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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
495e49e
·
verified ·
1 Parent(s): cbe1482

Record 18 verified HPC batch manifests

Browse files
Files changed (18) hide show
  1. manifests/batches/mathlib/000699.json +174 -0
  2. manifests/batches/mathlib/000700.json +400 -0
  3. manifests/batches/mathlib/000701.json +0 -0
  4. manifests/batches/mathlib/000703.json +931 -0
  5. manifests/batches/mathlib/000705.json +80 -0
  6. manifests/batches/mathlib/000706.json +610 -0
  7. manifests/batches/mathlib/000707.json +1296 -0
  8. manifests/batches/mathlib/000708.json +0 -0
  9. manifests/batches/numina/001458.json +44 -0
  10. manifests/batches/numina/001459.json +51 -0
  11. manifests/batches/numina/001460.json +58 -0
  12. manifests/batches/numina/001461.json +88 -0
  13. manifests/batches/numina/001462.json +44 -0
  14. manifests/batches/numina/001463.json +58 -0
  15. manifests/batches/numina/001465.json +44 -0
  16. manifests/batches/numina/001466.json +58 -0
  17. manifests/batches/numina/001467.json +51 -0
  18. manifests/batches/numina/001468.json +51 -0
manifests/batches/mathlib/000699.json ADDED
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+ ]
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manifests/batches/mathlib/000700.json ADDED
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+ "reason": "import_failure",
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+ "selection": {
235
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
236
+ "end": [
237
+ 255,
238
+ 94
239
+ ],
240
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean",
241
+ "full_name": "CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_inv_apply",
242
+ "start": [
243
+ 253,
244
+ 1
245
+ ],
246
+ "traced_tactics": [],
247
+ "url": "https://github.com/leanprover-community/mathlib4"
248
+ },
249
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean"
250
+ },
251
+ {
252
+ "error": "theorem has no selected tactic transitions",
253
+ "full_name": "CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_hom_apply",
254
+ "id": "CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_hom_apply",
255
+ "reason": "import_failure",
256
+ "selection": {
257
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
258
+ "end": [
259
+ 247,
260
+ 66
261
+ ],
262
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean",
263
+ "full_name": "CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_hom_apply",
264
+ "start": [
265
+ 244,
266
+ 1
267
+ ],
268
+ "traced_tactics": [],
269
+ "url": "https://github.com/leanprover-community/mathlib4"
270
+ },
271
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean"
272
+ },
273
+ {
274
+ "error": "theorem has no selected tactic transitions",
275
+ "full_name": "CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_inv",
276
+ "id": "CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_inv",
277
+ "reason": "import_failure",
278
+ "selection": {
279
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
280
+ "end": [
281
+ 259,
282
+ 84
283
+ ],
284
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean",
285
+ "full_name": "CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_inv",
286
+ "start": [
287
+ 257,
288
+ 1
289
+ ],
290
+ "traced_tactics": [],
291
+ "url": "https://github.com/leanprover-community/mathlib4"
292
+ },
293
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean"
294
+ },
295
+ {
296
+ "error": "theorem has no selected tactic transitions",
297
+ "full_name": "CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_inv_apply",
298
+ "id": "CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_inv_apply",
299
+ "reason": "import_failure",
300
+ "selection": {
301
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
302
+ "end": [
303
+ 263,
304
+ 94
305
+ ],
306
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean",
307
+ "full_name": "CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_inv_apply",
308
+ "start": [
309
+ 261,
310
+ 1
311
+ ],
312
+ "traced_tactics": [],
313
+ "url": "https://github.com/leanprover-community/mathlib4"
314
+ },
315
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean"
316
+ },
317
+ {
318
+ "error": "theorem has no selected tactic transitions",
319
+ "full_name": "CategoryTheory.FunctorToTypes.prod.lift_snd",
320
+ "id": "CategoryTheory.FunctorToTypes.prod.lift_snd",
321
+ "reason": "import_failure",
322
+ "selection": {
323
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
324
+ "end": [
325
+ 63,
326
+ 43
327
+ ],
328
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean",
329
+ "full_name": "CategoryTheory.FunctorToTypes.prod.lift_snd",
330
+ "start": [
331
+ 61,
332
+ 1
333
+ ],
334
+ "traced_tactics": [],
335
+ "url": "https://github.com/leanprover-community/mathlib4"
336
+ },
337
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean"
338
+ },
339
+ {
340
+ "error": "theorem has no selected tactic transitions",
341
+ "full_name": "CategoryTheory.FunctorToTypes.prod_ext",
342
+ "id": "CategoryTheory.FunctorToTypes.prod_ext",
343
+ "reason": "import_failure",
344
+ "selection": {
345
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
346
+ "end": [
347
+ 137,
348
+ 28
349
+ ],
350
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean",
351
+ "full_name": "CategoryTheory.FunctorToTypes.prod_ext",
352
+ "start": [
353
+ 135,
354
+ 1
355
+ ],
356
+ "traced_tactics": [],
357
+ "url": "https://github.com/leanprover-community/mathlib4"
358
+ },
359
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean"
360
+ }
361
+ ],
362
+ "input_proofs": 23,
363
+ "input_units": 2,
364
+ "proofs": 7,
365
+ "published_proofs": 7,
366
+ "published_transitions": 10,
367
+ "replay_failures": [],
368
+ "transitions": 10,
369
+ "validation_failures": [],
370
+ "validation_rejected_proofs": 0,
371
+ "zero_transition_proofs": 0
372
+ },
373
+ "shards": [
374
+ {
375
+ "path": "data/train/mathlib-000700-0000-595a419c97171966.parquet",
376
+ "sha256": "595a419c971719664f076dfa87a8715a8b343e2a93efb3c756f2c092f8125ead",
377
+ "bytes": 52708,
378
+ "rows": 10,
379
+ "revision": "cbe1482cb65ba353079b280907cc7e0382180ba2"
380
+ }
381
+ ],
382
+ "proof_ids": [
383
+ "mathlib:CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_fst",
384
+ "mathlib:CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_snd",
385
+ "mathlib:CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_hom",
386
+ "mathlib:CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_hom",
387
+ "mathlib:CategoryTheory.FunctorToTypes.prodMk_fst",
388
+ "mathlib:CategoryTheory.FunctorToTypes.prodMk_snd",
389
+ "mathlib:CategoryTheory.FunctorToTypes.prod_ext'"
390
+ ],
391
+ "proof_keys": [
392
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean\",null,null,\"CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_fst\"]",
393
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean\",null,null,\"CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_snd\"]",
394
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean\",null,null,\"CategoryTheory.FunctorToTypes.inl_comp_binaryCoproductIso_hom\"]",
395
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean\",null,null,\"CategoryTheory.FunctorToTypes.inr_comp_binaryCoproductIso_hom\"]",
396
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean\",null,null,\"CategoryTheory.FunctorToTypes.prodMk_fst\"]",
397
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean\",null,null,\"CategoryTheory.FunctorToTypes.prodMk_snd\"]",
398
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Limits/Shapes/FunctorToTypes.lean\",null,null,\"CategoryTheory.FunctorToTypes.prod_ext'\"]"
399
+ ]
400
+ }
manifests/batches/mathlib/000701.json ADDED
The diff for this file is too large to render. See raw diff
 
manifests/batches/mathlib/000703.json ADDED
@@ -0,0 +1,931 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000703",
4
+ "batch_fingerprint": "d9416501ff57e14ab9e464026cb90e8459f9abc4edc9ecb7f4f87d4dff353a6b",
5
+ "evidence": {
6
+ "batch_fingerprint": "d9416501ff57e14ab9e464026cb90e8459f9abc4edc9ecb7f4f87d4dff353a6b",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "CategoryTheory.NormalEpiCategory.mono_of_cancel_zero",
12
+ "id": "CategoryTheory.NormalEpiCategory.mono_of_cancel_zero",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 340,
18
+ 57
19
+ ],
20
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/NormalMono/Equalizers.lean",
21
+ "full_name": "CategoryTheory.NormalEpiCategory.mono_of_cancel_zero",
22
+ "start": [
23
+ 338,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/NormalMono/Equalizers.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "CategoryTheory.NormalMonoCategory.epi_of_zero_cancel",
34
+ "id": "CategoryTheory.NormalMonoCategory.epi_of_zero_cancel",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 174,
40
+ 60
41
+ ],
42
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/NormalMono/Equalizers.lean",
43
+ "full_name": "CategoryTheory.NormalMonoCategory.epi_of_zero_cancel",
44
+ "start": [
45
+ 172,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/NormalMono/Equalizers.lean"
52
+ },
53
+ {
54
+ "error": "no internal trace for tactic 'rw [\u2190 hm, Category.assoc, hw, comp_zero]'",
55
+ "full_name": "CategoryTheory.NormalMonoCategory.epi_of_zero_cokernel",
56
+ "id": "CategoryTheory.NormalMonoCategory.epi_of_zero_cokernel",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 162,
62
+ 35
63
+ ],
64
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/NormalMono/Equalizers.lean",
65
+ "full_name": "CategoryTheory.NormalMonoCategory.epi_of_zero_cokernel",
66
+ "start": [
67
+ 152,
68
+ 1
69
+ ],
70
+ "traced_tactics": [
71
+ {
72
+ "annotated_tactic": [
73
+ "\"simp\"",
74
+ "[]"
75
+ ],
76
+ "state_after": "no goals",
77
+ "state_before": "C : Type u_1\ninst\u271d\u2074 : Category.{?u.109385, u_1} C\ninst\u271d\u00b3 : HasZeroMorphisms C\ninst\u271d\u00b2 : HasFiniteProducts C\ninst\u271d\u00b9 : HasKernels C\ninst\u271d : NormalMonoCategory C\nX Y : C\nf : X \u27f6 Y\nZ : C\n\u22a2 f \u226b 0 = 0",
78
+ "tactic": "simp"
79
+ },
80
+ {
81
+ "annotated_tactic": [
82
+ "\"obtain \\u27e8W, w, hw, hl\\u27e9 := <a>normalMonoOfMono<\\/a> (<a>equalizer.\\u03b9<\\/a> u v)\"",
83
+ "[{\"full_name\":\"CategoryTheory.NormalMonoCategory.normalMonoOfMono\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/NormalMono\\/Basic.lean\",\"def_pos\":[132,3],\"def_end_pos\":[132,19]},{\"full_name\":\"CategoryTheory.Limits.equalizer.\\u03b9\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Equalizers.lean\",\"def_pos\":[776,22],\"def_end_pos\":[776,33]}]"
84
+ ],
85
+ "state_after": "case mk\nC : Type u_1\ninst\u271d\u2074 : Category.{u_2, u_1} C\ninst\u271d\u00b3 : HasZeroMorphisms C\ninst\u271d\u00b2 : HasFiniteProducts C\ninst\u271d\u00b9 : HasKernels C\ninst\u271d : NormalMonoCategory C\nX Y : C\nf : X \u27f6 Y\nZ : C\nl : IsColimit (CokernelCofork.of\u03c0 0 \u22ef)\nZ\u271d : C\nu v : Y \u27f6 Z\u271d\nhuv : f \u226b u = f \u226b v\nW : C\nw : Y \u27f6 W\nhw : equalizer.\u03b9 u v \u226b w = 0\nhl : IsLimit (KernelFork.of\u03b9 (equalizer.\u03b9 u v) hw)\n\u22a2 u = v",
86
+ "state_before": "C : Type u_1\ninst\u271d\u2074 : Category.{u_2, u_1} C\ninst\u271d\u00b3 : HasZeroMorphisms C\ninst\u271d\u00b2 : HasFiniteProducts C\ninst\u271d\u00b9 : HasKernels C\ninst\u271d : NormalMonoCategory C\nX Y : C\nf : X \u27f6 Y\nZ : C\nl : IsColimit (CokernelCofork.of\u03c0 0 \u22ef)\nZ\u271d : C\nu v : Y \u27f6 Z\u271d\nhuv : f \u226b u = f \u226b v\n\u22a2 u = v",
87
+ "tactic": "obtain \u27e8W, w, hw, hl\u27e9 := normalMonoOfMono (equalizer.\u03b9 u v)"
88
+ },
89
+ {
90
+ "annotated_tactic": [
91
+ "\"obtain \\u27e8m, hm\\u27e9 := <a>equalizer.lift'<\\/a> f huv\"",
92
+ "[{\"full_name\":\"CategoryTheory.Limits.equalizer.lift'\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Equalizers.lean\",\"def_pos\":[823,19],\"def_end_pos\":[823,34]}]"
93
+ ],
94
+ "state_after": "case mk.mk\nC : Type u_1\ninst\u271d\u2074 : Category.{u_2, u_1} C\ninst\u271d\u00b3 : HasZeroMorphisms C\ninst\u271d\u00b2 : HasFiniteProducts C\ninst\u271d\u00b9 : HasKernels C\ninst\u271d : NormalMonoCategory C\nX Y : C\nf : X \u27f6 Y\nZ : C\nl : IsColimit (CokernelCofork.of\u03c0 0 \u22ef)\nZ\u271d : C\nu v : Y \u27f6 Z\u271d\nhuv : f \u226b u = f \u226b v\nW : C\nw : Y \u27f6 W\nhw : equalizer.\u03b9 u v \u226b w = 0\nhl : IsLimit (KernelFork.of\u03b9 (equalizer.\u03b9 u v) hw)\nm : X \u27f6 equalizer u v\nhm : m \u226b equalizer.\u03b9 u v = f\n\u22a2 u = v",
95
+ "state_before": "case mk\nC : Type u_1\ninst\u271d\u2074 : Category.{u_2, u_1} C\ninst\u271d\u00b3 : HasZeroMorphisms C\ninst\u271d\u00b2 : HasFiniteProducts C\ninst\u271d\u00b9 : HasKernels C\ninst\u271d : NormalMonoCategory C\nX Y : C\nf : X \u27f6 Y\nZ : C\nl : IsColimit (CokernelCofork.of\u03c0 0 \u22ef)\nZ\u271d : C\nu v : Y \u27f6 Z\u271d\nhuv : f \u226b u = f \u226b v\nW : C\nw : Y \u27f6 W\nhw : equalizer.\u03b9 u v \u226b w = 0\nhl : IsLimit (KernelFork.of\u03b9 (equalizer.\u03b9 u v) hw)\n\u22a2 u = v",
96
+ "tactic": "obtain \u27e8m, hm\u27e9 := equalizer.lift' f huv"
97
+ },
98
+ {
99
+ "annotated_tactic": [
100
+ "\"have hwf : f \\u226b w = 0 := by rw [\\u2190 hm, <a>Category.assoc<\\/a>, hw, <a>comp_zero<\\/a>]\"",
101
+ "[{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.Limits.comp_zero\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/ZeroMorphisms.lean\",\"def_pos\":[66,9],\"def_end_pos\":[66,18]}]"
102
+ ],
103
+ "state_after": "case mk.mk\nC : Type u_1\ninst\u271d\u2074 : Category.{u_2, u_1} C\ninst\u271d\u00b3 : HasZeroMorphisms C\ninst\u271d\u00b2 : HasFiniteProducts C\ninst\u271d\u00b9 : HasKernels C\ninst\u271d : NormalMonoCategory C\nX Y : C\nf : X \u27f6 Y\nZ : C\nl : IsColimit (CokernelCofork.of\u03c0 0 \u22ef)\nZ\u271d : C\nu v : Y \u27f6 Z\u271d\nhuv : f \u226b u = f \u226b v\nW : C\nw : Y \u27f6 W\nhw : equalizer.\u03b9 u v \u226b w = 0\nhl : IsLimit (KernelFork.of\u03b9 (equalizer.\u03b9 u v) hw)\nm : X \u27f6 equalizer u v\nhm : m \u226b equalizer.\u03b9 u v = f\nhwf : f \u226b w = 0\n\u22a2 u = v",
104
+ "state_before": "case mk.mk\nC : Type u_1\ninst\u271d\u2074 : Category.{u_2, u_1} C\ninst\u271d\u00b3 : HasZeroMorphisms C\ninst\u271d\u00b2 : HasFiniteProducts C\ninst\u271d\u00b9 : HasKernels C\ninst\u271d : NormalMonoCategory C\nX Y : C\nf : X \u27f6 Y\nZ : C\nl : IsColimit (CokernelCofork.of\u03c0 0 \u22ef)\nZ\u271d : C\nu v : Y \u27f6 Z\u271d\nhuv : f \u226b u = f \u226b v\nW : C\nw : Y \u27f6 W\nhw : equalizer.\u03b9 u v \u226b w = 0\nhl : IsLimit (KernelFork.of\u03b9 (equalizer.\u03b9 u v) hw)\nm : X \u27f6 equalizer u v\nhm : m \u226b equalizer.\u03b9 u v = f\n\u22a2 u = v",
105
+ "tactic": "have hwf : f \u226b w = 0 := by rw [\u2190 hm, Category.assoc, hw, comp_zero]"
106
+ },
107
+ {
108
+ "annotated_tactic": [
109
+ "\"obtain \\u27e8n, hn\\u27e9 := <a>CokernelCofork.IsColimit.desc'<\\/a> l _ hwf\"",
110
+ "[{\"full_name\":\"CategoryTheory.Limits.CokernelCofork.IsColimit.desc'\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Kernels.lean\",\"def_pos\":[609,5],\"def_end_pos\":[609,35]}]"
111
+ ],
112
+ "state_after": "case mk.mk.mk\nC : Type u_1\ninst\u271d\u2074 : Category.{u_2, u_1} C\ninst\u271d\u00b3 : HasZeroMorphisms C\ninst\u271d\u00b2 : HasFiniteProducts C\ninst\u271d\u00b9 : HasKernels C\ninst\u271d : NormalMonoCategory C\nX Y : C\nf : X \u27f6 Y\nZ : C\nl : IsColimit (CokernelCofork.of\u03c0 0 \u22ef)\nZ\u271d : C\nu v : Y \u27f6 Z\u271d\nhuv : f \u226b u = f \u226b v\nW : C\nw : Y \u27f6 W\nhw : equalizer.\u03b9 u v \u226b w = 0\nhl : IsLimit (KernelFork.of\u03b9 (equalizer.\u03b9 u v) hw)\nm : X \u27f6 equalizer u v\nhm : m \u226b equalizer.\u03b9 u v = f\nhwf : f \u226b w = 0\nn : (CokernelCofork.of\u03c0 0 \u22ef).pt \u27f6 W\nhn : Cofork.\u03c0 (CokernelCofork.of\u03c0 0 \u22ef) \u226b n = w\n\u22a2 u = v",
113
+ "state_before": "case mk.mk\nC : Type u_1\ninst\u271d\u2074 : Category.{u_2, u_1} C\ninst\u271d\u00b3 : HasZeroMorphisms C\ninst\u271d\u00b2 : HasFiniteProducts C\ninst\u271d\u00b9 : HasKernels C\ninst\u271d : NormalMonoCategory C\nX Y : C\nf : X \u27f6 Y\nZ : C\nl : IsColimit (CokernelCofork.of\u03c0 0 \u22ef)\nZ\u271d : C\nu v : Y \u27f6 Z\u271d\nhuv : f \u226b u = f \u226b v\nW : C\nw : Y \u27f6 W\nhw : equalizer.\u03b9 u v \u226b w = 0\nhl : IsLimit (KernelFork.of\u03b9 (equalizer.\u03b9 u v) hw)\nm : X \u27f6 equalizer u v\nhm : m \u226b equalizer.\u03b9 u v = f\nhwf : f \u226b w = 0\n\u22a2 u = v",
114
+ "tactic": "obtain \u27e8n, hn\u27e9 := CokernelCofork.IsColimit.desc' l _ hwf"
115
+ },
116
+ {
117
+ "annotated_tactic": [
118
+ "\"rw [<a>Cofork.\\u03c0_of\\u03c0<\\/a>, <a>zero_comp<\\/a>] at hn\"",
119
+ "[{\"full_name\":\"CategoryTheory.Limits.Cofork.\\u03c0_of\\u03c0\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Equalizers.lean\",\"def_pos\":[387,9],\"def_end_pos\":[387,21]},{\"full_name\":\"CategoryTheory.Limits.zero_comp\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/ZeroMorphisms.lean\",\"def_pos\":[72,9],\"def_end_pos\":[72,18]}]"
120
+ ],
121
+ "state_after": "case mk.mk.mk\nC : Type u_1\ninst\u271d\u2074 : Category.{u_2, u_1} C\ninst\u271d\u00b3 : HasZeroMorphisms C\ninst\u271d\u00b2 : HasFiniteProducts C\ninst\u271d\u00b9 : HasKernels C\ninst\u271d : NormalMonoCategory C\nX Y : C\nf : X \u27f6 Y\nZ : C\nl : IsColimit (CokernelCofork.of\u03c0 0 \u22ef)\nZ\u271d : C\nu v : Y \u27f6 Z\u271d\nhuv : f \u226b u = f \u226b v\nW : C\nw : Y \u27f6 W\nhw : equalizer.\u03b9 u v \u226b w = 0\nhl : IsLimit (KernelFork.of\u03b9 (equalizer.\u03b9 u v) hw)\nm : X \u27f6 equalizer u v\nhm : m \u226b equalizer.\u03b9 u v = f\nhwf : f \u226b w = 0\nn : (CokernelCofork.of\u03c0 0 \u22ef).pt \u27f6 W\nhn : 0 = w\n\u22a2 u = v",
122
+ "state_before": "case mk.mk.mk\nC : Type u_1\ninst\u271d\u2074 : Category.{u_2, u_1} C\ninst\u271d\u00b3 : HasZeroMorphisms C\ninst\u271d\u00b2 : HasFiniteProducts C\ninst\u271d\u00b9 : HasKernels C\ninst\u271d : NormalMonoCategory C\nX Y : C\nf : X \u27f6 Y\nZ : C\nl : IsColimit (CokernelCofork.of\u03c0 0 \u22ef)\nZ\u271d : C\nu v : Y \u27f6 Z\u271d\nhuv : f \u226b u = f \u226b v\nW : C\nw : Y \u27f6 W\nhw : equalizer.\u03b9 u v \u226b w = 0\nhl : IsLimit (KernelFork.of\u03b9 (equalizer.\u03b9 u v) hw)\nm : X \u27f6 equalizer u v\nhm : m \u226b equalizer.\u03b9 u v = f\nhwf : f \u226b w = 0\nn : (CokernelCofork.of\u03c0 0 \u22ef).pt \u27f6 W\nhn : Cofork.\u03c0 (CokernelCofork.of\u03c0 0 \u22ef) \u226b n = w\n\u22a2 u = v",
123
+ "tactic": "rw [Cofork.\u03c0_of\u03c0, zero_comp] at hn"
124
+ },
125
+ {
126
+ "annotated_tactic": [
127
+ "\"have : <a>IsIso<\\/a> (<a>equalizer.\\u03b9<\\/a> u v) := by apply <a>isIso_limit_cone_parallelPair_of_eq<\\/a> hn.symm hl\"",
128
+ "[{\"full_name\":\"CategoryTheory.IsIso\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[272,7],\"def_end_pos\":[272,12]},{\"full_name\":\"CategoryTheory.Limits.equalizer.\\u03b9\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Equalizers.lean\",\"def_pos\":[776,22],\"def_end_pos\":[776,33]},{\"full_name\":\"CategoryTheory.Limits.isIso_limit_cone_parallelPair_of_eq\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Equalizers.lean\",\"def_pos\":[875,9],\"def_end_pos\":[875,44]}]"
129
+ ],
130
+ "state_after": "case mk.mk.mk\nC : Type u_1\ninst\u271d\u2074 : Category.{u_2, u_1} C\ninst\u271d\u00b3 : HasZeroMorphisms C\ninst\u271d\u00b2 : HasFiniteProducts C\ninst\u271d\u00b9 : HasKernels C\ninst\u271d : NormalMonoCategory C\nX Y : C\nf : X \u27f6 Y\nZ : C\nl : IsColimit (CokernelCofork.of\u03c0 0 \u22ef)\nZ\u271d : C\nu v : Y \u27f6 Z\u271d\nhuv : f \u226b u = f \u226b v\nW : C\nw : Y \u27f6 W\nhw : equalizer.\u03b9 u v \u226b w = 0\nhl : IsLimit (KernelFork.of\u03b9 (equalizer.\u03b9 u v) hw)\nm : X \u27f6 equalizer u v\nhm : m \u226b equalizer.\u03b9 u v = f\nhwf : f \u226b w = 0\nn : (CokernelCofork.of\u03c0 0 \u22ef).pt \u27f6 W\nhn : 0 = w\nthis : IsIso (equalizer.\u03b9 u v)\n\u22a2 u = v",
131
+ "state_before": "case mk.mk.mk\nC : Type u_1\ninst\u271d\u2074 : Category.{u_2, u_1} C\ninst\u271d\u00b3 : HasZeroMorphisms C\ninst\u271d\u00b2 : HasFiniteProducts C\ninst\u271d\u00b9 : HasKernels C\ninst\u271d : NormalMonoCategory C\nX Y : C\nf : X \u27f6 Y\nZ : C\nl : IsColimit (CokernelCofork.of\u03c0 0 \u22ef)\nZ\u271d : C\nu v : Y \u27f6 Z\u271d\nhuv : f \u226b u = f \u226b v\nW : C\nw : Y \u27f6 W\nhw : equalizer.\u03b9 u v \u226b w = 0\nhl : IsLimit (KernelFork.of\u03b9 (equalizer.\u03b9 u v) hw)\nm : X \u27f6 equalizer u v\nhm : m \u226b equalizer.\u03b9 u v = f\nhwf : f \u226b w = 0\nn : (CokernelCofork.of\u03c0 0 \u22ef).pt \u27f6 W\nhn : 0 = w\n\u22a2 u = v",
132
+ "tactic": "have : IsIso (equalizer.\u03b9 u v) := by apply isIso_limit_cone_parallelPair_of_eq hn.symm hl"
133
+ },
134
+ {
135
+ "annotated_tactic": [
136
+ "\"apply (<a>cancel_epi<\\/a> (<a>equalizer.\\u03b9<\\/a> u v)).1\"",
137
+ "[{\"full_name\":\"CategoryTheory.cancel_epi\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[306,9],\"def_end_pos\":[306,19]},{\"full_name\":\"CategoryTheory.Limits.equalizer.\\u03b9\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Equalizers.lean\",\"def_pos\":[776,22],\"def_end_pos\":[776,33]}]"
138
+ ],
139
+ "state_after": "case mk.mk.mk\nC : Type u_1\ninst\u271d\u2074 : Category.{u_2, u_1} C\ninst\u271d\u00b3 : HasZeroMorphisms C\ninst\u271d\u00b2 : HasFiniteProducts C\ninst\u271d\u00b9 : HasKernels C\ninst\u271d : NormalMonoCategory C\nX Y : C\nf : X \u27f6 Y\nZ : C\nl : IsColimit (CokernelCofork.of\u03c0 0 \u22ef)\nZ\u271d : C\nu v : Y \u27f6 Z\u271d\nhuv : f \u226b u = f \u226b v\nW : C\nw : Y \u27f6 W\nhw : equalizer.\u03b9 u v \u226b w = 0\nhl : IsLimit (KernelFork.of\u03b9 (equalizer.\u03b9 u v) hw)\nm : X \u27f6 equalizer u v\nhm : m \u226b equalizer.\u03b9 u v = f\nhwf : f \u226b w = 0\nn : (CokernelCofork.of\u03c0 0 \u22ef).pt \u27f6 W\nhn : 0 = w\nthis : IsIso (equalizer.\u03b9 u v)\n\u22a2 equalizer.\u03b9 u v \u226b u = equalizer.\u03b9 u v \u226b v",
140
+ "state_before": "case mk.mk.mk\nC : Type u_1\ninst\u271d\u2074 : Category.{u_2, u_1} C\ninst\u271d\u00b3 : HasZeroMorphisms C\ninst\u271d\u00b2 : HasFiniteProducts C\ninst\u271d\u00b9 : HasKernels C\ninst\u271d : NormalMonoCategory C\nX Y : C\nf : X \u27f6 Y\nZ : C\nl : IsColimit (CokernelCofork.of\u03c0 0 \u22ef)\nZ\u271d : C\nu v : Y \u27f6 Z\u271d\nhuv : f \u226b u = f \u226b v\nW : C\nw : Y \u27f6 W\nhw : equalizer.\u03b9 u v \u226b w = 0\nhl : IsLimit (KernelFork.of\u03b9 (equalizer.\u03b9 u v) hw)\nm : X \u27f6 equalizer u v\nhm : m \u226b equalizer.\u03b9 u v = f\nhwf : f \u226b w = 0\nn : (CokernelCofork.of\u03c0 0 \u22ef).pt \u27f6 W\nhn : 0 = w\nthis : IsIso (equalizer.\u03b9 u v)\n\u22a2 u = v",
141
+ "tactic": "apply (cancel_epi (equalizer.\u03b9 u v)).1"
142
+ },
143
+ {
144
+ "annotated_tactic": [
145
+ "\"exact <a>equalizer.condition<\\/a> _ _\"",
146
+ "[{\"full_name\":\"CategoryTheory.Limits.equalizer.condition\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Equalizers.lean\",\"def_pos\":[796,9],\"def_end_pos\":[796,28]}]"
147
+ ],
148
+ "state_after": "no goals",
149
+ "state_before": "case mk.mk.mk\nC : Type u_1\ninst\u271d\u2074 : Category.{u_2, u_1} C\ninst\u271d\u00b3 : HasZeroMorphisms C\ninst\u271d\u00b2 : HasFiniteProducts C\ninst\u271d\u00b9 : HasKernels C\ninst\u271d : NormalMonoCategory C\nX Y : C\nf : X \u27f6 Y\nZ : C\nl : IsColimit (CokernelCofork.of\u03c0 0 \u22ef)\nZ\u271d : C\nu v : Y \u27f6 Z\u271d\nhuv : f \u226b u = f \u226b v\nW : C\nw : Y \u27f6 W\nhw : equalizer.\u03b9 u v \u226b w = 0\nhl : IsLimit (KernelFork.of\u03b9 (equalizer.\u03b9 u v) hw)\nm : X \u27f6 equalizer u v\nhm : m \u226b equalizer.\u03b9 u v = f\nhwf : f \u226b w = 0\nn : (CokernelCofork.of\u03c0 0 \u22ef).pt \u27f6 W\nhn : 0 = w\nthis : IsIso (equalizer.\u03b9 u v)\n\u22a2 equalizer.\u03b9 u v \u226b u = equalizer.\u03b9 u v \u226b v",
150
+ "tactic": "exact equalizer.condition _ _"
151
+ },
152
+ {
153
+ "annotated_tactic": [
154
+ "\"rw [\\u2190 hm, <a>Category.assoc<\\/a>, hw, <a>comp_zero<\\/a>]\"",
155
+ "[{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.Limits.comp_zero\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/ZeroMorphisms.lean\",\"def_pos\":[66,9],\"def_end_pos\":[66,18]}]"
156
+ ],
157
+ "state_after": "no goals",
158
+ "state_before": "C : Type u_1\ninst\u271d\u2074 : Category.{u_2, u_1} C\ninst\u271d\u00b3 : HasZeroMorphisms C\ninst\u271d\u00b2 : HasFiniteProducts C\ninst\u271d\u00b9 : HasKernels C\ninst\u271d : NormalMonoCategory C\nX Y : C\nf : X \u27f6 Y\nZ : C\nl : IsColimit (CokernelCofork.of\u03c0 0 \u22ef)\nZ\u271d : C\nu v : Y \u27f6 Z\u271d\nhuv : f \u226b u = f \u226b v\nW : C\nw : Y \u27f6 W\nhw : equalizer.\u03b9 u v \u226b w = 0\nhl : IsLimit (KernelFork.of\u03b9 (equalizer.\u03b9 u v) hw)\nm : X \u27f6 equalizer u v\nhm : m \u226b equalizer.\u03b9 u v = f\n\u22a2 f \u226b w = 0",
159
+ "tactic": "rw [\u2190 hm, Category.assoc, hw, comp_zero]"
160
+ },
161
+ {
162
+ "annotated_tactic": [
163
+ "\"apply <a>isIso_limit_cone_parallelPair_of_eq<\\/a> hn.symm hl\"",
164
+ "[{\"full_name\":\"CategoryTheory.Limits.isIso_limit_cone_parallelPair_of_eq\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Equalizers.lean\",\"def_pos\":[875,9],\"def_end_pos\":[875,44]}]"
165
+ ],
166
+ "state_after": "no goals",
167
+ "state_before": "C : Type u_1\ninst\u271d\u2074 : Category.{u_2, u_1} C\ninst\u271d\u00b3 : HasZeroMorphisms C\ninst\u271d\u00b2 : HasFiniteProducts C\ninst\u271d\u00b9 : HasKernels C\ninst\u271d : NormalMonoCategory C\nX Y : C\nf : X \u27f6 Y\nZ : C\nl : IsColimit (CokernelCofork.of\u03c0 0 \u22ef)\nZ\u271d : C\nu v : Y \u27f6 Z\u271d\nhuv : f \u226b u = f \u226b v\nW : C\nw : Y \u27f6 W\nhw : equalizer.\u03b9 u v \u226b w = 0\nhl : IsLimit (KernelFork.of\u03b9 (equalizer.\u03b9 u v) hw)\nm : X \u27f6 equalizer u v\nhm : m \u226b equalizer.\u03b9 u v = f\nhwf : f \u226b w = 0\nn : (CokernelCofork.of\u03c0 0 \u22ef).pt \u27f6 W\nhn : 0 = w\n\u22a2 IsIso (equalizer.\u03b9 u v)",
168
+ "tactic": "apply isIso_limit_cone_parallelPair_of_eq hn.symm hl"
169
+ }
170
+ ],
171
+ "url": "https://github.com/leanprover-community/mathlib4"
172
+ },
173
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/NormalMono/Equalizers.lean"
174
+ },
175
+ {
176
+ "error": "theorem has no selected tactic transitions",
177
+ "full_name": "CategoryTheory.Limits.Cofan.IsColimit.fac",
178
+ "id": "CategoryTheory.Limits.Cofan.IsColimit.fac",
179
+ "reason": "import_failure",
180
+ "selection": {
181
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
182
+ "end": [
183
+ 166,
184
+ 28
185
+ ],
186
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
187
+ "full_name": "CategoryTheory.Limits.Cofan.IsColimit.fac",
188
+ "start": [
189
+ 162,
190
+ 1
191
+ ],
192
+ "traced_tactics": [],
193
+ "url": "https://github.com/leanprover-community/mathlib4"
194
+ },
195
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
196
+ },
197
+ {
198
+ "error": "theorem has no selected tactic transitions",
199
+ "full_name": "CategoryTheory.Limits.Cofan.IsColimit.hom_ext",
200
+ "id": "CategoryTheory.Limits.Cofan.IsColimit.hom_ext",
201
+ "reason": "import_failure",
202
+ "selection": {
203
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
204
+ "end": [
205
+ 170,
206
+ 30
207
+ ],
208
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
209
+ "full_name": "CategoryTheory.Limits.Cofan.IsColimit.hom_ext",
210
+ "start": [
211
+ 168,
212
+ 1
213
+ ],
214
+ "traced_tactics": [],
215
+ "url": "https://github.com/leanprover-community/mathlib4"
216
+ },
217
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
218
+ },
219
+ {
220
+ "error": "no internal trace for tactic 'simp'",
221
+ "full_name": "CategoryTheory.Limits.Cofan.isColimit_iff_isIso_sigmaDesc",
222
+ "id": "CategoryTheory.Limits.Cofan.isColimit_iff_isIso_sigmaDesc",
223
+ "reason": "import_failure",
224
+ "selection": {
225
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
226
+ "end": [
227
+ 306,
228
+ 6
229
+ ],
230
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
231
+ "full_name": "CategoryTheory.Limits.Cofan.isColimit_iff_isIso_sigmaDesc",
232
+ "start": [
233
+ 294,
234
+ 1
235
+ ],
236
+ "traced_tactics": [
237
+ {
238
+ "annotated_tactic": [
239
+ "\"refine \\u27e8fun h \\u21a6 \\u27e8<a>isColimitOfIsIsoSigmaDesc<\\/a> c\\u27e9, fun \\u27e8hc\\u27e9 \\u21a6 ?_\\u27e9\"",
240
+ "[{\"full_name\":\"CategoryTheory.Limits.Cofan.isColimitOfIsIsoSigmaDesc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Products.lean\",\"def_pos\":[289,5],\"def_end_pos\":[289,36]}]"
241
+ ],
242
+ "state_after": "\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3 : Type w\u2083\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nf : \u03b2 \u2192 C\ninst\u271d : HasCoproduct f\nc : Cofan f\nx\u271d : Nonempty (IsColimit c)\nhc : IsColimit c\n\u22a2 IsIso (Sigma.desc c.inj)",
243
+ "state_before": "\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3 : Type w\u2083\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nf : \u03b2 \u2192 C\ninst\u271d : HasCoproduct f\nc : Cofan f\n\u22a2 IsIso (Sigma.desc c.inj) \u2194 Nonempty (IsColimit c)",
244
+ "tactic": "refine \u27e8fun h \u21a6 \u27e8isColimitOfIsIsoSigmaDesc c\u27e9, fun \u27e8hc\u27e9 \u21a6 ?_\u27e9"
245
+ },
246
+ {
247
+ "annotated_tactic": [
248
+ "\"have : <a>IsIso<\\/a> (((<a>coproductIsCoproduct<\\/a> f).<a>coconePointUniqueUpToIso<\\/a> hc).<a>hom<\\/a> \\u226b hc.desc c) := by\\n simp; infer_instance\"",
249
+ "[{\"full_name\":\"CategoryTheory.IsIso\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[272,7],\"def_end_pos\":[272,12]},{\"full_name\":\"CategoryTheory.Limits.coproductIsCoproduct\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Products.lean\",\"def_pos\":[237,5],\"def_end_pos\":[237,25]},{\"full_name\":\"CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/IsLimit.lean\",\"def_pos\":[660,5],\"def_end_pos\":[660,29]},{\"full_name\":\"CategoryTheory.Iso.hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[53,3],\"def_end_pos\":[53,6]}]"
250
+ ],
251
+ "state_after": "\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3 : Type w\u2083\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nf : \u03b2 \u2192 C\ninst\u271d : HasCoproduct f\nc : Cofan f\nx\u271d : Nonempty (IsColimit c)\nhc : IsColimit c\nthis : IsIso (((coproductIsCoproduct f).coconePointUniqueUpToIso hc).hom \u226b hc.desc c)\n\u22a2 IsIso (Sigma.desc c.inj)",
252
+ "state_before": "\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3 : Type w\u2083\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nf : \u03b2 \u2192 C\ninst\u271d : HasCoproduct f\nc : Cofan f\nx\u271d : Nonempty (IsColimit c)\nhc : IsColimit c\n\u22a2 IsIso (Sigma.desc c.inj)",
253
+ "tactic": "have : IsIso (((coproductIsCoproduct f).coconePointUniqueUpToIso hc).hom \u226b hc.desc c) := by\n simp; infer_instance"
254
+ },
255
+ {
256
+ "annotated_tactic": [
257
+ "\"convert this\"",
258
+ "[]"
259
+ ],
260
+ "state_after": "case h.e'_5.h\n\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3 : Type w\u2083\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nf : \u03b2 \u2192 C\ninst\u271d : HasCoproduct f\nc : Cofan f\nx\u271d : Nonempty (IsColimit c)\nhc : IsColimit c\nthis : IsIso (((coproductIsCoproduct f).coconePointUniqueUpToIso hc).hom \u226b hc.desc c)\ne_3\u271d : \u2210 f = (mk (\u2210 f) (Sigma.\u03b9 f)).pt\n\u22a2 Sigma.desc c.inj = ((coproductIsCoproduct f).coconePointUniqueUpToIso hc).hom \u226b hc.desc c",
261
+ "state_before": "\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3 : Type w\u2083\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nf : \u03b2 \u2192 C\ninst\u271d : HasCoproduct f\nc : Cofan f\nx\u271d : Nonempty (IsColimit c)\nhc : IsColimit c\nthis : IsIso (((coproductIsCoproduct f).coconePointUniqueUpToIso hc).hom \u226b hc.desc c)\n\u22a2 IsIso (Sigma.desc c.inj)",
262
+ "tactic": "convert this"
263
+ },
264
+ {
265
+ "annotated_tactic": [
266
+ "\"ext\"",
267
+ "[]"
268
+ ],
269
+ "state_after": "case h.e'_5.h.h\n\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3 : Type w\u2083\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nf : \u03b2 \u2192 C\ninst\u271d : HasCoproduct f\nc : Cofan f\nx\u271d : Nonempty (IsColimit c)\nhc : IsColimit c\nthis : IsIso (((coproductIsCoproduct f).coconePointUniqueUpToIso hc).hom \u226b hc.desc c)\ne_3\u271d : \u2210 f = (mk (\u2210 f) (Sigma.\u03b9 f)).pt\nb\u271d : \u03b2\n\u22a2 Sigma.\u03b9 f b\u271d \u226b Sigma.desc c.inj =\n Sigma.\u03b9 f b\u271d \u226b ((coproductIsCoproduct f).coconePointUniqueUpToIso hc).hom \u226b hc.desc c",
270
+ "state_before": "case h.e'_5.h\n\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3 : Type w\u2083\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nf : \u03b2 \u2192 C\ninst\u271d : HasCoproduct f\nc : Cofan f\nx\u271d : Nonempty (IsColimit c)\nhc : IsColimit c\nthis : IsIso (((coproductIsCoproduct f).coconePointUniqueUpToIso hc).hom \u226b hc.desc c)\ne_3\u271d : \u2210 f = (mk (\u2210 f) (Sigma.\u03b9 f)).pt\n\u22a2 Sigma.desc c.inj = ((coproductIsCoproduct f).coconePointUniqueUpToIso hc).hom \u226b hc.desc c",
271
+ "tactic": "ext"
272
+ },
273
+ {
274
+ "annotated_tactic": [
275
+ "\"simp only [<a>colimit.\\u03b9_desc<\\/a>, <a>mk_pt<\\/a>, <a>mk_\\u03b9_app<\\/a>, <a>IsColimit.coconePointUniqueUpToIso<\\/a>,\\n <a>coproductIsCoproduct<\\/a>, <a>colimit.cocone_x<\\/a>, <a>Functor.mapIso_hom<\\/a>, <a>IsColimit.uniqueUpToIso_hom<\\/a>,\\n <a>Cocones.forget_map<\\/a>, <a>IsColimit.descCoconeMorphism_hom<\\/a>, <a>IsColimit.ofIsoColimit_desc<\\/a>,\\n <a>Cocones.ext_inv_hom<\\/a>, <a>Iso.refl_inv<\\/a>, <a>colimit.isColimit_desc<\\/a>, <a>Category.id_comp<\\/a>,\\n <a>IsColimit.desc_self<\\/a>, <a>Category.comp_id<\\/a>]\"",
276
+ "[{\"full_name\":\"CategoryTheory.Limits.colimit.\\u03b9_desc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/HasLimits.lean\",\"def_pos\":[789,9],\"def_end_pos\":[789,23]},{\"full_name\":\"CategoryTheory.Limits.Cofan.mk_pt\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Products.lean\",\"def_pos\":[68,10],\"def_end_pos\":[68,12]},{\"full_name\":\"CategoryTheory.Limits.Cofan.mk_\\u03b9_app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Products.lean\",\"def_pos\":[68,13],\"def_end_pos\":[68,18]},{\"full_name\":\"CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/IsLimit.lean\",\"def_pos\":[660,5],\"def_end_pos\":[660,29]},{\"full_name\":\"CategoryTheory.Limits.coproductIsCoproduct\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Products.lean\",\"def_pos\":[237,5],\"def_end_pos\":[237,25]},{\"full_name\":\"CategoryTheory.Limits.colimit.cocone_x\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/HasLimits.lean\",\"def_pos\":[752,9],\"def_end_pos\":[752,25]},{\"full_name\":\"CategoryTheory.Functor.mapIso_hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[622,3],\"def_end_pos\":[622,8]},{\"full_name\":\"CategoryTheory.Limits.IsColimit.uniqueUpToIso_hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/IsLimit.lean\",\"def_pos\":[646,3],\"def_end_pos\":[646,8]},{\"full_name\":\"CategoryTheory.Limits.Cocones.forget_map\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Cones.lean\",\"def_pos\":[655,3],\"def_end_pos\":[655,8]},{\"full_name\":\"CategoryTheory.Limits.IsColimit.descCoconeMorphism_hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/IsLimit.lean\",\"def_pos\":[609,3],\"def_end_pos\":[609,8]},{\"full_name\":\"CategoryTheory.Limits.IsColimit.ofIsoColimit_desc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/IsLimit.lean\",\"def_pos\":[695,9],\"def_end_pos\":[695,26]},{\"full_name\":\"CategoryTheory.Limits.Cocones.ext_inv_hom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Cones.lean\",\"def_pos\":[536,53],\"def_end_pos\":[536,58]},{\"full_name\":\"CategoryTheory.Iso.refl_inv\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[130,9],\"def_end_pos\":[130,14]},{\"full_name\":\"CategoryTheory.Limits.colimit.isColimit_desc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/HasLimits.lean\",\"def_pos\":[774,9],\"def_end_pos\":[774,31]},{\"full_name\":\"CategoryTheory.Category.id_comp\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[177,3],\"def_end_pos\":[177,10]},{\"full_name\":\"CategoryTheory.Limits.IsColimit.desc_self\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/IsLimit.lean\",\"def_pos\":[603,9],\"def_end_pos\":[603,18]},{\"full_name\":\"CategoryTheory.Category.comp_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[179,3],\"def_end_pos\":[179,10]}]"
277
+ ],
278
+ "state_after": "case h.e'_5.h.h\n\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3 : Type w\u2083\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nf : \u03b2 \u2192 C\ninst\u271d : HasCoproduct f\nc : Cofan f\nx\u271d : Nonempty (IsColimit c)\nhc : IsColimit c\nthis : IsIso (((coproductIsCoproduct f).coconePointUniqueUpToIso hc).hom \u226b hc.desc c)\ne_3\u271d : \u2210 f = (mk (\u2210 f) (Sigma.\u03b9 f)).pt\nb\u271d : \u03b2\n\u22a2 c.inj b\u271d = c.\u03b9.app { as := b\u271d }",
279
+ "state_before": "case h.e'_5.h.h\n\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3 : Type w\u2083\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nf : \u03b2 \u2192 C\ninst\u271d : HasCoproduct f\nc : Cofan f\nx\u271d : Nonempty (IsColimit c)\nhc : IsColimit c\nthis : IsIso (((coproductIsCoproduct f).coconePointUniqueUpToIso hc).hom \u226b hc.desc c)\ne_3\u271d : \u2210 f = (mk (\u2210 f) (Sigma.\u03b9 f)).pt\nb\u271d : \u03b2\n\u22a2 Sigma.\u03b9 f b\u271d \u226b Sigma.desc c.inj =\n Sigma.\u03b9 f b\u271d \u226b ((coproductIsCoproduct f).coconePointUniqueUpToIso hc).hom \u226b hc.desc c",
280
+ "tactic": "simp only [colimit.\u03b9_desc, mk_pt, mk_\u03b9_app, IsColimit.coconePointUniqueUpToIso,\n coproductIsCoproduct, colimit.cocone_x, Functor.mapIso_hom, IsColimit.uniqueUpToIso_hom,\n Cocones.forget_map, IsColimit.descCoconeMorphism_hom, IsColimit.ofIsoColimit_desc,\n Cocones.ext_inv_hom, Iso.refl_inv, colimit.isColimit_desc, Category.id_comp,\n IsColimit.desc_self, Category.comp_id]"
281
+ },
282
+ {
283
+ "annotated_tactic": [
284
+ "\"rfl\"",
285
+ "[]"
286
+ ],
287
+ "state_after": "no goals",
288
+ "state_before": "case h.e'_5.h.h\n\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3 : Type w\u2083\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nf : \u03b2 \u2192 C\ninst\u271d : HasCoproduct f\nc : Cofan f\nx\u271d : Nonempty (IsColimit c)\nhc : IsColimit c\nthis : IsIso (((coproductIsCoproduct f).coconePointUniqueUpToIso hc).hom \u226b hc.desc c)\ne_3\u271d : \u2210 f = (mk (\u2210 f) (Sigma.\u03b9 f)).pt\nb\u271d : \u03b2\n\u22a2 c.inj b\u271d = c.\u03b9.app { as := b\u271d }",
289
+ "tactic": "rfl"
290
+ },
291
+ {
292
+ "annotated_tactic": [
293
+ "\"simp\"",
294
+ "[]"
295
+ ],
296
+ "state_after": "\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3 : Type w\u2083\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nf : \u03b2 \u2192 C\ninst\u271d : HasCoproduct f\nc : Cofan f\nx\u271d : Nonempty (IsColimit c)\nhc : IsColimit c\n\u22a2 IsIso ((coproductIsCoproduct f).coconePointUniqueUpToIso hc).hom",
297
+ "state_before": "\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3 : Type w\u2083\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nf : \u03b2 \u2192 C\ninst\u271d : HasCoproduct f\nc : Cofan f\nx\u271d : Nonempty (IsColimit c)\nhc : IsColimit c\n\u22a2 IsIso (((coproductIsCoproduct f).coconePointUniqueUpToIso hc).hom \u226b hc.desc c)",
298
+ "tactic": "simp"
299
+ },
300
+ {
301
+ "annotated_tactic": [
302
+ "\"infer_instance\"",
303
+ "[]"
304
+ ],
305
+ "state_after": "no goals",
306
+ "state_before": "\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3 : Type w\u2083\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nf : \u03b2 \u2192 C\ninst\u271d : HasCoproduct f\nc : Cofan f\nx\u271d : Nonempty (IsColimit c)\nhc : IsColimit c\n\u22a2 IsIso ((coproductIsCoproduct f).coconePointUniqueUpToIso hc).hom",
307
+ "tactic": "infer_instance"
308
+ }
309
+ ],
310
+ "url": "https://github.com/leanprover-community/mathlib4"
311
+ },
312
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
313
+ },
314
+ {
315
+ "error": "theorem has no selected tactic transitions",
316
+ "full_name": "CategoryTheory.Limits.Fan.IsLimit.fac",
317
+ "id": "CategoryTheory.Limits.Fan.IsLimit.fac",
318
+ "reason": "import_failure",
319
+ "selection": {
320
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
321
+ "end": [
322
+ 141,
323
+ 26
324
+ ],
325
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
326
+ "full_name": "CategoryTheory.Limits.Fan.IsLimit.fac",
327
+ "start": [
328
+ 137,
329
+ 1
330
+ ],
331
+ "traced_tactics": [],
332
+ "url": "https://github.com/leanprover-community/mathlib4"
333
+ },
334
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
335
+ },
336
+ {
337
+ "error": "theorem has no selected tactic transitions",
338
+ "full_name": "CategoryTheory.Limits.Fan.IsLimit.hom_ext",
339
+ "id": "CategoryTheory.Limits.Fan.IsLimit.hom_ext",
340
+ "reason": "import_failure",
341
+ "selection": {
342
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
343
+ "end": [
344
+ 145,
345
+ 30
346
+ ],
347
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
348
+ "full_name": "CategoryTheory.Limits.Fan.IsLimit.hom_ext",
349
+ "start": [
350
+ 143,
351
+ 1
352
+ ],
353
+ "traced_tactics": [],
354
+ "url": "https://github.com/leanprover-community/mathlib4"
355
+ },
356
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
357
+ },
358
+ {
359
+ "error": "theorem has no selected tactic transitions",
360
+ "full_name": "CategoryTheory.Limits.Pi.isoLimit_hom_\u03c0",
361
+ "id": "CategoryTheory.Limits.Pi.isoLimit_hom_\u03c0",
362
+ "reason": "import_failure",
363
+ "selection": {
364
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
365
+ "end": [
366
+ 434,
367
+ 48
368
+ ],
369
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
370
+ "full_name": "CategoryTheory.Limits.Pi.isoLimit_hom_\u03c0",
371
+ "start": [
372
+ 431,
373
+ 1
374
+ ],
375
+ "traced_tactics": [],
376
+ "url": "https://github.com/leanprover-community/mathlib4"
377
+ },
378
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
379
+ },
380
+ {
381
+ "error": "theorem has no selected tactic transitions",
382
+ "full_name": "CategoryTheory.Limits.Pi.isoLimit_inv_\u03c0",
383
+ "id": "CategoryTheory.Limits.Pi.isoLimit_inv_\u03c0",
384
+ "reason": "import_failure",
385
+ "selection": {
386
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
387
+ "end": [
388
+ 429,
389
+ 48
390
+ ],
391
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
392
+ "full_name": "CategoryTheory.Limits.Pi.isoLimit_inv_\u03c0",
393
+ "start": [
394
+ 426,
395
+ 1
396
+ ],
397
+ "traced_tactics": [],
398
+ "url": "https://github.com/leanprover-community/mathlib4"
399
+ },
400
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
401
+ },
402
+ {
403
+ "error": "theorem has no selected tactic transitions",
404
+ "full_name": "CategoryTheory.Limits.Pi.map'_comp_\u03c0",
405
+ "id": "CategoryTheory.Limits.Pi.map'_comp_\u03c0",
406
+ "reason": "import_failure",
407
+ "selection": {
408
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
409
+ "end": [
410
+ 356,
411
+ 19
412
+ ],
413
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
414
+ "full_name": "CategoryTheory.Limits.Pi.map'_comp_\u03c0",
415
+ "start": [
416
+ 353,
417
+ 1
418
+ ],
419
+ "traced_tactics": [],
420
+ "url": "https://github.com/leanprover-community/mathlib4"
421
+ },
422
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
423
+ },
424
+ {
425
+ "error": "theorem has no selected tactic transitions",
426
+ "full_name": "CategoryTheory.Limits.Pi.map'_id",
427
+ "id": "CategoryTheory.Limits.Pi.map'_id",
428
+ "reason": "import_failure",
429
+ "selection": {
430
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
431
+ "end": [
432
+ 364,
433
+ 6
434
+ ],
435
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
436
+ "full_name": "CategoryTheory.Limits.Pi.map'_id",
437
+ "start": [
438
+ 361,
439
+ 1
440
+ ],
441
+ "traced_tactics": [],
442
+ "url": "https://github.com/leanprover-community/mathlib4"
443
+ },
444
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
445
+ },
446
+ {
447
+ "error": "theorem has no selected tactic transitions",
448
+ "full_name": "CategoryTheory.Limits.Sigma.hom_ext",
449
+ "id": "CategoryTheory.Limits.Sigma.hom_ext",
450
+ "reason": "import_failure",
451
+ "selection": {
452
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
453
+ "end": [
454
+ 229,
455
+ 35
456
+ ],
457
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
458
+ "full_name": "CategoryTheory.Limits.Sigma.hom_ext",
459
+ "start": [
460
+ 226,
461
+ 1
462
+ ],
463
+ "traced_tactics": [],
464
+ "url": "https://github.com/leanprover-community/mathlib4"
465
+ },
466
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
467
+ },
468
+ {
469
+ "error": "theorem has no selected tactic transitions",
470
+ "full_name": "CategoryTheory.Limits.Sigma.map'_id",
471
+ "id": "CategoryTheory.Limits.Sigma.map'_id",
472
+ "reason": "import_failure",
473
+ "selection": {
474
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
475
+ "end": [
476
+ 480,
477
+ 6
478
+ ],
479
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
480
+ "full_name": "CategoryTheory.Limits.Sigma.map'_id",
481
+ "start": [
482
+ 477,
483
+ 1
484
+ ],
485
+ "traced_tactics": [],
486
+ "url": "https://github.com/leanprover-community/mathlib4"
487
+ },
488
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
489
+ },
490
+ {
491
+ "error": "theorem has no selected tactic transitions",
492
+ "full_name": "CategoryTheory.Limits.Sigma.\u03b9_comp_map'",
493
+ "id": "CategoryTheory.Limits.Sigma.\u03b9_comp_map'",
494
+ "reason": "import_failure",
495
+ "selection": {
496
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
497
+ "end": [
498
+ 471,
499
+ 21
500
+ ],
501
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
502
+ "full_name": "CategoryTheory.Limits.Sigma.\u03b9_comp_map'",
503
+ "start": [
504
+ 467,
505
+ 1
506
+ ],
507
+ "traced_tactics": [],
508
+ "url": "https://github.com/leanprover-community/mathlib4"
509
+ },
510
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
511
+ },
512
+ {
513
+ "error": "no internal trace for tactic 'simp'",
514
+ "full_name": "CategoryTheory.Limits.Sigma.\u03b9_reindex_hom",
515
+ "id": "CategoryTheory.Limits.Sigma.\u03b9_reindex_hom",
516
+ "reason": "import_failure",
517
+ "selection": {
518
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
519
+ "end": [
520
+ 769,
521
+ 21
522
+ ],
523
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
524
+ "full_name": "CategoryTheory.Limits.Sigma.\u03b9_reindex_hom",
525
+ "start": [
526
+ 760,
527
+ 1
528
+ ],
529
+ "traced_tactics": [
530
+ {
531
+ "annotated_tactic": [
532
+ "\"dsimp [<a>Sigma.reindex<\\/a>]\"",
533
+ "[{\"full_name\":\"CategoryTheory.Limits.Sigma.reindex\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Products.lean\",\"def_pos\":[755,5],\"def_end_pos\":[755,18]}]"
534
+ ],
535
+ "state_after": "\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3\u271d : Type w\u2083\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\n\u03b3 : Type w'\n\u03b5 : \u03b2 \u2243 \u03b3\nf : \u03b3 \u2192 C\ninst\u271d\u00b9 : HasCoproduct f\ninst\u271d : HasCoproduct (f \u2218 \u21d1\u03b5)\nb : \u03b2\n\u22a2 \u03b9 (f \u2218 \u21d1\u03b5) b \u226b\n (HasColimit.isoOfEquivalence (Discrete.equivalence \u03b5)\n (Discrete.natIso fun x =>\n Iso.refl ((Discrete.functor f).obj ((Discrete.functor (Discrete.mk \u2218 \u21d1\u03b5)).obj x)))).hom =\n \u03b9 f (\u03b5 b)",
536
+ "state_before": "\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3\u271d : Type w\u2083\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\n\u03b3 : Type w'\n\u03b5 : \u03b2 \u2243 \u03b3\nf : \u03b3 \u2192 C\ninst\u271d\u00b9 : HasCoproduct f\ninst\u271d : HasCoproduct (f \u2218 \u21d1\u03b5)\nb : \u03b2\n\u22a2 \u03b9 (f \u2218 \u21d1\u03b5) b \u226b (reindex \u03b5 f).hom = \u03b9 f (\u03b5 b)",
537
+ "tactic": "dsimp [Sigma.reindex]"
538
+ },
539
+ {
540
+ "annotated_tactic": [
541
+ "\"simp only [<a>HasColimit.isoOfEquivalence_hom_\\u03c0<\\/a>, <a>Functor.id_obj<\\/a>, <a>Discrete.functor_obj<\\/a>,\\n <a>Function.comp_apply<\\/a>, <a>Discrete.equivalence_functor<\\/a>, <a>Discrete.equivalence_inverse<\\/a>,\\n <a>Functor.comp_obj<\\/a>, <a>Discrete.natIso_inv_app<\\/a>, <a>Iso.refl_inv<\\/a>, <a>Category.id_comp<\\/a>]\"",
542
+ "[{\"full_name\":\"CategoryTheory.Limits.HasColimit.isoOfEquivalence_hom_\\u03c0\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/HasLimits.lean\",\"def_pos\":[969,9],\"def_end_pos\":[969,42]},{\"full_name\":\"CategoryTheory.Functor.id_obj\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Basic.lean\",\"def_pos\":[94,9],\"def_end_pos\":[94,15]},{\"full_name\":\"CategoryTheory.Discrete.functor_obj\",\"def_path\":\"Mathlib\\/CategoryTheory\\/DiscreteCategory.lean\",\"def_pos\":[181,9],\"def_end_pos\":[181,20]},{\"full_name\":\"Function.comp_apply\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Core.lean\",\"def_pos\":[35,17],\"def_end_pos\":[35,36]},{\"full_name\":\"CategoryTheory.Discrete.equivalence_functor\",\"def_path\":\"Mathlib\\/CategoryTheory\\/DiscreteCategory.lean\",\"def_pos\":[255,3],\"def_end_pos\":[255,8]},{\"full_name\":\"CategoryTheory.Discrete.equivalence_inverse\",\"def_path\":\"Mathlib\\/CategoryTheory\\/DiscreteCategory.lean\",\"def_pos\":[255,3],\"def_end_pos\":[255,8]},{\"full_name\":\"CategoryTheory.Functor.comp_obj\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Functor\\/Basic.lean\",\"def_pos\":[110,9],\"def_end_pos\":[110,12]},{\"full_name\":\"CategoryTheory.Discrete.natIso_inv_app\",\"def_path\":\"Mathlib\\/CategoryTheory\\/DiscreteCategory.lean\",\"def_pos\":[218,3],\"def_end_pos\":[218,9]},{\"full_name\":\"CategoryTheory.Iso.refl_inv\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[130,9],\"def_end_pos\":[130,14]},{\"full_name\":\"CategoryTheory.Category.id_comp\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[177,3],\"def_end_pos\":[177,10]}]"
543
+ ],
544
+ "state_after": "\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3\u271d : Type w\u2083\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\n\u03b3 : Type w'\n\u03b5 : \u03b2 \u2243 \u03b3\nf : \u03b3 \u2192 C\ninst\u271d\u00b9 : HasCoproduct f\ninst\u271d : HasCoproduct (f \u2218 \u21d1\u03b5)\nb : \u03b2\n\u22a2 (Discrete.functor (f \u2218 \u21d1\u03b5)).map ((Discrete.equivalence \u03b5).unit.app { as := b }) \u226b\n colimit.\u03b9 (Discrete.functor f) { as := \u03b5 (\u03b5.symm (\u03b5 b)) } =\n \u03b9 f (\u03b5 b)",
545
+ "state_before": "\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3\u271d : Type w\u2083\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\n\u03b3 : Type w'\n\u03b5 : \u03b2 \u2243 \u03b3\nf : \u03b3 \u2192 C\ninst\u271d\u00b9 : HasCoproduct f\ninst\u271d : HasCoproduct (f \u2218 \u21d1\u03b5)\nb : \u03b2\n\u22a2 \u03b9 (f \u2218 \u21d1\u03b5) b \u226b\n (HasColimit.isoOfEquivalence (Discrete.equivalence \u03b5)\n (Discrete.natIso fun x =>\n Iso.refl ((Discrete.functor f).obj ((Discrete.functor (Discrete.mk \u2218 \u21d1\u03b5)).obj x)))).hom =\n \u03b9 f (\u03b5 b)",
546
+ "tactic": "simp only [HasColimit.isoOfEquivalence_hom_\u03c0, Functor.id_obj, Discrete.functor_obj,\n Function.comp_apply, Discrete.equivalence_functor, Discrete.equivalence_inverse,\n Functor.comp_obj, Discrete.natIso_inv_app, Iso.refl_inv, Category.id_comp]"
547
+ },
548
+ {
549
+ "annotated_tactic": [
550
+ "\"have h := <a>colimit.w<\\/a> (<a>Discrete.functor<\\/a> f) (<a>Discrete.eqToHom'<\\/a> (\\u03b5.apply_symm_apply (\\u03b5 b)))\"",
551
+ "[{\"full_name\":\"CategoryTheory.Limits.colimit.w\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/HasLimits.lean\",\"def_pos\":[758,9],\"def_end_pos\":[758,18]},{\"full_name\":\"CategoryTheory.Discrete.functor\",\"def_path\":\"Mathlib\\/CategoryTheory\\/DiscreteCategory.lean\",\"def_pos\":[172,5],\"def_end_pos\":[172,12]},{\"full_name\":\"CategoryTheory.Discrete.eqToHom'\",\"def_path\":\"Mathlib\\/CategoryTheory\\/DiscreteCategory.lean\",\"def_pos\":[149,8],\"def_end_pos\":[149,16]}]"
552
+ ],
553
+ "state_after": "\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3\u271d : Type w\u2083\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\n\u03b3 : Type w'\n\u03b5 : \u03b2 \u2243 \u03b3\nf : \u03b3 \u2192 C\ninst\u271d\u00b9 : HasCoproduct f\ninst\u271d : HasCoproduct (f \u2218 \u21d1\u03b5)\nb : \u03b2\nh :\n (Discrete.functor f).map (Discrete.eqToHom' \u22ef) \u226b colimit.\u03b9 (Discrete.functor f) { as := \u03b5 b } =\n colimit.\u03b9 (Discrete.functor f) { as := \u03b5 (\u03b5.symm (\u03b5 b)) }\n\u22a2 (Discrete.functor (f \u2218 \u21d1\u03b5)).map ((Discrete.equivalence \u03b5).unit.app { as := b }) \u226b\n colimit.\u03b9 (Discrete.functor f) { as := \u03b5 (\u03b5.symm (\u03b5 b)) } =\n \u03b9 f (\u03b5 b)",
554
+ "state_before": "\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3\u271d : Type w\u2083\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\n\u03b3 : Type w'\n\u03b5 : \u03b2 \u2243 \u03b3\nf : \u03b3 \u2192 C\ninst\u271d\u00b9 : HasCoproduct f\ninst\u271d : HasCoproduct (f \u2218 \u21d1\u03b5)\nb : \u03b2\n\u22a2 (Discrete.functor (f \u2218 \u21d1\u03b5)).map ((Discrete.equivalence \u03b5).unit.app { as := b }) \u226b\n colimit.\u03b9 (Discrete.functor f) { as := \u03b5 (\u03b5.symm (\u03b5 b)) } =\n \u03b9 f (\u03b5 b)",
555
+ "tactic": "have h := colimit.w (Discrete.functor f) (Discrete.eqToHom' (\u03b5.apply_symm_apply (\u03b5 b)))"
556
+ },
557
+ {
558
+ "annotated_tactic": [
559
+ "\"erw [\\u2190 h, <a>eqToHom_map<\\/a>, <a>eqToHom_map<\\/a>, <a>eqToHom_trans_assoc<\\/a>]\"",
560
+ "[{\"full_name\":\"CategoryTheory.eqToHom_map\",\"def_path\":\"Mathlib\\/CategoryTheory\\/EqToHom.lean\",\"def_pos\":[301,9],\"def_end_pos\":[301,20]},{\"full_name\":\"CategoryTheory.eqToHom_map\",\"def_path\":\"Mathlib\\/CategoryTheory\\/EqToHom.lean\",\"def_pos\":[301,9],\"def_end_pos\":[301,20]},{\"full_name\":\"CategoryTheory.eqToHom_trans_assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/EqToHom.lean\",\"def_pos\":[51,3],\"def_end_pos\":[51,25]}]"
561
+ ],
562
+ "state_after": "\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3\u271d : Type w\u2083\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\n\u03b3 : Type w'\n\u03b5 : \u03b2 \u2243 \u03b3\nf : \u03b3 \u2192 C\ninst\u271d\u00b9 : HasCoproduct f\ninst\u271d : HasCoproduct (f \u2218 \u21d1\u03b5)\nb : \u03b2\nh :\n (Discrete.functor f).map (Discrete.eqToHom' \u22ef) \u226b colimit.\u03b9 (Discrete.functor f) { as := \u03b5 b } =\n colimit.\u03b9 (Discrete.functor f) { as := \u03b5 (\u03b5.symm (\u03b5 b)) }\n\u22a2 eqToHom \u22ef \u226b colimit.\u03b9 (Discrete.functor f) { as := \u03b5 b } = \u03b9 f (\u03b5 b)\n\ncase p\n\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3\u271d : Type w\u2083\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\n\u03b3 : Type w'\n\u03b5 : \u03b2 \u2243 \u03b3\nf : \u03b3 \u2192 C\ninst\u271d\u00b9 : HasCoproduct f\ninst\u271d : HasCoproduct (f \u2218 \u21d1\u03b5)\nb : \u03b2\nh :\n (Discrete.functor f).map (Discrete.eqToHom' \u22ef) \u226b colimit.\u03b9 (Discrete.functor f) { as := \u03b5 b } =\n colimit.\u03b9 (Discrete.functor f) { as := \u03b5 (\u03b5.symm (\u03b5 b)) }\n\u22a2 { as := b } = { as := \u03b5.symm (\u03b5 b) }",
563
+ "state_before": "\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3\u271d : Type w\u2083\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\n\u03b3 : Type w'\n\u03b5 : \u03b2 \u2243 \u03b3\nf : \u03b3 \u2192 C\ninst\u271d\u00b9 : HasCoproduct f\ninst\u271d : HasCoproduct (f \u2218 \u21d1\u03b5)\nb : \u03b2\nh :\n (Discrete.functor f).map (Discrete.eqToHom' \u22ef) \u226b colimit.\u03b9 (Discrete.functor f) { as := \u03b5 b } =\n colimit.\u03b9 (Discrete.functor f) { as := \u03b5 (\u03b5.symm (\u03b5 b)) }\n\u22a2 (Discrete.functor (f \u2218 \u21d1\u03b5)).map ((Discrete.equivalence \u03b5).unit.app { as := b }) \u226b\n colimit.\u03b9 (Discrete.functor f) { as := \u03b5 (\u03b5.symm (\u03b5 b)) } =\n \u03b9 f (\u03b5 b)",
564
+ "tactic": "erw [\u2190 h, eqToHom_map, eqToHom_map, eqToHom_trans_assoc]"
565
+ },
566
+ {
567
+ "annotated_tactic": [
568
+ "\"all_goals { simp }\"",
569
+ "[]"
570
+ ],
571
+ "state_after": "no goals",
572
+ "state_before": "\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3\u271d : Type w\u2083\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\n\u03b3 : Type w'\n\u03b5 : \u03b2 \u2243 \u03b3\nf : \u03b3 \u2192 C\ninst\u271d\u00b9 : HasCoproduct f\ninst\u271d : HasCoproduct (f \u2218 \u21d1\u03b5)\nb : \u03b2\nh :\n (Discrete.functor f).map (Discrete.eqToHom' \u22ef) \u226b colimit.\u03b9 (Discrete.functor f) { as := \u03b5 b } =\n colimit.\u03b9 (Discrete.functor f) { as := \u03b5 (\u03b5.symm (\u03b5 b)) }\n\u22a2 eqToHom \u22ef \u226b colimit.\u03b9 (Discrete.functor f) { as := \u03b5 b } = \u03b9 f (\u03b5 b)\n\ncase p\n\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3\u271d : Type w\u2083\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\n\u03b3 : Type w'\n\u03b5 : \u03b2 \u2243 \u03b3\nf : \u03b3 \u2192 C\ninst\u271d\u00b9 : HasCoproduct f\ninst\u271d : HasCoproduct (f \u2218 \u21d1\u03b5)\nb : \u03b2\nh :\n (Discrete.functor f).map (Discrete.eqToHom' \u22ef) \u226b colimit.\u03b9 (Discrete.functor f) { as := \u03b5 b } =\n colimit.\u03b9 (Discrete.functor f) { as := \u03b5 (\u03b5.symm (\u03b5 b)) }\n\u22a2 { as := b } = { as := \u03b5.symm (\u03b5 b) }",
573
+ "tactic": "all_goals { simp }"
574
+ },
575
+ {
576
+ "annotated_tactic": [
577
+ "\"simp\"",
578
+ "[]"
579
+ ],
580
+ "state_after": "no goals",
581
+ "state_before": "case p\n\u03b2 : Type w\n\u03b1 : Type w\u2082\n\u03b3\u271d : Type w\u2083\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\n\u03b3 : Type w'\n\u03b5 : \u03b2 \u2243 \u03b3\nf : \u03b3 \u2192 C\ninst\u271d\u00b9 : HasCoproduct f\ninst\u271d : HasCoproduct (f \u2218 \u21d1\u03b5)\nb : \u03b2\nh :\n (Discrete.functor f).map (Discrete.eqToHom' \u22ef) \u226b colimit.\u03b9 (Discrete.functor f) { as := \u03b5 b } =\n colimit.\u03b9 (Discrete.functor f) { as := \u03b5 (\u03b5.symm (\u03b5 b)) }\n\u22a2 { as := b } = { as := \u03b5.symm (\u03b5 b) }",
582
+ "tactic": "simp"
583
+ }
584
+ ],
585
+ "url": "https://github.com/leanprover-community/mathlib4"
586
+ },
587
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
588
+ },
589
+ {
590
+ "error": "theorem has no selected tactic transitions",
591
+ "full_name": "CategoryTheory.Limits.cofan_mk_inj",
592
+ "id": "CategoryTheory.Limits.cofan_mk_inj",
593
+ "reason": "import_failure",
594
+ "selection": {
595
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
596
+ "end": [
597
+ 93,
598
+ 6
599
+ ],
600
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
601
+ "full_name": "CategoryTheory.Limits.cofan_mk_inj",
602
+ "start": [
603
+ 91,
604
+ 1
605
+ ],
606
+ "traced_tactics": [],
607
+ "url": "https://github.com/leanprover-community/mathlib4"
608
+ },
609
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
610
+ },
611
+ {
612
+ "error": "theorem has no selected tactic transitions",
613
+ "full_name": "CategoryTheory.Limits.fan_mk_proj",
614
+ "id": "CategoryTheory.Limits.fan_mk_proj",
615
+ "reason": "import_failure",
616
+ "selection": {
617
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
618
+ "end": [
619
+ 87,
620
+ 6
621
+ ],
622
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
623
+ "full_name": "CategoryTheory.Limits.fan_mk_proj",
624
+ "start": [
625
+ 86,
626
+ 1
627
+ ],
628
+ "traced_tactics": [],
629
+ "url": "https://github.com/leanprover-community/mathlib4"
630
+ },
631
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
632
+ },
633
+ {
634
+ "error": "theorem has no selected tactic transitions",
635
+ "full_name": "CategoryTheory.Limits.hasProducts_of_limit_fans",
636
+ "id": "CategoryTheory.Limits.hasProducts_of_limit_fans",
637
+ "reason": "import_failure",
638
+ "selection": {
639
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
640
+ "end": [
641
+ 646,
642
+ 68
643
+ ],
644
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
645
+ "full_name": "CategoryTheory.Limits.hasProducts_of_limit_fans",
646
+ "start": [
647
+ 640,
648
+ 1
649
+ ],
650
+ "traced_tactics": [],
651
+ "url": "https://github.com/leanprover-community/mathlib4"
652
+ },
653
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
654
+ },
655
+ {
656
+ "error": "theorem has no selected tactic transitions",
657
+ "full_name": "CategoryTheory.Limits.has_smallest_coproducts_of_hasCoproducts",
658
+ "id": "CategoryTheory.Limits.has_smallest_coproducts_of_hasCoproducts",
659
+ "reason": "import_failure",
660
+ "selection": {
661
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
662
+ "end": [
663
+ 637,
664
+ 100
665
+ ],
666
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
667
+ "full_name": "CategoryTheory.Limits.has_smallest_coproducts_of_hasCoproducts",
668
+ "start": [
669
+ 635,
670
+ 1
671
+ ],
672
+ "traced_tactics": [],
673
+ "url": "https://github.com/leanprover-community/mathlib4"
674
+ },
675
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
676
+ },
677
+ {
678
+ "error": "theorem has no selected tactic transitions",
679
+ "full_name": "CategoryTheory.Limits.has_smallest_products_of_hasProducts",
680
+ "id": "CategoryTheory.Limits.has_smallest_products_of_hasProducts",
681
+ "reason": "import_failure",
682
+ "selection": {
683
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
684
+ "end": [
685
+ 632,
686
+ 98
687
+ ],
688
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
689
+ "full_name": "CategoryTheory.Limits.has_smallest_products_of_hasProducts",
690
+ "start": [
691
+ 631,
692
+ 1
693
+ ],
694
+ "traced_tactics": [],
695
+ "url": "https://github.com/leanprover-community/mathlib4"
696
+ },
697
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
698
+ },
699
+ {
700
+ "error": "theorem has no selected tactic transitions",
701
+ "full_name": "CategoryTheory.Limits.piComparison_comp_\u03c0",
702
+ "id": "CategoryTheory.Limits.piComparison_comp_\u03c0",
703
+ "reason": "import_failure",
704
+ "selection": {
705
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
706
+ "end": [
707
+ 582,
708
+ 33
709
+ ],
710
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean",
711
+ "full_name": "CategoryTheory.Limits.piComparison_comp_\u03c0",
712
+ "start": [
713
+ 580,
714
+ 1
715
+ ],
716
+ "traced_tactics": [],
717
+ "url": "https://github.com/leanprover-community/mathlib4"
718
+ },
719
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Products.lean"
720
+ },
721
+ {
722
+ "error": "theorem has no selected tactic transitions",
723
+ "full_name": "CategoryTheory.Limits.\u03b9_comp_sigmaComparison",
724
+ "id": "CategoryTheory.Limits.\u03b9_comp_sigmaComparison",
725
+ "reason": "import_failure",
726
+ "selection": {
727
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
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+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/SplitCoequalizer.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "CategoryTheory.Limits.IsInitial.isIso_to",
34
+ "id": "CategoryTheory.Limits.IsInitial.isIso_to",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
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+ "end": [
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41
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42
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean",
43
+ "full_name": "CategoryTheory.Limits.IsInitial.isIso_to",
44
+ "start": [
45
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46
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47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "CategoryTheory.Limits.IsInitial.subsingleton_to",
56
+ "id": "CategoryTheory.Limits.IsInitial.subsingleton_to",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
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61
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62
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63
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64
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean",
65
+ "full_name": "CategoryTheory.Limits.IsInitial.subsingleton_to",
66
+ "start": [
67
+ 80,
68
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69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean"
74
+ },
75
+ {
76
+ "error": "theorem has no selected tactic transitions",
77
+ "full_name": "CategoryTheory.Limits.IsTerminal.isIso_from",
78
+ "id": "CategoryTheory.Limits.IsTerminal.isIso_from",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
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84
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85
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86
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean",
87
+ "full_name": "CategoryTheory.Limits.IsTerminal.isIso_from",
88
+ "start": [
89
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90
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91
+ ],
92
+ "traced_tactics": [],
93
+ "url": "https://github.com/leanprover-community/mathlib4"
94
+ },
95
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean"
96
+ },
97
+ {
98
+ "error": "theorem has no selected tactic transitions",
99
+ "full_name": "CategoryTheory.Limits.IsTerminal.subsingleton_to",
100
+ "id": "CategoryTheory.Limits.IsTerminal.subsingleton_to",
101
+ "reason": "import_failure",
102
+ "selection": {
103
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
104
+ "end": [
105
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106
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107
+ ],
108
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean",
109
+ "full_name": "CategoryTheory.Limits.IsTerminal.subsingleton_to",
110
+ "start": [
111
+ 198,
112
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113
+ ],
114
+ "traced_tactics": [],
115
+ "url": "https://github.com/leanprover-community/mathlib4"
116
+ },
117
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean"
118
+ },
119
+ {
120
+ "error": "theorem has no selected tactic transitions",
121
+ "full_name": "CategoryTheory.Limits.initial.strict_hom_ext",
122
+ "id": "CategoryTheory.Limits.initial.strict_hom_ext",
123
+ "reason": "import_failure",
124
+ "selection": {
125
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
126
+ "end": [
127
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128
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129
+ ],
130
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean",
131
+ "full_name": "CategoryTheory.Limits.initial.strict_hom_ext",
132
+ "start": [
133
+ 121,
134
+ 1
135
+ ],
136
+ "traced_tactics": [],
137
+ "url": "https://github.com/leanprover-community/mathlib4"
138
+ },
139
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean"
140
+ },
141
+ {
142
+ "error": "theorem has no selected tactic transitions",
143
+ "full_name": "CategoryTheory.Limits.initial.subsingleton_to",
144
+ "id": "CategoryTheory.Limits.initial.subsingleton_to",
145
+ "reason": "import_failure",
146
+ "selection": {
147
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
148
+ "end": [
149
+ 126,
150
+ 35
151
+ ],
152
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean",
153
+ "full_name": "CategoryTheory.Limits.initial.subsingleton_to",
154
+ "start": [
155
+ 125,
156
+ 1
157
+ ],
158
+ "traced_tactics": [],
159
+ "url": "https://github.com/leanprover-community/mathlib4"
160
+ },
161
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean"
162
+ },
163
+ {
164
+ "error": "theorem has no selected tactic transitions",
165
+ "full_name": "CategoryTheory.Limits.initialMul_inv",
166
+ "id": "CategoryTheory.Limits.initialMul_inv",
167
+ "reason": "import_failure",
168
+ "selection": {
169
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
170
+ "end": [
171
+ 154,
172
+ 24
173
+ ],
174
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean",
175
+ "full_name": "CategoryTheory.Limits.initialMul_inv",
176
+ "start": [
177
+ 153,
178
+ 1
179
+ ],
180
+ "traced_tactics": [],
181
+ "url": "https://github.com/leanprover-community/mathlib4"
182
+ },
183
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean"
184
+ },
185
+ {
186
+ "error": "theorem has no selected tactic transitions",
187
+ "full_name": "CategoryTheory.Limits.isInitialMul_inv",
188
+ "id": "CategoryTheory.Limits.isInitialMul_inv",
189
+ "reason": "import_failure",
190
+ "selection": {
191
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
192
+ "end": [
193
+ 111,
194
+ 17
195
+ ],
196
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean",
197
+ "full_name": "CategoryTheory.Limits.isInitialMul_inv",
198
+ "start": [
199
+ 109,
200
+ 1
201
+ ],
202
+ "traced_tactics": [],
203
+ "url": "https://github.com/leanprover-community/mathlib4"
204
+ },
205
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean"
206
+ },
207
+ {
208
+ "error": "no internal trace for tactic 'rfl'",
209
+ "full_name": "CategoryTheory.Limits.limit_\u03c0_isIso_of_is_strict_terminal",
210
+ "id": "CategoryTheory.Limits.limit_\u03c0_isIso_of_is_strict_terminal",
211
+ "reason": "import_failure",
212
+ "selection": {
213
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
214
+ "end": [
215
+ 237,
216
+ 11
217
+ ],
218
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean",
219
+ "full_name": "CategoryTheory.Limits.limit_\u03c0_isIso_of_is_strict_terminal",
220
+ "start": [
221
+ 206,
222
+ 1
223
+ ],
224
+ "traced_tactics": [
225
+ {
226
+ "annotated_tactic": [
227
+ "\"refine \\u27e8\\u27e8<a>limit.lift<\\/a> _ \\u27e8_, \\u27e8?_, ?_\\u27e9\\u27e9, ?_, ?_\\u27e9\\u27e9\"",
228
+ "[{\"full_name\":\"CategoryTheory.Limits.limit.lift\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/HasLimits.lean\",\"def_pos\":[181,5],\"def_end_pos\":[181,15]}]"
229
+ ],
230
+ "state_after": "case refine_1\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\n\u22a2 (X : J) \u2192 ((Functor.const J).obj (F.toPrefunctor.1 i)).obj X \u27f6 F.obj X\n\ncase refine_2\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\n\u22a2 \u2200 \u2983X Y : J\u2984 (f : X \u27f6 Y), ((Functor.const J).obj (F.toPrefunctor.1 i)).map f \u226b ?refine_1 Y = ?refine_1 X \u226b F.map f\n\ncase refine_3\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\n\u22a2 limit.\u03c0 F i \u226b limit.lift F { pt := F.toPrefunctor.1 i, \u03c0 := { app := ?refine_1, naturality := ?refine_2 } } =\n \ud835\udfd9 (limit F)\n\ncase refine_4\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\n\u22a2 limit.lift F { pt := F.toPrefunctor.1 i, \u03c0 := { app := ?refine_1, naturality := ?refine_2 } } \u226b limit.\u03c0 F i =\n \ud835\udfd9 (F.obj i)",
231
+ "state_before": "C : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\n\u22a2 IsIso (limit.\u03c0 F i)",
232
+ "tactic": "refine \u27e8\u27e8limit.lift _ \u27e8_, \u27e8?_, ?_\u27e9\u27e9, ?_, ?_\u27e9\u27e9"
233
+ },
234
+ {
235
+ "annotated_tactic": [
236
+ "\"exact fun j =>\\n <a>dite<\\/a> (j = i)\\n (fun h => <a>eqToHom<\\/a> (by cases h; rfl))\\n fun h => (H _ h).<a>from<\\/a> _\"",
237
+ "[{\"full_name\":\"dite\",\"def_path\":\".lake\\/packages\\/lean4\\/src\\/lean\\/Init\\/Prelude.lean\",\"def_pos\":[945,21],\"def_end_pos\":[945,25]},{\"full_name\":\"CategoryTheory.eqToHom\",\"def_path\":\"Mathlib\\/CategoryTheory\\/EqToHom.lean\",\"def_pos\":[43,5],\"def_end_pos\":[43,12]},{\"full_name\":\"CategoryTheory.Limits.IsTerminal.from\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Terminal.lean\",\"def_pos\":[157,5],\"def_end_pos\":[157,20]}]"
238
+ ],
239
+ "state_after": "no goals",
240
+ "state_before": "case refine_1\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\n\u22a2 (X : J) \u2192 ((Functor.const J).obj (F.toPrefunctor.1 i)).obj X \u27f6 F.obj X",
241
+ "tactic": "exact fun j =>\n dite (j = i)\n (fun h => eqToHom (by cases h; rfl))\n fun h => (H _ h).from _"
242
+ },
243
+ {
244
+ "annotated_tactic": [
245
+ "\"cases h\"",
246
+ "[]"
247
+ ],
248
+ "state_after": "case refl\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).obj i = F.obj i",
249
+ "state_before": "C : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj : J\nh : j = i\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).obj j = F.obj j",
250
+ "tactic": "cases h"
251
+ },
252
+ {
253
+ "annotated_tactic": [
254
+ "\"rfl\"",
255
+ "[]"
256
+ ],
257
+ "state_after": "no goals",
258
+ "state_before": "case refl\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).obj i = F.obj i",
259
+ "tactic": "rfl"
260
+ },
261
+ {
262
+ "annotated_tactic": [
263
+ "\"intro j k f\"",
264
+ "[]"
265
+ ],
266
+ "state_after": "case refine_2\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj k : J\nf : j \u27f6 k\n\u22a2 (((Functor.const J).obj (F.toPrefunctor.1 i)).map f \u226b\n if h : k = i then eqToHom \u22ef else (H k h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj k)) =\n (if h : j = i then eqToHom \u22ef else (H j h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j)) \u226b F.map f",
267
+ "state_before": "case refine_2\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\n\u22a2 \u2200 \u2983X Y : J\u2984 (f : X \u27f6 Y),\n (((Functor.const J).obj (F.toPrefunctor.1 i)).map f \u226b\n if h : Y = i then eqToHom \u22ef else (H Y h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj Y)) =\n (if h : X = i then eqToHom \u22ef else (H X h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj X)) \u226b F.map f",
268
+ "tactic": "intro j k f"
269
+ },
270
+ {
271
+ "annotated_tactic": [
272
+ "\"split_ifs with h h_1 h_1\"",
273
+ "[]"
274
+ ],
275
+ "state_after": "case pos\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj k : J\nf : j \u27f6 k\nh : k = i\nh_1 : j = i\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).map f \u226b eqToHom \u22ef = eqToHom \u22ef \u226b F.map f\n\ncase neg\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj k : J\nf : j \u27f6 k\nh : k = i\nh_1 : \u00acj = i\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).map f \u226b eqToHom \u22ef =\n (H j h_1).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j) \u226b F.map f\n\ncase pos\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj k : J\nf : j \u27f6 k\nh : \u00ack = i\nh_1 : j = i\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).map f \u226b\n (H k h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj k) =\n eqToHom \u22ef \u226b F.map f\n\ncase neg\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj k : J\nf : j \u27f6 k\nh : \u00ack = i\nh_1 : \u00acj = i\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).map f \u226b\n (H k h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj k) =\n (H j h_1).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j) \u226b F.map f",
276
+ "state_before": "case refine_2\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj k : J\nf : j \u27f6 k\n\u22a2 (((Functor.const J).obj (F.toPrefunctor.1 i)).map f \u226b\n if h : k = i then eqToHom \u22ef else (H k h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj k)) =\n (if h : j = i then eqToHom \u22ef else (H j h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j)) \u226b F.map f",
277
+ "tactic": "split_ifs with h h_1 h_1"
278
+ },
279
+ {
280
+ "annotated_tactic": [
281
+ "\"cases h\"",
282
+ "[]"
283
+ ],
284
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286
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295
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+ "annotated_tactic": [
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+ "tactic": "obtain rfl : f = \ud835\udfd9 _ := Subsingleton.elim _ _"
305
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+ {
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+ "annotated_tactic": [
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+ "\"simp\"",
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+ "state_before": "case pos.refl.refl\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).map (\ud835\udfd9 i) \u226b eqToHom \u22ef = eqToHom \u22ef \u226b F.map (\ud835\udfd9 i)",
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+ "tactic": "simp"
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+ {
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+ "annotated_tactic": [
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+ "\"cases h\"",
318
+ "[]"
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+ "state_after": "case neg.refl\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj : J\nh_1 : \u00acj = i\nf : j \u27f6 i\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).map f \u226b eqToHom \u22ef =\n (H j h_1).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j) \u226b F.map f",
321
+ "state_before": "case neg\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj k : J\nf : j \u27f6 k\nh : k = i\nh_1 : \u00acj = i\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).map f \u226b eqToHom \u22ef =\n (H j h_1).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j) \u226b F.map f",
322
+ "tactic": "cases h"
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+ },
324
+ {
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+ "annotated_tactic": [
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+ "\"erw [<a>Category.comp_id<\\/a>]\"",
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+ ],
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+ "state_after": "case neg.refl\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj : J\nh_1 : \u00acj = i\nf : j \u27f6 i\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).map f =\n (H j h_1).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j) \u226b F.map f",
330
+ "state_before": "case neg.refl\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj : J\nh_1 : \u00acj = i\nf : j \u27f6 i\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).map f \u226b eqToHom \u22ef =\n (H j h_1).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j) \u226b F.map f",
331
+ "tactic": "erw [Category.comp_id]"
332
+ },
333
+ {
334
+ "annotated_tactic": [
335
+ "\"haveI : <a>IsIso<\\/a> (F.map f) := (H _ h_1).<a>isIso_from<\\/a> _\"",
336
+ "[{\"full_name\":\"CategoryTheory.IsIso\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[272,7],\"def_end_pos\":[272,12]},{\"full_name\":\"CategoryTheory.Limits.IsTerminal.isIso_from\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/StrictInitial.lean\",\"def_pos\":[188,9],\"def_end_pos\":[188,30]}]"
337
+ ],
338
+ "state_after": "case neg.refl\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj : J\nh_1 : \u00acj = i\nf : j \u27f6 i\nthis : IsIso (F.map f)\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).map f =\n (H j h_1).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j) \u226b F.map f",
339
+ "state_before": "case neg.refl\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj : J\nh_1 : \u00acj = i\nf : j \u27f6 i\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).map f =\n (H j h_1).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j) \u226b F.map f",
340
+ "tactic": "haveI : IsIso (F.map f) := (H _ h_1).isIso_from _"
341
+ },
342
+ {
343
+ "annotated_tactic": [
344
+ "\"rw [\\u2190 <a>IsIso.comp_inv_eq<\\/a>]\"",
345
+ "[{\"full_name\":\"CategoryTheory.IsIso.comp_inv_eq\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Iso.lean\",\"def_pos\":[451,9],\"def_end_pos\":[451,20]}]"
346
+ ],
347
+ "state_after": "case neg.refl\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj : J\nh_1 : \u00acj = i\nf : j \u27f6 i\nthis : IsIso (F.map f)\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).map f \u226b inv (F.map f) =\n (H j h_1).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j)",
348
+ "state_before": "case neg.refl\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj : J\nh_1 : \u00acj = i\nf : j \u27f6 i\nthis : IsIso (F.map f)\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).map f =\n (H j h_1).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j) \u226b F.map f",
349
+ "tactic": "rw [\u2190 IsIso.comp_inv_eq]"
350
+ },
351
+ {
352
+ "annotated_tactic": [
353
+ "\"apply (H _ h_1).<a>hom_ext<\\/a>\"",
354
+ "[{\"full_name\":\"CategoryTheory.Limits.IsTerminal.hom_ext\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Terminal.lean\",\"def_pos\":[162,9],\"def_end_pos\":[162,27]}]"
355
+ ],
356
+ "state_after": "no goals",
357
+ "state_before": "case neg.refl\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj : J\nh_1 : \u00acj = i\nf : j \u27f6 i\nthis : IsIso (F.map f)\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).map f \u226b inv (F.map f) =\n (H j h_1).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j)",
358
+ "tactic": "apply (H _ h_1).hom_ext"
359
+ },
360
+ {
361
+ "annotated_tactic": [
362
+ "\"cases h_1\"",
363
+ "[]"
364
+ ],
365
+ "state_after": "case pos.refl\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nk : J\nh : \u00ack = i\nf : i \u27f6 k\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).map f \u226b\n (H k h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj k) =\n eqToHom \u22ef \u226b F.map f",
366
+ "state_before": "case pos\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj k : J\nf : j \u27f6 k\nh : \u00ack = i\nh_1 : j = i\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).map f \u226b\n (H k h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj k) =\n eqToHom \u22ef \u226b F.map f",
367
+ "tactic": "cases h_1"
368
+ },
369
+ {
370
+ "annotated_tactic": [
371
+ "\"apply (H _ h).<a>hom_ext<\\/a>\"",
372
+ "[{\"full_name\":\"CategoryTheory.Limits.IsTerminal.hom_ext\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Terminal.lean\",\"def_pos\":[162,9],\"def_end_pos\":[162,27]}]"
373
+ ],
374
+ "state_after": "no goals",
375
+ "state_before": "case pos.refl\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nk : J\nh : \u00ack = i\nf : i \u27f6 k\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).map f \u226b\n (H k h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj k) =\n eqToHom \u22ef \u226b F.map f",
376
+ "tactic": "apply (H _ h).hom_ext"
377
+ },
378
+ {
379
+ "annotated_tactic": [
380
+ "\"apply (H _ h).<a>hom_ext<\\/a>\"",
381
+ "[{\"full_name\":\"CategoryTheory.Limits.IsTerminal.hom_ext\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Terminal.lean\",\"def_pos\":[162,9],\"def_end_pos\":[162,27]}]"
382
+ ],
383
+ "state_after": "no goals",
384
+ "state_before": "case neg\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj k : J\nf : j \u27f6 k\nh : \u00ack = i\nh_1 : \u00acj = i\n\u22a2 ((Functor.const J).obj (F.toPrefunctor.1 i)).map f \u226b\n (H k h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj k) =\n (H j h_1).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j) \u226b F.map f",
385
+ "tactic": "apply (H _ h).hom_ext"
386
+ },
387
+ {
388
+ "annotated_tactic": [
389
+ "\"ext\"",
390
+ "[]"
391
+ ],
392
+ "state_after": "case refine_3.w\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj\u271d : J\n\u22a2 (limit.\u03c0 F i \u226b\n limit.lift F\n { pt := F.toPrefunctor.1 i,\n \u03c0 :=\n {\n app := fun j =>\n if h : j = i then eqToHom \u22ef else (H j h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j),\n naturality := \u22ef } }) \u226b\n limit.\u03c0 F j\u271d =\n \ud835\udfd9 (limit F) \u226b limit.\u03c0 F j\u271d",
393
+ "state_before": "case refine_3\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\n\u22a2 limit.\u03c0 F i \u226b\n limit.lift F\n { pt := F.toPrefunctor.1 i,\n \u03c0 :=\n {\n app := fun j =>\n if h : j = i then eqToHom \u22ef else (H j h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j),\n naturality := \u22ef } } =\n \ud835\udfd9 (limit F)",
394
+ "tactic": "ext"
395
+ },
396
+ {
397
+ "annotated_tactic": [
398
+ "\"rw [<a>assoc<\\/a>, <a>limit.lift_\\u03c0<\\/a>]\"",
399
+ "[{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.Limits.limit.lift_\\u03c0\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/HasLimits.lean\",\"def_pos\":[192,9],\"def_end_pos\":[192,21]}]"
400
+ ],
401
+ "state_after": "case refine_3.w\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj\u271d : J\n\u22a2 limit.\u03c0 F i \u226b\n { pt := F.toPrefunctor.1 i,\n \u03c0 :=\n {\n app := fun j =>\n if h : j = i then eqToHom \u22ef else (H j h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j),\n naturality := \u22ef } }.\u03c0.app\n j\u271d =\n \ud835\udfd9 (limit F) \u226b limit.\u03c0 F j\u271d",
402
+ "state_before": "case refine_3.w\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj\u271d : J\n\u22a2 (limit.\u03c0 F i \u226b\n limit.lift F\n { pt := F.toPrefunctor.1 i,\n \u03c0 :=\n {\n app := fun j =>\n if h : j = i then eqToHom \u22ef else (H j h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j),\n naturality := \u22ef } }) \u226b\n limit.\u03c0 F j\u271d =\n \ud835\udfd9 (limit F) \u226b limit.\u03c0 F j\u271d",
403
+ "tactic": "rw [assoc, limit.lift_\u03c0]"
404
+ },
405
+ {
406
+ "annotated_tactic": [
407
+ "\"dsimp only\"",
408
+ "[]"
409
+ ],
410
+ "state_after": "case refine_3.w\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj\u271d : J\n\u22a2 (limit.\u03c0 F i \u226b\n if h : j\u271d = i then eqToHom \u22ef else (H j\u271d h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j\u271d)) =\n \ud835\udfd9 (limit F) \u226b limit.\u03c0 F j\u271d",
411
+ "state_before": "case refine_3.w\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj\u271d : J\n\u22a2 limit.\u03c0 F i \u226b\n { pt := F.toPrefunctor.1 i,\n \u03c0 :=\n {\n app := fun j =>\n if h : j = i then eqToHom \u22ef else (H j h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j),\n naturality := \u22ef } }.\u03c0.app\n j\u271d =\n \ud835\udfd9 (limit F) \u226b limit.\u03c0 F j\u271d",
412
+ "tactic": "dsimp only"
413
+ },
414
+ {
415
+ "annotated_tactic": [
416
+ "\"split_ifs with h\"",
417
+ "[]"
418
+ ],
419
+ "state_after": "case pos\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj\u271d : J\nh : j\u271d = i\n\u22a2 limit.\u03c0 F i \u226b eqToHom \u22ef = \ud835\udfd9 (limit F) \u226b limit.\u03c0 F j\u271d\n\ncase neg\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj\u271d : J\nh : \u00acj\u271d = i\n\u22a2 limit.\u03c0 F i \u226b (H j\u271d h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j\u271d) = \ud835\udfd9 (limit F) \u226b limit.\u03c0 F j\u271d",
420
+ "state_before": "case refine_3.w\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj\u271d : J\n\u22a2 (limit.\u03c0 F i \u226b\n if h : j\u271d = i then eqToHom \u22ef else (H j\u271d h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j\u271d)) =\n \ud835\udfd9 (limit F) \u226b limit.\u03c0 F j\u271d",
421
+ "tactic": "split_ifs with h"
422
+ },
423
+ {
424
+ "annotated_tactic": [
425
+ "\"cases h\"",
426
+ "[]"
427
+ ],
428
+ "state_after": "case pos.refl\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\n\u22a2 limit.\u03c0 F i \u226b eqToHom \u22ef = \ud835\udfd9 (limit F) \u226b limit.\u03c0 F i",
429
+ "state_before": "case pos\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj\u271d : J\nh : j\u271d = i\n\u22a2 limit.\u03c0 F i \u226b eqToHom \u22ef = \ud835\udfd9 (limit F) \u226b limit.\u03c0 F j\u271d",
430
+ "tactic": "cases h"
431
+ },
432
+ {
433
+ "annotated_tactic": [
434
+ "\"rw [<a>id_comp<\\/a>, <a>eqToHom_refl<\\/a>]\"",
435
+ "[{\"full_name\":\"CategoryTheory.Category.id_comp\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[177,3],\"def_end_pos\":[177,10]},{\"full_name\":\"CategoryTheory.eqToHom_refl\",\"def_path\":\"Mathlib\\/CategoryTheory\\/EqToHom.lean\",\"def_pos\":[47,9],\"def_end_pos\":[47,21]}]"
436
+ ],
437
+ "state_after": "case pos.refl\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\n\u22a2 limit.\u03c0 F i \u226b \ud835\udfd9 (((Functor.const J).obj (F.toPrefunctor.1 i)).obj i) = limit.\u03c0 F i",
438
+ "state_before": "case pos.refl\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\n\u22a2 limit.\u03c0 F i \u226b eqToHom \u22ef = \ud835\udfd9 (limit F) \u226b limit.\u03c0 F i",
439
+ "tactic": "rw [id_comp, eqToHom_refl]"
440
+ },
441
+ {
442
+ "annotated_tactic": [
443
+ "\"exact <a>comp_id<\\/a> _\"",
444
+ "[{\"full_name\":\"CategoryTheory.Category.comp_id\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[179,3],\"def_end_pos\":[179,10]}]"
445
+ ],
446
+ "state_after": "no goals",
447
+ "state_before": "case pos.refl\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\n\u22a2 limit.\u03c0 F i \u226b \ud835\udfd9 (((Functor.const J).obj (F.toPrefunctor.1 i)).obj i) = limit.\u03c0 F i",
448
+ "tactic": "exact comp_id _"
449
+ },
450
+ {
451
+ "annotated_tactic": [
452
+ "\"apply (H _ h).<a>hom_ext<\\/a>\"",
453
+ "[{\"full_name\":\"CategoryTheory.Limits.IsTerminal.hom_ext\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/Shapes\\/Terminal.lean\",\"def_pos\":[162,9],\"def_end_pos\":[162,27]}]"
454
+ ],
455
+ "state_after": "no goals",
456
+ "state_before": "case neg\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\nj\u271d : J\nh : \u00acj\u271d = i\n\u22a2 limit.\u03c0 F i \u226b (H j\u271d h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j\u271d) = \ud835\udfd9 (limit F) \u226b limit.\u03c0 F j\u271d",
457
+ "tactic": "apply (H _ h).hom_ext"
458
+ },
459
+ {
460
+ "annotated_tactic": [
461
+ "\"rw [<a>limit.lift_\\u03c0<\\/a>]\"",
462
+ "[{\"full_name\":\"CategoryTheory.Limits.limit.lift_\\u03c0\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Limits\\/HasLimits.lean\",\"def_pos\":[192,9],\"def_end_pos\":[192,21]}]"
463
+ ],
464
+ "state_after": "case refine_4\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\n\u22a2 { pt := F.toPrefunctor.1 i,\n \u03c0 :=\n {\n app := fun j =>\n if h : j = i then eqToHom \u22ef else (H j h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j),\n naturality := \u22ef } }.\u03c0.app\n i =\n \ud835\udfd9 (F.obj i)",
465
+ "state_before": "case refine_4\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\n\u22a2 limit.lift F\n { pt := F.toPrefunctor.1 i,\n \u03c0 :=\n {\n app := fun j =>\n if h : j = i then eqToHom \u22ef else (H j h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j),\n naturality := \u22ef } } \u226b\n limit.\u03c0 F i =\n \ud835\udfd9 (F.obj i)",
466
+ "tactic": "rw [limit.lift_\u03c0]"
467
+ },
468
+ {
469
+ "annotated_tactic": [
470
+ "\"simp\"",
471
+ "[]"
472
+ ],
473
+ "state_after": "no goals",
474
+ "state_before": "case refine_4\nC : Type u\ninst\u271d\u2074 : Category.{v, u} C\ninst\u271d\u00b3 : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst\u271d\u00b2 : SmallCategory J\nF : J \u2964 C\ninst\u271d\u00b9 : HasLimit F\ni : J\nH : (j : J) \u2192 j \u2260 i \u2192 IsTerminal (F.obj j)\ninst\u271d : Subsingleton (i \u27f6 i)\n\u22a2 { pt := F.toPrefunctor.1 i,\n \u03c0 :=\n {\n app := fun j =>\n if h : j = i then eqToHom \u22ef else (H j h).from (((Functor.const J).obj (F.toPrefunctor.1 i)).obj j),\n naturality := \u22ef } }.\u03c0.app\n i =\n \ud835\udfd9 (F.obj i)",
475
+ "tactic": "simp"
476
+ }
477
+ ],
478
+ "url": "https://github.com/leanprover-community/mathlib4"
479
+ },
480
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean"
481
+ },
482
+ {
483
+ "error": "theorem has no selected tactic transitions",
484
+ "full_name": "CategoryTheory.Limits.mulInitial_inv",
485
+ "id": "CategoryTheory.Limits.mulInitial_inv",
486
+ "reason": "import_failure",
487
+ "selection": {
488
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
489
+ "end": [
490
+ 140,
491
+ 24
492
+ ],
493
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean",
494
+ "full_name": "CategoryTheory.Limits.mulInitial_inv",
495
+ "start": [
496
+ 139,
497
+ 1
498
+ ],
499
+ "traced_tactics": [],
500
+ "url": "https://github.com/leanprover-community/mathlib4"
501
+ },
502
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean"
503
+ },
504
+ {
505
+ "error": "theorem has no selected tactic transitions",
506
+ "full_name": "CategoryTheory.Limits.mulIsInitial_inv",
507
+ "id": "CategoryTheory.Limits.mulIsInitial_inv",
508
+ "reason": "import_failure",
509
+ "selection": {
510
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
511
+ "end": [
512
+ 98,
513
+ 17
514
+ ],
515
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean",
516
+ "full_name": "CategoryTheory.Limits.mulIsInitial_inv",
517
+ "start": [
518
+ 96,
519
+ 1
520
+ ],
521
+ "traced_tactics": [],
522
+ "url": "https://github.com/leanprover-community/mathlib4"
523
+ },
524
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean"
525
+ },
526
+ {
527
+ "error": "theorem has no selected tactic transitions",
528
+ "full_name": "CategoryTheory.Limits.terminal.strict_hom_ext",
529
+ "id": "CategoryTheory.Limits.terminal.strict_hom_ext",
530
+ "reason": "import_failure",
531
+ "selection": {
532
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
533
+ "end": [
534
+ 248,
535
+ 40
536
+ ],
537
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean",
538
+ "full_name": "CategoryTheory.Limits.terminal.strict_hom_ext",
539
+ "start": [
540
+ 247,
541
+ 1
542
+ ],
543
+ "traced_tactics": [],
544
+ "url": "https://github.com/leanprover-community/mathlib4"
545
+ },
546
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean"
547
+ },
548
+ {
549
+ "error": "theorem has no selected tactic transitions",
550
+ "full_name": "CategoryTheory.Limits.terminal.subsingleton_to",
551
+ "id": "CategoryTheory.Limits.terminal.subsingleton_to",
552
+ "reason": "import_failure",
553
+ "selection": {
554
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
555
+ "end": [
556
+ 252,
557
+ 37
558
+ ],
559
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean",
560
+ "full_name": "CategoryTheory.Limits.terminal.subsingleton_to",
561
+ "start": [
562
+ 251,
563
+ 1
564
+ ],
565
+ "traced_tactics": [],
566
+ "url": "https://github.com/leanprover-community/mathlib4"
567
+ },
568
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean"
569
+ }
570
+ ],
571
+ "input_proofs": 18,
572
+ "input_units": 2,
573
+ "proofs": 4,
574
+ "published_proofs": 4,
575
+ "published_transitions": 8,
576
+ "replay_failures": [],
577
+ "transitions": 8,
578
+ "validation_failures": [],
579
+ "validation_rejected_proofs": 0,
580
+ "zero_transition_proofs": 0
581
+ },
582
+ "shards": [
583
+ {
584
+ "path": "data/train/mathlib-000706-0000-0e656eb982a41aa5.parquet",
585
+ "sha256": "0e656eb982a41aa55076d0ec9c91f0976d672f8ebd033b5ff561501234c185da",
586
+ "bytes": 48032,
587
+ "rows": 3,
588
+ "revision": "cbe1482cb65ba353079b280907cc7e0382180ba2"
589
+ },
590
+ {
591
+ "path": "data/internal_test/mathlib-000706-0000-69ef449fe329d10d.parquet",
592
+ "sha256": "69ef449fe329d10d46671b10c4bb9424bee20ca6cff5fe7cc7264c64607052fb",
593
+ "bytes": 51014,
594
+ "rows": 5,
595
+ "revision": "cbe1482cb65ba353079b280907cc7e0382180ba2"
596
+ }
597
+ ],
598
+ "proof_ids": [
599
+ "mathlib:CategoryTheory.Limits.IsInitial.strict_hom_ext",
600
+ "mathlib:CategoryTheory.Limits.IsTerminal.strict_hom_ext",
601
+ "mathlib:CategoryTheory.Limits.hasStrictInitialObjects_of_initial_is_strict",
602
+ "mathlib:CategoryTheory.Limits.hasStrictTerminalObjects_of_terminal_is_strict"
603
+ ],
604
+ "proof_keys": [
605
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean\",null,null,\"CategoryTheory.Limits.IsInitial.strict_hom_ext\"]",
606
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean\",null,null,\"CategoryTheory.Limits.IsTerminal.strict_hom_ext\"]",
607
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean\",null,null,\"CategoryTheory.Limits.hasStrictInitialObjects_of_initial_is_strict\"]",
608
+ "[\"mathlib\",\"29dcec074de168ac2bf835a77ef68bbe069194c5\",\"Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean\",null,null,\"CategoryTheory.Limits.hasStrictTerminalObjects_of_terminal_is_strict\"]"
609
+ ]
610
+ }
manifests/batches/mathlib/000707.json ADDED
@@ -0,0 +1,1296 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "format": "leangpt-parquet-v2",
3
+ "batch": "mathlib/000707",
4
+ "batch_fingerprint": "17995cadeb232962cb97e600205df7a6918682c30ad909236fbb593cdc6065a9",
5
+ "evidence": {
6
+ "batch_fingerprint": "17995cadeb232962cb97e600205df7a6918682c30ad909236fbb593cdc6065a9",
7
+ "contamination_matches": [],
8
+ "failures": [
9
+ {
10
+ "error": "theorem has no selected tactic transitions",
11
+ "full_name": "CategoryTheory.StrongEpi.mk'",
12
+ "id": "CategoryTheory.StrongEpi.mk'",
13
+ "reason": "import_failure",
14
+ "selection": {
15
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
16
+ "end": [
17
+ 62,
18
+ 68
19
+ ],
20
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean",
21
+ "full_name": "CategoryTheory.StrongEpi.mk'",
22
+ "start": [
23
+ 57,
24
+ 1
25
+ ],
26
+ "traced_tactics": [],
27
+ "url": "https://github.com/leanprover-community/mathlib4"
28
+ },
29
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean"
30
+ },
31
+ {
32
+ "error": "theorem has no selected tactic transitions",
33
+ "full_name": "CategoryTheory.StrongMono.mk'",
34
+ "id": "CategoryTheory.StrongMono.mk'",
35
+ "reason": "import_failure",
36
+ "selection": {
37
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
38
+ "end": [
39
+ 78,
40
+ 64
41
+ ],
42
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean",
43
+ "full_name": "CategoryTheory.StrongMono.mk'",
44
+ "start": [
45
+ 74,
46
+ 1
47
+ ],
48
+ "traced_tactics": [],
49
+ "url": "https://github.com/leanprover-community/mathlib4"
50
+ },
51
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean"
52
+ },
53
+ {
54
+ "error": "theorem has no selected tactic transitions",
55
+ "full_name": "CategoryTheory.strongEpi_of_epi",
56
+ "id": "CategoryTheory.strongEpi_of_epi",
57
+ "reason": "import_failure",
58
+ "selection": {
59
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
60
+ "end": [
61
+ 217,
62
+ 39
63
+ ],
64
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean",
65
+ "full_name": "CategoryTheory.strongEpi_of_epi",
66
+ "start": [
67
+ 216,
68
+ 1
69
+ ],
70
+ "traced_tactics": [],
71
+ "url": "https://github.com/leanprover-community/mathlib4"
72
+ },
73
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean"
74
+ },
75
+ {
76
+ "error": "no internal trace for tactic 'simp only [Category.assoc, sq.w]'",
77
+ "full_name": "CategoryTheory.strongEpi_of_strongEpi",
78
+ "id": "CategoryTheory.strongEpi_of_strongEpi",
79
+ "reason": "import_failure",
80
+ "selection": {
81
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
82
+ "end": [
83
+ 123,
84
+ 92
85
+ ],
86
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean",
87
+ "full_name": "CategoryTheory.strongEpi_of_strongEpi",
88
+ "start": [
89
+ 114,
90
+ 1
91
+ ],
92
+ "traced_tactics": [
93
+ {
94
+ "annotated_tactic": [
95
+ "\"constructor\"",
96
+ "[]"
97
+ ],
98
+ "state_after": "case sq_hasLift\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d : StrongEpi (f \u226b g)\nX Y : C\nz : X \u27f6 Y\nx\u271d : Mono z\n\u22a2 \u2200 {f : Q \u27f6 X} {g_1 : R \u27f6 Y} (sq : CommSq f g z g_1), sq.HasLift",
99
+ "state_before": "C : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d : StrongEpi (f \u226b g)\nX Y : C\nz : X \u27f6 Y\nx\u271d : Mono z\n\u22a2 HasLiftingProperty g z",
100
+ "tactic": "constructor"
101
+ },
102
+ {
103
+ "annotated_tactic": [
104
+ "\"intro u v sq\"",
105
+ "[]"
106
+ ],
107
+ "state_after": "case sq_hasLift\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d : StrongEpi (f \u226b g)\nX Y : C\nz : X \u27f6 Y\nx\u271d : Mono z\nu : Q \u27f6 X\nv : R \u27f6 Y\nsq : CommSq u g z v\n\u22a2 sq.HasLift",
108
+ "state_before": "case sq_hasLift\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d : StrongEpi (f \u226b g)\nX Y : C\nz : X \u27f6 Y\nx\u271d : Mono z\n\u22a2 \u2200 {f : Q \u27f6 X} {g_1 : R \u27f6 Y} (sq : CommSq f g z g_1), sq.HasLift",
109
+ "tactic": "intro u v sq"
110
+ },
111
+ {
112
+ "annotated_tactic": [
113
+ "\"have h\\u2080 : (f \\u226b u) \\u226b z = (f \\u226b g) \\u226b v := by simp only [<a>Category.assoc<\\/a>, sq.w]\"",
114
+ "[{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]}]"
115
+ ],
116
+ "state_after": "case sq_hasLift\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d : StrongEpi (f \u226b g)\nX Y : C\nz : X \u27f6 Y\nx\u271d : Mono z\nu : Q \u27f6 X\nv : R \u27f6 Y\nsq : CommSq u g z v\nh\u2080 : (f \u226b u) \u226b z = (f \u226b g) \u226b v\n\u22a2 sq.HasLift",
117
+ "state_before": "case sq_hasLift\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d : StrongEpi (f \u226b g)\nX Y : C\nz : X \u27f6 Y\nx\u271d : Mono z\nu : Q \u27f6 X\nv : R \u27f6 Y\nsq : CommSq u g z v\n\u22a2 sq.HasLift",
118
+ "tactic": "have h\u2080 : (f \u226b u) \u226b z = (f \u226b g) \u226b v := by simp only [Category.assoc, sq.w]"
119
+ },
120
+ {
121
+ "annotated_tactic": [
122
+ "\"exact\\n <a>CommSq.HasLift.mk'<\\/a>\\n \\u27e8(<a>CommSq.mk<\\/a> h\\u2080).<a>lift<\\/a>, by\\n simp only [\\u2190 <a>cancel_mono<\\/a> z, <a>Category.assoc<\\/a>, <a>CommSq.fac_right<\\/a>, sq.w], by simp\\u27e9\"",
123
+ "[{\"full_name\":\"CategoryTheory.CommSq.HasLift.mk'\",\"def_path\":\"Mathlib\\/CategoryTheory\\/CommSq.lean\",\"def_pos\":[235,9],\"def_end_pos\":[235,12]},{\"full_name\":\"CategoryTheory.CommSq.mk\",\"def_path\":\"Mathlib\\/CategoryTheory\\/CommSq.lean\",\"def_pos\":[44,11],\"def_end_pos\":[44,17]},{\"full_name\":\"CategoryTheory.CommSq.lift\",\"def_path\":\"Mathlib\\/CategoryTheory\\/CommSq.lean\",\"def_pos\":[261,19],\"def_end_pos\":[261,23]},{\"full_name\":\"CategoryTheory.cancel_mono\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[310,9],\"def_end_pos\":[310,20]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.CommSq.fac_right\",\"def_path\":\"Mathlib\\/CategoryTheory\\/CommSq.lean\",\"def_pos\":[271,9],\"def_end_pos\":[271,18]}]"
124
+ ],
125
+ "state_after": "no goals",
126
+ "state_before": "case sq_hasLift\nC : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d : StrongEpi (f \u226b g)\nX Y : C\nz : X \u27f6 Y\nx\u271d : Mono z\nu : Q \u27f6 X\nv : R \u27f6 Y\nsq : CommSq u g z v\nh\u2080 : (f \u226b u) \u226b z = (f \u226b g) \u226b v\n\u22a2 sq.HasLift",
127
+ "tactic": "exact\n CommSq.HasLift.mk'\n \u27e8(CommSq.mk h\u2080).lift, by\n simp only [\u2190 cancel_mono z, Category.assoc, CommSq.fac_right, sq.w], by simp\u27e9"
128
+ },
129
+ {
130
+ "annotated_tactic": [
131
+ "\"simp only [<a>Category.assoc<\\/a>, sq.w]\"",
132
+ "[{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]}]"
133
+ ],
134
+ "state_after": "no goals",
135
+ "state_before": "C : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d : StrongEpi (f \u226b g)\nX Y : C\nz : X \u27f6 Y\nx\u271d : Mono z\nu : Q \u27f6 X\nv : R \u27f6 Y\nsq : CommSq u g z v\n\u22a2 (f \u226b u) \u226b z = (f \u226b g) \u226b v",
136
+ "tactic": "simp only [Category.assoc, sq.w]"
137
+ },
138
+ {
139
+ "annotated_tactic": [
140
+ "\"simp only [\\u2190 <a>cancel_mono<\\/a> z, <a>Category.assoc<\\/a>, <a>CommSq.fac_right<\\/a>, sq.w]\"",
141
+ "[{\"full_name\":\"CategoryTheory.cancel_mono\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[310,9],\"def_end_pos\":[310,20]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.CommSq.fac_right\",\"def_path\":\"Mathlib\\/CategoryTheory\\/CommSq.lean\",\"def_pos\":[271,9],\"def_end_pos\":[271,18]}]"
142
+ ],
143
+ "state_after": "no goals",
144
+ "state_before": "C : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d : StrongEpi (f \u226b g)\nX Y : C\nz : X \u27f6 Y\nx\u271d : Mono z\nu : Q \u27f6 X\nv : R \u27f6 Y\nsq : CommSq u g z v\nh\u2080 : (f \u226b u) \u226b z = (f \u226b g) \u226b v\n\u22a2 g \u226b \u22ef.lift = u",
145
+ "tactic": "simp only [\u2190 cancel_mono z, Category.assoc, CommSq.fac_right, sq.w]"
146
+ },
147
+ {
148
+ "annotated_tactic": [
149
+ "\"simp\"",
150
+ "[]"
151
+ ],
152
+ "state_after": "no goals",
153
+ "state_before": "C : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d : StrongEpi (f \u226b g)\nX Y : C\nz : X \u27f6 Y\nx\u271d : Mono z\nu : Q \u27f6 X\nv : R \u27f6 Y\nsq : CommSq u g z v\nh\u2080 : (f \u226b u) \u226b z = (f \u226b g) \u226b v\n\u22a2 \u22ef.lift \u226b z = v",
154
+ "tactic": "simp"
155
+ }
156
+ ],
157
+ "url": "https://github.com/leanprover-community/mathlib4"
158
+ },
159
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean"
160
+ },
161
+ {
162
+ "error": "theorem has no selected tactic transitions",
163
+ "full_name": "CategoryTheory.strongMono_of_mono",
164
+ "id": "CategoryTheory.strongMono_of_mono",
165
+ "reason": "import_failure",
166
+ "selection": {
167
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
168
+ "end": [
169
+ 221,
170
+ 42
171
+ ],
172
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean",
173
+ "full_name": "CategoryTheory.strongMono_of_mono",
174
+ "start": [
175
+ 220,
176
+ 1
177
+ ],
178
+ "traced_tactics": [],
179
+ "url": "https://github.com/leanprover-community/mathlib4"
180
+ },
181
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean"
182
+ },
183
+ {
184
+ "error": "no internal trace for tactic 'rw [\u2190 Category.assoc, eq_whisker sq.w, Category.assoc]'",
185
+ "full_name": "CategoryTheory.strongMono_of_strongMono",
186
+ "id": "CategoryTheory.strongMono_of_strongMono",
187
+ "reason": "import_failure",
188
+ "selection": {
189
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
190
+ "end": [
191
+ 135,
192
+ 96
193
+ ],
194
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean",
195
+ "full_name": "CategoryTheory.strongMono_of_strongMono",
196
+ "start": [
197
+ 127,
198
+ 1
199
+ ],
200
+ "traced_tactics": [
201
+ {
202
+ "annotated_tactic": [
203
+ "\"intros\"",
204
+ "[]"
205
+ ],
206
+ "state_after": "C : Type u\ninst\u271d\u00b2 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d\u00b9 : StrongMono (f \u226b g)\nX Y : C\nz : X \u27f6 Y\ninst\u271d : Epi z\n\u22a2 HasLiftingProperty z f",
207
+ "state_before": "C : Type u\ninst\u271d\u00b9 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d : StrongMono (f \u226b g)\nX Y : C\nz : X \u27f6 Y\n\u22a2 \u2200 [inst : Epi z], HasLiftingProperty z f",
208
+ "tactic": "intros"
209
+ },
210
+ {
211
+ "annotated_tactic": [
212
+ "\"constructor\"",
213
+ "[]"
214
+ ],
215
+ "state_after": "case sq_hasLift\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d\u00b9 : StrongMono (f \u226b g)\nX Y : C\nz : X \u27f6 Y\ninst\u271d : Epi z\n\u22a2 \u2200 {f_1 : X \u27f6 P} {g : Y \u27f6 Q} (sq : CommSq f_1 z f g), sq.HasLift",
216
+ "state_before": "C : Type u\ninst\u271d\u00b2 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d\u00b9 : StrongMono (f \u226b g)\nX Y : C\nz : X \u27f6 Y\ninst\u271d : Epi z\n\u22a2 HasLiftingProperty z f",
217
+ "tactic": "constructor"
218
+ },
219
+ {
220
+ "annotated_tactic": [
221
+ "\"intro u v sq\"",
222
+ "[]"
223
+ ],
224
+ "state_after": "case sq_hasLift\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d\u00b9 : StrongMono (f \u226b g)\nX Y : C\nz : X \u27f6 Y\ninst\u271d : Epi z\nu : X \u27f6 P\nv : Y \u27f6 Q\nsq : CommSq u z f v\n\u22a2 sq.HasLift",
225
+ "state_before": "case sq_hasLift\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d\u00b9 : StrongMono (f \u226b g)\nX Y : C\nz : X \u27f6 Y\ninst\u271d : Epi z\n\u22a2 \u2200 {f_1 : X \u27f6 P} {g : Y \u27f6 Q} (sq : CommSq f_1 z f g), sq.HasLift",
226
+ "tactic": "intro u v sq"
227
+ },
228
+ {
229
+ "annotated_tactic": [
230
+ "\"have h\\u2080 : u \\u226b f \\u226b g = z \\u226b v \\u226b g := by\\n rw [\\u2190 <a>Category.assoc<\\/a>, <a>eq_whisker<\\/a> sq.w, <a>Category.assoc<\\/a>]\"",
231
+ "[{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.eq_whisker\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[213,9],\"def_end_pos\":[213,19]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]}]"
232
+ ],
233
+ "state_after": "case sq_hasLift\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d\u00b9 : StrongMono (f \u226b g)\nX Y : C\nz : X \u27f6 Y\ninst\u271d : Epi z\nu : X \u27f6 P\nv : Y \u27f6 Q\nsq : CommSq u z f v\nh\u2080 : u \u226b f \u226b g = z \u226b v \u226b g\n\u22a2 sq.HasLift",
234
+ "state_before": "case sq_hasLift\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d\u00b9 : StrongMono (f \u226b g)\nX Y : C\nz : X \u27f6 Y\ninst\u271d : Epi z\nu : X \u27f6 P\nv : Y \u27f6 Q\nsq : CommSq u z f v\n\u22a2 sq.HasLift",
235
+ "tactic": "have h\u2080 : u \u226b f \u226b g = z \u226b v \u226b g := by\n rw [\u2190 Category.assoc, eq_whisker sq.w, Category.assoc]"
236
+ },
237
+ {
238
+ "annotated_tactic": [
239
+ "\"exact <a>CommSq.HasLift.mk'<\\/a> \\u27e8(<a>CommSq.mk<\\/a> h\\u2080).<a>lift<\\/a>, by simp, by simp [\\u2190 <a>cancel_epi<\\/a> z, sq.w]\\u27e9\"",
240
+ "[{\"full_name\":\"CategoryTheory.CommSq.HasLift.mk'\",\"def_path\":\"Mathlib\\/CategoryTheory\\/CommSq.lean\",\"def_pos\":[235,9],\"def_end_pos\":[235,12]},{\"full_name\":\"CategoryTheory.CommSq.mk\",\"def_path\":\"Mathlib\\/CategoryTheory\\/CommSq.lean\",\"def_pos\":[44,11],\"def_end_pos\":[44,17]},{\"full_name\":\"CategoryTheory.CommSq.lift\",\"def_path\":\"Mathlib\\/CategoryTheory\\/CommSq.lean\",\"def_pos\":[261,19],\"def_end_pos\":[261,23]},{\"full_name\":\"CategoryTheory.cancel_epi\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[306,9],\"def_end_pos\":[306,19]}]"
241
+ ],
242
+ "state_after": "no goals",
243
+ "state_before": "case sq_hasLift\nC : Type u\ninst\u271d\u00b2 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d\u00b9 : StrongMono (f \u226b g)\nX Y : C\nz : X \u27f6 Y\ninst\u271d : Epi z\nu : X \u27f6 P\nv : Y \u27f6 Q\nsq : CommSq u z f v\nh\u2080 : u \u226b f \u226b g = z \u226b v \u226b g\n\u22a2 sq.HasLift",
244
+ "tactic": "exact CommSq.HasLift.mk' \u27e8(CommSq.mk h\u2080).lift, by simp, by simp [\u2190 cancel_epi z, sq.w]\u27e9"
245
+ },
246
+ {
247
+ "annotated_tactic": [
248
+ "\"rw [\\u2190 <a>Category.assoc<\\/a>, <a>eq_whisker<\\/a> sq.w, <a>Category.assoc<\\/a>]\"",
249
+ "[{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]},{\"full_name\":\"CategoryTheory.eq_whisker\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[213,9],\"def_end_pos\":[213,19]},{\"full_name\":\"CategoryTheory.Category.assoc\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[181,3],\"def_end_pos\":[181,8]}]"
250
+ ],
251
+ "state_after": "no goals",
252
+ "state_before": "C : Type u\ninst\u271d\u00b2 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d\u00b9 : StrongMono (f \u226b g)\nX Y : C\nz : X \u27f6 Y\ninst\u271d : Epi z\nu : X \u27f6 P\nv : Y \u27f6 Q\nsq : CommSq u z f v\n\u22a2 u \u226b f \u226b g = z \u226b v \u226b g",
253
+ "tactic": "rw [\u2190 Category.assoc, eq_whisker sq.w, Category.assoc]"
254
+ },
255
+ {
256
+ "annotated_tactic": [
257
+ "\"simp\"",
258
+ "[]"
259
+ ],
260
+ "state_after": "no goals",
261
+ "state_before": "C : Type u\ninst\u271d\u00b2 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d\u00b9 : StrongMono (f \u226b g)\nX Y : C\nz : X \u27f6 Y\ninst\u271d : Epi z\nu : X \u27f6 P\nv : Y \u27f6 Q\nsq : CommSq u z f v\nh\u2080 : u \u226b f \u226b g = z \u226b v \u226b g\n\u22a2 z \u226b \u22ef.lift = u",
262
+ "tactic": "simp"
263
+ },
264
+ {
265
+ "annotated_tactic": [
266
+ "\"simp [\\u2190 <a>cancel_epi<\\/a> z, sq.w]\"",
267
+ "[{\"full_name\":\"CategoryTheory.cancel_epi\",\"def_path\":\"Mathlib\\/CategoryTheory\\/Category\\/Basic.lean\",\"def_pos\":[306,9],\"def_end_pos\":[306,19]}]"
268
+ ],
269
+ "state_after": "no goals",
270
+ "state_before": "C : Type u\ninst\u271d\u00b2 : Category.{v, u} C\nP Q R : C\nf : P \u27f6 Q\ng : Q \u27f6 R\ninst\u271d\u00b9 : StrongMono (f \u226b g)\nX Y : C\nz : X \u27f6 Y\ninst\u271d : Epi z\nu : X \u27f6 P\nv : Y \u27f6 Q\nsq : CommSq u z f v\nh\u2080 : u \u226b f \u226b g = z \u226b v \u226b g\n\u22a2 \u22ef.lift \u226b f = v",
271
+ "tactic": "simp [\u2190 cancel_epi z, sq.w]"
272
+ }
273
+ ],
274
+ "url": "https://github.com/leanprover-community/mathlib4"
275
+ },
276
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean"
277
+ },
278
+ {
279
+ "error": "theorem has no selected tactic transitions",
280
+ "full_name": "CategoryTheory.Limits.InitialMonoClass.of_initial",
281
+ "id": "CategoryTheory.Limits.InitialMonoClass.of_initial",
282
+ "reason": "import_failure",
283
+ "selection": {
284
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
285
+ "end": [
286
+ 564,
287
+ 51
288
+ ],
289
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean",
290
+ "full_name": "CategoryTheory.Limits.InitialMonoClass.of_initial",
291
+ "start": [
292
+ 562,
293
+ 1
294
+ ],
295
+ "traced_tactics": [],
296
+ "url": "https://github.com/leanprover-community/mathlib4"
297
+ },
298
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean"
299
+ },
300
+ {
301
+ "error": "theorem has no selected tactic transitions",
302
+ "full_name": "CategoryTheory.Limits.InitialMonoClass.of_isTerminal",
303
+ "id": "CategoryTheory.Limits.InitialMonoClass.of_isTerminal",
304
+ "reason": "import_failure",
305
+ "selection": {
306
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
307
+ "end": [
308
+ 571,
309
+ 100
310
+ ],
311
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean",
312
+ "full_name": "CategoryTheory.Limits.InitialMonoClass.of_isTerminal",
313
+ "start": [
314
+ 569,
315
+ 1
316
+ ],
317
+ "traced_tactics": [],
318
+ "url": "https://github.com/leanprover-community/mathlib4"
319
+ },
320
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean"
321
+ },
322
+ {
323
+ "error": "theorem has no selected tactic transitions",
324
+ "full_name": "CategoryTheory.Limits.InitialMonoClass.of_terminal",
325
+ "id": "CategoryTheory.Limits.InitialMonoClass.of_terminal",
326
+ "reason": "import_failure",
327
+ "selection": {
328
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
329
+ "end": [
330
+ 578,
331
+ 71
332
+ ],
333
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean",
334
+ "full_name": "CategoryTheory.Limits.InitialMonoClass.of_terminal",
335
+ "start": [
336
+ 576,
337
+ 1
338
+ ],
339
+ "traced_tactics": [],
340
+ "url": "https://github.com/leanprover-community/mathlib4"
341
+ },
342
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean"
343
+ },
344
+ {
345
+ "error": "no internal trace for tactic 'aesop_cat'",
346
+ "full_name": "CategoryTheory.Limits.IsInitial.hasInitial",
347
+ "id": "CategoryTheory.Limits.IsInitial.hasInitial",
348
+ "reason": "import_failure",
349
+ "selection": {
350
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
351
+ "end": [
352
+ 366,
353
+ 99
354
+ ],
355
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean",
356
+ "full_name": "CategoryTheory.Limits.IsInitial.hasInitial",
357
+ "start": [
358
+ 364,
359
+ 1
360
+ ],
361
+ "traced_tactics": [
362
+ {
363
+ "annotated_tactic": [
364
+ "\"aesop_cat\"",
365
+ "[]"
366
+ ],
367
+ "state_after": "no goals",
368
+ "state_before": "C : Type u\u2081\ninst\u271d : Category.{v\u2081, u\u2081} C\nX : C\nh : IsInitial X\nF : Discrete PEmpty.{1} \u2964 C\n\u22a2 (X_1 : Discrete PEmpty.{1}) \u2192 F.obj X_1 \u27f6 ((Functor.const (Discrete PEmpty.{1})).obj X).obj X_1",
369
+ "tactic": "aesop_cat"
370
+ },
371
+ {
372
+ "annotated_tactic": [
373
+ "\"aesop_cat\"",
374
+ "[]"
375
+ ],
376
+ "state_after": "no goals",
377
+ "state_before": "C : Type u\u2081\ninst\u271d : Category.{v\u2081, u\u2081} C\nX : C\nh : IsInitial X\nF : Discrete PEmpty.{1} \u2964 C\n\u22a2 \u2200 \u2983X_1 Y : Discrete PEmpty.{1}\u2984 (f : X_1 \u27f6 Y),\n F.map f \u226b id (Discrete.casesOn Y fun as => \u22ef.elim) =\n id (Discrete.casesOn X_1 fun as => \u22ef.elim) \u226b ((Functor.const (Discrete PEmpty.{1})).obj X).map f",
378
+ "tactic": "aesop_cat"
379
+ }
380
+ ],
381
+ "url": "https://github.com/leanprover-community/mathlib4"
382
+ },
383
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean"
384
+ },
385
+ {
386
+ "error": "theorem has no selected tactic transitions",
387
+ "full_name": "CategoryTheory.Limits.IsInitial.isSplitEpi_to",
388
+ "id": "CategoryTheory.Limits.IsInitial.isSplitEpi_to",
389
+ "reason": "import_failure",
390
+ "selection": {
391
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
392
+ "end": [
393
+ 204,
394
+ 41
395
+ ],
396
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean",
397
+ "full_name": "CategoryTheory.Limits.IsInitial.isSplitEpi_to",
398
+ "start": [
399
+ 203,
400
+ 1
401
+ ],
402
+ "traced_tactics": [],
403
+ "url": "https://github.com/leanprover-community/mathlib4"
404
+ },
405
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean"
406
+ },
407
+ {
408
+ "error": "theorem has no selected tactic transitions",
409
+ "full_name": "CategoryTheory.Limits.IsInitial.to_comp",
410
+ "id": "CategoryTheory.Limits.IsInitial.to_comp",
411
+ "reason": "import_failure",
412
+ "selection": {
413
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
414
+ "end": [
415
+ 189,
416
+ 16
417
+ ],
418
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean",
419
+ "full_name": "CategoryTheory.Limits.IsInitial.to_comp",
420
+ "start": [
421
+ 188,
422
+ 1
423
+ ],
424
+ "traced_tactics": [],
425
+ "url": "https://github.com/leanprover-community/mathlib4"
426
+ },
427
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean"
428
+ },
429
+ {
430
+ "error": "theorem has no selected tactic transitions",
431
+ "full_name": "CategoryTheory.Limits.IsInitial.to_self",
432
+ "id": "CategoryTheory.Limits.IsInitial.to_self",
433
+ "reason": "import_failure",
434
+ "selection": {
435
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
436
+ "end": [
437
+ 194,
438
+ 16
439
+ ],
440
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean",
441
+ "full_name": "CategoryTheory.Limits.IsInitial.to_self",
442
+ "start": [
443
+ 193,
444
+ 1
445
+ ],
446
+ "traced_tactics": [],
447
+ "url": "https://github.com/leanprover-community/mathlib4"
448
+ },
449
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean"
450
+ },
451
+ {
452
+ "error": "theorem has no selected tactic transitions",
453
+ "full_name": "CategoryTheory.Limits.IsTerminal.comp_from",
454
+ "id": "CategoryTheory.Limits.IsTerminal.comp_from",
455
+ "reason": "import_failure",
456
+ "selection": {
457
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
458
+ "end": [
459
+ 169,
460
+ 16
461
+ ],
462
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean",
463
+ "full_name": "CategoryTheory.Limits.IsTerminal.comp_from",
464
+ "start": [
465
+ 167,
466
+ 1
467
+ ],
468
+ "traced_tactics": [],
469
+ "url": "https://github.com/leanprover-community/mathlib4"
470
+ },
471
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean"
472
+ },
473
+ {
474
+ "error": "theorem has no selected tactic transitions",
475
+ "full_name": "CategoryTheory.Limits.IsTerminal.from_self",
476
+ "id": "CategoryTheory.Limits.IsTerminal.from_self",
477
+ "reason": "import_failure",
478
+ "selection": {
479
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
480
+ "end": [
481
+ 174,
482
+ 16
483
+ ],
484
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean",
485
+ "full_name": "CategoryTheory.Limits.IsTerminal.from_self",
486
+ "start": [
487
+ 173,
488
+ 1
489
+ ],
490
+ "traced_tactics": [],
491
+ "url": "https://github.com/leanprover-community/mathlib4"
492
+ },
493
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean"
494
+ },
495
+ {
496
+ "error": "no internal trace for tactic 'aesop_cat'",
497
+ "full_name": "CategoryTheory.Limits.IsTerminal.hasTerminal",
498
+ "id": "CategoryTheory.Limits.IsTerminal.hasTerminal",
499
+ "reason": "import_failure",
500
+ "selection": {
501
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
502
+ "end": [
503
+ 355,
504
+ 49
505
+ ],
506
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean",
507
+ "full_name": "CategoryTheory.Limits.IsTerminal.hasTerminal",
508
+ "start": [
509
+ 353,
510
+ 1
511
+ ],
512
+ "traced_tactics": [
513
+ {
514
+ "annotated_tactic": [
515
+ "\"aesop_cat\"",
516
+ "[]"
517
+ ],
518
+ "state_after": "no goals",
519
+ "state_before": "C : Type u\u2081\ninst\u271d : Category.{v\u2081, u\u2081} C\nX : C\nh : IsTerminal X\nF : Discrete PEmpty.{1} \u2964 C\n\u22a2 (X_1 : Discrete PEmpty.{1}) \u2192 ((Functor.const (Discrete PEmpty.{1})).obj X).obj X_1 \u27f6 F.obj X_1",
520
+ "tactic": "aesop_cat"
521
+ },
522
+ {
523
+ "annotated_tactic": [
524
+ "\"aesop_cat\"",
525
+ "[]"
526
+ ],
527
+ "state_after": "no goals",
528
+ "state_before": "C : Type u\u2081\ninst\u271d : Category.{v\u2081, u\u2081} C\nX : C\nh : IsTerminal X\nF : Discrete PEmpty.{1} \u2964 C\n\u22a2 \u2200 \u2983X_1 Y : Discrete PEmpty.{1}\u2984 (f : X_1 \u27f6 Y),\n ((Functor.const (Discrete PEmpty.{1})).obj X).map f \u226b id (Discrete.casesOn Y fun as => \u22ef.elim) =\n id (Discrete.casesOn X_1 fun as => \u22ef.elim) \u226b F.map f",
529
+ "tactic": "aesop_cat"
530
+ }
531
+ ],
532
+ "url": "https://github.com/leanprover-community/mathlib4"
533
+ },
534
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean"
535
+ },
536
+ {
537
+ "error": "theorem has no selected tactic transitions",
538
+ "full_name": "CategoryTheory.Limits.IsTerminal.isSplitMono_from",
539
+ "id": "CategoryTheory.Limits.IsTerminal.isSplitMono_from",
540
+ "reason": "import_failure",
541
+ "selection": {
542
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
543
+ "end": [
544
+ 199,
545
+ 44
546
+ ],
547
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean",
548
+ "full_name": "CategoryTheory.Limits.IsTerminal.isSplitMono_from",
549
+ "start": [
550
+ 198,
551
+ 1
552
+ ],
553
+ "traced_tactics": [],
554
+ "url": "https://github.com/leanprover-community/mathlib4"
555
+ },
556
+ "source_file": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean"
557
+ },
558
+ {
559
+ "error": "no internal trace for tactic 'aesop_cat'",
560
+ "full_name": "CategoryTheory.Limits.hasInitialChangeDiagram",
561
+ "id": "CategoryTheory.Limits.hasInitialChangeDiagram",
562
+ "reason": "import_failure",
563
+ "selection": {
564
+ "commit": "29dcec074de168ac2bf835a77ef68bbe069194c5",
565
+ "end": [
566
+ 311,
567
+ 75
568
+ ],
569
+ "file_path": "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean",
570
+ "full_name": "CategoryTheory.Limits.hasInitialChangeDiagram",
571
+ "start": [
572
+ 309,
573
+ 1
574
+ ],
575
+ "traced_tactics": [
576
+ {
577
+ "annotated_tactic": [
578
+ "\"aesop_cat\"",
579
+ "[]"
580
+ ],
581
+ "state_after": "no goals",
582
+ "state_before": "C : Type u\u2081\ninst\u271d : Category.{v\u2081, u\u2081} C\nX : C\nF\u2081 : Discrete PEmpty.{w + 1} \u2964 C\nF\u2082 : Discrete PEmpty.{w' + 1} \u2964 C\nh : HasColimit F\u2081\n\u22a2 (X : Discrete PEmpty.{w' + 1}) \u2192 F\u2082.obj X \u27f6 ((Functor.const (Discrete PEmpty.{w' + 1})).obj (colimit F\u2081)).obj X",
583
+ "tactic": "aesop_cat"
584
+ },
585
+ {
586
+ "annotated_tactic": [
587
+ "\"aesop_cat\"",
588
+ "[]"
589
+ ],
590
+ "state_after": "no goals",
591
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618
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620
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622
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642
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643
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644
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662
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663
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665
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666
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667
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687
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703
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704
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705
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706
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707
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724
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727
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728
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729
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730
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744
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745
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746
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747
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748
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749
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750
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751
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752
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753
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754
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760
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761
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762
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763
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765
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766
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767
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768
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769
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770
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771
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772
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773
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774
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775
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776
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777
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778
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784
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785
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788
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789
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790
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791
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792
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793
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794
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795
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797
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798
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799
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800
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801
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802
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803
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804
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806
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807
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808
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809
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810
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815
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816
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818
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819
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825
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830
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832
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833
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838
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841
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842
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843
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844
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846
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847
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848
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849
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850
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851
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852
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854
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861
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866
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867
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870
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871
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873
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874
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875
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876
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877
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878
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879
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882
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883
+ "tactic": "ext"
884
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885
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886
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887
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888
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889
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890
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