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Datasets:
HyperCactus0
/
LeanTransitionCorpus

Tasks:
Text Generation
Tags:
lean
lean4
automated-theorem-proving
theorem-proving
formal-mathematics
mathematics
License:
Dataset card Data Studio Files
xet
 Community
1
HyperCactus0 commited on
Commit
728453c
·
verified ·
1 Parent(s): 8acf782

Record 19 verified HPC batch manifests

Browse files
Files changed (19) hide show
  1. manifests/batches/deepseek/000451.json +148 -0
  2. manifests/batches/deepseek/000452.json +148 -0
  3. manifests/batches/deepseek/000453.json +148 -0
  4. manifests/batches/deepseek/000454.json +141 -0
  5. manifests/batches/deepseek/000455.json +166 -0
  6. manifests/batches/deepseek/000456.json +148 -0
  7. manifests/batches/deepseek/000457.json +148 -0
  8. manifests/batches/deepseek/000458.json +148 -0
  9. manifests/batches/mathlib/000380.json +0 -0
  10. manifests/batches/mathlib/000382.json +1147 -0
  11. manifests/batches/mathlib/000385.json +0 -0
  12. manifests/batches/mathlib/000386.json +0 -0
  13. manifests/batches/mathlib/000387.json +0 -0
  14. manifests/batches/numina/001140.json +52 -0
  15. manifests/batches/numina/001142.json +45 -0
  16. manifests/batches/numina/001143.json +52 -0
  17. manifests/batches/numina/001144.json +44 -0
  18. manifests/batches/numina/001145.json +51 -0
  19. manifests/batches/numina/001146.json +52 -0
manifests/batches/deepseek/000451.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "deepseek/000451",
4
+ "batch_fingerprint": "ee69b48a0a155106e1dd93456dae42d41a18965d8227ac86c06cc5429dcfa0db",
5
+ "evidence": {
6
+ "batch_fingerprint": "ee69b48a0a155106e1dd93456dae42d41a18965d8227ac86c06cc5429dcfa0db",
7
+ "contamination_matches": [],
8
+ "failures": [],
9
+ "input_proofs": 50,
10
+ "input_units": 50,
11
+ "proofs": 50,
12
+ "published_proofs": 50,
13
+ "published_transitions": 120,
14
+ "replay_failures": [],
15
+ "trace_mode": "individual",
16
+ "transitions": 120,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
20
+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/deepseek-000451-0000-4331f00c56600431.parquet",
24
+ "sha256": "4331f00c5660043194e6319979584e6c98ad40b35f1d835319fae8e870fe4c33",
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+ "bytes": 335401,
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+ "rows": 107,
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+ "revision": "8acf782729c74ca78799e9abc935e512ddf8cbb3"
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+ },
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+ {
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+ "path": "data/dev/deepseek-000451-0000-7cd38a9c3f1affce.parquet",
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+ "sha256": "7cd38a9c3f1affce72f83193ccb4b0cb5432723840ab5968bcc9a451eabe56a8",
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+ "bytes": 27445,
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+ "rows": 2,
34
+ "revision": "8acf782729c74ca78799e9abc935e512ddf8cbb3"
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+ },
36
+ {
37
+ "path": "data/internal_test/deepseek-000451-0000-58e654eedac36a15.parquet",
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+ "sha256": "58e654eedac36a15db37cf814f38a51dcb5eb048c9d6d28a95c6dd7f92abc781",
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+ "bytes": 59332,
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+ "rows": 11,
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+ "revision": "8acf782729c74ca78799e9abc935e512ddf8cbb3"
42
+ }
43
+ ],
44
+ "proof_ids": [
45
+ "deepseek:thm_22597",
46
+ "deepseek:thm_22598",
47
+ "deepseek:thm_22599",
48
+ "deepseek:thm_22600",
49
+ "deepseek:thm_22601",
50
+ "deepseek:thm_22602",
51
+ "deepseek:thm_22603",
52
+ "deepseek:thm_22604",
53
+ "deepseek:thm_22605",
54
+ "deepseek:thm_22606",
55
+ "deepseek:thm_22607",
56
+ "deepseek:thm_22608",
57
+ "deepseek:thm_22609",
58
+ "deepseek:thm_22610",
59
+ "deepseek:thm_22611",
60
+ "deepseek:thm_22612",
61
+ "deepseek:thm_22613",
62
+ "deepseek:thm_22614",
63
+ "deepseek:thm_22615",
64
+ "deepseek:thm_22616",
65
+ "deepseek:thm_22617",
66
+ "deepseek:thm_22618",
67
+ "deepseek:thm_22619",
68
+ "deepseek:thm_22620",
69
+ "deepseek:thm_22621",
70
+ "deepseek:thm_22622",
71
+ "deepseek:thm_22623",
72
+ "deepseek:thm_22624",
73
+ "deepseek:thm_22625",
74
+ "deepseek:thm_22626",
75
+ "deepseek:thm_22627",
76
+ "deepseek:thm_22628",
77
+ "deepseek:thm_22629",
78
+ "deepseek:thm_22630",
79
+ "deepseek:thm_22631",
80
+ "deepseek:thm_22632",
81
+ "deepseek:thm_22633",
82
+ "deepseek:thm_22634",
83
+ "deepseek:thm_22635",
84
+ "deepseek:thm_22636",
85
+ "deepseek:thm_22637",
86
+ "deepseek:thm_22638",
87
+ "deepseek:thm_22639",
88
+ "deepseek:thm_22640",
89
+ "deepseek:thm_22641",
90
+ "deepseek:thm_22642",
91
+ "deepseek:thm_22643",
92
+ "deepseek:thm_22644",
93
+ "deepseek:thm_22645",
94
+ "deepseek:thm_22646"
95
+ ],
96
+ "proof_keys": [
97
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022550.lean\",\"fc59e65efd8426cb93d625ba3ae4f08fbe8310bdaa9722d19ba168a16255380a\",0,\"thm_22597\"]",
98
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022551.lean\",\"e8ebc93c02c94465fee010068441465bcc071bc1e4ff4a66d876a463d5c1374d\",0,\"thm_22598\"]",
99
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022552.lean\",\"b9049af6b201af4b050c2c6fea860a87deee59ffd131c1582d8a4a85bffede6d\",0,\"thm_22599\"]",
100
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022553.lean\",\"adff243a8b6d3dff8210bab754a3639339130b6a89792db69dc00b1e20b0fa24\",0,\"thm_22600\"]",
101
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022554.lean\",\"263cb959ae4ba61ef0a192c9503a7ee9de77aee39fe93df54e78735b100f7716\",0,\"thm_22601\"]",
102
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022555.lean\",\"15cb4172e059728c7031595bb6e0056477c96885d71f8ac155f62e65277c57ef\",0,\"thm_22602\"]",
103
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022556.lean\",\"e93799f98dad3fe8773c3fdba9fd88dbdba767443ee85708546b9cecc4805599\",0,\"thm_22603\"]",
104
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022557.lean\",\"261c152ae4620e0b844aa44457a3f8d1737df63b563b4720bedcd0e86cc735d5\",0,\"thm_22604\"]",
105
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022558.lean\",\"0077aec43852e281534b41ad72c99833effab1ed0c7f14cbb0a405098cabe190\",0,\"thm_22605\"]",
106
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022559.lean\",\"014a040e6a96f5ff36c3781ec826cd57877d74c04cc0d231e496312879657d71\",0,\"thm_22606\"]",
107
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022560.lean\",\"b95ed88ff5e7605a789edb11c6a8bc51c56adcb68967a0c9e7cf5cf2b45c5e25\",0,\"thm_22607\"]",
108
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022561.lean\",\"7176518817e17181923baecaad64975514a2b8f1fdfea4f0208358e8b49b8de2\",0,\"thm_22608\"]",
109
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022562.lean\",\"43c104f68adbf4152347b96516ef4ed6451572efaa120d1c762c01b04eca2547\",0,\"thm_22609\"]",
110
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022563.lean\",\"fe1cec87eff2eb3b7e98229b76a0861e3e3bd9f2a574bf9ad46c932f7e254370\",0,\"thm_22610\"]",
111
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022564.lean\",\"16c041771283d93d25455854bb36284bd5f04eb29b950e77db8098a316ed9422\",0,\"thm_22611\"]",
112
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022565.lean\",\"738f525b3ace07be70a93cf05e3102acc42744db347bfdcb86f3e248a3080f8b\",0,\"thm_22612\"]",
113
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022566.lean\",\"64fce72cc8504329c98d17efed99fcf1073dfb0fcfd81d5062de302b581637f8\",0,\"thm_22613\"]",
114
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022567.lean\",\"a6fac0f8785c50a9421b480e7fc8af52aa3c731b211b88e2127f5ad6b4200132\",0,\"thm_22614\"]",
115
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022568.lean\",\"b0b5f4f67f9ea9e2fd3c56c251c95540f4b4a9bab451c560bdcd3f4b87dca512\",0,\"thm_22615\"]",
116
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022569.lean\",\"b0bd8f9259ed73231798cbf934af57467fb20f715736ff7090d053203601499c\",0,\"thm_22616\"]",
117
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022570.lean\",\"5b3ab09fbc678d985bb38349cd1223f378d48386970e9a22d65532ce10985100\",0,\"thm_22617\"]",
118
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022571.lean\",\"84c9bc7373e97265419501913558167c44a920de60679fe4a493dd8023e5fc00\",0,\"thm_22618\"]",
119
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022572.lean\",\"3c27470376cf6953e6f92b24e5da95e5f63a836a6a0852870d5592f98d5b2257\",0,\"thm_22619\"]",
120
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022573.lean\",\"2f618156f10f226603765d718f2495b29e661860c5495f159a4350cb30d02bd9\",0,\"thm_22620\"]",
121
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022574.lean\",\"47befda1bfcf6e3e665cf3c3bb31e83f5f641c5719dd2c510d942d72dba29e20\",0,\"thm_22621\"]",
122
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022575.lean\",\"af5ccbb94e82e155935a23c27444f1ab8566333c1a604e2356ffc12926ab8828\",0,\"thm_22622\"]",
123
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022576.lean\",\"c1cc6fa531f06801dd6410565149fbd1b637ea410288e294bb2a9aff1c22df14\",0,\"thm_22623\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022577.lean\",\"8afde6a2063d4bdaddb9d9bcccca4f44623acd622ae8076dd0376a8cf94ff4bf\",0,\"thm_22624\"]",
125
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022578.lean\",\"77c60b1c6be6ec01aa503e66505bbd56d33bc3f0d8a1c0a96486af81e88e1306\",0,\"thm_22625\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022579.lean\",\"016ca9d3abbee7d5377ce29ce28bb92ec332bcb4e10293c7597d278ecc6c300a\",0,\"thm_22626\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022580.lean\",\"f1f9b32924cba9d997090be4c2eaf2a7155af6b3ce1e86b3870ad40bbfe26f72\",0,\"thm_22627\"]",
128
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022581.lean\",\"9e52efe02c5a2653b90d4cf57fa89b3276ab9362da35bbeec899557278994870\",0,\"thm_22628\"]",
129
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022582.lean\",\"a0a279b13462bb91d786ebe48561c8f13197094252eb9adec669f03268ec0afa\",0,\"thm_22629\"]",
130
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022583.lean\",\"dd50bd2fee4f5bb93d3b33d8d8af2996714327580018c616a7fbbf0b3b496a12\",0,\"thm_22630\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022584.lean\",\"e8b2509e9fae445d0c05ddf7374805b34122115bdc55ffff03ce549ab4d9f636\",0,\"thm_22631\"]",
132
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022585.lean\",\"8b1a45a85ccbace71aa7e9f8d148094e1ab2cc47db2c2f30d98a79d92408259f\",0,\"thm_22632\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022586.lean\",\"96b0802ef9a6120a4a64c4c4a16a050446d5ecbb82409ff552339851eb8d5ba1\",0,\"thm_22633\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022587.lean\",\"84b9e7e33f7b6f2fda34f676bb52ea1f178205bb9593cc3a55c15c4ad9e1a920\",0,\"thm_22634\"]",
135
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022588.lean\",\"49327ac760143f0db9bedc10a44b6104c510978fb860f0e00f48e6757c3affb3\",0,\"thm_22635\"]",
136
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022589.lean\",\"1c8fa9d553e61fdc0d8eaffdbb302ac81c8c92e5e185dfcc539346fc0ea8bbc4\",0,\"thm_22636\"]",
137
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022590.lean\",\"85ce23ce4c75e4ea349285455158e1a8dd24c63974dec16503c90753943ce308\",0,\"thm_22637\"]",
138
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022591.lean\",\"be10afc17a0d8ee9077f62c5af9ae68a8b617103d042b8fe108320d5481c7e45\",0,\"thm_22638\"]",
139
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022592.lean\",\"da1d925512a8fcd8cb177fdc3222c8b1cb6c81af1be715ba058cf46bc670f786\",0,\"thm_22639\"]",
140
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022593.lean\",\"9d4a3d50a561d3fa04ee684567095179e4734f58477e1e4990597d237ee59207\",0,\"thm_22640\"]",
141
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022594.lean\",\"4e283886c40d355ee263e57a7c7637abee4ad84018e7071bb71649a1c6574ce4\",0,\"thm_22641\"]",
142
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022595.lean\",\"1b207901ab377be6df998254bd9f1a20f464192012e11ea2a7c766fff5b4dd92\",0,\"thm_22642\"]",
143
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022596.lean\",\"38b8b75010c5433be6d3b5acea93524e8124cd0b9b0a5a9318c7891179ecc30c\",0,\"thm_22643\"]",
144
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022597.lean\",\"5496cd2a17575ed17dc9c7f0c71c1e96781380b47b370447178d7ffc1639b01e\",0,\"thm_22644\"]",
145
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022598.lean\",\"d48e78b42ce2a9f77ac4edbd0b926e535bed76f9367ce84356d15a126383d042\",0,\"thm_22645\"]",
146
+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022599.lean\",\"0af0e68dc32bd4a2607d420e27fd8641241e13c40eda73a13ce146dbb1f56d91\",0,\"thm_22646\"]"
147
+ ]
148
+ }
manifests/batches/deepseek/000452.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ {
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+ "format": "leangpt-parquet-v2",
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+ "batch": "deepseek/000452",
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+ "batch_fingerprint": "9065dbac64d77ac9ad04bb0676a60013efacbb51d6f882a46fd9311e0aec6607",
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+ "evidence": {
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+ "batch_fingerprint": "9065dbac64d77ac9ad04bb0676a60013efacbb51d6f882a46fd9311e0aec6607",
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+ "contamination_matches": [],
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+ "failures": [],
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+ "input_proofs": 50,
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+ "input_units": 50,
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+ "proofs": 50,
12
+ "published_proofs": 50,
13
+ "published_transitions": 111,
14
+ "replay_failures": [],
15
+ "trace_mode": "individual",
16
+ "transitions": 111,
17
+ "validation_failures": [],
18
+ "validation_rejected_proofs": 0,
19
+ "zero_transition_proofs": 0
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+ },
21
+ "shards": [
22
+ {
23
+ "path": "data/train/deepseek-000452-0000-c2159a8bcf9701d2.parquet",
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+ "sha256": "c2159a8bcf9701d22ae17c77fb980cfa409f296e15f73b03fd56100e8f04f2ff",
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+ "bytes": 294582,
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+ "rows": 93,
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+ "revision": "8acf782729c74ca78799e9abc935e512ddf8cbb3"
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+ },
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+ {
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+ "path": "data/dev/deepseek-000452-0000-a7532c79ef9aa8c0.parquet",
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+ "sha256": "a7532c79ef9aa8c0921de76f9e55f22fcdce22a6bf7dd96db3b31d143176f7b4",
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+ "bytes": 40031,
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+ "rows": 7,
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+ "revision": "8acf782729c74ca78799e9abc935e512ddf8cbb3"
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+ },
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+ {
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+ "path": "data/internal_test/deepseek-000452-0000-c7e218e764921938.parquet",
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+ "sha256": "c7e218e7649219388f2caa843f786eff2e2c1a1f86128e9b03bb523db91ec072",
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+ "bytes": 43933,
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+ "rows": 11,
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+ "revision": "8acf782729c74ca78799e9abc935e512ddf8cbb3"
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+ }
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+ ],
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+ "proof_ids": [
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+ "deepseek:thm_22650",
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+ "deepseek:thm_22652",
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+ "deepseek:thm_22653",
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+ "deepseek:thm_22654",
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+ "deepseek:thm_22658",
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+ "deepseek:thm_22663",
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+ "deepseek:thm_22665",
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+ "deepseek:thm_22666",
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+ "deepseek:thm_22668",
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+ "deepseek:thm_22669",
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+ "deepseek:thm_22670",
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+ "deepseek:thm_22671",
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+ "deepseek:thm_22672",
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+ "deepseek:thm_22673",
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+ "deepseek:thm_22674",
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+ "deepseek:thm_22675",
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+ "deepseek:thm_22676",
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+ "deepseek:thm_22677",
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+ "deepseek:thm_22678",
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+ "deepseek:thm_22679",
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+ "deepseek:thm_22680",
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+ "deepseek:thm_22681",
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+ "deepseek:thm_22682",
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+ "deepseek:thm_22683",
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+ "deepseek:thm_22684",
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+ "deepseek:thm_22685",
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+ "deepseek:thm_22686",
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+ "deepseek:thm_22687",
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+ "deepseek:thm_22688",
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+ "deepseek:thm_22689",
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+ "deepseek:thm_22690",
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+ "deepseek:thm_22691",
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+ "deepseek:thm_22692",
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+ "deepseek:thm_22693",
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+ "deepseek:thm_22694",
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+ "deepseek:thm_22695",
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+ "deepseek:thm_22696"
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+ ],
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+ "proof_keys": [
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022632.lean\",\"3123d6f526e71ae2261ef8a22eb9c20a7ea61537bc819e8576823c23a90a879d\",0,\"thm_22679\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022635.lean\",\"c741531b9db203f46d3ddbc9edffa3720cae702bba634b1d7327ef67dcfaf70c\",0,\"thm_22682\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022640.lean\",\"938bcaab9e7312647756c53e7e58557a5d89cdc08a88abf35f99daf077d9401c\",0,\"thm_22687\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022641.lean\",\"dde77556efdaaa142679220a0aef59e6df867ac35c628059b702155e6964f4f8\",0,\"thm_22688\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022643.lean\",\"974c8f2a929db6700f4189664e160e3ea2d45634f74bacdcee5f210c71f02fac\",0,\"thm_22690\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022644.lean\",\"1c7cf59c15bbac4286ca5bb64c86dacbe9fe10a8caf22440b53f8742c2323612\",0,\"thm_22691\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022645.lean\",\"ffb7edededcb93ba07b6d0e4b9b40d7e03e0821664e3ca5b35721a0510ef1c43\",0,\"thm_22692\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022647.lean\",\"d8ec497d7c255a186db56ee439ee27eedef7b38f370a80c10335b0e728dc8b5f\",0,\"thm_22694\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022648.lean\",\"8ada42389228dbb985837c9ab67fc76ee6c1fec3d2926c6a9721e017c752bf8a\",0,\"thm_22695\"]",
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147
+ ]
148
+ }
manifests/batches/deepseek/000453.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ {
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+ "format": "leangpt-parquet-v2",
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+ "batch": "deepseek/000453",
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+ "batch_fingerprint": "590435bf28400f8f23aadf1d0a06c4f63fbdd548c03a9606eaba33f49ee82b0a",
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+ "evidence": {
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+ "batch_fingerprint": "590435bf28400f8f23aadf1d0a06c4f63fbdd548c03a9606eaba33f49ee82b0a",
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+ "contamination_matches": [],
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+ "failures": [],
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+ "input_proofs": 50,
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+ "input_units": 50,
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+ "proofs": 50,
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+ "published_proofs": 50,
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+ "published_transitions": 123,
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+ "replay_failures": [],
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+ "trace_mode": "individual",
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+ "transitions": 123,
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+ "validation_failures": [],
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+ "validation_rejected_proofs": 0,
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+ "zero_transition_proofs": 0
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+ },
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+ "shards": [
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+ {
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+ "path": "data/train/deepseek-000453-0000-77df0613e39c3065.parquet",
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+ "sha256": "77df0613e39c306543e970593cc5de9d446403b149165233656920b6d4c6de70",
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+ "path": "data/dev/deepseek-000453-0000-3a5ed471790a0828.parquet",
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+ "path": "data/internal_test/deepseek-000453-0000-729e4c4d4e67013d.parquet",
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+ }
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+ ],
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+ "proof_ids": [
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+ "deepseek:thm_22697",
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+ "deepseek:thm_22699",
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+ "deepseek:thm_22700",
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+ "deepseek:thm_22701",
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+ "deepseek:thm_22702",
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+ "deepseek:thm_22703",
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+ "deepseek:thm_22704",
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+ "deepseek:thm_22705",
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+ "deepseek:thm_22706",
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+ "deepseek:thm_22707",
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+ "deepseek:thm_22708",
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+ "deepseek:thm_22709",
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+ "deepseek:thm_22710",
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+ "deepseek:thm_22713",
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+ "deepseek:thm_22721",
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+ "deepseek:thm_22722",
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+ "deepseek:thm_22723",
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+ "deepseek:thm_22724",
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+ "deepseek:thm_22728",
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+ "deepseek:thm_22729",
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+ "deepseek:thm_22730",
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+ "deepseek:thm_22731",
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+ "deepseek:thm_22732",
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+ "deepseek:thm_22734",
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+ "deepseek:thm_22738",
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+ "deepseek:thm_22740",
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+ "deepseek:thm_22741",
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+ "deepseek:thm_22744",
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+ "deepseek:thm_22745",
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+ "deepseek:thm_22746"
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+ ],
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+ "proof_keys": [
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022650.lean\",\"913fb349248898d98b9f4c8b25597a7c5b19fbe309bdf1f5cd63256a1f5f795b\",0,\"thm_22697\"]",
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147
+ ]
148
+ }
manifests/batches/deepseek/000454.json ADDED
@@ -0,0 +1,141 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ {
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+ "batch_fingerprint": "b452fe6ff0cf6ae8685e8c0a5dc5e5506c604e7b56996e56ccc5c5cf0612f83a",
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+ "contamination_matches": [],
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+ "replay_failures": [],
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+ "trace_mode": "individual",
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+ "transitions": 114,
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+ "validation_failures": [],
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+ "path": "data/train/deepseek-000454-0000-cf307851d40b631c.parquet",
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+ "deepseek:thm_22794",
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+ ],
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022746.lean\",\"3240f8b734fa1d1d9c729edb5e74e013df2fec61a289a056dbb14ca954d44bf9\",0,\"thm_22793\"]",
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+ "[\"deepseek\",\"1ee889f608fb12ba3596757ee91a60acd663ea81\",\"Full/Proof_022747.lean\",\"f8684a0d5a170eea519cc717db93d569f57ed075b960d1328f72da12b3c8a35e\",0,\"thm_22794\"]",
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140
+ ]
141
+ }
manifests/batches/deepseek/000455.json ADDED
@@ -0,0 +1,166 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ {
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+ "batch": "deepseek/000455",
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+ "batch_fingerprint": "dec46a7449bd85fe3fd085b85fc02a4f85d6a2ef71778daac8984059534b2527",
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+ "evidence": {
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+ "contamination_matches": [],
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+ {
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+ "error": "final replayable tactic does not close all goals",
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+ "id": "thm_22826",
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+ "index": 22779,
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+ "reason": "import_failure",
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+ "selection": {
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+ "file_path": "Full/Proof_022779.lean",
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+ "id": "thm_22826",
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+ "index": 22779,
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+ "metadata": {
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+ "declaration_kind": "theorem",
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+ "source_dataset": "deepseek",
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+ "theorem_name": "thm_22826",
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manifests/batches/deepseek/000458.json ADDED
@@ -0,0 +1,148 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ }
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+ "batch": "mathlib/000382",
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+ "batch_fingerprint": "2ec341796355338727a3f3a7b49be62f3ab298d5f0b23f40e127add12db88e87",
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+ {
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+ "error": "theorem has no selected tactic transitions",
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+ },
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+ "source_file": "Mathlib/AlgebraicTopology/SimplicialSet/Monoidal.lean"
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+ },
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+ {
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+ "error": "theorem has no selected tactic transitions",
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+ "full_name": "SSet.associator_inv_app_apply",
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+ "id": "SSet.associator_inv_app_apply",
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+ "reason": "import_failure",
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+ "url": "https://github.com/leanprover-community/mathlib4"
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+ },
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+ "source_file": "Mathlib/AlgebraicTopology/SimplicialSet/Monoidal.lean"
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+ },
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+ {
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+ "error": "theorem has no selected tactic transitions",
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+ "id": "SSet.leftUnitor_hom_app_apply",
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+ "reason": "import_failure",
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+ },
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+ "source_file": "Mathlib/AlgebraicTopology/SimplicialSet/Monoidal.lean"
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+ },
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+ {
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+ "error": "theorem has no selected tactic transitions",
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+ "full_name": "SSet.leftUnitor_inv_app_apply",
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+ "id": "SSet.leftUnitor_inv_app_apply",
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+ "reason": "import_failure",
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+ ],
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+ "url": "https://github.com/leanprover-community/mathlib4"
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+ },
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+ "source_file": "Mathlib/AlgebraicTopology/SimplicialSet/Monoidal.lean"
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+ },
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+ {
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+ "error": "theorem has no selected tactic transitions",
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+ "full_name": "SSet.rightUnitor_hom_app_apply",
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+ "id": "SSet.rightUnitor_hom_app_apply",
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+ "reason": "import_failure",
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+ ],
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+ "url": "https://github.com/leanprover-community/mathlib4"
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+ },
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+ "source_file": "Mathlib/AlgebraicTopology/SimplicialSet/Monoidal.lean"
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+ },
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+ {
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+ "error": "theorem has no selected tactic transitions",
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+ "full_name": "SSet.rightUnitor_inv_app_apply",
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+ "id": "SSet.rightUnitor_inv_app_apply",
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+ "reason": "import_failure",
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+ "url": "https://github.com/leanprover-community/mathlib4"
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+ },
139
+ "source_file": "Mathlib/AlgebraicTopology/SimplicialSet/Monoidal.lean"
140
+ },
141
+ {
142
+ "error": "theorem has no selected tactic transitions",
143
+ "full_name": "SSet.tensorHom_app_apply",
144
+ "id": "SSet.tensorHom_app_apply",
145
+ "reason": "import_failure",
146
+ "selection": {
147
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
148
+ "end": [
149
+ 50,
150
+ 56
151
+ ],
152
+ "file_path": "Mathlib/AlgebraicTopology/SimplicialSet/Monoidal.lean",
153
+ "full_name": "SSet.tensorHom_app_apply",
154
+ "start": [
155
+ 47,
156
+ 1
157
+ ],
158
+ "traced_tactics": [],
159
+ "url": "https://github.com/leanprover-community/mathlib4"
160
+ },
161
+ "source_file": "Mathlib/AlgebraicTopology/SimplicialSet/Monoidal.lean"
162
+ },
163
+ {
164
+ "error": "theorem has no selected tactic transitions",
165
+ "full_name": "SSet.whiskerLeft_app_apply",
166
+ "id": "SSet.whiskerLeft_app_apply",
167
+ "reason": "import_failure",
168
+ "selection": {
169
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
170
+ "end": [
171
+ 55,
172
+ 48
173
+ ],
174
+ "file_path": "Mathlib/AlgebraicTopology/SimplicialSet/Monoidal.lean",
175
+ "full_name": "SSet.whiskerLeft_app_apply",
176
+ "start": [
177
+ 52,
178
+ 1
179
+ ],
180
+ "traced_tactics": [],
181
+ "url": "https://github.com/leanprover-community/mathlib4"
182
+ },
183
+ "source_file": "Mathlib/AlgebraicTopology/SimplicialSet/Monoidal.lean"
184
+ },
185
+ {
186
+ "error": "theorem has no selected tactic transitions",
187
+ "full_name": "SSet.whiskerRight_app_apply",
188
+ "id": "SSet.whiskerRight_app_apply",
189
+ "reason": "import_failure",
190
+ "selection": {
191
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
192
+ "end": [
193
+ 60,
194
+ 48
195
+ ],
196
+ "file_path": "Mathlib/AlgebraicTopology/SimplicialSet/Monoidal.lean",
197
+ "full_name": "SSet.whiskerRight_app_apply",
198
+ "start": [
199
+ 57,
200
+ 1
201
+ ],
202
+ "traced_tactics": [],
203
+ "url": "https://github.com/leanprover-community/mathlib4"
204
+ },
205
+ "source_file": "Mathlib/AlgebraicTopology/SimplicialSet/Monoidal.lean"
206
+ },
207
+ {
208
+ "error": "no internal trace for tactic 'ext'",
209
+ "full_name": "SimplicialObject.Split.Hom.ext",
210
+ "id": "SimplicialObject.Split.Hom.ext",
211
+ "reason": "import_failure",
212
+ "selection": {
213
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
214
+ "end": [
215
+ 363,
216
+ 14
217
+ ],
218
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
219
+ "full_name": "SimplicialObject.Split.Hom.ext",
220
+ "start": [
221
+ 352,
222
+ 1
223
+ ],
224
+ "traced_tactics": [
225
+ {
226
+ "annotated_tactic": [
227
+ "\"rcases \\u03a6\\u2081 with \\u27e8F\\u2081, f\\u2081, c\\u2081\\u27e9\"",
228
+ "[]"
229
+ ],
230
+ "state_after": "case mk\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\n\u03a6\u2082 : S\u2081.Hom S\u2082\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = \u03a6\u2082.f n\n\u22a2 { F := F\u2081, f := f\u2081, comm := c\u2081 } = \u03a6\u2082",
231
+ "state_before": "C : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\n\u03a6\u2081 \u03a6\u2082 : S\u2081.Hom S\u2082\nh : \u2200 (n : \u2115), \u03a6\u2081.f n = \u03a6\u2082.f n\n\u22a2 \u03a6\u2081 = \u03a6\u2082",
232
+ "tactic": "rcases \u03a6\u2081 with \u27e8F\u2081, f\u2081, c\u2081\u27e9"
233
+ },
234
+ {
235
+ "annotated_tactic": [
236
+ "\"rcases \\u03a6\\u2082 with \\u27e8F\\u2082, f\\u2082, c\\u2082\\u27e9\"",
237
+ "[]"
238
+ ],
239
+ "state_after": "case mk.mk\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nF\u2082 : S\u2081.X \u27f6 S\u2082.X\nf\u2082 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2082 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] } = f\u2082 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = { F := F\u2082, f := f\u2082, comm := c\u2082 }.f n\n\u22a2 { F := F\u2081, f := f\u2081, comm := c\u2081 } = { F := F\u2082, f := f\u2082, comm := c\u2082 }",
240
+ "state_before": "case mk\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\n\u03a6\u2082 : S\u2081.Hom S\u2082\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = \u03a6\u2082.f n\n\u22a2 { F := F\u2081, f := f\u2081, comm := c\u2081 } = \u03a6\u2082",
241
+ "tactic": "rcases \u03a6\u2082 with \u27e8F\u2082, f\u2082, c\u2082\u27e9"
242
+ },
243
+ {
244
+ "annotated_tactic": [
245
+ "\"have h' : f\\u2081 = f\\u2082 := by\\n ext\\n apply h\"",
246
+ "[]"
247
+ ],
248
+ "state_after": "case mk.mk\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nF\u2082 : S\u2081.X \u27f6 S\u2082.X\nf\u2082 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2082 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] } = f\u2082 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = { F := F\u2082, f := f\u2082, comm := c\u2082 }.f n\nh' : f\u2081 = f\u2082\n\u22a2 { F := F\u2081, f := f\u2081, comm := c\u2081 } = { F := F\u2082, f := f\u2082, comm := c\u2082 }",
249
+ "state_before": "case mk.mk\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nF\u2082 : S\u2081.X \u27f6 S\u2082.X\nf\u2082 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2082 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] } = f\u2082 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = { F := F\u2082, f := f\u2082, comm := c\u2082 }.f n\n\u22a2 { F := F\u2081, f := f\u2081, comm := c\u2081 } = { F := F\u2082, f := f\u2082, comm := c\u2082 }",
250
+ "tactic": "have h' : f\u2081 = f\u2082 := by\n ext\n apply h"
251
+ },
252
+ {
253
+ "annotated_tactic": [
254
+ "\"subst h'\"",
255
+ "[]"
256
+ ],
257
+ "state_after": "case mk.mk\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nF\u2082 : S\u2081.X \u27f6 S\u2082.X\nc\u2082 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = { F := F\u2082, f := f\u2081, comm := c\u2082 }.f n\n\u22a2 { F := F\u2081, f := f\u2081, comm := c\u2081 } = { F := F\u2082, f := f\u2081, comm := c\u2082 }",
258
+ "state_before": "case mk.mk\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nF\u2082 : S\u2081.X \u27f6 S\u2082.X\nf\u2082 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2082 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] } = f\u2082 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = { F := F\u2082, f := f\u2082, comm := c\u2082 }.f n\nh' : f\u2081 = f\u2082\n\u22a2 { F := F\u2081, f := f\u2081, comm := c\u2081 } = { F := F\u2082, f := f\u2082, comm := c\u2082 }",
259
+ "tactic": "subst h'"
260
+ },
261
+ {
262
+ "annotated_tactic": [
263
+ "\"simp only [mk.injEq, <a>and_true<\\/a>]\"",
264
+ "[{\"full_name\":\"and_true\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/SimpLemmas.lean\",\"def_pos\":[104,17],\"def_end_pos\":[104,25]}]"
265
+ ],
266
+ "state_after": "case mk.mk\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nF\u2082 : S\u2081.X \u27f6 S\u2082.X\nc\u2082 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = { F := F\u2082, f := f\u2081, comm := c\u2082 }.f n\n\u22a2 F\u2081 = F\u2082",
267
+ "state_before": "case mk.mk\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nF\u2082 : S\u2081.X \u27f6 S\u2082.X\nc\u2082 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = { F := F\u2082, f := f\u2081, comm := c\u2082 }.f n\n\u22a2 { F := F\u2081, f := f\u2081, comm := c\u2081 } = { F := F\u2082, f := f\u2081, comm := c\u2082 }",
268
+ "tactic": "simp only [mk.injEq, and_true]"
269
+ },
270
+ {
271
+ "annotated_tactic": [
272
+ "\"apply S\\u2081.s.hom_ext\"",
273
+ "[]"
274
+ ],
275
+ "state_after": "case mk.mk.h\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nF\u2082 : S\u2081.X \u27f6 S\u2082.X\nc\u2082 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = { F := F\u2082, f := f\u2081, comm := c\u2082 }.f n\n\u22a2 \u2200 (n : \u2115), S\u2081.s.\u03c6 F\u2081 n = S\u2081.s.\u03c6 F\u2082 n",
276
+ "state_before": "case mk.mk\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nF\u2082 : S\u2081.X \u27f6 S\u2082.X\nc\u2082 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = { F := F\u2082, f := f\u2081, comm := c\u2082 }.f n\n\u22a2 F\u2081 = F\u2082",
277
+ "tactic": "apply S\u2081.s.hom_ext"
278
+ },
279
+ {
280
+ "annotated_tactic": [
281
+ "\"intro n\"",
282
+ "[]"
283
+ ],
284
+ "state_after": "case mk.mk.h\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nF\u2082 : S\u2081.X \u27f6 S\u2082.X\nc\u2082 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = { F := F\u2082, f := f\u2081, comm := c\u2082 }.f n\nn : \u2115\n\u22a2 S\u2081.s.\u03c6 F\u2081 n = S\u2081.s.\u03c6 F\u2082 n",
285
+ "state_before": "case mk.mk.h\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nF\u2082 : S\u2081.X \u27f6 S\u2082.X\nc\u2082 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = { F := F\u2082, f := f\u2081, comm := c\u2082 }.f n\n\u22a2 \u2200 (n : \u2115), S\u2081.s.\u03c6 F\u2081 n = S\u2081.s.\u03c6 F\u2082 n",
286
+ "tactic": "intro n"
287
+ },
288
+ {
289
+ "annotated_tactic": [
290
+ "\"dsimp\"",
291
+ "[]"
292
+ ],
293
+ "state_after": "case mk.mk.h\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nF\u2082 : S\u2081.X \u27f6 S\u2082.X\nc\u2082 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = { F := F\u2082, f := f\u2081, comm := c\u2082 }.f n\nn : \u2115\n\u22a2 S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] }",
294
+ "state_before": "case mk.mk.h\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nF\u2082 : S\u2081.X \u27f6 S\u2082.X\nc\u2082 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = { F := F\u2082, f := f\u2081, comm := c\u2082 }.f n\nn : \u2115\n\u22a2 S\u2081.s.\u03c6 F\u2081 n = S\u2081.s.\u03c6 F\u2082 n",
295
+ "tactic": "dsimp"
296
+ },
297
+ {
298
+ "annotated_tactic": [
299
+ "\"rw [c\\u2081, c\\u2082]\"",
300
+ "[]"
301
+ ],
302
+ "state_after": "no goals",
303
+ "state_before": "case mk.mk.h\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nF\u2082 : S\u2081.X \u27f6 S\u2082.X\nc\u2082 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = { F := F\u2082, f := f\u2081, comm := c\u2082 }.f n\nn : \u2115\n\u22a2 S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] }",
304
+ "tactic": "rw [c\u2081, c\u2082]"
305
+ },
306
+ {
307
+ "annotated_tactic": [
308
+ "\"ext\"",
309
+ "[]"
310
+ ],
311
+ "state_after": "case h\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nF\u2082 : S\u2081.X \u27f6 S\u2082.X\nf\u2082 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2082 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] } = f\u2082 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = { F := F\u2082, f := f\u2082, comm := c\u2082 }.f n\nx\u271d : \u2115\n\u22a2 f\u2081 x\u271d = f\u2082 x\u271d",
312
+ "state_before": "C : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nF\u2082 : S\u2081.X \u27f6 S\u2082.X\nf\u2082 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2082 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] } = f\u2082 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = { F := F\u2082, f := f\u2082, comm := c\u2082 }.f n\n\u22a2 f\u2081 = f\u2082",
313
+ "tactic": "ext"
314
+ },
315
+ {
316
+ "annotated_tactic": [
317
+ "\"apply h\"",
318
+ "[]"
319
+ ],
320
+ "state_after": "no goals",
321
+ "state_before": "case h\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nS\u2081 S\u2082 : Split C\nF\u2081 : S\u2081.X \u27f6 S\u2082.X\nf\u2081 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2081 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2081.app { unop := [n] } = f\u2081 n \u226b S\u2082.s.\u03b9 n\nF\u2082 : S\u2081.X \u27f6 S\u2082.X\nf\u2082 : (n : \u2115) \u2192 S\u2081.s.N n \u27f6 S\u2082.s.N n\nc\u2082 : \u2200 (n : \u2115), S\u2081.s.\u03b9 n \u226b F\u2082.app { unop := [n] } = f\u2082 n \u226b S\u2082.s.\u03b9 n\nh : \u2200 (n : \u2115), { F := F\u2081, f := f\u2081, comm := c\u2081 }.f n = { F := F\u2082, f := f\u2082, comm := c\u2082 }.f n\nx\u271d : \u2115\n\u22a2 f\u2081 x\u271d = f\u2082 x\u271d",
322
+ "tactic": "apply h"
323
+ }
324
+ ],
325
+ "url": "https://github.com/leanprover-community/mathlib4"
326
+ },
327
+ "source_file": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean"
328
+ },
329
+ {
330
+ "error": "theorem has no selected tactic transitions",
331
+ "full_name": "SimplicialObject.Split.comp_F",
332
+ "id": "SimplicialObject.Split.comp_F",
333
+ "reason": "import_failure",
334
+ "selection": {
335
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
336
+ "end": [
337
+ 413,
338
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339
+ ],
340
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
341
+ "full_name": "SimplicialObject.Split.comp_F",
342
+ "start": [
343
+ 411,
344
+ 1
345
+ ],
346
+ "traced_tactics": [],
347
+ "url": "https://github.com/leanprover-community/mathlib4"
348
+ },
349
+ "source_file": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean"
350
+ },
351
+ {
352
+ "error": "theorem has no selected tactic transitions",
353
+ "full_name": "SimplicialObject.Split.comp_f",
354
+ "id": "SimplicialObject.Split.comp_f",
355
+ "reason": "import_failure",
356
+ "selection": {
357
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
358
+ "end": [
359
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360
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361
+ ],
362
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
363
+ "full_name": "SimplicialObject.Split.comp_f",
364
+ "start": [
365
+ 418,
366
+ 1
367
+ ],
368
+ "traced_tactics": [],
369
+ "url": "https://github.com/leanprover-community/mathlib4"
370
+ },
371
+ "source_file": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean"
372
+ },
373
+ {
374
+ "error": "theorem has no selected tactic transitions",
375
+ "full_name": "SimplicialObject.Split.hom_ext",
376
+ "id": "SimplicialObject.Split.hom_ext",
377
+ "reason": "import_failure",
378
+ "selection": {
379
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
380
+ "end": [
381
+ 389,
382
+ 16
383
+ ],
384
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
385
+ "full_name": "SimplicialObject.Split.hom_ext",
386
+ "start": [
387
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388
+ 1
389
+ ],
390
+ "traced_tactics": [],
391
+ "url": "https://github.com/leanprover-community/mathlib4"
392
+ },
393
+ "source_file": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean"
394
+ },
395
+ {
396
+ "error": "theorem has no selected tactic transitions",
397
+ "full_name": "SimplicialObject.Split.id_F",
398
+ "id": "SimplicialObject.Split.id_F",
399
+ "reason": "import_failure",
400
+ "selection": {
401
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
402
+ "end": [
403
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404
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405
+ ],
406
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
407
+ "full_name": "SimplicialObject.Split.id_F",
408
+ "start": [
409
+ 400,
410
+ 1
411
+ ],
412
+ "traced_tactics": [],
413
+ "url": "https://github.com/leanprover-community/mathlib4"
414
+ },
415
+ "source_file": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean"
416
+ },
417
+ {
418
+ "error": "theorem has no selected tactic transitions",
419
+ "full_name": "SimplicialObject.Split.id_f",
420
+ "id": "SimplicialObject.Split.id_f",
421
+ "reason": "import_failure",
422
+ "selection": {
423
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
424
+ "end": [
425
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426
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427
+ ],
428
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
429
+ "full_name": "SimplicialObject.Split.id_f",
430
+ "start": [
431
+ 406,
432
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433
+ ],
434
+ "traced_tactics": [],
435
+ "url": "https://github.com/leanprover-community/mathlib4"
436
+ },
437
+ "source_file": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean"
438
+ },
439
+ {
440
+ "error": "no internal trace for tactic 'dsimp at h'",
441
+ "full_name": "SimplicialObject.Splitting.IndexSet.eqId_iff_eq",
442
+ "id": "SimplicialObject.Splitting.IndexSet.eqId_iff_eq",
443
+ "reason": "import_failure",
444
+ "selection": {
445
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
446
+ "end": [
447
+ 140,
448
+ 25
449
+ ],
450
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
451
+ "full_name": "SimplicialObject.Splitting.IndexSet.eqId_iff_eq",
452
+ "start": [
453
+ 127,
454
+ 1
455
+ ],
456
+ "traced_tactics": [
457
+ {
458
+ "annotated_tactic": [
459
+ "\"constructor\"",
460
+ "[]"
461
+ ],
462
+ "state_after": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.EqId \u2192 A.fst = \u0394\n\ncase mpr\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.fst = \u0394 \u2192 A.EqId",
463
+ "state_before": "C : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.EqId \u2194 A.fst = \u0394",
464
+ "tactic": "constructor"
465
+ },
466
+ {
467
+ "annotated_tactic": [
468
+ "\"intro h\"",
469
+ "[]"
470
+ ],
471
+ "state_after": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A.EqId\n\u22a2 A.fst = \u0394",
472
+ "state_before": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.EqId \u2192 A.fst = \u0394",
473
+ "tactic": "intro h"
474
+ },
475
+ {
476
+ "annotated_tactic": [
477
+ "\"dsimp at h\"",
478
+ "[]"
479
+ ],
480
+ "state_after": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A = id \u0394\n\u22a2 A.fst = \u0394",
481
+ "state_before": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A.EqId\n\u22a2 A.fst = \u0394",
482
+ "tactic": "dsimp at h"
483
+ },
484
+ {
485
+ "annotated_tactic": [
486
+ "\"rw [h]\"",
487
+ "[]"
488
+ ],
489
+ "state_after": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A = id \u0394\n\u22a2 (id \u0394).fst = \u0394",
490
+ "state_before": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A = id \u0394\n\u22a2 A.fst = \u0394",
491
+ "tactic": "rw [h]"
492
+ },
493
+ {
494
+ "annotated_tactic": [
495
+ "\"rfl\"",
496
+ "[]"
497
+ ],
498
+ "state_after": "no goals",
499
+ "state_before": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A = id \u0394\n\u22a2 (id \u0394).fst = \u0394",
500
+ "tactic": "rfl"
501
+ },
502
+ {
503
+ "annotated_tactic": [
504
+ "\"intro h\"",
505
+ "[]"
506
+ ],
507
+ "state_after": "case mpr\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A.fst = \u0394\n\u22a2 A.EqId",
508
+ "state_before": "case mpr\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.fst = \u0394 \u2192 A.EqId",
509
+ "tactic": "intro h"
510
+ },
511
+ {
512
+ "annotated_tactic": [
513
+ "\"rcases A with \\u27e8_, \\u27e8f, hf\\u27e9\\u27e9\"",
514
+ "[]"
515
+ ],
516
+ "state_after": "case mpr.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\n\u0394 fst\u271d : SimplexCategory\u1d52\u1d56\nf : \u0394.unop \u27f6 fst\u271d.unop\nhf : Epi f\nh : \u27e8fst\u271d, \u27e8f, hf\u27e9\u27e9.fst = \u0394\n\u22a2 EqId \u27e8fst\u271d, \u27e8f, hf\u27e9\u27e9",
517
+ "state_before": "case mpr\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A.fst = \u0394\n\u22a2 A.EqId",
518
+ "tactic": "rcases A with \u27e8_, \u27e8f, hf\u27e9\u27e9"
519
+ },
520
+ {
521
+ "annotated_tactic": [
522
+ "\"simp only at h\"",
523
+ "[]"
524
+ ],
525
+ "state_after": "case mpr.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\n\u0394 fst\u271d : SimplexCategory\u1d52\u1d56\nf : \u0394.unop \u27f6 fst\u271d.unop\nhf : Epi f\nh : fst\u271d = \u0394\n\u22a2 EqId \u27e8fst\u271d, \u27e8f, hf\u27e9\u27e9",
526
+ "state_before": "case mpr.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\n\u0394 fst\u271d : SimplexCategory\u1d52\u1d56\nf : \u0394.unop \u27f6 fst\u271d.unop\nhf : Epi f\nh : \u27e8fst\u271d, \u27e8f, hf\u27e9\u27e9.fst = \u0394\n\u22a2 EqId \u27e8fst\u271d, \u27e8f, hf\u27e9\u27e9",
527
+ "tactic": "simp only at h"
528
+ },
529
+ {
530
+ "annotated_tactic": [
531
+ "\"subst h\"",
532
+ "[]"
533
+ ],
534
+ "state_after": "case mpr.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\nfst\u271d : SimplexCategory\u1d52\u1d56\nf : fst\u271d.unop \u27f6 fst\u271d.unop\nhf : Epi f\n\u22a2 EqId \u27e8fst\u271d, \u27e8f, hf\u27e9\u27e9",
535
+ "state_before": "case mpr.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\n\u0394 fst\u271d : SimplexCategory\u1d52\u1d56\nf : \u0394.unop \u27f6 fst\u271d.unop\nhf : Epi f\nh : fst\u271d = \u0394\n\u22a2 EqId \u27e8fst\u271d, \u27e8f, hf\u27e9\u27e9",
536
+ "tactic": "subst h"
537
+ },
538
+ {
539
+ "annotated_tactic": [
540
+ "\"refine <a>ext<\\/a> _ _ <a>rfl<\\/a> ?_\"",
541
+ "[{\"full_name\":\"SimplicialObject.Splitting.IndexSet.ext\",\"def_path\":\"Mathlib\\/AlgebraicTopology\\/SplitSimplicialObject.lean\",\"def_pos\":[77,9],\"def_end_pos\":[77,12]},{\"full_name\":\"rfl\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[294,22],\"def_end_pos\":[294,25]}]"
542
+ ],
543
+ "state_after": "case mpr.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\nfst\u271d : SimplexCategory\u1d52\u1d56\nf : fst\u271d.unop \u27f6 fst\u271d.unop\nhf : Epi f\n\u22a2 e \u27e8fst\u271d, \u27e8f, hf\u27e9\u27e9 \u226b eqToHom \u22ef = (id fst\u271d).e",
544
+ "state_before": "case mpr.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\nfst\u271d : SimplexCategory\u1d52\u1d56\nf : fst\u271d.unop \u27f6 fst\u271d.unop\nhf : Epi f\n\u22a2 EqId \u27e8fst\u271d, \u27e8f, hf\u27e9\u27e9",
545
+ "tactic": "refine ext _ _ rfl ?_"
546
+ },
547
+ {
548
+ "annotated_tactic": [
549
+ "\"haveI := hf\"",
550
+ "[]"
551
+ ],
552
+ "state_after": "case mpr.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\nfst\u271d : SimplexCategory\u1d52\u1d56\nf : fst\u271d.unop \u27f6 fst\u271d.unop\nhf this : Epi f\n\u22a2 e \u27e8fst\u271d, \u27e8f, hf\u27e9\u27e9 \u226b eqToHom \u22ef = (id fst\u271d).e",
553
+ "state_before": "case mpr.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\nfst\u271d : SimplexCategory\u1d52\u1d56\nf : fst\u271d.unop \u27f6 fst\u271d.unop\nhf : Epi f\n\u22a2 e \u27e8fst\u271d, \u27e8f, hf\u27e9\u27e9 \u226b eqToHom \u22ef = (id fst\u271d).e",
554
+ "tactic": "haveI := hf"
555
+ },
556
+ {
557
+ "annotated_tactic": [
558
+ "\"simp only [<a>eqToHom_refl<\\/a>, <a>comp_id<\\/a>]\"",
559
+ "[{\"full_name\":\"CategoryTheory.eqToHom_refl\",\"def_path\":\"Mathlib\\/CategoryTheory\\/EqToHom.lean\",\"def_pos\":[47,9],\"def_end_pos\":[47,21]},{\"full_name\":\"CategoryTheory.Category.comp_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[179,3],\"def_end_pos\":[179,10]}]"
560
+ ],
561
+ "state_after": "case mpr.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\nfst\u271d : SimplexCategory\u1d52\u1d56\nf : fst\u271d.unop \u27f6 fst\u271d.unop\nhf this : Epi f\n\u22a2 e \u27e8fst\u271d, \u27e8f, hf\u27e9\u27e9 = (id fst\u271d).e",
562
+ "state_before": "case mpr.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\nfst\u271d : SimplexCategory\u1d52\u1d56\nf : fst\u271d.unop \u27f6 fst\u271d.unop\nhf this : Epi f\n\u22a2 e \u27e8fst\u271d, \u27e8f, hf\u27e9\u27e9 \u226b eqToHom \u22ef = (id fst\u271d).e",
563
+ "tactic": "simp only [eqToHom_refl, comp_id]"
564
+ },
565
+ {
566
+ "annotated_tactic": [
567
+ "\"exact <a>eq_id_of_epi<\\/a> f\"",
568
+ "[{\"full_name\":\"SimplexCategory.eq_id_of_epi\",\"def_path\":\"Mathlib\\/AlgebraicTopology\\/SimplexCategory.lean\",\"def_pos\":[793,9],\"def_end_pos\":[793,21]}]"
569
+ ],
570
+ "state_after": "no goals",
571
+ "state_before": "case mpr.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.3430, u_1} C\nfst\u271d : SimplexCategory\u1d52\u1d56\nf : fst\u271d.unop \u27f6 fst\u271d.unop\nhf this : Epi f\n\u22a2 e \u27e8fst\u271d, \u27e8f, hf\u27e9\u27e9 = (id fst\u271d).e",
572
+ "tactic": "exact eq_id_of_epi f"
573
+ }
574
+ ],
575
+ "url": "https://github.com/leanprover-community/mathlib4"
576
+ },
577
+ "source_file": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean"
578
+ },
579
+ {
580
+ "error": "no internal trace for tactic 'rw [h]'",
581
+ "full_name": "SimplicialObject.Splitting.IndexSet.eqId_iff_len_eq",
582
+ "id": "SimplicialObject.Splitting.IndexSet.eqId_iff_len_eq",
583
+ "reason": "import_failure",
584
+ "selection": {
585
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
586
+ "end": [
587
+ 151,
588
+ 12
589
+ ],
590
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
591
+ "full_name": "SimplicialObject.Splitting.IndexSet.eqId_iff_len_eq",
592
+ "start": [
593
+ 143,
594
+ 1
595
+ ],
596
+ "traced_tactics": [
597
+ {
598
+ "annotated_tactic": [
599
+ "\"rw [<a>eqId_iff_eq<\\/a>]\"",
600
+ "[{\"full_name\":\"SimplicialObject.Splitting.IndexSet.eqId_iff_eq\",\"def_path\":\"Mathlib\\/AlgebraicTopology\\/SplitSimplicialObject.lean\",\"def_pos\":[127,9],\"def_end_pos\":[127,20]}]"
601
+ ],
602
+ "state_after": "C : Type u_1\ninst\u271d : Category.{?u.3816, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.fst = \u0394 \u2194 A.fst.unop.len = \u0394.unop.len",
603
+ "state_before": "C : Type u_1\ninst\u271d : Category.{?u.3816, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.EqId \u2194 A.fst.unop.len = \u0394.unop.len",
604
+ "tactic": "rw [eqId_iff_eq]"
605
+ },
606
+ {
607
+ "annotated_tactic": [
608
+ "\"constructor\"",
609
+ "[]"
610
+ ],
611
+ "state_after": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.3816, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.fst = \u0394 \u2192 A.fst.unop.len = \u0394.unop.len\n\ncase mpr\nC : Type u_1\ninst\u271d : Category.{?u.3816, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.fst.unop.len = \u0394.unop.len \u2192 A.fst = \u0394",
612
+ "state_before": "C : Type u_1\ninst\u271d : Category.{?u.3816, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.fst = \u0394 \u2194 A.fst.unop.len = \u0394.unop.len",
613
+ "tactic": "constructor"
614
+ },
615
+ {
616
+ "annotated_tactic": [
617
+ "\"intro h\"",
618
+ "[]"
619
+ ],
620
+ "state_after": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.3816, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A.fst = \u0394\n\u22a2 A.fst.unop.len = \u0394.unop.len",
621
+ "state_before": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.3816, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.fst = \u0394 \u2192 A.fst.unop.len = \u0394.unop.len",
622
+ "tactic": "intro h"
623
+ },
624
+ {
625
+ "annotated_tactic": [
626
+ "\"rw [h]\"",
627
+ "[]"
628
+ ],
629
+ "state_after": "no goals",
630
+ "state_before": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.3816, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A.fst = \u0394\n\u22a2 A.fst.unop.len = \u0394.unop.len",
631
+ "tactic": "rw [h]"
632
+ },
633
+ {
634
+ "annotated_tactic": [
635
+ "\"intro h\"",
636
+ "[]"
637
+ ],
638
+ "state_after": "case mpr\nC : Type u_1\ninst\u271d : Category.{?u.3816, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A.fst.unop.len = \u0394.unop.len\n\u22a2 A.fst = \u0394",
639
+ "state_before": "case mpr\nC : Type u_1\ninst\u271d : Category.{?u.3816, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.fst.unop.len = \u0394.unop.len \u2192 A.fst = \u0394",
640
+ "tactic": "intro h"
641
+ },
642
+ {
643
+ "annotated_tactic": [
644
+ "\"rw [\\u2190 <a>unop_inj_iff<\\/a>]\"",
645
+ "[{\"full_name\":\"Opposite.unop_inj_iff\",\"def_path\":\"Mathlib\\/Data\\/Opposite.lean\",\"def_pos\":[77,9],\"def_end_pos\":[77,21]}]"
646
+ ],
647
+ "state_after": "case mpr\nC : Type u_1\ninst\u271d : Category.{?u.3816, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A.fst.unop.len = \u0394.unop.len\n\u22a2 A.fst.unop = \u0394.unop",
648
+ "state_before": "case mpr\nC : Type u_1\ninst\u271d : Category.{?u.3816, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A.fst.unop.len = \u0394.unop.len\n\u22a2 A.fst = \u0394",
649
+ "tactic": "rw [\u2190 unop_inj_iff]"
650
+ },
651
+ {
652
+ "annotated_tactic": [
653
+ "\"ext\"",
654
+ "[]"
655
+ ],
656
+ "state_after": "case mpr.a\nC : Type u_1\ninst\u271d : Category.{?u.3816, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A.fst.unop.len = \u0394.unop.len\n\u22a2 A.fst.unop.len = \u0394.unop.len",
657
+ "state_before": "case mpr\nC : Type u_1\ninst\u271d : Category.{?u.3816, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A.fst.unop.len = \u0394.unop.len\n\u22a2 A.fst.unop = \u0394.unop",
658
+ "tactic": "ext"
659
+ },
660
+ {
661
+ "annotated_tactic": [
662
+ "\"exact h\"",
663
+ "[]"
664
+ ],
665
+ "state_after": "no goals",
666
+ "state_before": "case mpr.a\nC : Type u_1\ninst\u271d : Category.{?u.3816, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A.fst.unop.len = \u0394.unop.len\n\u22a2 A.fst.unop.len = \u0394.unop.len",
667
+ "tactic": "exact h"
668
+ }
669
+ ],
670
+ "url": "https://github.com/leanprover-community/mathlib4"
671
+ },
672
+ "source_file": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean"
673
+ },
674
+ {
675
+ "error": "no internal trace for tactic 'dsimp at h'",
676
+ "full_name": "SimplicialObject.Splitting.IndexSet.eqId_iff_mono",
677
+ "id": "SimplicialObject.Splitting.IndexSet.eqId_iff_mono",
678
+ "reason": "import_failure",
679
+ "selection": {
680
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
681
+ "end": [
682
+ 171,
683
+ 27
684
+ ],
685
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
686
+ "full_name": "SimplicialObject.Splitting.IndexSet.eqId_iff_mono",
687
+ "start": [
688
+ 162,
689
+ 1
690
+ ],
691
+ "traced_tactics": [
692
+ {
693
+ "annotated_tactic": [
694
+ "\"constructor\"",
695
+ "[]"
696
+ ],
697
+ "state_after": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.4635, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.EqId \u2192 Mono A.e\n\ncase mpr\nC : Type u_1\ninst\u271d : Category.{?u.4635, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 Mono A.e \u2192 A.EqId",
698
+ "state_before": "C : Type u_1\ninst\u271d : Category.{?u.4635, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.EqId \u2194 Mono A.e",
699
+ "tactic": "constructor"
700
+ },
701
+ {
702
+ "annotated_tactic": [
703
+ "\"intro h\"",
704
+ "[]"
705
+ ],
706
+ "state_after": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.4635, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A.EqId\n\u22a2 Mono A.e",
707
+ "state_before": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.4635, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.EqId \u2192 Mono A.e",
708
+ "tactic": "intro h"
709
+ },
710
+ {
711
+ "annotated_tactic": [
712
+ "\"dsimp at h\"",
713
+ "[]"
714
+ ],
715
+ "state_after": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.4635, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A = id \u0394\n\u22a2 Mono A.e",
716
+ "state_before": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.4635, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A.EqId\n\u22a2 Mono A.e",
717
+ "tactic": "dsimp at h"
718
+ },
719
+ {
720
+ "annotated_tactic": [
721
+ "\"subst h\"",
722
+ "[]"
723
+ ],
724
+ "state_after": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.4635, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\n\u22a2 Mono (id \u0394).e",
725
+ "state_before": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.4635, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A = id \u0394\n\u22a2 Mono A.e",
726
+ "tactic": "subst h"
727
+ },
728
+ {
729
+ "annotated_tactic": [
730
+ "\"dsimp only [<a>id<\\/a>, <a>e<\\/a>]\"",
731
+ "[{\"full_name\":\"SimplicialObject.Splitting.IndexSet.id\",\"def_path\":\"Mathlib\\/AlgebraicTopology\\/SplitSimplicialObject.lean\",\"def_pos\":[111,5],\"def_end_pos\":[111,7]},{\"full_name\":\"SimplicialObject.Splitting.IndexSet.e\",\"def_path\":\"Mathlib\\/AlgebraicTopology\\/SplitSimplicialObject.lean\",\"def_pos\":[67,5],\"def_end_pos\":[67,6]}]"
732
+ ],
733
+ "state_after": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.4635, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\n\u22a2 Mono (\ud835\udfd9 \u0394.unop)",
734
+ "state_before": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.4635, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\n\u22a2 Mono (id \u0394).e",
735
+ "tactic": "dsimp only [id, e]"
736
+ },
737
+ {
738
+ "annotated_tactic": [
739
+ "\"infer_instance\"",
740
+ "[]"
741
+ ],
742
+ "state_after": "no goals",
743
+ "state_before": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.4635, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\n\u22a2 Mono (\ud835\udfd9 \u0394.unop)",
744
+ "tactic": "infer_instance"
745
+ },
746
+ {
747
+ "annotated_tactic": [
748
+ "\"intro h\"",
749
+ "[]"
750
+ ],
751
+ "state_after": "case mpr\nC : Type u_1\ninst\u271d : Category.{?u.4635, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : Mono A.e\n\u22a2 A.EqId",
752
+ "state_before": "case mpr\nC : Type u_1\ninst\u271d : Category.{?u.4635, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 Mono A.e \u2192 A.EqId",
753
+ "tactic": "intro h"
754
+ },
755
+ {
756
+ "annotated_tactic": [
757
+ "\"rw [<a>eqId_iff_len_le<\\/a>]\"",
758
+ "[{\"full_name\":\"SimplicialObject.Splitting.IndexSet.eqId_iff_len_le\",\"def_path\":\"Mathlib\\/AlgebraicTopology\\/SplitSimplicialObject.lean\",\"def_pos\":[154,9],\"def_end_pos\":[154,24]}]"
759
+ ],
760
+ "state_after": "case mpr\nC : Type u_1\ninst\u271d : Category.{?u.4635, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : Mono A.e\n\u22a2 \u0394.unop.len \u2264 A.fst.unop.len",
761
+ "state_before": "case mpr\nC : Type u_1\ninst\u271d : Category.{?u.4635, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : Mono A.e\n\u22a2 A.EqId",
762
+ "tactic": "rw [eqId_iff_len_le]"
763
+ },
764
+ {
765
+ "annotated_tactic": [
766
+ "\"exact <a>len_le_of_mono<\\/a> h\"",
767
+ "[{\"full_name\":\"SimplexCategory.len_le_of_mono\",\"def_path\":\"Mathlib\\/AlgebraicTopology\\/SimplexCategory.lean\",\"def_pos\":[573,9],\"def_end_pos\":[573,23]}]"
768
+ ],
769
+ "state_after": "no goals",
770
+ "state_before": "case mpr\nC : Type u_1\ninst\u271d : Category.{?u.4635, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : Mono A.e\n\u22a2 \u0394.unop.len \u2264 A.fst.unop.len",
771
+ "tactic": "exact len_le_of_mono h"
772
+ }
773
+ ],
774
+ "url": "https://github.com/leanprover-community/mathlib4"
775
+ },
776
+ "source_file": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean"
777
+ },
778
+ {
779
+ "error": "theorem has no selected tactic transitions",
780
+ "full_name": "SimplicialObject.Splitting.IndexSet.ext'",
781
+ "id": "SimplicialObject.Splitting.IndexSet.ext'",
782
+ "reason": "import_failure",
783
+ "selection": {
784
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
785
+ "end": [
786
+ 74,
787
+ 46
788
+ ],
789
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
790
+ "full_name": "SimplicialObject.Splitting.IndexSet.ext'",
791
+ "start": [
792
+ 74,
793
+ 1
794
+ ],
795
+ "traced_tactics": [],
796
+ "url": "https://github.com/leanprover-community/mathlib4"
797
+ },
798
+ "source_file": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean"
799
+ },
800
+ {
801
+ "error": "theorem has no selected tactic transitions",
802
+ "full_name": "SimplicialObject.Splitting.IndexSet.fac_pull",
803
+ "id": "SimplicialObject.Splitting.IndexSet.fac_pull",
804
+ "reason": "import_failure",
805
+ "selection": {
806
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
807
+ "end": [
808
+ 195,
809
+ 14
810
+ ],
811
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
812
+ "full_name": "SimplicialObject.Splitting.IndexSet.fac_pull",
813
+ "start": [
814
+ 194,
815
+ 1
816
+ ],
817
+ "traced_tactics": [],
818
+ "url": "https://github.com/leanprover-community/mathlib4"
819
+ },
820
+ "source_file": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean"
821
+ },
822
+ {
823
+ "error": "theorem has no selected tactic transitions",
824
+ "full_name": "SimplicialObject.Splitting.cofan_inj_eq",
825
+ "id": "SimplicialObject.Splitting.cofan_inj_eq",
826
+ "reason": "import_failure",
827
+ "selection": {
828
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
829
+ "end": [
830
+ 245,
831
+ 64
832
+ ],
833
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
834
+ "full_name": "SimplicialObject.Splitting.cofan_inj_eq",
835
+ "start": [
836
+ 244,
837
+ 1
838
+ ],
839
+ "traced_tactics": [],
840
+ "url": "https://github.com/leanprover-community/mathlib4"
841
+ },
842
+ "source_file": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean"
843
+ },
844
+ {
845
+ "error": "theorem has no selected tactic transitions",
846
+ "full_name": "SimplicialObject.Splitting.hom_ext'",
847
+ "id": "SimplicialObject.Splitting.hom_ext'",
848
+ "reason": "import_failure",
849
+ "selection": {
850
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
851
+ "end": [
852
+ 270,
853
+ 48
854
+ ],
855
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
856
+ "full_name": "SimplicialObject.Splitting.hom_ext'",
857
+ "start": [
858
+ 268,
859
+ 1
860
+ ],
861
+ "traced_tactics": [],
862
+ "url": "https://github.com/leanprover-community/mathlib4"
863
+ },
864
+ "source_file": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean"
865
+ }
866
+ ],
867
+ "input_proofs": 32,
868
+ "input_units": 2,
869
+ "proofs": 10,
870
+ "published_proofs": 7,
871
+ "published_transitions": 11,
872
+ "replay_failures": [],
873
+ "transitions": 29,
874
+ "validation_failures": [
875
+ {
876
+ "errors": [
877
+ "internal transition boundary mismatch",
878
+ "internal transition boundary mismatch"
879
+ ],
880
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
881
+ "proof_id": "mathlib:SimplicialObject.Splitting.IndexSet.eqId_iff_len_le",
882
+ "provenance": {
883
+ "selection": {
884
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
885
+ "end": [
886
+ 159,
887
+ 64
888
+ ],
889
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
890
+ "full_name": "SimplicialObject.Splitting.IndexSet.eqId_iff_len_le",
891
+ "start": [
892
+ 154,
893
+ 1
894
+ ],
895
+ "traced_tactics": [
896
+ {
897
+ "annotated_tactic": [
898
+ "\"rw [<a>eqId_iff_len_eq<\\/a>]\"",
899
+ "[{\"full_name\":\"SimplicialObject.Splitting.IndexSet.eqId_iff_len_eq\",\"def_path\":\"Mathlib\\/AlgebraicTopology\\/SplitSimplicialObject.lean\",\"def_pos\":[143,9],\"def_end_pos\":[143,24]}]"
900
+ ],
901
+ "state_after": "C : Type u_1\ninst\u271d : Category.{?u.3929, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.fst.unop.len = \u0394.unop.len \u2194 \u0394.unop.len \u2264 A.fst.unop.len",
902
+ "state_before": "C : Type u_1\ninst\u271d : Category.{?u.3929, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.EqId \u2194 \u0394.unop.len \u2264 A.fst.unop.len",
903
+ "tactic": "rw [eqId_iff_len_eq]"
904
+ },
905
+ {
906
+ "annotated_tactic": [
907
+ "\"constructor\"",
908
+ "[]"
909
+ ],
910
+ "state_after": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.3929, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.fst.unop.len = \u0394.unop.len \u2192 \u0394.unop.len \u2264 A.fst.unop.len\n\ncase mpr\nC : Type u_1\ninst\u271d : Category.{?u.3929, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 \u0394.unop.len \u2264 A.fst.unop.len \u2192 A.fst.unop.len = \u0394.unop.len",
911
+ "state_before": "C : Type u_1\ninst\u271d : Category.{?u.3929, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.fst.unop.len = \u0394.unop.len \u2194 \u0394.unop.len \u2264 A.fst.unop.len",
912
+ "tactic": "constructor"
913
+ },
914
+ {
915
+ "annotated_tactic": [
916
+ "\"intro h\"",
917
+ "[]"
918
+ ],
919
+ "state_after": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.3929, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A.fst.unop.len = \u0394.unop.len\n\u22a2 \u0394.unop.len \u2264 A.fst.unop.len",
920
+ "state_before": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.3929, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 A.fst.unop.len = \u0394.unop.len \u2192 \u0394.unop.len \u2264 A.fst.unop.len",
921
+ "tactic": "intro h"
922
+ },
923
+ {
924
+ "annotated_tactic": [
925
+ "\"rw [h]\"",
926
+ "[]"
927
+ ],
928
+ "state_after": "no goals",
929
+ "state_before": "case mp\nC : Type u_1\ninst\u271d : Category.{?u.3929, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\nh : A.fst.unop.len = \u0394.unop.len\n\u22a2 \u0394.unop.len \u2264 A.fst.unop.len",
930
+ "tactic": "rw [h]"
931
+ },
932
+ {
933
+ "annotated_tactic": [
934
+ "\"exact <a>le_antisymm<\\/a> (<a>len_le_of_epi<\\/a> (<a>inferInstance<\\/a> : <a>Epi<\\/a> A.e))\"",
935
+ "[{\"full_name\":\"le_antisymm\",\"def_path\":\"Mathlib\\/Init\\/Order\\/Defs.lean\",\"def_pos\":[188,9],\"def_end_pos\":[188,20]},{\"full_name\":\"SimplexCategory.len_le_of_epi\",\"def_path\":\"Mathlib\\/AlgebraicTopology\\/SimplexCategory.lean\",\"def_pos\":[584,9],\"def_end_pos\":[584,22]},{\"full_name\":\"inferInstance\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[99,8],\"def_end_pos\":[99,21]},{\"full_name\":\"CategoryTheory.Epi\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[285,7],\"def_end_pos\":[285,10]}]"
936
+ ],
937
+ "state_after": "no goals",
938
+ "state_before": "case mpr\nC : Type u_1\ninst\u271d : Category.{?u.3929, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 \u0394.unop.len \u2264 A.fst.unop.len \u2192 A.fst.unop.len = \u0394.unop.len",
939
+ "tactic": "exact le_antisymm (len_le_of_epi (inferInstance : Epi A.e))"
940
+ }
941
+ ],
942
+ "url": "https://github.com/leanprover-community/mathlib4"
943
+ }
944
+ },
945
+ "theorem_name": "SimplicialObject.Splitting.IndexSet.eqId_iff_len_le"
946
+ },
947
+ {
948
+ "errors": [
949
+ "internal transition boundary mismatch"
950
+ ],
951
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
952
+ "proof_id": "mathlib:SimplicialObject.Splitting.IndexSet.ext",
953
+ "provenance": {
954
+ "selection": {
955
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
956
+ "end": [
957
+ 84,
958
+ 17
959
+ ],
960
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
961
+ "full_name": "SimplicialObject.Splitting.IndexSet.ext",
962
+ "start": [
963
+ 77,
964
+ 1
965
+ ],
966
+ "traced_tactics": [
967
+ {
968
+ "annotated_tactic": [
969
+ "\"rw [h\\u2081]\"",
970
+ "[]"
971
+ ],
972
+ "state_after": "no goals",
973
+ "state_before": "C : Type u_1\ninst\u271d : Category.{?u.799, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA A\u2081 A\u2082 : IndexSet \u0394\nh\u2081 : A\u2081.fst = A\u2082.fst\n\u22a2 A\u2081.fst.unop = A\u2082.fst.unop",
974
+ "tactic": "rw [h\u2081]"
975
+ },
976
+ {
977
+ "annotated_tactic": [
978
+ "\"rcases A\\u2081 with \\u27e8\\u0394\\u2081, \\u27e8\\u03b1\\u2081, h\\u03b1\\u2081\\u27e9\\u27e9\"",
979
+ "[]"
980
+ ],
981
+ "state_after": "case mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.799, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA A\u2082 : IndexSet \u0394\n\u0394\u2081 : SimplexCategory\u1d52\u1d56\n\u03b1\u2081 : \u0394.unop \u27f6 \u0394\u2081.unop\nh\u03b1\u2081 : Epi \u03b1\u2081\nh\u2081 : \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9.fst = A\u2082.fst\nh\u2082 : e \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9 \u226b eqToHom \u22ef = A\u2082.e\n\u22a2 \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9 = A\u2082",
982
+ "state_before": "C : Type u_1\ninst\u271d : Category.{?u.799, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA A\u2081 A\u2082 : IndexSet \u0394\nh\u2081 : A\u2081.fst = A\u2082.fst\nh\u2082 : A\u2081.e \u226b eqToHom \u22ef = A\u2082.e\n\u22a2 A\u2081 = A\u2082",
983
+ "tactic": "rcases A\u2081 with \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9"
984
+ },
985
+ {
986
+ "annotated_tactic": [
987
+ "\"rcases A\\u2082 with \\u27e8\\u0394\\u2082, \\u27e8\\u03b1\\u2082, h\\u03b1\\u2082\\u27e9\\u27e9\"",
988
+ "[]"
989
+ ],
990
+ "state_after": "case mk.mk.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.799, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u0394\u2081 : SimplexCategory\u1d52\u1d56\n\u03b1\u2081 : \u0394.unop \u27f6 \u0394\u2081.unop\nh\u03b1\u2081 : Epi \u03b1\u2081\n\u0394\u2082 : SimplexCategory\u1d52\u1d56\n\u03b1\u2082 : \u0394.unop \u27f6 \u0394\u2082.unop\nh\u03b1\u2082 : Epi \u03b1\u2082\nh\u2081 : \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9.fst = \u27e8\u0394\u2082, \u27e8\u03b1\u2082, h\u03b1\u2082\u27e9\u27e9.fst\nh\u2082 : e \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9 \u226b eqToHom \u22ef = e \u27e8\u0394\u2082, \u27e8\u03b1\u2082, h\u03b1\u2082\u27e9\u27e9\n\u22a2 \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9 = \u27e8\u0394\u2082, \u27e8\u03b1\u2082, h\u03b1\u2082\u27e9\u27e9",
991
+ "state_before": "case mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.799, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA A\u2082 : IndexSet \u0394\n\u0394\u2081 : SimplexCategory\u1d52\u1d56\n\u03b1\u2081 : \u0394.unop \u27f6 \u0394\u2081.unop\nh\u03b1\u2081 : Epi \u03b1\u2081\nh\u2081 : \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9.fst = A\u2082.fst\nh\u2082 : e \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9 \u226b eqToHom \u22ef = A\u2082.e\n\u22a2 \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9 = A\u2082",
992
+ "tactic": "rcases A\u2082 with \u27e8\u0394\u2082, \u27e8\u03b1\u2082, h\u03b1\u2082\u27e9\u27e9"
993
+ },
994
+ {
995
+ "annotated_tactic": [
996
+ "\"simp only at h\\u2081\"",
997
+ "[]"
998
+ ],
999
+ "state_after": "case mk.mk.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.799, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u0394\u2081 : SimplexCategory\u1d52\u1d56\n\u03b1\u2081 : \u0394.unop \u27f6 \u0394\u2081.unop\nh\u03b1\u2081 : Epi \u03b1\u2081\n\u0394\u2082 : SimplexCategory\u1d52\u1d56\n\u03b1\u2082 : \u0394.unop \u27f6 \u0394\u2082.unop\nh\u03b1\u2082 : Epi \u03b1\u2082\nh\u2081 : \u0394\u2081 = \u0394\u2082\nh\u2082 : e \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9 \u226b eqToHom \u22ef = e \u27e8\u0394\u2082, \u27e8\u03b1\u2082, h\u03b1\u2082\u27e9\u27e9\n\u22a2 \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9 = \u27e8\u0394\u2082, \u27e8\u03b1\u2082, h\u03b1\u2082\u27e9\u27e9",
1000
+ "state_before": "case mk.mk.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.799, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u0394\u2081 : SimplexCategory\u1d52\u1d56\n\u03b1\u2081 : \u0394.unop \u27f6 \u0394\u2081.unop\nh\u03b1\u2081 : Epi \u03b1\u2081\n\u0394\u2082 : SimplexCategory\u1d52\u1d56\n\u03b1\u2082 : \u0394.unop \u27f6 \u0394\u2082.unop\nh\u03b1\u2082 : Epi \u03b1\u2082\nh\u2081 : \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9.fst = \u27e8\u0394\u2082, \u27e8\u03b1\u2082, h\u03b1\u2082\u27e9\u27e9.fst\nh\u2082 : e \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9 \u226b eqToHom \u22ef = e \u27e8\u0394\u2082, \u27e8\u03b1\u2082, h\u03b1\u2082\u27e9\u27e9\n\u22a2 \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9 = \u27e8\u0394\u2082, \u27e8\u03b1\u2082, h\u03b1\u2082\u27e9\u27e9",
1001
+ "tactic": "simp only at h\u2081"
1002
+ },
1003
+ {
1004
+ "annotated_tactic": [
1005
+ "\"subst h\\u2081\"",
1006
+ "[]"
1007
+ ],
1008
+ "state_after": "case mk.mk.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.799, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u0394\u2081 : SimplexCategory\u1d52\u1d56\n\u03b1\u2081 : \u0394.unop \u27f6 \u0394\u2081.unop\nh\u03b1\u2081 : Epi \u03b1\u2081\n\u03b1\u2082 : \u0394.unop \u27f6 \u0394\u2081.unop\nh\u03b1\u2082 : Epi \u03b1\u2082\nh\u2082 : e \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9 \u226b eqToHom \u22ef = e \u27e8\u0394\u2081, \u27e8\u03b1\u2082, h\u03b1\u2082\u27e9\u27e9\n\u22a2 \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9 = \u27e8\u0394\u2081, \u27e8\u03b1\u2082, h\u03b1\u2082\u27e9\u27e9",
1009
+ "state_before": "case mk.mk.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.799, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u0394\u2081 : SimplexCategory\u1d52\u1d56\n\u03b1\u2081 : \u0394.unop \u27f6 \u0394\u2081.unop\nh\u03b1\u2081 : Epi \u03b1\u2081\n\u0394\u2082 : SimplexCategory\u1d52\u1d56\n\u03b1\u2082 : \u0394.unop \u27f6 \u0394\u2082.unop\nh\u03b1\u2082 : Epi \u03b1\u2082\nh\u2081 : \u0394\u2081 = \u0394\u2082\nh\u2082 : e \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9 \u226b eqToHom \u22ef = e \u27e8\u0394\u2082, \u27e8\u03b1\u2082, h\u03b1\u2082\u27e9\u27e9\n\u22a2 \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9 = \u27e8\u0394\u2082, \u27e8\u03b1\u2082, h\u03b1\u2082\u27e9\u27e9",
1010
+ "tactic": "subst h\u2081"
1011
+ },
1012
+ {
1013
+ "annotated_tactic": [
1014
+ "\"simp only [<a>eqToHom_refl<\\/a>, <a>comp_id<\\/a>, <a>IndexSet.e<\\/a>] at h\\u2082\"",
1015
+ "[{\"full_name\":\"CategoryTheory.eqToHom_refl\",\"def_path\":\"Mathlib\\/CategoryTheory\\/EqToHom.lean\",\"def_pos\":[47,9],\"def_end_pos\":[47,21]},{\"full_name\":\"CategoryTheory.Category.comp_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[179,3],\"def_end_pos\":[179,10]},{\"full_name\":\"SimplicialObject.Splitting.IndexSet.e\",\"def_path\":\"Mathlib\\/AlgebraicTopology\\/SplitSimplicialObject.lean\",\"def_pos\":[67,5],\"def_end_pos\":[67,6]}]"
1016
+ ],
1017
+ "state_after": "case mk.mk.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.799, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u0394\u2081 : SimplexCategory\u1d52\u1d56\n\u03b1\u2081 : \u0394.unop \u27f6 \u0394\u2081.unop\nh\u03b1\u2081 : Epi \u03b1\u2081\n\u03b1\u2082 : \u0394.unop \u27f6 \u0394\u2081.unop\nh\u03b1\u2082 : Epi \u03b1\u2082\nh\u2082 : \u03b1\u2081 = \u03b1\u2082\n\u22a2 \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9 = \u27e8\u0394\u2081, \u27e8\u03b1\u2082, h\u03b1\u2082\u27e9\u27e9",
1018
+ "state_before": "case mk.mk.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.799, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u0394\u2081 : SimplexCategory\u1d52\u1d56\n\u03b1\u2081 : \u0394.unop \u27f6 \u0394\u2081.unop\nh\u03b1\u2081 : Epi \u03b1\u2081\n\u03b1\u2082 : \u0394.unop \u27f6 \u0394\u2081.unop\nh\u03b1\u2082 : Epi \u03b1\u2082\nh\u2082 : e \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9 \u226b eqToHom \u22ef = e \u27e8\u0394\u2081, \u27e8\u03b1\u2082, h\u03b1\u2082\u27e9\u27e9\n\u22a2 \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9 = \u27e8\u0394\u2081, \u27e8\u03b1\u2082, h\u03b1\u2082\u27e9\u27e9",
1019
+ "tactic": "simp only [eqToHom_refl, comp_id, IndexSet.e] at h\u2082"
1020
+ },
1021
+ {
1022
+ "annotated_tactic": [
1023
+ "\"simp only [h\\u2082]\"",
1024
+ "[]"
1025
+ ],
1026
+ "state_after": "no goals",
1027
+ "state_before": "case mk.mk.mk.mk\nC : Type u_1\ninst\u271d : Category.{?u.799, u_1} C\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u0394\u2081 : SimplexCategory\u1d52\u1d56\n\u03b1\u2081 : \u0394.unop \u27f6 \u0394\u2081.unop\nh\u03b1\u2081 : Epi \u03b1\u2081\n\u03b1\u2082 : \u0394.unop \u27f6 \u0394\u2081.unop\nh\u03b1\u2082 : Epi \u03b1\u2082\nh\u2082 : \u03b1\u2081 = \u03b1\u2082\n\u22a2 \u27e8\u0394\u2081, \u27e8\u03b1\u2081, h\u03b1\u2081\u27e9\u27e9 = \u27e8\u0394\u2081, \u27e8\u03b1\u2082, h\u03b1\u2082\u27e9\u27e9",
1028
+ "tactic": "simp only [h\u2082]"
1029
+ }
1030
+ ],
1031
+ "url": "https://github.com/leanprover-community/mathlib4"
1032
+ }
1033
+ },
1034
+ "theorem_name": "SimplicialObject.Splitting.IndexSet.ext"
1035
+ },
1036
+ {
1037
+ "errors": [
1038
+ "internal transition boundary mismatch"
1039
+ ],
1040
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
1041
+ "proof_id": "mathlib:SimplicialObject.Splitting.hom_ext",
1042
+ "provenance": {
1043
+ "selection": {
1044
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
1045
+ "end": [
1046
+ 280,
1047
+ 38
1048
+ ],
1049
+ "file_path": "Mathlib/AlgebraicTopology/SplitSimplicialObject.lean",
1050
+ "full_name": "SimplicialObject.Splitting.hom_ext",
1051
+ "start": [
1052
+ 273,
1053
+ 1
1054
+ ],
1055
+ "traced_tactics": [
1056
+ {
1057
+ "annotated_tactic": [
1058
+ "\"ext \\u0394\"",
1059
+ "[]"
1060
+ ],
1061
+ "state_after": "case h\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nX Y : SimplicialObject C\ns : Splitting X\nf g : X \u27f6 Y\nh : \u2200 (n : \u2115), s.\u03c6 f n = s.\u03c6 g n\n\u0394 : SimplexCategory\u1d52\u1d56\n\u22a2 f.app \u0394 = g.app \u0394",
1062
+ "state_before": "C : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nX Y : SimplicialObject C\ns : Splitting X\nf g : X \u27f6 Y\nh : \u2200 (n : \u2115), s.\u03c6 f n = s.\u03c6 g n\n\u22a2 f = g",
1063
+ "tactic": "ext \u0394"
1064
+ },
1065
+ {
1066
+ "annotated_tactic": [
1067
+ "\"apply s.hom_ext'\"",
1068
+ "[]"
1069
+ ],
1070
+ "state_after": "case h.h\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nX Y : SimplicialObject C\ns : Splitting X\nf g : X \u27f6 Y\nh : \u2200 (n : \u2115), s.\u03c6 f n = s.\u03c6 g n\n\u0394 : SimplexCategory\u1d52\u1d56\n\u22a2 \u2200 (A : IndexSet \u0394), (s.cofan \u0394).inj A \u226b f.app \u0394 = (s.cofan \u0394).inj A \u226b g.app \u0394",
1071
+ "state_before": "case h\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nX Y : SimplicialObject C\ns : Splitting X\nf g : X \u27f6 Y\nh : \u2200 (n : \u2115), s.\u03c6 f n = s.\u03c6 g n\n\u0394 : SimplexCategory\u1d52\u1d56\n\u22a2 f.app \u0394 = g.app \u0394",
1072
+ "tactic": "apply s.hom_ext'"
1073
+ },
1074
+ {
1075
+ "annotated_tactic": [
1076
+ "\"intro A\"",
1077
+ "[]"
1078
+ ],
1079
+ "state_after": "case h.h\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nX Y : SimplicialObject C\ns : Splitting X\nf g : X \u27f6 Y\nh : \u2200 (n : \u2115), s.\u03c6 f n = s.\u03c6 g n\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 (s.cofan \u0394).inj A \u226b f.app \u0394 = (s.cofan \u0394).inj A \u226b g.app \u0394",
1080
+ "state_before": "case h.h\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nX Y : SimplicialObject C\ns : Splitting X\nf g : X \u27f6 Y\nh : \u2200 (n : \u2115), s.\u03c6 f n = s.\u03c6 g n\n\u0394 : SimplexCategory\u1d52\u1d56\n\u22a2 \u2200 (A : IndexSet \u0394), (s.cofan \u0394).inj A \u226b f.app \u0394 = (s.cofan \u0394).inj A \u226b g.app \u0394",
1081
+ "tactic": "intro A"
1082
+ },
1083
+ {
1084
+ "annotated_tactic": [
1085
+ "\"induction' \\u0394 using <a>Opposite.rec<\\/a> with \\u0394\"",
1086
+ "[{\"full_name\":\"Opposite.rec\",\"def_path\":\"Mathlib\\/Data\\/Opposite.lean\",\"def_pos\":[35,11],\"def_end_pos\":[35,19]}]"
1087
+ ],
1088
+ "state_after": "case h.h.op\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nX Y : SimplicialObject C\ns : Splitting X\nf g : X \u27f6 Y\nh : \u2200 (n : \u2115), s.\u03c6 f n = s.\u03c6 g n\n\u0394 : SimplexCategory\nA : IndexSet { unop := \u0394 }\n\u22a2 (s.cofan { unop := \u0394 }).inj A \u226b f.app { unop := \u0394 } = (s.cofan { unop := \u0394 }).inj A \u226b g.app { unop := \u0394 }",
1089
+ "state_before": "case h.h\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nX Y : SimplicialObject C\ns : Splitting X\nf g : X \u27f6 Y\nh : \u2200 (n : \u2115), s.\u03c6 f n = s.\u03c6 g n\n\u0394 : SimplexCategory\u1d52\u1d56\nA : IndexSet \u0394\n\u22a2 (s.cofan \u0394).inj A \u226b f.app \u0394 = (s.cofan \u0394).inj A \u226b g.app \u0394",
1090
+ "tactic": "induction' \u0394 using Opposite.rec with \u0394"
1091
+ },
1092
+ {
1093
+ "annotated_tactic": [
1094
+ "\"induction' \\u0394 using <a>SimplexCategory.rec<\\/a> with n\"",
1095
+ "[{\"full_name\":\"SimplexCategory.rec\",\"def_path\":\"Mathlib\\/AlgebraicTopology\\/SimplexCategory.lean\",\"def_pos\":[89,15],\"def_end_pos\":[89,18]}]"
1096
+ ],
1097
+ "state_after": "case h.h.op.h\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nX Y : SimplicialObject C\ns : Splitting X\nf g : X \u27f6 Y\nh : \u2200 (n : \u2115), s.\u03c6 f n = s.\u03c6 g n\nn : \u2115\nA : IndexSet { unop := [n] }\n\u22a2 (s.cofan { unop := [n] }).inj A \u226b f.app { unop := [n] } = (s.cofan { unop := [n] }).inj A \u226b g.app { unop := [n] }",
1098
+ "state_before": "case h.h.op\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nX Y : SimplicialObject C\ns : Splitting X\nf g : X \u27f6 Y\nh : \u2200 (n : \u2115), s.\u03c6 f n = s.\u03c6 g n\n\u0394 : SimplexCategory\nA : IndexSet { unop := \u0394 }\n\u22a2 (s.cofan { unop := \u0394 }).inj A \u226b f.app { unop := \u0394 } = (s.cofan { unop := \u0394 }).inj A \u226b g.app { unop := \u0394 }",
1099
+ "tactic": "induction' \u0394 using SimplexCategory.rec with n"
1100
+ },
1101
+ {
1102
+ "annotated_tactic": [
1103
+ "\"simp only [s.cofan_inj_comp_app, h]\"",
1104
+ "[]"
1105
+ ],
1106
+ "state_after": "no goals",
1107
+ "state_before": "case h.h.op.h\nC : Type u_1\ninst\u271d : Category.{u_2, u_1} C\nX Y : SimplicialObject C\ns : Splitting X\nf g : X \u27f6 Y\nh : \u2200 (n : \u2115), s.\u03c6 f n = s.\u03c6 g n\nn : \u2115\nA : IndexSet { unop := [n] }\n\u22a2 (s.cofan { unop := [n] }).inj A \u226b f.app { unop := [n] } = (s.cofan { unop := [n] }).inj A \u226b g.app { unop := [n] }",
1108
+ "tactic": "simp only [s.cofan_inj_comp_app, h]"
1109
+ }
1110
+ ],
1111
+ "url": "https://github.com/leanprover-community/mathlib4"
1112
+ }
1113
+ },
1114
+ "theorem_name": "SimplicialObject.Splitting.hom_ext"
1115
+ }
1116
+ ],
1117
+ "validation_rejected_proofs": 3,
1118
+ "zero_transition_proofs": 0
1119
+ },
1120
+ "shards": [
1121
+ {
1122
+ "path": "data/train/mathlib-000382-0000-3cadbce2db2651ca.parquet",
1123
+ "sha256": "3cadbce2db2651ca5e153739716286ebb0fa19a191ff5caf8b77fc3588365fe4",
1124
+ "bytes": 72094,
1125
+ "rows": 11,
1126
+ "revision": "8acf782729c74ca78799e9abc935e512ddf8cbb3"
1127
+ }
1128
+ ],
1129
+ "proof_ids": [
1130
+ "mathlib:SimplicialObject.Split.cofan_inj_naturality_symm",
1131
+ "mathlib:SimplicialObject.Split.congr_F",
1132
+ "mathlib:SimplicialObject.Split.congr_f",
1133
+ "mathlib:SimplicialObject.Splitting.cofan_inj_comp_app",
1134
+ "mathlib:SimplicialObject.Splitting.cofan_inj_epi_naturality",
1135
+ "mathlib:SimplicialObject.Splitting.cofan_inj_id",
1136
+ "mathlib:SimplicialObject.Splitting.\u03b9_desc"
1137
+ ],
1138
+ "proof_keys": [
1139
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/AlgebraicTopology/SplitSimplicialObject.lean\",null,null,\"SimplicialObject.Split.cofan_inj_naturality_symm\"]",
1140
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/AlgebraicTopology/SplitSimplicialObject.lean\",null,null,\"SimplicialObject.Split.congr_F\"]",
1141
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/AlgebraicTopology/SplitSimplicialObject.lean\",null,null,\"SimplicialObject.Split.congr_f\"]",
1142
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/AlgebraicTopology/SplitSimplicialObject.lean\",null,null,\"SimplicialObject.Splitting.cofan_inj_comp_app\"]",
1143
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/AlgebraicTopology/SplitSimplicialObject.lean\",null,null,\"SimplicialObject.Splitting.cofan_inj_epi_naturality\"]",
1144
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/AlgebraicTopology/SplitSimplicialObject.lean\",null,null,\"SimplicialObject.Splitting.cofan_inj_id\"]",
1145
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/AlgebraicTopology/SplitSimplicialObject.lean\",null,null,\"SimplicialObject.Splitting.\u03b9_desc\"]"
1146
+ ]
1147
+ }
manifests/batches/mathlib/000385.json ADDED
The diff for this file is too large to render. See raw diff
 
manifests/batches/mathlib/000386.json ADDED
The diff for this file is too large to render. See raw diff
 
manifests/batches/mathlib/000387.json ADDED
The diff for this file is too large to render. See raw diff
 
manifests/batches/numina/001140.json ADDED
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+ {
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+ "format": "leangpt-parquet-v2",
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+ "validation_rejected_proofs": 0,
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+ },
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+ "shards": [
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+ {
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+ "path": "data/train/numina-001140-0000-70f547940e650c9a.parquet",
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+ "revision": "8acf782729c74ca78799e9abc935e512ddf8cbb3"
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+ },
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+ "path": "data/internal_test/numina-001140-0000-9bb976796061de63.parquet",
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+ "numina:0a47d39b-fbeb-5c0a-89cf-8e4db5219bf6",
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+ "numina:9b443b57-3290-5e2d-a5af-7e60fc8eeb55",
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+ "numina:ea506f64-d77b-5edd-be1b-c4437d1a35f8",
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+ "numina:f5ae32e3-70c1-5975-b8b2-f8ed5e8d4542"
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+ ],
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+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005700.lean\",\"550cc6f513892e8d0abd8380dc437149720846f6a0975527864b7c25d65d52dc\",2,\"number_theory_249846\"]",
47
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005701.lean\",\"803eac20b7b5a54368d5e263d172dcc93a7d5af90fbc07eb0e3c509e5f592399\",0,\"algebra_107072\"]",
48
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005702.lean\",\"2bd45e33e87a30ed65a702686e86425206ff0f3b136937ff4ec39b9e42dd1b90\",2,\"algebra_241734\"]",
49
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005703.lean\",\"c4a7660220e24681860b2c4cbf1c3debbcbab8bca70af0fd38de439d9ce52eff\",0,\"algebra_677\"]",
50
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005704.lean\",\"58dd37d11a080bf58ddc9597fe7b28881e795052d33db2d4e3d3fafd46011781\",0,\"number_theory_683\"]"
51
+ ]
52
+ }
manifests/batches/numina/001142.json ADDED
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1
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+ "numina:493febe5-b25b-54c0-90b9-abd19304edeb",
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+ "numina:5c1cd10b-8faa-5aa1-b538-58ab4e11baaa",
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+ "numina:7d301df5-a2b5-5d5c-b008-b726c03e170b",
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+ "numina:b4cd2b7c-5763-52af-b292-46aa4e7ce291",
36
+ "numina:bab55aa6-302b-538e-ae3a-b5ea4c64b5a8"
37
+ ],
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+ "proof_keys": [
39
+ "[\"numina\",\"51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94\",\"Full/Proof_005710.lean\",\"95c65ccf4a328e18420e7afcab309edbaefb624bd4669f69be1188bb71d483da\",2,\"number_theory_191070\"]",
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