OAI/Analysis/NuclearUltrapower/SOSCertificate.lean

GitHub source file

369 declarations, 0 contain sorry, 0 declared as axioms

  1. def OAI.NuclearUltrapower.SL3Certificate.q0 line 10
  2. def OAI.NuclearUltrapower.SL3Certificate.q1 line 11
  3. def OAI.NuclearUltrapower.SL3Certificate.q2 line 12
  4. def OAI.NuclearUltrapower.SL3Certificate.q3 line 13
  5. def OAI.NuclearUltrapower.SL3Certificate.q4 line 14
  6. def OAI.NuclearUltrapower.SL3Certificate.q5 line 15
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  9. def OAI.NuclearUltrapower.SL3Certificate.q8 line 18
  10. def OAI.NuclearUltrapower.SL3Certificate.q9 line 19
  11. def OAI.NuclearUltrapower.SL3Certificate.q10 line 20
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  13. def OAI.NuclearUltrapower.SL3Certificate.q12 line 22
  14. def OAI.NuclearUltrapower.SL3Certificate.q13 line 23
  15. def OAI.NuclearUltrapower.SL3Certificate.q14 line 24
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  21. def OAI.NuclearUltrapower.SL3Certificate.q20 line 30
  22. def OAI.NuclearUltrapower.SL3Certificate.q21 line 31
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  32. def OAI.NuclearUltrapower.SL3Certificate.q31 line 41
  33. def OAI.NuclearUltrapower.SL3Certificate.q32 line 42
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  40. def OAI.NuclearUltrapower.SL3Certificate.q39 line 49
  41. def OAI.NuclearUltrapower.SL3Certificate.q40 line 50
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  51. def OAI.NuclearUltrapower.SL3Certificate.q50 line 60
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  60. def OAI.NuclearUltrapower.SL3Certificate.q59 line 69
  61. def OAI.NuclearUltrapower.SL3Certificate.q60 line 70
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  67. def OAI.NuclearUltrapower.SL3Certificate.q66 line 76
  68. def OAI.NuclearUltrapower.SL3Certificate.q67 line 77
  69. def OAI.NuclearUltrapower.SL3Certificate.q68 line 78
  70. def OAI.NuclearUltrapower.SL3Certificate.q69 line 79
  71. def OAI.NuclearUltrapower.SL3Certificate.q70 line 80
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  113. def OAI.NuclearUltrapower.SL3Certificate.q112 line 122
  114. def OAI.NuclearUltrapower.SL3Certificate.q113 line 123
  115. def OAI.NuclearUltrapower.SL3Certificate.q114 line 124
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  121. def OAI.NuclearUltrapower.SL3Certificate.q120 line 130
  122. def OAI.NuclearUltrapower.SL3Certificate.columns line 131
  123. def OAI.NuclearUltrapower.SL3Certificate.g0 line 132
  124. def OAI.NuclearUltrapower.SL3Certificate.g1 line 133
  125. def OAI.NuclearUltrapower.SL3Certificate.g2 line 134
  126. def OAI.NuclearUltrapower.SL3Certificate.g3 line 135
  127. def OAI.NuclearUltrapower.SL3Certificate.g4 line 136
  128. def OAI.NuclearUltrapower.SL3Certificate.g5 line 137
  129. def OAI.NuclearUltrapower.SL3Certificate.g6 line 138
  130. def OAI.NuclearUltrapower.SL3Certificate.g7 line 139
  131. def OAI.NuclearUltrapower.SL3Certificate.g8 line 140
  132. def OAI.NuclearUltrapower.SL3Certificate.g9 line 141
  133. def OAI.NuclearUltrapower.SL3Certificate.g10 line 142
  134. def OAI.NuclearUltrapower.SL3Certificate.g11 line 143
  135. def OAI.NuclearUltrapower.SL3Certificate.g12 line 144
  136. def OAI.NuclearUltrapower.SL3Certificate.g13 line 145
  137. def OAI.NuclearUltrapower.SL3Certificate.g14 line 146
  138. def OAI.NuclearUltrapower.SL3Certificate.g15 line 147
  139. def OAI.NuclearUltrapower.SL3Certificate.g16 line 148
  140. def OAI.NuclearUltrapower.SL3Certificate.g17 line 149
  141. def OAI.NuclearUltrapower.SL3Certificate.g18 line 150
  142. def OAI.NuclearUltrapower.SL3Certificate.g19 line 151
  143. def OAI.NuclearUltrapower.SL3Certificate.g20 line 152
  144. def OAI.NuclearUltrapower.SL3Certificate.g21 line 153
  145. def OAI.NuclearUltrapower.SL3Certificate.g22 line 154
  146. def OAI.NuclearUltrapower.SL3Certificate.g23 line 155
  147. def OAI.NuclearUltrapower.SL3Certificate.g24 line 156
  148. def OAI.NuclearUltrapower.SL3Certificate.g25 line 157
  149. def OAI.NuclearUltrapower.SL3Certificate.g26 line 158
  150. def OAI.NuclearUltrapower.SL3Certificate.g27 line 159
  151. def OAI.NuclearUltrapower.SL3Certificate.g28 line 160
  152. def OAI.NuclearUltrapower.SL3Certificate.g29 line 161
  153. def OAI.NuclearUltrapower.SL3Certificate.g30 line 162
  154. def OAI.NuclearUltrapower.SL3Certificate.g31 line 163
  155. def OAI.NuclearUltrapower.SL3Certificate.g32 line 164
  156. def OAI.NuclearUltrapower.SL3Certificate.g33 line 165
  157. def OAI.NuclearUltrapower.SL3Certificate.g34 line 166
  158. def OAI.NuclearUltrapower.SL3Certificate.g35 line 167
  159. def OAI.NuclearUltrapower.SL3Certificate.g36 line 168
  160. def OAI.NuclearUltrapower.SL3Certificate.g37 line 169
  161. def OAI.NuclearUltrapower.SL3Certificate.g38 line 170
  162. def OAI.NuclearUltrapower.SL3Certificate.g39 line 171
  163. def OAI.NuclearUltrapower.SL3Certificate.g40 line 172
  164. def OAI.NuclearUltrapower.SL3Certificate.g41 line 173
  165. def OAI.NuclearUltrapower.SL3Certificate.g42 line 174
  166. def OAI.NuclearUltrapower.SL3Certificate.g43 line 175
  167. def OAI.NuclearUltrapower.SL3Certificate.g44 line 176
  168. def OAI.NuclearUltrapower.SL3Certificate.g45 line 177
  169. def OAI.NuclearUltrapower.SL3Certificate.g46 line 178
  170. def OAI.NuclearUltrapower.SL3Certificate.g47 line 179
  171. def OAI.NuclearUltrapower.SL3Certificate.g48 line 180
  172. def OAI.NuclearUltrapower.SL3Certificate.g49 line 181
  173. def OAI.NuclearUltrapower.SL3Certificate.g50 line 182
  174. def OAI.NuclearUltrapower.SL3Certificate.g51 line 183
  175. def OAI.NuclearUltrapower.SL3Certificate.g52 line 184
  176. def OAI.NuclearUltrapower.SL3Certificate.g53 line 185
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  178. def OAI.NuclearUltrapower.SL3Certificate.g55 line 187
  179. def OAI.NuclearUltrapower.SL3Certificate.g56 line 188
  180. def OAI.NuclearUltrapower.SL3Certificate.g57 line 189
  181. def OAI.NuclearUltrapower.SL3Certificate.g58 line 190
  182. def OAI.NuclearUltrapower.SL3Certificate.g59 line 191
  183. def OAI.NuclearUltrapower.SL3Certificate.g60 line 192
  184. def OAI.NuclearUltrapower.SL3Certificate.g61 line 193
  185. def OAI.NuclearUltrapower.SL3Certificate.g62 line 194
  186. def OAI.NuclearUltrapower.SL3Certificate.g63 line 195
  187. def OAI.NuclearUltrapower.SL3Certificate.g64 line 196
  188. def OAI.NuclearUltrapower.SL3Certificate.g65 line 197
  189. def OAI.NuclearUltrapower.SL3Certificate.g66 line 198
  190. def OAI.NuclearUltrapower.SL3Certificate.g67 line 199
  191. def OAI.NuclearUltrapower.SL3Certificate.g68 line 200
  192. def OAI.NuclearUltrapower.SL3Certificate.g69 line 201
  193. def OAI.NuclearUltrapower.SL3Certificate.g70 line 202
  194. def OAI.NuclearUltrapower.SL3Certificate.g71 line 203
  195. def OAI.NuclearUltrapower.SL3Certificate.g72 line 204
  196. def OAI.NuclearUltrapower.SL3Certificate.g73 line 205
  197. def OAI.NuclearUltrapower.SL3Certificate.g74 line 206
  198. def OAI.NuclearUltrapower.SL3Certificate.g75 line 207
  199. def OAI.NuclearUltrapower.SL3Certificate.g76 line 208
  200. def OAI.NuclearUltrapower.SL3Certificate.g77 line 209
  201. def OAI.NuclearUltrapower.SL3Certificate.g78 line 210
  202. def OAI.NuclearUltrapower.SL3Certificate.g79 line 211
  203. def OAI.NuclearUltrapower.SL3Certificate.g80 line 212
  204. def OAI.NuclearUltrapower.SL3Certificate.g81 line 213
  205. def OAI.NuclearUltrapower.SL3Certificate.g82 line 214
  206. def OAI.NuclearUltrapower.SL3Certificate.g83 line 215
  207. def OAI.NuclearUltrapower.SL3Certificate.g84 line 216
  208. def OAI.NuclearUltrapower.SL3Certificate.g85 line 217
  209. def OAI.NuclearUltrapower.SL3Certificate.g86 line 218
  210. def OAI.NuclearUltrapower.SL3Certificate.g87 line 219
  211. def OAI.NuclearUltrapower.SL3Certificate.g88 line 220
  212. def OAI.NuclearUltrapower.SL3Certificate.g89 line 221
  213. def OAI.NuclearUltrapower.SL3Certificate.g90 line 222
  214. def OAI.NuclearUltrapower.SL3Certificate.g91 line 223
  215. def OAI.NuclearUltrapower.SL3Certificate.g92 line 224
  216. def OAI.NuclearUltrapower.SL3Certificate.g93 line 225
  217. def OAI.NuclearUltrapower.SL3Certificate.g94 line 226
  218. def OAI.NuclearUltrapower.SL3Certificate.g95 line 227
  219. def OAI.NuclearUltrapower.SL3Certificate.g96 line 228
  220. def OAI.NuclearUltrapower.SL3Certificate.g97 line 229
  221. def OAI.NuclearUltrapower.SL3Certificate.g98 line 230
  222. def OAI.NuclearUltrapower.SL3Certificate.g99 line 231
  223. def OAI.NuclearUltrapower.SL3Certificate.g100 line 232
  224. def OAI.NuclearUltrapower.SL3Certificate.g101 line 233
  225. def OAI.NuclearUltrapower.SL3Certificate.g102 line 234
  226. def OAI.NuclearUltrapower.SL3Certificate.g103 line 235
  227. def OAI.NuclearUltrapower.SL3Certificate.g104 line 236
  228. def OAI.NuclearUltrapower.SL3Certificate.g105 line 237
  229. def OAI.NuclearUltrapower.SL3Certificate.g106 line 238
  230. def OAI.NuclearUltrapower.SL3Certificate.g107 line 239
  231. def OAI.NuclearUltrapower.SL3Certificate.g108 line 240
  232. def OAI.NuclearUltrapower.SL3Certificate.g109 line 241
  233. def OAI.NuclearUltrapower.SL3Certificate.g110 line 242
  234. def OAI.NuclearUltrapower.SL3Certificate.g111 line 243
  235. def OAI.NuclearUltrapower.SL3Certificate.g112 line 244
  236. def OAI.NuclearUltrapower.SL3Certificate.g113 line 245
  237. def OAI.NuclearUltrapower.SL3Certificate.g114 line 246
  238. def OAI.NuclearUltrapower.SL3Certificate.g115 line 247
  239. def OAI.NuclearUltrapower.SL3Certificate.g116 line 248
  240. def OAI.NuclearUltrapower.SL3Certificate.g117 line 249
  241. def OAI.NuclearUltrapower.SL3Certificate.g118 line 250
  242. def OAI.NuclearUltrapower.SL3Certificate.g119 line 251
  243. def OAI.NuclearUltrapower.SL3Certificate.g120 line 252
  244. def OAI.NuclearUltrapower.SL3Certificate.gram line 253
  245. def OAI.NuclearUltrapower.SL3Certificate.dot line 254
  246. def OAI.NuclearUltrapower.SL3Certificate.addVec line 258
  247. def OAI.NuclearUltrapower.SL3Certificate.sumVec line 263
  248. theorem OAI.NuclearUltrapower.SL3Certificate.augmentation line 267
  249. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_0 line 268
  250. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_1 line 269
  251. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_2 line 270
  252. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_3 line 271
  253. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_4 line 272
  254. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_5 line 273
  255. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_6 line 274
  256. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_7 line 275
  257. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_8 line 276
  258. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_9 line 277
  259. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_10 line 278
  260. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_11 line 279
  261. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_12 line 280
  262. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_13 line 281
  263. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_14 line 282
  264. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_15 line 283
  265. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_16 line 284
  266. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_17 line 285
  267. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_18 line 286
  268. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_19 line 287
  269. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_20 line 288
  270. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_21 line 289
  271. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_22 line 290
  272. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_23 line 291
  273. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_24 line 292
  274. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_25 line 293
  275. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_26 line 294
  276. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_27 line 295
  277. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_28 line 296
  278. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_29 line 297
  279. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_30 line 298
  280. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_31 line 299
  281. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_32 line 300
  282. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_33 line 301
  283. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_34 line 302
  284. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_35 line 303
  285. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_36 line 304
  286. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_37 line 305
  287. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_38 line 306
  288. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_39 line 307
  289. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_40 line 308
  290. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_41 line 309
  291. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_42 line 310
  292. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_43 line 311
  293. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_44 line 312
  294. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_45 line 313
  295. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_46 line 314
  296. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_47 line 315
  297. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_48 line 316
  298. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_49 line 317
  299. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_50 line 318
  300. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_51 line 319
  301. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_52 line 320
  302. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_53 line 321
  303. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_54 line 322
  304. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_55 line 323
  305. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_56 line 324
  306. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_57 line 325
  307. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_58 line 326
  308. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_59 line 327
  309. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_60 line 328
  310. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_61 line 329
  311. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_62 line 330
  312. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_63 line 331
  313. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_64 line 332
  314. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_65 line 333
  315. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_66 line 334
  316. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_67 line 335
  317. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_68 line 336
  318. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_69 line 337
  319. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_70 line 338
  320. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_71 line 339
  321. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_72 line 340
  322. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_73 line 341
  323. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_74 line 342
  324. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_75 line 343
  325. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_76 line 344
  326. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_77 line 345
  327. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_78 line 346
  328. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_79 line 347
  329. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_80 line 348
  330. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_81 line 349
  331. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_82 line 350
  332. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_83 line 351
  333. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_84 line 352
  334. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_85 line 353
  335. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_86 line 354
  336. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_87 line 355
  337. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_88 line 356
  338. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_89 line 357
  339. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_90 line 358
  340. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_91 line 359
  341. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_92 line 360
  342. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_93 line 361
  343. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_94 line 362
  344. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_95 line 363
  345. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_96 line 364
  346. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_97 line 365
  347. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_98 line 366
  348. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_99 line 367
  349. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_100 line 368
  350. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_101 line 369
  351. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_102 line 370
  352. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_103 line 371
  353. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_104 line 372
  354. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_105 line 373
  355. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_106 line 374
  356. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_107 line 375
  357. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_108 line 376
  358. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_109 line 377
  359. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_110 line 378
  360. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_111 line 379
  361. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_112 line 380
  362. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_113 line 381
  363. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_114 line 382
  364. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_115 line 383
  365. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_116 line 384
  366. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_117 line 385
  367. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_118 line 386
  368. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_119 line 387
  369. theorem OAI.NuclearUltrapower.SL3Certificate.gram_row_120 line 388