CoeSort

📁 Source: Mathlib/Data/Set/CoeSort.lean

Statistics

Metric	Count
Definitions Elem, instCoeSortType	2
Theorems elem_mem	1
Total	3

Set

Definitions

Name	Category	Theorems
Elem 📖	CompOp	3433 math math: linearIndependent_set_coe_iff, IsLocalization.AtPrime.coe_primeSpectrumOrderIso_symm_apply_asIdeal, Fintype.all_card_le_rel_image_card_iff_exists_injective, NumberField.Ideal.ramificationIdx_primesOverSpanEquivMonicFactorsMod_symm_apply', Polynomial.Gal.galActionHom_restrict, mem_list_sum, iUnion_eq_range_sigma, TemperedDistribution.lineDerivOpCLM_eq, SimpleGraph.instIsEmptyElemForallObjOppositeFinsetComponentComplFunctorEndOfFinite, TopologicalSpace.IsOpenCover.isInducing_iff_restrictPreimage, continuousSMul_sphere_ball, instCompactSpaceElemClosedBallOfProperSpace, LowerSemicontinuousOn.inter_biInter_preimage_Iic_eq_empty_iff_exists_finset, MeasureTheory.Lp.toTemperedDistributionCLM_apply, ContinuousMap.HomotopyRel.prod_apply, ContinuousMap.tendsto_compactOpen_restrict, TemperedDistribution.fourierInv_toTemperedDistributionCLM_eq, CategoryTheory.Presieve.ofArrows_eq_ofArrows_uncurry, Ici.coe_bot, cfcₙ_def, Affine.Simplex.altitudeFoot_restrict, AddCircle.coe_equivIco_mk_apply, NNReal.orderIsoIccZeroCoe_apply_coe_coe, Matroid.instNonemptyElemSetSetOfAndIsFlatSubsetInterE, tsum_setProd_singleton_right, Order.IsNormal.apply_of_isSuccLimit, Topology.RelCWComplex.Subcomplex.union', Finset.coe_sort_coe, SetTheory.PGame.default_nim_one_rightMoves_eq, Field.Emb.Cardinal.equivLim_coherence, Submonoid.mem_closure_iff_of_fintype, continuous_cfcₙHomSuperset_left, Iic.coe_sInf, Ideal.comap_fiberIsoOfBijectiveResidueField_apply, MeromorphicOn.codiscrete_setOf_meromorphicOrderAt_eq_zero_or_top, Cardinal.mk_sUnion_le, CategoryTheory.CoreSmallCategoryOfSet.functor_obj, CategoryTheory.Limits.SingleObj.Types.sections.equivFixedPoints_apply_coe, completelyRegularSpace_iff_isOpen, OrderIso.map_csInf, Module.rank_def, Preorder.measurable_restrictLe, Filter.HasBasis.liminf_eq_ite, Real.iInf_Ioi_eq_iInf_rat_gt, MapsTo.iterate_restrict, norm_cfcₙHom, Algebra.lift_cardinalMk_adjoin_le, Path.subpath_self, polynomialFunctions.eq_adjoin_X, functorToTypes_obj, IsPathConnected.exists_path_through_family', CategoryTheory.regularTopology.EqualizerCondition.bijective_mapToEqualizer_pullback', IsDedekindDomain.HeightOneSpectrum.equivPrimesOver_apply, Subgroup.IsComplement.equiv_fst_eq_iff_leftCosetEquivalence, card_fintypeInsertOfNotMem, Profinite.NobelingProof.GoodProducts.sum_to_range, Dynamics.coverEntropy_restrict, bernsteinApproximation.apply_zero, unitInterval.sigmoid_le_iff, Nontrivial.coe_sort, Module.Basis.reindexRange_self, ContinuousMap.compactOpen_eq_iInf_induced, Cardinal.mk_insert_le, CategoryTheory.CoreSmallCategoryOfSet.instIsEquivalenceElemObjSmallCategoryOfSetFunctor, Matrix.IsHermitian.isClosedEmbedding_cfcAux, Cardinal.le_mk_iff_exists_subset, IsDiscrete.to_subtype, SimpleGraph.Subgraph.deleteVerts_mono', Nimber.instSmallElemInvSet, IsSelfAdjoint.commute_cfcHom, IsOfFinOrder.natCard_powers_le_orderOf, instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, SimpleGraph.ConnectedComponent.maximal_connected_induce_supp, Ideal.toCharacterSpace_apply_eq_zero_of_mem, inclusion_comp_inclusion, Subgroup.index_center_le_pow, NonUnitalIsometricContinuousFunctionalCalculus.isometric, AlgebraicGeometry.iSup_affineOpens_eq_top, Cardinal.mk_emptyCollection_iff, unitInterval.symmHomeomorph_apply, cfcₙHom_apply_mem_elemental, SimpleGraph.coe_induceHom, NumberField.Ideal.inertiaDeg_primesOverSpanEquivMonicFactorsMod_symm_apply, Localization.algebraMap_injective_of_span_eq_top, tendsto_tsum_div_pow_atTop_integral, SimpleGraph.incidenceSetEquivNeighborSet_apply_coe, Trivialization.preimageHomeomorph_symm_apply, IsMinOn.iInf_eq, Path.continuousMapClass, Matroid.restrictSubtype_indep_iff, ProbabilityTheory.IsMeasurableRatCDF.iInf_rat_gt_eq, Equiv.Set.union_symm_apply_left, PrimeSpectrum.preimageEquivFiber_symm_apply_coe, SSet.Subcomplex.Pairing.instFiniteSubtypeElemNIIAncestralRel, Fintype.card_ofFinset, unitInterval.volume_Ioo, exteriorPower.basis_apply, image_val_iUnion, unitInterval.volume_Iic, norm_eq_iInf_iff_real_inner_le_zero, UniformOnFun.gen_eq_preimage_restrict, nhds_ne_subtype_neBot_iff, ContinuousMap.HomotopyWith.coe_toContinuousMap, instNoMaxOrderElemIoi, CategoryTheory.SmallObject.SuccStruct.extendToSucc_map_le_succ, linearIndependent_le_span, Cardinal.mk_preimage_of_injective_of_subset_range, NumberField.prod_nonarchAbsVal_eq, MeasurableSpace.Subtype.separatesPoints, rank_le_card_isVisible, SSet.horn₃₁.desc.multicofork_π_two, unitInterval.volume_def, unitInterval.sigmoid_lt, Summable.sum_add_tsum_compl, Module.free_iff_set, CategoryTheory.SmallCategoryOfSet.id_def, Profinite.NobelingProof.projRestricts_comp_projRestrict, AlgebraicGeometry.Scheme.Hom.fiberHomeo_apply, Polynomial.Gal.smul_def, Trivialization.domExtend_source, LipschitzOnWith.mapsToRestrict, Ioo.infinite, definable_iff_empty_definable_with_params, Metric.unitSphere.coe_one, Topology.IsClosedEmbedding.inclusion, Function.Fiber.map_eq_image, mem_nhdsSet_subtype_iff_nhdsSetWithin, Profinite.NobelingProof.injective_πs', Height.mulHeight₁_eq, ModelWithCorners.instIsEmptyElemBoundaryOfBoundarylessManifold, Ordinal.Iio_one_default_eq, tprod_subtype_mulSupport, Finite.Set.subset, Finite.Set.finite_image, IsClosedMap.isEvenlyCovered_of_openPartialHomeomorph, continuousSMul_sphere_sphere, spectrum.instCompactSpace, small_union, MeasurableSpace.instFinite_countablePartition, Module.Basis.range_ofVectorSpace, LSeries.term_convolution', nhds_ne_subtype_eq_bot_iff, SSet.Subcomplex.Pairing.IsProper.isUniquelyCodimOneFace, volume_set_coe_def, Filter.mem_iInf, ENNReal.tsum_set_const, Submodule.generators_card, Metric.contractibleSpace_ball, instNonemptyRange, Matroid.Indep.cardinalMk_le_cRk_of_subset, SimpleGraph.Subgraph.coeSubgraph_injective, imageFactorization_injective_iff, ApproximatesLinearOn.lipschitz, Polynomial.card_rootSet_le_derivative, discreteTopology_subtype_iff', Cardinal.extend_function_finite, restrictPreimage_surjective, Polynomial.Gal.restrict_smul, Cardinal.mk_preimage_of_subset_range_lift, Subgroup.transferTransversal_apply, unitInterval.strictAnti_symm, CategoryTheory.Subfunctor.Subpresheaf.toPresheaf_obj, instNoMinOrderElemIic, ContinuousMap.attachBound_apply_coe, Finsupp.supportedEquivFinsupp_symm_single, Cardinal.mk_Iio_real, Metric.PiNatEmbed.continuous_distDenseSeq_inv, ProbabilityTheory.unitInterval.cdf_eq_real, SimpleGraph.IsAcyclic.induce, AddAction.mem_addSubgroup_orbit_iff, normalizedFactorsEquivOfQuotEquiv_emultiplicity_eq_emultiplicity, range_inclusion, Path.extend_extends, AlgebraicGeometry.Scheme.IdealSheafData.ideal_sSup, natCard_smul_set₀, ContinuousLinearMap.iSup_rayleigh_eq_iSup_rayleigh_sphere, GenLoop.fromLoop_apply, NumberField.Ideal.inertiaDeg_primesOverSpanEquivMonicFactorsMod_symm_apply', Affine.Simplex.restrict_reindex, range_IciExtend, EquicontinuousOn.tendsto_uniformOnFun_iff_pi', Ideal.coe_smul_primesOver_mk_eq_map_galRestrict, Affine.Simplex.faceOppositeCentroid_restrict, ODE.FunSpace.isUniformInducing_toContinuousMap, Icc.coe_zero, IsProperMap.restrict, ContinuousFunctionalCalculus.compactSpace_spectrum, CategoryTheory.PreGaloisCategory.endEquivSectionsFibers_π, Polynomial.Gal.galActionHom_injective, Iic.isCompactElement, exteriorPower.coe_basis, OrderIso.sumLexIicIoi_symm_apply_of_lt, Trivialization.codExtend_source, tprod_image, Subgroup.IsComplement.coe_equiv_snd_eq_one_iff_mem, stdSimplexHomeomorphUnitInterval_symm_apply_coe, exists_set_linearIndependent_of_isDomain, exteriorPower.ιMulti_family_linearIndependent_field, Cardinal.mk_preimage_equiv_lift, MeasureTheory.UniformIntegrable.uniformIntegrable_of_tendstoInMeasure, Ici.coe_inf, Finset.multipliable, principalSegIioIicOfLE_toRelEmbedding, MeasureTheory.measurable_restrict_cylinderEvents, Algebra.IsAlgebraic.trdeg_le_cardinalMk, idealFactorsEquivOfQuotEquiv_mem_normalizedFactors_of_mem_normalizedFactors, Profinite.NobelingProof.Products.span_nil_eq_top, preimage_val_eq_univ_of_subset, MeasureTheory.measure_biUnion, SimpleGraph.Subgraph.verts_coeSubgraph, QuasispectrumRestricts.compactSpace, MeasureTheory.UniformIntegrable.uniformIntegrable_of_ae_tendsto, Field.Emb.Cardinal.directed_filtration, ContinuousMapZero.toContinuousMap_id, FiniteExhaustion.instFiniteElemCoeNat, PiNat.exists_retraction_subtype_of_isClosed, isClosedEmbedding_cfcₙAux, image_coe_eq_restrict_image, CategoryTheory.Limits.Types.limitCone_pt, CategoryTheory.Functor.sectionsFunctor_obj, ContinuousMapZero.id_toFun, coe_factor_orderIso_map_eq_one_iff, WeakDual.CharacterSpace.instIsEmpty, AddSubgroup.IsComplement.card_mul_card, SimpleGraph.walkLengthTwoEquivCommonNeighbors_symm_apply_coe, isMin_of_pred_notMem, OrdConnected.IicExtend, Finite.coeSort_toFinset, countable_iff_exists_surjective, small_biInter, MeasureTheory.Measure.toSphere_apply_aux, AddSubgroup.IsComplement.quotientAddGroupMk_leftQuotientEquiv, powersetCard.isPretransitive, NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm_apply_fst, unitInterval.toNNReal_continuous, IsComplete.completeSpace_coe, TermDefinable₁.const, SimplexCategory.toTopObj_one_coe_add_coe_eq_one, linearIndependent_le_span', encard_univ_coe, Profinite.NobelingProof.GoodProducts.linearIndependent_iff_union_smaller, Topology.IsInducing.restrictPreimage, cauchySeq_finset_iff_nat_tsum_vanishing, NormedSpace.sphere_nonempty_rclike, exteriorPower.basis_repr_ne, Profinite.NobelingProof.coe_πs, ContinuousMap.Homotopy.apply_zero_path, SetLike.coe_sort_coe, selfAdjoint.expUnitaryPathToOne_apply, powersetCard.ofFinEmb_surjective, HomotopyGroup.symmAt_indep, SimpleGraph.exists_bijective_of_forall_ncard_le, Finite.multipliable_compl_iff, Finite.Set.finite_of_finite_image, Fintype.card_range_le, instTietzeExtensionUnitBall, AddCircle.equivIccQuot_comp_mk_eq_toIcoMod, TopologicalSpace.noetherian_univ_iff, subset_sSup_emptyset, genericPoints.component_injective, ENNReal.tsum_iUnion_le_tsum, Complex.UnitDisc.instSMulCommClass_closedBall_circle, TemperedDistribution.lineDerivOp_fourier_eq, PrimeSpectrum.discreteTopology_iff_finite_isMaximal_and_sInf_le_nilradical, MeasureTheory.measure_biUnion_le, set_fintype_card_eq_univ_iff, Complex.UnitDisc.instSMulCommClass_closedBall_left, contMDiff_neg_sphere, StarAlgebra.elemental.characterSpaceToSpectrum_coe, MeasurableSet.standardBorel, CategoryTheory.Subfunctor.toFunctor_obj, Function.Embedding.sumSet_apply, pow_image_of_prime_by_factor_orderIso_dvd, ContinuousMap.HomotopyWith.prop', Countable.exists_pos_hasSum_le, ODE.FunSpace.range_toContinuousMap, WeakDual.CharacterSpace.apply_mem_spectrum, PFun.preimage_asSubtype, nonempty_Icc_subtype, tsum_setProd_singleton_left, Span.repr_def, Equiv.sigmaPreimageEquiv_symm_apply_snd_coe, StarConvex.contractibleSpace, HasCardinalLT.Set.functor_obj, surjOn_iff_surjective, Multipliable.subtype, CommGrpCat.hasLimit_iff_small_sections, instSMulCommClass_sphere_sphere_sphere, projIic_surjective, uniformity_setCoe, Subgroup.IsComplement.equiv_snd_eq_self_iff_mem, Fintype.mem_span_image_iff_exists_fun, Affine.Simplex.restrict_map_restrict, unitInterval.pos_iff_ne_zero, Path.Homotopy.map_apply, WeakDual.CharacterSpace.ext_iff, encard_preimage_val_le_encard_left, CategoryTheory.Limits.opCompYonedaSectionsEquiv_symm_apply_coe, Path.pi_coe, Pretrivialization.restrictPreimage_target, Flow.orbit_restrict, termDefinable_empty_withConstants_iff, CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_self_succ, CategoryTheory.Limits.yonedaCompLimIsoCocones_inv_app, strictMonoOn_projIic, FirstOrder.Language.coe_con, isCompact_iff_compactSpace, Nat.coe_orderEmbeddingOfSet, unitInterval.coe_symmMeasurableEquiv, genericPoints.equiv_symm_apply, Ordinal.card_iSup_Iio_le_sum_card, Profinite.NobelingProof.instSubsingletonLocallyConstantElemForallBoolEmptyCollectionSetInt, Ordinal.enum_symm_apply_coe, Function.Embedding.sumSet_range, TemperedDistribution.smulLeftCLM_compL_smulLeftCLM, CategoryTheory.Limits.MulticospanIndex.sectionsEquiv_symm_apply_val, SimpleGraph.isClique_iff_induce_eq, Path.range_subpathAux, orthonormal_empty, unitInterval.volume_Ico, IccExtend_eq_self, Cardinal.le_aleph0_iff_set_countable, Filter.HasBasis.iInf, SimpleGraph.map_edgeFinset_induce_of_support_subset, CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSet_id, CategoryTheory.SmallObject.SuccStruct.arrowMk_iterationFunctor_map, Path.ext_iff, MulAction.quotient_out_smul_fixedPoints, ContinuousMap.HomotopyLike.map_zero_left, hasSum_subtype_iff_of_support_subset, ContinuousMap.Homotopy.evalAt_eq, isLindelof_iff_isLindelof_univ, Ordinal.enum_zero_le, Topology.IsEmbedding.inclusion, PrimitiveSpectrum.isTopologicalBasis_relativeLower, LinearMap.le_rank_iff_exists_linearIndependent, SimpleGraph.IsCompleteBetween.induce, CategoryTheory.Limits.coyonedaCompLimIsoCones_inv_app, val_comp_inclusion, exteriorPower.ιMulti_family_span_fixedDegree_of_span, Equiv.ofLeftInverse_apply_coe, Subtype.dense_iff, CategoryTheory.Subgroupoid.inclusion_inj_on_objects, Equiv.finsuppUnique_symm_apply_support_val, coe_neg_closedBall, Cardinal.mk_preimage_equiv, isLindelof_iff_lindelofSpace, instContinuousNegElemBallOfNat, Dense.ciSup, UniformOnFun.isometry_restrict, equicontinuous_restrict_iff, isChain_coe_univ_iff, MvPolynomial.prime_rename_iff, Equiv.Set.rangeInl_symm_apply_coe, Finite.card_lt_card, Module.Basis.coe_extendLe, polynomialFunctions_separatesPoints, Cardinal.mk_univ, LinearIndepOn.linearIndependent_restrict, Ordinal.enum_lt_enum, powersetCard.mem_mulActionHom_compl, Finite.summable, Subgroup.IsComplement.equiv_one, CategoryTheory.Functor.WellOrderInductionData.surjective, DirectedOn.le_ciInf_set_iff, Cardinal.mk_monotone, MeasureTheory.Measure.toSphere_real_apply_univ, restrictPreimage_isClosedEmbedding, SSet.horn₃₂.desc.multicofork_π_one, Topology.IsInducing.codRestrict, tsum_range, unitInterval.volume_apply, Finsupp.mem_span_iff_linearCombination, instIsManifoldRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc, Metric.unitBall.instContinuousMul, PrimeSpectrum.instQuasiSoberElemZeroLocus, Countable.exists_surjective, AlgebraicIndependent.iff_adjoin_image_compl, setBasisOfLinearIndependentOfCardEqFinrank_repr_apply, Icc.nonneg, coe_eq_subtype, Besicovitch.exists_closedBall_covering_tsum_measure_le, Profinite.NobelingProof.Products.max_eq_eval, OrderIso.sumLexIioIci_symm_apply_Ici, DFinsupp.mk_neg, Language.start_toDFA, Topology.RelCWComplex.Subcomplex.union, MvPolynomial.supportedEquivMvPolynomial_symm_X, Metric.contractibleSpace_closedBall, cfcHom_continuous, polynomialFunctions.starClosure_topologicalClosure, cfcL_apply, small_inter_of_left, Equiv.Perm.OnCycleFactors.kerParam_range_card, SSet.Subcomplex.Pairing.dim_p, exists_dist_slope_lt_pairwiseDisjoint_hasSum, AlgebraicGeometry.Scheme.IdealSheafData.ideal_mul, PointwiseConvergenceCLM.tendsto_nhds, AddSubgroup.IsComplement.card_right, isPreconnected_iff_preconnectedSpace, quasispectrum.coe_zero, MeasureTheory.lintegral_biUnion, Order.le_cof, isPreirreducible_iff_preirreducibleSpace, Profinite.NobelingProof.Products.eval_πs, Summable.nat_tsum_vanishing, Equiv.Set.image_apply, Cardinal.mk_le_one_iff_set_subsingleton, QuotientAddGroup.equivIocMod_zero, Fintype.card_Iic, unitInterval.sigmoid_strictMono, CategoryTheory.Subobject.wideCospan_map_term, rangeFactorization_bijective, Icc_isBoundaryPoint_bot, ENat.card_image_of_injOn, Equiv.Perm.OnCycleFactors.kerParam_injective, Topology.IsLocallyConstructible.iff_of_isOpenCover, TangentBundle.symmL_trivializationAt_eq_core, CategoryTheory.Limits.MulticospanIndex.sectionsEquiv_apply_coe, SimpleGraph.Preconnected.induce_of_degree_eq_one, cfcHom_nonneg_iff, Homeomorph.contDiff_unitBall, CategoryTheory.Subgroupoid.inclusion_refl, Finset.summable, gelfandStarTransform_naturality, Orthonormal.exists_hilbertBasis_extension, IsOpenMap.restrictPreimage, Matroid.restrictSubtype_isBasis_iff, ringKrullDim_quotient, Metric.sphere_isEmpty_of_subsingleton, gelfandStarTransform_apply_apply, MeasureTheory.lintegral_countable, TopologicalSpace.Fiber.sigmaIsoHom_inj, MapsTo.coe_restrict, rank_span_set, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_dvd_norm_le, Profinite.NobelingProof.GoodProducts.injective, Polynomial.Gal.mapRoots_bijective, stereographic'_source, Subgroup.exists_left_transversal_of_le, cfc_apply_mkD, IsClosed.isCompletelyPseudoMetrizableSpace, Subfield.cardinalMk_closure_le_max, SimpleGraph.card_set_walk_length_eq, unitInterval.symm_le_symm, Matroid.InvariantCardinalRank.forall_card_isBasis_diff, cfcₙ_eq_cfcₙL_mkD, TangentBundle.continuousLinearMapAt_trivializationAt_eq_core, Icc.infinite, stdSimplexHomeomorphUnitInterval_zero, affineIndependent_set_iff_linearIndependent_vsub, algebraicIndependent_bounded_of_finset_algebraicIndependent_bounded, Function.MulExact.iff_rangeFactorization, Submodule.mem_ideal_smul_span_iff_exists_sum', image_val_inter, CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.inductiveSystem_obj, DirectSum.mk_smul, Ioc.coe_pow, Matroid.IsBase.cardinalMk_le_cRank, surjective_onto_image, Module.Basis.ofSpan_subset, Ordinal.one_toPGame_leftMoves_default_eq, GenLoop.homotopyTo_apply, SSet.Subcomplex.Pairing.isUniquelyCodimOneFace, Profinite.NobelingProof.spanFunctorIsoIndexFunctor_hom_app_hom_hom_apply_coe, SSet.Subcomplex.Pairing.WeakRankFunction.wf_ancestralRel, Path.Homotopy.continuous_transAssocReparamAux, Nucleus.restrict_toFun, IsCyclotomicExtension.Rat.nrComplexPlaces_eq_totient_div_two, Cardinal.le_mk_iff_exists_set, DirectSum.mk_injective, AlgebraicGeometry.Scheme.Hom.irreducibleComponentsEquiv_symm_apply_coe, restrictPreimage_isOpenEmbedding, Filter.tendsto_Iic_atBot, AntilipschitzWith.to_rightInvOn, Matroid.Indep.exists_eq_image_of_mapSetEmbedding, MonoidHom.fiberEquivKer_symm_apply, Cardinal.mk_image_embedding, compl_mem_codiscrete_iff, Path.Homotopy.target, restrictPreimage_bijective, CategoryTheory.TransfiniteCompositionOfShape.iic_isoBot, CompactlyCoherentSpace.isOpen_iff, HasProd.tprod_fiberwise, gelfandTransform_bijective, StrictMono.orderIso_apply, Cardinal.infinite_pigeonhole, Finite.Set.finite_diff, HasCardinalLT.Set.cocone_pt, ContinuousMap.concatCM_left, AddCircle.equivIco_coe_eq, AddMonoidHom.fiberEquiv_symm_apply, Equiv.ofLeftInverse_symm_apply, SimpleGraph.isContained_iff_exists_iso_subgraph, SimpleGraph.card_incidenceSet_eq_degree, IsModularLattice.complementedLattice_Ici, cfcHom_isClosedEmbedding, unitInterval.symmMeasurableEquiv_apply, mfderivWithin_projIcc_one, RestrictedProduct.isOpenEmbedding_structureMap, Cardinal.le_range_of_union_finset_eq_top, TemperedDistribution.smulLeftCLM_neg, HomotopyGroup.isUnital_auxGroup, Matroid.IsBasis'.cardinalMk_eq, totallyDisconnectedSpace_subtype_iff, SimpleGraph.Subgraph.image_coe_edgeSet_coe, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_norm_eq_mul_torsion, encard_preimage_val_le_encard_right, Affine.Simplex.circumradius_restrict, IsOpenMap.codRestrict, ENNReal.tsum_biUnion_le, PointwiseConvergenceCLM.postcomp_apply, Path.delayReflRight_zero, CategoryTheory.GradedObject.instFiniteElemProdNatPreimageHAddFstSndSingletonSet, AlgebraicGeometry.IsAffineOpen.self_le_iSup_basicOpen_iff, OrderIso.map_csSup_of_directedOn, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_assoc, isScalarTower_closedBall_closedBall_closedBall, CategoryTheory.Limits.compYonedaSectionsEquiv_apply_app, Affine.Simplex.medial_restrict, Profinite.NobelingProof.GoodProducts.equiv_toFun_eq_eval, cauchySeq_finset_iff_nat_tprod_vanishing, SpectrumRestricts.compactSpace, Function.HasTemperateGrowth.toTemperedDistribution_apply, OrderHom.nextFixed_le, isAtomic_iff_forall_isAtomic_Iic, Cardinal.infinite_pigeonhole_card_lt, SimpleGraph.card_commonNeighbors_le_degree_left, Order.IsSuccLimit.iSup_Iio, powersetCard.coe_coe, isScalarTower_sphere_closedBall_closedBall, Icc.disjoint_iff, powersetCard.faithfulSMul, linearIndependent_comp_subtype_iff, FirstOrder.Language.addEmptyConstants_symm_isExpansionOn, tprod_setProd_singleton_left, SimpleGraph.Subgraph.nontrivial_verts_of_degree_ne_zero, ContinuousMap.HomotopyWith.apply_one, cardinal_eq_of_mem_nhds_zero, monotone_projIic, definable_iff_exists_formula_sum, Profinite.NobelingProof.Products.eval_πs', Profinite.NobelingProof.GoodProducts.span_sum, Profinite.NobelingProof.GoodProducts.range_equiv_factorization, Cardinal.mk_subset_ge_of_subset_image_lift, BoxIntegral.unitPartition.integralSum_eq_tsum_div, image_restrictPreimage, Ici.isAtom_iff, Equiv.Set.insert_symm_apply_inr, CategoryTheory.SmallObject.SuccStruct.arrowMap_refl, Topology.CWComplex.Subcomplex.cell_def, Matroid.instRankFiniteElemRestrictSubtype, Fintype.card_range, small_empty, Matroid.cRank_eq_iSup_cardinalMk_indep, uniformEquicontinuous_restrict_iff, powersetCard.compl_symm, CategoryTheory.GradedObject.CofanMapObjFun.inj_iso_hom, Path.Homotopy.eval_zero, Icc_isInteriorPoint_interior, tsum_eq_tsum_diff_singleton, Cardinal.mk_emptyCollection, PiTensorProduct.projectiveSeminorm_apply, Nat.count_le_cardinal, instInfiniteElemIoiOfNoMaxOrder, sUnion_eq_iUnion, Pi.Colex.sSup_apply, Finite.Set.finite_insert, Cardinal.mk_preimage_down, Pretrivialization.domExtend_baseSet, SimpleGraph.IsSRGWith.card_neighborFinset_union_eq, cfcₙ_apply_mkD, exists_hilbertBasis, Matroid.IsBasis.cardinalMk_diff_comm, AddAction.orbitZMultiplesEquiv_symm_apply', PrimeSpectrum.coe_preimageHomeomorphFiber_apply_asIdeal, CompactlyCoherentSpace.isClosed_iff, cfcₙHom_id, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t_assoc, TemperedDistribution.instLineDerivLeftSMulReal, Subgroup.rank_closure_finite_le_nat_card, Cardinal.mk_div_le, MapsTo.coe_iterate_restrict, ContinuousOn.restrict_mapsTo, SimpleGraph.Walk.map_induce_induceHomOfLE, tendsto_card_div_pow_atTop_volume, affineSpan_eq_affineSpan_lineMap_units, SSet.nonDegenerateEquivOfIso_symm_apply_coe, CategoryTheory.GradedObject.instFiniteElemProdNatSetOfEqHAddFstSnd, Subgroup.quotientCentralizerEmbedding_apply, Module.Basis.extendLe_subset, NumberField.mixedEmbedding.fundamentalCone.integerSetQuotEquivAssociates_apply, CantorScheme.Disjoint.map_injective, Cardinal.mk_union_add_mk_inter, AlgebraicIndependent.adjoin_iff_disjoint, Module.Basis.mk_range_eq_rank, Pi.induced_restrict, SimpleGraph.induceUnivIso_apply, nonempty_coe_sort, TemperedDistribution.fourierInv_lineDerivOp_eq, mfderivWithin_comp_projIcc_one, AddAction.orbitZMultiplesEquiv_symm_apply, Ordinal.iSup_succ, BoundedContinuousFunction.restrict_apply, SimplexCategory.continuous_toTopMap, VitaliFamily.FineSubfamilyOn.measure_le_tsum, Module.Basis.le_span, antitoneOn_iff_antitone, initialSegIic_toFun, ContinuousMap.HomotopyRel.refl_apply, SimpleGraph.extend_finset_to_connected, iInf_range', preimage_coe_mem_nhds_subtype, coe_biUnionEqSigmaOfDisjoint_symm_apply, WithTop.tendsto_untop, Equiv.Set.univ_symm_apply, unitInterval.qRight_one_left, ContinuousMap.Homotopy.ulift_apply, Filter.mem_cardinaleGenerate_iff, Real.continuous_tan, MeasureTheory.continuous_diracProbaEquiv, SimpleGraph.Copy.range_toSubgraph, Continuous.restrict, MulAction.sum_card_fixedBy_eq_card_orbits_mul_card_group, ZSpan.quotientEquiv_apply_mk, Equiv.Set.insert_apply_left, OrderIso.setIsotypicComponents_apply, GenLoop.loopHomeo_apply, Polynomial.instSMulCommClassElemRootSet, MeasureTheory.Measure.sum_add_sum_compl, Function.Embedding.sigmaSet_apply, Equiv.coe_ofInjective_symm, IsLocalization.AtPrime.coe_primeSpectrumOrderIso_apply_coe_asIdeal, CategoryTheory.HomOrthogonal.matrixDecomposition_id, lipschitzOnWith_iff_restrict, Matroid.restrictSubtype_ground, OpenPartialHomeomorph.homeomorphOfImageSubsetSource_symm_apply, Metric.unitSphere.coe_mul, IccLeftChart_extend_interior_pos, Cardinal.mk_iUnion_le_sum_mk_lift, Ordinal.enum_le_enum', Profinite.NobelingProof.fin_comap_jointlySurjective, Equiv.Perm.sign_of_cycleType_eq_replicate, PrimeSpectrum.coe_preimageOrderIsoFiber_symm_apply_coe_asIdeal, ContinuousLinearMap.iInf_rayleigh_eq_iInf_rayleigh_sphere, image_val_union, Cardinal.mk_image_embedding_lift, Filter.HasBasis.limsup_eq_ite, restrictPreimage_isEmbedding, UpperSemicontinuousOn.inter_biInter_preimage_Ici_eq_empty_iff_exists_finset, EquicontinuousOn.inducing_uniformOnFun_iff_pi', Module.End.eigenvectors_linearIndependent, Path.delayReflLeft_one, range_restrictPreimage, Matroid.isClosed_iff_isFlat, TopologicalSpace.Subtype.secondCountableTopology, ENNReal.tsum_biUnion, IsCompactOperator.codRestrict, TemperedDistribution.instFourierAdd, Finset.hasSum_support, ProbabilityTheory.setBernoulli_one, CategoryTheory.TransfiniteCompositionOfShape.ici_F, IsCyclotomicExtension.Rat.absdiscr_prime_pow, powersetCard.stabilizer_coe, Finite.Set.finite_sep, isBigO_norm_Icc_restrict_atTop, Equiv.Perm.VectorsProdEqOne.vectorEquiv_apply_coe, Matroid.restrictSubtype_dual', SimpleGraph.Partition.colorable, cfcHom_le_iff, SimpleGraph.card_neighborSet_eq_degree, Module.Basis.reindexRange_repr', Equiv.Perm.VectorsProdEqOne.card, cfcHom_id, SimpleGraph.IsTree.coe_subgraphOfAdj, tsum_subtype, Finite.Set.finite_seq, Summable.subtype, ContinuousMap.HomotopyRel.trans_apply, PointwiseConvergenceCLM.instLocallyConvexSpace, Cardinal.mk_iUnion_eq_sum_mk, Module.Basis.reindexRange_repr, AlgebraicGeometry.pointEquivClosedPoint_apply_coe, finprod_set_coe_eq_finprod_mem, Topology.RelCWComplex.Subcomplex.union_closedCell, TemperedDistribution.instFourierSMul, OrderIso.sumLexIicIoi_symm_apply_of_le, range_cfcₙHom, Profinite.NobelingProof.GoodProducts.spanFin, Profinite.NobelingProof.succ_exact, NormedField.denselyOrdered_range_norm, small_set_zero, MulAction.instIsPretransitiveElemOrbit_1, Ideal.nonempty_minimalPrimes, ContinuousMap.mkD_of_continuousOn, coe_neg_sphere, isSigmaCompact_iff_isSigmaCompact_univ, Pi.Lex.sInf_apply, Affine.Simplex.ninePointCircle_restrict, instPathConnectedSpaceElemForallRealStdSimplexOfNonempty, Subgroup.IsComplement.equiv_mul_left_of_mem, SSet.horn₃₁.desc.multicofork_pt, natCard_add_le, CategoryTheory.SmallObject.SuccStruct.extendToSuccObjIso_hom_naturality_assoc, Subgroup.smul_leftQuotientEquiv, OpenPartialHomeomorph.toHomeomorphSourceTarget_apply_coe, hasSum_subtype_iff_indicator, FilterBasis.eq_iInf_principal, AlgebraicGeometry.Scheme.IdealSheafData.ideal_pow, Pretrivialization.restrictPreimage'_target, discreteTopology_of_noAccPts, Function.Exact.rangeFactorization, principalSegIioIicOfLE_top, SetTheory.PGame.toRightMovesNim_one_symm, Filter.HasBasis.limsup_eq_sInf_iUnion_iInter, Profinite.NobelingProof.GoodProducts.smaller_factorization, Cardinal.mk_le_iff_forall_finset_subset_card_le, InjOn.imageFactorization_injective, SimpleGraph.ConnectedComponent.even_card_of_isPerfectMatching, ZLattice.covolume.tendsto_card_div_pow, ContinuousMap.Homotopy.cast_apply, SimpleGraph.Subgraph.coe_degree, Path.toHomotopyConst_apply, OrderHom.le_prevFixed, unitInterval.measurePreserving_symm, SimpleGraph.nonempty_singletonSubgraph_verts, ContinuousMap.mkD_of_not_continuousOn, spectrum.gelfandTransform_eq, stereographic_apply_neg, SimpleGraph.Adj.card_commonNeighbors_lt_degree, NumberField.mixedEmbedding.fundamentalCone.integerSetEquiv_apply_fst, Affine.Simplex.face_restrict, Module.Basis.reindexRange_apply, Icc.codisjoint_iff, Icc_chartedSpaceChartAt_of_le_top, TemperedDistribution.delta_apply, Pi.uniformSpace_comap_restrict, exists_basis_of_pairing_ne_zero, Path.extend_apply, SimpleGraph.Embedding.mapNeighborSet_apply_coe, Cardinal.mk_union_le_aleph0, Affine.Simplex.interior_restrict, linearIndependent_restrict_iff, Submodule.spanRank_span_of_linearIndepOn, Submodule.spanRank_span_le_card, GaloisConnection.l_ciSup_set_of_directedOn, surjective_codRestrict, MulAction.orbitRel.Quotient.mem_subgroup_orbit_iff, Profinite.NobelingProof.πs'_apply_apply, aemeasurable_restrict_iff_comap_subtype, LinearIndepOn.linearIndependent, projIic_surjOn, QuasiconvexOn.isPreconnected_preimage_subtype, stdSimplex.eq_one_of_unique, EisensteinSeries.gammaSetDivGcdSigmaEquiv_symm_eq, powersetCard.instInfinite, WeakDual.CharacterSpace.instNonUnitalAlgHomClass, range_stereographic_symm, AffineSubspace.inclusion_linear, Cardinal.small_Iio, SimpleGraph.ConnectedComponent.maximal_connected_induce_iff, TemperedDistribution.instContinuousFourier, ZFSet.coeEquiv_apply_coe, injective_codRestrict, Cardinal.mk_setProd, Bornology.IsBounded.boundedSpace_val, WeakDual.CharacterSpace.continuousMapEval_bijective, CategoryTheory.ObjectProperty.instIsClosedUnderColimitsOfShapeColimitsCardinalClosureCategoryFamily, AddSubgroup.isComplement_addSubgroup_left_iff_bijective, Cardinal.mk_strictMonoOn, Matroid.cRk_le_cardinalMk, MonoidAlgebra.mvPolynomial_aeval_of_surjective_of_closure, AddMonoidAlgebra.mvPolynomial_aeval_of_surjective_of_closure, isOpenEmbedding_stereographic_symm, HolderOnWith.holderWith, powersetCard.nontrivial_iff, small_sub, Filter.mem_cocardinal, SSet.Subcomplex.Pairing.RankFunction.wf_ancestralRel, continuousMap_mem_polynomialFunctions_closure, measurableEmbedding_sigmoid, SubAddAction.ofFixingAddSubgroup.append_left, SimplexCategory.toTop_obj, Polynomial.card_rootSet_eq_natDegree_iff_of_splits, powersetCard.isPretransitive_alternatingGroup, lipschitzOnWith_cfc_fun_of_subset, HomotopyGroup.transAt_indep, instNonemptyElemInsert, unitInterval.toNNReal_zero, Cardinal.mk_biUnion_le_lift, IsDedekindDomain.primesOverEquivPrimesOver_inertiagDeg_eq, tendsto_comp_coe_Iio_atTop, CategoryTheory.Presieve.preZeroHypercover_I₀, ContinuousMap.Homotopy.compContinuousMap_apply, Cardinal.mk_range_eq_of_injective, Subgroup.IsComplement.equiv_snd_eq_iff_rightCosetEquivalence, TopologicalSpace.IsOpenCover.isClosedEmbedding_iff_restrictPreimage, Path.cast_coe, ContinuousMap.Homotopy.comp_apply, surjective_mapsTo_image_restrict, normalizedFactorsEquivOfQuotEquiv_symm, CategoryTheory.SmallObject.SuccStruct.restrictionLTOfCoconeIso_inv_app, Finite.Set.finite_range, StronglyLocallyContractibleSpace.contractible_basis, Trivialization.restrictPreimage'_source, Path.ofLine_mem, completelyNormalSpace_iff_forall_normalSpace, Monoid.fg_iff_exists_freeMonoid_hom_surjective, contractible_subset_basis, IsOpen.polishSpace, continuous_rangeFactorization_iff, Homeomorph.coe_unitBall_apply_zero, hallMatchingsOn.nonempty, gelfandStarTransform_symm_apply, card_derangements_invariant, CategoryTheory.Functor.bijective_sectionsPrecomp, isIrreducible_iff_irreducibleSpace, iSup_subtype'', Cardinal.mk_inv, unitSphereToUnits_apply_coe, Flow.coe_restrict_apply, coe_fintypeCard, le_ciSup_set, SimplexCategory.toTop_map, Fintype.card_setUniv, isQuotientMap_projIcc, SimpleGraph.Walk.map_mapToSubgraph_eq_induce, powersetCard.isPretransitive_of_isMultiplyPretransitive', SSet.Subcomplex.Pairing.IsRegular.wf, NumberField.mixedEmbedding.fundamentalCone.integerSetTorsionSMul_smul_coe, instNonemptyTop, powersetCard.addAction_stabilizer_coe, TopologicalSpace.IsOpenCover.isHomeomorph_iff_restrictPreimage, CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_eq, Real.coe_expOrderIso_apply, CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan_inj, Path.subpathAux_one, SchwartzMap.delta_apply, Path.continuous_delayReflRight, MeasureTheory.Measure.restrict_biUnion_le, biInter_eq_iInter, Finite.Set.finite_image2, AddMonoidHom.fiberEquivKer_apply, powersetCard.addActionHom_of_embedding_surjective, unitInterval.lt_one_iff_ne_one, measurableEmbedding_sigmoid_comp_embeddingReal, MeasureTheory.exists_subset_real_measurableEquiv, unitInterval.lt_symm_comm, MeasureTheory.UnifIntegrable.unifIntegrable_of_tendstoInMeasure, GenLoop.instContinuousEval, stdSimplex.map_coe, Path.Homotopy.hcomp_half, Profinite.NobelingProof.Products.eval_eq, Homeomorph.Set.univ_symm_apply_coe, Filter.tendsto_comp_val_Iic_atBot, Icc.convexCombo_one, SSet.Subcomplex.PairingCore.pairing_p_equivII, Path.Homotopy.hcomp_apply, CategoryTheory.Subgroupoid.coe_comp_coe, Nontrivial.infsep_eq_iInf, ENNReal.tsum_set_one, FilterBasis.nonempty_sets, SimpleGraph.Subgraph.coe_adj, genericPoints.component_surjective, hasProd_subtype_iff_mulIndicator, Path.continuous_delayReflLeft, tendsto_Ioi_atBot, Path.Homotopy.symm_apply, AddSubgroup.IsComplement.mk''_rightQuotientEquiv, LipschitzWith.projIcc, CategoryTheory.SmallObject.SuccStruct.extendToSuccObjIso_hom_naturality, SSet.instFiniteElemObjOppositeSimplexCategoryOpMkNonDegenerateOfFinite, WeakDual.CharacterSpace.homeoEval_naturality, CommMonCat.instSmallElemForallObjCompMonCatForget₂MonoidHomCarrierCarrierForgetSections, semicontinuous_restrict_iff, Finset.card_preimage_eq_sum_card_image_eq, unitInterval.volume_uIcc, multipliable_subtype_and_compl, Cardinal.mk_image_eq_of_injOn_lift, Path.instContinuousEvalElemRealUnitInterval, Fin.coe_of_injective_castSucc_symm, isClosedMap_restrict_of_compactSpace, unitInterval.volume_Ici, PrimitiveSpectrum.hull_inf, Subgroup.isComplement_subgroup_left_iff_existsUnique_quotientMk'', PointwiseConvergenceCLM.instT2Space, Function.Embedding.optionEmbeddingEquiv_apply_snd_coe, Matroid.closure_eq_subtypeClosure, Subgroup.card_commutator_le_of_finite_commutatorSet, Multipliable.tprod_vanishing, Path.Homotopy.eval_apply, Cardinal.mk_compl_finset_of_infinite, CategoryTheory.Limits.instHasIterationOfShapeElemIic, Path.Homotopy.transAssocReparamAux_zero, small_image, surjective_onto_range, MonoidHom.fiberEquiv_symm_apply, SimpleGraph.chromaticNumber_eq_iInf, Ordinal.veblen_of_ne_zero, Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype, Finset.tprod_subtype', Cardinal.card_iUnion_lt_iff_forall_of_isRegular, Fintype.card_Ici, ContinuousMap.coe_restrict, monovaryOn_iff_monovary, CategoryTheory.TransfiniteCompositionOfShape.iic_isColimit, Cardinal.mk_univ_quaternionAlgebra, Module.Basis.range_extendLe, Matroid.instFinitaryElemRestrictSubtype, CompleteLattice.Iic_coatomic_of_compact_element, alternatingGroup.stabilizer.surjective_toPerm, IsPathConnected.exists_path_through_family, ContinuousMap.Homotopy.apply_one_path, MeasureTheory.Measure.toSphere_apply_univ, isLocalHomeomorph_iff_isOpenEmbedding_restrict, Nonempty.to_subtype, IsClosedMap.restrictPreimage, Function.Injective.codRestrict, SimpleGraph.ConnectedComponent.odd_matches_node_outside, AlgebraicGeometry.Scheme.IdealSheafData.ideal_bot, iUnion_coe_set, Submodule.exists_span_set_card_eq_spanRank, Module.Basis.reindexRange_repr_self, ENNReal.orderIsoIicOneBirational_apply_coe, unitInterval.volume_uIoo, Nat.card_image_of_injective, Int.card_fintype_Ioo_of_lt, subset_sInf_emptyset, IsCoveringMap.liftPath_const, uniformContinuousOn_iff_restrict, Pretrivialization.restrictPreimage_toFun, AlgebraicIndependent.adjoin_of_disjoint, ContinuousAt.restrictPreimage, Affine.Simplex.altitude_restrict_eq_comap_subtype, Module.Basis.subset_extendLe, Cardinal.mk_image_eq_lift, SimplexCategory.toTop₀_map, unitSphereToUnits_injective, not_nonempty_iff_eq_empty', AddSubgroup.isComplement_iff_existsUnique_neg_add_mem, Subgroup.IsComplement.finite_right_iff, topologicalKrullDim_subspace_le, ContinuousMap.HomotopyRel.compContinuousMap_apply, Setoid.IsPartition.ncard_eq_finsum, powersetCard.exists_mem_notMem, Cardinal.mk_iUnion_le_sum_mk, cfcₙAux_id, FirstOrder.Language.Substructure.lift_card_closure_le_card_term, maximal_orthonormal_iff_basis_of_finiteDimensional, Profinite.NobelingProof.Products.evalFacProps, PrimeSpectrum.preimageEquivFiber_apply_asIdeal, stereographic'_target, Fintype.card_Icc, CategoryTheory.Limits.Types.Small.limitCone_pt, exists_linearIndepOn_of_lt_rank, sInter_eq_iInter, Equiv.Perm.card_fixedPoints_modEq, Trivialization.domExtend_symm_apply, ConvexOn.sSup_of_countable_affine_eq, SimpleGraph.IsContained.exists_iso_subgraph, Cardinal.mk_surjective_eq_arrow_of_le, continuousSMul_closedBall_ball, DirectedOn.ciSup_set_le_iff, PiTensorProduct.bddBelow_projectiveSemiNormAux, projIcc_eq_one, IsClosed.sigmaCompactSpace, Pretrivialization.codExtend_baseSet, rangeSplitting_injective, Fintype.card_Ioo, Cardinal.mk_bounded_set_le, Path.mul_apply, tsum_image, MeromorphicOn.isClopen_setOf_meromorphicOrderAt_eq_top, Equiv.Set.union_apply_left, PointwiseConvergenceCLM.isEmbedding_coeFn, Ico.coe_inf, Real.uniformContinuous_inv, tsum_subtype_eq_of_support_subset, ContinuousMap.HomotopyLike.toContinuousMapClass, subsingleton_coe_of_subsingleton, isScalarTower_sphere_sphere_sphere, CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan_inj, SimpleGraph.induceHom_id, CategoryTheory.SmallObject.SuccStruct.extendToSuccRestrictionLEIso_hom_app, multipliable_subtype_iff_mulIndicator, IsCoveringMapOn.isCoveringMap_restrictPreimage, Pretrivialization.codExtend_target, Matrix.instFiniteSpectrum, isometry_cfcₙHom, CategoryTheory.Limits.Types.isLimitEquivSections_apply, Ico.coe_bot, PrimitiveSpectrum.hull_finsetInf, frequently_nhds_subtype_iff, card_union_le, MeasurableEmbedding.equivRange_apply, StarAlgebra.elemental.bijective_characterSpaceToSpectrum, SimpleGraph.Subgraph.isAcyclic_coe_bot, Matroid.IsBase.cardinalMk_eq_cRank, Ico.coe_zero, HahnSeries.SummableFamily.finite_co_support_prod_smul, bernstein.variance, AddSubgroup.card_add_eq_card_addSubgroup_add_card_quotient, EuclideanSpace.instIsManifoldSphere, OrderIso.sumLexIioIci_symm_apply_Iio, Topology.reorderRestrictProd_restrict_compl, CategoryTheory.SmallObject.SuccStruct.Iteration.subsingleton.MapEq.w, Function.Embedding.sumSet_preimage_inr, MeasurableSpace.cardinal_generateMeasurableRec_le, IsClosedMap.mapsToRestrict, Dynamics.coverEntropy_restrict_subset, bernstein_apply, eq_finite_iUnion_of_finite_subset_iUnion, infIccOrderIsoIccSup_apply_coe, gelfandTransform_map_star, MeasureTheory.measurableEmbedding_of_fderivWithin, polynomialFunctions.starClosure_eq_adjoin_X, card_commutatorSet_closureCommutatorRepresentatives, DirectedOn.isGLB_ciInf_set, isCompact_iff_isCompact_univ, MeasureTheory.StronglyMeasurable.separableSpace_range_union_singleton, TangentBundle.coordChange_model_space, SSet.horn₃₁.desc.multicofork_π_two_assoc, PointwiseConvergenceCLM.isInducing_inducingFn, FirstOrder.Language.constantsOnMap_inclusion_isExpansionOn, CategoryTheory.SmallObject.SuccStruct.extendToSucc_obj_eq, AlgebraicGeometry.Scheme.directedAffineCover_I₀, CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.inductiveSystem_map, projIci_surjective, FirstOrder.Language.Term.realize_restrictVarLeft', IsOfFinAddOrder.natCard_multiples_le_addOrderOf, AlgebraicGeometry.Scheme.Opens.toScheme_carrier, Trivialization.codExtend_apply, PrimitiveSpectrum.gc_closureOperator, ContinuousMap.aeStronglyMeasurable_restrict_mkD_restrict_of_uncurry, iUnion_eq_range_psigma, MeasureTheory.Measure.instIsFiniteMeasureElemSphereOfNatRealToSphere, Subgroup.IsComplement.leftCosetEquivalence_equiv_fst, GenLoop.ext_iff, MeasurableEmbedding.measurable_rangeSplitting, infsep_eq_iInf, Function.Embedding.coe_sigmaSet, Topology.CWComplex.Subcomplex.union, monotoneOn_iff_monotone, InverseSystem.invLimEquiv_apply_coe, CategoryTheory.SmallObject.SuccStruct.ofCoconeObjIso_hom_naturality, iSup_range', powersetCard.mem_coe_iff, IsClosed.preimage_val, cfcₙHom_predicate, Matroid.instFiniteElemERestrictSubtype, Topology.IsCoherentWith.isClosed_iff, Submodule.norm_eq_iInf_iff_real_inner_eq_zero, ENNReal.tsum_union_le, unitInterval.measurable_symm, Monoid.PushoutI.NormalWord.cons_head, SSet.horn₃₁.desc.multicofork_π_zero_assoc, Cardinal.mk_image_le, LinearMap.toMatrix_reindexRange, Metric.PiNatEmbed.separation, TopologicalSpace.MetrizableSpace.subtype, unitInterval.continuous_sigmoid, TopologicalSpace.IsSeparable.secondCountableTopology, SimpleGraph.Subgraph.preconnected_iff, IsDedekindDomain.primesOverEquivPrimesOver_apply, Finite.Set.finite_inter_of_right, ContinuousMap.HomotopyWith.coeFn_injective, toFinite_toFinset, Equiv.Perm.card_isConj_eq, inTangentCoordinates_eq, Profinite.NobelingProof.projRestricts_eq_id, CategoryTheory.SmallObject.SuccStruct.Iteration.obj_bot, Real.log_of_pos, Iic.coe_inf, Complex.UnitDisc.coe_closedBall_smul, Icc.coe_mul, Metric.unitClosedBall.coe_mul, AddSubgroup.IsComplement.existsUnique, exists_basis_of_pairing_eq_zero, SSet.Subcomplex.yonedaEquiv_coe, Ioc.coe_top, TemperedDistribution.fourier_toTemperedDistributionCLM_eq, ContinuousMap.restrictPreimage_apply, principalSegIio_toRelEmbedding, AlgebraicGeometry.Scheme.IdealSheafData.le_ofIdeals_iff, SimpleGraph.Subgraph.IsMatching.toEdge.surjective, Subgroup.IsComplement.equiv_fst_eq_self_of_mem_of_one_mem, Cardinal.small_Icc, DFinsupp.mk_zero, ProbabilityTheory.IsGaussianProcess.restrict, SimpleGraph.Walk.induce_cons, Path.Homotopy.transAssocReparamAux_one, OrderIso.setCongr_symm_apply, CategoryTheory.SmallObject.SuccStruct.Iteration.subsingleton.MapEq.tgt, IsOpen.locallyConnectedSpace, Valuation.Integers.not_denselyOrdered_of_isPrincipalIdealRing, Finite.Set.finite_union, injOn_iff_injective, CategoryTheory.Functor.toEventualRanges_obj, SimplexCategory.toTop₀_obj, opEquiv_self_symm_apply_coe, LocallyLipschitzOn.restrict, AddCircle.equivIccQuot_comp_mk_eq_toIocMod, small_single, SimplexCategory.toTopObj_one_add_eq_one, Matroid.IsBase.cardinalMk_eq, HallMarriageTheorem.hall_cond_of_restrict, WeakDual.CharacterSpace.coe_coe, contMDiff_subtype_coe_Icc, Nat.card_preimage_of_injOn, ContinuousFunctionalCalculus.exists_cfc_of_predicate, infIooOrderIsoIooSup_symm_apply_coe, Profinite.IndexFunctor.surjective_π_app, AddSubgroup.rank_closure_finite_le_nat_card, Path.Homotopy.transReflReparamAux_one, IsAtomic.Set.Iic.isAtomic, NumberField.mixedEmbedding.fundamentalCone.integerSetTorsionSMul_stabilizer, AlgebraicGeometry.IsAffineOpen.self_le_basicOpen_union_iff, Profinite.NobelingProof.GoodProducts.injective_sum_to, Subgroup.smul_apply_eq_smul_apply_inv_smul, EquicontinuousOn.isClosed_range_pi_of_uniformOnFun', Affine.Simplex.ExcenterExists.touchpointWeights_restrict, Icc_chartedSpaceChartAt, IsGδ.of_t2Space_locallyCompactSpace, EulerProduct.prod_filter_prime_geometric_eq_tsum_factoredNumbers, powersetCard.coe_ofFinEmb, IsMaxOn.iSup_eq, Matroid.IsBasis.cardinalMk_le_cRk, IsLocallyClosed.locallyCompactSpace, PointwiseConvergenceCLM.equivWeakDual_apply, SimpleGraph.isTree_iff_connected_and_card, ContinuousMap.Homotopy.extend_apply_coe, MeasureTheory.lintegral_subtype_comap, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered, TemperedDistribution.fourierTransformInv_toTemperedDistributionCLM_eq, ContinuousMap.Homotopy.evalAt_apply, SetTheory.PGame.moveRight_nim, directedOn_iff_isCodirectedOrder, Profinite.NobelingProof.iso_map_bijective, Subgroup.IsComplement.equiv_fst_eq_one_of_mem_of_one_mem, BoundedContinuousFunction.exists_norm_eq_restrict_eq_of_closed, Iic.complementedLattice_iff, Matroid.mapSetEmbedding_indep_iff', instIsStronglyCoatomicElemOfOrdConnected, isCoatomic_iff_forall_isCoatomic_Ici, SimpleGraph.Connected.exists_preconnected_induce_compl_singleton_of_finite, AddCircle.continuous_equivIoc_symm, instSMulCommClass_sphere_closedBall_closedBall, CategoryTheory.SmallCategoryCardinalLT.hasCardinalLT, KummerDedekind.emultiplicity_factors_map_eq_emultiplicity, ENNReal.orderIsoIicCoe_symm_apply_coe, stdSimplex.continuous_map, Fin.cycleIcc_to_cycleRange, Pretrivialization.codExtend_source, SSet.stdSimplex.nonDegenerateEquiv_apply_apply, Equiv.Set.univPi_symm_apply_coe, CategoryTheory.SmallObject.SuccStruct.ofCoconeObjIso_hom_naturality_assoc, CategoryTheory.Functor.sectionsEquivHom_naturality, MeasureTheory.integrableOn_iff_comap_subtypeVal, ProbabilityTheory.measurable_countablePartitionSet_subtype, MeasureTheory.diracProba_comp_diracProbaEquiv_symm_eq_val, Filter.frequently_cocardinal, rightInverse_rangeSplitting, countable_coe_iff, ContinuousMap.Homotopy.symm_apply, IsCyclotomicExtension.Rat.discr, unitInterval.volume_Icc, CategoryTheory.Subgroupoid.isThin_iff, DirectSum.mk_apply_of_notMem, TopCat.hasLimit_iff_small_sections, Ici.coe_sup, iInf_subtype'', preimage_val_iInter, small_sInter, Trivialization.domExtend_baseSet, PNat.card_fintype_uIcc, unitInterval.range_sigmoid, Path.source', inclusion_eq_id, Subtype.irreducibleSpace, HNNExtension.NormalWord.unitsSMulGroup_snd, Filter.Germ.isConstant_comp_subtype, Equiv.Set.rangeInr_apply_inr, Ordinal.card_iSup_Iio_le_card_mul_iSup, SchwartzMap.toTemperedDistributionCLM_apply_apply, cfc_def, InjOn.injective, Order.exists_orderEmbedding_insert, ComplexShape.symmetryEquiv_apply_coe, Subgroup.isComplement_iff_existsUnique, isLindelof_iff_LindelofSpace, ComplexShape.symmetryEquiv_symm_apply_coe, GaloisConnection.l_csSup_of_directedOn, CategoryTheory.Limits.Types.limitCone_π_app, Subgroup.IsComplement.equiv_snd_eq_self_of_mem_of_one_mem, Cardinal.mk_smul_set, EulerProduct.prod_primesBelow_tsum_eq_tsum_smoothNumbers, denseRange_inclusion_iff, isMax_of_succ_notMem, unitInterval.mul_le_left, GenLoop.continuous_fromLoop, Cardinal.infinite_pigeonhole_card, Ordinal.small_Iic, codRestrict_range_surjective, CategoryTheory.Limits.whiskeringLimYonedaIsoCones_inv_app_app, Metric.unitBall.coe_eq_zero, Cardinal.mk_iUnion_eq_sum_mk_lift, Profinite.NobelingProof.projRestricts_eq_comp, TemperedDistribution.smulLeftCLM_sub, stdSimplex.vertex_coe, Affine.Simplex.ExcenterExists.excenter_restrict, Commute.cfcₙHom, CategoryTheory.SmallObject.SuccStruct.Iteration.congr_obj, MonoidHom.fiberEquivKer_apply, Subsingleton.coe_sort, isEmpty_coe_sort, AddAction.orbit.coe_vadd, FGModuleCat.FGModuleCatCoevaluation_apply_one, SSet.Subcomplex.mem_nonDegenerate_iff, StrictMono.denselyOrdered_range, continuousSMul_sphere_closedBall, IsClosed.two_pow_mk_le_two_pow_mk_dense, AddGroup.card_nsmul_eq_card_nsmul_card_univ, QuasilinearOn.isPreconnected_preimage_subtype, Subgroup.rank_commutator_le_card, Nat.card_univ, MulAction.coe_quotient_smul_fixedPoints, Module.Basis.range_extend, Path.reparam_id, Metric.sphere.compactSpace, isUniformInducing_rangeFactorization_iff, SimpleGraph.Subgraph.map_hom_top, ContinuousAt.codRestrict, PointwiseConvergenceCLM.equivWeakDual_symm_apply, MeasurableSpace.Subtype.countablySeparated, instDenselyOrdered, Ico.nonneg, ContractingWith.restrict, MapsTo.restrict_eq_codRestrict, Icc.coe_pow, CategoryTheory.Functor.IsWellOrderContinuous.nonempty_isColimit, SimpleGraph.induce_pair_connected_of_adj, WeakDual.CharacterSpace.coe_toNonUnitalAlgHom, genericPoints.equiv_apply, Convex.contractibleSpace, lipschitzOnWith_cfc_fun, MeasureTheory.UnifIntegrable.unifIntegrable_of_ae_tendsto, Trivialization.restrictPreimage'_baseSet, CategoryTheory.Limits.opCompYonedaSectionsEquiv_apply_app, Equiv.Set.sumCompl_symm_apply_of_mem, Isometry.isometryEquivOnRange_toEquiv, OpenPartialHomeomorph.isOpenEmbedding_restrict, Path.uniformContinuous, Nat.Subtype.lt_succ_iff_le, Fintype.card_of_finset', InfiniteGalois.proj_adjoin_singleton_val, isScalarTower_closedBall_ball_ball, ciSup_Iic, Cardinal.mk_image2_le, Subgroup.IsComplement.equiv_snd_eq_one_of_mem_of_one_mem, Nat.card_coe_set_eq, ContinuousMap.HomotopyWith.trans_apply, Path.image_extend_of_subset, Equiv.Set.sumCompl_symm_apply, Stonean.extremallyDisconnected_pullback, Profinite.NobelingProof.Products.eval_πs_image', UniformOnFun.continuous_rng_iff, AlgebraicGeometry.affineOpensRestrict_apply_coe_coe, OrderIso.sumLexIicIoi_symm_apply_Iic, GenLoop.toLoop_apply, MulAction.orbitRel.Quotient.orbit.coe_smul, Nimber.small_Ioo, Preorder.measurable_restrictLe₂, SimpleGraph.incidenceSetEquivNeighborSet_symm_apply_coe, SimpleGraph.card_commonNeighbors_le_degree_right, powersetCard.coe_map, Matroid.IsBasis'.cardinalMk_eq_cRk, ODE.FunSpace.toContinuousMap_apply_eq_apply, sInf_apply, MeasurableSet.exists_measurable_proj, CategoryTheory.Subgroupoid.hom.faithful, CategoryTheory.HomOrthogonal.matrixDecompositionLinearEquiv_symm_apply, MonoidAlgebra.freeAlgebra_lift_of_surjective_of_closure, SimpleGraph.adjMatrix_pow_apply_eq_card_walk, Topology.reorderRestrictProd_of_mem, AddSubgroup.isComplement_addSubgroup_right_iff_bijective, Affine.Simplex.map_altitude_restrict, UniformContinuous.rangeFactorization, Affine.Simplex.faceOpposite_restrict, Ico.coe_eq_zero, Algebra.quasiFiniteAt_iff_isOpen_singleton_fiber, ConvexOn.sSup_of_nat_affine_eq, NumberField.mixedEmbedding.fundamentalCone.quotIntNorm_apply, IsLUB.ciSup_set_eq, ncard_coe, Cardinal.mk_preimage_of_subset_range, coe_pred_of_mem, Profinite.NobelingProof.factors_prod_eq_basis_of_ne, Ico.infinite, mkFactorOrderIsoOfFactorDvdEquiv_apply_coe, AddSubgroup.isComplement_addSubgroup_right_iff_existsUnique_quotientAddGroupMk, CategoryTheory.Limits.SingleObj.Types.limitEquivFixedPoints_symm_apply, Iic.disjoint_iff, SetTheory.PGame.default_nim_one_leftMoves_eq, tprod_singleton, Path.Homotopy.trans_assoc_reparam, Cardinal.mk_Icc_real, card_ne_eq, Subgroup.IsComplement.equiv_fst_mul_equiv_snd, natCard_pos, Int.card_fintype_Icc_of_le, Topology.IsEmbedding.restrict, small_sep, Profinite.NobelingProof.continuous_projRestrict, SimpleGraph.Reachable.coe_coeSubgraph, IsPGroup.card_modEq_card_fixedPoints, CategoryTheory.Limits.MultispanShape.ofLinearOrder_L, Subsingleton.cardinalMk_le_one, IntermediateField.cardinalMk_adjoin_le, QuotientAddGroup.equivIcoMod_symm_apply, Matroid.cRank_le_iff, sum_indicator_eventually_eq_card, HomotopyGroup.mul_spec, instNoMinOrderElemIoo, restrict_comp_codRestrict, Icc.coe_iInf, Equiv.Perm.stabilizer_isPreprimitive, WeakDual.CharacterSpace.coe_toCLM, CategoryTheory.SmallObject.coconeOfLE_pt, CategoryTheory.Limits.compCoyonedaSectionsEquiv_symm_apply_coe, SimpleGraph.map_neighborFinset_induce_of_neighborSet_subset, AlgebraicGeometry.Scheme.IdealSheafData.ofIdeals_mono, Affine.Simplex.exradius_restrict, SimpleGraph.degree_induce_support, TopologicalSpace.Fiber.sigmaIsoHom_apply, isUniformEmbedding_set_inclusion, IsUniformInducing.rangeFactorization, IsEvenlyCovered.toTrivialization_apply, AffineIndependent.subtype, range_cfcₙ_eq_range_cfcₙHom, powersetCard.mem_ofFinEmb_iff_mem_range, ContinuousMap.adjoin_id_eq_span_one_union, Real.sinOrderIso_apply, Matroid.Indep.cardinalMk_le_isBasis, StrictMono.codRestrict, Nat.Subtype.lt_succ_self, Profinite.NobelingProof.continuous_CC'₁, MeasurableSpace.CountablySeparated.subtype_iff, Finite.card_image_le, powersetCard.ofFinEmbEquiv_symm_apply, Cardinal.mk_neg, IsCyclotomicExtension.Rat.absdiscr_prime_pow_succ, LipschitzOnWith.to_restric_mapsTo, embeddingOfSubset_apply_coe, Ordinal.cof_eq', Cardinal.le_mk_diff_add_mk, iccHomeoI_apply_coe, SimpleGraph.Subgraph.deleteEdges_coe_eq, SSet.Subcomplex.mem_degenerate_iff, Equiv.Perm.sign_of_pow_two_eq_one, AddAction.minimalPeriod_eq_card, Matrix.IsHermitian.cfcAux_apply, Fin.coe_of_injective_castLE_symm, CategoryTheory.SmallObject.ιFunctorObj_eq, powersetCard.mem_compl, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric, ContinuousMap.nhds_compactOpen_eq_iInf_nhds_induced, SimpleGraph.Connected.induce_compl_singleton_of_degree_eq_one, UniformOnFun.topologicalSpace_eq, Path.extend_range, instContinuousNegElemSphereOfNat, Ordinal.le_enum_succ, Finite.card_toFinset, Ordinal.opow_limit, unitInterval.symm_one, Cardinal.mk_sum_compl, GenLoop.fromLoop_symm_toLoop, Order.coheight_eq_krullDim_Ici, coe_comp_rangeFactorization, Pretrivialization.codExtend'_toFun, EulerProduct.prod_primesBelow_geometric_eq_tsum_smoothNumbers, SimpleGraph.IsTree.coe_singletonSubgraph, IsPGroup.card_orbit, SSet.skeleton_succ, Cardinal.preAleph_limit, CategoryTheory.HomOrthogonal.matrixDecompositionLinearEquiv_apply, SSet.Subcomplex.iSup_ofSimplex_nonDegenerate_eq_top, Path.delayReflLeft_zero, SimpleGraph.Hom.mapEdgeSet.injective, IsCoveringMapOn.restrictPreimage, SimpleGraph.card_neighborSet_toSubgraph, Subgroup.IsComplement.equiv_symm_apply, Subgroup.card_commutator_dvd_index_center_pow, IsLindelof.elim_nhds_subcover', CategoryTheory.Limits.compCoyonedaSectionsEquiv_apply_app, AddSubgroup.center_eq_infi', IsDedekindDomain.primesOverEquivPrimesOver_ramificationIdx_eq, comap_subtype_coe_apply, GaloisConnection.u_csInf, preimage_val_image_val_eq_self, DirectedOn.isLUB_ciSup_set, AddSubgroup.IsComplement.rightQuotientEquiv_apply, LinearIndependent.span_repr_eq, CategoryTheory.GradedObject.CofanMapObjFun.ιMapObj_iso_inv, Matroid.IsBasis'.cardinalMk_diff_comm, toFinset_card, cardinal_eq_of_isOpen, card_range_of_injective, Ordinal.enum_typein, Ici.disjoint_iff, instFiniteElemProdCommutatorRepresentatives, Matrix.instFiniteElemRealSpectrum, unitInterval.symmMeasurableEquiv_symm_apply, Nonempty.natCard_pos, inr_comp_cfcₙHom_eq_cfcₙAux, unitInterval.qRight_zero_right, exteriorPower.ιMultiDual_apply_ιMulti, Cardinal.card_lt_card_of_left_finite, SimpleGraph.induceHom_injective, Profinite.NobelingProof.GoodProducts.span, SimpleGraph.Subgraph.coe_deleteEdges_le, preimage_liftCover, CategoryTheory.Sheaf.ΓObjEquivSections_naturality_symm, linearIndependent_bounded_of_finset_linearIndependent_bounded, Trivialization.codExtend'_target, OrderIso.sumLexIicIoi_symm_apply_Ioi, IsCoveringMap.monodromy_refl, CategoryTheory.SmallCategoryOfSet.comp_def, IsCyclotomicExtension.Rat.discr_prime_pow_succ, IsLocalization.Away.span_range_mulNumerator_eq_top, isLocalHomeomorphOn_iff_isOpenEmbedding_restrict, Ici.codisjoint_iff, Matroid.restrictSubtype_inter_indep_iff, range_restrict, Subfield.cardinalMk_closure, CategoryTheory.Limits.Types.limitEquivSections_symm_apply, SimpleGraph.Subgraph.spanningCoeEquivCoeOfSpanning_apply_coe, range_insert, unitInterval.mul_le_right, instNoMinOrderElemIio, natCard_smul_set, RestrictedProduct.nhds_eq_map_structureMap, infinite_coe_iff, exists_polynomial_near_continuousMap, isSimpleOrder_Iic_iff_isAtom, SimpleGraph.nonempty_subgraphOfAdj_verts, PMF.toMeasure_uniformOfFintype_apply, AddGrpCat.hasLimit_iff_small_sections, exteriorPower.ιMulti_family_eq_coe_comp, Path.isUniformEmbedding_coe, Profinite.NobelingProof.GoodProducts.linearIndependent_iff_smaller, unitInterval.symmHomeomorph_symm_apply, Subtype.connectedSpace, SimpleGraph.Subgraph.Preconnected.coe, Equiv.Set.sumDiffSubset_symm_apply_of_notMem, Homeomorph.image_apply_coe, Path.range_subpath, homeomorphUnitSphereProd_symm_apply_coe, PointwiseConvergenceCLM.coeLMₛₗ_apply, powersetCard.mulActionHom_compl_mulActionHom_compl, unitInterval.continuous_qRight, card_derangements_fin_add_two, ZLattice.covolume.tendsto_card_le_div', AddSubgroup.vadd_leftQuotientEquiv, ApproximatesLinearOn.lipschitz_sub, Cardinal.mk_set_eq_one_iff, image_eq_range, Path.symm_apply, Int.card_fintype_Ioc_of_le, Icc.instIsCancelMulZero, Icc.mul_le_left, le_rank_iff_exists_linearIndependent, Cardinal.mk_union_of_disjoint, unitInterval.nonneg', IsOpen.inter_preimage_val_iff, DirectSum.mk_apply_of_mem, opEquiv_self_apply_coe, MeasureTheory.Measure.Subtype.volume_def, Cardinal.small_Ioo, unitInterval.le_one', tendstoLocallyUniformlyOn_iff_tendstoLocallyUniformly_comp_coe, ContinuousOn.measurableEmbedding, sigmaToiUnion_bijective, card_singleton_prod, SimpleGraph.dartOfNeighborSet_injective, Path.Homotopy.trans_apply, unitInterval.symm_le_comm, strictMonoOn_projIcc, Order.height_eq_krullDim_Iic, measurable_restrict₂, Metric.PiNatEmbed.exists_closed_embedding_to_hilbert_cube, Function.Surjective.restrictPreimage, Equiv.ofInjective_symm_apply, GrpCat.hasLimit_iff_small_sections, Cardinal.mk_powerset, unitInterval.instTietzeExtension, TemperedDistribution.instLineDerivSMulReal, univ.nonempty, PointwiseConvergenceCLM.continuousEvalConst, MeasureTheory.Measure.volume_subtype_coe_le_volume, Continuous.rangeFactorization, Topology.continuous_reorderRestrictProd, IsOpen.locallyCompactSpace, BooleanSubalgebra.mem_closure_iff_sup_sdiff, Height.mulHeight_eq, IsOpenMap.mapsToRestrict, Metric.unitBall.instIsLeftCancelMulZero, Subgroup.IsComplement.existsUnique, MeasureTheory.Measure.toTemperedDistribution_apply, WeakDual.CharacterSpace.compContinuousMap_apply, tprod_univ, Function.MulExact.rangeFactorization, lipschitzOnWith_cfcₙ_fun, Affine.Simplex.circumcenter_restrict, TangentBundle.chartAt, powersetCard.coe_nonempty_iff, Finite.multipliable, PointwiseConvergenceCLM.coeLM_apply, powersetCard.faithfulVAdd, Topology.IsOpenEmbedding.restrictPreimage, SimpleGraph.Connected.card_vert_le_card_edgeSet_add_one, Filter.tendsto_Ioi_atTop, Affine.Simplex.height_restrict, exists_union_disjoint_cardinal_eq_of_even, ae_restrict_iff_subtype, Path.Homotopy.continuous_reflTransSymmAux, AddMonoid.fg_iff_exists_freeAddMonoid_hom_surjective, Path.inv_apply, MeasureTheory.measurableEquiv_range_coe_nat_of_infinite_of_countable, coe_succ_of_mem, pred_notMem_iff_isMin, injective_iff_injective_of_iUnion_eq_univ, small_image2, Ordinal.accPt_subtype, tangentBundleCore_coordChange_model_space, small_inter_of_right, continuous_cfcHomSuperset_left, EuclideanGeometry.orthogonalProjection_affineSpan_singleton, card_prod_singleton, ContinuousMap.Homotopy.trans_apply, tprod_setProd_singleton_right, ContinuousMap.HomotopyRel.symm_apply, Cardinal.mk_range_le, PiTensorProduct.injectiveSeminorm_apply, Homeomorph.unitBall_apply_coe, FirstOrder.Language.Substructure.reduct_withConstants, Cardinal.mk_range_inr, continuous_IccExtend_iff, Finite.to_subtype, Path.refl_apply, Affine.Simplex.instNonemptyElemComplSetSingletonOfNontrivial, Ideal.nonempty_primesOver, stdSimplex.ext_iff, IccLeftChart_extend_bot, Path.range_segment, IsSimplyConnected.simplyConnectedSpace, Cardinal.mk_image_eq, trdeg_eq_iSup_cardinalMk_isTranscendenceBasis, TemperedDistribution.fourier_lineDerivOp_eq, IsClosed.isCompletelyMetrizableSpace, cfcₙHom_isClosedEmbedding, Finset.hasSum, finite_coe_iff, MulAction.isPreprimitive_stabilizer_subgroup, Ioc.infinite, Trivialization.codExtend'_apply, ProbabilityTheory.setBernoulli_zero, tsum_congr_set_coe, Ideal.isPretransitive_of_isGalois, Equiv.Set.image_symm_preimage, Ideal.coe_smul_primesOver_mk, CategoryTheory.SmallObject.SuccStruct.Iteration.obj_succ, IsCoatomic.Set.Ici.isCoatomic, Path.continuous_uncurry_iff, TopologicalSpace.noetherianSpace_set_iff, Icc.le_one, small_pair, CategoryTheory.HomOrthogonal.matrixDecomposition_comp, AlgebraicGeometry.isCompactOpen_iff_eq_finset_affine_union, AlgebraicGeometry.IsAffineOpen.iSup_basicOpen_eq_self_iff, AffineBasis.exists_affineBasis, Ici.coe_top, unitInterval.qRight_zero_left, bernsteinApproximation.apply_one, CategoryTheory.TransfiniteCompositionOfShape.ici_isoBot, Iic.coe_iInf, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric, Subgroup.IsComplement.card_mul_card, Module.isLocallyConstant_rankAtStalk_freeLocus, Subgroup.IsComplement.rightCosetEquivalence_equiv_snd, CategoryTheory.CoreSmallCategoryOfSet.functor_map, Height.AdmissibleAbsValues.mulSupport_finite, IsClosed.locallyCompactSpace, Pretrivialization.restrictPreimage'_baseSet, PrincipalSeg.orderIsoIio_apply_coe, Equiv.Set.rangeSplittingImageEquiv_symm_apply_coe, MulAction.orbitRel.Quotient.subgroup_quotient_eq_iff, coe_smul_fixedPoints_of_normal, Path.prod_coe, cfcₙHom_le_iff, cauchySeq_finset_iff_tprod_vanishing, bernstein_nonneg, Module.Basis.extend_apply_self, stereographic_neg_apply, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, default_coe_singleton, VitaliFamily.FineSubfamilyOn.covering_disjoint_subtype, Seminorm.coe_sSup_eq', CategoryTheory.SmallObject.SuccStruct.extendToSucc.obj_eq, powersetCard.mulActionHom_compl_bijective, Cardinal.mk_Iic_real, OrderHom.nextFixed_le_iff, isAntichain_preimage_subtypeVal, SSet.Subcomplex.PairingCore.equivI_apply_coe, Profinite.NobelingProof.GoodProducts.linearIndependent_iff_sum, preimage_val_sInter_eq_sInter, CategoryTheory.TransfiniteCompositionOfShape.iic_F, tangentBundleCore_coordChange, AddSubgroup.isComplement_addSubgroup_left_iff_existsUnique_quotientMk'', Ordinal.typein_enum, CategoryTheory.SmallObject.SuccStruct.restrictionLTOfCoconeIso_hom_app, Manifold.riemannianEDist_def, EulerProduct.prod_filter_prime_tsum_eq_tsum_factoredNumbers, Cardinal.mk_strictMono, instNonemptyElemWeakDualComplexCharacterSpaceOfNontrivial, SimpleGraph.induceHomOfLE_apply, coe_snd_unionEqSigmaOfDisjoint, CategoryTheory.Limits.Types.Small.limitCone_pt_ext_iff, instNoMaxOrderElemIco, isScalarTower_sphere_sphere_closedBall, CategoryTheory.Limits.Types.Small.limitCone_π_app, Complex.UnitDisc.instSMulCommClass_closedBall_right, MulAction.mem_subgroup_orbit_iff, Icc.isCompl_iff, Equiv.Perm.card_fixedPoints, card_lt_card, Topology.image_snd_preimageImageRestrict, OrderIso.map_csInf_of_directedOn, Filter.tendsto_Iio_atBot, PrincipalSeg.subrelIso_symm_apply, TemperedDistribution.laplacian_eq_sum, CategoryTheory.MorphismProperty.ofHoms_homFamily, Cardinal.small_Ioc, chainHeight_coe_univ_lt, unitInterval.instIsProbabilityMeasureElemRealVolume, Multipliable.nat_tprod_vanishing, Nat.Subtype.orderIsoOfNat_apply, CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSet_comp, tangentBundleCore.isContMDiff, MultilinearMap.iteratedFDeriv_aux, CategoryTheory.SmallObject.SuccStruct.arrowι_def, Topology.IsEmbedding.toHomeomorph_apply_coe, Isometry.isometryEquivOnRange_apply, OrdConnected.isSuccArchimedean, TemperedDistribution.instContinuousLineDeriv, AddCommMonCat.instSmallElemForallObjCompMonCatForget₂AddMonoidHomCarrierCarrierForgetSections, Ideal.isPretransitive_of_isGaloisGroup, cfc_eq_cfcL_mkD, Nat.card_mono, natCard_inv, ApproximatesLinearOn.antilipschitz, OrderIso.sumLexIicIoi_apply_inr, unitInterval.symm_eq_zero, lowerHemicontinuous_restrict_iff, termDefinable₁_iff_exists_term, Nat.card_image_of_injOn, stdSimplexHomeomorphUnitInterval_apply_coe, Matroid.map_val_restrictSubtype_eq, AddGroupSeminorm.coe_sSup_apply, linearIndependent_set_iff_affineIndependent_vadd_union_singleton, Iic.coe_biInf, Equiv.Set.univ_apply, Iic.coe_sSup, Complex.UnitDisc.instIsScalarTower_closedBall, SimpleGraph.dart_fst_fiber, directedOn_iff_isDirectedOrder, Homeomorph.Set.prod_apply, Metric.sphere.instContinuousMul, stdSimplex.instSubsingletonElemForall, AlgebraicGeometry.IsOpenImmersion.affineOpensEquiv_apply_coe_coe, CategoryTheory.SmallObject.restrictionLE_map, small_mul, homeomorphSphereProd_symm_apply_coe, range_codRestrict, nonempty_Iic_subtype, Subtype.coe_image_of_subset, Cardinal.mk_smul_set₀, CategoryTheory.SmallObject.SuccStruct.arrowMap_ofCocone_to_top, Submodule.mem_span_iff_of_fintype, ContinuousMap.aeStronglyMeasurable_mkD_restrict_of_uncurry, CategoryTheory.SmallObject.SuccStruct.Iteration.mapObj_trans_assoc, Affine.Simplex.incenter_restrict, ContinuousMap.Homotopy.curry_apply, unitInterval.sigmoid_injective, MulAction.orbitZPowersEquiv_symm_apply, cfcHomSuperset_apply, isScalarTower_sphere_sphere_ball, stdSimplex.sum_eq_one, card_image_of_injective, SimpleGraph.Walk.map_mapToSubgraph_hom, Pretrivialization.restrictPreimage_source, MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd, MeasureTheory.Measure.instSigmaFiniteElemRealIoiOfNatVolumeIoiPow, powersetCard.addActionHom_singleton_bijective, Sym2.card_diagSet_compl, Summable.tsum_subtype_le, Summable.tsum_subtype_add_tsum_subtype_compl, Matroid.cRk_le_iff, cfcₙHom_eq_cfcₙ_extend, range_cfc_eq_range_cfcHom, MeasureTheory.Measure.exists_sum_smul_dirac, isChain_preimage_subtypeVal, instContinuousNegElemClosedBallOfNat, Matroid.Indep.cardinalMk_le_cRank, FirstOrder.Language.BoundedFormula.realize_restrictFreeVar', boundedSpace_val_set_iff, IsOpen.preimage_val, Path.Homotopy.transReflReparamAux_zero, AddCircle.measurePreserving_equivIoc, PrimitiveSpectrum.preimage_upperClosure_compl_finset, Circle.argEquiv_symm_apply, elem_mem, Matroid.mapSetEmbedding_indep_iff, nonempty_Ico_sdiff, MulAction.instIsPretransitiveElemOrbit, homeomorphUnitSphereProd_apply_fst_coe, Icc.coe_iSup, Countable.le_aleph0, Profinite.NobelingProof.e_mem_of_eq_true, OrdConnected.isStronglyAtomic, MeasurableSpace.cardinal_measurableSet_le_continuum, Iic.coe_sup, CategoryTheory.SmallObject.SuccStruct.extendToSuccRestrictionLEIso_inv_app, AlgebraicGeometry.Scheme.IdealSheafData.ideal_top, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_left, powersetCard.coe_compl, Topology.IsEmbedding.restrictPreimage, Finset.hasProd_support, Path.Homotopy.cast_apply, small_div, contMDiffWithinAt_comp_projIcc_iff, DirectedOn.le_ciSup_set, Trivialization.proj_clift, Profinite.IndexFunctor.map_comp_π_app, WithZero.denselyOrdered_set_iff_subsingleton, ContinuousMap.continuous_restrict, isGLB_ciInf_set, IsClosed.two_pow_mk_lt_continuum, sInf_eq_iInf', HasCountableSeparatingOn.subtype_iff, ContinuousMap.Homotopy.extend_apply_of_mem_I, Ordinal.mk_Iio_ordinal, idealFactorsEquivOfQuotEquiv_symm, Metric.unitSphere.coe_inv, Profinite.NobelingProof.πs_apply_apply, small_setProd, rangeFactorization_surjective, AddAction.orbitRel.Quotient.orbit.coe_vadd, GenLoop.toLoop_apply_coe, EquicontinuousOn.comap_uniformOnFun_eq, CategoryTheory.GradedObject.CofanMapObjFun.inj_iso_hom_assoc, Module.Basis.coe_ofVectorSpace, Function.Embedding.sigmaSet_range, countable_iff_exists_injective, Nat.equivProdNatSmoothNumbers_apply', rank_span_le, Profinite.NobelingProof.GoodProducts.finsuppSum_mem_span_eval, Pretrivialization.domExtend_invFun, AlgebraicGeometry.isCompact_and_isOpen_iff_finite_and_eq_biUnion_affineOpens, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, Ordinal.ToType.mk_symm_apply_coe, SimpleGraph.Iso.mapNeighborSet_apply_coe, Icc.coe_eq_zero, Matroid.Indep.cardinalMk_le_isBasis', mem_of_mem_image_val, Equiv.image_strictAnti, IsCyclotomicExtension.Rat.natAbs_discr, Metric.PiNatEmbed.continuous_distDenseSeq, Pairwise.subtype, Affine.Simplex.inradius_restrict, Equiv.Set.rangeSplittingImageEquiv_apply_coe_coe, Finsupp.supportedEquivFinsupp_symm_apply_coe_support_val, Nat.nth_apply_eq_orderIsoOfNat, isScalarTower_sphere_closedBall_ball, Ordinal.bddAbove_iff_small, bernstein.z_zero, Profinite.NobelingProof.GoodProducts.linearIndependent, Subgroup.IsComplement.card_right, Cardinal.mk_univ_real, Path.Homotopy.coeFn_injective, SimpleGraph.Walk.map_mapToSubgraph_eq_induce_id, Cardinal.beth_limit, TemperedDistribution.smulLeftCLM_add, Cardinal.mk_subset_mk_lt_cof, exteriorPower.ιMulti_family_span_of_span, unitInterval.image_coe_preimage_symm, antivaryOn_iff_antivary, ProperVAdd.isProperMap_vadd_pair_set, Homeomorph.image_symm_apply_coe, Profinite.NobelingProof.GoodProducts.square_commutes, ENNReal.orderIsoUnitIntervalBirational_apply_coe, CategoryTheory.TransfiniteCompositionOfShape.ici_isColimit, Nonempty.coe_sort, cfcₙHom_map_quasispectrum, HahnSeries.SummableFamily.finite_co_support_prod_mul, Equiv.Perm.OnCycleFactors.cycleType_kerParam_apply_apply, exists_set_linearIndependent, Ordinal.enum_succ_eq_top, CategoryTheory.SmallObject.SuccStruct.Iteration.arrowSucc_eq, finsum_set_coe_eq_finsum_mem, Cardinal.mk_biUnion_le, LipschitzWith.restrict, coe_eq_image_val, SimpleGraph.card_commonNeighbors_lt_card_verts, Real.fromBinary_surjective, IsOpenMap.restrict, CategoryTheory.Functor.sectionsEquivHom_naturality_symm, SmoothPartitionOfUnity.exists_isSubordinate_chartAt_source_of_isClosed, ContinuousOn.continuous_restrict_iff_continuous_uniformOnFun, CompletelyRegularSpace.completely_regular, Subgroup.transferTransversal_apply', GenLoop.loopHomeo_symm_apply, SimpleGraph.map_neighborFinset_induce, Function.Fiber.mem_iff_eq_image, stdSimplex.instNonemptyElemForall, PointwiseConvergenceCLM.precomp_apply, SimpleGraph.Subgraph.hom_injective, emultiplicity_prime_eq_emultiplicity_image_by_factor_orderIso, MulAction.orbitEquivQuotientStabilizer_symm_apply, Ideal.exists_subset_radical_span_sup_of_subset_radical_sup, OrdConnected.IciExtend, Function.Bijective.restrictPreimage, Homeomorph.Set.prod_symm_apply_coe, BoxIntegral.IntegrationParams.RCond.min, small_insert, CategoryTheory.SmallObject.SuccStruct.ofCocone_obj_eq_pt, ContinuousMap.HomotopyWith.ext_iff, Convex.locPathConnectedSpace, Icc_chartedSpaceChartAt_of_top_le, Equiv.ofInjective_apply, natCard_vadd_set, Filter.hasBasis_cocardinal, spec_cfcₙAux, Profinite.NobelingProof.spanFinBasis.span, card_empty, OrdConnected.restrict, tendsto_nhdsWithin_iff_subtype, comp_rangeSplitting, Iic.instIsCompactlyGenerated, SimpleGraph.card_support_deleteIncidenceSet, Cardinal.mk_bounded_subset_le, oneTangentSpaceIcc_def, Finsupp.linearCombination_restrict, CategoryTheory.SmallObject.SuccStruct.Iteration.mapObj_refl, cfcHom_eq_cfc_extend, powersetCard.coe_addActionHom_of_embedding, Path.continuous, MeasureTheory.Filtration.piFinset_eq_comap_restrict, ZSpan.fractRestrict_surjective, multipliable_iff_nat_tprod_vanishing, IccRightChart_extend_top_mem_frontier, Metric.unitSphere.coe_zpow, CategoryTheory.Limits.Types.Small.limitConeIsLimit_lift, emultiplicity_prime_le_emultiplicity_image_by_factor_orderIso, tendsto_comp_coe_Ioo_atBot, exteriorPower.basis_coord, preimage_coe_coe_diagonal, Filter.tendsto_comp_val_Iio_atBot, SimpleGraph.induce_singleton_eq_top, stdSimplex.zero_le, einfsep_eq_iInf, Path.source_mem_range, SSet.horn_eq_iSup, Pi.continuous_restrict, Ordinal.cof_type_le, IsCyclotomicExtension.Rat.absdiscr_prime, ContinuousMap.HomotopyLike.map_one_left, IsEvenlyCovered.restrictPreimage, Polynomial.card_rootSet_eq_natDegree, ZLattice.covolume.tendsto_card_div_pow', Path.neg_apply, StrictMonoOn.strictMono, Function.Injective.restrictPreimage, Path.target_mem_range, Cardinal.mk_le_mk_of_subset, small_diff, Cardinal.mk_range_eq_lift, Cardinal.mk_iUnion_le_lift, continuous_inclusion, MeasurableSpace.cardinal_generateMeasurable_le_continuum, measurable_restrict_apply, Matroid.instRankPosElemERestrictSubtype, unitInterval.tendsto_sigmoid_atTop, OrderIso.sumLexIicIoi_apply_inl, CategoryTheory.SmallObject.SuccStruct.ofCocone_map_to_top, Nat.equivProdNatFactoredNumbers_apply, Complex.UnitDisc.coe_smul_closedBall, isClosed_preimage_val_coborder, Function.Embedding.sumSet_preimage_inl, PathConnectedSpace.exists_path_through_family, stereographic_target, Ordinal.small_Icc, Metric.unitClosedBall.coe_eq_zero, TemperedDistribution.fourierTransform_apply, OpenPartialHomeomorph.secondCountableTopology_source, Subgroup.IsComplement.coe_equiv_fst_eq_one_iff_mem, Affine.Simplex.centroid_restrict, SpectrumRestricts.starAlgHom_apply, PrimeSpectrum.coe_primesOverOrderIsoFiber_apply_asIdeal, unitInterval.symm_zero, PrimitiveSpectrum.closedsGC_closureOperator, natCard_neg, HolderWith.restrict_iff, instNoMinOrderElemIoi, NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates_eq_iff, Ordinal.derivFamily_limit, PNat.card_fintype_Ioo, Nimber.small_Ioc, infIooOrderIsoIooSup_apply_coe, OpenPartialHomeomorph.homeomorphOfImageSubsetSource_apply, GrpCat.instSmallElemForallObjCompMonCatForget₂MonoidHomCarrierCarrierForgetSections, Trivialization.restrictPreimage'_target, Cardinal.mk_set_le, cfcₙHomSuperset_id, strictMonoOn_projIci, finite_diff_iUnion_Ioo', FirstOrder.Language.Term.realize_con, Equiv.Set.Equiv.strictMono_setCongr, MeasureTheory.Measure.toSphereBallBound_mul_measureReal_unitBall_le_toSphere_ball, Cardinal.mk_range_inl, CategoryTheory.Limits.preservesColimitsOfShape_of_preservesWellOrderContinuousOfShape, Trivialization.restrictPreimage'_apply, CategoryTheory.Limits.limitCompYonedaIsoCocone_inv, Equiv.Set.sumDiffSubset_apply_inr, SimpleGraph.IsSRGWith.of_adj, tprod_subtype_eq_of_mulSupport_subset, QuotientAddGroup.equivIocMod_symm_apply, UniformOnFun.uniformContinuous_restrict, range_projIic, Module.Free.exists_set, Module.Basis.range_ofSpan, SubMulAction.ofFixingSubgroup.append_left, instIsEmptyElemEmptyCollection, BoundedContinuousFunction.coe_restrict, tendstoUniformlyOn_iff_restrict, small_univ, CategoryTheory.Limits.coneOfSectionCompYoneda_π, Matroid.restrictSubtype_indep_iff_of_subset, IsCompact.elim_nhds_subcover', SimpleGraph.preconnected_induce_iff, Monotone.codRestrict, DirectedOn.ciInf_set_le, Matroid.IsBase.cardinalMk_diff_comm, bijective_iff_bijective_of_iUnion_eq_univ, Commute.cfcHom, Infinite.exists_union_disjoint_cardinal_eq_of_infinite, countable_infinite_iff_nonempty_denumerable, coe_unionEqSigmaOfDisjoint_symm_apply, IsCyclotomicExtension.Rat.discr_prime_pow, Affine.Simplex.orthogonalProjectionSpan_restrict, SimpleGraph.lineGraph_bot, Ordinal.enum_le_enum, Submodule.annihilator_span, SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl, GaloisConnection.l_csSup, Seminorm.coe_sSup_eq, SSet.horn₃₂.desc.multicofork_π_zero_assoc, Path.subpathAux_continuous, GaloisConnection.u_csInf_of_directedOn, MeasureTheory.setLIntegral_subtype, SimpleGraph.isIndepSet_induce, unitInterval.subtype_Ici_eq_Icc, AlgebraicGeometry.Scheme.IdealSheafData.ideal_iInf, AddSubgroup.isComplement_iff_existsUnique, TangentBundle.trivializationAt_eq_localTriv, multipliable_iff_tprod_vanishing, Cardinal.exists_infinite_fiber, unitInterval.symm_lt_comm, SimpleGraph.Subgraph.connected_iff', setBasisOfTopLeSpanOfCardEqFinrank_repr_apply, Cardinal.mk_sep, AddAction.orbitEquivQuotientStabilizer_symm_apply, nnnorm_cfcₙHom, MeasureTheory.Measure.Subtype.volume_univ, stdSimplex.vertex_injective, unitInterval.coe_lt_one, ContinuousMultilinearMap.iteratedFDerivComponent_apply, preimage_val_sInter, Filter.eventually_cocardinal, Polynomial.Gal.galAction_isPretransitive, succ_notMem_iff_isMax, Affine.Simplex.setInterior_restrict, unitInterval.sigmoid_lt_iff, IsClosed.inter_preimage_val_iff, Nimber.small_Icc, CategoryTheory.SmallObject.SuccStruct.Iteration.subsingleton.MapEq.src, instNoMinOrderElemIoc, mdifferentiableWithinAt_comp_projIcc_iff, Pi.induced_restrict_sUnion, Ideal.span_range_pow_eq_top, unitInterval.subtype_Iio_eq_Ico, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, ZLattice.covolume.tendsto_card_le_div, Subgroup.IsComplement.card_left, SimpleGraph.connected_induce_iff, QuasiconcaveOn.isPreconnected_preimage_subtype, cfc_apply, HomotopyGroup.one_def, powersetCard.addAction_faithful, isSigmaCompact_iff_sigmaCompactSpace, ContinuousMap.mkD_apply_of_continuousOn, isLUB_ciSup_set, MonomialOrder.div_set, AnalyticOnNhd.isClopen_setOf_analyticOrderAt_eq_top, DFinsupp.lmk_apply, NNReal.orderIsoIccZeroCoe_symm_apply_coe, Path.target', nonempty_iff_ne_empty', UniformOnFun.edist_eq_pi_restrict, Iic.coe_iSup, Cardinal.mk_univ_complex, instTietzeExtensionUnitClosedBall, Measurable.measurableSet_preimage_iff_preimage_val, Real.coe_comp_expOrderIso, WeakDual.metrizable_of_isCompact, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, MulAction.mem_fixedPoints_iff_card_orbit_eq_one, CategoryTheory.HomOrthogonal.matrixDecompositionAddEquiv_symm_apply, mem_nhds_subtype_iff_nhdsWithin, coe_snd_biUnionEqSigmaOfDisjoint, Affine.Simplex.excenterWeights_restrict, AddMonoidHom.fiberEquiv_apply, AddGrpCat.instSmallElemForallObjCompMonCatForget₂AddMonoidHomCarrierCarrierForgetSections, image_val_iInter, inclusion_injective, IsGLB.ciInf_set_eq, MulAction.orbit.coe_smul, measurable_restrict, ContinuousMap.Homotopy.extend_of_mem_I, PrimitiveSpectrum.isOpen_iff, MonotoneOn.monotone, AddGroup.fg_iff_exists_freeAddGroup_hom_surjective, CategoryTheory.SmallObject.πFunctorObj_eq, stereographic_source, HasCardinalLT.Set.cocone_ι_app, t5Space_iff_forall_t4Space, MulAction.orbitZPowersEquiv_symm_apply', alternatingGroup.stabilizer_isPreprimitive, IsCoveringMap.monodromyFunctor_obj, SimpleGraph.degree_induce_of_neighborSet_subset, Icc.coe_inf, subset_preimage_val_image_val_iff, IsCompact.elim_nhdsWithin_subcover', MeasurableSpace.cardinal_measurableSet_le, IsOpen.locPathConnectedSpace, lipschitzOnWith_cfcₙ_fun_of_subset, SimpleGraph.induceHom_comp, iSup_succ, CategoryTheory.SmallObject.SuccStruct.ofCocone_obj_eq, AnalyticOnNhd.codiscrete_setOf_analyticOrderAt_eq_zero_or_top, nonempty_Iio_subtype, AddMonoidHom.fiberEquivKer_symm_apply, polynomialFunctions_coe, AddAction.card_orbit_mul_card_stabilizer_eq_card_addGroup, Finset.centroid_eq_centroid_image_of_inj_on, FirstOrder.Language.Substructure.coe_withConstants, MeasurableSpace.cardinal_generateMeasurable_le, isClosedEmbedding_cfcₙHom_of_cfcHom, continuousOn_iff_continuous_restrict, tprod_subtype, iccLeftChart_extend_zero, WeakDual.ker_isMaximal, powersetCard.mem_ofFinEmbEquiv_iff_mem_range, Trivialization.domExtend_target, Affine.Simplex.median_restrict, Measurable.rangeFactorization, Equiv.Set.insert_symm_apply_inl, Ioc.coe_eq_one, IsSelfAdjoint.commute_cfcₙHom, CategoryTheory.Limits.limitCompCoyonedaIsoCone_inv, Ordinal.small_Ioc, TopologicalSpace.Opens.IsBasis.isOpenCover, eq_univ_of_image_val_eq, QuasispectrumRestricts.nonUnitalStarAlgHom_apply, Finset.prod_set_coe, EulerProduct.norm_tsum_factoredNumbers_sub_tsum_lt, tangentBundleCore_baseSet, OrderHom.le_prevFixed_iff, set_fintype_card_le_univ, Nimber.small_Iic, card_le_card, PrimeSpectrum.coe_preimageOrderIsoFiber_apply_asIdeal, AddSubmonoid.mem_closure_iff_of_fintype, ContinuousMap.exists_tendsto_compactOpen_iff_forall, ConvexOn.real_sSup_of_countable_affine_eq, unitInterval.volume_Ioc, IsOpen.baireSpace, unitInterval.coe_pos, monotone_projIcc, Equiv.Set.rangeInl_apply_inl, isLocallyClosed_tfae, Icc.coe_one, Equiv.Set.rangeInr_symm_apply_coe, Filter.HasBasis.liminf_eq_sSup_iUnion_iInter, ENNReal.sum_add_tsum_compl, lowerSemicontinuous_restrict_iff, Cardinal.small_Iic, mkFactorOrderIsoOfFactorDvdEquiv_symm_apply_coe, NonUnitalContinuousFunctionalCalculus.exists_cfc_of_predicate, Cardinal.mk_surjective_eq_zero_iff, subset_sSup_def, CategoryTheory.Limits.SingleObj.Types.limitEquivFixedPoints_apply_coe, stdSimplexHomeomorphUnitInterval_one, MeasureTheory.Measure.restrict_biUnion, image_val_compl, UniformOnFun.uniformContinuous_restrict_toFun, Cardinal.mk_mul_le, FirstOrder.Language.distinctConstantsTheory_eq_iUnion, Ordinal.lift_card_sInf_compl_le, AlgebraicGeometry.Scheme.IdealSheafData.coe_support_eq_eq_iInter_zeroLocus, Cardinal.bddAbove_iff_small, instFiniteElemSubtypeMemSubgroupClosureCommutatorRepresentativesCommutatorSet, ContinuousMap.Homotopy.continuous, Path.trans_apply, ContinuousMap.Homotopy.affine_apply, SSet.horn.multicoequalizerDiagram, CategoryTheory.Subgroupoid.coe_inv_coe', ENNReal.tsum_biUnion', Profinite.NobelingProof.continuous_projRestricts, AddCircle.liftIoc_eq_lift_Icc, FreeGroup.startsWith.smul_def, ZSpan.quotientEquiv.symm_apply, emultiplicity_normalizedFactorsEquivSpanNormalizedFactors_symm_eq_emultiplicity, Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtype, Subgroup.isComplement_subgroup_left_iff_bijective, Multipliable.prod_mul_tprod_compl, iSup_Iio_eq_self_iff_isSuccPrelimit, continuousAt_codRestrict_iff, Ideal.coe_smul_primesOver_eq_map_galRestrict, CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.arrowMap_functor, Affine.Simplex.closedInterior_restrict, InverseSystem.piLTLim_symm_apply, summable_subtype_and_compl, Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype, small_subset, Path.trans_range, coe_setBasisOfLinearIndependentOfCardEqFinrank, IsCoveringMap.monodromy_bijective, CategoryTheory.SmallObject.SuccStruct.Iteration.obj_limit, powersetCard.nontrivial', cfcHom_isStrictlyPositive_iff, Pi.continuous_restrict_apply, partialSups_eq_ciSup_Iic, Nat.Subtype.ofNat_range, Path.symm_subpath, CategoryTheory.SmallObject.SuccStruct.extendToSucc_map, Profinite.NobelingProof.GoodProducts.smaller_mono, Cardinal.mk_vadd_set, idealFactorsEquivOfQuotEquiv_is_dvd_iso, piCongrLeft_comp_restrict, FiniteGaloisIntermediateField.adjoin_simple_map_algEquiv, CategoryTheory.GradedObject.CofanMapObjFun.ιMapObj_iso_inv_assoc, WeakDual.CharacterSpace.mem_spectrum_iff_exists, Function.Embedding.optionEmbeddingEquiv_symm_apply, Algebra.SubmersivePresentation.basisKaehler_apply, SimpleGraph.Coloring.card_colorClasses_le, OrderEmbedding.orderIso_apply, strictMono_restrict, eventually_nhds_subtype_iff, image_val_preimage_val_subset_self, Iic.codisjoint_iff, Cardinal.preBeth_limit, HomotopyGroup.inv_spec, SetCoe.countable, PathConnectedSpace.exists_path_through_family', AddCircle.equivIoc_coe_eq, powersetCard.nontrivial, SSet.horn₃₁.desc.multicofork_π_three_assoc, Ordinal.enum_zero_eq_bot, exteriorPower.basis_repr_apply, discreteTopology_subtype_iff, IsClosedMap.codRestrict, ContinuousOn.restrict, instSMulCommClass_sphere_ball_ball, Metric.unitSphere.coe_pow, Pretrivialization.restrictPreimage'_toFun, Path.range_coe, nhdsWithin_subtype_eq_bot_iff, MvPolynomial.weightedDecomposition.decompose'_eq, Continuous.codRestrict, separatesPoints_continuous_of_t35Space_Icc, iccHomeoI_symm_apply_coe, Submodule.coe_mapIic_apply, exists_union_disjoint_cardinal_eq_iff, NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_symm_apply, HasCardinalLT.Set.functor_map_coe, SetTheory.PGame.toLeftMovesNim_symm_lt, Trivialization.preimageHomeomorph_apply, separableSpace_univ, TopologicalSpace.IsSeparable.separableSpace, Equiv.Set.sumDiffSubset_symm_apply_of_mem, TemperedDistribution.instFourierInvSMul, TopologicalSpace.IsOpenCover.denseRange_iff_restrictPreimage, Matroid.restrictSubtype_ground_isBasis_iff, MapsTo.range_restrict, ContinuousMap.norm_restrict_mono_set, tangentBundleCore_localTriv_baseSet, MeasureTheory.locallyIntegrable_comap, tendsto_comp_coe_Ioo_atTop, SSet.horn₃₁.desc.multicofork_π_zero, cast_ncard, FirstOrder.Language.Substructure.mem_withConstants, cfc_apply_pi, IsLowerSet.isUpperSet_preimage_coe, MeasureTheory.tsum_measure_preimage_singleton, MeasureTheory.exists_nat_measurableEquiv_range_coe_fin_of_finite, Trivialization.restrictPreimage_source, nonempty_Ico_subtype, Affine.Simplex.mongePoint_restrict, Equiv.image_strictMono, PNat.card_fintype_Ioc, ProbabilityTheory.IsRatCondKernelCDFAux.integrable_iInf_rat_gt, IsLocalHomeomorphOn.discreteTopology_image_iff, MeasurableSpace.measurableEquiv_nat_bool_of_countablyGenerated, Path.add_apply, Profinite.NobelingProof.GoodProducts.linearIndependentEmpty, StrictMonoOn.restrict, ContinuousMap.comp_attachBound_mem_closure, instIsStronglyAtomicElemOfOrdConnected, Matroid.restrictSubtype_ground_isBase_iff, MeasureTheory.restrict_map_withDensity_abs_det_fderiv_eq_addHaar, Metric.unitBall.coe_mul, TemperedDistribution.instFourierInvAdd, instNonemptyElemImage, Subgroup.isComplement_iff_existsUnique_inv_mul_mem, OrderIso.map_ciSup_set, Homeomorph.Set.univ_apply, MapsTo.lipschitzOnWith_iff_restrict, Affine.Simplex.eulerPoint_restrict, UniformOnFun.edist_continuousRestrict, Equiv.Set.image_symm_apply, DFinsupp.mk_add, Path.map_coe, ContinuousMap.Homotopy.coe_toContinuousMap, Trivialization.preimageSingletonHomeomorph_symm_apply, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply_eq_span, ContinuousMap.continuousOn_mkD_restrict_of_uncurry, ContinuousMap.Homotopy.apply_zero, ContinuousMap.tendsto_compactOpen_iff_forall, TemperedDistribution.fourierInv_apply, chainHeight_coe_univ_le, IsCompact.isClosed_image_restrict, Matrix.IsHermitian.cfcAux_id, SimpleGraph.Subgraph.spanningCoeEquivCoeOfSpanning_symm_apply, cfcₙAux_mem_range_inr, PNat.card_fintype_Ico, ContinuousMap.adjoin_id_eq_span_one_add, AffineSubspace.coe_inclusion_apply, Subgroup.exists_right_transversal_of_le, CategoryTheory.TransfiniteCompositionOfShape.iic_incl_app, AddCircle.continuous_equivIco_symm, Equiv.Perm.OnCycleFactors.kerParam_range_eq_centralizer_of_count_le_one, Matroid.Spanning.cRank_le_cardinalMk, codRestrict_restrict, Ico.coe_mul, Language.mem_accept_toDFA, MeasurableEmbedding.equivRange_symm_apply_mk, Affine.Simplex.ExcenterExists.touchpoint_restrict, Path.subpath_continuous_family, AffineSubspace.signedInfDist_singleton, Subtype.preirreducibleSpace, IsProperMap.restrictPreimage, MeasurableSpace.countablySeparated_subtype_of_hasCountableSeparatingOn, Ordinal.iSup_Iio_eq_bsup, IsCyclotomicExtension.Rat.nrRealPlaces_eq_zero, ContinuousMap.continuous_mkD_restrict_of_uncurry, BoundedContinuousFunction.dist_extend_extend, coe_subset, PointwiseConvergenceCLM.tendsto_nhds_atTop, TemperedDistribution.fourierTransform_toTemperedDistributionCLM_eq, instFiniteElemSubmoduleIsotypicComponentsOfIsNoetherian, AddCircle.continuousAt_equivIoc, JoinedIn.somePath_mem, Fin.card_range_le, FirstOrder.Language.addEmptyConstants_is_expansion_on', Metric.unitBall.instIsRightCancelMulZero, TemperedDistribution.instLineDerivAdd, AddEquiv.finsuppUnique_symm_apply_support_val, SetTheory.PGame.moveLeft_toLeftMovesNim, toENat_cardinalMk, Topology.IsEmbedding.homeomorphOfSubsetRange_apply_coe, uniformContinuous_rangeFactorization_iff, CategoryTheory.GradedObject.mapBifunctorRightUnitorCofan_inj_assoc, Affine.Simplex.excenterWeightsUnnorm_restrict, tendstoUniformlyOn_iff_tendstoUniformly_comp_coe, Filter.tendsto_comp_val_Ici_atTop, range_projIci, restrictPreimage_isInducing, powersetCard.isPreprimitive_perm, Filter.cocardinal_inf_principal_neBot_iff, Metric.contractibleSpace_eball, small_set_one, IsLocalHomeomorphOn.discreteTopology_of_image, Equiv.Perm.VectorsProdEqOne.vectorEquiv_symm_apply, tendsto_Ioo_atBot, CategoryTheory.SmallObject.SuccStruct.extendToSucc_obj_succ_eq, IsModularLattice.isModularLattice_Ici, imageFactorization_surjective, CategoryTheory.Subgroupoid.coe_inv_coe, PrimitiveSpectrum.isClosed_iff, Icc.coe_bot, Path.Homotopy.continuous_transReflReparamAux, cantorToHilbert_continuous, Nat.card_eq_card_toFinset, cfcHomSuperset_id, Ordinal.instIsEmptyIioZero, natCard_mul_le, Metric.unitClosedBall.coe_one, Finite.nonempty_fintype, Function.Embedding.toEquivRange_symm_apply_self, continuous_projIcc, MeasureTheory.Measure.le_count_apply, instCountablySeparatedElemOfHasCountableSeparatingOnIsOpen, ENNReal.orderIsoIicCoe_apply_coe, Cardinal.mk_preimage_of_injective_of_subset_range_lift, TemperedDistribution.instLineDerivSMulComplex, instNoMaxOrderElemIoo, Nat.card_image_equiv, Cardinal.extend_function, OrderIso.sumLexIioIci_symm_apply_of_ge, AlgebraicGeometry.Scheme.IdealSheafData.ideal_sup, Group.card_pow_eq_card_pow_card_univ, AddAction.sum_card_fixedBy_eq_card_orbits_mul_card_addGroup, powersetCard.isPretransitive_of_isMultiplyPretransitive, Ordinal.toPGame_moveLeft, preimage_val_sUnion, ContinuousMap.Homotopy.prod_apply, Path.refl_range, map_uniformity_set_coe, ContinuousMap.HomotopyWith.prop, MeasureTheory.integral_subtype, Finset.restrict_preimage, ContinuousMap.restrict_apply_mk, SSet.horn₃₂.desc.multicofork_π_three, CategoryTheory.Limits.Concrete.small_sections_of_hasLimit, Fintype.card_uIcc, Module.exists_ltSeries_support_isMaximal_last_of_ltSeries_support, stdSimplex.add_eq_one, Polynomial.instIsScalarTowerElemRootSet, Finite.Set.finite_inter_of_left, Path.id_apply, MeasureTheory.integral_countable, DirectedOn.isCodirectedOrder, sigmaToiUnion_injective, isBigO_norm_Icc_restrict_atBot, Function.Injective.hasSum_range_iff, Nat.Subtype.coe_bot, Order.cof_le, DiscreteTopology.of_subset, ContinuousMap.HomotopyWith.refl_apply, exteriorPower.map_comp_ιMulti_family, Nimber.small_Ico, FreeCommRing.restriction_of, Trivialization.restrictPreimage_baseSet, TemperedDistribution.laplacian_toTemperedDistributionCLM_eq, Profinite.NobelingProof.GoodProducts.span_iff_products, Equiv.setCongr_apply, cfcₙHom_continuous, HasCardinalLT.Set.instIsCardinalFiltered, Finset.prod_finset_coe, Module.Basis.ofVectorSpace_apply_self, ODE.FunSpace.continuous, MeasureTheory.measure_sUnion₀, IsDedekindDomain.primesOverEquivPrimesOver_symm_apply, WeakDual.gelfandTransform_apply_apply, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_tsum, Icc.monotone_addNSMul, Pretrivialization.codExtend'_target, AntilipschitzWith.restrict, AlgebraicGeometry.Scheme.IdealSheafData.ideal_mono, MeasureTheory.tendsto_diracProbaEquivSymm_iff_tendsto, nonempty_Ioi_subtype, CategoryTheory.SmallObject.SuccStruct.Iteration.congr_map, Equiv.Set.insert_apply_right, Finsupp.restrictSupportEquiv_symm_single, powersetCard.isPreprimitive_alternatingGroup, Path.source, summable_iff_tsum_vanishing, FiniteExhaustion.finite', Topology.IsQuotientMap.restrictPreimage_isOpen, SimpleGraph.IsAcyclic.subgraph, SimpleGraph.Copy.toSubgraph_surjOn, AlgebraicGeometry.Scheme.IdealSheafData.ideal_iSup, SimpleGraph.Walk.support_induce, cfcₙHomSuperset_continuous, SimpleGraph.Iso.mapNeighborSet_symm_apply_coe, Profinite.NobelingProof.GoodProducts.sum_equiv_comp_eval_eq_elim, Path.coe_toContinuousMap, OpenPartialHomeomorph.subtypeRestr_symm_eqOn_of_le, bernsteinApproximation_uniform, iUnion_finset_eq_set, SSet.nonDegenerateEquivOfIso_apply_coe, ContinuousMap.Homotopy.map_one_left, AddCircle.continuousAt_equivIco, projIci_surjOn, Matroid.IsBasis.cardinalMk_eq_cRk, CategoryTheory.OrthogonalReflection.D₁.ι_comp_t, Language.step_toDFA, Pretrivialization.restrictPreimage'_source, Finsupp.supportedEquivFinsupp_symm_apply_coe, StrictAntiOn.strictAnti, mem_list_prod, Filter.frequently_cocardinal_mem, continuousSMul_closedBall_closedBall, IntermediateField.lift_cardinalMk_adjoin_le, cfcₙ_apply_pi, ContinuousMap.Homotopy.apply_one, subsingleton_coe, Finsupp.supportedEquivFinsupp_apply_support_val, TopologicalSpace.Fiber.sigmaIsoHom_surj, Ordinal.relIso_enum', ContinuousMapZero.mkD_of_not_continuousOn, Fintype.card_Ioc, ContinuousMap.hasFiniteIntegral_mkD_restrict_of_bound, Finite.summable_compl_iff, instWellFoundedGTElemRangeBound, projIcc_surjective, PointwiseConvergenceCLM.tendsto_iff_forall_tendsto, biUnion_eq_iUnion, Equiv.Set.sumCompl_apply_inr, GenLoop.Homotopic.equiv, Iic.coe_top, ContinuousMap.injective_restrict, CategoryTheory.SmallObject.SuccStruct.arrowSucc_extendToSucc, Cardinal.mk_add_le, subset_of_image_val_subset_image_val, contMDiffOn_comp_projIcc_iff, Matroid.restrictSubtype_dual, Trivialization.sourceHomeomorphBaseSetProd_symm_apply, Path.truncate_const_continuous_family, IsOpen.isOpenMap_inclusion, summable_subtype_iff_indicator, CategoryTheory.SmallObject.SuccStruct.arrowMap_ofCocone, nonempty_Ioo_subtype, LipschitzOnWith.to_restrict, OrderIso.map_csSup, AddCircle.openPartialHomeomorphCoe_symm_apply, Nat.factorizationEquiv_inv_apply, SimpleGraph.card_commonNeighbors_top, isPathConnected_iff_pathConnectedSpace, SimpleGraph.Subgraph.edgeSet_coe, isClopen_preimage_val, VitaliFamily.FineSubfamilyOn.measure_le_tsum_of_absolutelyContinuous, Pi.uniformSpace_comap_restrict_sUnion, TopologicalSpace.NoetherianSpace.set, ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral_iInf_rat_gt, hasProd_subtype_iff_of_mulSupport_subset, FiniteGaloisIntermediateField.adjoin_simple_map_algHom, CategoryTheory.MorphismProperty.IsSmall.small_toSet, finite_def, CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.functor_obj, TopologicalSpace.IsOpenCover.isEmbedding_iff_restrictPreimage, Cardinal.mk_Ioo_real, exists_norm_eq_iInf_of_complete_convex, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_fst, powersetCard.card, tsum_setElem_eq_tsum_setElem_diff, Filter.principal_subtype, Polynomial.rootSet.coe_smul, unitInterval.sigmoid_monotone, Finset.prod_congr_set, CategoryTheory.Limits.Types.limitEquivSections_apply, CategoryTheory.Subobject.leInfCone_π_app_none, continuousWithinAt_iff_continuousAt_restrict, card_derangements_eq_numDerangements, Function.Fiber.eq_fiber_image, CategoryTheory.Limits.Types.hasLimit_iff_small_sections, Equiv.image_antitone, WithTop.denselyOrdered_set_iff_subsingleton, AlgebraicGeometry.isCompact_iff_finite_and_eq_biUnion_affineOpens, Metric.unitSphere.coe_div, card_derangements_fin_eq_numDerangements, Topology.IsClosedEmbedding.restrictPreimage, NonUnitalContinuousFunctionalCalculus.compactSpace_quasispectrum, TermDefinable.const, Cardinal.mk_insert, Subgroup.IsComplement.equiv_mul_right_of_mem, CategoryTheory.Functor.sectionsEquivHom_apply_app, cfc_eq_cfcL, lipschitzOnWith_restrict, NatOrdinal.small_Ioc, pairwise_subtype_iff_pairwise_set, stereographic_apply, powersetCard.mulActionHom_singleton_bijective, Fintype.card_Ioi, Cardinal.mk_bounded_set_le_of_infinite, StieltjesFunction.iInf_Ioi_eq, Subgroup.isComplement_iff_existsUnique_mul_inv_mem, homeomorphSphereProd_apply_snd_coe, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, Matroid.Indep.cRk_eq_cardinalMk, Countable.to_subtype, ciInf_set_le, Finite.Set.finite_replacement, natCard_graphOn, instSMulCommClass_closedBall_closedBall_ball, AlgebraicGeometry.Scheme.Hom.irreducibleComponentsEquiv_apply_coe, Fintype.card_Iio, CategoryTheory.Limits.coneOfSectionCompCoyoneda_π, Metric.eball_contractible, Topology.IsOpenEmbedding.restrict, Monotone.restrict, tprod_congr_set_coe, isDiscrete_iff_discreteTopology, stdSimplexEquivIcc_apply_coe, Complex.UnitDisc.instSMulCommClass_circle_closedBall, polynomialFunctions.topologicalClosure, BijOn.bijective, Function.Exact.iff_rangeFactorization, Cardinal.mk_set_eq_nat_iff_finset, Setoid.card_classes_ker_le, NumberField.Ideal.ramificationIdx_primesOverSpanEquivMonicFactorsMod_symm_apply, Dense.ciInf', Finsupp.restrictSupportEquiv_apply, AlgebraicGeometry.Scheme.IdealSheafData.ideal_inf, AddAction.instIsPretransitiveElemOrbit, Subgroup.IsComplement.mk''_rightQuotientEquiv, ContinuousMap.concatCM_right, Matrix.submatrix_gram, Ordinal.small_Ioo, Path.Homotopy.trans_refl_reparam, isClosed_preimage_val, exists_set_linearIndependent_of_lt_rank, ContinuousMap.Homotopy.congr_fun, Finite.lt_aleph0, Path.extend_extends', Icc.coe_eq_one, NatOrdinal.small_Iio, Ordinal.ToType.mk_apply, equicontinuousAt_restrict_iff, Subtype.preconnectedSpace, Complex.continuous_tan, Cardinal.small_Ico, ProperSMul.isProperMap_smul_pair_set, Iic.isCompl_iff, Multipliable.tprod_subtype_le, QuotientGroup.card_preimage_mk, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, unitInterval.instNoAtomsElemRealVolume, instInfiniteElemIciOfNoMaxOrder, MeasureTheory.Lp.toTemperedDistribution_toLp_eq, cfcHom_predicate, powersetCard.mulAction_faithful, coe_setOf, small_neg, WeakDual.CharacterSpace.continuousMapEval_apply_apply, IsClosed.weaklyLocallyCompactSpace, leftInverse_rangeSplitting, isScalarTower_sphere_ball_ball, Function.Embedding.invOfMemRange_surjective, Ordinal.small_Iio, Path.truncate_continuous_family, Iic.coe_biSup, TopologicalSpace.Fiber.instCompactSpaceElemValSetMemRangeCoeLocallyConstantPreimageSingleton, exteriorPower.basis_repr, OrderIso.sumLexIioIci_apply_inl, ContinuousOn.mapsToRestrict, spectrum.instCompactSpaceNNReal, Cardinal.mk_set_eq_zero_iff, Matroid.isFlat_iff_isClosed, tprod_setElem_eq_tprod_setElem_diff, Cardinal.mk_Ici_real, Module.Basis.exists_basis, Profinite.NobelingProof.CC_comp_zero, rangeFactorization_injective, CategoryTheory.Functor.eval_section_injective_of_eventually_injective, exists_infinite_discreteTopology, Polynomial.Splits.toPermHom_apply_eq_one_or_isSwap_of_ncard_le_of_mem_inertia, IsClosed.mk_lt_continuum, Subgroup.center_eq_infi', Metric.contractibleSpace_closedEBall, Topology.IsEmbedding.codRestrict, TemperedDistribution.laplacian_apply_apply, ContinuousMap.HomotopyWith.symm_apply, IsLocalHomeomorph.discreteTopology_range_iff, powersetCard.coe_mulActionHom_compl, powersetCard.instFiniteElemFinset, Ioi.coe_sup, IsModularLattice.isModularLattice_Iic, TemperedDistribution.smulLeftCLM_smulLeftCLM_apply, SimpleGraph.Walk.induce_nil, ContinuousMap.IccExtendCM_of_mem, AlgebraicGeometry.affineOpensRestrict_symm_apply_coe, ApproximatesLinearOn.injective, ENat.card_image_of_injective, le_ciInf_set_iff, Ici.isCompl_iff, KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, Profinite.NobelingProof.eval_eq_πJ, OrdConnected.isPredArchimedean, instInfiniteElemIicOfNoMinOrder, ContinuousMap.polynomial_comp_attachBound, Profinite.NobelingProof.continuous_CC'₀, GaloisConnection.u_ciInf_set, FirstOrder.Language.Substructure.closure_withConstants_eq, OrderIso.setCongr_apply, tendsto_Ioo_atTop, SimpleGraph.isNIndepSet_induce, ProbabilityTheory.measurable_memPartitionSet_subtype, cardinal_eq_of_mem_nhds, SSet.horn₃₂.desc.multicofork_pt, norm_cfcHom, IsClosedMap.restrict, Profinite.NobelingProof.Products.evalFacProp, PrimeSpectrum.coe_preimageHomeomorphFiber_symm_apply_coe_asIdeal, PointwiseConvergenceCLM.hasBasis_nhds_zero, Nat.equivProdNatFactoredNumbers_apply', AlgebraicGeometry.Scheme.IdealSheafData.ideal_ofIdeals_le, Finset.hasProd, Pi.continuous_restrict₂, TemperedDistribution.lineDerivOp_apply_apply, QuotientAddGroup.equivIcoMod_zero, denselyOrdered_set_iff_subsingleton, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, CategoryTheory.SmallCategoryCardinalLT.exists_equivalence, CategoryTheory.SmallObject.restrictionLT_obj, WeakDual.CharacterSpace.equivAlgHom_coe, ContinuousMap.HomotopyWith.continuous, CategoryTheory.Limits.HasIterationOfShape.hasColimitsOfShape_of_isSuccLimit, small_range, OrderIso.map_ciSup_set_of_directedOn, AddSubgroup.mem_closure_iff_of_fintype, Subgroup.IsComplement.equiv_mul_right, Cardinal.mk_singleton, ZLattice.covolume.tendsto_card_le_div'', TemperedDistribution.lineDerivOp_fourierInv_eq, image_val_diff, AlgebraicGeometry.IsAffineOpen.basicOpen_union_eq_self_iff, Types.monoOverEquivalenceSet_unitIso, homeomorphUnitSphereProd_apply_snd_coe, IsLocalHomeomorph.isTopologicalBasis, Profinite.NobelingProof.Products.evalCons, AlgebraicIndependent.iff_adjoin_image, TopologicalSpace.Opens.isOpenEmbedding_of_le, GeneralizingMap.restrictPreimage, NormedField.denselyOrdered_range_nnnorm, Trivialization.codExtend_target, instNonemptyElemCommutatorSet, Pretrivialization.restrictPreimage_baseSet, CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument.preservesColimit, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn, MeasureTheory.continuous_diracProbaEquivSymm, Multipliable.tprod_subtype_mul_tprod_subtype_compl, Equiv.Set.sumDiffSubset_apply_inl, IsGδ.baireSpace_of_dense, NatOrdinal.small_Ico, AddSubgroup.vadd_apply_eq_vadd_apply_neg_vadd, QuotientAddGroup.equivIcoMod_coe, IccExtend_range, Basis.le_span'', FreeGroup.Orbit.duplicate, CategoryTheory.SmallObject.restrictionLE_obj, OrderIso.map_ciInf_set_of_directedOn, unitInterval.symm_lt_symm, Module.Basis.ofSpan_apply_self, basis_le_span', SimpleGraph.induceUnivIso_symm_apply_coe, ENat.card_coe_set_eq, Ordinal.cof_eq, IsEvenlyCovered.of_openPartialHomeomorph, ContinuousMap.Homotopy.ext_iff, Equiv.Perm.stabilizer.surjective_toPerm, Int.card_fintype_Ico_of_le, Subtype.preimage_coe_compl', Polynomial.Splits.surjective_toPermHom_of_iSup_inertia_eq_top, Path.delayReflRight_one, Equiv.Set.sumCompl_apply_inl, Cardinal.mk_univ_quaternion_of_infinite, Ordinal.to_leftMoves_one_toPGame_symm, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, Equiv.Perm.OnCycleFactors.kerParam_range_le_centralizer, cfcₙ_eq_cfcₙL, Matroid.map_val_restrictSubtype_ground_eq, Profinite.NobelingProof.one_sub_e_mem_of_false, PrimitiveSpectrum.hull_sSup, Metric.unitClosedBall.coe_pow, Finite.Set.finite_prod, surjOn_iff_exists_map_subtype, WeakDual.CharacterSpace.instAlgHomClass, UniformOnFun.edist_eq_restrict_sUnion, Module.Basis.extendLe_apply_self, stereographic'_symm_apply, image_image_val_eq_restrict_image, CategoryTheory.Subgroupoid.inclusion_trans, ContinuousOn.tendsto_restrict_iff_tendstoUniformlyOn, IsCompact.elim_nhds_subcover_nhdsSet', ContinuousMap.HomotopyRel.cast_apply, Metric.unitClosedBall.instIsCancelMulZero, ENNReal.tsum_fiberwise, cfcₙL_apply, Finite.convexHull_eq_image, homeomorphSphereProd_apply_fst_coe, MeasureTheory.Measure.volumeIoiPow_apply_Iio, SimpleGraph.lineGraph_adj_iff_exists, Countable.totallySeparatedSpace, SimpleGraph.edgeSet_univ_card, MeasureTheory.Lp.toTemperedDistribution_apply, projIcc_surjOn, cfcHomSuperset_continuous, TemperedDistribution.smulLeftCLM_const, Path.subpathAux_zero, GaloisConnection.l_ciSup_set, initialSegIicIicOfLE_toFun_coe, Algebra.cardinalMk_adjoin_le, ciSup_set_le_iff, SimpleGraph.card_edgeFinset_induce_support, tendsto_card_div_pow_atTop_volume', Subgroup.transferTransversal_apply'', ContinuousMap.HomotopyWith.coe_toHomotopy, AddSubgroup.exists_right_transversal_of_le, SSet.Subcomplex.PairingCore.ancestralRel_iff, NatOrdinal.small_Ioo, PrimeSpectrum.coe_primesOverOrderIsoFiber_symm_apply_coe, CategoryTheory.SmallObject.restrictionLT_map, CategoryTheory.SmallObject.SuccStruct.ofCocone_map, Path.Homotopy.eval_one, HallMarriageTheorem.hall_cond_of_compl, TemperedDistribution.smulLeftCLM_sum, Metric.unitClosedBall.instContinuousMul, discreteTopology_union, ContinuousMap.HomotopyRel.eq_fst, AddSubgroup.IsComplement.finite_right_iff, CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.arrowMap_functor_to_top, HallMarriageTheorem.hall_cond_of_erase, ContinuousMap.elemental_id_eq_top, DFinsupp.mk_sub, Ordinal.enum_inj, Function.Embedding.coe_sumSet, SimpleGraph.Walk.map_induce, Path.target, MeasureTheory.Measure.toSphereBallBound_mul_measure_unitBall_le_toSphere_ball, Cardinal.mk_surjective_eq_zero_iff_lift, Icc.mul_le_right, Metric.unitClosedBall.coe_eq_one, unitInterval.instNontrivialElemReal, Cardinal.mk_image_eq_of_injOn, CategoryTheory.Subgroupoid.hom.inj_on_objects, gelfandTransform_isometry, PairwiseDisjoint.range, Path.Homotopy.source, Profinite.NobelingProof.injective_πs, Equiv.sigmaPreimageEquiv_symm_apply_fst, WeakDual.CharacterSpace.compContinuousMap_comp, TopologicalSpace.Subtype.firstCountableTopology, sInf_image', CategoryTheory.SmallObject.SuccStruct.iterationFunctor_obj, polynomialFunctions_closure_eq_top', SimpleGraph.degree_induce_of_support_subset, TemperedDistribution.instContinuousFourierInv, SimpleGraph.induceHomOfLE_toHom, SimpleGraph.Embedding.mapEdgeSet_apply, AffineIndependent.range, natCard_div_le, Cardinal.countable_iff_lt_aleph_one, hasProd_subtype_comap_iff_of_mulSupport_subset, bernstein.z_last, bernstein.probability, completelyRegularSpace_iff, stdSimplexEquivIcc_symm_apply_coe, unitInterval.univ_eq_Icc, functorToTypes_map, SSet.Subcomplex.PairingCore.equivII_apply_coe, Subgroup.isComplement_subgroup_right_iff_existsUnique_quotientGroupMk, Subgroup.card_mul_eq_card_subgroup_mul_card_quotient, Nat.card_image_le, Ideal.comap_fiberIsoOfBijectiveResidueField_symm, Pi.Colex.sInf_apply, SimpleGraph.Reachable.coe_toSubgraph, FirstOrder.Language.Substructure.subset_closure_withConstants, ContinuousMap.polynomial_comp_attachBound_mem, range_cfcHom, Cardinal.mk_diff_add_mk, Finset.sum_congr_set, PointwiseConvergenceCLM.evalCLM_apply, Fintype.card_Ico, Ioc.coe_one, rank_closureCommutatorRepresentatives_le, TemperedDistribution.fourier_apply, tprod_eq_tprod_diff_singleton, Countable.nonempty_encodable, principalSegIio_toFun, AntitoneOn.monotone, nnnorm_cfcHom, CategoryTheory.Functor.toPreimages_obj, Iio.coe_inf, Profinite.NobelingProof.coe_πs', unitInterval.subtype_Iic_eq_Icc, iUnion_of_singleton_coe, WeakDual.CharacterSpace.equivAlgHom_symm_coe, NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates_surjective, transfiniteIterate_limit, WithBot.denselyOrdered_set_iff_subsingleton, SimpleGraph.Subgraph.inclusion_apply_coe, ContinuousMap.HomotopyWith.apply_zero, OrdConnected.isStronglyCoatomic, Equiv.self_comp_ofInjective_symm, CategoryTheory.HomOrthogonal.matrixDecompositionAddEquiv_apply, Profinite.NobelingProof.GoodProducts.range_equiv_smaller_toFun_bijective, linearIndependent_le_span'', sSup_image', NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_apply, MeasureTheory.measure_sUnion, IsUpperSet.isLowerSet_preimage_coe, IsEvenlyCovered.mem_toTrivialization_baseSet, ZFSet.vonNeumann_of_isSuccPrelimit, Filter.tendsto_comp_val_Ioi_atTop, exists_compact_surjective_zorn_subset, SchwartzMap.coe_apply, compactSpace_Icc, ENNReal.tsum_mono_subtype, CategoryTheory.Limits.PreservesWellOrderContinuousOfShape.preservesColimitsOfShape, Trivialization.sourceHomeomorphBaseSetProd_apply, UniformOnFun.edist_continuousRestrict_of_singleton, PrimitiveSpectrum.hull_iSup, DiscreteTopology.preimage_of_continuous_injective, AffineBasis.exists_affine_subbasis, Cardinal.mk_image_le_lift, StarAlgebra.elemental.continuous_characterSpaceToSpectrum, map_prime_of_factor_orderIso, projIcc_eq_zero, Field.Emb.Cardinal.iSup_filtration, Group.fg_iff_exists_freeGroup_hom_surjective, Cardinal.aleph_limit, RestrictedProduct.nhds_zero_eq_map_structureMap, Metric.unitBall.instIsCancelMulZero, ContinuousMap.Homotopy.refl_apply, ContinuousMap.HomotopyWith.cast_apply, CategoryTheory.SmallObject.coconeOfLE_ι_app, Matroid.restrictSubtype_isBase_iff, OrderIso.setIsotypicComponents_symm_apply, SimpleGraph.Subgraph.coeSubgraph_adj, Cardinal.mk_Ico_real, Subgroup.IsComplement.rightQuotientEquiv_apply, instSMulCommClass_sphere_closedBall_ball, SimpleGraph.Iso.mapEdgeSet_apply, MeasureTheory.Measure.toSphere_eq_zero_iff_finrank, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, ProbabilityTheory.iInf_rat_gt_defaultRatCDF, Matroid.invariantCardinalRank_iff, MapsTo.restrict_commutes, t5Space_iff_forall_isOpen_t4Space, rank_span, range_IicExtend, stdSimplex.le_one, unitInterval.sigmoid_pos, InverseSystem.invLimEquiv_symm_apply_coe, AlgebraicGeometry.Scheme.IdealSheafData.ideal_biInf, image_restrict, ContinuousMap.compactOpen_le_induced, IsClosed.completeSpace_coe, TemperedDistribution.smulLeftCLM_smul, CategoryTheory.Limits.SingleObj.Types.sections.equivFixedPoints_symm_apply_coe, isScalarTower_closedBall_closedBall_ball, HasCardinalLT.Set.instIsFilteredOfFactIsRegular, Metric.infDist_eq_iInf, unitInterval.symm_involutive, sigmaToiUnion_surjective, Subgroup.IsComplement.equiv_fst_eq_mul_inv, Cardinal.mk_union_le, IsClosed.mk_lt_two_pow_mk_dense, ProperSpace.of_isClosed, Path.subpath_zero_one, OrderIso.map_ciInf_set, Subtype.preimage_val_subset_preimage_val_iff, tsum_singleton, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, PointwiseConvergenceCLM.withSeminorms, Ioc.coe_mul, ContMDiff.codRestrict_sphere, iInter_coe_set, unitInterval.volume_uIoc, Function.Embedding.sigmaSet_preimage, Real.uniformContinuous_mul, SimpleGraph.card_edgeSet, completelyNormalSpace_iff_forall_isOpen_normalSpace, Finset.sum_set_coe, Profinite.NobelingProof.list_prod_apply, SimpleGraph.induce_adj, Topology.IsEmbedding.toHomeomorph_symm_apply, Subgroup.IsComplement.leftQuotientEquiv_apply, inclusion_le_inclusion, instFinite_memPartition, Topology.isEmbedding_sigmoid, SimpleGraph.Connected.exists_connected_induce_compl_singleton_of_finite_nontrivial, restrictPreimage_injective, UniformOnFun.isUniformInducing_pi_restrict, IsClosed.polishSpace, Path.segment_apply, Finite.card_range_le, MvPolynomial.exists_restrict_to_vars, Path.Homotopy.symm₂_apply, algebraicIndependent_comp_subtype, coe_neg_ball, exteriorPower.ιMulti_family_linearIndependent_ofBasis, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsum, IsCyclotomicExtension.Rat.discr_prime, Metric.instTietzeExtensionClosedBall, AddAction.mem_fixedPoints_iff_card_orbit_eq_one, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, Icc.coe_top, GroupSeminorm.coe_sSup_apply, TopologicalSpace.IsOpenCover.isOpenEmbedding_iff_restrictPreimage, SimpleGraph.Reachable.coe_subgraphMap, AntilipschitzWith.codRestrict, TemperedDistribution.derivCLM_apply_apply, AddSubgroup.exists_left_transversal_of_le, Group.nat_card_center_add_sum_card_noncenter_eq_card, Equiv.image_symm_apply_coe, Nat.totient_eq_card_lt_and_coprime, PointwiseConvergenceCLM.hasBasis_nhds_zero_of_basis, LinearMap.toMatrixAlgEquiv_reindexRange, Trivialization.restrictPreimage_apply, Matroid.mapSetEmbedding_ground, CategoryTheory.sheafHomSectionsEquiv_symm_apply_coe_apply, Pi.Lex.sSup_apply, Fintype.card_compl_set, chainHeight_coe_univ, Function.Fiber.fiber_nonempty, infIccOrderIsoIccSup_symm_apply_coe, SimpleGraph.Subgraph.Adj.coe, Nat.nth_eq_orderIsoOfNat, ContDiffPointwiseHolderAt.zero_exponent_iff, unitInterval.tendsto_sigmoid_atBot, Pretrivialization.codExtend_toFun, TopologicalSpace.IsOpenCover.isClosedMap_iff_restrictPreimage, BoundedContinuousFunction.exists_norm_eq_restrict_eq, MonoidHom.fiberEquiv_apply, CategoryTheory.regularTopology.EqualizerCondition.bijective_mapToEqualizer_pullback, TangentBundle.chartAt_toPartialEquiv, Finite.exists_infinite_fiber, powersetCard.mem_range_ofFinEmbEquiv_symm_iff_mem, SimpleGraph.Subgraph.Connected.induce_verts, CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan_inj_assoc, IsometricContinuousFunctionalCalculus.isometric, Equiv.image_apply_coe, SSet.Subcomplex.Pairing.instIsWellFoundedElemNIIAncestralRel, ContinuousMap.instCompactSpaceElemCoeCompacts, Trivialization.codExtend'_baseSet, ConvexOn.exists_affine_le_of_lt, completeSpace_coe_iff_isComplete, SimpleGraph.Subgraph.hom_apply, Function.Injective.hasProd_range_iff, ContinuousLinearMap.toPointwiseConvergenceCLM_apply, NatOrdinal.small_Icc, ContinuousMap.Homotopy.curry_one, Pi.uniformContinuous_restrict, Ordinal.veblenWith_of_ne_zero, CategoryTheory.Subgroupoid.inclusion_faithful, Metric.unitClosedBall.coe_zero, SSet.Subcomplex.Pairing.wf, upperHemicontinuousOn_iff_restrict, unitInterval.subtype_Ioi_eq_Ioc, MvPolynomial.supportedEquivMvPolynomial_symm_C, Ioc.le_one, card_singleton, Subgroup.IsComplement.card_mul, SimpleGraph.killCopies_def, AddSubgroup.IsComplement.card_left, Subgroup.IsComplement.finite_left_iff, Matroid.IsBasis.cardinalMk_eq, exteriorPower.ιMulti_family_span, Height.AdmissibleAbsValues.product_formula, ContinuousMap.HomotopyRel.pi_apply, stdSimplex.instNontrivialElemForall, Infinite.card_eq_zero, Nimber.small_Iio, ConvexOn.real_sSup_of_nat_affine_eq, Cardinal.mk_univ_quaternion, volume_image_subtype_coe, Cardinal.mk_preimage_of_injective_lift, CategoryTheory.Sheaf.ΓObjEquivSections_naturality, Cardinal.mk_Ioc_real, WeakDual.CharacterSpace.exists_apply_eq_zero, UniformOnFun.hasBasis_uniformity_of_basis_aux₁, SSet.Subcomplex.Pairing.exists_or, WithTop.continuous_untop, CategoryTheory.SmallObject.preservesColimit, Subgroup.IsComplement.equiv_mul_left, Function.Embedding.toEquivRange_apply, HasRankNullity.exists_set_linearIndependent, Metric.instTietzeExtensionBall, isQuasiSeparated_iff_quasiSeparatedSpace, quasispectrum.instCompactSpaceNNReal, tsum_subtype_support, MulAction.card_orbit_mul_card_stabilizer_eq_card_group, TemperedDistribution.fourierTransformInv_apply, Preorder.piCongrLeft_comp_restrictLe, hasProd_subtype_mulSupport, cfcₙHom_of_cfcHom_map_quasispectrum, MeasureTheory.lintegral_biUnion₀, powersetCard.ncard_eq, WeakDual.CharacterSpace.compContinuousMap_id, inclusion_lt_inclusion, small_univ_iff, IntermediateField.Lifts.carrier_union, Ordinal.familyOfBFamily'_enum, Summable.tsum_vanishing, DirectedOn.isDirectedOrder, instSMulCommClass_sphere_sphere_closedBall, Equiv.Perm.OnCycleFactors.kerParam_range_eq, Module.Basis.coe_extend, subset_sInf_def, Equiv.sigmaPreimageEquiv_apply, Finset.sum_finset_coe, Matroid.mapSetEquiv_indep_iff, TopologicalSpace.PseudoMetrizableSpace.subtype, Topology.CWComplex.Subcomplex.union_closedCell, Pretrivialization.codExtend'_source, Profinite.NobelingProof.GoodProducts.linearIndependent_iff_range, Nat.Subtype.coe_comp_ofNat_range, IsNoetherian.coeSort_finsetBasisIndex, Affine.Simplex.restrict_map_subtype, Polynomial.toContinuousMapOn_apply, continuous_stereoInvFun, Matroid.Indep.cardinalMk_le_isBase, IsEvenlyCovered.discreteTopology_fiber, countable_iff_nonempty_encodable, SimpleGraph.Subgraph.IsInduced.isIndContained, AEMeasurable.subtype_mk, stdSimplexEquivIcc_one, Equiv.Set.union_apply_right, Trivialization.codExtend'_source, ZLattice.covolume.tendsto_card_div_pow'', Profinite.NobelingProof.GoodProducts.max_eq_eval, Nat.card_preimage_of_injective, instIsCountablyGeneratedProdElemUniformity, CategoryTheory.Subgroupoid.inclusion_comp_embedding, Module.Basis.mk_eq_spanRank, Equiv.apply_ofInjective_symm, SSet.horn₃₂.desc.multicofork_π_zero, polynomialFunctions_closure_eq_top, Ideal.coe_smul_primesOver, IsLocallyClosed.isOpen_preimage_val_closure, isSimpleOrder_Ici_iff_isCoatom, Finsupp.supportedEquivFinsupp_symm_apply_coe_apply, AlgebraicGeometry.pointEquivClosedPoint_symm_apply_coe, cfcₙHomSuperset_apply, ConjClasses.card_carrier, Ordinal.enum_zero_le', InverseSystem.piLTLim_apply, Ordinal.toLeftMovesToPGame_symm_lt, SSet.horn₃₂.desc.multicofork_π_three_assoc, cfcₙ_apply, SimpleGraph.walkLengthTwoEquivCommonNeighbors_apply_coe, IsClosed.isClosedMap_inclusion, unitInterval.symm_eq_one, Icc.coe_sup, IsModularLattice.complementedLattice_Iic, SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_not_adj_compl, SSet.horn₃₂.desc.multicofork_π_one_assoc, SetTheory.PGame.moveLeft_nim, Filter.tendsto_Ici_atTop, Stonean.extremallyDisconnected_preimage, CategoryTheory.SmallObject.hasColimitsOfShape_discrete, PMF.toOuterMeasure_uniformOfFintype_apply, Function.Embedding.codRestrict_apply, SimpleGraph.card_edgeFinset_induce_of_support_subset, linearIndependent_le_span_aux', Ordinal.familyOfBFamily_enum, SimpleGraph.induce_top, instSMulCommClass_closedBall_closedBall_closedBall, Equiv.Set.union_symm_apply_right, Setoid.quotientEquivClasses_mk_eq, IsEvenlyCovered.to_isEvenlyCovered_preimage, Cardinal.mk_preimage_of_injective, PointwiseConvergenceCLM.isUniformEmbedding_coeFn, Subgroup.IsComplement.equiv_snd_eq_inv_mul, range_projIcc, Cardinal.mk_range_eq, mem_normalizedFactors_factor_orderIso_of_mem_normalizedFactors, cfcHom_eq_of_isStarNormal, CategoryTheory.SmallObject.SuccStruct.Iteration.prop_map_succ, SMul.smul_stabilizer_def, Equiv.Set.univPi_apply_coe, Ioc.codisjoint_iff, Monotone.rangeFactorization, Equiv.image_monotone, ENNReal.tsum_iUnion_le, AlgebraicGeometry.Scheme.IdealSheafData.strictMono_ideal, CategoryTheory.TransfiniteCompositionOfShape.ici_incl, Topology.reorderRestrictProd_of_compl, instNoMaxOrderElemIci, Language.accepts_toDFA, Finsupp.supportedEquivFinsupp_apply_apply, Path.Homotopy.refl_apply, small_iInter, Real.log_of_ne_zero, AddCircle.liftIco_eq_lift_Icc, PNat.card_fintype_Icc, omegaLimit_eq_iInter, hasSum_subtype_comap_iff_of_support_subset, SSet.stdSimplex.nonDegenerateEquiv_symm_apply_coe, Iic.isCoatom_iff, Trivialization.codExtend_baseSet, HasCardinalLT.Set.isFiltered_of_aleph0_le, MulAction.minimalPeriod_eq_card, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, AddAction.instIsPretransitiveElemOrbit_1, Topology.RelCWComplex.Subcomplex.cell_def, card_image_of_inj_on, unitInterval.symm_bijective, cfcHom_map_spectrum, EisensteinSeries.gammaSetDivGcdEquiv_eq, Matroid.IsBasis'.cardinalMk_le_cRk, Path.symm_range, unitInterval.sigmoid_lt_one, Affine.Simplex.restrict_map_inclusion, ciInf_Ici, Order.IsSuccPrelimit.iSup_Iio, Dense.ciSup', upperSemicontinuousOn_iff_restrict, AlgebraicGeometry.Scheme.Hom.fiberι_fiberHomeo_symm, GenLoop.boundary, IccRightChart_extend_top, GenLoop.homotopyFrom_apply, GenLoop.const_apply, Pretrivialization.codExtend'_baseSet, Submodule.exists_norm_eq_iInf_of_complete_subspace, nontrivial_coe_sort, Pretrivialization.domExtend_source, Profinite.NobelingProof.GoodProducts.linearIndependentSingleton, stdSimplex.instCompactSpace_coe, small_add, FirstOrder.Language.map_constants_inclusion_isExpansionOn, Continuous.restrictPreimage, NatOrdinal.small_Iic, Submodule.FG.spanRank_le_iff_exists_span_set_card_le, orderTopology_of_ordConnected, powersetCard.mem_map_iff_mem_range, IsCoveringMap.restrictPreimage, Subgroup.isComplement_subgroup_right_iff_bijective, imageFactorization_eq, AddAction.orbitRel.Quotient.mem_addSubgroup_orbit_iff, ConvexOn.sSup_affine_eq, Equiv.Set.sumCompl_symm_apply_compl, boundary_Icc, range_singleton, AlgebraicGeometry.Scheme.AffineZariskiSite.presieveOfSections_eq_ofArrows, image_val_preimage_restrictPreimage, Preorder.piCongrLeft_comp_frestrictLe, cfcₙHom_nonneg_iff, algebraicIndependent_image, MeasurableSet.of_subtype_image, Ordinal.IsNormal.apply_of_isSuccLimit, powersetCard.coe_mulActionHom_of_embedding, Metric.unitBall.coe_zero, GenLoop.fromLoop_coe, strictAntiOn_iff_strictAnti, Subsingleton.denselyOrdered, Ordinal.small_Ico, summable_partition, Preorder.continuous_restrictLe, CategoryTheory.PreZeroHypercover.shrink_I₀, Ico.disjoint_iff, Profinite.NobelingProof.Products.eval_πs_image, LinearMap.le_rank_iff_exists_linearIndependent_finset, instSMulCommClass_sphere_sphere_ball, Iic.coe_bot, AlgebraicGeometry.Scheme.Opens.toSpecΓ_preimage_zeroLocus, UniformOnFun.lipschitzWith_restrict, unitInterval.sigmoid_le, MeasureTheory.Measure.toSphere.instIsOpenPosMeasure, SSet.horn₃₁.desc.multicofork_π_three, ENNReal.tsum_biUnion_le_tsum, PrimitiveSpectrum.gc, isTranscendenceBasis_image, Cardinal.card_lt_card_of_right_finite, sSup_apply, SimpleGraph.Walk.IsEulerian.card_odd_degree, Infinite.to_subtype, nonempty_Ioc_subtype, Cardinal.lt_aleph0_iff_set_finite, Matroid.instNonemptyElemERestrictSubtype, unitInterval.qRight_one_right, Finsupp.restrictSupportEquiv_symm_apply_coe, TopologicalSpace.IsCompletelyMetrizableSpace.univ, Ioc.coe_sup, GenLoop.homotopicTo, InnerProductSpace.gramSchmidtNormed_orthonormal', Cardinal.mk_subset_ge_of_subset_image, alternatingGroup.stabilizer_subgroup_isPreprimitive, MapsTo.restrict_surjective_iff, CategoryTheory.Limits.opHomCompWhiskeringLimYonedaIsoCocones_inv_app_app, Nat.Subtype.ofNat_surjective, continuousFunctionalCalculus_map_id, IsModularLattice.complementedLattice_Icc, Subgroup.IsComplement.equiv_fst_eq_self_iff_mem, NonarchAddGroupSeminorm.coe_sSup_apply, SimpleGraph.map_edgeFinset_induce, tsum_univ, surjective_iff_surjective_of_iUnion_eq_univ, CategoryTheory.SmallObject.SuccStruct.Iteration.mapObj_trans, cauchySeq_finset_iff_tsum_vanishing, boundary_product, powersetCard.mulActionHom_of_embedding_surjective, isBigO_norm_restrict_cocompact, preimage_rangeSplitting, AddSubgroup.isComplement_iff_existsUnique_add_neg_mem, OrderIso.sumLexIioIci_apply_inr, continuum_le_cardinal_of_isOpen, linearIndependent_empty, omegaLimit_eq_iInter_inter, GenLoop.continuous_toLoop, Equiv.Perm.OnCycleFactors.kerParam_apply, ConvexOn.real_sSup_affine_eq, SimpleGraph.Subgraph.inclusion.injective, card_insert, UniformOnFun.hasBasis_uniformity_of_basis_aux₂, Trivialization.preimageSingletonHomeomorph_apply, preimage_iUnionLift, ContinuousMap.Homotopy.congr_arg, OrderIso.sumLexIioIci_symm_apply_of_lt, SimpleGraph.edgeFinset_card, CategoryTheory.Limits.Types.isLimit_iff_bijective_sectionOfCone, unitInterval.le_symm_comm, GenLoop.fromLoop_trans_toLoop, Circle.argEquiv_apply_coe, Cardinal.mk_iUnion_le, ConvexIndependent.subtype, Cardinal.mk_Ioi_real, hasSum_singleton, Complex.UnitDisc.instIsScalarTower_closedBall_closedBall, isAntichain_coe_univ_iff, Cardinal.finset_card_lt_aleph0, Topology.restrict_compl_reorderRestrictProd, Real.fromBinary_continuous, tprod_range, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply, ENNReal.orderIsoIicOneBirational_symm_apply, DFinsupp.mk_smul, Equiv.setCongr_symm_apply, CantorScheme.VanishingDiam.map_continuous, MapsTo.restrict_inj, Iic.eq_top_iff, SetTheory.PGame.moveRight_toRightMovesNim, Unitary.path_apply, nonempty_Ici_subtype, TemperedDistribution.laplacianCLM_apply, hallMatchingsOn.finite, CategoryTheory.Limits.Multifork.toSections_fac, Equiv.Perm.card_isConj_mul_eq, Polynomial.toContinuousMapOnAlgHom_apply, Cardinal.iSup_mk_le_mk_iUnion, mem_codiscrete_subtype_iff_mem_codiscreteWithin, Profinite.NobelingProof.factors_prod_eq_basis, Ordinal.le_cof_type, SimpleGraph.Iso.mapEdgeSet_symm_apply, Path.truncate_range, SSet.Subcomplex.PairingCore.pairing_p_symm_equivI, ContinuousMap.Homotopy.map_zero_left, unitInterval.continuous_symm, Cardinal.mk_range_le_lift, image_val_sUnion, MeasureTheory.Measure.infinitePi_map_restrict', StructureGroupoid.restriction_mem_maximalAtlas_subtype, CategoryTheory.Presheaf.FamilyOfElementsOnObjects.IsCompatible.existsUnique_section, Dense.ciInf, powersetCard.coe_smul, IccLeftChart_extend_bot_mem_frontier, AddMonoidAlgebra.freeAlgebra_lift_of_surjective_of_closure, ODE.FunSpace.lipschitzWith, MeasureTheory.Measure.infinitePi_pi_of_countable, cfcHom_apply_mem_elemental, tendsto_comp_coe_Ioi_atBot, Equiv.Set.sumCompl_symm_apply_of_notMem, Icc_isBoundaryPoint_top, Preorder.continuous_restrictLe₂, Ordinal.relIso_enum, powersetCard.coe_nontrivial_iff, Profinite.NobelingProof.factors_prod_eq_basis_of_eq, MeasureTheory.Lp.toTemperedDistribution_smul_eq, summable_iff_nat_tsum_vanishing, ContinuousMap.coe_IccExtend, Nat.equivProdNatSmoothNumbers_apply, EulerProduct.norm_tsum_smoothNumbers_sub_tsum_lt, monotone_projIci, GaloisConnection.u_ciInf_set_of_directedOn, Cardinal.mk_univ_quaternionAlgebra_of_infinite, FirstOrder.Language.Substructure.lift_card_closure_le, FirstOrder.Language.Term.realize_restrictVar', Profinite.NobelingProof.GoodProducts.union, tangentBundleCore_indexAt, MeasureTheory.Measure.toSphere_apply_univ', WeakDual.CharacterSpace.instStarHomClass, AddSubgroup.IsComplement.finite_left_iff, ContinuousAt.restrict, Subgroup.IsComplement.quotientGroupMk_leftQuotientEquiv, powersetCard.exists_mem_notMem_iff_ne, hasSum_subtype_support, unitInterval.toNNReal_one, FirstOrder.Language.card_le_of_model_distinctConstantsTheory, Seminorm.sSup_apply, AddSubgroup.IsComplement.leftQuotientEquiv_apply, Finset.instNonemptyElemCoeInsert, IsOpen.stronglyLocallyContractibleSpace, EquicontinuousOn.isUniformInducing_uniformOnFun_iff_pi', SimplexCategory.toTopObj_zero_apply_zero, TopologicalSpace.IsOpenCover.generalizingMap_iff_restrictPreimage, surjective_stereographic, exists_injOn_iff_injective, Monoid.PushoutI.NormalWord.cons_toList, unitInterval.symm_symmMeasurableEquiv, PointedCone.dual_eq_iInter_dual_singleton, natCard_sub_le, Path.Homotopic.concat_subpath, instInfiniteElemIioOfNoMinOrder, ProbabilityTheory.IsRatStieltjesPoint.iInf_rat_gt_eq, IsDedekindDomain.selmerGroup.valuation_ker_eq, CategoryTheory.OrthogonalReflection.D₂.multispanIndex_snd, FiniteGaloisIntermediateField.adjoin_simple_le_iff, instNoMaxOrderElemIio, small_powerset, SetTheory.PGame.toRightMovesNim_symm_lt, Nat.card_range_of_injective, exteriorPower.basis_repr_self, sSup_eq_iSup', preimage_restrictPreimage, Cardinal.mk_sub_le, Pretrivialization.domExtend_target, SimpleGraph.Walk.connected_induce_support, instIsManifoldIcc, CategoryTheory.SmallObject.SuccStruct.Iteration.arrow_mk_mapObj, TemperedDistribution.smulLeftCLM_apply_apply, OpenPartialHomeomorph.toHomeomorphSourceTarget_symm_apply_coe, Subgroup.mem_closure_iff_of_fintype, Cardinal.mk_surjective_eq_arrow_of_lift_le, GenLoop.instContinuousEvalConst, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformly, Finsupp.lsubtypeDomain_apply, CompletelyRegularSpace.completely_regular_isOpen, Dynamics.dynEntourage_eq_inter_Ico, SimpleGraph.Subgraph.coe_hom, locallyLipschitzOn_iff_restrict, unitInterval.volume_Iio, contMDiffOn_projIcc, SSet.skeletonOfMono_succ, QuotientAddGroup.equivIocMod_coe, TopologicalSpace.IsOpenCover.isOpenMap_iff_restrictPreimage, Profinite.NobelingProof.surjective_projRestricts, Ioo.coe_mul, Real.coe_sinOrderIso_apply, AlgebraicGeometry.Scheme.IdealSheafData.supportSet_eq_iInter_zeroLocus, RestrictedProduct.isEmbedding_structureMap, emultiplicity_normalizedFactorsEquivSpanNormalizedFactors_eq_emultiplicity, Topology.IsCoherentWith.isOpen_iff, AddAction.orbitRel.Quotient.addSubgroup_quotient_eq_iff, map_nhdsSet_subtype_val, powersetCard.coe_vadd, Cardinal.mk_Iio_ord_toType, Affine.Simplex.restrict_points_coe, measurable_inclusion, Icc.convexCombo_zero, SimpleGraph.Subgraph.coe_deleteEdges_eq, AddCommGrpCat.hasLimit_iff_small_sections, Affine.Simplex.excenterExists_restrict, AlgebraicGeometry.IsOpenImmersion.affineOpensEquiv_symm_apply_coe, MeasureTheory.Measure.toSphere_eq_zero_iff, MvPolynomial.decomposition.decompose'_eq, Function.Injective.invOfMemRange_surjective, SetTheory.PGame.toLeftMovesNim_one_symm, AlgebraicGeometry.Scheme.affineBasicOpen_le, nontrivial_mono, ContinuousMap.HomotopyRel.eq_snd, bernsteinApproximation.apply, quasispectrum.instCompactSpace, tendsto_Iio_atTop, Filter.mem_cardinalGenerate_iff, isometry_cfcHom, ApproximatesLinearOn.continuous, ContinuousMap.Homotopy.curry_zero, tangentBundleCore_coordChange_achart, Metric.sphere.instIsTopologicalGroup, Module.Basis.coe_ofSpan, powersetCard.ofFinEmbEquiv_apply, hasProd_singleton, Ordinal.enum_type, OrderIso.map_minimal_mem, Metric.PiNatEmbed.exists_embedding_to_hilbert_cube, CategoryTheory.Limits.Types.isLimitEquivSections_symm_apply, MeasureTheory.measure_biUnion₀, SimpleGraph.Subgraph.restrict_adj, SimpleGraph.Subgraph.coe_isContained, Profinite.NobelingProof.GoodProducts.max_eq_eval_unapply, NumberField.mixedEmbedding.fundamentalCone.intNorm_idealSetEquiv_apply, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, CategoryTheory.Functor.eval_section_surjective_of_surjective, Ordinal.one_toType_eq, Algebra.rank_adjoin_le, CategoryTheory.Limits.hasColimitsOfShape_of_isSuccLimit, WeakDual.CharacterSpace.instContinuousLinearMapClass, Equiv.Perm.OnCycleFactors.sign_kerParam_apply_apply, OrderIso.map_maximal_mem, Homeomorph.unitBall_symm_apply, Metric.ball_contractible, SimpleGraph.Subgraph.Connected.coe, ProbabilityTheory.Kernel.traj_eq_prod, principalSegIio_top, Ordinal.toPGame_moveLeft', Profinite.NobelingProof.succ_mono, stdSimplexEquivIcc_zero, Measurable.measurable_comp_iff_restrict, Trivialization.restrictPreimage_target, Finset.tsum_subtype', Dynamics.coverEntropyInf_restrict_subset, Icc.instZeroLEOneClass, eq_sUnion_finset_of_isTopologicalBasis_of_isCompact_open, Nat.card_eq_card_finite_toFinset, Function.Embedding.optionEmbeddingEquiv_apply_fst, FreeCommRing.map_subtype_val_restriction, SimpleGraph.card_edgeFinset_induce_compl_singleton, isConnected_iff_connectedSpace, CategoryTheory.Limits.compYonedaSectionsEquiv_symm_apply_coe, HasSum.tsum_fiberwise, strictMonoOn_iff_strictMono, KummerDedekind.normalizedFactorsMapEquivNormalizedFactorsMinPolyMk_symm_apply_eq_span, unitInterval.instConnectedSpaceElemReal, SimpleGraph.Subgraph.coe_bot, IsCoveringMap.liftPath_trans, TopologicalSpace.NoetherianSpace.range, ContinuousMap.restrict_apply, isSimplyConnected_iff_exists_homotopy_refl_forall_mem, unitInterval.volume_Ioi
instCoeSortType 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
elem_mem 📖	mathematical	—	Elem	—	—

---

← Back to Index