Upload 19 files
Browse files- .gitattributes +6 -0
- novel_premises/test.json +3 -0
- novel_premises/test_formal_informal.json +0 -0
- novel_premises/test_formal_informal_metadata.json +712 -0
- novel_premises/train.json +3 -0
- novel_premises/train_formal_informal.json +3 -0
- novel_premises/train_formal_informal_metadata.json +0 -0
- novel_premises/val.json +3 -0
- novel_premises/val_formal_informal.json +0 -0
- novel_premises/val_formal_informal_metadata.json +663 -0
- random/test.json +0 -0
- random/test_formal_informal.json +0 -0
- random/test_formal_informal_metadata.json +1022 -0
- random/train.json +3 -0
- random/train_formal_informal.json +3 -0
- random/train_formal_informal_metadata.json +0 -0
- random/val.json +0 -0
- random/val_formal_informal.json +0 -0
- random/val_formal_informal_metadata.json +987 -0
- test-example.json +0 -0
.gitattributes
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@@ -53,3 +53,9 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
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*.jpg filter=lfs diff=lfs merge=lfs -text
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*.jpeg filter=lfs diff=lfs merge=lfs -text
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*.jpg filter=lfs diff=lfs merge=lfs -text
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*.jpeg filter=lfs diff=lfs merge=lfs -text
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*.webp filter=lfs diff=lfs merge=lfs -text
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novel_premises/test.json filter=lfs diff=lfs merge=lfs -text
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novel_premises/train_formal_informal.json filter=lfs diff=lfs merge=lfs -text
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novel_premises/train.json filter=lfs diff=lfs merge=lfs -text
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novel_premises/val.json filter=lfs diff=lfs merge=lfs -text
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random/train_formal_informal.json filter=lfs diff=lfs merge=lfs -text
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random/train.json filter=lfs diff=lfs merge=lfs -text
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novel_premises/test.json
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version https://git-lfs.github.com/spec/v1
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oid sha256:6082dcb54d04990051bd4c959a434ecd2b168f937352fbdb60bd094a86867d58
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size 17025440
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novel_premises/test_formal_informal.json
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novel_premises/test_formal_informal_metadata.json
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{
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"total_valid_proofs": 2000,
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114 |
+
"Set.mapsTo_prod_map_diagonal",
|
115 |
+
"Set.image_mulSingle_Icc_left",
|
116 |
+
"MeasureTheory.Measure.FiniteSpanningSetsIn.ext",
|
117 |
+
"MeasureTheory.Integrable.comp_div",
|
118 |
+
"Real.volume_pi_le_prod_diam",
|
119 |
+
"MeasureTheory.mem_disjointed_spanningSetsIndex",
|
120 |
+
"Set.EqOn.piecewise_ite",
|
121 |
+
"Set.isUnit_singleton",
|
122 |
+
"Finmap.mem_union",
|
123 |
+
"Finset.sup_himp_right",
|
124 |
+
"Finset.max_mem_insert_bot_image_coe",
|
125 |
+
"Finset.inf'_const",
|
126 |
+
"Rel.image_core_gc",
|
127 |
+
"Finset.inf'_sup_inf'",
|
128 |
+
"Finset.nontrivial_iff_ne_singleton",
|
129 |
+
"Array.SatisfiesM_mapM'",
|
130 |
+
"Primrec.nat_double_succ",
|
131 |
+
"ContinuousOn.integral_sub_linear_isLittleO_ae",
|
132 |
+
"MeasureTheory.pdf.integral_mul_eq_integral",
|
133 |
+
"MeasureTheory.withDensity\u1d65_sub'",
|
134 |
+
"Int.neg_lt_sub_right_of_lt_add",
|
135 |
+
"Int.emod_lt_of_pos",
|
136 |
+
"MeasureTheory.snorm'_eq_zero_iff",
|
137 |
+
"MeasureTheory.snorm_congr_norm_ae",
|
138 |
+
"Set.nontrivial_of_exists_lt",
|
139 |
+
"Setoid.isPartition_classes",
|
140 |
+
"Option.some_orElse'",
|
141 |
+
"MvPolynomial.map_rightInverse",
|
142 |
+
"Finset.piecewise_mem_Icc_of_mem_of_mem",
|
143 |
+
"RegularExpression.one_def",
|
144 |
+
"ZMod.cast_pow'",
|
145 |
+
"MeasurableSpace.monotone_comap",
|
146 |
+
"MeasureTheory.Measure.snd_map_prod_mk",
|
147 |
+
"Primrec.list_reverse",
|
148 |
+
"ManyOneEquiv.of_equiv",
|
149 |
+
"Set.encard_lt_top_iff",
|
150 |
+
"IsOpen.exists_lt_isClosed",
|
151 |
+
"MeasureTheory.integrableOn_finset_iUnion",
|
152 |
+
"Finset.sup_eq_union",
|
153 |
+
"TypeVec.casesCons_append1",
|
154 |
+
"MeasureTheory.TendstoInMeasure.congr",
|
155 |
+
"Int.ediv_mul_cancel",
|
156 |
+
"generateFrom_measurableSet_of_generatePiSystem",
|
157 |
+
"ProbabilityTheory.IndepSets.bUnion",
|
158 |
+
"MeasureTheory.integral_integral_sub'",
|
159 |
+
"Finset.mem_pi",
|
160 |
+
"Int.add_lt_add_iff_right",
|
161 |
+
"String.utf8GetAux_addChar_right_cancel",
|
162 |
+
"Vector.removeNth_insertNth",
|
163 |
+
"intervalIntegral.integral_hasDerivAt_of_tendsto_ae_left",
|
164 |
+
"Set.singleton_eq_singleton_iff",
|
165 |
+
"MeasureTheory.ofReal_set_integral_one",
|
166 |
+
"MeasureTheory.Lp.const_mem_Lp",
|
167 |
+
"MeasureTheory.inducedOuterMeasure_eq",
|
168 |
+
"Set.union_diff_cancel_right",
|
169 |
+
"Finset.sdiff_ssubset",
|
170 |
+
"MeasureTheory.Measure.hausdorffMeasure_le_liminf_sum",
|
171 |
+
"String.isEmpty_iff",
|
172 |
+
"MeasureTheory.pdf_eq_zero_of_not_measurable",
|
173 |
+
"Finset.not_mem_of_max_lt",
|
174 |
+
"Finset.disjUnion_product",
|
175 |
+
"List.infix_of_mem_join",
|
176 |
+
"equivalence_of_manyOneEquiv",
|
177 |
+
"MeasureTheory.condexpInd_disjoint_union_apply",
|
178 |
+
"Sum.map_comp_map",
|
179 |
+
"ENNReal.essSup_add_le",
|
180 |
+
"aeSeq.measurable",
|
181 |
+
"Finset.aemeasurable_prod'",
|
182 |
+
"UnionFind.lt_rankMax'",
|
183 |
+
"PFun.preimage_union",
|
184 |
+
"MeasureTheory.Integrable.integral_condKernel",
|
185 |
+
"MeasureTheory.Egorov.notConvergentSeq_measurableSet",
|
186 |
+
"Finset.Icc_subset_Ioc_iff",
|
187 |
+
"MeasureTheory.Measure.le_count_apply",
|
188 |
+
"Std.RBNode.lowerBound?_mem_lb",
|
189 |
+
"PMF.toMeasure_ofMultiset_apply",
|
190 |
+
"ZMod.lift_comp_castAddHom",
|
191 |
+
"MeasureTheory.OuterMeasure.union",
|
192 |
+
"Int.neg_le_sub_right_of_le_add",
|
193 |
+
"Finset.card_product",
|
194 |
+
"Int.fdiv_nonneg",
|
195 |
+
"Std.PairingHeapImp.Heap.deleteMin_fst",
|
196 |
+
"ProbabilityTheory.indep_of_indep_of_le_right",
|
197 |
+
"RegularExpression.matches'_pow",
|
198 |
+
"MeasurableSpace.monotone_map",
|
199 |
+
"ZMod.int_cast_cast",
|
200 |
+
"Fin.pred_mk",
|
201 |
+
"Subtype.equivalence",
|
202 |
+
"intervalIntegral.integral_mono",
|
203 |
+
"Finset.eq_empty_of_ssubset_singleton",
|
204 |
+
"MeasureTheory.measure_add_measure_compl",
|
205 |
+
"Finset.powerset_injective",
|
206 |
+
"Finset.card_le_diff_of_interleaved",
|
207 |
+
"Int.dvd_iff_mod_eq_zero",
|
208 |
+
"Set.image3_congr'",
|
209 |
+
"Std.RBSet.mem_insert_of_mem",
|
210 |
+
"MeasureTheory.AEDisjoint.mono_ae",
|
211 |
+
"MvPolynomial.monomial_one_dvd_iff_modMonomial_eq_zero",
|
212 |
+
"Finset.pi_empty",
|
213 |
+
"toNat_manyOneReducible",
|
214 |
+
"MeasureTheory.ext_of_generate_finite",
|
215 |
+
"Finset.Nonempty.to_subtype",
|
216 |
+
"MeasureTheory.volume_pi_ball",
|
217 |
+
"MeasureTheory.Filtration.const_apply",
|
218 |
+
"PProd.forall'",
|
219 |
+
"MeasureTheory.OuterMeasure.map_iInf_le",
|
220 |
+
"MeasureTheory.dominatedFinMeasAdditive_condexpInd",
|
221 |
+
"Finset.singleton_mul_inter",
|
222 |
+
"NFA.eval_append_singleton",
|
223 |
+
"Quotient.choice_eq",
|
224 |
+
"MeasureTheory.set_integral_condexpInd",
|
225 |
+
"measurable_sInf",
|
226 |
+
"Set.subset_image_symmDiff",
|
227 |
+
"MeasureTheory.integrable_of_fintype",
|
228 |
+
"FiniteInter.finiteInterClosure_finiteInter",
|
229 |
+
"MeasureTheory.Adapted.stoppedProcess",
|
230 |
+
"intervalIntegral.intervalIntegral_pos_of_pos",
|
231 |
+
"Quotient.liftOn\u2082_mk",
|
232 |
+
"MeasureTheory.ae_le_trim_iff",
|
233 |
+
"MeasureTheory.integrableOn_add_measure",
|
234 |
+
"Finset.set_biInter_singleton",
|
235 |
+
"ENNReal.measurable_toReal",
|
236 |
+
"MeasureTheory.condexp_stopping_time_ae_eq_restrict_eq_of_countable",
|
237 |
+
"Set.countable_isTop",
|
238 |
+
"Finset.inf_id_set_eq_sInter",
|
239 |
+
"Nat.Coprime.gcd_both",
|
240 |
+
"Function.Injective.pprod_map",
|
241 |
+
"Measurable.measurable_comp_iff_restrict",
|
242 |
+
"Setoid.eqvGen_mono",
|
243 |
+
"String.get?_of_valid",
|
244 |
+
"volume_regionBetween_eq_integral",
|
245 |
+
"ProbabilityTheory.iIndepFun.indepFun_prod_range_succ",
|
246 |
+
"Primcodable.mem_range_encode",
|
247 |
+
"Nat.Partrec.Code.smn",
|
248 |
+
"intervalIntegral.integral_hasFDerivAt",
|
249 |
+
"MeasureTheory.Lp.simpleFunc.aemeasurable",
|
250 |
+
"MvPolynomial.eval_pow",
|
251 |
+
"MeasureTheory.measurePreserving_prod_inv_mul_swap",
|
252 |
+
"Set.range_diff_image",
|
253 |
+
"Part.mem_bind_iff",
|
254 |
+
"Finset.sdiff_sdiff_left'",
|
255 |
+
"Set.ordConnected_uIoc",
|
256 |
+
"Holor.cprank_upper_bound",
|
257 |
+
"MvPolynomial.support_sum",
|
258 |
+
"Complex.volume_preserving_equiv_real_prod",
|
259 |
+
"MeasureTheory.Lp.simpleFunc.boundedSMul",
|
260 |
+
"Turing.ToPartrec.stepNormal_eval",
|
261 |
+
"MeasureTheory.continuous_condexpIndL1",
|
262 |
+
"Finset.univ_mul_univ",
|
263 |
+
"Finmap.lookup_union_left",
|
264 |
+
"Int.le_sub_one_of_lt",
|
265 |
+
"List.subset_append_of_subset_right",
|
266 |
+
"Set.pairwise_eq_iff_exists_eq",
|
267 |
+
"Multiset.map_finset_sup",
|
268 |
+
"MeasureTheory.volume_preserving_piFinSuccAboveEquiv",
|
269 |
+
"MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_image",
|
270 |
+
"Set.Countable.insert",
|
271 |
+
"essSup_const",
|
272 |
+
"ack_inj_left",
|
273 |
+
"Fin.coe_clamp",
|
274 |
+
"Finset.filter_congr",
|
275 |
+
"intervalIntegral.integral_comp_mul_deriv",
|
276 |
+
"MeasureTheory.setLaverage_lt_top",
|
277 |
+
"MeasurableSpace.mkOfClosure_sets",
|
278 |
+
"MeasureTheory.L1.norm_Integral_le_one",
|
279 |
+
"MeasureTheory.setIntegral_setAverage_sub",
|
280 |
+
"Function.Injective.comp_injOn",
|
281 |
+
"Set.ordConnected_iInter",
|
282 |
+
"intervalIntegral.continuous_of_dominated_interval",
|
283 |
+
"Std.RBSet.forIn_eq_forIn_toList",
|
284 |
+
"MeasureTheory.BorelCantelli.integrable_process",
|
285 |
+
"Finset.image\u2082_image_left_anticomm",
|
286 |
+
"MvPolynomial.mul_X_divMonomial",
|
287 |
+
"not_and_self_iff",
|
288 |
+
"MvPolynomial.aeval_eq_zero",
|
289 |
+
"equivalence_of_oneOneEquiv",
|
290 |
+
"MvPolynomial.X_mul_divMonomial",
|
291 |
+
"MeasureTheory.FinMeasAdditive.smul_measure_iff",
|
292 |
+
"ProbabilityTheory.variance_smul",
|
293 |
+
"MeasureTheory.integral_inter_add_diff",
|
294 |
+
"ZNum.cast_zero'",
|
295 |
+
"Turing.PartrecToTM2.tr_ret_halt",
|
296 |
+
"PEquiv.single_trans_single_of_ne",
|
297 |
+
"ProbabilityTheory.iIndepFun.condexp_natural_ae_eq_of_lt",
|
298 |
+
"ne_self_iff_false",
|
299 |
+
"set_integral_re_add_im",
|
300 |
+
"Int.lt_add_of_neg_lt_sub_right",
|
301 |
+
"Turing.Tape.exists_mk'",
|
302 |
+
"Finmap.lookup_union_right",
|
303 |
+
"vectorEx_iff_exists",
|
304 |
+
"OneOneReducible.disjoin_left",
|
305 |
+
"MeasureTheory.meas_le_ae_eq_meas_lt",
|
306 |
+
"ProbabilityTheory.measure_zero_or_one_of_measurableSet_limsup_atBot",
|
307 |
+
"vectorAll_iff_forall",
|
308 |
+
"ProbabilityTheory.Indep.symm",
|
309 |
+
"QuotientGroup.measurable_coe",
|
310 |
+
"ProbabilityTheory.indep_iSup_of_antitone",
|
311 |
+
"ComputablePred.halting_problem_not_re",
|
312 |
+
"Finset.mem_uIcc_of_le",
|
313 |
+
"MeasureTheory.hasFiniteIntegral_neg_iff",
|
314 |
+
"MvPolynomial.aeval_X_left_apply",
|
315 |
+
"MvPolynomial.aevalTower_toAlgHom",
|
316 |
+
"MeasureTheory.mem\u2112p_neg_iff",
|
317 |
+
"MeasureTheory.lowerCrossingTime_stabilize'",
|
318 |
+
"Finset.inf_mem",
|
319 |
+
"MeasureTheory.integral_integral_sub",
|
320 |
+
"PMF.toMeasure_ofFinset_apply",
|
321 |
+
"DomMulAct.smul_Lp_ae_eq",
|
322 |
+
"MeasureTheory.Measure.bind_zero_right'",
|
323 |
+
"MeasureTheory.isMulLeftInvariant_map_smul",
|
324 |
+
"MeasureTheory.isMulRightInvariant_map_smul",
|
325 |
+
"DFA.eval_append_singleton",
|
326 |
+
"Subtype.coind_bijective",
|
327 |
+
"MeasureTheory.L1.setToL1_lipschitz",
|
328 |
+
"PosNum.cast_pos",
|
329 |
+
"Finset.insert_inj",
|
330 |
+
"AEMeasurable.comp_quasiMeasurePreserving",
|
331 |
+
"Std.RBSet.mem_of_mem_toList",
|
332 |
+
"ZMod.nat_cast_val",
|
333 |
+
"TypeVec.drop_append1'",
|
334 |
+
"MeasureTheory.tendstoUniformlyOn_of_ae_tendsto",
|
335 |
+
"Int.fmod_nonneg",
|
336 |
+
"Quot.liftOn\u2082_mk",
|
337 |
+
"ComputablePred.halting_problem",
|
338 |
+
"stronglyMeasurable_const_smul_iff\u2080",
|
339 |
+
"Prod.map_id",
|
340 |
+
"ZMod.lift_comp_coe",
|
341 |
+
"Nat.mul_lt_mul'",
|
342 |
+
"Finset.self_mem_range_succ",
|
343 |
+
"Nat.Coprime.pow",
|
344 |
+
"MeasureTheory.Measure.ofMeasurable_apply",
|
345 |
+
"Fin.subNat_addNat",
|
346 |
+
"MeasureTheory.NullMeasurableSet.insert",
|
347 |
+
"MvPolynomial.coeff_sum",
|
348 |
+
"Set.Ioo_infinite",
|
349 |
+
"Set.dual_ordConnected",
|
350 |
+
"ProbabilityTheory.kernel.integral_integral_sub",
|
351 |
+
"MeasureTheory.volume_pi_closedBall",
|
352 |
+
"MvPolynomial.eval\u2082Hom_bind\u2082",
|
353 |
+
"Int.div_mul_cancel",
|
354 |
+
"MeasureTheory.mem_spanningSetsIndex",
|
355 |
+
"MeasureTheory.Integrable.lintegral_lt_top",
|
356 |
+
"ManyOneDegree.liftOn_eq",
|
357 |
+
"MeasureTheory.average_pair",
|
358 |
+
"PFun.preimage_inter",
|
359 |
+
"Measurable.sumMap",
|
360 |
+
"Finset.uIcc_of_not_ge",
|
361 |
+
"Ctop.coe_mk",
|
362 |
+
"Finset.set_biInter_inter",
|
363 |
+
"Std.RBSet.empty_eq",
|
364 |
+
"MeasureTheory.VectorMeasure.restrict_le_restrict_iff",
|
365 |
+
"String.get!_eq_get",
|
366 |
+
"Computability.unary_decode_encode_nat",
|
367 |
+
"MeasureTheory.Lp.tendsto_Lp_of_tendsto_\u2112p",
|
368 |
+
"measurable_subtype_coe",
|
369 |
+
"Sum.getRight_inr",
|
370 |
+
"Set.restrict_piecewise",
|
371 |
+
"AEMeasurable.indicator\u2080",
|
372 |
+
"Primrec.list_indexOf",
|
373 |
+
"MeasureTheory.aestronglyMeasurable'_condexpInd",
|
374 |
+
"MeasureTheory.Measure.lintegral_bind",
|
375 |
+
"ProbabilityTheory.indepSet_iff_measure_inter_eq_mul",
|
376 |
+
"Finset.insert_inj_on",
|
377 |
+
"MeasurableSet.nhdsWithin_isMeasurablyGenerated",
|
378 |
+
"MeasureTheory.setLintegral_setLaverage",
|
379 |
+
"Array.toArray_data",
|
380 |
+
"Set.image_add_const_Ioo",
|
381 |
+
"eq_borel_upgradeStandardBorel",
|
382 |
+
"Fin.castSucc_ne_zero_iff",
|
383 |
+
"Finset.inter_left_idem",
|
384 |
+
"torusMap_zero_radius",
|
385 |
+
"Fin.succ_succ_ne_one",
|
386 |
+
"PosNum.div'_to_nat",
|
387 |
+
"Finset.ssubset_of_ssubset_of_subset",
|
388 |
+
"PEquiv.injective_of_forall_isSome",
|
389 |
+
"Finset.comp_inf_eq_inf_comp_of_is_total",
|
390 |
+
"Fin.eq_succ_of_ne_zero",
|
391 |
+
"Semiquot.mem_pure'",
|
392 |
+
"Fin.val_inj",
|
393 |
+
"Finset.map_inl_disjUnion_map_inr",
|
394 |
+
"intervalIntegral.integral_interval_sub_left",
|
395 |
+
"List.sublist_nil",
|
396 |
+
"MeasureTheory.Measure.join_dirac",
|
397 |
+
"Quotient.liftOn\u2082'_mk",
|
398 |
+
"Set.smul_set_univ\u2080",
|
399 |
+
"MvPolynomial.monomial_finsupp_sum_index",
|
400 |
+
"MeasureTheory.integrable_smul_iff",
|
401 |
+
"MeasurableSet.compl",
|
402 |
+
"MvPolynomial.X_injective",
|
403 |
+
"Set.disjoint_compl_right_iff_subset",
|
404 |
+
"Finset.union_mul_inter_subset",
|
405 |
+
"Set.Finite.countable",
|
406 |
+
"List.reverse_sublist",
|
407 |
+
"Set.image_eq_preimage_of_inverse",
|
408 |
+
"Set.Nonempty.inv",
|
409 |
+
"ProbabilityTheory.iIndepFun.mul",
|
410 |
+
"Set.image_mulSingle_uIcc_right",
|
411 |
+
"MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left'",
|
412 |
+
"MeasureTheory.L1.norm_setToL1_le_mul_norm'",
|
413 |
+
"List.pairwiseDisjoint_iff_coe_toFinset_pairwise_disjoint",
|
414 |
+
"MeasureTheory.le_sub_of_le_upcrossingsBefore",
|
415 |
+
"ProbabilityTheory.indep_iff_forall_indepSet",
|
416 |
+
"MvPolynomial.algHom_ext",
|
417 |
+
"String.lt_next'",
|
418 |
+
"PosNum.mod'_to_nat",
|
419 |
+
"List.forM_cons'",
|
420 |
+
"measurableSet_Ico",
|
421 |
+
"Finset.strictAnti_iff'",
|
422 |
+
"MeasureTheory.L1.SimpleFunc.setToL1S_smul_left",
|
423 |
+
"MeasureTheory.AEEqFun.compQuasiMeasurePreserving_mk",
|
424 |
+
"Finset.min_mem_insert_top_image_coe",
|
425 |
+
"Quotient.map\u2082_mk",
|
426 |
+
"Function.Injective.subsingleton_image_iff",
|
427 |
+
"Monotone.intervalIntegrable",
|
428 |
+
"Finset.inf_himp_right",
|
429 |
+
"Finset.antitone_iff'",
|
430 |
+
"Std.RBSet.single_toList",
|
431 |
+
"MeasureTheory.inducedOuterMeasure_eq'",
|
432 |
+
"MeasureTheory.Measure.FiniteAtFilter.filter_mono_ae",
|
433 |
+
"Finset.sort_empty",
|
434 |
+
"Set.subset_image_union",
|
435 |
+
"SatisfiesM.seqLeft",
|
436 |
+
"List.take_length",
|
437 |
+
"Std.RBSet.size_eq",
|
438 |
+
"Set.MulAntidiagonal.finite_of_isWf",
|
439 |
+
"Quot.lift\u2082_mk",
|
440 |
+
"IsUnit.measurable_const_smul_iff",
|
441 |
+
"Set.IciExtend_self",
|
442 |
+
"isPiSystem_generatePiSystem",
|
443 |
+
"Std.RBSet.mem_iff_find?",
|
444 |
+
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445 |
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446 |
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447 |
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448 |
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449 |
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450 |
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451 |
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452 |
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453 |
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454 |
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455 |
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456 |
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457 |
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458 |
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459 |
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460 |
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461 |
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462 |
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463 |
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464 |
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465 |
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466 |
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467 |
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468 |
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469 |
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470 |
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471 |
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472 |
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473 |
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474 |
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475 |
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476 |
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477 |
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478 |
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479 |
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480 |
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481 |
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482 |
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483 |
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484 |
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485 |
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486 |
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487 |
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488 |
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489 |
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490 |
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491 |
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492 |
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493 |
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494 |
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495 |
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496 |
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497 |
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498 |
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499 |
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500 |
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501 |
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502 |
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503 |
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504 |
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505 |
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506 |
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507 |
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508 |
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509 |
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510 |
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511 |
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512 |
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513 |
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514 |
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515 |
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516 |
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517 |
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518 |
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519 |
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520 |
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521 |
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522 |
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523 |
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524 |
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525 |
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526 |
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527 |
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528 |
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529 |
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530 |
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|
531 |
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532 |
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"Finset.inf_singleton",
|
533 |
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534 |
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535 |
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536 |
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537 |
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538 |
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539 |
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540 |
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|
541 |
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|
542 |
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543 |
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544 |
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545 |
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546 |
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547 |
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548 |
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549 |
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|
550 |
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|
551 |
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|
552 |
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553 |
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554 |
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555 |
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556 |
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|
557 |
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|
558 |
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|
559 |
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560 |
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561 |
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562 |
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563 |
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564 |
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565 |
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566 |
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567 |
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568 |
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569 |
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570 |
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571 |
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572 |
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573 |
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574 |
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575 |
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576 |
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577 |
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578 |
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579 |
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580 |
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581 |
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582 |
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583 |
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584 |
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585 |
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586 |
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587 |
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588 |
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589 |
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590 |
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591 |
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592 |
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593 |
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594 |
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595 |
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596 |
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597 |
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598 |
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599 |
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600 |
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601 |
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602 |
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603 |
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604 |
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605 |
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606 |
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607 |
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608 |
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609 |
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610 |
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611 |
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612 |
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613 |
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614 |
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615 |
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616 |
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617 |
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618 |
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619 |
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620 |
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621 |
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625 |
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626 |
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627 |
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628 |
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629 |
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630 |
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631 |
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632 |
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633 |
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635 |
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636 |
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642 |
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643 |
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644 |
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645 |
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646 |
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650 |
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652 |
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653 |
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654 |
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655 |
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656 |
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657 |
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658 |
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659 |
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660 |
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661 |
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662 |
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663 |
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664 |
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665 |
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666 |
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667 |
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668 |
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669 |
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670 |
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671 |
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672 |
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673 |
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674 |
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|
675 |
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|
676 |
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|
677 |
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|
678 |
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|
679 |
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|
680 |
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|
681 |
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|
682 |
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|
683 |
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|
684 |
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|
685 |
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|
686 |
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|
687 |
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|
688 |
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|
689 |
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|
690 |
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|
691 |
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|
692 |
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|
693 |
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|
694 |
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|
695 |
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|
696 |
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|
697 |
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|
698 |
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|
699 |
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|
700 |
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|
701 |
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|
702 |
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|
703 |
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|
704 |
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|
705 |
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|
706 |
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|
707 |
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|
708 |
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|
709 |
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"Int.gcd_greatest",
|
710 |
+
"Int.sign_mul_natAbs"
|
711 |
+
]
|
712 |
+
}
|
novel_premises/train.json
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ADDED
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novel_premises/val.json
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novel_premises/val_formal_informal_metadata.json
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|
|
|
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|
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|
|
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|
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|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
1 |
+
{
|
2 |
+
"total_valid_proofs": 2000,
|
3 |
+
"total_no_tactics": 656,
|
4 |
+
"deliminter": "**",
|
5 |
+
"no_tactics": [
|
6 |
+
"MeasureTheory.SimpleFunc.sum_measure_preimage_singleton",
|
7 |
+
"MvPolynomial.pderiv_one",
|
8 |
+
"MeasureTheory.Measure.ae_ae_of_ae_prod",
|
9 |
+
"AddAction.zmultiplesQuotientStabilizerEquiv_symm_apply",
|
10 |
+
"MeasureTheory.upperCrossingTime_lt_of_le_upcrossingsBefore",
|
11 |
+
"MeasurableSpace.comap_not",
|
12 |
+
"MeasureTheory.Submartingale.pos",
|
13 |
+
"ProbabilityTheory.IndepSets.bInter",
|
14 |
+
"Set.infinite_iff_exists_lt",
|
15 |
+
"MeasureTheory.Measure.FiniteAtFilter.exists_mem_basis",
|
16 |
+
"MeasureTheory.AECover.lintegral_tendsto_of_countably_generated",
|
17 |
+
"Finset.set_biInter_finset_image",
|
18 |
+
"ProbabilityTheory.indep_iSup_of_disjoint",
|
19 |
+
"indicator_ae_eq_of_ae_eq_set",
|
20 |
+
"intervalIntegrable_const",
|
21 |
+
"MeasureTheory.volume_measurePreserving_piCongrLeft",
|
22 |
+
"Set.image_swap_eq_preimage_swap",
|
23 |
+
"intervalIntegral.integral_zero_ae",
|
24 |
+
"MeasurableEmbedding.comap_preimage",
|
25 |
+
"List.findIdx_get?_eq_get_of_exists",
|
26 |
+
"List.drop_subset",
|
27 |
+
"Filter.Tendsto.eventually_intervalIntegrable",
|
28 |
+
"Finset.disjSum_mono",
|
29 |
+
"measurable_const_smul_iff\u2080",
|
30 |
+
"MeasureTheory.Measure.eqOn_Icc_of_ae_eq",
|
31 |
+
"Primrec.list_headI",
|
32 |
+
"MeasureTheory.norm_condexpL2_le_one",
|
33 |
+
"Turing.PartrecToTM2.tr_supports",
|
34 |
+
"MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le'",
|
35 |
+
"String.toString_toSubstring",
|
36 |
+
"Set.piecewise_mem_Icc'",
|
37 |
+
"MeasureTheory.map_div_right_ae",
|
38 |
+
"List.pairwise_disjoint_of_coe_toFinset_pairwiseDisjoint",
|
39 |
+
"MeasureTheory.AECover.inter_restrict",
|
40 |
+
"MeasureTheory.AEDisjoint.of_null_left",
|
41 |
+
"Set.empty_ssubset_singleton",
|
42 |
+
"List.count_eq_zero",
|
43 |
+
"PFun.core_inter",
|
44 |
+
"intervalIntegral.integral_ofReal",
|
45 |
+
"MeasureTheory.inducedOuterMeasure_eq_extend'",
|
46 |
+
"Finset.fold_sup_bot_singleton",
|
47 |
+
"Finset.inf_top",
|
48 |
+
"List.mem_erase_of_ne",
|
49 |
+
"Std.TransCmp.lt_trans",
|
50 |
+
"Finset.filter_union_filter_neg_eq",
|
51 |
+
"Set.inter_symmDiff_distrib_right",
|
52 |
+
"Part.induction_on",
|
53 |
+
"Finset.mem_inter",
|
54 |
+
"MvPolynomial.aevalTower_comp_C",
|
55 |
+
"MeasureTheory.L1.setToL1_eq_setToL1'",
|
56 |
+
"Finset.subset_smul_finset_iff\u2080",
|
57 |
+
"MvPolynomial.pderiv_eq_zero_of_not_mem_vars",
|
58 |
+
"Part.mem_coe",
|
59 |
+
"Classical.not_forall",
|
60 |
+
"Finset.sym_singleton",
|
61 |
+
"intervalIntegral.integrableOn_deriv_of_nonneg",
|
62 |
+
"Finmap.lookup_erase_ne",
|
63 |
+
"Set.Iio_add_bij",
|
64 |
+
"AEMeasurable.isGLB",
|
65 |
+
"Finset.image\u2082_congr'",
|
66 |
+
"Set.Finite.disjoint_toFinset",
|
67 |
+
"Finset.inf'_congr",
|
68 |
+
"Turing.PointedMap.mk_val",
|
69 |
+
"Set.mem_ite_univ_right",
|
70 |
+
"PosNum.of_to_nat",
|
71 |
+
"MvPolynomial.degrees_C",
|
72 |
+
"Primrec.nat_add",
|
73 |
+
"Sum.getLeft_inl",
|
74 |
+
"MeasureTheory.Egorov.notConvergentSeq_antitone",
|
75 |
+
"Finset.inf_erase_top",
|
76 |
+
"Set.image_add_const_Ico",
|
77 |
+
"MeasureTheory.Measure.finiteAt_nhdsWithin",
|
78 |
+
"Set.IicExtend_self",
|
79 |
+
"Int.mul_self_lt_mul_self",
|
80 |
+
"MeasureTheory.Measure.haar.haarContent_apply",
|
81 |
+
"Set.RightInvOn.congr_right",
|
82 |
+
"Finset.card_le_card_mul_right",
|
83 |
+
"MeasureTheory.SimpleFunc.lintegral_map",
|
84 |
+
"intervalIntegral.deriv_integral_of_tendsto_ae_right",
|
85 |
+
"Finset.Ioo_subset_Iic_self",
|
86 |
+
"MeasureTheory.Measure.eqOn_Ico_of_ae_eq",
|
87 |
+
"Finset.min_mono",
|
88 |
+
"SatisfiesM.trivial",
|
89 |
+
"MvPolynomial.join\u2082_comp_map",
|
90 |
+
"Turing.PartrecToTM2.tr_respects",
|
91 |
+
"MeasureTheory.measure_pos_iff_nonempty_of_smulInvariant",
|
92 |
+
"Primrec.eq",
|
93 |
+
"Set.Finite.nullMeasurableSet_sInter",
|
94 |
+
"manyOneReducible_toNat_toNat",
|
95 |
+
"MeasureTheory.Measure.eqOn_Ioo_of_ae_eq",
|
96 |
+
"StrictMono.strictMonoOn_IicExtend",
|
97 |
+
"Finset.not_mem_of_lt_min",
|
98 |
+
"MeasureTheory.ProgMeasurable.stoppedProcess",
|
99 |
+
"Set.iInter_iUnion_of_antitone",
|
100 |
+
"Nat.sub_le_iff_le_add",
|
101 |
+
"MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono",
|
102 |
+
"Int.emod_nonneg",
|
103 |
+
"aemeasurable_iUnion_iff",
|
104 |
+
"Set.InvOn.mono",
|
105 |
+
"MeasureTheory.Lp.simpleFunc.denseInducing",
|
106 |
+
"ProbabilityTheory.indepSets_of_indepSets_of_le_right",
|
107 |
+
"Finset.uIcc_toDual",
|
108 |
+
"Finset.product_disjUnion",
|
109 |
+
"MeasureTheory.SimpleFunc.eapprox_comp",
|
110 |
+
"Turing.BlankRel.equivalence",
|
111 |
+
"Fin.pred_mk_succ'",
|
112 |
+
"Set.Infinite.of_smul_set",
|
113 |
+
"Complex.measurable_arg",
|
114 |
+
"essInf_const",
|
115 |
+
"String.set_of_valid",
|
116 |
+
"Finset.pi_const_singleton",
|
117 |
+
"Set.piecewise_op\u2082",
|
118 |
+
"Num.add_of_nat",
|
119 |
+
"String.next_of_valid",
|
120 |
+
"intervalIntegral.norm_integral_le_of_norm_le_const",
|
121 |
+
"Set.vsub_self_mono",
|
122 |
+
"ZMod.cast_sub'",
|
123 |
+
"USize.mod_toNat",
|
124 |
+
"Finset.empty_disjSum",
|
125 |
+
"MeasureTheory.volume_measurePreserving_sumPiEquivProdPi",
|
126 |
+
"Finset.Ioc_subset_Ici_self",
|
127 |
+
"Set.mul_subset_iff_left",
|
128 |
+
"MeasurableSpace.ext",
|
129 |
+
"MeasureTheory.condexpL1Clm_of_aestronglyMeasurable'",
|
130 |
+
"MeasureTheory.lintegral_sub_le",
|
131 |
+
"Int.eq_one_of_mul_eq_one_right",
|
132 |
+
"intervalIntegral.tsum_intervalIntegral_eq_of_summable_norm",
|
133 |
+
"Setoid.exists_of_mem_partition",
|
134 |
+
"Finset.sdiff_eq_self_of_disjoint",
|
135 |
+
"Set.image3_mono",
|
136 |
+
"Primrec.nat_casesOn",
|
137 |
+
"MeasureTheory.eventually_mem_spanningSets",
|
138 |
+
"Trunc.out_eq",
|
139 |
+
"MeasureTheory.norm_condexpInd_le",
|
140 |
+
"MeasureTheory.NullMeasurableSet.mono_ac",
|
141 |
+
"MvPolynomial.mkDerivation_X",
|
142 |
+
"Measurable.eq_mp",
|
143 |
+
"Set.nontrivial_of_nontrivial_coe",
|
144 |
+
"MeasureTheory.Adapted.stronglyMeasurable_stoppedProcess",
|
145 |
+
"AEMeasurable.mono_measure",
|
146 |
+
"MeasureTheory.L1.setToL1_eq_setToL1SCLM",
|
147 |
+
"MeasureTheory.L1.SimpleFunc.setToL1S_congr_left",
|
148 |
+
"Primrec.vector_ofFn'",
|
149 |
+
"MeasureTheory.Measure.IsHaarMeasure.smul",
|
150 |
+
"Num.cast_succ",
|
151 |
+
"Std.RBNode.Balanced.depth_bound",
|
152 |
+
"Finset.erase_injOn",
|
153 |
+
"MeasureTheory.integral_union_eq_left_of_forall",
|
154 |
+
"List.exists_or_eq_self_of_eraseP",
|
155 |
+
"Set.disjoint_image_of_injective",
|
156 |
+
"USize.div_toNat",
|
157 |
+
"String.str_eq",
|
158 |
+
"MeasureTheory.Mem\u2112p.inf",
|
159 |
+
"MeasureTheory.map_mul_left_eq_self",
|
160 |
+
"QuotientGroup.measurable_from_quotient",
|
161 |
+
"MvPolynomial.X_divMonomial",
|
162 |
+
"Set.mapsTo_union",
|
163 |
+
"MvPolynomial.X_dvd_iff_modMonomial_eq_zero",
|
164 |
+
"MeasureTheory.stronglyMeasurable_of_fintype",
|
165 |
+
"MeasureTheory.set_integral_eq_integral_of_forall_compl_eq_zero",
|
166 |
+
"Monotone.IciExtend",
|
167 |
+
"Std.HashMap.Imp.Buckets.update_size",
|
168 |
+
"Option.map_eq_none",
|
169 |
+
"MeasureTheory.OuterMeasure.iUnion_eq_of_caratheodory",
|
170 |
+
"MvPolynomial.eval_rename_prod_mk",
|
171 |
+
"MeasureTheory.locallyIntegrable_zero",
|
172 |
+
"MeasureTheory.NullMeasurableSet.measurable_of_complete",
|
173 |
+
"Part.some_injective",
|
174 |
+
"Finset.empty_ssubset_singleton",
|
175 |
+
"Finset.card_erase_le",
|
176 |
+
"Option.orElse_eq_some'",
|
177 |
+
"List.disjoint_of_disjoint_cons_right",
|
178 |
+
"PEquiv.ofSet_eq_some_iff",
|
179 |
+
"Finset.inf_apply",
|
180 |
+
"Int.neg_units_ne_self",
|
181 |
+
"Set.image_mulSingle_uIcc_left",
|
182 |
+
"MeasureTheory.Measure.MeasurePreserving.zpow",
|
183 |
+
"AEMeasurable.edist",
|
184 |
+
"MeasureTheory.LocallyIntegrable.smul",
|
185 |
+
"Set.nontrivial_iff_exists_lt",
|
186 |
+
"Set.Finite.toFinset_insert'",
|
187 |
+
"MeasureTheory.Measure.finiteAt_nhds",
|
188 |
+
"MeasureTheory.VectorMeasure.MutuallySingular.smul_left",
|
189 |
+
"surjOn_Iic_of_monotone_surjective",
|
190 |
+
"IsOpen.exists_lt_isCompact",
|
191 |
+
"MeasureTheory.SimpleFunc.measurableSet_preimage",
|
192 |
+
"Int.div_nonpos",
|
193 |
+
"Set.pi_piecewise",
|
194 |
+
"MeasureTheory.snormEssSup_lt_top_of_ae_bound",
|
195 |
+
"Setoid.eqvGen_eq",
|
196 |
+
"MeasureTheory.FinStronglyMeasurable.add",
|
197 |
+
"Set.sigma_subset_iff",
|
198 |
+
"Int.ModEq.mul",
|
199 |
+
"MeasureTheory.measurableSet_of_null",
|
200 |
+
"Nat.exists_mul_emod_eq_one_of_coprime",
|
201 |
+
"Int.le_add_of_neg_le_sub_right",
|
202 |
+
"tendsto_measure_cthickening_of_isCompact",
|
203 |
+
"IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul'",
|
204 |
+
"deriv_circleMap_ne_zero",
|
205 |
+
"Finset.sym_fill_mem",
|
206 |
+
"MeasureTheory.finStronglyMeasurable_iff_stronglyMeasurable_and_exists_set_sigmaFinite",
|
207 |
+
"intervalIntegral.integral_congr_ae",
|
208 |
+
"MeasureTheory.upperCrossingTime_lt_succ",
|
209 |
+
"MeasureTheory.martingale_of_set_integral_eq_succ",
|
210 |
+
"Option.map\u2082_curry",
|
211 |
+
"MeasureTheory.martingale_nat",
|
212 |
+
"MeasureTheory.integrable_of_intervalIntegral_norm_tendsto",
|
213 |
+
"Finset.mul_subset_iff_left",
|
214 |
+
"MeasureTheory.Lp.coeFn_posPart",
|
215 |
+
"MeasCat.coe_of",
|
216 |
+
"Set.Finite.toFinset_eq_univ",
|
217 |
+
"Finset.disjSum_empty",
|
218 |
+
"Int.lt_add_of_neg_lt_sub_left",
|
219 |
+
"PMF.support_countable",
|
220 |
+
"Finset.empty_subset",
|
221 |
+
"Quotient.out_inj",
|
222 |
+
"MeasureTheory.stronglyMeasurable_of_isEmpty",
|
223 |
+
"Finset.mem_sort",
|
224 |
+
"MvPolynomial.pderiv_C",
|
225 |
+
"MeasureTheory.ae_dirac_iff",
|
226 |
+
"Turing.PartrecToTM2.trNat_default",
|
227 |
+
"measurable_of_measurable_on_compl_finite",
|
228 |
+
"MeasureTheory.integral_Ico_eq_integral_Ioo",
|
229 |
+
"MeasureTheory.hausdorffMeasure_measurePreserving_piFinTwo",
|
230 |
+
"MeasurableSet.induction_on_open",
|
231 |
+
"Turing.PartrecToTM2.tr_read",
|
232 |
+
"Fin.lastCases_last",
|
233 |
+
"MeasureTheory.OuterMeasure.restrict_le_self",
|
234 |
+
"Setoid.mkClasses_classes",
|
235 |
+
"Finset.sort_sorted_lt",
|
236 |
+
"Turing.TM0.map_init",
|
237 |
+
"Set.exists_seq_cover_iff_countable",
|
238 |
+
"ProbabilityTheory.condexp_ae_eq_integral_condDistrib'",
|
239 |
+
"Multiset.coe_keys",
|
240 |
+
"TypeVec.append1_cases_append1",
|
241 |
+
"Set.countable_isBot",
|
242 |
+
"Set.ordConnected_iff_uIcc_subset_left",
|
243 |
+
"Setoid.IsPartition.pairwiseDisjoint",
|
244 |
+
"Int.le_add_of_neg_le_sub_left",
|
245 |
+
"MeasureTheory.integral_Iic_eq_integral_Iio",
|
246 |
+
"MeasureTheory.Measure.sigmaFinite_of_le",
|
247 |
+
"MeasureTheory.Measure.ae_sum_iff",
|
248 |
+
"Set.toFinset_smul_set",
|
249 |
+
"MvPolynomial.modMonomial_add_divMonomial_single",
|
250 |
+
"MeasurableSet.exists_lt_isCompact_of_ne_top",
|
251 |
+
"Finmap.mem_insert",
|
252 |
+
"MeasureTheory.nullMeasurableSet_insert",
|
253 |
+
"MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left",
|
254 |
+
"OneOneReducible.of_equiv",
|
255 |
+
"Vector.not_mem_zero",
|
256 |
+
"String.revPosOfAux_eq",
|
257 |
+
"Int.shiftLeft_sub",
|
258 |
+
"Function.insert_injOn",
|
259 |
+
"MvPolynomial.induction_on''",
|
260 |
+
"Finset.card_image_iff",
|
261 |
+
"Set.Finite.iSup_biInf_of_antitone",
|
262 |
+
"Finpartition.isPartition_parts",
|
263 |
+
"MeasureTheory.laverage_one",
|
264 |
+
"MeasureTheory.integrable_stoppedProcess",
|
265 |
+
"Int.lt.intro",
|
266 |
+
"aestronglyMeasurable_const_smul_iff\u2080",
|
267 |
+
"Set.subset_union_compl_iff_inter_subset",
|
268 |
+
"CFilter.coe_mk",
|
269 |
+
"ProbabilityTheory.measure_zero_or_one_of_measurableSet_limsup_atTop",
|
270 |
+
"MeasureTheory.Lp.norm_zero",
|
271 |
+
"Set.infinite_of_not_bddBelow",
|
272 |
+
"Int.bit1_ne_bit0",
|
273 |
+
"Finset.monotone_filter_right",
|
274 |
+
"MeasureTheory.Measure.restrict_restrict'",
|
275 |
+
"Nat.lt_min",
|
276 |
+
"MeasureTheory.ProbabilityMeasure.toFiniteMeasure_embedding",
|
277 |
+
"Part.bind_defined",
|
278 |
+
"Finsupp.mem_pi",
|
279 |
+
"MeasureTheory.Measure.IsFiniteMeasure.IicSnd",
|
280 |
+
"Finset.induction_on_pi_min",
|
281 |
+
"MeasureTheory.Lp.mem_boundedContinuousFunction_iff",
|
282 |
+
"MeasureTheory.integrable_toReal_of_lintegral_ne_top",
|
283 |
+
"Std.PairingHeapImp.Heap.WF.combine",
|
284 |
+
"Finset.inf_attach",
|
285 |
+
"Set.PairwiseDisjoint.insert_of_not_mem",
|
286 |
+
"ProbabilityTheory.indep_of_indep_of_le_left",
|
287 |
+
"Rel.preimage_def",
|
288 |
+
"List.exists_of_modifyNthTail",
|
289 |
+
"Set.image_mulSingle_Ioo_right",
|
290 |
+
"MvPolynomial.mapAlgHom_coe_ringHom",
|
291 |
+
"sign_pow",
|
292 |
+
"torusIntegral_const_mul",
|
293 |
+
"intervalIntegral.integral_hasDerivAt_left",
|
294 |
+
"Finset.card_erase_lt_of_mem",
|
295 |
+
"Nat.le_of_mod_lt",
|
296 |
+
"Pairwise.subset_of_biUnion_subset_biUnion",
|
297 |
+
"AEMeasurable.add_measure",
|
298 |
+
"Set.countable_univ_iff",
|
299 |
+
"IsUnit.aestronglyMeasurable_const_smul_iff",
|
300 |
+
"Sum.liftRel_subrelation_lex",
|
301 |
+
"generatePiSystem_eq",
|
302 |
+
"Finset.disjSups_subset_iff",
|
303 |
+
"Int.sign_coe_nat_of_nonzero",
|
304 |
+
"MvPolynomial.aeval_eq_constantCoeff_of_vars",
|
305 |
+
"List.tail!_cons",
|
306 |
+
"circleMap_ne_mem_ball",
|
307 |
+
"PMF.toMeasure_pure_apply",
|
308 |
+
"Finset.card_erase_add_one",
|
309 |
+
"Finset.mulAntidiagonal_mono_left",
|
310 |
+
"Finset.piecewise_idem_left",
|
311 |
+
"MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left'",
|
312 |
+
"MeasureTheory.Adapted.progMeasurable_of_continuous",
|
313 |
+
"PEquiv.single_trans_of_eq_none",
|
314 |
+
"Finset.sup_himp_left",
|
315 |
+
"MeasureTheory.Measure.addHaar_preimage_continuousLinearEquiv",
|
316 |
+
"MeasureTheory.pdf.quasiMeasurePreserving_hasPDF'",
|
317 |
+
"MvPolynomial.modMonomial_add_divMonomial",
|
318 |
+
"MeasureTheory.measurePreserving_prod_div",
|
319 |
+
"Computability.FinEncoding.card_le_aleph0",
|
320 |
+
"MeasureTheory.measurePreserving_prod_inv_mul",
|
321 |
+
"List.count_replicate_self",
|
322 |
+
"Set.image_mulSingle_Ico_right",
|
323 |
+
"MvPolynomial.aeval_bind\u2081",
|
324 |
+
"MeasureTheory.le_measure_liminf_of_limsup_measure_compl_le",
|
325 |
+
"MeasurableSet.image_inclusion",
|
326 |
+
"Turing.PartrecToTM2.trNat_natEnd",
|
327 |
+
"ProbabilityTheory.aestronglyMeasurable'_integral_condDistrib",
|
328 |
+
"ack_strictMono_left",
|
329 |
+
"MeasureTheory.Measure.count_eq_zero_iff'",
|
330 |
+
"Fin.ofNat'_zero_val",
|
331 |
+
"Std.RBSet.mem_toList_unique",
|
332 |
+
"MvPolynomial.derivation_eq_of_forall_mem_vars",
|
333 |
+
"Primrec.pred",
|
334 |
+
"MeasureTheory.L1.SimpleFunc.setToL1S_add_left",
|
335 |
+
"Finset.card_le_card_sdiff_add_card",
|
336 |
+
"Set.image_mulSingle_Icc_right",
|
337 |
+
"intervalIntegral.derivWithin_integral_left",
|
338 |
+
"Vector.mapAccumr\u2082_eq_map\u2082_of_unused_state",
|
339 |
+
"List.exists_of_set'",
|
340 |
+
"MeasureTheory.Measure.NullMeasurableSet.subtype_coe",
|
341 |
+
"Std.AssocList.erase_toList",
|
342 |
+
"Option.orElse_eq_none'",
|
343 |
+
"Nat.max_eq_max",
|
344 |
+
"Std.RBNode.lowerBound?_le",
|
345 |
+
"Finset.sup_inf",
|
346 |
+
"MeasureTheory.isClosed_aeStronglyMeasurable'",
|
347 |
+
"Set.insert_union_distrib",
|
348 |
+
"Set.image2_vsub",
|
349 |
+
"StrictMono.strictMonoOn_IccExtend",
|
350 |
+
"Part.mem_mk_iff",
|
351 |
+
"iff_true_right",
|
352 |
+
"Setoid.eq_of_mem_eqv_class",
|
353 |
+
"Int.toNat_sub_toNat_neg",
|
354 |
+
"MeasureTheory.condexpInd_smul'",
|
355 |
+
"MeasureTheory.set_lintegral_lt_top_of_isCompact",
|
356 |
+
"Int.succ_neg_nat_succ",
|
357 |
+
"MeasureTheory.Lp.continuous_posPart",
|
358 |
+
"Int.mul_self_le_mul_self",
|
359 |
+
"Turing.reaches_total",
|
360 |
+
"Finset.disjiUnion_map_sigma_mk",
|
361 |
+
"Nat.div_gcd_pos_of_pos_right",
|
362 |
+
"MeasureTheory.aecover_Iio_of_Iic",
|
363 |
+
"Fin.exists_fin_two",
|
364 |
+
"ProbabilityTheory.IndepSets.inter",
|
365 |
+
"String.revPosOf_eq",
|
366 |
+
"Finset.set_biInter_insert_update",
|
367 |
+
"MeasureTheory.volume_preserving_pi_empty",
|
368 |
+
"Finset.inf_of_mem",
|
369 |
+
"Set.map_eq_of_subset",
|
370 |
+
"MeasureTheory.OuterMeasure.ofFunction_eq_sSup",
|
371 |
+
"Set.finite_preimage_inl_and_inr",
|
372 |
+
"ProbabilityTheory.IndepSets.indepSet_of_mem",
|
373 |
+
"Set.image_add_const_Ioc",
|
374 |
+
"Turing.PartrecToTM2.tr_pred",
|
375 |
+
"MeasureTheory.ProbabilityMeasure.tendsto_nhds_iff_toFiniteMeasure_tendsto_nhds",
|
376 |
+
"MeasureTheory.Lp.coeFn_abs",
|
377 |
+
"Int.mod_mul_right_mod",
|
378 |
+
"PFun.lift_injective",
|
379 |
+
"MeasureTheory.L1.SimpleFunc.setToL1SCLM_const",
|
380 |
+
"Int.sub_one_lt_of_le",
|
381 |
+
"MeasureTheory.uniformIntegrable_subsingleton",
|
382 |
+
"MeasureTheory.integral_integral_add",
|
383 |
+
"List.ne_nil_of_drop_ne_nil",
|
384 |
+
"MeasureTheory.VectorMeasure.of_iUnion_nonpos",
|
385 |
+
"Finset.uIcc_subset_uIcc_iff_le",
|
386 |
+
"Part.eq_get_iff_mem",
|
387 |
+
"MeasureTheory.set_lintegral_mono'",
|
388 |
+
"ZMod.addOrderOf_one",
|
389 |
+
"Set.Ioo.infinite",
|
390 |
+
"Std.RBSet.mem_congr",
|
391 |
+
"ProbabilityTheory.iIndepFun.indepFun_prod",
|
392 |
+
"Measurable.measurable_comp_iff_of_surjective",
|
393 |
+
"Finset.inf_eq_sInf_image",
|
394 |
+
"Finset.mem_sdiff",
|
395 |
+
"Finset.set_biInter_option_toFinset",
|
396 |
+
"MvPolynomial.eval_mem",
|
397 |
+
"List.toFinset_surjective",
|
398 |
+
"MvPolynomial.renameEquiv_refl",
|
399 |
+
"MeasureTheory.Measure.isHaarMeasure_of_isCompact_nonempty_interior",
|
400 |
+
"Set.Ioc.infinite",
|
401 |
+
"Finset.min'_lt_of_mem_erase_min'",
|
402 |
+
"Finset.op_smul_finset_mul_eq_mul_smul_finset",
|
403 |
+
"Int.sign_eq_one_iff_pos",
|
404 |
+
"Set.inclusion_eq_id",
|
405 |
+
"MeasureTheory.Measure.integral_comp_div",
|
406 |
+
"Set.compl_image_set_of",
|
407 |
+
"MeasureTheory.ProbabilityMeasure.tendsto_measure_of_null_frontier_of_tendsto'",
|
408 |
+
"Std.HashMap.Imp.WF_iff",
|
409 |
+
"OneOneReducible.disjoin_right",
|
410 |
+
"ContinuousAt.stronglyMeasurableAtFilter",
|
411 |
+
"MvPolynomial.is_id",
|
412 |
+
"MvPolynomial.aevalTower_comp_algebraMap",
|
413 |
+
"MeasureTheory.Measure.join_map_dirac",
|
414 |
+
"Filter.Realizer.tendsto_iff",
|
415 |
+
"String.get'_eq",
|
416 |
+
"MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left'",
|
417 |
+
"Std.AssocList.findEntry?_eq",
|
418 |
+
"MeasureTheory.Measure.countable_meas_level_set_pos",
|
419 |
+
"MeasureTheory.Mem\u2112p.ofReal",
|
420 |
+
"Nat.strongRecOn_eq",
|
421 |
+
"ZMod.ringHom_rightInverse",
|
422 |
+
"Subtype.equiv_iff",
|
423 |
+
"strictAntiOn_Ici_of_lt_pred",
|
424 |
+
"Set.mem_image_elim_on",
|
425 |
+
"String.utf8Len_reverse",
|
426 |
+
"MeasureTheory.progMeasurable_of_tendsto",
|
427 |
+
"ForInStep.bind_done",
|
428 |
+
"MeasureTheory.inducedOuterMeasure_eq_extend",
|
429 |
+
"Set.InjOn.cancel_left",
|
430 |
+
"IsUnit.integrable_smul_iff",
|
431 |
+
"measure_closure_of_null_frontier",
|
432 |
+
"Finset.insert_sdiff_insert",
|
433 |
+
"List.mem_singleton",
|
434 |
+
"Set.inter_diff_distrib_right",
|
435 |
+
"Turing.BlankRel.refl",
|
436 |
+
"Finset.mul_subset_iff_right",
|
437 |
+
"UFModel.Models.size_eq",
|
438 |
+
"MeasureTheory.VectorMeasure.measurable_of_not_zero_le_restrict",
|
439 |
+
"MvPolynomial.divMonomial_monomial",
|
440 |
+
"MeasureTheory.Lp.coeFn_sub",
|
441 |
+
"MeasureTheory.weightedSMul_union",
|
442 |
+
"MeasureTheory.set_integral_congr\u2080",
|
443 |
+
"ProbabilityTheory.indep_iSup_of_monotone",
|
444 |
+
"MeasureTheory.adapted_martingalePart",
|
445 |
+
"Finmap.union_toFinmap",
|
446 |
+
"Finset.sup_singleton",
|
447 |
+
"Finset.mem_sigma",
|
448 |
+
"ProbabilityTheory.indep_bot_left",
|
449 |
+
"MeasureTheory.integral_integral_add'",
|
450 |
+
"Finset.disjSum_strictMono_left",
|
451 |
+
"ProbabilityTheory.IndepSets.union_iff",
|
452 |
+
"MeasureTheory.Measure.pi_eq",
|
453 |
+
"Array.foldr_push'",
|
454 |
+
"MeasureTheory.Measure.le_hausdorffMeasure",
|
455 |
+
"Turing.TM2to1.tr_eval_dom",
|
456 |
+
"MeasureTheory.Lp.mem_Lp_of_ae_le",
|
457 |
+
"List.filter_eq'",
|
458 |
+
"PMF.toOuterMeasure_mono",
|
459 |
+
"integral_pair",
|
460 |
+
"MeasureTheory.hausdorffMeasure_measurePreserving_funUnique",
|
461 |
+
"MeasureTheory.Lp.norm_neg",
|
462 |
+
"MeasureTheory.hasFiniteIntegral_add_measure",
|
463 |
+
"Std.PairingHeapImp.Heap.WF.singleton",
|
464 |
+
"Quot.map\u2082_mk",
|
465 |
+
"Finset.smul_mem_smul_finset_iff",
|
466 |
+
"MvPolynomial.eval_sub",
|
467 |
+
"Set.Finite.eq_of_subset_of_encard_le'",
|
468 |
+
"Set.encard_strictMono",
|
469 |
+
"Finset.mem_inv_smul_finset_iff\u2080",
|
470 |
+
"Set.abs_sub_left_of_mem_uIcc",
|
471 |
+
"Quotient.hrecOn'_mk''",
|
472 |
+
"Set.restrict_eq_restrict_iff",
|
473 |
+
"Nat.exists_eq_succ_of_ne_zero",
|
474 |
+
"ProbabilityTheory.iIndepFun.indepFun_finset_prod_of_not_mem",
|
475 |
+
"MeasureTheory.Mem\u2112p.of_le_mul",
|
476 |
+
"Set.infinite_mul",
|
477 |
+
"MeasureTheory.VectorMeasure.ext",
|
478 |
+
"StrictMono.strictMonoOn_IciExtend",
|
479 |
+
"List.mem_of_mem_erase",
|
480 |
+
"Set.countable_iff_exists_surjective",
|
481 |
+
"Set.SurjOn.union_union",
|
482 |
+
"List.append_right_inj",
|
483 |
+
"Finset.inf'_map",
|
484 |
+
"MeasureTheory.setAverage_const",
|
485 |
+
"Finset.mem_erase",
|
486 |
+
"aemeasurable_biInf",
|
487 |
+
"MeasurableEmbedding.of_measurable_inverse",
|
488 |
+
"MeasureTheory.Lp.simpleFunc.aestronglyMeasurable",
|
489 |
+
"MeasureTheory.VectorMeasure.MutuallySingular.neg_left_iff",
|
490 |
+
"ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun",
|
491 |
+
"ULower.down_computable",
|
492 |
+
"List.count_le_count_cons",
|
493 |
+
"MeasureTheory.FinStronglyMeasurable.sub",
|
494 |
+
"Set.bijOn_empty",
|
495 |
+
"List.reverseAux_eq",
|
496 |
+
"measurable_tProd_elim'",
|
497 |
+
"Trunc.eq",
|
498 |
+
"Finset.filter_subset",
|
499 |
+
"ContinuousMap.toLp_injective",
|
500 |
+
"ProbabilityTheory.IsFiniteKernel.bound_ne_top",
|
501 |
+
"Finset.fold_ite",
|
502 |
+
"Set.nontrivial_iff_pair_subset",
|
503 |
+
"Set.mul_subset_iff_right",
|
504 |
+
"PEquiv.single_trans_single",
|
505 |
+
"Set.pairwiseDisjoint_pi",
|
506 |
+
"List.infix_nil",
|
507 |
+
"MeasureTheory.volume_preserving_piEquivPiSubtypeProd",
|
508 |
+
"Finset.mem_uIcc_of_ge",
|
509 |
+
"Real.volume_pi_Ico",
|
510 |
+
"Finset.image_image\u2082_right_anticomm",
|
511 |
+
"Finset.inf_inf",
|
512 |
+
"IndexedPartition.index_some",
|
513 |
+
"Set.coe_singletonOneHom",
|
514 |
+
"ProbabilityTheory.kernel.ae_ae_of_ae_compProd",
|
515 |
+
"Primrec.vector_get'",
|
516 |
+
"ProbabilityTheory.condCount_of_univ",
|
517 |
+
"Nat.recDiagOn_zero_succ",
|
518 |
+
"Set.eq_of_subset_of_card_le",
|
519 |
+
"MeasureTheory.Lp.mem_Lp_of_nnnorm_ae_le_mul",
|
520 |
+
"Finset.insert_ne_empty",
|
521 |
+
"Std.RBSet.find?_insert_of_eq",
|
522 |
+
"Set.Finite.bddBelow_biUnion",
|
523 |
+
"WithBot.preimage_coe_bot",
|
524 |
+
"Finset.inter_subset_ite",
|
525 |
+
"MeasureTheory.L1.SimpleFunc.setToL1S_zero_left",
|
526 |
+
"Set.eqOn_comp_right_iff",
|
527 |
+
"MeasureTheory.set_integral_eq_zero_of_forall_eq_zero",
|
528 |
+
"Std.RBSet.foldlM_eq_foldlM_toList",
|
529 |
+
"MeasureTheory.withDensity_mul",
|
530 |
+
"String.get_of_valid",
|
531 |
+
"MeasureTheory.aecover_Ioo_of_Ioo",
|
532 |
+
"ProbabilityTheory.iIndepSet.indep_generateFrom_lt",
|
533 |
+
"MeasureTheory.Measure.QuasiMeasurePreserving.exists_preimage_eq_of_preimage_ae",
|
534 |
+
"measurable_of_empty",
|
535 |
+
"MvPolynomial.as_sum",
|
536 |
+
"aemeasurable_restrict_of_monotoneOn",
|
537 |
+
"Array.mapIdx_induction'",
|
538 |
+
"Partrec\u2082.unpaired'",
|
539 |
+
"MeasureTheory.integral_Ici_eq_integral_Ioi",
|
540 |
+
"Set.restrict_piecewise_compl",
|
541 |
+
"MeasureTheory.Lp.simpleFunc.toLp_toSimpleFunc",
|
542 |
+
"Opposite.equivToOpposite_coe",
|
543 |
+
"Sum.range_eq",
|
544 |
+
"Computable.equiv\u2082",
|
545 |
+
"Finset.nonempty_uIcc",
|
546 |
+
"MeasureTheory.VectorMeasure.AbsolutelyContinuous.refl",
|
547 |
+
"MvPolynomial.constantCoeff_comp_algebraMap",
|
548 |
+
"Nat.lt_log2_self",
|
549 |
+
"aemeasurable_restrict_of_measurable_subtype",
|
550 |
+
"Erased.join_eq_out",
|
551 |
+
"MeasureTheory.integrable_add_measure",
|
552 |
+
"MeasureTheory.AEStronglyMeasurable.mem\u2112p_truncation",
|
553 |
+
"ProbabilityTheory.iIndepFun.indepFun",
|
554 |
+
"Set.ncard_image_iff",
|
555 |
+
"Set.disjoint_left_ordSeparatingSet",
|
556 |
+
"Primrec.nat_sqrt",
|
557 |
+
"Fin.castLE_comp_castLE",
|
558 |
+
"LipschitzWith.hausdorffMeasure_image_le",
|
559 |
+
"MulAction.zpowersQuotientStabilizerEquiv_symm_apply",
|
560 |
+
"MeasureTheory.Integrable.aefinStronglyMeasurable",
|
561 |
+
"MeasureTheory.OuterMeasure.ext",
|
562 |
+
"Finmap.lookup_erase",
|
563 |
+
"MeasureTheory.SignedMeasure.existsNatOneDivLTMeasure_of_not_negative",
|
564 |
+
"Finset.inf'_biUnion",
|
565 |
+
"Set.iInter_iUnion_of_monotone",
|
566 |
+
"Set.RightInvOn.mapsTo",
|
567 |
+
"Turing.Tape.map_mk\u2081",
|
568 |
+
"MeasureTheory.Measure.QuasiMeasurePreserving.mono",
|
569 |
+
"MeasureTheory.OuterMeasure.boundedBy_eq_self",
|
570 |
+
"Part.coe_toFinset",
|
571 |
+
"MeasureTheory.StronglyMeasurable.ite",
|
572 |
+
"ProbabilityTheory.kernel.integral_integral_sub'",
|
573 |
+
"Set.countable_univ_pi",
|
574 |
+
"Turing.PartrecToTM2.trNum_natEnd",
|
575 |
+
"Finset.pair_comm",
|
576 |
+
"MeasureTheory.lintegral_strict_mono_of_ae_le_of_ae_lt_on",
|
577 |
+
"Fin.lastCases_castSucc",
|
578 |
+
"MeasureTheory.SimpleFunc.FinMeasSupp.pair",
|
579 |
+
"Int.sign_ofNat_of_nonzero",
|
580 |
+
"MeasureTheory.tendsto_measure_of_null_frontier",
|
581 |
+
"MeasureTheory.FiniteMeasure.tendsto_testAgainstNN_of_le_const",
|
582 |
+
"MeasureTheory.integrableOn_Ioi_of_intervalIntegral_norm_tendsto",
|
583 |
+
"MvPolynomial.support_sub",
|
584 |
+
"RegularExpression.zero_def",
|
585 |
+
"Part.getOrElse_none",
|
586 |
+
"Int.add_lt_add",
|
587 |
+
"MeasureTheory.L1.SimpleFunc.setToL1S_zero_left'",
|
588 |
+
"MvPolynomial.modMonomial_X",
|
589 |
+
"Num.minFac_to_nat",
|
590 |
+
"PMF.mem_support_filter_iff",
|
591 |
+
"Nat.recDiagOn_succ_zero",
|
592 |
+
"MeasureTheory.SignedMeasure.zero_mem_measureOfNegatives",
|
593 |
+
"ContinuousMap.toLp_norm_eq_toLp_norm_coe",
|
594 |
+
"Finset.isPwo_support_mulAntidiagonal",
|
595 |
+
"MvPolynomial.bind\u2082_bind\u2082",
|
596 |
+
"MvPolynomial.killCompl_rename_app",
|
597 |
+
"MeasureTheory.integral_Icc_eq_integral_Ico",
|
598 |
+
"Quot.factor_mk_eq",
|
599 |
+
"Std.BitVec.ofNat_eq_ofNat",
|
600 |
+
"Vector3.consElim_cons",
|
601 |
+
"MeasureTheory.SimpleFunc.FinMeasSupp.map\u2082",
|
602 |
+
"PMF.toMeasure_bind_apply",
|
603 |
+
"MeasureTheory.upperCrossingTime_eq_of_bound_le",
|
604 |
+
"String.Iterator.Valid.toEnd",
|
605 |
+
"IndexedPartition.proj_eq_iff",
|
606 |
+
"MeasureTheory.Measure.MutuallySingular.add_right",
|
607 |
+
"Std.RBNode.Path.zoom_fill",
|
608 |
+
"PosNum.cast_to_znum",
|
609 |
+
"MeasureTheory.locallyIntegrableOn_const",
|
610 |
+
"exists\u2084_congr",
|
611 |
+
"exists\u2085_congr",
|
612 |
+
"MeasureTheory.Measure.ae_sum_iff'",
|
613 |
+
"MeasureTheory.Integrable.comp_div_left",
|
614 |
+
"Fin.val_ne_iff",
|
615 |
+
"aemeasurable_const_smul_iff\u2080",
|
616 |
+
"Std.RBSet.mem_insert_of_mem_toList",
|
617 |
+
"Finset.pimage_mono",
|
618 |
+
"MeasureTheory.measure_pos_iff_nonempty_of_isMulLeftInvariant",
|
619 |
+
"IndexedPartition.equivQuotient_index_apply",
|
620 |
+
"MvPolynomial.X_mul_modMonomial",
|
621 |
+
"MeasureTheory.measure_isOpen_pos_of_smulInvariant_of_ne_zero",
|
622 |
+
"Vector.mOfFn_part_some",
|
623 |
+
"USize.modn_toNat",
|
624 |
+
"Nat.Coprime.gcd_mul",
|
625 |
+
"Set.image_finset_prod",
|
626 |
+
"ProbabilityTheory.stronglyMeasurable_condexpKernel",
|
627 |
+
"Set.image_mulSingle_Ioc_left",
|
628 |
+
"ComputablePred.computable_of_oneOneReducible",
|
629 |
+
"Ctop.Realizer.ext",
|
630 |
+
"Primrec.nat_sub",
|
631 |
+
"Set.MulAntidiagonal.eq_of_fst_le_fst_of_snd_le_snd",
|
632 |
+
"measurable_of_restrict_of_restrict_compl",
|
633 |
+
"Set.piecewise_mem_Icc",
|
634 |
+
"Set.piecewise_range_comp",
|
635 |
+
"MeasureTheory.VectorMeasure.of_disjoint_iUnion",
|
636 |
+
"Set.disjoint_image_iff",
|
637 |
+
"Set.injOn_iff_invFunOn_image_image_eq_self",
|
638 |
+
"MeasureTheory.Measure.comap\u2097_eq_comap",
|
639 |
+
"BoundedContinuousFunction.Lp_norm_le",
|
640 |
+
"Rat.divInt_zero",
|
641 |
+
"Set.compl_subset_compl",
|
642 |
+
"MeasureTheory.quasiMeasurePreserving_div",
|
643 |
+
"MeasureTheory.Measure.count_singleton",
|
644 |
+
"intervalIntegral.deriv_integral_of_tendsto_ae_left",
|
645 |
+
"Decidable.imp_iff_not_or",
|
646 |
+
"PMF.support_filter",
|
647 |
+
"Set.fst_image_sigma",
|
648 |
+
"Primrec.nat_mul",
|
649 |
+
"MeasureTheory.Ico_ae_eq_Ioc",
|
650 |
+
"MvPolynomial.monomial_modMonomial",
|
651 |
+
"MvPolynomial.coeff_X_mul",
|
652 |
+
"TypeVec.typevecCasesNil\u2082_appendFun",
|
653 |
+
"Set.singleton_pi'",
|
654 |
+
"Set.range_eval",
|
655 |
+
"Finset.min'_le",
|
656 |
+
"measurableSet_le",
|
657 |
+
"TypeVec.typevecCasesCons\u2082_appendFun",
|
658 |
+
"Set.countable_iff_exists_injective",
|
659 |
+
"Nat.eq_or_lt_of_not_lt",
|
660 |
+
"AEMeasurable.iUnion",
|
661 |
+
"String.next'_eq"
|
662 |
+
]
|
663 |
+
}
|
random/test.json
ADDED
The diff for this file is too large to render.
See raw diff
|
|
random/test_formal_informal.json
ADDED
The diff for this file is too large to render.
See raw diff
|
|
random/test_formal_informal_metadata.json
ADDED
@@ -0,0 +1,1022 @@
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|
1 |
+
{
|
2 |
+
"total_valid_proofs": 2000,
|
3 |
+
"total_no_tactics": 1015,
|
4 |
+
"deliminter": "**",
|
5 |
+
"no_tactics": [
|
6 |
+
"LaurentPolynomial.isUnit_T",
|
7 |
+
"PartENat.toWithTop_some",
|
8 |
+
"Finset.coe_smul",
|
9 |
+
"GenLoop.continuous_fromLoop",
|
10 |
+
"Int.neg_eq_neg",
|
11 |
+
"Polynomial.degree_sum_fin_lt",
|
12 |
+
"SimpleGraph.Walk.edges_bypass_subset",
|
13 |
+
"PrimeSpectrum.closedEmbedding_comap_of_surjective",
|
14 |
+
"Filter.tendsto_fst",
|
15 |
+
"IsMaxOn.norm_add_self",
|
16 |
+
"Rat.cast_sub",
|
17 |
+
"Set.finite_le_nat",
|
18 |
+
"Finset.eq_univ_of_forall",
|
19 |
+
"RingEquiv.trans_apply",
|
20 |
+
"CategoryTheory.ConcreteCategory.surjective_of_epi_of_preservesPushout",
|
21 |
+
"AlgEquiv.ext_iff",
|
22 |
+
"RingCon.coe_nsmul",
|
23 |
+
"MvPolynomial.coeToMvPowerSeries.ringHom_apply",
|
24 |
+
"FreimanHom.comp_id",
|
25 |
+
"ContinuousAt.vsub",
|
26 |
+
"Multiset.ndinsert_zero",
|
27 |
+
"Rat.mkRat_num_den",
|
28 |
+
"MeasureTheory.AEStronglyMeasurable.restrict",
|
29 |
+
"LinearMap.SeparatingLeft.toMatrix\u2082",
|
30 |
+
"Cardinal.pow_cast_right",
|
31 |
+
"t1Space_iff_continuous_cofinite_of",
|
32 |
+
"Antitone.pairwise_disjoint_on_Ioc_pred",
|
33 |
+
"continuous_quotient_mk'",
|
34 |
+
"Finset.smul_finset_union",
|
35 |
+
"Subsingleton.antitone'",
|
36 |
+
"LocalHomeomorph.symm_image_target_inter_eq",
|
37 |
+
"DoubleCentralizer.toProdMulOpposite_injective",
|
38 |
+
"Submodule.mk_quotientEquivOfIsCompl_apply",
|
39 |
+
"Filter.prod_mono_left",
|
40 |
+
"Seminorm.ext",
|
41 |
+
"List.isPrefixOf_cons\u2082",
|
42 |
+
"Cardinal.toNat_eq_iff",
|
43 |
+
"Polynomial.continuousWithinAt_aeval",
|
44 |
+
"Directed.mono",
|
45 |
+
"NonUnitalSubsemiring.mk'_toAddSubmonoid",
|
46 |
+
"Filter.inf_principal_neBot_iff",
|
47 |
+
"Filter.eventually_of_mem",
|
48 |
+
"Relation.TransGen.head",
|
49 |
+
"MvPolynomial.eval\u2082_zero_apply",
|
50 |
+
"LowerSet.coe_div",
|
51 |
+
"Finset.mem_uIcc_of_le",
|
52 |
+
"ofAdd_smul",
|
53 |
+
"IsMonoidHom.id",
|
54 |
+
"deriv_sqrt",
|
55 |
+
"IsROrC.conj_bit0",
|
56 |
+
"Order.pred_succ_of_not_isMax",
|
57 |
+
"TwoPointing.sum_fst",
|
58 |
+
"SmoothBumpFunction.hasCompactSupport",
|
59 |
+
"UpperHalfPlane.im_ne_zero",
|
60 |
+
"Filter.eventuallyEq_bind",
|
61 |
+
"Mathlib.Meta.Positivity.pow_zero_pos",
|
62 |
+
"CategoryTheory.Subgroupoid.isThin_iff",
|
63 |
+
"CategoryTheory.ActionCategory.\u03c0_map",
|
64 |
+
"coe_basisOfLinearIndependentOfCardEqFinrank",
|
65 |
+
"fderivWithin_pi",
|
66 |
+
"HasDerivWithinAt.const_sub",
|
67 |
+
"WithBot.toDual_lt_iff",
|
68 |
+
"le_iSup'",
|
69 |
+
"LocalHomeomorph.secondCountableTopology_source",
|
70 |
+
"IsLowerSet.le_card_inter_finset",
|
71 |
+
"supIrred_ofDual",
|
72 |
+
"ContinuousMultilinearMap.nnnorm_ofSubsingleton",
|
73 |
+
"Hyperreal.coe_ne_zero",
|
74 |
+
"SetTheory.PGame.zero_lt_one",
|
75 |
+
"IsCompact.isLUB_sSup",
|
76 |
+
"IsBoundedBilinearMap.differentiableOn",
|
77 |
+
"tendsto_atTop_of_eventually_const",
|
78 |
+
"Basis.algebraMap_injective",
|
79 |
+
"ContinuousAt.exp",
|
80 |
+
"StarSubalgebra.map_mono",
|
81 |
+
"tsum_sigma'",
|
82 |
+
"norm_le_norm_add_const_of_dist_le'",
|
83 |
+
"Equiv.sumArrowEquivProdArrow_apply_fst",
|
84 |
+
"Set.iUnion_vsub_left_image",
|
85 |
+
"CategoryTheory.Subobject.underlyingIso_hom_comp_eq_mk",
|
86 |
+
"Real.volume_pi_Ioo",
|
87 |
+
"BoundedLatticeHom.coe_id",
|
88 |
+
"OrderIso.map_csInf",
|
89 |
+
"SetSemiring.add_def",
|
90 |
+
"Metric.isOpen_thickening",
|
91 |
+
"IsClosed.compl_mem_nhds",
|
92 |
+
"isOpen_Ioo",
|
93 |
+
"HasFDerivAt.csin",
|
94 |
+
"ContinuousMap.gen_inter",
|
95 |
+
"NonUnitalSubring.mem_carrier",
|
96 |
+
"CircleDeg1Lift.coe_mul",
|
97 |
+
"WellFoundedLT.fix_eq",
|
98 |
+
"IsCyclotomicExtension.finiteDimensional",
|
99 |
+
"Multiset.count_zero",
|
100 |
+
"Polynomial.eval\u2082_finset_prod",
|
101 |
+
"lt_or_lt_iff_ne",
|
102 |
+
"Equiv.coe_vaddConst_symm",
|
103 |
+
"AEMeasurable.const_inf",
|
104 |
+
"Ordinal.nfp_eq_self",
|
105 |
+
"Nat.Odd.of_mul_right",
|
106 |
+
"Set.mapsTo_iInter_iInter",
|
107 |
+
"Urysohns.CU.left_U_subset_right_C",
|
108 |
+
"FirstOrder.Language.BoundedFormula.IsAtomic.relabel",
|
109 |
+
"abelianizationCongr_of",
|
110 |
+
"MonoidHom.ker_restrict",
|
111 |
+
"MeasureTheory.measure_toMeasurable_union",
|
112 |
+
"ContinuousWithinAt.mem_closure",
|
113 |
+
"IsLocalMaxOn.sup",
|
114 |
+
"Rep.MonoidalCategory.braiding_inv_apply",
|
115 |
+
"MultilinearMap.map_update_zero",
|
116 |
+
"commutatorElement_self",
|
117 |
+
"LinearMap.fst_surjective",
|
118 |
+
"LinearMap.IsRefl.flip_isRefl_iff",
|
119 |
+
"Equiv.Perm.VectorsProdEqOne.zero_eq",
|
120 |
+
"IsCompact.isGreatest_sSup",
|
121 |
+
"Set.image_add_const_Icc",
|
122 |
+
"Colex.eq_iff",
|
123 |
+
"Ordinal.typein_enum",
|
124 |
+
"QuadraticForm.complex_equivalent",
|
125 |
+
"affineSpan_le",
|
126 |
+
"MeasureTheory.integral_iUnion_ae",
|
127 |
+
"ContinuousWithinAt.comp'",
|
128 |
+
"RePred.of_eq",
|
129 |
+
"Bool.decide_false_iff",
|
130 |
+
"Metric.self_subset_cthickening",
|
131 |
+
"MvPolynomial.aeval_def",
|
132 |
+
"lt_of_eq_of_lt",
|
133 |
+
"WithBot.add_coe_eq_bot_iff",
|
134 |
+
"Set.iUnion_or",
|
135 |
+
"Covby.image",
|
136 |
+
"Subalgebra.restrictScalars_toSubmodule",
|
137 |
+
"Asymptotics.isBigO_pure",
|
138 |
+
"reflexive_oneOneReducible",
|
139 |
+
"nhds_right'_le_nhds_ne",
|
140 |
+
"Algebra.trace_apply",
|
141 |
+
"Btw.btw.antisymm",
|
142 |
+
"CategoryTheory.mop_comp",
|
143 |
+
"iInf_congr_Prop",
|
144 |
+
"Monotone.strictMono_of_injective",
|
145 |
+
"Convex.image_deriv",
|
146 |
+
"PrimeSpectrum.vanishingIdeal_union",
|
147 |
+
"Lists'.mem_of_subset",
|
148 |
+
"Finite.card_pos",
|
149 |
+
"IsROrC.re_add_im",
|
150 |
+
"Set.eq_or_ssubset_of_subset",
|
151 |
+
"AffineIsometryEquiv.coe_mul",
|
152 |
+
"Part.get_mem",
|
153 |
+
"TensorProduct.AlgebraTensorModule.tensorTensorTensorComm_tmul",
|
154 |
+
"Real.Angle.continuous_sin",
|
155 |
+
"Int.card_Icc",
|
156 |
+
"IsLocalization.lift_id",
|
157 |
+
"FractionalIdeal.div_zero",
|
158 |
+
"summable_sum",
|
159 |
+
"FormalMultilinearSeries.norm_mul_pow_le_of_lt_radius",
|
160 |
+
"Num.succ_to_nat",
|
161 |
+
"UpperSet.coe_subset_coe",
|
162 |
+
"Complementeds.coe_bot",
|
163 |
+
"AEMeasurable.div_const",
|
164 |
+
"FirstOrder.Language.Equiv.coe_toEmbedding",
|
165 |
+
"Matrix.isUnit_of_left_inverse",
|
166 |
+
"selfZpow_of_nonneg",
|
167 |
+
"AList.keys_erase",
|
168 |
+
"CategoryTheory.Functor.const.unop_functor_op_obj_map",
|
169 |
+
"UniformFun.hasBasis_nhds",
|
170 |
+
"ContinuousMap.HomotopyEquiv.continuous",
|
171 |
+
"ONote.opow_def",
|
172 |
+
"AlgEquiv.coe_algHom",
|
173 |
+
"SimpleGraph.singleton_disjoint_neighborFinset",
|
174 |
+
"edist_ofMul",
|
175 |
+
"Std.RBNode.insert_toList_zoom_nil",
|
176 |
+
"Mathlib.Tactic.ComputeDegree.natDegree_C_le",
|
177 |
+
"mulIndicator_eventuallyLE_mulIndicator",
|
178 |
+
"lt_inv_of_neg",
|
179 |
+
"PerfectClosure.induction_on",
|
180 |
+
"ComplexShape.down_mk",
|
181 |
+
"inv_add_inv",
|
182 |
+
"InfHom.ext",
|
183 |
+
"OrderEmbedding.isCoatom_of_map_top_of_image",
|
184 |
+
"Std.RBNode.cmpEq.RootOrdered_congr",
|
185 |
+
"nndist_midpoint_midpoint_le",
|
186 |
+
"EuclideanGeometry.oangle_eq_zero_iff_oangle_rev_eq_zero",
|
187 |
+
"Ordinal.mod_mod",
|
188 |
+
"Matrix.submatrix_mul_equiv",
|
189 |
+
"LinearMap.map_neg",
|
190 |
+
"Std.RBNode.Path.Ordered.insert",
|
191 |
+
"Finset.Subset.trans",
|
192 |
+
"Finset.pi_const_singleton",
|
193 |
+
"IsGalois.integral",
|
194 |
+
"MeasureTheory.Lp.stronglyMeasurable",
|
195 |
+
"NonUnitalStarSubalgebra.toNonUnitalSubalgebra_inj",
|
196 |
+
"RelEmbedding.codRestrict_apply",
|
197 |
+
"FiniteDimensional.nontrivial_of_finrank_pos",
|
198 |
+
"ContDiff.rpow_const_of_ne",
|
199 |
+
"transGen_of_succ_of_ne",
|
200 |
+
"Set.preimage_singleton_eq_empty",
|
201 |
+
"lcm_dvd_lcm_mul_left",
|
202 |
+
"Bornology.IsBounded.smul\u2080",
|
203 |
+
"selfAdjoint.val_pow",
|
204 |
+
"NatOrdinal.toOrdinal_symm_eq",
|
205 |
+
"Isometry.uniformContinuous",
|
206 |
+
"ContinuousLinearEquiv.continuousWithinAt",
|
207 |
+
"continuousAt_id",
|
208 |
+
"Disjoint.exists_mem_filter_basis",
|
209 |
+
"Nat.ArithmeticFunction.vonMangoldt_eq_zero_iff",
|
210 |
+
"List.IsPrefix.trans",
|
211 |
+
"coe_inv_unitSphere",
|
212 |
+
"Metric.preimage_mul_left_closedBall",
|
213 |
+
"Subalgebra.center_toSubsemiring",
|
214 |
+
"Algebra.surjective_algebraMap_iff",
|
215 |
+
"closure_diff_intrinsicFrontier",
|
216 |
+
"CliffordAlgebra.reverse_mem_evenOdd_iff",
|
217 |
+
"Submodule.orthogonal_gc",
|
218 |
+
"List.destutter_pair",
|
219 |
+
"Int.ofNat_mul_negSucc",
|
220 |
+
"codisjoint_map_orderIso_iff",
|
221 |
+
"Set.preimage_pi",
|
222 |
+
"Ordinal.toNatOrdinal_zero",
|
223 |
+
"AlternatingMap.map_eq_zero_of_eq",
|
224 |
+
"MeasureTheory.integrableOn_condexpL2_of_measure_ne_top",
|
225 |
+
"mul_lt_mul\u2080",
|
226 |
+
"Filter.BoundedAtFilter.smul",
|
227 |
+
"Subsemiring.le_pointwise_smul_iff\u2080",
|
228 |
+
"Submodule.restrictScalars_top",
|
229 |
+
"Set.eq_empty_of_isEmpty",
|
230 |
+
"CategoryTheory.Sieve.pullback_pushforward_le",
|
231 |
+
"Path.coe_mk",
|
232 |
+
"Matrix.trace_fin_two",
|
233 |
+
"mul_one_eq_id",
|
234 |
+
"Iic_mem_nhds",
|
235 |
+
"Filter.eventually_ne_atBot",
|
236 |
+
"intermediate_value_Ioc",
|
237 |
+
"ContinuousOrderHom.id_comp",
|
238 |
+
"MeasureTheory.Measure.IsComplete.out",
|
239 |
+
"LocalHomeomorph.preimage_interior",
|
240 |
+
"ModelWithCorners.coe_extChartAt_transDiffeomorph",
|
241 |
+
"LipschitzWith.mul_end",
|
242 |
+
"Ordnode.Valid'.node",
|
243 |
+
"HasStrictFDerivAt.cos",
|
244 |
+
"ProbabilityTheory.kernel.prodMkLeft_apply'",
|
245 |
+
"Filter.isAtom_pure",
|
246 |
+
"nhds_bind_nhdsWithin",
|
247 |
+
"EuclideanGeometry.cospherical_empty",
|
248 |
+
"Real.contDiffAt_rpow_const_of_ne",
|
249 |
+
"Polynomial.rootMultiplicity_zero",
|
250 |
+
"Set.vsub_subset_vsub_left",
|
251 |
+
"IsBoundedBilinearMap.map_sub_left",
|
252 |
+
"Set.iUnion_ge_eq_iUnion_nat_add",
|
253 |
+
"Con.toSetoid_inj",
|
254 |
+
"AlgHom.toLieHom_comp",
|
255 |
+
"IsLocalizedModule.fromLocalizedModule'_mk",
|
256 |
+
"OptionT.goto_mkLabel",
|
257 |
+
"Complementeds.mk_top",
|
258 |
+
"MeasureTheory.SimpleFunc.inf_apply",
|
259 |
+
"Sylow.coe_comapOfKerIsPGroup",
|
260 |
+
"Smooth.snd",
|
261 |
+
"CategoryTheory.Functor.essImage.ofNatIso",
|
262 |
+
"Continuous.nndist",
|
263 |
+
"dense_univ",
|
264 |
+
"CategoryTheory.Abelian.comp_epiDesc",
|
265 |
+
"NonUnitalSubsemiring.gc_map_comap",
|
266 |
+
"CategoryTheory.Limits.Multiequalizer.condition",
|
267 |
+
"OrderIso.image_symm_image",
|
268 |
+
"List.Sublist.length_le",
|
269 |
+
"ContinuousConstSMul.secondCountableTopology",
|
270 |
+
"Finset.inr_mem_disjSum",
|
271 |
+
"UniformSpace.Completion.uniformEmbedding_coe",
|
272 |
+
"Matrix.kroneckerMap_reindex_right",
|
273 |
+
"Iff.not_left",
|
274 |
+
"MvPolynomial.monomial_sum_one",
|
275 |
+
"Absorbs.add",
|
276 |
+
"measurable_smul_const",
|
277 |
+
"MeasureTheory.mem_lpMeas_indicatorConstLp",
|
278 |
+
"Filter.NeBot.zero_div_nonneg",
|
279 |
+
"mem_integralClosure_iff_mem_FG",
|
280 |
+
"CategoryTheory.NatTrans.naturality_app",
|
281 |
+
"ContinuousLinearEquiv.mdifferentiableOn",
|
282 |
+
"nndist_triangle",
|
283 |
+
"VectorPrebundle.smoothCoordChange_apply",
|
284 |
+
"Filter.comap_cofinite_le",
|
285 |
+
"Metric.closedBall_subset_closedBall'",
|
286 |
+
"AddValuation.ext_iff",
|
287 |
+
"UniformEmbedding.comp",
|
288 |
+
"LinearMap.map_smul\u2082",
|
289 |
+
"Symmetric.swap_eq",
|
290 |
+
"IsMetricSeparated.union_right",
|
291 |
+
"FirstOrder.Language.Substructure.le_comap_of_map_le",
|
292 |
+
"Nat.mul_lt_mul'",
|
293 |
+
"AddMonoidHom.extension_coe",
|
294 |
+
"IsROrC.algebraMap_eq_ofReal",
|
295 |
+
"List.foldr_nil",
|
296 |
+
"SymAlg.mul_def",
|
297 |
+
"inf_right_comm",
|
298 |
+
"inv_ball",
|
299 |
+
"Antitone.le_leftLim",
|
300 |
+
"Prod.fst_comp_toSigma",
|
301 |
+
"Ordinal.enumOrd_def_nonempty",
|
302 |
+
"IsMin.Iio_eq",
|
303 |
+
"IsLocalMinOn.min",
|
304 |
+
"DifferentiableOn.analyticOn",
|
305 |
+
"TopCat.Presheaf.isSheaf_iff_isSheafEqualizerProducts",
|
306 |
+
"Option.to_list_none",
|
307 |
+
"GeneralizedContinuedFraction.convergent_eq_conts_a_div_conts_b",
|
308 |
+
"NNReal.summable_mk",
|
309 |
+
"SemidirectProduct.inv_right",
|
310 |
+
"Finset.compl_eq_univ_iff",
|
311 |
+
"Matrix.blockDiagonal_apply_ne",
|
312 |
+
"Basis.card_le_card_of_submodule",
|
313 |
+
"Set.mem_sigma_iff",
|
314 |
+
"Vector.mapAccumr_cons",
|
315 |
+
"Order.Cofinal.le_above",
|
316 |
+
"Subsemigroup.map_strictMono_of_injective",
|
317 |
+
"csSup_Iic",
|
318 |
+
"Monoid.coe_one",
|
319 |
+
"ZMod.injective_valMinAbs",
|
320 |
+
"intervalIntegral.integral_nonneg_of_ae",
|
321 |
+
"measurable_mem",
|
322 |
+
"Submodule.toAddSubmonoid_toNatSubmodule",
|
323 |
+
"dNext_comp_left",
|
324 |
+
"Cardinal.lift_mk_shrink",
|
325 |
+
"IsIntegral.sum",
|
326 |
+
"CategoryTheory.Presheaf.isSheaf_of_isTerminal",
|
327 |
+
"NonemptyInterval.ext_iff",
|
328 |
+
"ProjectiveSpectrum.mem_coe_basicOpen",
|
329 |
+
"ModuleCat.piIsoPi_inv_kernel_\u03b9",
|
330 |
+
"Function.Injective.hasLeftInverse",
|
331 |
+
"Subsemigroup.mem_closure",
|
332 |
+
"WithBot.Icc_bot_coe",
|
333 |
+
"Std.RBNode.Path.Balanced.insert",
|
334 |
+
"CategoryTheory.Preadditive.hasCoequalizers_of_hasCokernels",
|
335 |
+
"Filter.Tendsto.mono_right",
|
336 |
+
"Filter.Tendsto.nndist",
|
337 |
+
"ContinuousMap.congr_fun",
|
338 |
+
"isCompactOperator_iff_isCompact_closure_image_closedBall",
|
339 |
+
"Relation.TransGen.head'",
|
340 |
+
"CategoryTheory.Limits.coequalizer.condition",
|
341 |
+
"Set.Ioc_subset_Ioo_union_Icc",
|
342 |
+
"Subgroup.mem_closure",
|
343 |
+
"isOpen_extChartAt_source",
|
344 |
+
"AddMonoidAlgebra.le_infDegree_add",
|
345 |
+
"DFinsupp.sumAddHom_zero",
|
346 |
+
"Filter.tendsto_add_atTop_nat",
|
347 |
+
"PicardLindelof.FunSpace.uniformInducing_toContinuousMap",
|
348 |
+
"MulAction.orbit_smul_subset",
|
349 |
+
"max_mul_mul_le_max_mul_max'",
|
350 |
+
"Submodule.span_insert_eq_span",
|
351 |
+
"SimpleGraph.mem_cliqueFinset_iff",
|
352 |
+
"HasDerivAt.arsinh",
|
353 |
+
"Matrix.UnitaryGroup.toLin'_one",
|
354 |
+
"Codisjoint.himp_le_of_right_le",
|
355 |
+
"bit0_eq_zero",
|
356 |
+
"Fin.pos",
|
357 |
+
"Std.RBNode.insert_toList_zoom_node",
|
358 |
+
"IntermediateField.mem_mk",
|
359 |
+
"MeasureTheory.measurableEmbedding_of_fderivWithin",
|
360 |
+
"InitialSeg.trans_apply",
|
361 |
+
"List.rel_sections",
|
362 |
+
"Submodule.mul_comm",
|
363 |
+
"AlternatingMap.curryLeft_smul",
|
364 |
+
"bddAbove_smul_iff_of_pos",
|
365 |
+
"OrderDual.Preorder.dual_dual",
|
366 |
+
"Int.not_irrational",
|
367 |
+
"left_mem_affineSpan_pair",
|
368 |
+
"AddSubgroup.mem_smul_pointwise_iff_exists",
|
369 |
+
"CategoryTheory.Idempotents.app_p_comm",
|
370 |
+
"SetLike.exists",
|
371 |
+
"Fintype.exists_le_card_fiber_of_mul_le_card",
|
372 |
+
"Filter.blimsup_eq",
|
373 |
+
"Continuous.inv\u2080",
|
374 |
+
"Continuous.exp",
|
375 |
+
"MeasureTheory.quasiMeasurePreserving_div",
|
376 |
+
"isConnected_Ico",
|
377 |
+
"Subtype.coe_sup",
|
378 |
+
"SimpleGraph.swap_mem_interedges_iff",
|
379 |
+
"IsROrC.I_mul_I",
|
380 |
+
"MeasureTheory.SimpleFunc.mem\u2112p_iff",
|
381 |
+
"ENNReal.inv_limsup",
|
382 |
+
"Algebra.TensorProduct.map_comp",
|
383 |
+
"div_mem_comm_iff",
|
384 |
+
"Set.exists_image_iff",
|
385 |
+
"Nat.digits_zero_zero",
|
386 |
+
"NonUnitalAlgebra.inf_toNonUnitalSubsemiring",
|
387 |
+
"iInf_ne_top_subtype",
|
388 |
+
"Complex.zero_lt_real",
|
389 |
+
"AddSubgroup.pointwise_smul_le_pointwise_smul_iff",
|
390 |
+
"RingHom.ker_ne_top",
|
391 |
+
"MulAction.Supports.mono",
|
392 |
+
"Nat.Prime.ne_one",
|
393 |
+
"QuotientGroup.homQuotientZPowOfHom_id",
|
394 |
+
"continuousWithinAt_const",
|
395 |
+
"derivWithin_pow'",
|
396 |
+
"Set.Nonempty.inv",
|
397 |
+
"Finset.singleton_one",
|
398 |
+
"Equiv.Perm.ofSubtype_apply_coe",
|
399 |
+
"LieEquiv.refl_symm",
|
400 |
+
"Function.one_lt_const",
|
401 |
+
"measure_Ico_lt_top",
|
402 |
+
"CategoryTheory.Functor.initial_natIso_iff",
|
403 |
+
"ENNReal.top_ne_zero",
|
404 |
+
"frontier_Iic_subset",
|
405 |
+
"OrderIso.ext",
|
406 |
+
"Filter.comap_embedding_atBot",
|
407 |
+
"AlgEquiv.restrictScalars_apply",
|
408 |
+
"IsUnit.mul_left_eq_zero",
|
409 |
+
"smul_vsub_rev_vadd_mem_affineSpan_pair",
|
410 |
+
"Filter.EventuallyEq.differentiableAt_iff",
|
411 |
+
"nonempty_measurable_superset",
|
412 |
+
"Set.iInter_plift_down",
|
413 |
+
"SimpleGraph.edgeDensity_le_one",
|
414 |
+
"Finsupp.not_mem_graph_snd_zero",
|
415 |
+
"normUnit_eq_one",
|
416 |
+
"not_imp_eq_of_eq_false_right",
|
417 |
+
"AlgHom.one_apply",
|
418 |
+
"iInf_iInf_eq_right",
|
419 |
+
"Finset.Nonempty.sym",
|
420 |
+
"AddCommGroupCat.asHom_apply",
|
421 |
+
"PSet.Equiv.symm",
|
422 |
+
"SeparatedNhds.preimage",
|
423 |
+
"CliffordAlgebraQuaternion.toQuaternion_ofQuaternion",
|
424 |
+
"Finsupp.prod_antidiagonal_swap",
|
425 |
+
"LocalHomeomorph.image_source_eq_target",
|
426 |
+
"Std.BinomialHeap.Imp.Heap.WF.merge",
|
427 |
+
"lowerClosure_eq_bot_iff",
|
428 |
+
"compl_sup_compl_le",
|
429 |
+
"Stream'.Seq.mem_cons_of_mem",
|
430 |
+
"measurableEmbedding_const_smul\u2080",
|
431 |
+
"iff_true_iff",
|
432 |
+
"AlgebraicGeometry.quasiCompact_stableUnderBaseChange",
|
433 |
+
"EsakiaHom.ext",
|
434 |
+
"NonUnitalSubalgebra.coe_map",
|
435 |
+
"CategoryTheory.finitaryExtensive_of_preserves_and_reflects",
|
436 |
+
"Finset.min_insert",
|
437 |
+
"Set.ordConnected_uIoc",
|
438 |
+
"Asymptotics.IsBigO.pow",
|
439 |
+
"Monotone.map_csInf",
|
440 |
+
"GenLoop.continuous_toLoop",
|
441 |
+
"Quotient.exact'",
|
442 |
+
"eq_of_abs_sub_nonpos",
|
443 |
+
"FormalMultilinearSeries.apply_order_ne_zero'",
|
444 |
+
"IsHausdorff.haus",
|
445 |
+
"ProbabilityTheory.IndepSets.union_iff",
|
446 |
+
"FirstOrder.Language.Substructure.map_inf_comap_of_surjective",
|
447 |
+
"FractionalIdeal.one_mem_one",
|
448 |
+
"isCompl_toDual_iff",
|
449 |
+
"smul_inv''",
|
450 |
+
"Cardinal.toNat_apply_of_lt_aleph0",
|
451 |
+
"Metric.equicontinuous_of_continuity_modulus",
|
452 |
+
"StarSubalgebra.centralizer_le",
|
453 |
+
"List.Sorted.get_strictMono",
|
454 |
+
"ContractingWith.efixedPoint_mem'",
|
455 |
+
"MeasureTheory.Integrable.norm",
|
456 |
+
"Sum.Lex.inl_lt_inl_iff",
|
457 |
+
"MeasureTheory.ProbabilityMeasure.tendsto_nhds_iff_toFiniteMeasure_tendsto_nhds",
|
458 |
+
"List.Sublist.count_le",
|
459 |
+
"min_one",
|
460 |
+
"Finset.eq_of_mem_slice",
|
461 |
+
"MvPolynomial.IsWeightedHomogeneous.add",
|
462 |
+
"Int.ofNat_eq_zero",
|
463 |
+
"contMDiffAt_const",
|
464 |
+
"Subring.prod_mono",
|
465 |
+
"Set.diff_diff_cancel_left",
|
466 |
+
"Set.mapsTo_prod_map_diagonal",
|
467 |
+
"VectorAllP.imp",
|
468 |
+
"Equiv.Perm.support_refl",
|
469 |
+
"IsLocallyConstant.iff_isOpen_fiber",
|
470 |
+
"Polynomial.fderivWithin_aeval",
|
471 |
+
"CategoryTheory.IsFilteredOrEmpty.of_isRightAdjoint",
|
472 |
+
"MonotoneOn.Ico",
|
473 |
+
"QuadraticForm.linMulLin_comp",
|
474 |
+
"LocallyConstant.coe_desc",
|
475 |
+
"IsLprojection.le_def",
|
476 |
+
"CategoryTheory.Faithful.div_faithful",
|
477 |
+
"HNNExtension.NormalWord.consRecOn_ofGroup",
|
478 |
+
"isG\u03b4_empty",
|
479 |
+
"ack_le_iff_right",
|
480 |
+
"Tuple.antitone_pair_of_not_sorted",
|
481 |
+
"Matrix.isDiag_iff_diagonal_diag",
|
482 |
+
"AddValuation.map_add",
|
483 |
+
"CoheytingHom.coe_id",
|
484 |
+
"CategoryTheory.Limits.image.isoStrongEpiMono_inv_comp_mono",
|
485 |
+
"Prod.uIcc_eq",
|
486 |
+
"Finsupp.mapRange.linearEquiv_apply",
|
487 |
+
"DifferentiableOn.hasFDerivAt",
|
488 |
+
"decidableEq_inr_neg",
|
489 |
+
"DifferentiableWithinAt.sub_const",
|
490 |
+
"AEMeasurable.indicator",
|
491 |
+
"MeasureTheory.AEStronglyMeasurable.indicator",
|
492 |
+
"span_gramSchmidt_Iio",
|
493 |
+
"Set.bounded_gt_Ioo",
|
494 |
+
"Finset.ssubset_of_ssubset_of_subset",
|
495 |
+
"Set.Infinite.of_smul_set",
|
496 |
+
"DifferentiableAt.sinh",
|
497 |
+
"Set.Subsingleton.coe_sort",
|
498 |
+
"ContMDiffAt.smul",
|
499 |
+
"MulAction.fixed_eq_iInter_fixedBy",
|
500 |
+
"upperSemicontinuousOn_const",
|
501 |
+
"Finset.singleton_ne_empty",
|
502 |
+
"List.some_nthLe_eq",
|
503 |
+
"UpperHalfPlane.continuous_re",
|
504 |
+
"Subalgebra.coe_sub",
|
505 |
+
"Embedding.isSeparable_preimage",
|
506 |
+
"Complex.continuousOn_tan",
|
507 |
+
"Sum.Lex.inl_le_inr",
|
508 |
+
"WithTop.forall",
|
509 |
+
"Set.Finite.einfsep_pos",
|
510 |
+
"Ideal.mem_span_singleton'",
|
511 |
+
"MeasureTheory.Ioo_ae_eq_Ioc'",
|
512 |
+
"CategoryTheory.Equivalence.functor_map_inj_iff",
|
513 |
+
"HasFPowerSeriesOnBall.add",
|
514 |
+
"CategoryTheory.IsDetector.isSeparator",
|
515 |
+
"Set.mem_sep_iff",
|
516 |
+
"List.mem_keys_of_mem_keys_kerase",
|
517 |
+
"IsCompactOperator.clm_comp",
|
518 |
+
"EuclideanHalfSpace.ext",
|
519 |
+
"NonUnitalStarAlgebra.map_top",
|
520 |
+
"Set.finite_range_findGreatest",
|
521 |
+
"Filter.Tendsto.zpow",
|
522 |
+
"MeasurableEmbedding.comap_eq",
|
523 |
+
"HasFPowerSeriesOnBall.analyticAt",
|
524 |
+
"CauSeq.lim_le",
|
525 |
+
"Int.div_mul_cancel",
|
526 |
+
"Complex.nnnorm_int",
|
527 |
+
"Subsemigroup.map_map",
|
528 |
+
"HasFDerivWithinAt.mono_of_mem",
|
529 |
+
"Set.Icc_subset_Ioi_iff",
|
530 |
+
"Algebra.toSubsemiring_eq_top",
|
531 |
+
"Set.mem_union_left",
|
532 |
+
"LinearPMap.adjoint_apply_eq",
|
533 |
+
"not_eq_of_eq_true",
|
534 |
+
"elementalStarAlgebra.isClosed",
|
535 |
+
"Matrix.toLin'_apply",
|
536 |
+
"Ordinal.blsub_id",
|
537 |
+
"measurable_quotient_mk'",
|
538 |
+
"EuclideanGeometry.left_ne_right_of_oangle_eq_pi_div_two",
|
539 |
+
"isClopen_compl_iff",
|
540 |
+
"LieSubalgebra.mem_mk_iff",
|
541 |
+
"Ici_toDual",
|
542 |
+
"antivaryOn_toDual_right",
|
543 |
+
"Asymptotics.SuperpolynomialDecay.mul_param_zpow",
|
544 |
+
"Cardinal.mk_out",
|
545 |
+
"Module.Ray.someRayVector_ray",
|
546 |
+
"OrderMonoidHom.toMonoidHom_eq_coe",
|
547 |
+
"Fin.forall_fin_succ_pi",
|
548 |
+
"apply_wcovby_apply_iff",
|
549 |
+
"Subtype.mk_le_mk",
|
550 |
+
"StarSubalgebra.range_le",
|
551 |
+
"ContinuousOrderHom.coe_id",
|
552 |
+
"IntervalIntegrable.aestronglyMeasurable",
|
553 |
+
"AntisymmRel.trans_wcovby",
|
554 |
+
"Continuous.prod_mk",
|
555 |
+
"HasStrictFDerivAt.eq_implicitFunctionOfComplemented",
|
556 |
+
"Matrix.of_add_of",
|
557 |
+
"ContinuousMap.one_comp",
|
558 |
+
"CategoryTheory.Limits.IsZero.eq_of_tgt",
|
559 |
+
"\u03b5NFA.start_one",
|
560 |
+
"CategoryTheory.Limits.WalkingPair.equivBool_symm_apply_false",
|
561 |
+
"Matrix.conjTranspose_list_prod",
|
562 |
+
"Nat.sqrt_add_eq'",
|
563 |
+
"SetTheory.PGame.moveRight_nim'",
|
564 |
+
"Turing.Tape.write_nth",
|
565 |
+
"Hyperreal.Infinite.ne_zero",
|
566 |
+
"SimpleGraph.Subgraph.neighborSet_sup",
|
567 |
+
"CategoryTheory.isIso_of_epi_of_nonzero",
|
568 |
+
"MeasureTheory.Measure.coe_add",
|
569 |
+
"Option.Mem.leftUnique",
|
570 |
+
"Quot.liftOn\u2082_mk",
|
571 |
+
"CochainComplex.mkHom_f_1",
|
572 |
+
"div_neg_of_pos_of_neg",
|
573 |
+
"RingHom.Finite.of_surjective",
|
574 |
+
"Finset.ne_empty_of_mem",
|
575 |
+
"FractionalIdeal.map_comp",
|
576 |
+
"CircleDeg1Lift.monotone",
|
577 |
+
"Finset.disjiUnion_cons",
|
578 |
+
"CategoryTheory.op_zsmul",
|
579 |
+
"Ordinal.nat_cast_succ",
|
580 |
+
"IsROrC.conj_re",
|
581 |
+
"Set.div_eq_empty",
|
582 |
+
"MvPolynomial.counit_surjective",
|
583 |
+
"CauSeq.Completion.mk_mul",
|
584 |
+
"Submodule.quotEquivOfEq_mk",
|
585 |
+
"Continuous.Icc_extend'",
|
586 |
+
"Function.Injective.sum_elim",
|
587 |
+
"RingHom.map_list_prod",
|
588 |
+
"ENNReal.essSup_const_mul",
|
589 |
+
"Std.RBSet.mkRBSet_eq",
|
590 |
+
"Ideal.IsPrime.radical_le_iff",
|
591 |
+
"NonUnitalStarSubalgebra.mem_toNonUnitalSubalgebra",
|
592 |
+
"Set.image_iInter_subset",
|
593 |
+
"pathComponent_symm",
|
594 |
+
"MeasureTheory.ProbabilityMeasure.toFiniteMeasure_embedding",
|
595 |
+
"Hindman.exists_FP_of_finite_cover",
|
596 |
+
"Prefunctor.pathStar_apply",
|
597 |
+
"Set.Nonempty.of_mul_left",
|
598 |
+
"Nat.bit0_lt_bit1",
|
599 |
+
"Hyperreal.InfinitePos.pos",
|
600 |
+
"CliffordAlgebra.EquivEven.Q'_apply",
|
601 |
+
"SemiNormedGroupCat.explicitCokernelDesc_zero",
|
602 |
+
"StrictMono.orderIsoOfSurjective_symm_apply_self",
|
603 |
+
"OrderIso.toFun_eq_coe",
|
604 |
+
"LinearMap.mulRight_toAddMonoidHom",
|
605 |
+
"MulAut.mul_apply",
|
606 |
+
"WithBot.le_of_add_le_add_right",
|
607 |
+
"ExistsContDiffBumpBase.u_smooth",
|
608 |
+
"StrictMonoOn.comp_strictAntiOn",
|
609 |
+
"CentroidHom.toAddMonoidHom_eq_coe",
|
610 |
+
"SetSemiring.up_down",
|
611 |
+
"IsCoatom.le_iff",
|
612 |
+
"IsCompact.totallyBounded",
|
613 |
+
"isBoundedBilinearMap_smulRight",
|
614 |
+
"IsMax.Ici_eq",
|
615 |
+
"Finset.forall_of_forall_insert",
|
616 |
+
"MonotoneOn.quasiconvexOn",
|
617 |
+
"Subfield.closure_le",
|
618 |
+
"NumberField.Units.dirichletUnitTheorem.seq_norm_ne_zero",
|
619 |
+
"Ultrafilter.em",
|
620 |
+
"AlternatingMap.curryLeft_add",
|
621 |
+
"pi_nnnorm_const'",
|
622 |
+
"Int.nonneg_of_pos",
|
623 |
+
"contDiffWithinAt_inter",
|
624 |
+
"Finsupp.support_neg",
|
625 |
+
"Abelianization.lift.unique",
|
626 |
+
"Unitization.inr_zero",
|
627 |
+
"ENNReal.coe_lt_top",
|
628 |
+
"SmoothBumpFunction.nhds_basis_support",
|
629 |
+
"Set.center_eq_univ",
|
630 |
+
"WithTop.toDual_symm_apply",
|
631 |
+
"Finset.div_inter_subset",
|
632 |
+
"LinearIsometryEquiv.norm_map",
|
633 |
+
"BotHom.coe_comp",
|
634 |
+
"isOpen_uniformity",
|
635 |
+
"SemidirectProduct.inr_injective",
|
636 |
+
"Nat.cast_min",
|
637 |
+
"Derivation.sub_apply",
|
638 |
+
"Complex.normSq_eq_zero",
|
639 |
+
"ContMDiffOn.congr",
|
640 |
+
"Fin.prod_univ_zero",
|
641 |
+
"Order.bot_lt_succ",
|
642 |
+
"IsScalarTower.coe_toAlgHom",
|
643 |
+
"parallelogram_law_with_nnnorm",
|
644 |
+
"Rat.zero_den",
|
645 |
+
"Finset.codisjoint_inf_right",
|
646 |
+
"Finsupp.comapSMul_single",
|
647 |
+
"FirstOrder.Language.Equiv.toEmbedding_toHom",
|
648 |
+
"Commute.multiset_sum_left",
|
649 |
+
"Finset.monotone_filter_left",
|
650 |
+
"DFinsupp.not_mem_neLocus",
|
651 |
+
"isClopen_biInter_finset",
|
652 |
+
"continuous_empty_function",
|
653 |
+
"Set.Ioo_subset_Ico_self",
|
654 |
+
"ConvexCone.Salient.anti",
|
655 |
+
"Submodule.map_smul''",
|
656 |
+
"IsROrC.continuous_normSq",
|
657 |
+
"Set.sInf_eq_sInter",
|
658 |
+
"ContDiffWithinAt.cos",
|
659 |
+
"Polynomial.degree_lt_wf",
|
660 |
+
"PSet.equiv_iff_mem",
|
661 |
+
"CategoryTheory.ihom.coev_ev",
|
662 |
+
"CategoryTheory.Limits.Bicone.toCone_\u03c0_app_mk",
|
663 |
+
"Real.hasDerivAt_arcsin",
|
664 |
+
"SetLike.homogeneous_coe",
|
665 |
+
"Field.subset_closure",
|
666 |
+
"lowerSemicontinuous_iff_isOpen_preimage",
|
667 |
+
"HasDerivAt.tendsto_punctured_nhds",
|
668 |
+
"CategoryTheory.Subgroupoid.map_comap_le",
|
669 |
+
"Multiset.of_mem_filter",
|
670 |
+
"MeasureTheory.AEDisjoint.of_null_right",
|
671 |
+
"extChartAt_preimage_mem_nhdsWithin",
|
672 |
+
"ApplicativeTransformation.preserves_pure",
|
673 |
+
"Set.Subsingleton.measurableSet",
|
674 |
+
"Set.Bounded.mono",
|
675 |
+
"MulPosMono.toMulPosStrictMono",
|
676 |
+
"inf_le_bihimp",
|
677 |
+
"IsometryEquiv.symm_trans_apply",
|
678 |
+
"Real.pi_div_two_eq_arcsin",
|
679 |
+
"deriv_sq_norm_ne_zero",
|
680 |
+
"Filter.eventuallyEq_principal",
|
681 |
+
"ContinuousLinearMap.coe_restrictScalars",
|
682 |
+
"Finset.fold_singleton",
|
683 |
+
"IsCoatom.lt_iff",
|
684 |
+
"ContinuousOrderHom.comp_id",
|
685 |
+
"Matrix.fromBlocks_apply\u2081\u2081",
|
686 |
+
"IsClopen.isClosed",
|
687 |
+
"LieModuleHom.add_apply",
|
688 |
+
"Finset.Icc_subset_Icc_left",
|
689 |
+
"Complex.I_re",
|
690 |
+
"frobenius_sub",
|
691 |
+
"LinearMap.IsAlt.self_eq_zero",
|
692 |
+
"CliffordAlgebra.EquivEven.reverse_e0",
|
693 |
+
"NonUnitalAlgHom.subtype_comp_codRestrict",
|
694 |
+
"star_intCast",
|
695 |
+
"Filter.exists_eventuallyEq_const_of_forall_separating",
|
696 |
+
"Int.eq_of_associated_of_nonneg",
|
697 |
+
"Finset.mem_union_left",
|
698 |
+
"Fin.val_two",
|
699 |
+
"lowerBounds_mono",
|
700 |
+
"HolderOnWith.ediam_image_inter_le_of_le",
|
701 |
+
"edist_dist",
|
702 |
+
"StrictConcaveOn.inf",
|
703 |
+
"CategoryTheory.Limits.BinaryBicone.fstKernelFork_\u03b9",
|
704 |
+
"TensorProduct.lid_tmul",
|
705 |
+
"MeasurableSpace.generateFrom_sup_generateFrom",
|
706 |
+
"ContinuousAt.rpow_const",
|
707 |
+
"Subalgebra.coe_restrictScalars",
|
708 |
+
"TrivSqZeroExt.inl_add",
|
709 |
+
"Equiv.Perm.VectorsProdEqOne.rotate_zero",
|
710 |
+
"ENNReal.continuous_nnreal_sub",
|
711 |
+
"Finset.mul_univ_of_one_mem",
|
712 |
+
"PowerSeries.coe_X",
|
713 |
+
"Set.image_subtype_val_Ioo_subset",
|
714 |
+
"Metric.isometry_inl",
|
715 |
+
"Ideal.le_map_of_comap_le_of_surjective",
|
716 |
+
"embedding_of_embedding_compose",
|
717 |
+
"LieSubalgebra.span_empty",
|
718 |
+
"hammingNorm_lt_one",
|
719 |
+
"SubMulAction.mem_carrier",
|
720 |
+
"Monoid.End.coe_pow",
|
721 |
+
"IsROrC.I_mul_I_of_nonzero",
|
722 |
+
"MeasureTheory.Integrable.integral_condDistrib",
|
723 |
+
"MeasureTheory.StronglyMeasurable.div",
|
724 |
+
"pow_ne_zero",
|
725 |
+
"MeasurableEquiv.coe_smul\u2080",
|
726 |
+
"Even.mul_left",
|
727 |
+
"BoxIntegral.Prepartition.le_biUnionIndex",
|
728 |
+
"MeasureTheory.Submartingale.sum_mul_sub'",
|
729 |
+
"iteratedFDeriv_add_apply'",
|
730 |
+
"QuotientGroup.homQuotientZPowOfHom_comp_of_rightInverse",
|
731 |
+
"SimpleGraph.Reachable.trans",
|
732 |
+
"zero_smul",
|
733 |
+
"RingEquiv.toMonoidHom_commutes",
|
734 |
+
"le_of_neg_of_one_div_le_one_div",
|
735 |
+
"CategoryTheory.IsCofilteredOrEmpty.of_initial",
|
736 |
+
"IsLeast.isGLB",
|
737 |
+
"EMetric.diam_eq_zero_iff",
|
738 |
+
"Antitone.vecCons",
|
739 |
+
"Set.image3_congr'",
|
740 |
+
"LatticeOrderedGroup.m_neg_part_def",
|
741 |
+
"MeasureTheory.SimpleFunc.inv_apply",
|
742 |
+
"LinearMap.range_toAddSubmonoid",
|
743 |
+
"LinearMap.detAux_id",
|
744 |
+
"min_lt_iff",
|
745 |
+
"Submodule.mem_div_iff_forall_mul_mem",
|
746 |
+
"ModuleCat.monoidalClosed_curry",
|
747 |
+
"List.Forall\u2082.mp",
|
748 |
+
"CategoryTheory.\u03bc_inv_naturality",
|
749 |
+
"Asymptotics.IsLittleO.add",
|
750 |
+
"CategoryTheory.FreeBicategory.mk_id",
|
751 |
+
"Set.diff_univ",
|
752 |
+
"ContinuousMultilinearMap.coe_restrictScalars",
|
753 |
+
"prod_mk_mem_compRel",
|
754 |
+
"Real.Angle.cos_coe",
|
755 |
+
"nhds_eq_nhds_emetric_ball",
|
756 |
+
"Std.RBNode.Stream.toList_nil",
|
757 |
+
"Set.ordConnected_biInter",
|
758 |
+
"VectorBundleCore.mem_localTriv_source",
|
759 |
+
"MeasureTheory.Measure.measure_Ioo_eq_zero",
|
760 |
+
"mul_left_cancel''",
|
761 |
+
"AbstractCompletion.continuous_map",
|
762 |
+
"LipschitzOnWith.edist_le_mul_of_le",
|
763 |
+
"ContinuousOrderHom.coe_copy",
|
764 |
+
"DiffContOnCl.const_smul",
|
765 |
+
"Asymptotics.superpolynomialDecay_iff_abs_tendsto_zero",
|
766 |
+
"IsGenericPoint.specializes_iff_mem",
|
767 |
+
"CauSeq.mul_pos",
|
768 |
+
"ContinuousMultilinearMap.bounds_bddBelow",
|
769 |
+
"MeasureTheory.Measure.lintegral_bind",
|
770 |
+
"PrimeMultiset.coeNat_injective",
|
771 |
+
"List.argmin_singleton",
|
772 |
+
"Subsemiring.center_eq_top",
|
773 |
+
"IsLUB.exists_between_sub_self",
|
774 |
+
"WithLp.equiv_symm_single",
|
775 |
+
"AntitoneOn.convex_le",
|
776 |
+
"inducing_subtype_val",
|
777 |
+
"Subgroup.mem_iSup_of_mem",
|
778 |
+
"NonUnitalStarSubalgebra.coe_center",
|
779 |
+
"Set.image2_subset_iff",
|
780 |
+
"MvPolynomial.le_weightedTotalDegree",
|
781 |
+
"EReal.coe_sub",
|
782 |
+
"Finset.inf'_insert",
|
783 |
+
"MeasureTheory.LocallyIntegrableOn.add",
|
784 |
+
"Polynomial.SplittingField.splits",
|
785 |
+
"monotone_of_deriv_nonneg",
|
786 |
+
"List.dProdIndex_nil",
|
787 |
+
"CategoryTheory.MonoidalClosed.homEquiv_symm_apply_eq",
|
788 |
+
"NormedAddGroupHom.smul_apply",
|
789 |
+
"MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono",
|
790 |
+
"MeasureTheory.map_mul_right_eq_self",
|
791 |
+
"ENNReal.mul_left_mono",
|
792 |
+
"UpperSet.prod_sup",
|
793 |
+
"selfAdjoint.val_one",
|
794 |
+
"Filter.map\u2082_map_left_anticomm",
|
795 |
+
"Multiset.monotone_filter_left",
|
796 |
+
"ContinuousLinearMap.map_smul_of_tower",
|
797 |
+
"Disjoint.dual",
|
798 |
+
"Subsemigroup.le_comap_of_map_le",
|
799 |
+
"AbstractCompletion.extend_comp_coe",
|
800 |
+
"WithTop.ofDual_apply_top",
|
801 |
+
"Pi.default_def",
|
802 |
+
"List.singleton_eq",
|
803 |
+
"CocompactMap.coe_copy",
|
804 |
+
"Subgroup.map_inf_le",
|
805 |
+
"Filter.HasBasis.clusterPt_iff",
|
806 |
+
"ENNReal.inv_liminf",
|
807 |
+
"Algebra.TensorProduct.productMap_left",
|
808 |
+
"IsPreconnected.intermediate_value",
|
809 |
+
"RingEquiv.toNonUnitalRingHom_refl",
|
810 |
+
"Submodule.sInf_coe",
|
811 |
+
"Orthonormal.toSubtypeRange",
|
812 |
+
"LocalHomeomorph.contDiff_unitBallBall_symm",
|
813 |
+
"SupHom.dual_id",
|
814 |
+
"TypeVec.lastFun_subtypeVal",
|
815 |
+
"isMinFilter_dual_iff",
|
816 |
+
"CategoryTheory.GrothendieckTopology.Subpresheaf.sheafify_sheafify",
|
817 |
+
"CategoryTheory.Preadditive.forkOfKernelFork_\u03b9",
|
818 |
+
"USize.modn_toNat",
|
819 |
+
"SetTheory.PGame.numeric_zero",
|
820 |
+
"Function.minimalPeriod_id",
|
821 |
+
"CliffordAlgebraComplex.Q_apply",
|
822 |
+
"IsTorsion.quotient_iff",
|
823 |
+
"Subring.toSubsemiring_injective",
|
824 |
+
"Monoid.CoprodI.NeWord.singleton_last",
|
825 |
+
"Ideal.isPrime_of_irreducible_absNorm",
|
826 |
+
"MeasureTheory.MeasurePreserving.prod",
|
827 |
+
"Equiv.eq_symm_comp",
|
828 |
+
"Units.isSMulRegular",
|
829 |
+
"Finite.one_lt_card",
|
830 |
+
"IsClosed.upperSemicontinuousOn_indicator",
|
831 |
+
"Subsingleton.strictMono",
|
832 |
+
"MvPolynomial.vars_one",
|
833 |
+
"CategoryTheory.Limits.Multicoequalizer.multicofork_\u03b9_app_right",
|
834 |
+
"mul_eq_zero_comm",
|
835 |
+
"NonUnitalSubsemiring.mem_closure_iff",
|
836 |
+
"LocalHomeomorph.EqOnSource.eqOn",
|
837 |
+
"Function.is_periodic_id",
|
838 |
+
"LinearMap.mulRight_apply",
|
839 |
+
"List.Chain'.take",
|
840 |
+
"Set.symmDiff_def",
|
841 |
+
"Smooth.smul",
|
842 |
+
"SimpleGraph.Walk.darts_cons",
|
843 |
+
"IsROrC.conj_I",
|
844 |
+
"ContinuousAlternatingMap.map_piecewise_add",
|
845 |
+
"SlashInvariantForm.coe_zero",
|
846 |
+
"MeasureTheory.AEEqFun.lintegral_mk",
|
847 |
+
"Set.inter_compl_self",
|
848 |
+
"cauchySeq_tendsto_of_complete",
|
849 |
+
"Cubic.ne_zero_of_b_ne_zero",
|
850 |
+
"wellFounded_antisymmetrization_iff",
|
851 |
+
"isIrreducible_singleton",
|
852 |
+
"Subgroup.prod_mono_right",
|
853 |
+
"Quaternion.mul_coe_eq_smul",
|
854 |
+
"tendsto_pow_atTop_nhds_0_of_abs_lt_1",
|
855 |
+
"ConjAct.toConjAct_mul",
|
856 |
+
"Function.Commute.comp_right",
|
857 |
+
"Filter.Germ.le_def",
|
858 |
+
"Set.eqOn_comp_right_iff",
|
859 |
+
"Monovary.sum_comp_perm_smul_le_sum_smul",
|
860 |
+
"MvPolynomial.constantCoeff_smul",
|
861 |
+
"AlgHom.range_comp",
|
862 |
+
"CategoryTheory.Functor.const.opObjUnop_hom_app",
|
863 |
+
"GroupFilterBasis.prod_subset_self",
|
864 |
+
"MeasureTheory.SimpleFunc.bind_apply",
|
865 |
+
"TopHom.ext",
|
866 |
+
"Function.Surjective.of_comp_iff",
|
867 |
+
"SetTheory.PGame.Impartial.equiv_zero_iff_le",
|
868 |
+
"Nat.div2_zero",
|
869 |
+
"Sum.getLeft?_inl",
|
870 |
+
"AlternatingMap.domDomCongr_perm",
|
871 |
+
"Filter.coext",
|
872 |
+
"Matrix.conjTranspose_list_sum",
|
873 |
+
"coeFn_fourierLp",
|
874 |
+
"Filter.prod_mono_right",
|
875 |
+
"BoxIntegral.Prepartition.iUnion_biUnionTagged",
|
876 |
+
"NNRat.toNNRat_mono",
|
877 |
+
"uniformContinuous_toMul",
|
878 |
+
"contDiffOn_succ_of_fderiv_apply",
|
879 |
+
"MeasureTheory.AEStronglyMeasurable.inv",
|
880 |
+
"RingHom.asBoolAlg_id",
|
881 |
+
"BoundedContinuousFunction.dist_toContinuousMap",
|
882 |
+
"HilbertBasis.tsum_inner_mul_inner",
|
883 |
+
"tendsto_ceil_atTop",
|
884 |
+
"SimpleGraph.Walk.length_concat",
|
885 |
+
"MeasureTheory.condexpL1_congr_ae",
|
886 |
+
"IsBaseChange.inductionOn",
|
887 |
+
"FirstOrder.Language.Substructure.cg_closure",
|
888 |
+
"ModelWithCorners.right_inv",
|
889 |
+
"Cardinal.toNat_lt_of_lt_of_lt_aleph0",
|
890 |
+
"isOpen_gt'",
|
891 |
+
"Disjoint.inf_right",
|
892 |
+
"Filter.mem_inf_iff",
|
893 |
+
"LocalHomeomorph.refl_prod_refl",
|
894 |
+
"Cardinal.mk_preimage_of_injective_of_subset_range_lift",
|
895 |
+
"PerfectClosure.liftOn_mk",
|
896 |
+
"Set.iInter\u2082_mono'",
|
897 |
+
"LipschitzWith.continuous_compLp",
|
898 |
+
"LinearEquivClass.range",
|
899 |
+
"continuous_const",
|
900 |
+
"DFinsupp.neLocus_add_left",
|
901 |
+
"Order.Ideal.carrier_eq_coe",
|
902 |
+
"Traversable.foldlm_map",
|
903 |
+
"Subsemiring.range_fst",
|
904 |
+
"Set.add_mem_Ioc_iff_left",
|
905 |
+
"MeasureTheory.ae_eq_univ",
|
906 |
+
"AddSubgroup.pointwise_smul_le_iff\u2080",
|
907 |
+
"total_of",
|
908 |
+
"ModularGroup.lcRow0_apply",
|
909 |
+
"Monotone.map_sSup_of_continuousAt'",
|
910 |
+
"StrictMono.minimal_of_minimal_image",
|
911 |
+
"ContinuousMap.HomotopyEquiv.toFun_eq_coe",
|
912 |
+
"PicardLindelof.continuousOn",
|
913 |
+
"Finset.prod_range_add_div_prod_range",
|
914 |
+
"NonUnitalStarSubalgebra.coe_centralizer",
|
915 |
+
"LocalEquiv.prod_target",
|
916 |
+
"Set.preimage_comp_eq",
|
917 |
+
"LinearPMap.map_smul",
|
918 |
+
"Set.biUnion_lt_succ",
|
919 |
+
"Antivary.antivaryOn",
|
920 |
+
"convex_Ioi",
|
921 |
+
"Int.eq_of_mul_eq_one",
|
922 |
+
"Setoid.mkClasses_classes",
|
923 |
+
"Nat.recDiagAux_succ_succ",
|
924 |
+
"WithTop.coe_mono",
|
925 |
+
"Function.update_inv",
|
926 |
+
"Set.Icc_union_Ico_eq_Ico",
|
927 |
+
"balanced_iInter",
|
928 |
+
"FirstOrder.Language.BoundedFormula.realize_rel",
|
929 |
+
"Set.biInter_eq_iInter",
|
930 |
+
"Set.Icc.coe_pow",
|
931 |
+
"Int.covby_iff_succ_eq",
|
932 |
+
"FreeLieAlgebra.liftAux_map_mul",
|
933 |
+
"Con.comap_rel",
|
934 |
+
"Equiv.emptySum_apply_inr",
|
935 |
+
"hasBasis_nhdsSet_Ici_Ioi",
|
936 |
+
"Set.image_mulSingle_Ioc_left",
|
937 |
+
"LocalEquiv.prod_source",
|
938 |
+
"isTotallySeparated_singleton",
|
939 |
+
"Filter.tendsto_atTop_add_nonneg_right",
|
940 |
+
"QuasiconcaveOn.inf",
|
941 |
+
"isOpenMap_ofDual",
|
942 |
+
"finprod_false",
|
943 |
+
"Subsemigroup.coe_bot",
|
944 |
+
"bihimp_right_surjective",
|
945 |
+
"PrimeSpectrum.comap_singleton_isClosed_of_isIntegral",
|
946 |
+
"Finset.insert_subset_insert",
|
947 |
+
"MeasureTheory.aestronglyMeasurable_one",
|
948 |
+
"Subring.pointwise_smul_subset_iff",
|
949 |
+
"IsOpenMap.nhds_le",
|
950 |
+
"Set.nontrivial_iff_exists_lt",
|
951 |
+
"Monotone.Ici",
|
952 |
+
"RingHom.congr_fun",
|
953 |
+
"iInf_mono",
|
954 |
+
"PerfectionMap.hom_ext",
|
955 |
+
"Set.wellFoundedOn_singleton",
|
956 |
+
"coe_mul_unitClosedBall",
|
957 |
+
"upperClosure_empty",
|
958 |
+
"BoundedContinuousFunction.dist_mkOfCompact",
|
959 |
+
"CategoryTheory.Groupoid.isIsomorphic_iff_nonempty_hom",
|
960 |
+
"OpenEmbedding.comp",
|
961 |
+
"LinearEquiv.ofLinear_symm_apply",
|
962 |
+
"himp_le_himp_right",
|
963 |
+
"LipschitzWith.ae_differentiableAt_real",
|
964 |
+
"forall_of_ball",
|
965 |
+
"ContinuousLinearMap.adjointAux_apply",
|
966 |
+
"Set.isSimpleOrder_Iic_iff_isAtom",
|
967 |
+
"SetTheory.PGame.leftMoves_add",
|
968 |
+
"Function.not_lt_argmin",
|
969 |
+
"isLeast_univ",
|
970 |
+
"MeasureTheory.Adapted.progMeasurable_of_discrete",
|
971 |
+
"WellFounded.rank_lt_of_rel",
|
972 |
+
"Finset.erase_mem_shadow",
|
973 |
+
"Subalgebra.mem_centralizer_iff",
|
974 |
+
"Filter.le_vsub_iff",
|
975 |
+
"Set.Ioc.coe_pow",
|
976 |
+
"CategoryTheory.Monoidal.rightUnitor_inv_app",
|
977 |
+
"AddMonoidHom.mul_apply",
|
978 |
+
"AlgebraicGeometry.PresheafedSpace.stalkMap_germ'",
|
979 |
+
"ContinuousLinearEquiv.equivOfInverse_apply",
|
980 |
+
"CategoryTheory.yonedaEquiv_apply",
|
981 |
+
"Or.symm",
|
982 |
+
"ContDiff.restrict_scalars",
|
983 |
+
"Ordinal.nat_cast_pos",
|
984 |
+
"QuaternionAlgebra.nat_cast_re",
|
985 |
+
"PartitionOfUnity.le_one",
|
986 |
+
"LocalHomeomorph.image_open_of_open'",
|
987 |
+
"MonoidHomClass.continuous_of_bound",
|
988 |
+
"antitone_const",
|
989 |
+
"tsum_mul_tsum",
|
990 |
+
"Polynomial.degree_one",
|
991 |
+
"Zsqrtd.coe_int_sub",
|
992 |
+
"MeasureTheory.Measure.MutuallySingular.smul_nnreal",
|
993 |
+
"compl_singleton_mem_nhds_iff",
|
994 |
+
"DualNumber.snd_eps",
|
995 |
+
"FixedPoints.minpoly_eq_minpoly",
|
996 |
+
"Ordnode.Valid.merge",
|
997 |
+
"Set.mapsTo_empty",
|
998 |
+
"Set.EqOn.comp_right",
|
999 |
+
"Option.map_id''",
|
1000 |
+
"MeasureTheory.measure_mono_null",
|
1001 |
+
"MonoidHom.map_finprod_of_injective",
|
1002 |
+
"Set.Ioc.coe_mul",
|
1003 |
+
"tendsto_ceil_left_pure_ceil",
|
1004 |
+
"CliffordAlgebra.\u03b9_comp_lift",
|
1005 |
+
"lineMap_le_left_iff_le",
|
1006 |
+
"Set.iInter_comm",
|
1007 |
+
"Associates.out_injective",
|
1008 |
+
"ContinuousLinearMap.op_norm_le_of_shell",
|
1009 |
+
"PLift.up_surjective",
|
1010 |
+
"SetTheory.Game.PGame.equiv_iff_game_eq",
|
1011 |
+
"Set.mk_preimage_sigma_eq_empty",
|
1012 |
+
"Dense.exists_lt",
|
1013 |
+
"ContDiffAt.inversion",
|
1014 |
+
"TypeVec.dropFun_appendFun",
|
1015 |
+
"Set.image2_vsub",
|
1016 |
+
"zpow_lt_zpow",
|
1017 |
+
"MeasureTheory.integral_Ioi_of_hasDerivAt_of_nonpos'",
|
1018 |
+
"nndist_lineMap_right",
|
1019 |
+
"Action.sum_hom",
|
1020 |
+
"Rack.op_act_op_eq"
|
1021 |
+
]
|
1022 |
+
}
|
random/train.json
ADDED
@@ -0,0 +1,3 @@
|
|
|
|
|
|
|
|
|
1 |
+
version https://git-lfs.github.com/spec/v1
|
2 |
+
oid sha256:2cb44d3a1b0dd03423fed44f5cc2f232fd63e406cbfb26bf0afdc14f9698febe
|
3 |
+
size 325746355
|
random/train_formal_informal.json
ADDED
@@ -0,0 +1,3 @@
|
|
|
|
|
|
|
|
|
1 |
+
version https://git-lfs.github.com/spec/v1
|
2 |
+
oid sha256:d1627f8e2b9cfe904c4465abf82c237a4218dbd2617ca3adb17b52fec27992b8
|
3 |
+
size 133494488
|
random/train_formal_informal_metadata.json
ADDED
The diff for this file is too large to render.
See raw diff
|
|
random/val.json
ADDED
The diff for this file is too large to render.
See raw diff
|
|
random/val_formal_informal.json
ADDED
The diff for this file is too large to render.
See raw diff
|
|
random/val_formal_informal_metadata.json
ADDED
@@ -0,0 +1,987 @@
|
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|
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|
|
|
|
1 |
+
{
|
2 |
+
"total_valid_proofs": 2000,
|
3 |
+
"total_no_tactics": 980,
|
4 |
+
"deliminter": "**",
|
5 |
+
"no_tactics": [
|
6 |
+
"PrimeSpectrum.zeroLocus_union",
|
7 |
+
"Multiset.toDFinsupp_inj",
|
8 |
+
"NNRat.coe_le_coe",
|
9 |
+
"Int.floor_lt",
|
10 |
+
"AlgEquiv.toLieEquiv_apply",
|
11 |
+
"Antitone.directed_le",
|
12 |
+
"Differentiable.clm_comp",
|
13 |
+
"MeasureTheory.AEEqFun.coeFn_div",
|
14 |
+
"Int.two_dvd_ne_zero",
|
15 |
+
"imp_imp_imp",
|
16 |
+
"AnalyticAt.neg",
|
17 |
+
"LocalHomeomorph.nhdsWithin_target_inter",
|
18 |
+
"Measurable.sinh",
|
19 |
+
"HomologicalComplex.id_f",
|
20 |
+
"Finsupp.lex_def",
|
21 |
+
"LocalHomeomorph.restr_trans",
|
22 |
+
"FreeMonoid.smul_def",
|
23 |
+
"AddEquiv.coe_toLinearEquiv",
|
24 |
+
"contMDiffWithinAt_univ",
|
25 |
+
"LinearMap.comp_smul",
|
26 |
+
"ContMDiff.comp_contMDiffOn",
|
27 |
+
"StarSubalgebra.coe_sInf",
|
28 |
+
"RingEquiv.coe_monoidHom_trans",
|
29 |
+
"Part.mod_def",
|
30 |
+
"BoxIntegral.TaggedPrepartition.distortion_disjUnion",
|
31 |
+
"Set.Iic_bot",
|
32 |
+
"Finset.weightedVSub_const_smul",
|
33 |
+
"CompositionSeries.coe_append",
|
34 |
+
"Subgroup.comap_le_comap_of_surjective",
|
35 |
+
"FiberBundleCore.localTrivAsLocalEquiv_coe",
|
36 |
+
"WithBot.some_eq_coe",
|
37 |
+
"UpperHalfPlane.continuous_coe",
|
38 |
+
"OrderMonoidHom.coe_mul",
|
39 |
+
"Continuous.restrictPreimage",
|
40 |
+
"Set.sups_nonempty",
|
41 |
+
"LinearIsometryEquiv.coe_refl",
|
42 |
+
"SemidirectProduct.inl_inj",
|
43 |
+
"ContinuousOn.fin_insertNth",
|
44 |
+
"LinearMap.isIntegral",
|
45 |
+
"IsTop.Iic_eq",
|
46 |
+
"LocalHomeomorph.injOn",
|
47 |
+
"Sum.Ioc_inl_inl",
|
48 |
+
"Int.ofNat_div",
|
49 |
+
"Order.pred_le",
|
50 |
+
"equivalence_of_manyOneEquiv",
|
51 |
+
"HahnSeries.single_ne_zero",
|
52 |
+
"Matrix.vec_single_eq_const",
|
53 |
+
"Commute.symm",
|
54 |
+
"EuclideanGeometry.concyclic_pair",
|
55 |
+
"Matrix.updateColumn_ne",
|
56 |
+
"AddCommGroup.ModEq.sub_left",
|
57 |
+
"QuotientAddGroup.equivIcoMod_coe",
|
58 |
+
"List.set_nil",
|
59 |
+
"List.disjoint_of_subset_left",
|
60 |
+
"ProbabilityTheory.indepSets_of_indepSets_of_le_left",
|
61 |
+
"Subsingleton.eq_univ_of_nonempty",
|
62 |
+
"mdifferentiable_const",
|
63 |
+
"Subtype.mk_lt_mk",
|
64 |
+
"Option.none_orElse",
|
65 |
+
"sInf_image2_eq_sSup_sSup",
|
66 |
+
"NFA.eval_append_singleton",
|
67 |
+
"lowerSemicontinuous_ciSup",
|
68 |
+
"symm_trans_mem_contDiffGroupoid",
|
69 |
+
"intervalIntegral.integral_nonneg",
|
70 |
+
"PrimeSpectrum.zeroLocus_singleton_one",
|
71 |
+
"Set.Ioc_eq_empty_of_le",
|
72 |
+
"ContinuousAlternatingMap.toContinuousMultilinearMap_add",
|
73 |
+
"Real.continuousOn_exp",
|
74 |
+
"ONote.NF.snd",
|
75 |
+
"Vector.replicate_succ",
|
76 |
+
"List.exists_of_length_succ",
|
77 |
+
"isMaxOn_const",
|
78 |
+
"Set.ssubset_of_ssubset_of_subset",
|
79 |
+
"SetTheory.PGame.le_of_le_of_equiv",
|
80 |
+
"Matrix.isDiag_zero",
|
81 |
+
"CategoryTheory.Limits.pushout.condition",
|
82 |
+
"Set.infs_sups_subset_left",
|
83 |
+
"AlgebraicGeometry.StructureSheaf.stalkToFiberRingHom_germ'",
|
84 |
+
"AntitoneOn.map_bddAbove",
|
85 |
+
"CategoryTheory.Idempotents.karoubiUniversal_functor_eq",
|
86 |
+
"RingEquiv.prodProdProdComm_toAddEquiv",
|
87 |
+
"IsSimpleModule.congr",
|
88 |
+
"IsLinearMap.convexHull_image",
|
89 |
+
"BoxIntegral.Prepartition.not_mem_bot",
|
90 |
+
"AffineSubspace.SSameSide.trans",
|
91 |
+
"Set.mulIndicator_empty'",
|
92 |
+
"Polynomial.Monic.irreducible_of_degree_eq_one",
|
93 |
+
"Std.RBNode.find?_some_memP",
|
94 |
+
"MeasureTheory.Measure.measurable_bind'",
|
95 |
+
"NonUnitalStarAlgHom.range_comp_le_range",
|
96 |
+
"Fin.insertNth_sub",
|
97 |
+
"LinearMap.quotKerEquivRange_apply_mk",
|
98 |
+
"MeasureTheory.restrict_Ioo_eq_restrict_Ico",
|
99 |
+
"DomMulAct.mk_smul_addMonoidHom_apply",
|
100 |
+
"Ring.lie_def",
|
101 |
+
"IsBot.mono",
|
102 |
+
"Submodule.restrictScalars_injective",
|
103 |
+
"Multiset.subset_iff",
|
104 |
+
"Embedding.t3Space",
|
105 |
+
"Nat.dvd_sub_mod",
|
106 |
+
"Finset.card_mul_eq_card_mul",
|
107 |
+
"IsLeftRegular.right_of_commute",
|
108 |
+
"QuaternionAlgebra.coe_nat_cast",
|
109 |
+
"EuclideanGeometry.orthogonalProjection_mem_orthogonal",
|
110 |
+
"Ordinal.sup_le",
|
111 |
+
"ProbabilityTheory.kernel.indepSets_of_indepSets_of_le_left",
|
112 |
+
"Option.iget_mem",
|
113 |
+
"zpow_bit0_pos",
|
114 |
+
"QuotientGroup.map_id",
|
115 |
+
"isCompact_accumulate",
|
116 |
+
"IsometryEquiv.mulLeft_symm",
|
117 |
+
"CircleDeg1Lift.translationNumber_le_ceil_sub",
|
118 |
+
"NonUnitalAlgebra.mem_top",
|
119 |
+
"MeasurableEquiv.restrict_map",
|
120 |
+
"Lean.Elab.Command.$n_def",
|
121 |
+
"Localization.mk_eq_mk_iff",
|
122 |
+
"Filter.tendsto_iInf'",
|
123 |
+
"Submonoid.subset_closure",
|
124 |
+
"minimals_inter_subset",
|
125 |
+
"equivalence_of_oneOneEquiv",
|
126 |
+
"String.next_of_valid",
|
127 |
+
"CategoryTheory.Presieve.bind_comp",
|
128 |
+
"Int.negSucc_mul_ofNat",
|
129 |
+
"Hyperreal.infiniteNeg_mul_of_not_infinitesimal_neg_infinitePos",
|
130 |
+
"Metric.closure_sphere",
|
131 |
+
"SameRay.nonneg_smul_left",
|
132 |
+
"MonoidHom.coe_comp",
|
133 |
+
"MulAction.card_eq_sum_card_group_div_card_stabilizer",
|
134 |
+
"CategoryTheory.Limits.mono_of_isLimit_fork",
|
135 |
+
"List.maximum_eq_none",
|
136 |
+
"ENat.one_le_iff_pos",
|
137 |
+
"List.getI_append_right",
|
138 |
+
"Polynomial.isRoot_of_aeval_algebraMap_eq_zero",
|
139 |
+
"Set.einfsep_pair_eq_inf",
|
140 |
+
"CategoryTheory.Limits.Types.Limit.map_\u03c0_apply'",
|
141 |
+
"CategoryTheory.Monad.leftAdjoint_forget",
|
142 |
+
"reflection_inv",
|
143 |
+
"Continuous.comp_aestronglyMeasurable",
|
144 |
+
"MeasurableSpace.isPiSystem_measurableSet",
|
145 |
+
"Thunk.prod_get_snd",
|
146 |
+
"CategoryTheory.sum.inverseAssociator_obj_inl",
|
147 |
+
"WithOne.cases_on",
|
148 |
+
"IsCompl.inf_sup",
|
149 |
+
"SimpleGraph.ConnectedComponent.connectedComponentMk_mem",
|
150 |
+
"HasStrictFDerivAt.exists_lipschitzOnWith",
|
151 |
+
"Submodule.closure_le_toAddSubmonoid_span",
|
152 |
+
"Order.Ideal.IsProper.ne_top",
|
153 |
+
"Continuous.if",
|
154 |
+
"Matrix.circulant_add",
|
155 |
+
"prod_finprod_comm",
|
156 |
+
"UpperSet.compl_le_compl",
|
157 |
+
"StrictMono.coe_orderIsoOfSurjective",
|
158 |
+
"Num.toZNumNeg_succ",
|
159 |
+
"RingHom.finite_iff_isIntegral_and_finiteType",
|
160 |
+
"Dilation.ext",
|
161 |
+
"Quaternion.mul_star_eq_coe",
|
162 |
+
"LatticeHom.cancel_right",
|
163 |
+
"DFinsupp.subtypeDomain_zero",
|
164 |
+
"Set.Ico_eq_empty",
|
165 |
+
"Int.natAbs_ne_zero_of_ne_zero",
|
166 |
+
"Matrix.blockDiagonal_inj",
|
167 |
+
"Polynomial.mod_def",
|
168 |
+
"IsROrC.ofReal_ofNat",
|
169 |
+
"Finset.insert_val",
|
170 |
+
"OpenEmbedding.continuous",
|
171 |
+
"Ideal.map_comap_le",
|
172 |
+
"Finset.Nat.antidiagonalTuple_two",
|
173 |
+
"ManyOneEquiv.congr_right",
|
174 |
+
"Equiv.Perm.sign_trans_trans_symm",
|
175 |
+
"CategoryTheory.section_comp_right",
|
176 |
+
"AlgebraicGeometry.IsOpenImmersion.to_iso",
|
177 |
+
"BilinForm.toMatrixAux_apply",
|
178 |
+
"Nat.ArithmeticFunction.one_one",
|
179 |
+
"Set.WellFoundedOn.mono'",
|
180 |
+
"Matrix.TransvectionStruct.det",
|
181 |
+
"NNReal.zero_rpow",
|
182 |
+
"ContinuousLinearEquiv.map_add",
|
183 |
+
"ProbabilityTheory.IdentDistrib.const_mul",
|
184 |
+
"Complex.not_le_zero_iff",
|
185 |
+
"MeasureTheory.AEStronglyMeasurable.mem\u2112p_truncation",
|
186 |
+
"uniformity_basis_edist_nnreal_le",
|
187 |
+
"SetTheory.PGame.add_right_neg_equiv",
|
188 |
+
"SimpleGraph.sum_degrees_eq_twice_card_edges",
|
189 |
+
"CategoryTheory.Limits.HasImage.of_arrow_iso",
|
190 |
+
"Mathlib.Meta.Positivity.mul_nonneg_of_nonneg_of_pos",
|
191 |
+
"AddEquiv.mapMatrix_symm",
|
192 |
+
"powersMulHom_apply",
|
193 |
+
"Equiv.Perm.IsCycle.zpowersEquivSupport_apply",
|
194 |
+
"Set.mem_insert_iff",
|
195 |
+
"Matrix.eq_zero_of_forall_pow_sum_mul_pow_eq_zero",
|
196 |
+
"ZFSet.mem_sUnion",
|
197 |
+
"MeasureTheory.AECover.integral_eq_of_tendsto_of_nonneg_ae",
|
198 |
+
"Matrix.kroneckerTMul_zero",
|
199 |
+
"TopologicalSpace.subset_trans",
|
200 |
+
"Set.image_add_const_Ioo",
|
201 |
+
"OrderMonoidHom.comp_mul",
|
202 |
+
"exists_unique_iff_exists",
|
203 |
+
"Filter.map_smul",
|
204 |
+
"Hausdorffification.induction_on",
|
205 |
+
"Stream'.map_eq_apply",
|
206 |
+
"Submonoid.inv_bot",
|
207 |
+
"MulOpposite.unop_add",
|
208 |
+
"Turing.PartrecToTM2.trNat_natEnd",
|
209 |
+
"Primrec.succ",
|
210 |
+
"one_sub_div",
|
211 |
+
"iSup_ite",
|
212 |
+
"Matrix.kronecker_one",
|
213 |
+
"Ideal.coeff_zero_mem_comap_of_root_mem",
|
214 |
+
"List.findSome?_cons",
|
215 |
+
"ContinuousLinearMap.hasFDerivAt_of_bilinear",
|
216 |
+
"Rat.ofNat_num",
|
217 |
+
"LinearMap.toContinuousLinearMap\u2081_coe",
|
218 |
+
"Module.End.generalizedEigenspace_le_generalizedEigenspace_finrank",
|
219 |
+
"Setoid.finite_classes_ker",
|
220 |
+
"Collinear.finiteDimensional_direction_affineSpan",
|
221 |
+
"EMetric.preimage_mul_left_ball",
|
222 |
+
"ConjAct.forall",
|
223 |
+
"isSeparable_tower_top_of_isSeparable",
|
224 |
+
"Metric.isBounded_range_of_tendsto_cofinite",
|
225 |
+
"LieModule.coe_linearMap_maxTrivLinearMapEquivLieModuleHom_symm",
|
226 |
+
"Summable.op",
|
227 |
+
"RingHom.congr_arg",
|
228 |
+
"IsGLB.mem_of_isClosed",
|
229 |
+
"continuous_nnnorm'",
|
230 |
+
"Polynomial.derivative_add",
|
231 |
+
"ne_iff_lt_iff_le",
|
232 |
+
"Balanced.union",
|
233 |
+
"hasMFDerivWithinAt_extChartAt",
|
234 |
+
"MvPolynomial.support_sum_monomial_coeff",
|
235 |
+
"Filter.top_mul_top",
|
236 |
+
"ContinuousLinearMap.op_norm_le_of_nhds_zero",
|
237 |
+
"IndexedPartition.exists_mem",
|
238 |
+
"lowerBounds_upperClosure",
|
239 |
+
"MeasureTheory.OuterMeasure.map_iInf_le",
|
240 |
+
"ContinuousMap.Homotopic.prodMk",
|
241 |
+
"Matrix.mul_mul_left",
|
242 |
+
"EuclideanGeometry.oangle_rev",
|
243 |
+
"LucasLehmer.norm_num_ext.isNat_not_lucasLehmerTest",
|
244 |
+
"PEquiv.trans_assoc",
|
245 |
+
"Module.Ray.ind",
|
246 |
+
"CategoryTheory.Limits.MultispanIndex.multispan_map_snd",
|
247 |
+
"Finset.card_powerset",
|
248 |
+
"one_lt_pow_iff",
|
249 |
+
"finite_iff_nonempty_fintype",
|
250 |
+
"FiniteField.card'",
|
251 |
+
"Metric.continuous_infNndist_pt",
|
252 |
+
"RingEquiv.sofLeftInverse'_apply",
|
253 |
+
"LieHom.zero_apply",
|
254 |
+
"Subgroup.IsComplement'.disjoint",
|
255 |
+
"IsROrC.conjCle_apply",
|
256 |
+
"FractionalIdeal.coeToSet_coeToSubmodule",
|
257 |
+
"TrivSqZeroExt.snd_neg",
|
258 |
+
"QuadraticForm.coeFn_neg",
|
259 |
+
"Finset.Icc_subset_Ioc_iff",
|
260 |
+
"MeasureTheory.Integrable.lintegral_lt_top",
|
261 |
+
"Submodule.eq_top_iff'",
|
262 |
+
"BoundedOrderHom.coe_comp_orderHom",
|
263 |
+
"AlternatingMap.map_zero",
|
264 |
+
"isClosedMap_ofDual",
|
265 |
+
"InitialSeg.Antisymm.aux",
|
266 |
+
"Function.invFunOn_eq",
|
267 |
+
"IntermediateField.adjoin_nat",
|
268 |
+
"Polynomial.cyclotomic'_ne_zero",
|
269 |
+
"MeasureTheory.SimpleFunc.coe_const",
|
270 |
+
"Function.onFun_apply",
|
271 |
+
"Finsupp.total_id_surjective",
|
272 |
+
"CategoryTheory.Functor.mapPresheaf_obj_presheaf",
|
273 |
+
"antivaryOn_id_iff",
|
274 |
+
"Derivation.mk_coe",
|
275 |
+
"Set.Nonempty.vsub",
|
276 |
+
"MeasureTheory.BorelCantelli.integrable_process",
|
277 |
+
"RingHom.map_add",
|
278 |
+
"ProbabilityTheory.iIndepFun.indepFun_finset_prod_of_not_mem",
|
279 |
+
"LinearMap.splittingOfFunOnFintypeSurjective_injective",
|
280 |
+
"Subsemiring.coe_add",
|
281 |
+
"isOpenMap_snd",
|
282 |
+
"toMul_sum",
|
283 |
+
"PrimeSpectrum.zeroLocus_radical",
|
284 |
+
"PhragmenLindelof.eqOn_quadrant_I",
|
285 |
+
"IsSimpleOrder.eq_bot_of_lt",
|
286 |
+
"AlgHom.ext_of_adjoin_eq_top",
|
287 |
+
"Mathlib.Meta.Positivity.nnreal_coe_pos",
|
288 |
+
"Submodule.inner_right_of_mem_orthogonal",
|
289 |
+
"ProbabilityTheory.IndepSets.inter",
|
290 |
+
"AffineIsometryEquiv.dist_map",
|
291 |
+
"FreeMonoid.toList_symm",
|
292 |
+
"Subsemigroup.mem_top",
|
293 |
+
"inv_lt_one_of_one_lt",
|
294 |
+
"LowerSemicontinuous.measurable",
|
295 |
+
"Perfection.hom_ext",
|
296 |
+
"isUnit_iff_forall_dvd",
|
297 |
+
"FirstOrder.Language.age.hereditary",
|
298 |
+
"Cardinal.power_zero",
|
299 |
+
"Continuous.dist",
|
300 |
+
"Submodule.span_span",
|
301 |
+
"EReal.bot_sub",
|
302 |
+
"Continuous.smul",
|
303 |
+
"RingEquiv.ofLeftInverse_symm_apply",
|
304 |
+
"Real.arsinh_inj",
|
305 |
+
"Finset.EquitableOn.le_add_one",
|
306 |
+
"Function.Commute.iterate_iterate_self",
|
307 |
+
"OnePoint.infty_mem_opensOfCompl",
|
308 |
+
"Nat.fib_bit0_succ",
|
309 |
+
"NNReal.coe_zero",
|
310 |
+
"Matrix.zero_empty",
|
311 |
+
"ModuleCat.MonoidalCategory.hom_apply",
|
312 |
+
"CauSeq.add_apply",
|
313 |
+
"Finset.isLeast_min'",
|
314 |
+
"Tropical.injective_untrop",
|
315 |
+
"LinearEquiv.ofEq_symm",
|
316 |
+
"connectedComponents_lift_unique'",
|
317 |
+
"holderWith_one",
|
318 |
+
"Set.prod_self_ssubset_prod_self",
|
319 |
+
"ConvexCone.mem_closure",
|
320 |
+
"SmoothBumpCovering.toSmoothPartitionOfUnity_eq_mul_prod",
|
321 |
+
"indicator_ae_eq_restrict",
|
322 |
+
"AlternatingMap.coe_domDomCongr",
|
323 |
+
"Set.range_restrict",
|
324 |
+
"ENNReal.nhdsWithin_Ioi_coe_neBot",
|
325 |
+
"Int.one_le_abs",
|
326 |
+
"HomotopyCategory.quotient_obj_as",
|
327 |
+
"ValuationSubring.mem_pointwise_smul_iff_inv_smul_mem",
|
328 |
+
"OneOneEquiv.le_congr_left",
|
329 |
+
"Submodule.complete_of_finiteDimensional",
|
330 |
+
"Function.Embedding.coe_quotientOut",
|
331 |
+
"smoothOn_pi_space",
|
332 |
+
"TrivSqZeroExt.continuous_snd",
|
333 |
+
"MeasureTheory.tendstoInMeasure_of_tendsto_Lp",
|
334 |
+
"Set.bijective_iff_bijOn_univ",
|
335 |
+
"NonUnitalRingHom.coe_mul",
|
336 |
+
"Finset.max_le",
|
337 |
+
"isGreatest_Ioc",
|
338 |
+
"SmoothBumpFunction.tsupport_subset_extChartAt_source",
|
339 |
+
"Ordinal.type_preimage",
|
340 |
+
"ContinuousOn.const_smul",
|
341 |
+
"Polynomial.map_multiset_prod",
|
342 |
+
"Function.mulSupport_max",
|
343 |
+
"MeasureTheory.Integrable.congr'",
|
344 |
+
"BoxIntegral.Box.ne_of_disjoint_coe",
|
345 |
+
"MeasureTheory.IsFundamentalDomain.restrict_restrict",
|
346 |
+
"Homeomorph.continuousMapOfUnique_apply",
|
347 |
+
"IsLocalization.surj",
|
348 |
+
"Finsupp.sub_single_one_add",
|
349 |
+
"Finset.union_subset_union_left",
|
350 |
+
"Hamming.ofHamming_neg",
|
351 |
+
"factorial_tendsto_atTop",
|
352 |
+
"Submodule.coe_inner",
|
353 |
+
"CategoryTheory.op_tensorObj",
|
354 |
+
"RingHom.map_iterate_frobenius",
|
355 |
+
"DenseEmbedding.mk'",
|
356 |
+
"Dilation.tendsto_nhds_iff",
|
357 |
+
"BoxIntegral.Box.measurableSet_Icc",
|
358 |
+
"Codisjoint.eq_top",
|
359 |
+
"AlgebraicTopology.DoldKan.PInfty_f_0",
|
360 |
+
"div_lt_div_right'",
|
361 |
+
"HasFDerivAt.norm_sq",
|
362 |
+
"Filter.tendsto_iff_forall_eventually_mem",
|
363 |
+
"Sum.inl_le_inl_iff",
|
364 |
+
"swap_comp_bipointedToPointedSnd",
|
365 |
+
"and_iff_left_iff_imp",
|
366 |
+
"closure_smul",
|
367 |
+
"Ideal.mul_le",
|
368 |
+
"eventually_norm_pow_le",
|
369 |
+
"NonUnitalSubring.closure_univ",
|
370 |
+
"Subalgebra.centralizer_le",
|
371 |
+
"AffineMap.lineMap_apply_module'",
|
372 |
+
"FirstOrder.Language.Formula.realize_inf",
|
373 |
+
"CategoryTheory.AdditiveFunctor.ofLeftExact_map",
|
374 |
+
"Nat.lt_succ_of_lt",
|
375 |
+
"Set.eval_image_univ_pi",
|
376 |
+
"Nat.gcd_gcd_self_right_left",
|
377 |
+
"CategoryTheory.Limits.span_map_fst",
|
378 |
+
"List.mem_of_mem_erase",
|
379 |
+
"PowerSeries.map_id",
|
380 |
+
"IsPrimePow.two_le",
|
381 |
+
"Wcovby.snd",
|
382 |
+
"MultilinearMap.map_smul",
|
383 |
+
"IsExposed.isCompact",
|
384 |
+
"MeasureTheory.snormEssSup_const_smul_le",
|
385 |
+
"Balanced.smul_eq",
|
386 |
+
"Coheyting.boundary_bot",
|
387 |
+
"SimpleGraph.Walk.isPath_def",
|
388 |
+
"UpperHalfPlane.im_pos",
|
389 |
+
"Matrix.fromBlocks_apply\u2081\u2082",
|
390 |
+
"continuousAt_star",
|
391 |
+
"Matrix.blockDiag'_smul",
|
392 |
+
"IsROrC.ofReal_re",
|
393 |
+
"Prod.fst_toSigma",
|
394 |
+
"Submodule.carrier_inj",
|
395 |
+
"min_left_commutative",
|
396 |
+
"CategoryTheory.IsPullback.of_hasBinaryProduct'",
|
397 |
+
"LinearEquiv.symm_conj_apply",
|
398 |
+
"LinearEquiv.ofSubmodule'_apply",
|
399 |
+
"Ordnode.Valid'.of_lt",
|
400 |
+
"CategoryTheory.Limits.limLax_obj'",
|
401 |
+
"List.card_nil",
|
402 |
+
"IsSepClosed.exists_aeval_eq_zero",
|
403 |
+
"CategoryTheory.IsPushout.of_isColimit'",
|
404 |
+
"GroupNorm.sup_apply",
|
405 |
+
"MulOpposite.op_add",
|
406 |
+
"SpectralMap.comp_id",
|
407 |
+
"Primrec.nat_rec\u2081",
|
408 |
+
"ENNReal.inv_lt_inv'",
|
409 |
+
"Con.lift_surjective_of_surjective",
|
410 |
+
"NonUnitalSubalgebra.coe_prod",
|
411 |
+
"continuousWithinAt_left_of_monotoneOn_of_exists_between",
|
412 |
+
"Stream'.head_zip",
|
413 |
+
"Equiv.Perm.card_cycleType_pos",
|
414 |
+
"Metric.ball_infDist_compl_subset",
|
415 |
+
"Set.countable_iff_exists_injective",
|
416 |
+
"Asymptotics.isLittleO_abs_right",
|
417 |
+
"measurable_from_top",
|
418 |
+
"SimpleGraph.ConnectedComponent.exact",
|
419 |
+
"Ordinal.toPGame_injective",
|
420 |
+
"derivWithin_mul_const",
|
421 |
+
"ApproximatesLinearOn.closedBall_subset_target",
|
422 |
+
"Hamming.nnnorm_eq_hammingNorm",
|
423 |
+
"Polynomial.commute_X",
|
424 |
+
"Option.mem_def",
|
425 |
+
"fderiv_clm_comp",
|
426 |
+
"gal_mul_isSolvable",
|
427 |
+
"Quiver.symmetrify_reverse",
|
428 |
+
"Real.openEmbedding_exp",
|
429 |
+
"Submodule.iSup_mul",
|
430 |
+
"contMDiffOn_extChartAt",
|
431 |
+
"FractionalIdeal.coeIdeal_bot",
|
432 |
+
"Ordinal.nadd_le_nadd_iff_left",
|
433 |
+
"ContDiffAt.contDiffBump",
|
434 |
+
"WithTop.coe_untop'_le",
|
435 |
+
"Filter.le_map\u2082_iff",
|
436 |
+
"nndist_triangle_left",
|
437 |
+
"MonotoneOn.set_prod",
|
438 |
+
"hasBinaryProducts_of_hasTerminal_and_pullbacks",
|
439 |
+
"has_deriv_within_taylorWithinEval_at_Icc",
|
440 |
+
"List.destutter_nil",
|
441 |
+
"RingEquiv.restrictRootsOfUnity_symm",
|
442 |
+
"Sum.getLeft_inl",
|
443 |
+
"MeasureTheory.AEEqFun.coeFn_compMeasurePreserving",
|
444 |
+
"AlgebraicTopology.DoldKan.PInfty_f",
|
445 |
+
"DirectSum.decompose_add",
|
446 |
+
"IntermediateField.inf_toSubfield",
|
447 |
+
"le_imp_le_of_lt_imp_lt",
|
448 |
+
"BilinForm.isRefl_neg",
|
449 |
+
"WithOne.coe_unone",
|
450 |
+
"Polynomial.constantCoeff_coe",
|
451 |
+
"true_imp_iff",
|
452 |
+
"NonUnitalSubsemiring.coe_mul",
|
453 |
+
"WithOne.coe_mul",
|
454 |
+
"Ne.ne_or_ne",
|
455 |
+
"Subalgebra.pointwise_smul_toSubsemiring",
|
456 |
+
"measurableSet_closedBall",
|
457 |
+
"Set.union_star",
|
458 |
+
"Ordinal.bsup_lt_ord_lift",
|
459 |
+
"Filter.Frequently.mem_of_closed",
|
460 |
+
"Matrix.diagonal_kronecker",
|
461 |
+
"intervalIntegral.integral_hasDerivWithinAt_right",
|
462 |
+
"t1Space_iff_disjoint_pure_nhds",
|
463 |
+
"Fin.induction_zero",
|
464 |
+
"DirectSum.of_zero_smul",
|
465 |
+
"mul_inf",
|
466 |
+
"Set.Nonempty.of_infs_right",
|
467 |
+
"StarAlgHom.copy_eq",
|
468 |
+
"ContinuousOn.continuousAt",
|
469 |
+
"bddAbove_singleton",
|
470 |
+
"PrincipalSeg.codRestrict_top",
|
471 |
+
"CliffordAlgebra.changeForm_comp_changeForm",
|
472 |
+
"Turing.Tape.mk'_right",
|
473 |
+
"Hyperreal.coe_ofNat",
|
474 |
+
"Complex.continuousOn_sin",
|
475 |
+
"MeasureTheory.ProbabilityMeasure.toWeakDualBCNN_continuous",
|
476 |
+
"isUnit_exp_of_mem_ball",
|
477 |
+
"Nonneg.coe_add",
|
478 |
+
"CauSeq.const_pos",
|
479 |
+
"QuadraticForm.Equivalent.prod",
|
480 |
+
"Asymptotics.IsBigO.mono",
|
481 |
+
"DomMulAct.smul_monoidHom_apply",
|
482 |
+
"Subsemiring.coe_one",
|
483 |
+
"ContinuousLinearMap.le_of_op_norm\u2082_le_of_le",
|
484 |
+
"mapsTo_extChartAt",
|
485 |
+
"Set.iUnion_unpair",
|
486 |
+
"Con.inf_def",
|
487 |
+
"Matrix.UnitaryGroup.coe_toGL",
|
488 |
+
"Set.sUnion_subset_sUnion",
|
489 |
+
"MeasureTheory.Martingale.supermartingale",
|
490 |
+
"Encodable.decode_nat",
|
491 |
+
"ULiftable.up_down",
|
492 |
+
"Filter.Iio_mem_atBot",
|
493 |
+
"ContDiffAt.comp",
|
494 |
+
"Function.id_def",
|
495 |
+
"Matrix.toBilin'_toMatrix'",
|
496 |
+
"Multiset.mem_dedup",
|
497 |
+
"Hyperreal.infinitePos_iff_infinite_and_pos",
|
498 |
+
"CategoryTheory.nonempty_isLeftAdjoint_iff_hasTerminal_costructuredArrow",
|
499 |
+
"LocalHomeomorph.trans_source",
|
500 |
+
"TypeVec.appendFun_inj",
|
501 |
+
"Metric.self_subset_thickening",
|
502 |
+
"Polynomial.mem_map_range",
|
503 |
+
"NonUnitalSubsemiring.mem_center_iff",
|
504 |
+
"add_tsub_cancel_iff_le",
|
505 |
+
"Filter.EventuallyEq.rfl",
|
506 |
+
"MeasureTheory.Measure.Subtype.volume_def",
|
507 |
+
"Function.Surjective.forall\u2083",
|
508 |
+
"FiniteField.X_pow_card_pow_sub_X_ne_zero",
|
509 |
+
"exists_nhds_one_split",
|
510 |
+
"Set.nonempty_Ioo",
|
511 |
+
"FundamentalGroupoidFunctor.coneDiscreteComp_obj_mapCone",
|
512 |
+
"Nat.choose_mono",
|
513 |
+
"Dilation.coe_mk",
|
514 |
+
"FractionalIdeal.mul_right_strictMono",
|
515 |
+
"isAtomic_iff_isCoatomic",
|
516 |
+
"Antitone.map_sInf_of_continuousAt'",
|
517 |
+
"ContinuousLinearMap.extendTo\ud835\udd5c'_apply",
|
518 |
+
"Primrec\u2082.encode_iff",
|
519 |
+
"CategoryTheory.Sieve.pushforward_apply_comp",
|
520 |
+
"LinearMap.coe_mul",
|
521 |
+
"IsROrC.normSq_one",
|
522 |
+
"Vector.empty_toList_eq_ff",
|
523 |
+
"String.isEmpty_iff",
|
524 |
+
"Subring.pointwise_smul_def",
|
525 |
+
"AlgebraicTopology.DoldKan.PInfty_f_naturality",
|
526 |
+
"Function.surjective_eval",
|
527 |
+
"MeasureTheory.L1.SimpleFunc.setToL1SCLM_nonneg",
|
528 |
+
"map_mk_unit_aux",
|
529 |
+
"ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun''",
|
530 |
+
"quotientMap_iff",
|
531 |
+
"HasStrictDerivAt.sqrt",
|
532 |
+
"MulAction.exists_smul_eq",
|
533 |
+
"card_sylow_eq_card_quotient_normalizer",
|
534 |
+
"Asymptotics.IsBigOWith.exists_pos",
|
535 |
+
"ConvexBody.coe_smul",
|
536 |
+
"NormedAddGroupHom.coe_inj_iff",
|
537 |
+
"LieHom.rangeRestrict_apply",
|
538 |
+
"LinearMap.ker_fst",
|
539 |
+
"Subfield.mk_le_mk",
|
540 |
+
"MeasureTheory.set_integral_congr\u2080",
|
541 |
+
"CategoryTheory.Limits.WidePullbackShape.hom_id",
|
542 |
+
"TopologicalSpace.gc_generateFrom",
|
543 |
+
"List.Disjoint.symm",
|
544 |
+
"csInf_le_csInf",
|
545 |
+
"IsTotal.swap",
|
546 |
+
"BilinForm.toQuadraticForm_apply",
|
547 |
+
"mul_le_one",
|
548 |
+
"fixingSubmonoid_fixedPoints_gc",
|
549 |
+
"Equiv.permCongr_apply",
|
550 |
+
"ENNReal.coe_one",
|
551 |
+
"CategoryTheory.Subobject.lift_mk",
|
552 |
+
"Std.RBNode.WF.depth_bound",
|
553 |
+
"Path.extend_range",
|
554 |
+
"Computation.terminates_map_iff",
|
555 |
+
"OrderMonoidWithZeroHom.coe_id",
|
556 |
+
"Set.inter_vsub_union_subset_union",
|
557 |
+
"Encodable.encode_prod_val",
|
558 |
+
"lcm_assoc",
|
559 |
+
"ConvexCone.comap_comap",
|
560 |
+
"CategoryTheory.Abelian.image.fac",
|
561 |
+
"LocalHomeomorph.MDifferentiable.ker_mfderiv_eq_bot",
|
562 |
+
"ContinuousMap.smul_apply",
|
563 |
+
"LineDifferentiableAt.lineDifferentiableWithinAt",
|
564 |
+
"IsSepClosed.splits_domain",
|
565 |
+
"IntermediateField.adjoin.finiteDimensional",
|
566 |
+
"NonUnitalSubsemiring.centralizer_univ",
|
567 |
+
"DifferentiableOn.ccos",
|
568 |
+
"IsPreconnected.intermediate_value_Ici",
|
569 |
+
"Interval.coe_inj",
|
570 |
+
"mem_extremePoints",
|
571 |
+
"EMetric.diam_ball",
|
572 |
+
"sInfHom.cancel_right",
|
573 |
+
"Finset.sdiff_union_self_eq_union",
|
574 |
+
"IsCompact.nonempty_iInter_of_sequence_nonempty_compact_closed",
|
575 |
+
"LinearEquiv.mapMatrix_trans",
|
576 |
+
"Antitone.mul",
|
577 |
+
"Complex.UnitDisc.abs_ne_one",
|
578 |
+
"ContMDiffAt.of_le",
|
579 |
+
"Measurable.mul'",
|
580 |
+
"sdiff_le'",
|
581 |
+
"IsAntichain.maximals_lowerClosure",
|
582 |
+
"HahnSeries.neg_coeff",
|
583 |
+
"LieHom.map_lie",
|
584 |
+
"polynomialFunctions.starClosure_topologicalClosure",
|
585 |
+
"CompactExhaustion.isClosed",
|
586 |
+
"AlgebraicGeometry.locallyOfFiniteType_respectsIso",
|
587 |
+
"RingTopology.coinduced_continuous",
|
588 |
+
"Computable.list_reverse",
|
589 |
+
"MeasureTheory.Measure.countable_meas_pos_of_disjoint_of_meas_iUnion_ne_top",
|
590 |
+
"Computation.eq_thinkN'",
|
591 |
+
"BilinForm.isSymm_zero",
|
592 |
+
"DFA.eval_singleton",
|
593 |
+
"AlgebraicGeometry.LocallyRingedSpace.\u0393_obj",
|
594 |
+
"IsLocalExtr.congr",
|
595 |
+
"LucasLehmer.mersenne_int_ne_zero",
|
596 |
+
"CategoryTheory.Limits.wideCoequalizer.\u03c0_desc",
|
597 |
+
"MulOpposite.op_comp_unop",
|
598 |
+
"MeasureTheory.JordanDecomposition.real_smul_nonneg",
|
599 |
+
"Multiset.inf_mono",
|
600 |
+
"IntermediateField.val_mk",
|
601 |
+
"Subsemiring.smul_mem_pointwise_smul_iff\u2080",
|
602 |
+
"AffineSubspace.sSameSide_smul_vsub_vadd_right",
|
603 |
+
"Matrix.smul_of",
|
604 |
+
"AffineBasis.card_eq_finrank_add_one",
|
605 |
+
"NonUnitalStarAlgHom.inr_apply",
|
606 |
+
"CategoryTheory.Limits.WalkingPair.swap_symm_apply_ff",
|
607 |
+
"Stream'.WSeq.of_mem_append",
|
608 |
+
"IsUnit.unit_spec",
|
609 |
+
"Filter.le_lift",
|
610 |
+
"ProbabilityTheory.iIndepFun.mul",
|
611 |
+
"Algebra.TensorProduct.assoc_toLinearEquiv",
|
612 |
+
"nhds_ofMul",
|
613 |
+
"Set.Ioi_inter_Iio",
|
614 |
+
"LinearEquiv.ext",
|
615 |
+
"IsFreeGroup.lift'_eq_freeGroup_lift",
|
616 |
+
"PowerSeries.evalNegHom_X",
|
617 |
+
"Subgroup.one_lt_card_iff_ne_bot",
|
618 |
+
"Set.image_image2_right_comm",
|
619 |
+
"Set.Finite.isPwo",
|
620 |
+
"FreeMonoid.toList_of_mul",
|
621 |
+
"CategoryTheory.Limits.initialMonoClass_of_disjoint_coproducts",
|
622 |
+
"Set.Icc_subset_Ici_self",
|
623 |
+
"ENNReal.toReal_le_of_le_ofReal",
|
624 |
+
"CategoryTheory.Functor.sum_map_inl",
|
625 |
+
"Lists'.Subset.trans",
|
626 |
+
"image_le_of_deriv_right_le_deriv_boundary",
|
627 |
+
"AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toSheafedSpace_toPresheafedSpace",
|
628 |
+
"BilinForm.Nondegenerate.toMatrix'",
|
629 |
+
"MulHom.id_comp",
|
630 |
+
"toIcoMod_mem_Ico",
|
631 |
+
"IsLocallyConstant.eq_const",
|
632 |
+
"Iff.to_eq",
|
633 |
+
"IsROrC.ofRealClm_apply",
|
634 |
+
"NonUnitalAlgebra.adjoin_induction",
|
635 |
+
"MeasureTheory.integral_Iic_eq_integral_Iio",
|
636 |
+
"Equiv.Perm.smul_def",
|
637 |
+
"Set.Nonempty.left",
|
638 |
+
"Quot.congr_mk",
|
639 |
+
"LinearMap.toMatrixAlgEquiv'_symm",
|
640 |
+
"Filter.HasBasis.inf",
|
641 |
+
"CauSeq.Completion.mk_pow",
|
642 |
+
"IsIdempotentElem.coe_zero",
|
643 |
+
"iSup_mono'",
|
644 |
+
"MeasureTheory.IsStoppingTime.measurableSet_lt_of_countable",
|
645 |
+
"String.next'_eq",
|
646 |
+
"antitone_vecCons",
|
647 |
+
"Finset.inter_val",
|
648 |
+
"EMetric.cauchySeq_iff_NNReal",
|
649 |
+
"Complex.mem_reProdIm",
|
650 |
+
"Submodule.span_eq_of_le",
|
651 |
+
"GaloisConnection.u_inf",
|
652 |
+
"NonUnitalSubring.sInf_toSubsemigroup",
|
653 |
+
"AddMonoidAlgebra.single_mul_apply_of_not_exists_add",
|
654 |
+
"Vector.toList_injective",
|
655 |
+
"LinearIsometry.map_neg",
|
656 |
+
"IsometryEquiv.dist_eq",
|
657 |
+
"IsLocalization.mk'_eq_iff_eq'",
|
658 |
+
"AddMonoidAlgebra.supDegree_add_le",
|
659 |
+
"MeasureTheory.Measure.restrict_restrict",
|
660 |
+
"SupHom.comp_apply",
|
661 |
+
"mul_lt_mul_left",
|
662 |
+
"Mathlib.Tactic.LinearCombination.c_mul_pf",
|
663 |
+
"Nat.lt_pow_iff_log_lt",
|
664 |
+
"SetTheory.PGame.sub_congr",
|
665 |
+
"Basis.coe_algebraMapCoeffs",
|
666 |
+
"Set.iUnion_mul_right_image",
|
667 |
+
"CategoryTheory.isoWhiskerRight_inv",
|
668 |
+
"Cardinal.ord_card_unbounded'",
|
669 |
+
"Finset.card_powersetCard",
|
670 |
+
"deriv_ne_zero",
|
671 |
+
"ContinuousAt.preimage_mem_nhds",
|
672 |
+
"Equiv.Perm.sumCongr_mul",
|
673 |
+
"CategoryTheory.GrothendieckTopology.pullback_stable",
|
674 |
+
"ContinuousLinearMap.continuous",
|
675 |
+
"WithTop.succ_coe",
|
676 |
+
"MeasureTheory.SimpleFunc.lintegral_zero",
|
677 |
+
"CategoryTheory.endofunctorMonoidalCategory_tensorUnit_obj",
|
678 |
+
"Multiset.zero_bind",
|
679 |
+
"Set.OrdConnected.preimage_coe_nnreal_real",
|
680 |
+
"MultilinearMap.uncurrySum_aux_apply",
|
681 |
+
"TopologicalSpace.Opens.mk_univ",
|
682 |
+
"sq_pos_of_ne_zero",
|
683 |
+
"LinearMap.compl\u2081\u2082_apply",
|
684 |
+
"Int.castRingHom_int",
|
685 |
+
"or_iff_left",
|
686 |
+
"Hyperreal.IsSt.le",
|
687 |
+
"StrictAntiOn.le_iff_le",
|
688 |
+
"Int.ofNat_add_one_out",
|
689 |
+
"Polynomial.map_monic_ne_zero",
|
690 |
+
"Std.RBSet.find?_some_mem",
|
691 |
+
"MonoidHom.transferSylow_eq_pow",
|
692 |
+
"Nat.ceil_le",
|
693 |
+
"Finsupp.toMultiset_toFinsupp",
|
694 |
+
"Complex.abs_sub_eq",
|
695 |
+
"LinearMap.toMatrix_apply'",
|
696 |
+
"Asymptotics.IsBigO.congr_right",
|
697 |
+
"StrictMonoOn.continuousWithinAt_right_of_surjOn",
|
698 |
+
"Real.tan_arctan",
|
699 |
+
"Set.infs_infs_infs_comm",
|
700 |
+
"not_isCoprime_zero_zero",
|
701 |
+
"Pell.yn_ge_n",
|
702 |
+
"Submonoid.LocalizationMap.AwayMap.lift_comp",
|
703 |
+
"MvPolynomial.esymm_eq_sum_subtype",
|
704 |
+
"measurable_infNndist",
|
705 |
+
"Pi.lex_eq_finsupp_lex",
|
706 |
+
"vsub_right_injective",
|
707 |
+
"Ultrafilter.mem_coe",
|
708 |
+
"ClosureOperator.closure_sup_closure_left",
|
709 |
+
"Fin.cast_castAdd_right",
|
710 |
+
"SMul.comp.smulCommClass'",
|
711 |
+
"SimpleGraph.Iso.map_adj_iff",
|
712 |
+
"MeasureTheory.Measure.absolutelyContinuous_of_eq",
|
713 |
+
"FreeSemigroup.mul_map_seq",
|
714 |
+
"Module.End.natCast_apply",
|
715 |
+
"Filter.map\u2082_mono_right",
|
716 |
+
"AlgEquiv.mk_coe'",
|
717 |
+
"LinearEquiv.coe_coe",
|
718 |
+
"analyticOn_congr'",
|
719 |
+
"GromovHausdorff.isometry_optimalGHInjr",
|
720 |
+
"Ideal.IsPrime.mul_le",
|
721 |
+
"OpenSubgroup.toOpens_inf",
|
722 |
+
"ContinuousOpenMap.ext",
|
723 |
+
"MulOpposite.unop_one",
|
724 |
+
"AlgHom.coe_mk'",
|
725 |
+
"Int.zero_mul",
|
726 |
+
"CategoryTheory.Idempotents.DoldKan.equivalence_functor",
|
727 |
+
"Finset.card_le_card_mul_left",
|
728 |
+
"CategoryTheory.whiskerLeft_twice",
|
729 |
+
"Real.smoothTransition.continuousAt",
|
730 |
+
"FirstOrder.Language.funMap_eq_coe_constants",
|
731 |
+
"star_mul'",
|
732 |
+
"Fin.leftInverse_cast",
|
733 |
+
"MeasureTheory.Measure.QuasiMeasurePreserving.mono_left",
|
734 |
+
"Ici_mem_nhds",
|
735 |
+
"Set.SurjOn.cancel_right",
|
736 |
+
"Subtype.val_prop",
|
737 |
+
"Function.const_le_one_of_le_one",
|
738 |
+
"Continuous.cpow",
|
739 |
+
"Pi.prod_snd_fst",
|
740 |
+
"ENNReal.coe_ne_zero",
|
741 |
+
"Multiset.ndinter_subset_left",
|
742 |
+
"BiheytingHom.toFun_eq_coe_aux",
|
743 |
+
"LatticeHom.coe_id",
|
744 |
+
"Filter.tendsto_atTop_of_add_bdd_above_left'",
|
745 |
+
"closure_eq_cluster_pts",
|
746 |
+
"NNReal.rpow_sub",
|
747 |
+
"leftInverse_div_mul_left",
|
748 |
+
"Function.Antiperiodic.nat_even_mul_periodic",
|
749 |
+
"AddCommGroup.ModEq.add_zsmul",
|
750 |
+
"Ideal.is_fg_degreeLE",
|
751 |
+
"Subsemiring.prod_mem",
|
752 |
+
"Metric.iUnion_ball_nat",
|
753 |
+
"LiouvilleWith.add_int",
|
754 |
+
"Int.fmod_nonneg'",
|
755 |
+
"LinearMap.toAffineMap_linear",
|
756 |
+
"LinearMap.ext_on_range",
|
757 |
+
"HasMFDerivWithinAt.continuousWithinAt",
|
758 |
+
"MonoidHom.coprod_apply",
|
759 |
+
"MeasureTheory.Lp.simpleFunc.measurable",
|
760 |
+
"LinearMap.ker_id",
|
761 |
+
"Multiset.erase_cons_head",
|
762 |
+
"CategoryTheory.e_assoc",
|
763 |
+
"CauSeq.le_total",
|
764 |
+
"LatticeHom.coe_comp_sup_hom",
|
765 |
+
"Antitone.tendsto_alternating_series_of_tendsto_zero",
|
766 |
+
"List.Perm.nodup_iff",
|
767 |
+
"borel_eq_generateFrom_Ici",
|
768 |
+
"NonUnitalSubsemiring.map_id",
|
769 |
+
"Subgroup.relindex_ne_zero_trans",
|
770 |
+
"false_imp_iff",
|
771 |
+
"AffineSubspace.not_wSameSide_bot",
|
772 |
+
"MonoidWithZeroHom.coe_inj",
|
773 |
+
"SimpleGraph.Path.isTrail",
|
774 |
+
"Part.one_mem_one",
|
775 |
+
"strictMonoOn_toDual_comp_iff",
|
776 |
+
"Prime.associated_of_dvd",
|
777 |
+
"fderiv.comp",
|
778 |
+
"InfHom.copy_eq",
|
779 |
+
"Primrec.comp\u2082",
|
780 |
+
"IndexedPartition.proj_out",
|
781 |
+
"LinearPMap.isClosable_iff_exists_closed_extension",
|
782 |
+
"TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd",
|
783 |
+
"continuousWithinAt_Iio_iff_Iic",
|
784 |
+
"NNReal.summable_Lp_add",
|
785 |
+
"ContinuousAlternatingMap.ofSubsingleton_toAlternatingMap",
|
786 |
+
"List.join_splitWrtComposition",
|
787 |
+
"Algebra.adjoin_eq_of_le",
|
788 |
+
"IsMaxOn.on_preimage",
|
789 |
+
"Nat.dvd_ord_proj_of_dvd",
|
790 |
+
"AlgEquiv.toLieEquiv_symm_apply",
|
791 |
+
"multiplicity.eq_of_associated_left",
|
792 |
+
"bihimp_def",
|
793 |
+
"Submonoid.toAddSubmonoid_closure",
|
794 |
+
"MeasureTheory.AEStronglyMeasurable.iUnion",
|
795 |
+
"MvPolynomial.map_rightInverse",
|
796 |
+
"OrderHom.isFixedPt_gfp",
|
797 |
+
"nndist_midpoint_midpoint_le'",
|
798 |
+
"Hyperreal.infiniteNeg_add_infiniteNeg",
|
799 |
+
"Finset.sups_infs_subset_left",
|
800 |
+
"mem_maximals_setOf_iff",
|
801 |
+
"Int.self_sub_fract",
|
802 |
+
"monotone_Iic",
|
803 |
+
"FirstOrder.Language.toFun_embedding_empty",
|
804 |
+
"Set.union_subset_iff",
|
805 |
+
"MeasureTheory.snorm_indicator_const",
|
806 |
+
"Finset.Nonempty.image\u2082",
|
807 |
+
"Ultrafilter.inf_neBot_iff",
|
808 |
+
"nhds_mono",
|
809 |
+
"MeasureTheory.StronglyMeasurable.const_smul'",
|
810 |
+
"ContinuousMap.HomotopyWith.ext",
|
811 |
+
"MonotoneOn.max",
|
812 |
+
"differentiable_star_iff",
|
813 |
+
"Set.SurjOn.mapsTo_compl",
|
814 |
+
"Filter.Tendsto.pow",
|
815 |
+
"IsEquivalent.summable_iff",
|
816 |
+
"List.choose_mem",
|
817 |
+
"IsCoprime.pow",
|
818 |
+
"IntermediateField.range_val",
|
819 |
+
"NormedSpace.toLocallyConvexSpace'",
|
820 |
+
"List.getLast?_singleton",
|
821 |
+
"ContinuousLinearMap.mkOfIsCompactOperator_mem_compactOperator",
|
822 |
+
"MultilinearMap.add_apply",
|
823 |
+
"OrderMonoidWithZeroHom.comp_assoc",
|
824 |
+
"CategoryTheory.Functor.eq_of_iso",
|
825 |
+
"HahnSeries.C_eq_algebraMap",
|
826 |
+
"CircleDeg1Lift.iterate_mono",
|
827 |
+
"Filter.Germ.abs_def",
|
828 |
+
"CategoryTheory.Presieve.IsSheafFor.isSeparatedFor",
|
829 |
+
"MonoidHom.coe_mker",
|
830 |
+
"LinearEquiv.coe_ofInvolutive",
|
831 |
+
"Primrec.nat_casesOn",
|
832 |
+
"FirstOrder.Language.Substructure.mem_closure",
|
833 |
+
"MeasureTheory.tsum_meas_le_meas_iUnion_of_disjoint",
|
834 |
+
"mem_nhdsSet_interior",
|
835 |
+
"Set.image_preimage",
|
836 |
+
"IsLowerSet.top_mem",
|
837 |
+
"Cycle.Chain.eq_nil_of_well_founded",
|
838 |
+
"List.Perm.eqv",
|
839 |
+
"WithLp.equiv_pi_apply",
|
840 |
+
"Ordinal.type_lift_preimage_aux",
|
841 |
+
"Part.left_dom_of_div_dom",
|
842 |
+
"HasDerivAt.hasDerivWithinAt",
|
843 |
+
"two_mul_le_add_sq",
|
844 |
+
"KaehlerDifferential.map_D",
|
845 |
+
"List.SublistForall\u2082.prod_le_prod'",
|
846 |
+
"Disjoint.inf_right'",
|
847 |
+
"Multiset.erase_zero",
|
848 |
+
"Polynomial.natDegree_cubic",
|
849 |
+
"subset_lowerBounds_upperBounds",
|
850 |
+
"Finset.isG\u03b4_compl",
|
851 |
+
"Field.closure_mono",
|
852 |
+
"LinearMap.coprod_zero_left",
|
853 |
+
"List.Pairwise.chain'",
|
854 |
+
"isTorsion_of_finite",
|
855 |
+
"algebraMap_exp_comm_of_mem_ball",
|
856 |
+
"MeasureTheory.Measure.top_add",
|
857 |
+
"Set.mulIndicator_one'",
|
858 |
+
"Set.pairwiseDisjoint_union",
|
859 |
+
"BoxIntegral.Box.le_iff_bounds",
|
860 |
+
"ofBoolAlg_sup",
|
861 |
+
"MeasureTheory.snormEssSup_le_of_ae_nnnorm_bound",
|
862 |
+
"Fintype.card_set",
|
863 |
+
"Ioo_mem_nhdsWithin_Ioi'",
|
864 |
+
"Real.add_neg_lt_sSup",
|
865 |
+
"Set.mk_mem_sigma",
|
866 |
+
"IsExtrFilter.comp_mono",
|
867 |
+
"Cardinal.isRegular_cof",
|
868 |
+
"RingHom.sclosure_preimage_le",
|
869 |
+
"Submodule.map_pow",
|
870 |
+
"Set.iUnion_congr_Prop",
|
871 |
+
"RelEmbedding.coe_trans",
|
872 |
+
"MeasureTheory.Lp.coeFn_inf",
|
873 |
+
"Part.get_eq_of_mem",
|
874 |
+
"FreeGroup.lift.of_eq",
|
875 |
+
"RingHom.mk_coe",
|
876 |
+
"BotHom.bot_apply",
|
877 |
+
"Matrix.UnitaryGroup.inv_apply",
|
878 |
+
"NonUnitalSubsemiring.toSubsemigroup_strictMono",
|
879 |
+
"Pi.monoidHom_injective",
|
880 |
+
"ContinuousLinearMap.coe_sub'",
|
881 |
+
"Mathlib.Meta.NormNum.jacobiSymNat.qr\u2083_mod",
|
882 |
+
"Filter.tendsto_neg_const_mul_pow_atTop",
|
883 |
+
"List.formPerm_cons_cons",
|
884 |
+
"Convex.lineMap_mem",
|
885 |
+
"CategoryTheory.IsIso.comp_inv_eq",
|
886 |
+
"hasDerivWithinAt_inter'",
|
887 |
+
"Equiv.comp_bijective",
|
888 |
+
"Set.ite_mono",
|
889 |
+
"Units.eq_inv_of_mul_eq_one_right",
|
890 |
+
"BumpCovering.sum_toPartitionOfUnity_eq",
|
891 |
+
"DoubleCentralizer.sub_fst",
|
892 |
+
"exists_succ_iterate_or",
|
893 |
+
"AddSubmonoid.toNatSubmodule_symm",
|
894 |
+
"OrderEmbedding.coe_ofMapLEIff",
|
895 |
+
"MonoidHom.map_zpow'",
|
896 |
+
"List.not_lt_of_mem_argmax",
|
897 |
+
"Dilation.coe_mul",
|
898 |
+
"PiTensorProduct.add_tprodCoeff'",
|
899 |
+
"Filter.tendsto_pure_left",
|
900 |
+
"IsLocalization.mk'_eq_iff_eq_mul",
|
901 |
+
"tsub_add_eq_add_tsub",
|
902 |
+
"IsROrC.hasSum_conj",
|
903 |
+
"Additive.isAddMonoidHom",
|
904 |
+
"TopCat.presheafToTypes_map",
|
905 |
+
"Con.conGen_mono",
|
906 |
+
"ContinuousLinearMap.hasBasis_nhds_zero",
|
907 |
+
"Set.infs_eq_empty",
|
908 |
+
"RingEquiv.mapMatrix_refl",
|
909 |
+
"Fintype.card_eq_zero",
|
910 |
+
"TopologicalSpace.Closeds.coe_sInf",
|
911 |
+
"CategoryTheory.InjectiveResolution.complex_d_comp",
|
912 |
+
"forall_const",
|
913 |
+
"CategoryTheory.Pi.isoApp_trans",
|
914 |
+
"imp_congr_ctx",
|
915 |
+
"TopCat.Presheaf.germ_res",
|
916 |
+
"ConvexOn.add_const",
|
917 |
+
"Subsemigroup.closure_iUnion",
|
918 |
+
"Ideal.mul_mem_mul",
|
919 |
+
"ContMDiff.clm_apply",
|
920 |
+
"Flow.map_add",
|
921 |
+
"ofLex_inj",
|
922 |
+
"LinearIsometryEquiv.comp_hasFDerivAt_iff'",
|
923 |
+
"Monoid.CoprodI.Word.smul_def",
|
924 |
+
"Set.prod_subset_preimage_snd",
|
925 |
+
"List.mem_of_mem_take",
|
926 |
+
"LocallyBoundedMap.comp_assoc",
|
927 |
+
"ContDiffAt.inv",
|
928 |
+
"List.nil_infix",
|
929 |
+
"ONote.NFBelow_zero",
|
930 |
+
"MeasureTheory.SimpleFunc.const_mul_eq_map",
|
931 |
+
"Set.preimage_subset_image_of_inverse",
|
932 |
+
"UpperSet.coe_top",
|
933 |
+
"Nat.nth_le_nth_of_lt_card",
|
934 |
+
"CategoryTheory.Limits.Types.limitEquivSections_symm_apply",
|
935 |
+
"EventuallyLE.countable_iInter",
|
936 |
+
"ofDual_max",
|
937 |
+
"IsMinOn.iInf_eq",
|
938 |
+
"Filter.NeBot.not_disjoint",
|
939 |
+
"CategoryTheory.leOfHom_homOfLE",
|
940 |
+
"ENNReal.max_zero_left",
|
941 |
+
"ExteriorAlgebra.toTrivSqZeroExt_\u03b9",
|
942 |
+
"Continuous.pow",
|
943 |
+
"Zspan.fract_mem_fundamentalDomain",
|
944 |
+
"MeasureTheory.Integrable.prod_right_ae",
|
945 |
+
"Substring.ValidFor.startPos",
|
946 |
+
"LinearMap.IsSymm.ortho_comm",
|
947 |
+
"Action.functorCategoryMonoidalEquivalence.inverse_map",
|
948 |
+
"Algebra.isAlgebraic_of_larger_base_of_injective",
|
949 |
+
"PartENat.get_eq_iff_eq_some",
|
950 |
+
"LinearEquiv.piCongrRight_trans",
|
951 |
+
"Interval.coe_injective",
|
952 |
+
"LieModuleHom.neg_apply",
|
953 |
+
"hasContinuousInv\u2080_of_hasSmoothInv\u2080",
|
954 |
+
"Tropical.untrop_inj_iff",
|
955 |
+
"Dvd.dvd.zero_modEq_nat",
|
956 |
+
"Computation.get_eq_of_promises",
|
957 |
+
"Subalgebra.coe_pointwise_smul",
|
958 |
+
"Function.surjective_pi_map",
|
959 |
+
"List.chain'_iff_pairwise",
|
960 |
+
"comap_coe_Ioo_nhdsWithin_Ioi",
|
961 |
+
"sInf_sUnion",
|
962 |
+
"Matrix.det_pow",
|
963 |
+
"isUpperSet_Ioi",
|
964 |
+
"btw_rfl_left",
|
965 |
+
"Function.LeftInverse.leftInvOn",
|
966 |
+
"CategoryTheory.Iso.refl_symm",
|
967 |
+
"iteratedFDerivWithin_inter",
|
968 |
+
"CategoryTheory.Limits.IsZero.hasZeroObject",
|
969 |
+
"Ideal.le_comap_mul",
|
970 |
+
"Int.natAbs_eq",
|
971 |
+
"Filter.frequently_map",
|
972 |
+
"Multiset.Pi.cons_ne",
|
973 |
+
"CategoryTheory.RanIsSheafOfCoverLifting.gluedLimitCone_\u03c0_app",
|
974 |
+
"NonUnitalSubring.toNonUnitalSubsemiring_mono",
|
975 |
+
"OrderMonoidWithZeroHom.mk_coe",
|
976 |
+
"upperBounds_Iic",
|
977 |
+
"Polynomial.fderiv_aeval",
|
978 |
+
"mul_le_of_le_of_le_one",
|
979 |
+
"Subgroup.Normal.eq_bot_or_eq_top",
|
980 |
+
"Polynomial.splits_iff_exists_multiset",
|
981 |
+
"CategoryTheory.Equivalence.Equivalence_mk'_unit",
|
982 |
+
"Ordnode.Valid.right",
|
983 |
+
"cast_proof_irrel",
|
984 |
+
"Quaternion.exp_coe",
|
985 |
+
"PosMulMono.toPosMulReflectLT"
|
986 |
+
]
|
987 |
+
}
|
test-example.json
ADDED
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|
|