cb8a.parquet",
31
+ "sha256": "660685847ca2cb8aeccc51be78ef122df2db901c8e3da9e0e6402679e1fdbacb",
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+ "bytes": 38191,
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+ "rows": 6,
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+ "revision": "03bde7f2d1ad989476e75d92008e2f729cf4919a"
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+ },
36
+ {
37
+ "path": "data/internal_test/deepseek-000549-0000-cffae3d49a127d15.parquet",
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+ "sha256": "cffae3d49a127d1562750d08aef651c04d464eb7dd3ae85beb1f7403e3f46c9a",
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+ "bytes": 56509,
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+ "rows": 13,
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+ "revision": "03bde7f2d1ad989476e75d92008e2f729cf4919a"
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+ }
43
+ ],
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+ "proof_ids": [
45
+ "deepseek:thm_27498",
46
+ "deepseek:thm_27499",
47
+ "deepseek:thm_27500",
48
+ "deepseek:thm_27501",
49
+ "deepseek:thm_27502",
50
+ "deepseek:thm_27503",
51
+ "deepseek:thm_27504",
52
+ "deepseek:thm_27505",
53
+ "deepseek:thm_27506",
54
+ "deepseek:thm_27507",
55
+ "deepseek:thm_27508",
56
+ "deepseek:thm_27509",
57
+ "deepseek:thm_27510",
58
+ "deepseek:thm_27511",
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+ "deepseek:thm_27512",
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+ "deepseek:thm_27513",
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+ "deepseek:thm_27514",
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+ "deepseek:thm_27515",
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+ "deepseek:thm_27516",
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+ "deepseek:thm_27517",
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+ "deepseek:thm_27518",
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+ "deepseek:thm_27519",
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+ "deepseek:thm_27520",
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+ "deepseek:thm_27521",
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+ "deepseek:thm_27522",
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+ "deepseek:thm_27523",
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+ "deepseek:thm_27524",
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+ "deepseek:thm_27525",
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+ "deepseek:thm_27526",
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+ "deepseek:thm_27527",
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+ "deepseek:thm_27528",
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+ "deepseek:thm_27529",
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+ "deepseek:thm_27530",
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+ "deepseek:thm_27531",
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+ "deepseek:thm_27532",
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+ "deepseek:thm_27533",
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+ "deepseek:thm_27534",
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+ "deepseek:thm_27535",
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+ "deepseek:thm_27536",
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+ "deepseek:thm_27537",
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+ "deepseek:thm_27538",
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+ "deepseek:thm_27539",
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+ "deepseek:thm_27540",
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+ "deepseek:thm_27541",
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+ "deepseek:thm_27542",
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+ "deepseek:thm_27543",
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+ "deepseek:thm_27544",
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+ "deepseek:thm_27545",
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+ "deepseek:thm_27546",
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+ "deepseek:thm_27547"
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+ ],
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+ "proof_keys": [
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027451.lean\",\"32da0ba18fb19ca46ce399f875c656539e9b0b8e7fc33985e579ff162813602e\",0,\"thm_27499\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027452.lean\",\"f040487ee239f493190e5ee3ca3263094f7ce7f05a034f7f75bb2c6a4607e1b6\",0,\"thm_27500\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027461.lean\",\"3bf51e4b8a53d9995948d86795a039d9508d44e35e53a5b971c08c883b1d4de1\",0,\"thm_27509\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027462.lean\",\"8547e8b100cb4c390bac5a2d2d375ca400ad245cce465f3280d8801ca54280e4\",0,\"thm_27510\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027464.lean\",\"8e2077848e5d392df5cf7495093e42ebc21a8b7dd0f663b7a8e3741ee6ce7f46\",0,\"thm_27512\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027491.lean\",\"b22a0bff68e601e8b18ea49253b601f49c426ed940cd4b396ceb470e41213aac\",0,\"thm_27539\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027492.lean\",\"19493cfeab880535337e103a4602789f1ea547232b6163616b2aefb0ff3a5e25\",0,\"thm_27540\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027497.lean\",\"0679b074ad8f6e54af2a255a884669d14125e418535e4ff3b9426961022d7fbf\",0,\"thm_27545\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_027498.lean\",\"57bd195a412492e3fde6f620e4f0e09f619620139ea2c46cb8fa30b9b5ce9de1\",0,\"thm_27546\"]",
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147
+ ]
148
+ }
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+ ]
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1
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+ "error": "theorem has no selected tactic transitions",
583
+ "full_name": "DifferentiableWithinAt.norm",
584
+ "id": "DifferentiableWithinAt.norm",
585
+ "reason": "import_failure",
586
+ "selection": {
587
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
588
+ "end": [
589
+ 278,
590
+ 87
591
+ ],
592
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
593
+ "full_name": "DifferentiableWithinAt.norm",
594
+ "start": [
595
+ 276,
596
+ 1
597
+ ],
598
+ "traced_tactics": [],
599
+ "url": "https://github.com/leanprover-community/mathlib4"
600
+ },
601
+ "source_file": "Mathlib/Analysis/InnerProductSpace/Calculus.lean"
602
+ },
603
+ {
604
+ "error": "theorem has no selected tactic transitions",
605
+ "full_name": "DifferentiableWithinAt.norm_sq",
606
+ "id": "DifferentiableWithinAt.norm_sq",
607
+ "reason": "import_failure",
608
+ "selection": {
609
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
610
+ "end": [
611
+ 273,
612
+ 87
613
+ ],
614
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
615
+ "full_name": "DifferentiableWithinAt.norm_sq",
616
+ "start": [
617
+ 271,
618
+ 1
619
+ ],
620
+ "traced_tactics": [],
621
+ "url": "https://github.com/leanprover-community/mathlib4"
622
+ },
623
+ "source_file": "Mathlib/Analysis/InnerProductSpace/Calculus.lean"
624
+ },
625
+ {
626
+ "error": "theorem has no selected tactic transitions",
627
+ "full_name": "HasFDerivAt.inner",
628
+ "id": "HasFDerivAt.inner",
629
+ "reason": "import_failure",
630
+ "selection": {
631
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
632
+ "end": [
633
+ 106,
634
+ 74
635
+ ],
636
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
637
+ "full_name": "HasFDerivAt.inner",
638
+ "start": [
639
+ 104,
640
+ 1
641
+ ],
642
+ "traced_tactics": [],
643
+ "url": "https://github.com/leanprover-community/mathlib4"
644
+ },
645
+ "source_file": "Mathlib/Analysis/InnerProductSpace/Calculus.lean"
646
+ },
647
+ {
648
+ "error": "theorem has no selected tactic transitions",
649
+ "full_name": "HasFDerivAt.norm_sq",
650
+ "id": "HasFDerivAt.norm_sq",
651
+ "reason": "import_failure",
652
+ "selection": {
653
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
654
+ "end": [
655
+ 228,
656
+ 54
657
+ ],
658
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
659
+ "full_name": "HasFDerivAt.norm_sq",
660
+ "start": [
661
+ 226,
662
+ 1
663
+ ],
664
+ "traced_tactics": [],
665
+ "url": "https://github.com/leanprover-community/mathlib4"
666
+ },
667
+ "source_file": "Mathlib/Analysis/InnerProductSpace/Calculus.lean"
668
+ },
669
+ {
670
+ "error": "theorem has no selected tactic transitions",
671
+ "full_name": "HasFDerivWithinAt.inner",
672
+ "id": "HasFDerivWithinAt.inner",
673
+ "reason": "import_failure",
674
+ "selection": {
675
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
676
+ "end": [
677
+ 96,
678
+ 92
679
+ ],
680
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
681
+ "full_name": "HasFDerivWithinAt.inner",
682
+ "start": [
683
+ 92,
684
+ 1
685
+ ],
686
+ "traced_tactics": [],
687
+ "url": "https://github.com/leanprover-community/mathlib4"
688
+ },
689
+ "source_file": "Mathlib/Analysis/InnerProductSpace/Calculus.lean"
690
+ },
691
+ {
692
+ "error": "theorem has no selected tactic transitions",
693
+ "full_name": "HasFDerivWithinAt.norm_sq",
694
+ "id": "HasFDerivWithinAt.norm_sq",
695
+ "reason": "import_failure",
696
+ "selection": {
697
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
698
+ "end": [
699
+ 236,
700
+ 72
701
+ ],
702
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
703
+ "full_name": "HasFDerivWithinAt.norm_sq",
704
+ "start": [
705
+ 234,
706
+ 1
707
+ ],
708
+ "traced_tactics": [],
709
+ "url": "https://github.com/leanprover-community/mathlib4"
710
+ },
711
+ "source_file": "Mathlib/Analysis/InnerProductSpace/Calculus.lean"
712
+ },
713
+ {
714
+ "error": "theorem has no selected tactic transitions",
715
+ "full_name": "HasStrictFDerivAt.inner",
716
+ "id": "HasStrictFDerivAt.inner",
717
+ "reason": "import_failure",
718
+ "selection": {
719
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
720
+ "end": [
721
+ 101,
722
+ 80
723
+ ],
724
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
725
+ "full_name": "HasStrictFDerivAt.inner",
726
+ "start": [
727
+ 99,
728
+ 1
729
+ ],
730
+ "traced_tactics": [],
731
+ "url": "https://github.com/leanprover-community/mathlib4"
732
+ },
733
+ "source_file": "Mathlib/Analysis/InnerProductSpace/Calculus.lean"
734
+ },
735
+ {
736
+ "error": "theorem has no selected tactic transitions",
737
+ "full_name": "Homeomorph.contDiff_unitBall",
738
+ "id": "Homeomorph.contDiff_unitBall",
739
+ "reason": "import_failure",
740
+ "selection": {
741
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
742
+ "end": [
743
+ 395,
744
+ 42
745
+ ],
746
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
747
+ "full_name": "Homeomorph.contDiff_unitBall",
748
+ "start": [
749
+ 394,
750
+ 1
751
+ ],
752
+ "traced_tactics": [],
753
+ "url": "https://github.com/leanprover-community/mathlib4"
754
+ },
755
+ "source_file": "Mathlib/Analysis/InnerProductSpace/Calculus.lean"
756
+ },
757
+ {
758
+ "error": "no internal trace for tactic 'rwa [mem_ball_zero_iff, \u2190 _root_.abs_one, \u2190 abs_norm, \u2190 sq_lt_sq, one_pow, \u2190 sub_pos] at hy'",
759
+ "full_name": "PartialHomeomorph.contDiffOn_univUnitBall_symm",
760
+ "id": "PartialHomeomorph.contDiffOn_univUnitBall_symm",
761
+ "reason": "import_failure",
762
+ "selection": {
763
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
764
+ "end": [
765
+ 392,
766
+ 61
767
+ ],
768
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
769
+ "full_name": "PartialHomeomorph.contDiffOn_univUnitBall_symm",
770
+ "start": [
771
+ 384,
772
+ 1
773
+ ],
774
+ "traced_tactics": [
775
+ {
776
+ "annotated_tactic": [
777
+ "\"apply <a>ContDiffAt.contDiffWithinAt<\\/a>\"",
778
+ "[{\"full_name\":\"ContDiffAt.contDiffWithinAt\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/ContDiff\\/Defs.lean\",\"def_pos\":[1375,9],\"def_end_pos\":[1375,36]}]"
779
+ ],
780
+ "state_after": "case h\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\ny : E\nhy : y \u2208 ball 0 1\n\u22a2 ContDiffAt \u211d n (\u2191univUnitBall.symm) y",
781
+ "state_before": "n : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\ny : E\nhy : y \u2208 ball 0 1\n\u22a2 ContDiffWithinAt \u211d n (\u2191univUnitBall.symm) (ball 0 1) y",
782
+ "tactic": "apply ContDiffAt.contDiffWithinAt"
783
+ },
784
+ {
785
+ "annotated_tactic": [
786
+ "\"suffices <a>ContDiffAt<\\/a> \\u211d n (fun y : E => (\\u221a(1 - \\u2016y\\u2016 ^ 2 : \\u211d))\\u207b\\u00b9) y from this.smul <a>contDiffAt_id<\\/a>\"",
787
+ "[{\"full_name\":\"ContDiffAt\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/ContDiff\\/Defs.lean\",\"def_pos\":[1361,5],\"def_end_pos\":[1361,15]},{\"full_name\":\"contDiffAt_id\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/ContDiff\\/Basic.lean\",\"def_pos\":[191,9],\"def_end_pos\":[191,22]}]"
788
+ ],
789
+ "state_after": "case h\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\ny : E\nhy : y \u2208 ball 0 1\n\u22a2 ContDiffAt \u211d n (fun y => (\u221a(1 - \u2016y\u2016 ^ 2))\u207b\u00b9) y",
790
+ "state_before": "case h\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\ny : E\nhy : y \u2208 ball 0 1\n\u22a2 ContDiffAt \u211d n (\u2191univUnitBall.symm) y",
791
+ "tactic": "suffices ContDiffAt \u211d n (fun y : E => (\u221a(1 - \u2016y\u2016 ^ 2 : \u211d))\u207b\u00b9) y from this.smul contDiffAt_id"
792
+ },
793
+ {
794
+ "annotated_tactic": [
795
+ "\"have h : (0 : \\u211d) < (1 : \\u211d) - \\u2016(y : E)\\u2016 ^ 2 := by\\n rwa [<a>mem_ball_zero_iff<\\/a>, \\u2190 <a>_root_.abs_one<\\/a>, \\u2190 <a>abs_norm<\\/a>, \\u2190 <a>sq_lt_sq<\\/a>, <a>one_pow<\\/a>, \\u2190 <a>sub_pos<\\/a>] at hy\"",
796
+ "[{\"full_name\":\"mem_ball_zero_iff\",\"def_path\":\"Mathlib\\/Analysis\\/Normed\\/Group\\/Basic.lean\",\"def_pos\":[620,3],\"def_end_pos\":[620,14]},{\"full_name\":\"abs_one\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Ring\\/Abs.lean\",\"def_pos\":[42,15],\"def_end_pos\":[42,22]},{\"full_name\":\"abs_norm\",\"def_path\":\"Mathlib\\/Analysis\\/Normed\\/Group\\/Basic.lean\",\"def_pos\":[476,30],\"def_end_pos\":[476,38]},{\"full_name\":\"sq_lt_sq\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Ring\\/Abs.lean\",\"def_pos\":[116,7],\"def_end_pos\":[116,15]},{\"full_name\":\"one_pow\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[696,39],\"def_end_pos\":[696,46]},{\"full_name\":\"sub_pos\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Defs.lean\",\"def_pos\":[886,30],\"def_end_pos\":[886,37]}]"
797
+ ],
798
+ "state_after": "case h\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\ny : E\nhy : y \u2208 ball 0 1\nh : 0 < 1 - \u2016y\u2016 ^ 2\n\u22a2 ContDiffAt \u211d n (fun y => (\u221a(1 - \u2016y\u2016 ^ 2))\u207b\u00b9) y",
799
+ "state_before": "case h\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\ny : E\nhy : y \u2208 ball 0 1\n\u22a2 ContDiffAt \u211d n (fun y => (\u221a(1 - \u2016y\u2016 ^ 2))\u207b\u00b9) y",
800
+ "tactic": "have h : (0 : \u211d) < (1 : \u211d) - \u2016(y : E)\u2016 ^ 2 := by\n rwa [mem_ball_zero_iff, \u2190 _root_.abs_one, \u2190 abs_norm, \u2190 sq_lt_sq, one_pow, \u2190 sub_pos] at hy"
801
+ },
802
+ {
803
+ "annotated_tactic": [
804
+ "\"refine <a>ContDiffAt.inv<\\/a> ?_ (Real.sqrt_ne_zero'.mpr h)\"",
805
+ "[{\"full_name\":\"ContDiffAt.inv\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/ContDiff\\/Basic.lean\",\"def_pos\":[1806,16],\"def_end_pos\":[1806,30]}]"
806
+ ],
807
+ "state_after": "case h\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\ny : E\nhy : y \u2208 ball 0 1\nh : 0 < 1 - \u2016y\u2016 ^ 2\n\u22a2 ContDiffAt \u211d n (fun y => \u221a(1 - \u2016y\u2016 ^ 2)) y",
808
+ "state_before": "case h\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\ny : E\nhy : y \u2208 ball 0 1\nh : 0 < 1 - \u2016y\u2016 ^ 2\n\u22a2 ContDiffAt \u211d n (fun y => (\u221a(1 - \u2016y\u2016 ^ 2))\u207b\u00b9) y",
809
+ "tactic": "refine ContDiffAt.inv ?_ (Real.sqrt_ne_zero'.mpr h)"
810
+ },
811
+ {
812
+ "annotated_tactic": [
813
+ "\"refine (<a>contDiffAt_sqrt<\\/a> h.ne').<a>comp<\\/a> y ?_\"",
814
+ "[{\"full_name\":\"Real.contDiffAt_sqrt\",\"def_path\":\"Mathlib\\/Analysis\\/SpecialFunctions\\/Sqrt.lean\",\"def_pos\":[65,9],\"def_end_pos\":[65,24]},{\"full_name\":\"ContDiffAt.comp\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/ContDiff\\/Basic.lean\",\"def_pos\":[730,16],\"def_end_pos\":[730,31]}]"
815
+ ],
816
+ "state_after": "case h\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\ny : E\nhy : y \u2208 ball 0 1\nh : 0 < 1 - \u2016y\u2016 ^ 2\n\u22a2 ContDiffAt \u211d n (fun y => 1 - \u2016y\u2016 ^ 2) y",
817
+ "state_before": "case h\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\ny : E\nhy : y \u2208 ball 0 1\nh : 0 < 1 - \u2016y\u2016 ^ 2\n\u22a2 ContDiffAt \u211d n (fun y => \u221a(1 - \u2016y\u2016 ^ 2)) y",
818
+ "tactic": "refine (contDiffAt_sqrt h.ne').comp y ?_"
819
+ },
820
+ {
821
+ "annotated_tactic": [
822
+ "\"exact contDiffAt_const.sub (<a>contDiff_norm_sq<\\/a> \\u211d).<a>contDiffAt<\\/a>\"",
823
+ "[{\"full_name\":\"contDiff_norm_sq\",\"def_path\":\"Mathlib\\/Analysis\\/InnerProductSpace\\/Calculus.lean\",\"def_pos\":[151,9],\"def_end_pos\":[151,25]},{\"full_name\":\"ContDiff.contDiffAt\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/ContDiff\\/Defs.lean\",\"def_pos\":[1469,9],\"def_end_pos\":[1469,28]}]"
824
+ ],
825
+ "state_after": "no goals",
826
+ "state_before": "case h\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\ny : E\nhy : y \u2208 ball 0 1\nh : 0 < 1 - \u2016y\u2016 ^ 2\n\u22a2 ContDiffAt \u211d n (fun y => 1 - \u2016y\u2016 ^ 2) y",
827
+ "tactic": "exact contDiffAt_const.sub (contDiff_norm_sq \u211d).contDiffAt"
828
+ },
829
+ {
830
+ "annotated_tactic": [
831
+ "\"rwa [<a>mem_ball_zero_iff<\\/a>, \\u2190 <a>_root_.abs_one<\\/a>, \\u2190 <a>abs_norm<\\/a>, \\u2190 <a>sq_lt_sq<\\/a>, <a>one_pow<\\/a>, \\u2190 <a>sub_pos<\\/a>] at hy\"",
832
+ "[{\"full_name\":\"mem_ball_zero_iff\",\"def_path\":\"Mathlib\\/Analysis\\/Normed\\/Group\\/Basic.lean\",\"def_pos\":[620,3],\"def_end_pos\":[620,14]},{\"full_name\":\"abs_one\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Ring\\/Abs.lean\",\"def_pos\":[42,15],\"def_end_pos\":[42,22]},{\"full_name\":\"abs_norm\",\"def_path\":\"Mathlib\\/Analysis\\/Normed\\/Group\\/Basic.lean\",\"def_pos\":[476,30],\"def_end_pos\":[476,38]},{\"full_name\":\"sq_lt_sq\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Ring\\/Abs.lean\",\"def_pos\":[116,7],\"def_end_pos\":[116,15]},{\"full_name\":\"one_pow\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[696,39],\"def_end_pos\":[696,46]},{\"full_name\":\"sub_pos\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Group\\/Defs.lean\",\"def_pos\":[886,30],\"def_end_pos\":[886,37]}]"
833
+ ],
834
+ "state_after": "no goals",
835
+ "state_before": "n : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\ny : E\nhy : y \u2208 ball 0 1\n\u22a2 0 < 1 - \u2016y\u2016 ^ 2",
836
+ "tactic": "rwa [mem_ball_zero_iff, \u2190 _root_.abs_one, \u2190 abs_norm, \u2190 sq_lt_sq, one_pow, \u2190 sub_pos] at hy"
837
+ }
838
+ ],
839
+ "url": "https://github.com/leanprover-community/mathlib4"
840
+ },
841
+ "source_file": "Mathlib/Analysis/InnerProductSpace/Calculus.lean"
842
+ },
843
+ {
844
+ "error": "theorem has no selected tactic transitions",
845
+ "full_name": "PartialHomeomorph.contDiff_unitBallBall",
846
+ "id": "PartialHomeomorph.contDiff_unitBallBall",
847
+ "reason": "import_failure",
848
+ "selection": {
849
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
850
+ "end": [
851
+ 405,
852
+ 48
853
+ ],
854
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
855
+ "full_name": "PartialHomeomorph.contDiff_unitBallBall",
856
+ "start": [
857
+ 404,
858
+ 1
859
+ ],
860
+ "traced_tactics": [],
861
+ "url": "https://github.com/leanprover-community/mathlib4"
862
+ },
863
+ "source_file": "Mathlib/Analysis/InnerProductSpace/Calculus.lean"
864
+ },
865
+ {
866
+ "error": "theorem has no selected tactic transitions",
867
+ "full_name": "PartialHomeomorph.contDiff_unitBallBall_symm",
868
+ "id": "PartialHomeomorph.contDiff_unitBallBall_symm",
869
+ "reason": "import_failure",
870
+ "selection": {
871
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
872
+ "end": [
873
+ 408,
874
+ 48
875
+ ],
876
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
877
+ "full_name": "PartialHomeomorph.contDiff_unitBallBall_symm",
878
+ "start": [
879
+ 407,
880
+ 1
881
+ ],
882
+ "traced_tactics": [],
883
+ "url": "https://github.com/leanprover-community/mathlib4"
884
+ },
885
+ "source_file": "Mathlib/Analysis/InnerProductSpace/Calculus.lean"
886
+ },
887
+ {
888
+ "error": "no internal trace for tactic 'positivity'",
889
+ "full_name": "PartialHomeomorph.contDiff_univUnitBall",
890
+ "id": "PartialHomeomorph.contDiff_univUnitBall",
891
+ "reason": "import_failure",
892
+ "selection": {
893
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
894
+ "end": [
895
+ 382,
896
+ 75
897
+ ],
898
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
899
+ "full_name": "PartialHomeomorph.contDiff_univUnitBall",
900
+ "start": [
901
+ 378,
902
+ 1
903
+ ],
904
+ "traced_tactics": [
905
+ {
906
+ "annotated_tactic": [
907
+ "\"suffices <a>ContDiff<\\/a> \\u211d n fun x : E => (\\u221a(1 + \\u2016x\\u2016 ^ 2 : \\u211d))\\u207b\\u00b9 from this.smul <a>contDiff_id<\\/a>\"",
908
+ "[{\"full_name\":\"ContDiff\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/ContDiff\\/Defs.lean\",\"def_pos\":[1443,5],\"def_end_pos\":[1443,13]},{\"full_name\":\"contDiff_id\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/ContDiff\\/Basic.lean\",\"def_pos\":[183,9],\"def_end_pos\":[183,20]}]"
909
+ ],
910
+ "state_after": "n : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\n\u22a2 ContDiff \u211d n fun x => (\u221a(1 + \u2016x\u2016 ^ 2))\u207b\u00b9",
911
+ "state_before": "n : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\n\u22a2 ContDiff \u211d n \u2191univUnitBall",
912
+ "tactic": "suffices ContDiff \u211d n fun x : E => (\u221a(1 + \u2016x\u2016 ^ 2 : \u211d))\u207b\u00b9 from this.smul contDiff_id"
913
+ },
914
+ {
915
+ "annotated_tactic": [
916
+ "\"have h : \\u2200 x : E, (0 : \\u211d) < (1 : \\u211d) + \\u2016x\\u2016 ^ 2 := fun x => by positivity\"",
917
+ "[]"
918
+ ],
919
+ "state_after": "n : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nh : \u2200 (x : E), 0 < 1 + \u2016x\u2016 ^ 2\n\u22a2 ContDiff \u211d n fun x => (\u221a(1 + \u2016x\u2016 ^ 2))\u207b\u00b9",
920
+ "state_before": "n : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\n\u22a2 ContDiff \u211d n fun x => (\u221a(1 + \u2016x\u2016 ^ 2))\u207b\u00b9",
921
+ "tactic": "have h : \u2200 x : E, (0 : \u211d) < (1 : \u211d) + \u2016x\u2016 ^ 2 := fun x => by positivity"
922
+ },
923
+ {
924
+ "annotated_tactic": [
925
+ "\"refine <a>ContDiff.inv<\\/a> ?_ fun x => Real.sqrt_ne_zero'.mpr (h x)\"",
926
+ "[{\"full_name\":\"ContDiff.inv\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/ContDiff\\/Basic.lean\",\"def_pos\":[1811,9],\"def_end_pos\":[1811,21]}]"
927
+ ],
928
+ "state_after": "n : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nh : \u2200 (x : E), 0 < 1 + \u2016x\u2016 ^ 2\n\u22a2 ContDiff \u211d n fun x => \u221a(1 + \u2016x\u2016 ^ 2)",
929
+ "state_before": "n : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nh : \u2200 (x : E), 0 < 1 + \u2016x\u2016 ^ 2\n\u22a2 ContDiff \u211d n fun x => (\u221a(1 + \u2016x\u2016 ^ 2))\u207b\u00b9",
930
+ "tactic": "refine ContDiff.inv ?_ fun x => Real.sqrt_ne_zero'.mpr (h x)"
931
+ },
932
+ {
933
+ "annotated_tactic": [
934
+ "\"exact (contDiff_const.add <| <a>contDiff_norm_sq<\\/a> \\u211d).<a>sqrt<\\/a> fun x => (h x).<a>ne'<\\/a>\"",
935
+ "[{\"full_name\":\"contDiff_norm_sq\",\"def_path\":\"Mathlib\\/Analysis\\/InnerProductSpace\\/Calculus.lean\",\"def_pos\":[151,9],\"def_end_pos\":[151,25]},{\"full_name\":\"ContDiff.sqrt\",\"def_path\":\"Mathlib\\/Analysis\\/SpecialFunctions\\/Sqrt.lean\",\"def_pos\":[175,9],\"def_end_pos\":[175,22]},{\"full_name\":\"LT.lt.ne'\",\"def_path\":\"Mathlib\\/Order\\/Basic.lean\",\"def_pos\":[306,9],\"def_end_pos\":[306,12]}]"
936
+ ],
937
+ "state_after": "no goals",
938
+ "state_before": "n : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nh : \u2200 (x : E), 0 < 1 + \u2016x\u2016 ^ 2\n\u22a2 ContDiff \u211d n fun x => \u221a(1 + \u2016x\u2016 ^ 2)",
939
+ "tactic": "exact (contDiff_const.add <| contDiff_norm_sq \u211d).sqrt fun x => (h x).ne'"
940
+ },
941
+ {
942
+ "annotated_tactic": [
943
+ "\"positivity\"",
944
+ "[]"
945
+ ],
946
+ "state_after": "no goals",
947
+ "state_before": "n : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nx : E\n\u22a2 0 < 1 + \u2016x\u2016 ^ 2",
948
+ "tactic": "positivity"
949
+ }
950
+ ],
951
+ "url": "https://github.com/leanprover-community/mathlib4"
952
+ },
953
+ "source_file": "Mathlib/Analysis/InnerProductSpace/Calculus.lean"
954
+ },
955
+ {
956
+ "error": "theorem has no selected tactic transitions",
957
+ "full_name": "contDiffAt_inner",
958
+ "id": "contDiffAt_inner",
959
+ "reason": "import_failure",
960
+ "selection": {
961
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
962
+ "end": [
963
+ 62,
964
+ 37
965
+ ],
966
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
967
+ "full_name": "contDiffAt_inner",
968
+ "start": [
969
+ 61,
970
+ 1
971
+ ],
972
+ "traced_tactics": [],
973
+ "url": "https://github.com/leanprover-community/mathlib4"
974
+ },
975
+ "source_file": "Mathlib/Analysis/InnerProductSpace/Calculus.lean"
976
+ },
977
+ {
978
+ "error": "theorem has no selected tactic transitions",
979
+ "full_name": "contDiff_inner",
980
+ "id": "contDiff_inner",
981
+ "reason": "import_failure",
982
+ "selection": {
983
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
984
+ "end": [
985
+ 58,
986
+ 38
987
+ ],
988
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
989
+ "full_name": "contDiff_inner",
990
+ "start": [
991
+ 57,
992
+ 1
993
+ ],
994
+ "traced_tactics": [],
995
+ "url": "https://github.com/leanprover-community/mathlib4"
996
+ },
997
+ "source_file": "Mathlib/Analysis/InnerProductSpace/Calculus.lean"
998
+ },
999
+ {
1000
+ "error": "theorem has no selected tactic transitions",
1001
+ "full_name": "deriv_inner_apply",
1002
+ "id": "deriv_inner_apply",
1003
+ "reason": "import_failure",
1004
+ "selection": {
1005
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1006
+ "end": [
1007
+ 148,
1008
+ 46
1009
+ ],
1010
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
1011
+ "full_name": "deriv_inner_apply",
1012
+ "start": [
1013
+ 145,
1014
+ 1
1015
+ ],
1016
+ "traced_tactics": [],
1017
+ "url": "https://github.com/leanprover-community/mathlib4"
1018
+ },
1019
+ "source_file": "Mathlib/Analysis/InnerProductSpace/Calculus.lean"
1020
+ },
1021
+ {
1022
+ "error": "theorem has no selected tactic transitions",
1023
+ "full_name": "differentiable_inner",
1024
+ "id": "differentiable_inner",
1025
+ "reason": "import_failure",
1026
+ "selection": {
1027
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1028
+ "end": [
1029
+ 66,
1030
+ 46
1031
+ ],
1032
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
1033
+ "full_name": "differentiable_inner",
1034
+ "start": [
1035
+ 65,
1036
+ 1
1037
+ ],
1038
+ "traced_tactics": [],
1039
+ "url": "https://github.com/leanprover-community/mathlib4"
1040
+ },
1041
+ "source_file": "Mathlib/Analysis/InnerProductSpace/Calculus.lean"
1042
+ },
1043
+ {
1044
+ "error": "theorem has no selected tactic transitions",
1045
+ "full_name": "fderivInnerCLM_apply",
1046
+ "id": "fderivInnerCLM_apply",
1047
+ "reason": "import_failure",
1048
+ "selection": {
1049
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1050
+ "end": [
1051
+ 52,
1052
+ 6
1053
+ ],
1054
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
1055
+ "full_name": "fderivInnerCLM_apply",
1056
+ "start": [
1057
+ 51,
1058
+ 1
1059
+ ],
1060
+ "traced_tactics": [],
1061
+ "url": "https://github.com/leanprover-community/mathlib4"
1062
+ },
1063
+ "source_file": "Mathlib/Analysis/InnerProductSpace/Calculus.lean"
1064
+ }
1065
+ ],
1066
+ "input_proofs": 66,
1067
+ "input_units": 2,
1068
+ "proofs": 23,
1069
+ "published_proofs": 20,
1070
+ "published_transitions": 39,
1071
+ "replay_failures": [],
1072
+ "transitions": 59,
1073
+ "validation_failures": [
1074
+ {
1075
+ "errors": [
1076
+ "internal transition boundary mismatch",
1077
+ "internal transition boundary mismatch"
1078
+ ],
1079
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
1080
+ "proof_id": "mathlib:PartialHomeomorph.contDiffOn_univBall_symm",
1081
+ "provenance": {
1082
+ "selection": {
1083
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1084
+ "end": [
1085
+ 421,
1086
+ 45
1087
+ ],
1088
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
1089
+ "full_name": "PartialHomeomorph.contDiffOn_univBall_symm",
1090
+ "start": [
1091
+ 415,
1092
+ 1
1093
+ ],
1094
+ "traced_tactics": [
1095
+ {
1096
+ "annotated_tactic": [
1097
+ "\"unfold <a>univBall<\\/a>\"",
1098
+ "[{\"full_name\":\"PartialHomeomorph.univBall\",\"def_path\":\"Mathlib\\/Analysis\\/NormedSpace\\/HomeomorphBall.lean\",\"def_pos\":[122,5],\"def_end_pos\":[122,13]}]"
1099
+ ],
1100
+ "state_after": "n : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nc : E\nr : \u211d\n\u22a2 ContDiffOn \u211d n\n (\u2191(if h : 0 < r then univUnitBall.trans' (unitBallBall c r h) \u22ef\n else (IsometryEquiv.vaddConst c).toHomeomorph.toPartialHomeomorph).symm)\n (ball c r)",
1101
+ "state_before": "n : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nc : E\nr : \u211d\n\u22a2 ContDiffOn \u211d n (\u2191(univBall c r).symm) (ball c r)",
1102
+ "tactic": "unfold univBall"
1103
+ },
1104
+ {
1105
+ "annotated_tactic": [
1106
+ "\"split_ifs with h\"",
1107
+ "[]"
1108
+ ],
1109
+ "state_after": "case pos\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nc : E\nr : \u211d\nh : 0 < r\n\u22a2 ContDiffOn \u211d n (\u2191(univUnitBall.trans' (unitBallBall c r h) \u22ef).symm) (ball c r)\n\ncase neg\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nc : E\nr : \u211d\nh : \u00ac0 < r\n\u22a2 ContDiffOn \u211d n (\u2191(IsometryEquiv.vaddConst c).toHomeomorph.toPartialHomeomorph.symm) (ball c r)",
1110
+ "state_before": "n : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nc : E\nr : \u211d\n\u22a2 ContDiffOn \u211d n\n (\u2191(if h : 0 < r then univUnitBall.trans' (unitBallBall c r h) \u22ef\n else (IsometryEquiv.vaddConst c).toHomeomorph.toPartialHomeomorph).symm)\n (ball c r)",
1111
+ "tactic": "split_ifs with h"
1112
+ },
1113
+ {
1114
+ "annotated_tactic": [
1115
+ "\"refine contDiffOn_univUnitBall_symm.comp (<a>contDiff_unitBallBall_symm<\\/a> h).<a>contDiffOn<\\/a> ?_\"",
1116
+ "[{\"full_name\":\"PartialHomeomorph.contDiff_unitBallBall_symm\",\"def_path\":\"Mathlib\\/Analysis\\/InnerProductSpace\\/Calculus.lean\",\"def_pos\":[407,9],\"def_end_pos\":[407,35]},{\"full_name\":\"ContDiff.contDiffOn\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/ContDiff\\/Defs.lean\",\"def_pos\":[1485,9],\"def_end_pos\":[1485,28]}]"
1117
+ ],
1118
+ "state_after": "case pos\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nc : E\nr : \u211d\nh : 0 < r\n\u22a2 ball c r \u2286 \u2191(unitBallBall c r h).symm \u207b\u00b9' ball 0 1",
1119
+ "state_before": "case pos\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nc : E\nr : \u211d\nh : 0 < r\n\u22a2 ContDiffOn \u211d n (\u2191(univUnitBall.trans' (unitBallBall c r h) \u22ef).symm) (ball c r)",
1120
+ "tactic": "refine contDiffOn_univUnitBall_symm.comp (contDiff_unitBallBall_symm h).contDiffOn ?_"
1121
+ },
1122
+ {
1123
+ "annotated_tactic": [
1124
+ "\"rw [\\u2190 <a>unitBallBall_source<\\/a> c r h, \\u2190 <a>unitBallBall_target<\\/a> c r h]\"",
1125
+ "[{\"full_name\":\"PartialHomeomorph.unitBallBall_source\",\"def_path\":\"Mathlib\\/Analysis\\/NormedSpace\\/HomeomorphBall.lean\",\"def_pos\":[109,3],\"def_end_pos\":[109,9]},{\"full_name\":\"PartialHomeomorph.unitBallBall_target\",\"def_path\":\"Mathlib\\/Analysis\\/NormedSpace\\/HomeomorphBall.lean\",\"def_pos\":[109,3],\"def_end_pos\":[109,9]}]"
1126
+ ],
1127
+ "state_after": "case pos\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nc : E\nr : \u211d\nh : 0 < r\n\u22a2 (unitBallBall c r h).target \u2286 \u2191(unitBallBall c r h).symm \u207b\u00b9' (unitBallBall c r h).source",
1128
+ "state_before": "case pos\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nc : E\nr : \u211d\nh : 0 < r\n\u22a2 ball c r \u2286 \u2191(unitBallBall c r h).symm \u207b\u00b9' ball 0 1",
1129
+ "tactic": "rw [\u2190 unitBallBall_source c r h, \u2190 unitBallBall_target c r h]"
1130
+ },
1131
+ {
1132
+ "annotated_tactic": [
1133
+ "\"apply <a>PartialHomeomorph.symm_mapsTo<\\/a>\"",
1134
+ "[{\"full_name\":\"PartialHomeomorph.symm_mapsTo\",\"def_path\":\"Mathlib\\/Topology\\/PartialHomeomorph.lean\",\"def_pos\":[178,19],\"def_end_pos\":[178,30]}]"
1135
+ ],
1136
+ "state_after": "no goals",
1137
+ "state_before": "case pos\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nc : E\nr : \u211d\nh : 0 < r\n\u22a2 (unitBallBall c r h).target \u2286 \u2191(unitBallBall c r h).symm \u207b\u00b9' (unitBallBall c r h).source",
1138
+ "tactic": "apply PartialHomeomorph.symm_mapsTo"
1139
+ },
1140
+ {
1141
+ "annotated_tactic": [
1142
+ "\"exact contDiffOn_id.sub <a>contDiffOn_const<\\/a>\"",
1143
+ "[{\"full_name\":\"contDiffOn_const\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/ContDiff\\/Basic.lean\",\"def_pos\":[94,9],\"def_end_pos\":[94,25]}]"
1144
+ ],
1145
+ "state_after": "no goals",
1146
+ "state_before": "case neg\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nc : E\nr : \u211d\nh : \u00ac0 < r\n\u22a2 ContDiffOn \u211d n (\u2191(IsometryEquiv.vaddConst c).toHomeomorph.toPartialHomeomorph.symm) (ball c r)",
1147
+ "tactic": "exact contDiffOn_id.sub contDiffOn_const"
1148
+ }
1149
+ ],
1150
+ "url": "https://github.com/leanprover-community/mathlib4"
1151
+ }
1152
+ },
1153
+ "theorem_name": "PartialHomeomorph.contDiffOn_univBall_symm"
1154
+ },
1155
+ {
1156
+ "errors": [
1157
+ "internal transition boundary mismatch",
1158
+ "internal transition boundary mismatch"
1159
+ ],
1160
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
1161
+ "proof_id": "mathlib:PartialHomeomorph.contDiff_univBall",
1162
+ "provenance": {
1163
+ "selection": {
1164
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1165
+ "end": [
1166
+ 413,
1167
+ 41
1168
+ ],
1169
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Calculus.lean",
1170
+ "full_name": "PartialHomeomorph.contDiff_univBall",
1171
+ "start": [
1172
+ 410,
1173
+ 1
1174
+ ],
1175
+ "traced_tactics": [
1176
+ {
1177
+ "annotated_tactic": [
1178
+ "\"unfold <a>univBall<\\/a>\"",
1179
+ "[{\"full_name\":\"PartialHomeomorph.univBall\",\"def_path\":\"Mathlib\\/Analysis\\/NormedSpace\\/HomeomorphBall.lean\",\"def_pos\":[122,5],\"def_end_pos\":[122,13]}]"
1180
+ ],
1181
+ "state_after": "n : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nc : E\nr : \u211d\n\u22a2 ContDiff \u211d n\n \u2191(if h : 0 < r then univUnitBall.trans' (unitBallBall c r h) \u22ef\n else (IsometryEquiv.vaddConst c).toHomeomorph.toPartialHomeomorph)",
1182
+ "state_before": "n : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nc : E\nr : \u211d\n\u22a2 ContDiff \u211d n \u2191(univBall c r)",
1183
+ "tactic": "unfold univBall"
1184
+ },
1185
+ {
1186
+ "annotated_tactic": [
1187
+ "\"split_ifs with h\"",
1188
+ "[]"
1189
+ ],
1190
+ "state_after": "case pos\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nc : E\nr : \u211d\nh : 0 < r\n\u22a2 ContDiff \u211d n \u2191(univUnitBall.trans' (unitBallBall c r h) \u22ef)\n\ncase neg\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nc : E\nr : \u211d\nh : \u00ac0 < r\n\u22a2 ContDiff \u211d n \u2191(IsometryEquiv.vaddConst c).toHomeomorph.toPartialHomeomorph",
1191
+ "state_before": "n : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nc : E\nr : \u211d\n\u22a2 ContDiff \u211d n\n \u2191(if h : 0 < r then univUnitBall.trans' (unitBallBall c r h) \u22ef\n else (IsometryEquiv.vaddConst c).toHomeomorph.toPartialHomeomorph)",
1192
+ "tactic": "split_ifs with h"
1193
+ },
1194
+ {
1195
+ "annotated_tactic": [
1196
+ "\"exact (<a>contDiff_unitBallBall<\\/a> h).<a>comp<\\/a> <a>contDiff_univUnitBall<\\/a>\"",
1197
+ "[{\"full_name\":\"PartialHomeomorph.contDiff_unitBallBall\",\"def_path\":\"Mathlib\\/Analysis\\/InnerProductSpace\\/Calculus.lean\",\"def_pos\":[404,9],\"def_end_pos\":[404,30]},{\"full_name\":\"ContDiff.comp\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/ContDiff\\/Basic.lean\",\"def_pos\":[676,9],\"def_end_pos\":[676,22]},{\"full_name\":\"PartialHomeomorph.contDiff_univUnitBall\",\"def_path\":\"Mathlib\\/Analysis\\/InnerProductSpace\\/Calculus.lean\",\"def_pos\":[378,9],\"def_end_pos\":[378,48]}]"
1198
+ ],
1199
+ "state_after": "no goals",
1200
+ "state_before": "case pos\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nc : E\nr : \u211d\nh : 0 < r\n\u22a2 ContDiff \u211d n \u2191(univUnitBall.trans' (unitBallBall c r h) \u22ef)",
1201
+ "tactic": "exact (contDiff_unitBallBall h).comp contDiff_univUnitBall"
1202
+ },
1203
+ {
1204
+ "annotated_tactic": [
1205
+ "\"exact contDiff_id.add <a>contDiff_const<\\/a>\"",
1206
+ "[{\"full_name\":\"contDiff_const\",\"def_path\":\"Mathlib\\/Analysis\\/Calculus\\/ContDiff\\/Basic.lean\",\"def_pos\":[86,9],\"def_end_pos\":[86,23]}]"
1207
+ ],
1208
+ "state_after": "no goals",
1209
+ "state_before": "case neg\nn : \u2115\u221e\nE : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \u211d E\nc : E\nr : \u211d\nh : \u00ac0 < r\n\u22a2 ContDiff \u211d n \u2191(IsometryEquiv.vaddConst c).toHomeomorph.toPartialHomeomorph",
1210
+ "tactic": "exact contDiff_id.add contDiff_const"
1211
+ }
1212
+ ],
1213
+ "url": "https://github.com/leanprover-community/mathlib4"
1214
+ }
1215
+ },
1216
+ "theorem_name": "PartialHomeomorph.contDiff_univBall"
1217
+ },
1218
+ {
1219
+ "errors": [
1220
+ "internal transition boundary mismatch",
1221
+ "internal transition boundary mismatch",
1222
+ "internal transition boundary mismatch",
1223
+ "internal transition boundary mismatch"
1224
+ ],
1225
+ "file_path": "Mathlib/Analysis/InnerProductSpace/ConformalLinearMap.lean",
1226
+ "proof_id": "mathlib:isConformalMap_iff",
1227
+ "provenance": {
1228
+ "selection": {
1229
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1230
+ "end": [
1231
+ 43,
1232
+ 47
1233
+ ],
1234
+ "file_path": "Mathlib/Analysis/InnerProductSpace/ConformalLinearMap.lean",
1235
+ "full_name": "isConformalMap_iff",
1236
+ "start": [
1237
+ 29,
1238
+ 1
1239
+ ],
1240
+ "traced_tactics": [
1241
+ {
1242
+ "annotated_tactic": [
1243
+ "\"constructor\"",
1244
+ "[]"
1245
+ ],
1246
+ "state_after": "case mp\nE : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nf : E \u2192L[\u211d] F\n\u22a2 IsConformalMap f \u2192 \u2203 c, 0 < c \u2227 \u2200 (u v : E), \u27eaf u, f v\u27eb_\u211d = c * \u27eau, v\u27eb_\u211d\n\ncase mpr\nE : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nf : E \u2192L[\u211d] F\n\u22a2 (\u2203 c, 0 < c \u2227 \u2200 (u v : E), \u27eaf u, f v\u27eb_\u211d = c * \u27eau, v\u27eb_\u211d) \u2192 IsConformalMap f",
1247
+ "state_before": "E : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nf : E \u2192L[\u211d] F\n\u22a2 IsConformalMap f \u2194 \u2203 c, 0 < c \u2227 \u2200 (u v : E), \u27eaf u, f v\u27eb_\u211d = c * \u27eau, v\u27eb_\u211d",
1248
+ "tactic": "constructor"
1249
+ },
1250
+ {
1251
+ "annotated_tactic": [
1252
+ "\"rintro \\u27e8c\\u2081, hc\\u2081, li, rfl\\u27e9\"",
1253
+ "[]"
1254
+ ],
1255
+ "state_after": "case mp.intro.intro.intro\nE : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nc\u2081 : \u211d\nhc\u2081 : c\u2081 \u2260 0\nli : E \u2192\u2097\u1d62[\u211d] F\n\u22a2 \u2203 c, 0 < c \u2227 \u2200 (u v : E), \u27ea(c\u2081 \u2022 li.toContinuousLinearMap) u, (c\u2081 \u2022 li.toContinuousLinearMap) v\u27eb_\u211d = c * \u27eau, v\u27eb_\u211d",
1256
+ "state_before": "case mp\nE : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nf : E \u2192L[\u211d] F\n\u22a2 IsConformalMap f \u2192 \u2203 c, 0 < c \u2227 \u2200 (u v : E), \u27eaf u, f v\u27eb_\u211d = c * \u27eau, v\u27eb_\u211d",
1257
+ "tactic": "rintro \u27e8c\u2081, hc\u2081, li, rfl\u27e9"
1258
+ },
1259
+ {
1260
+ "annotated_tactic": [
1261
+ "\"refine \\u27e8c\\u2081 * c\\u2081, <a>mul_self_pos<\\/a>.2 hc\\u2081, fun u v => ?_\\u27e9\"",
1262
+ "[{\"full_name\":\"mul_self_pos\",\"def_path\":\"Mathlib\\/Algebra\\/Order\\/Ring\\/Defs.lean\",\"def_pos\":[1126,9],\"def_end_pos\":[1126,21]}]"
1263
+ ],
1264
+ "state_after": "case mp.intro.intro.intro\nE : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nc\u2081 : \u211d\nhc\u2081 : c\u2081 \u2260 0\nli : E \u2192\u2097\u1d62[\u211d] F\nu v : E\n\u22a2 \u27ea(c\u2081 \u2022 li.toContinuousLinearMap) u, (c\u2081 \u2022 li.toContinuousLinearMap) v\u27eb_\u211d = c\u2081 * c\u2081 * \u27eau, v\u27eb_\u211d",
1265
+ "state_before": "case mp.intro.intro.intro\nE : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nc\u2081 : \u211d\nhc\u2081 : c\u2081 \u2260 0\nli : E \u2192\u2097\u1d62[\u211d] F\n\u22a2 \u2203 c, 0 < c \u2227 \u2200 (u v : E), \u27ea(c\u2081 \u2022 li.toContinuousLinearMap) u, (c\u2081 \u2022 li.toContinuousLinearMap) v\u27eb_\u211d = c * \u27eau, v\u27eb_\u211d",
1266
+ "tactic": "refine \u27e8c\u2081 * c\u2081, mul_self_pos.2 hc\u2081, fun u v => ?_\u27e9"
1267
+ },
1268
+ {
1269
+ "annotated_tactic": [
1270
+ "\"simp only [<a>real_inner_smul_left<\\/a>, <a>real_inner_smul_right<\\/a>, <a>mul_assoc<\\/a>, <a>coe_smul'<\\/a>,\\n <a>coe_toContinuousLinearMap<\\/a>, <a>Pi.smul_apply<\\/a>, <a>inner_map_map<\\/a>]\"",
1271
+ "[{\"full_name\":\"real_inner_smul_left\",\"def_path\":\"Mathlib\\/Analysis\\/InnerProductSpace\\/Basic.lean\",\"def_pos\":[468,9],\"def_end_pos\":[468,29]},{\"full_name\":\"real_inner_smul_right\",\"def_path\":\"Mathlib\\/Analysis\\/InnerProductSpace\\/Basic.lean\",\"def_pos\":[481,9],\"def_end_pos\":[481,30]},{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]},{\"full_name\":\"ContinuousLinearMap.coe_smul'\",\"def_path\":\"Mathlib\\/Topology\\/Algebra\\/Module\\/Basic.lean\",\"def_pos\":[602,9],\"def_end_pos\":[602,18]},{\"full_name\":\"LinearIsometry.coe_toContinuousLinearMap\",\"def_path\":\"Mathlib\\/Analysis\\/NormedSpace\\/LinearIsometry.lean\",\"def_pos\":[365,9],\"def_end_pos\":[365,34]},{\"full_name\":\"Pi.smul_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Pi\\/Basic.lean\",\"def_pos\":[129,60],\"def_end_pos\":[129,70]},{\"full_name\":\"LinearIsometry.inner_map_map\",\"def_path\":\"Mathlib\\/Analysis\\/InnerProductSpace\\/Basic.lean\",\"def_pos\":[1256,9],\"def_end_pos\":[1256,37]}]"
1272
+ ],
1273
+ "state_after": "no goals",
1274
+ "state_before": "case mp.intro.intro.intro\nE : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nc\u2081 : \u211d\nhc\u2081 : c\u2081 \u2260 0\nli : E \u2192\u2097\u1d62[\u211d] F\nu v : E\n\u22a2 \u27ea(c\u2081 \u2022 li.toContinuousLinearMap) u, (c\u2081 \u2022 li.toContinuousLinearMap) v\u27eb_\u211d = c\u2081 * c\u2081 * \u27eau, v\u27eb_\u211d",
1275
+ "tactic": "simp only [real_inner_smul_left, real_inner_smul_right, mul_assoc, coe_smul',\n coe_toContinuousLinearMap, Pi.smul_apply, inner_map_map]"
1276
+ },
1277
+ {
1278
+ "annotated_tactic": [
1279
+ "\"rintro \\u27e8c\\u2081, hc\\u2081, huv\\u27e9\"",
1280
+ "[]"
1281
+ ],
1282
+ "state_after": "case mpr.intro.intro\nE : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nf : E \u2192L[\u211d] F\nc\u2081 : \u211d\nhc\u2081 : 0 < c\u2081\nhuv : \u2200 (u v : E), \u27eaf u, f v\u27eb_\u211d = c\u2081 * \u27eau, v\u27eb_\u211d\n\u22a2 IsConformalMap f",
1283
+ "state_before": "case mpr\nE : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nf : E \u2192L[\u211d] F\n\u22a2 (\u2203 c, 0 < c \u2227 \u2200 (u v : E), \u27eaf u, f v\u27eb_\u211d = c * \u27eau, v\u27eb_\u211d) \u2192 IsConformalMap f",
1284
+ "tactic": "rintro \u27e8c\u2081, hc\u2081, huv\u27e9"
1285
+ },
1286
+ {
1287
+ "annotated_tactic": [
1288
+ "\"obtain \\u27e8c, hc, rfl\\u27e9 : \\u2203 c : \\u211d, 0 < c \\u2227 c\\u2081 = c * c :=\\n \\u27e8\\u221ac\\u2081, <a>Real.sqrt_pos<\\/a>.2 hc\\u2081, (<a>Real.mul_self_sqrt<\\/a> hc\\u2081.le).<a>symm<\\/a>\\u27e9\"",
1289
+ "[{\"full_name\":\"Real.sqrt_pos\",\"def_path\":\"Mathlib\\/Data\\/Real\\/Sqrt.lean\",\"def_pos\":[319,9],\"def_end_pos\":[319,17]},{\"full_name\":\"Real.mul_self_sqrt\",\"def_path\":\"Mathlib\\/Data\\/Real\\/Sqrt.lean\",\"def_pos\":[166,9],\"def_end_pos\":[166,22]},{\"full_name\":\"Eq.symm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[323,9],\"def_end_pos\":[323,16]}]"
1290
+ ],
1291
+ "state_after": "case mpr.intro.intro.intro.intro\nE : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nf : E \u2192L[\u211d] F\nc : \u211d\nhc : 0 < c\nhc\u2081 : 0 < c * c\nhuv : \u2200 (u v : E), \u27eaf u, f v\u27eb_\u211d = c * c * \u27eau, v\u27eb_\u211d\n\u22a2 IsConformalMap f",
1292
+ "state_before": "case mpr.intro.intro\nE : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nf : E \u2192L[\u211d] F\nc\u2081 : \u211d\nhc\u2081 : 0 < c\u2081\nhuv : \u2200 (u v : E), \u27eaf u, f v\u27eb_\u211d = c\u2081 * \u27eau, v\u27eb_\u211d\n\u22a2 IsConformalMap f",
1293
+ "tactic": "obtain \u27e8c, hc, rfl\u27e9 : \u2203 c : \u211d, 0 < c \u2227 c\u2081 = c * c :=\n \u27e8\u221ac\u2081, Real.sqrt_pos.2 hc\u2081, (Real.mul_self_sqrt hc\u2081.le).symm\u27e9"
1294
+ },
1295
+ {
1296
+ "annotated_tactic": [
1297
+ "\"refine \\u27e8c, hc.ne', (c\\u207b\\u00b9 \\u2022 f : E \\u2192\\u2097[\\u211d] F).<a>isometryOfInner<\\/a> fun u v => ?_, ?_\\u27e9\"",
1298
+ "[{\"full_name\":\"LinearMap.isometryOfInner\",\"def_path\":\"Mathlib\\/Analysis\\/InnerProductSpace\\/Basic.lean\",\"def_pos\":[1272,5],\"def_end_pos\":[1272,30]}]"
1299
+ ],
1300
+ "state_after": "case mpr.intro.intro.intro.intro.refine_1\nE : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nf : E \u2192L[\u211d] F\nc : \u211d\nhc : 0 < c\nhc\u2081 : 0 < c * c\nhuv : \u2200 (u v : E), \u27eaf u, f v\u27eb_\u211d = c * c * \u27eau, v\u27eb_\u211d\nu v : E\n\u22a2 \u27ea(c\u207b\u00b9 \u2022 \u2191f) u, (c\u207b\u00b9 \u2022 \u2191f) v\u27eb_\u211d = \u27eau, v\u27eb_\u211d\n\ncase mpr.intro.intro.intro.intro.refine_2\nE : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nf : E \u2192L[\u211d] F\nc : \u211d\nhc : 0 < c\nhc\u2081 : 0 < c * c\nhuv : \u2200 (u v : E), \u27eaf u, f v\u27eb_\u211d = c * c * \u27eau, v\u27eb_\u211d\n\u22a2 f = c \u2022 ((c\u207b\u00b9 \u2022 \u2191f).isometryOfInner \u22ef).toContinuousLinearMap",
1301
+ "state_before": "case mpr.intro.intro.intro.intro\nE : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nf : E \u2192L[\u211d] F\nc : \u211d\nhc : 0 < c\nhc\u2081 : 0 < c * c\nhuv : \u2200 (u v : E), \u27eaf u, f v\u27eb_\u211d = c * c * \u27eau, v\u27eb_\u211d\n\u22a2 IsConformalMap f",
1302
+ "tactic": "refine \u27e8c, hc.ne', (c\u207b\u00b9 \u2022 f : E \u2192\u2097[\u211d] F).isometryOfInner fun u v => ?_, ?_\u27e9"
1303
+ },
1304
+ {
1305
+ "annotated_tactic": [
1306
+ "\"simp only [<a>real_inner_smul_left<\\/a>, <a>real_inner_smul_right<\\/a>, huv, <a>mul_assoc<\\/a>, <a>coe_smul<\\/a>,\\n <a>inv_mul_cancel_left\\u2080<\\/a> hc.ne', <a>LinearMap.smul_apply<\\/a>, <a>ContinuousLinearMap.coe_coe<\\/a>]\"",
1307
+ "[{\"full_name\":\"real_inner_smul_left\",\"def_path\":\"Mathlib\\/Analysis\\/InnerProductSpace\\/Basic.lean\",\"def_pos\":[468,9],\"def_end_pos\":[468,29]},{\"full_name\":\"real_inner_smul_right\",\"def_path\":\"Mathlib\\/Analysis\\/InnerProductSpace\\/Basic.lean\",\"def_pos\":[481,9],\"def_end_pos\":[481,30]},{\"full_name\":\"mul_assoc\",\"def_path\":\"Mathlib\\/Algebra\\/Group\\/Defs.lean\",\"def_pos\":[289,9],\"def_end_pos\":[289,18]},{\"full_name\":\"ContinuousLinearMap.coe_smul\",\"def_path\":\"Mathlib\\/Topology\\/Algebra\\/Module\\/Basic.lean\",\"def_pos\":[596,9],\"def_end_pos\":[596,17]},{\"full_name\":\"inv_mul_cancel_left\\u2080\",\"def_path\":\"Mathlib\\/Algebra\\/GroupWithZero\\/Basic.lean\",\"def_pos\":[302,9],\"def_end_pos\":[302,29]},{\"full_name\":\"LinearMap.smul_apply\",\"def_path\":\"Mathlib\\/Algebra\\/Module\\/LinearMap\\/Defs.lean\",\"def_pos\":[831,9],\"def_end_pos\":[831,19]},{\"full_name\":\"ContinuousLinearMap.coe_coe\",\"def_path\":\"Mathlib\\/Topology\\/Algebra\\/Module\\/Basic.lean\",\"def_pos\":[527,9],\"def_end_pos\":[527,16]}]"
1308
+ ],
1309
+ "state_after": "no goals",
1310
+ "state_before": "case mpr.intro.intro.intro.intro.refine_1\nE : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nf : E \u2192L[\u211d] F\nc : \u211d\nhc : 0 < c\nhc\u2081 : 0 < c * c\nhuv : \u2200 (u v : E), \u27eaf u, f v\u27eb_\u211d = c * c * \u27eau, v\u27eb_\u211d\nu v : E\n\u22a2 \u27ea(c\u207b\u00b9 \u2022 \u2191f) u, (c\u207b\u00b9 \u2022 \u2191f) v\u27eb_\u211d = \u27eau, v\u27eb_\u211d",
1311
+ "tactic": "simp only [real_inner_smul_left, real_inner_smul_right, huv, mul_assoc, coe_smul,\n inv_mul_cancel_left\u2080 hc.ne', LinearMap.smul_apply, ContinuousLinearMap.coe_coe]"
1312
+ },
1313
+ {
1314
+ "annotated_tactic": [
1315
+ "\"ext1 x\"",
1316
+ "[]"
1317
+ ],
1318
+ "state_after": "case mpr.intro.intro.intro.intro.refine_2.h\nE : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nf : E \u2192L[\u211d] F\nc : \u211d\nhc : 0 < c\nhc\u2081 : 0 < c * c\nhuv : \u2200 (u v : E), \u27eaf u, f v\u27eb_\u211d = c * c * \u27eau, v\u27eb_\u211d\nx : E\n\u22a2 f x = (c \u2022 ((c\u207b\u00b9 \u2022 \u2191f).isometryOfInner \u22ef).toContinuousLinearMap) x",
1319
+ "state_before": "case mpr.intro.intro.intro.intro.refine_2\nE : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nf : E \u2192L[\u211d] F\nc : \u211d\nhc : 0 < c\nhc\u2081 : 0 < c * c\nhuv : \u2200 (u v : E), \u27eaf u, f v\u27eb_\u211d = c * c * \u27eau, v\u27eb_\u211d\n\u22a2 f = c \u2022 ((c\u207b\u00b9 \u2022 \u2191f).isometryOfInner \u22ef).toContinuousLinearMap",
1320
+ "tactic": "ext1 x"
1321
+ },
1322
+ {
1323
+ "annotated_tactic": [
1324
+ "\"exact (<a>smul_inv_smul\\u2080<\\/a> hc.ne' (f x)).<a>symm<\\/a>\"",
1325
+ "[{\"full_name\":\"smul_inv_smul\\u2080\",\"def_path\":\"Mathlib\\/GroupTheory\\/GroupAction\\/Group.lean\",\"def_pos\":[212,9],\"def_end_pos\":[212,23]},{\"full_name\":\"Eq.symm\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[323,9],\"def_end_pos\":[323,16]}]"
1326
+ ],
1327
+ "state_after": "no goals",
1328
+ "state_before": "case mpr.intro.intro.intro.intro.refine_2.h\nE : Type u_1\nF : Type u_2\ninst\u271d\u00b3 : NormedAddCommGroup E\ninst\u271d\u00b2 : NormedAddCommGroup F\ninst\u271d\u00b9 : InnerProductSpace \u211d E\ninst\u271d : InnerProductSpace \u211d F\nf : E \u2192L[\u211d] F\nc : \u211d\nhc : 0 < c\nhc\u2081 : 0 < c * c\nhuv : \u2200 (u v : E), \u27eaf u, f v\u27eb_\u211d = c * c * \u27eau, v\u27eb_\u211d\nx : E\n\u22a2 f x = (c \u2022 ((c\u207b\u00b9 \u2022 \u2191f).isometryOfInner \u22ef).toContinuousLinearMap) x",
1329
+ "tactic": "exact (smul_inv_smul\u2080 hc.ne' (f x)).symm"
1330
+ }
1331
+ ],
1332
+ "url": "https://github.com/leanprover-community/mathlib4"
1333
+ }
1334
+ },
1335
+ "theorem_name": "isConformalMap_iff"
1336
+ }
1337
+ ],
1338
+ "validation_rejected_proofs": 3,
1339
+ "zero_transition_proofs": 0
1340
+ },
1341
+ "shards": [
1342
+ {
1343
+ "path": "data/train/mathlib-000483-0000-2156b15290726855.parquet",
1344
+ "sha256": "2156b15290726855221108874ffca304cfd3d23258251e24084f27163b9f0eca",
1345
+ "bytes": 220060,
1346
+ "rows": 33,
1347
+ "revision": "03bde7f2d1ad989476e75d92008e2f729cf4919a"
1348
+ },
1349
+ {
1350
+ "path": "data/internal_test/mathlib-000483-0000-9e461007359a22b7.parquet",
1351
+ "sha256": "9e461007359a22b78b8ed58a4e0d70073eb37f25337aa73cabdd7cc4c569257a",
1352
+ "bytes": 126346,
1353
+ "rows": 6,
1354
+ "revision": "03bde7f2d1ad989476e75d92008e2f729cf4919a"
1355
+ }
1356
+ ],
1357
+ "proof_ids": [
1358
+ "mathlib:ContDiffWithinAt.dist",
1359
+ "mathlib:DifferentiableAt.dist",
1360
+ "mathlib:DifferentiableWithinAt.dist",
1361
+ "mathlib:HasDerivAt.inner",
1362
+ "mathlib:HasDerivAt.norm_sq",
1363
+ "mathlib:HasDerivWithinAt.inner",
1364
+ "mathlib:contDiffAt_euclidean",
1365
+ "mathlib:contDiffAt_norm",
1366
+ "mathlib:contDiffOn_euclidean",
1367
+ "mathlib:contDiffWithinAt_euclidean",
1368
+ "mathlib:contDiff_euclidean",
1369
+ "mathlib:contDiff_norm_sq",
1370
+ "mathlib:differentiableAt_euclidean",
1371
+ "mathlib:differentiableOn_euclidean",
1372
+ "mathlib:differentiableWithinAt_euclidean",
1373
+ "mathlib:differentiable_euclidean",
1374
+ "mathlib:fderiv_inner_apply",
1375
+ "mathlib:hasFDerivWithinAt_euclidean",
1376
+ "mathlib:hasStrictFDerivAt_euclidean",
1377
+ "mathlib:hasStrictFDerivAt_norm_sq"
1378
+ ],
1379
+ "proof_keys": [
1380
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"ContDiffWithinAt.dist\"]",
1381
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"DifferentiableAt.dist\"]",
1382
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"DifferentiableWithinAt.dist\"]",
1383
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"HasDerivAt.inner\"]",
1384
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"HasDerivAt.norm_sq\"]",
1385
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"HasDerivWithinAt.inner\"]",
1386
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"contDiffAt_euclidean\"]",
1387
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"contDiffAt_norm\"]",
1388
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"contDiffOn_euclidean\"]",
1389
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"contDiffWithinAt_euclidean\"]",
1390
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"contDiff_euclidean\"]",
1391
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"contDiff_norm_sq\"]",
1392
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"differentiableAt_euclidean\"]",
1393
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"differentiableOn_euclidean\"]",
1394
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"differentiableWithinAt_euclidean\"]",
1395
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"differentiable_euclidean\"]",
1396
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"fderiv_inner_apply\"]",
1397
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"hasFDerivWithinAt_euclidean\"]",
1398
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"hasStrictFDerivAt_euclidean\"]",
1399
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/Analysis/InnerProductSpace/Calculus.lean\",null,null,\"hasStrictFDerivAt_norm_sq\"]"
1400
+ ]
1401
+ }
manifests/batches/mathlib/000484.json ADDED
@@ -0,0 +1,457 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000484",
4
+ "batch_fingerprint": "becedc2c027d19f4829df554a647aeec2a56c8d7dc2ab6afb5198ec5a9b3be66",
5
+ "evidence": {
6
+ "batch_fingerprint": "becedc2c027d19f4829df554a647aeec2a56c8d7dc2ab6afb5198ec5a9b3be66",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "no internal trace for tactic 'conv_rhs => rw [\u2190 inner_conj_symm]'",
11
+ "full_name": "InnerProductSpace.ext_inner_left_basis",
12
+ "id": "InnerProductSpace.ext_inner_left_basis",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 90,
18
+ 29
19
+ ],
20
+ "file_path": "Mathlib/Analysis/InnerProductSpace/Dual.lean",
21
+ "full_name": "InnerProductSpace.ext_inner_left_basis",
22
+ "start": [
23
+ 81,
24
+ 1
25
+ ],
26
+ "traced_tactics": [
27
+ {
28
+ "annotated_tactic": [
29
+ "\"apply (<a>toDualMap<\\/a> \\ud835\\udd5c E).map_eq_iff.mp\"",
30
+ "[{\"full_name\":\"InnerProductSpace.toDualMap\",\"def_path\":\"Mathlib\\/Analysis\\/InnerProductSpace\\/Dual.lean\",\"def_pos\":[63,5],\"def_end_pos\":[63,14]}]"
31
+ ],
32
+ "state_after": "\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u00b2 : RCLike \ud835\udd5c\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \ud835\udd5c E\n\u03b9 : Type u_3\nx y : E\nb : Basis \u03b9 \ud835\udd5c E\nh : \u2200 (i : \u03b9), \u27eab i, x\u27eb_\ud835\udd5c = \u27eab i, y\u27eb_\ud835\udd5c\n\u22a2 (toDualMap \ud835\udd5c E) x = (toDualMap \ud835\udd5c E) y",
33
+ "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u00b2 : RCLike \ud835\udd5c\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \ud835\udd5c E\n\u03b9 : Type u_3\nx y : E\nb : Basis \u03b9 \ud835\udd5c E\nh : \u2200 (i : \u03b9), \u27eab i, x\u27eb_\ud835\udd5c = \u27eab i, y\u27eb_\ud835\udd5c\n\u22a2 x = y",
34
+ "tactic": "apply (toDualMap \ud835\udd5c E).map_eq_iff.mp"
35
+ },
36
+ {
37
+ "annotated_tactic": [
38
+ "\"refine (<a>Function.Injective.eq_iff<\\/a> <a>ContinuousLinearMap.coe_injective<\\/a>).<a>mp<\\/a> (<a>Basis.ext<\\/a> b ?_)\"",
39
+ "[{\"full_name\":\"Function.Injective.eq_iff\",\"def_path\":\"Mathlib\\/Logic\\/Function\\/Basic.lean\",\"def_pos\":[85,9],\"def_end_pos\":[85,25]},{\"full_name\":\"ContinuousLinearMap.coe_injective\",\"def_path\":\"Mathlib\\/Topology\\/Algebra\\/Module\\/Basic.lean\",\"def_pos\":[404,9],\"def_end_pos\":[404,22]},{\"full_name\":\"Iff.mp\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[118,3],\"def_end_pos\":[118,5]},{\"full_name\":\"Basis.ext\",\"def_path\":\"Mathlib\\/LinearAlgebra\\/Basis.lean\",\"def_pos\":[273,9],\"def_end_pos\":[273,12]}]"
40
+ ],
41
+ "state_after": "\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u00b2 : RCLike \ud835\udd5c\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \ud835\udd5c E\n\u03b9 : Type u_3\nx y : E\nb : Basis \u03b9 \ud835\udd5c E\nh : \u2200 (i : \u03b9), \u27eab i, x\u27eb_\ud835\udd5c = \u27eab i, y\u27eb_\ud835\udd5c\n\u22a2 \u2200 (i : \u03b9), \u2191((toDualMap \ud835\udd5c E) x) (b i) = \u2191((toDualMap \ud835\udd5c E) y) (b i)",
42
+ "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u00b2 : RCLike \ud835\udd5c\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \ud835\udd5c E\n\u03b9 : Type u_3\nx y : E\nb : Basis \u03b9 \ud835\udd5c E\nh : \u2200 (i : \u03b9), \u27eab i, x\u27eb_\ud835\udd5c = \u27eab i, y\u27eb_\ud835\udd5c\n\u22a2 (toDualMap \ud835\udd5c E) x = (toDualMap \ud835\udd5c E) y",
43
+ "tactic": "refine (Function.Injective.eq_iff ContinuousLinearMap.coe_injective).mp (Basis.ext b ?_)"
44
+ },
45
+ {
46
+ "annotated_tactic": [
47
+ "\"intro i\"",
48
+ "[]"
49
+ ],
50
+ "state_after": "\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u00b2 : RCLike \ud835\udd5c\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \ud835\udd5c E\n\u03b9 : Type u_3\nx y : E\nb : Basis \u03b9 \ud835\udd5c E\nh : \u2200 (i : \u03b9), \u27eab i, x\u27eb_\ud835\udd5c = \u27eab i, y\u27eb_\ud835\udd5c\ni : \u03b9\n\u22a2 \u2191((toDualMap \ud835\udd5c E) x) (b i) = \u2191((toDualMap \ud835\udd5c E) y) (b i)",
51
+ "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u00b2 : RCLike \ud835\udd5c\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \ud835\udd5c E\n\u03b9 : Type u_3\nx y : E\nb : Basis \u03b9 \ud835\udd5c E\nh : \u2200 (i : \u03b9), \u27eab i, x\u27eb_\ud835\udd5c = \u27eab i, y\u27eb_\ud835\udd5c\n\u22a2 \u2200 (i : \u03b9), \u2191((toDualMap \ud835\udd5c E) x) (b i) = \u2191((toDualMap \ud835\udd5c E) y) (b i)",
52
+ "tactic": "intro i"
53
+ },
54
+ {
55
+ "annotated_tactic": [
56
+ "\"simp only [<a>ContinuousLinearMap.coe_coe<\\/a>]\"",
57
+ "[{\"full_name\":\"ContinuousLinearMap.coe_coe\",\"def_path\":\"Mathlib\\/Topology\\/Algebra\\/Module\\/Basic.lean\",\"def_pos\":[527,9],\"def_end_pos\":[527,16]}]"
58
+ ],
59
+ "state_after": "\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u00b2 : RCLike \ud835\udd5c\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \ud835\udd5c E\n\u03b9 : Type u_3\nx y : E\nb : Basis \u03b9 \ud835\udd5c E\nh : \u2200 (i : \u03b9), \u27eab i, x\u27eb_\ud835\udd5c = \u27eab i, y\u27eb_\ud835\udd5c\ni : \u03b9\n\u22a2 ((toDualMap \ud835\udd5c E) x) (b i) = ((toDualMap \ud835\udd5c E) y) (b i)",
60
+ "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u00b2 : RCLike \ud835\udd5c\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \ud835\udd5c E\n\u03b9 : Type u_3\nx y : E\nb : Basis \u03b9 \ud835\udd5c E\nh : \u2200 (i : \u03b9), \u27eab i, x\u27eb_\ud835\udd5c = \u27eab i, y\u27eb_\ud835\udd5c\ni : \u03b9\n\u22a2 \u2191((toDualMap \ud835\udd5c E) x) (b i) = \u2191((toDualMap \ud835\udd5c E) y) (b i)",
61
+ "tactic": "simp only [ContinuousLinearMap.coe_coe]"
62
+ },
63
+ {
64
+ "annotated_tactic": [
65
+ "\"rw [<a>toDualMap_apply<\\/a>, <a>toDualMap_apply<\\/a>]\"",
66
+ "[{\"full_name\":\"InnerProductSpace.toDualMap_apply\",\"def_path\":\"Mathlib\\/Analysis\\/InnerProductSpace\\/Dual.lean\",\"def_pos\":[70,9],\"def_end_pos\":[70,24]},{\"full_name\":\"InnerProductSpace.toDualMap_apply\",\"def_path\":\"Mathlib\\/Analysis\\/InnerProductSpace\\/Dual.lean\",\"def_pos\":[70,9],\"def_end_pos\":[70,24]}]"
67
+ ],
68
+ "state_after": "\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u00b2 : RCLike \ud835\udd5c\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \ud835\udd5c E\n\u03b9 : Type u_3\nx y : E\nb : Basis \u03b9 \ud835\udd5c E\nh : \u2200 (i : \u03b9), \u27eab i, x\u27eb_\ud835\udd5c = \u27eab i, y\u27eb_\ud835\udd5c\ni : \u03b9\n\u22a2 \u27eax, b i\u27eb_\ud835\udd5c = \u27eay, b i\u27eb_\ud835\udd5c",
69
+ "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u00b2 : RCLike \ud835\udd5c\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \ud835\udd5c E\n\u03b9 : Type u_3\nx y : E\nb : Basis \u03b9 \ud835\udd5c E\nh : \u2200 (i : \u03b9), \u27eab i, x\u27eb_\ud835\udd5c = \u27eab i, y\u27eb_\ud835\udd5c\ni : \u03b9\n\u22a2 ((toDualMap \ud835\udd5c E) x) (b i) = ((toDualMap \ud835\udd5c E) y) (b i)",
70
+ "tactic": "rw [toDualMap_apply, toDualMap_apply]"
71
+ },
72
+ {
73
+ "annotated_tactic": [
74
+ "\"rw [\\u2190 <a>inner_conj_symm<\\/a>]\"",
75
+ "[{\"full_name\":\"inner_conj_symm\",\"def_path\":\"Mathlib\\/Analysis\\/InnerProductSpace\\/Basic.lean\",\"def_pos\":[432,9],\"def_end_pos\":[432,24]}]"
76
+ ],
77
+ "state_after": "\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u00b2 : RCLike \ud835\udd5c\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \ud835\udd5c E\n\u03b9 : Type u_3\nx y : E\nb : Basis \u03b9 \ud835\udd5c E\nh : \u2200 (i : \u03b9), \u27eab i, x\u27eb_\ud835\udd5c = \u27eab i, y\u27eb_\ud835\udd5c\ni : \u03b9\n\u22a2 (starRingEnd \ud835\udd5c) \u27eab i, x\u27eb_\ud835\udd5c = \u27eay, b i\u27eb_\ud835\udd5c",
78
+ "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u00b2 : RCLike \ud835\udd5c\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \ud835\udd5c E\n\u03b9 : Type u_3\nx y : E\nb : Basis \u03b9 \ud835\udd5c E\nh : \u2200 (i : \u03b9), \u27eab i, x\u27eb_\ud835\udd5c = \u27eab i, y\u27eb_\ud835\udd5c\ni : \u03b9\n\u22a2 \u27eax, b i\u27eb_\ud835\udd5c = \u27eay, b i\u27eb_\ud835\udd5c",
79
+ "tactic": "rw [\u2190 inner_conj_symm]"
80
+ },
81
+ {
82
+ "annotated_tactic": [
83
+ "\"conv_rhs => rw [\\u2190 <a>inner_conj_symm<\\/a>]\"",
84
+ "[{\"full_name\":\"inner_conj_symm\",\"def_path\":\"Mathlib\\/Analysis\\/InnerProductSpace\\/Basic.lean\",\"def_pos\":[432,9],\"def_end_pos\":[432,24]}]"
85
+ ],
86
+ "state_after": "\ud835\udd5c : Type u_1\nE : Type u_2\ninst\u271d\u00b2 : RCLike \ud835\udd5c\ninst\u271d\u00b9 : NormedAddCommGroup E\ninst\u271d : InnerProductSpace \ud835\udd5c E\n\u03b9 : Type u_3\nx y : E\nb : Basis \u03b9 \ud835\udd5c E\nh : \u2200 (i : \u03b9), \u27eab i, x\u27eb_\ud835\udd5c = \u27eab i, y\u27eb_\ud835\udd5c\ni : \u03b9\n\u22a2 (starRingEnd \ud835\udd5c) \u27eab i, x\u27eb_\ud835\udd5c = (starRingEnd \ud835\udd5c) \u27eab i, y\u27eb_\ud835\udd5c",
87
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92
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105
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144
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153
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164
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165
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+ "id": "InnerProductSpace.innerSL_norm",
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+ "reason": "import_failure",
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+ "id": "InnerProductSpace.toDual_apply",
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226
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248
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249
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250
+ },
251
+ {
252
+ "error": "theorem has no selected tactic transitions",
253
+ "full_name": "Euclidean.ball_mem_nhds",
254
+ "id": "Euclidean.ball_mem_nhds",
255
+ "reason": "import_failure",
256
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263
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270
+ },
271
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272
+ },
273
+ {
274
+ "error": "theorem has no selected tactic transitions",
275
+ "full_name": "Euclidean.ball_subset_closedBall",
276
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277
+ "reason": "import_failure",
278
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279
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285
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286
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289
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290
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291
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292
+ },
293
+ "source_file": "Mathlib/Analysis/InnerProductSpace/EuclideanDist.lean"
294
+ },
295
+ {
296
+ "error": "theorem has no selected tactic transitions",
297
+ "full_name": "Euclidean.closedBall_eq_preimage",
298
+ "id": "Euclidean.closedBall_eq_preimage",
299
+ "reason": "import_failure",
300
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301
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314
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315
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316
+ },
317
+ {
318
+ "error": "theorem has no selected tactic transitions",
319
+ "full_name": "Euclidean.closedBall_mem_nhds",
320
+ "id": "Euclidean.closedBall_mem_nhds",
321
+ "reason": "import_failure",
322
+ "selection": {
323
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
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328
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329
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334
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336
+ },
337
+ "source_file": "Mathlib/Analysis/InnerProductSpace/EuclideanDist.lean"
338
+ },
339
+ {
340
+ "error": "theorem has no selected tactic transitions",
341
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342
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343
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344
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345
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351
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355
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358
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359
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360
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361
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362
+ "error": "theorem has no selected tactic transitions",
363
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364
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366
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380
+ },
381
+ "source_file": "Mathlib/Analysis/InnerProductSpace/EuclideanDist.lean"
382
+ },
383
+ {
384
+ "error": "theorem has no selected tactic transitions",
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+ "full_name": "Euclidean.mem_ball_self",
386
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+ "reason": "import_failure",
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395
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400
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401
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402
+ },
403
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404
+ }
405
+ ],
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+ "input_proofs": 23,
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+ "input_units": 2,
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+ "proofs": 10,
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+ "published_proofs": 10,
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+ "published_transitions": 21,
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+ "replay_failures": [],
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+ "transitions": 21,
413
+ "validation_failures": [],
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+ "validation_rejected_proofs": 0,
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+ "zero_transition_proofs": 0
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+ },
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+ "shards": [
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+ {
419
+ "path": "data/train/mathlib-000484-0000-6d4d8632e7bf9229.parquet",
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+ "revision": "03bde7f2d1ad989476e75d92008e2f729cf4919a"
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+ }
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+ ],
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+ "proof_ids": [
434
+ "mathlib:ContDiff.euclidean_dist",
435
+ "mathlib:Euclidean.closedBall_eq_image",
436
+ "mathlib:Euclidean.closure_ball",
437
+ "mathlib:Euclidean.exists_pos_lt_subset_ball",
438
+ "mathlib:Euclidean.isCompact_closedBall",
439
+ "mathlib:Euclidean.nhds_basis_ball",
440
+ "mathlib:Euclidean.nhds_basis_closedBall",
441
+ "mathlib:InnerProductSpace.continuousLinearMapOfBilin_apply",
442
+ "mathlib:InnerProductSpace.toDual_symm_apply",
443
+ "mathlib:InnerProductSpace.unique_continuousLinearMapOfBilin"
444
+ ],
445
+ "proof_keys": [
446
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447
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+ ]
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+ }
manifests/batches/numina/001238.json ADDED
@@ -0,0 +1,52 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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