Notation

📁 Source: Mathlib/Order/Notation.lean

Statistics

Metric	Count
Definitions Bot, bot, Compl, compl, HImp, himp, HNot, hnot, HasCompl, compl, delabInf, delabSup, Top, top, «term_ᶜ», «term_⇨_», «term_⊓_», «term_⊔_», «term⊤», «term⊥», «term￢_»	21
Theorems ext, ext_iff, ext, ext_iff, ext, ext_iff, ext, ext_iff, bot_nonempty, top_nonempty	10
Total	31

Bot

Definitions

Name	Category	Theorems
bot 📖	CompOp	2298 math, 1 bridge math: Ideal.mem_bot, CongruenceSubgroup.Gamma_zero_bot, Filter.Realizer.bot_σ, SimpleGraph.locallyLinear_bot, Finset.bot_eq_empty, EReal.continuousAt_add_coe_bot, le_bot_iff, Algebra.range_ofId, sInf_univ, Filter.tendsto_Ico_pure_bot, PNat.bot_eq_one, CategoryTheory.sheafBotEquivalence_functor, EReal.exp_bot, LieModule.trivial_iff_lower_central_eq_bot, SimpleGraph.cliqueSet_bot, Subalgebra.LinearDisjoint.inf_eq_bot, WithBot.mul_bot', SModEq.bot, Submonoid.mrange_inr', Set.Ici.coe_bot, AddSubgroup.closure_empty, Submodule.rTensorOne_symm_apply, BooleanSubalgebra.val_bot, IsAtom.lt_iff, LaurentPolynomial.degree_C_mul_T_ite, MonoidHom.comap_bot, coinduced_bot, AlgebraicGeometry.Scheme.bot_mem_grothendieckTopology, Finset.Ico_bot, LieAlgebra.IsKilling.iInf_ker_weight_eq_bot, Submonoid.map_inr, Finpartition.empty_parts, CategoryTheory.Subgroupoid.full_empty, YoungDiagram.cells_bot, Submodule.QuotientBot.infinite, Ideal.comap_bot_le_of_injective, AddSubmonoid.prod_eq_bot_iff, min_eq_bot, MonoidHom.mker_snd, AddSubgroup.ofAddUnits_bot, EReal.bot_mul_coe_of_neg, NonUnitalSubsemiring.mem_bot, Subgroup.ofUnits_bot, Concept.intent_bot, Subgroup.isComplement'_top_left, stronglyMeasurableAt_bot, iSupIndep.injOn_iInf, IntermediateField.LinearDisjoint.iff_inf_eq_bot, MeasurableSpace.comap_const, Submodule.bot_coe, Filter.inf_principal_eq_bot_iff_comap, Filter.isBounded_bot, nhds_bot_basis, Submodule.le_annihilator_iff, Filter.bot_mul, PrimeSpectrum.asIdeal_bot, AddSubmonoid.bot_prod_bot, SimpleGraph.killCopies_bot, WithBot.sum_eq_bot_iff, alternatingGroup.eq_bot_of_card_le_two, WithBot.not_coe_le_bot, IsNoetherian.disjoint_partialSups_eventually_bot, FirstOrder.Language.Formula.realize_bot, Disjoint.le_bot, AddSubgroup.zero_smul, le_sdiff_right, partialSups_succ', Submodule.subsingleton_iff_eq_bot, SimpleGraph.Subgraph.neighborSet_bot, Submodule.comm_trans_lTensorOne, LieAlgebra.derivedLength_zero, Filter.map₂_bot_right, IntermediateField.coe_algebraMap_over_bot, WithBot.orderIsoPUnitSumLex_symm_inl, ENNReal.log_eq_bot_iff, RingCon.toCon_eq_bot, WithBotTop.rec_bot, NonUnitalStarAlgebra.mem_bot, Ideal.iInf_pow_smul_eq_bot_of_isLocalRing, IsDedekindDomain.HeightOneSpectrum.iInf_localization_eq_bot, grade_bot, Seminorm.bot_eq_zero, Equiv.Perm.support_prod_of_pairwise_disjoint, Ideal.under_bot, Filter.bot_sub, lt_compl_self, WithTop.toDual_top, Additive.ofMul_bot, Algebra.adjoin_singleton_intCast, BoundedOrderHomClass.map_bot, BotHom.bot_apply, SimpleGraph.cliqueFree_two, min_bot_left, BoxIntegral.Box.splitUpper_eq_bot, IsCompl.inf_left_eq_bot_iff, nhds_ne_subtype_eq_bot_iff, Submonoid.powers_one, EReal.sub_top, LieSubmodule.bot_toSubmodule, algebraicIndependent_iff_ker_eq_bot, SupHom.bot_apply, EReal.bot_mul_coe_of_pos, AddSubgroup.closure_singleton_zero, AddMonoidAlgebra.supDegree_single, MeasurableSpace.comap_bot, Submodule.LinearDisjoint.bot_right, codisjoint_bot, AddSubmonoid.eq_bot_of_subsingleton, InfHom.bot_apply, Submodule.mul_annihilator, SimpleGraph.eccent_bot, Interval.div_bot, TopologicalSpace.Clopens.coe_bot, inf_inf_sdiff, ProperCone.innerDual_univ, DiscreteQuotient.proj_bot_inj, Submonoid.mrange_inl', WithBot.subtypeOrderIso_symm_apply, PEquiv.single_trans_of_eq_none, SummationFilter.neBot_or_eq_bot, Lagrange.degree_basisDivisor_self, ArchimedeanClass.closedBallAddSubgroup_top, List.foldr_max_of_ne_nil, MeasureTheory.hittingAfter_bot_le_iff, AlgebraicGeometry.LocallyRingedSpace.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, LieModule.traceForm_eq_sum_genWeightSpaceOf, AlgebraicGeometry.Scheme.Hom.preimage_bot, IntermediateField.coe_bot, Submodule.smul_bot, Submodule.mulMap_one_right_eq, Module.supportDim_eq_bot_iff_subsingleton, AddSubmonoid.multiples_zero, Submodule.restrictScalars_eq_bot_iff, Geometry.SimplicialComplex.space_bot, Filter.tendsto_bot, Booleanisation.comp_bot, bot_sdiff, IntermediateField.lift_insepDegree_bot', AddSubgroup.bot_toAddSubmonoid, ConvexCone.coe_eq_empty, LieAlgebra.isSolvable_iff_int, SimpleGraph.copyCount_bot, CategoryTheory.isCoseparating_empty_of_thin, Disjoint.eq_bot_of_ge, NonUnitalAlgebra.coe_bot, bot_lt_of_lt, BoxIntegral.Box.coe_bot, WithBot.eq_bot_iff_forall_ne, EReal.forall, sSup_eq_bot, LieModuleHom.ker_eq_bot, WithBot.eq_bot_iff_forall_lt, NonUnitalStarAlgebra.coe_bot, Submodule.mk_eq_bot, DirectSum.isInternal_ne_bot_iff, OrderDual.ofDual_bot, IsCompl.bihimp_eq_bot, iSup_false, algebraicClosure.algebraicClosure_eq_bot, SimpleGraph.bot_not_connected, Subring.closure_singleton_intCast, Sublattice.pi_univ_eq_bot_iff, AffineSubspace.comap_bot, PUnit.bot_eq, Filter.map_bot, AddSubgroup.pi_bot, Finsupp.bot_eq_zero, EReal.top_div_of_neg_ne_bot, Filter.cardinalInterFilter_bot, Filter.pi_inf_principal_univ_pi_eq_bot, bot_lt_iSup, Ring.DimensionLEOne.eq_bot_of_lt, ClopenUpperSet.coe_bot, Subsemiring.op_eq_bot, Subring.closure_singleton_one, WithBot.range_coe, bot_lt_isotypicComponent, IsGaloisGroup.fixingSubgroup_top, Multiset.sup_zero, CategoryTheory.Presieve.isSheaf_bot, Filter.bot_vsub, LieSubmodule.bot_lie, Filter.bot_smul, AddSubgroup.normal_bot, AddSubgroup.eq_bot_of_card_eq, MeasurableSpace.generateFrom_empty, Set.accumulate_bot, TruncatedWittVector.iInf_ker_truncate, Filter.map₂_bot_left, vectorSpan_eq_bot_iff_subsingleton, LieSubmodule.lie_abelian_iff_lie_self_eq_bot, IsGaloisGroup.fixedPoints_top, Sublattice.coe_bot, RingCon.comap_bot, AlgebraicIndependent.repr_ker, MeasureTheory.condLExp_bot', Submodule.pi_univ_bot, CategoryTheory.Functor.WellOrderInductionData.Extension.map_zero, TwoSidedIdeal.matrix_jacobson_bot, Submodule.restrictScalars_bot, Ideal.bot_lt_of_maximal, IsLowerSet.bot_mem, IntermediateField.botEquiv_symm, Subalgebra.op_bot, YoungDiagram.coe_bot, CategoryTheory.isCodetecting_empty_of_groupoid, RootPairing.invtRootSubmodule.bot_mem, Subgroup.op_bot, AddSubgroup.bot_prod_bot, WithZero.zero_eq_bot, Ideal.isPrime_iff_bot_or_prime, Algebra.adjoin_singleton_algebraMap, Ideal.span_singleton_eq_bot, CategoryTheory.TransfiniteCompositionOfShape.fac_assoc, LieAlgebra.hasTrivialRadical_iff, Subsemiring.mem_bot, IntermediateField.relfinrank_bot_right, LieAlgebra.IsKilling.corootSpace_eq_bot_iff, Coheyting.boundary_top, LTSeries.exists_relSeries_covBy_and_head_eq_bot_and_last_eq_bot, AlgebraicGeometry.Scheme.IdealSheafData.radical_bot, LieSubmodule.isNilpotent_iff_exists_lcs_eq_bot, Subgroup.map_one_eq_bot, LieSubalgebra.subsingleton_bot, Fintype.linearIndependent_iff', exists_le_isAssociatedPrime_of_isNoetherianRing, Submonoid.units_bot, InfiniteGalois.mem_bot_iff_fixed, LieSubalgebra.bot_coe, LieModule.nilpotencyLength_eq_succ_iff, LowerSet.bot_prod, ProbabilityTheory.condIndep_bot_left, CategoryTheory.Functor.WellOrderInductionData.surjective, Subgroup.pi_bot, Interval.bot_add, InnerProductSpace.gramSchmidt_bot, Polynomial.IsSplittingField.splits_iff, RingHom.ker_equiv, Partition.bot_notMem, Submodule.map₂_bot_right, Subgroup.unop_eq_bot, himp_bot, NumberField.InfinitePlace.IsUnramified.stabilizer_eq_bot, TopologicalSpace.Compacts.isClopen_singleton_bot, Filter.EventuallyConst.bot, bot_lt_affineSpan, LieModuleHom.ker_id, Filter.tendsto_Ioo_pure_bot, PrimeSpectrum.denseRange_comap_iff_minimalPrimes, EReal.neg_eq_top_iff, AddMonoidHom.ker_fst, AddSubgroup.closure_eq_bot_iff, LinearGrowth.linearGrowthInf_bot, SupHom.coe_bot, LowerSet.bot_lt_Iic, StarSubalgebra.bot_toSubalgebra, bot_uniformity, EReal.continuousAt_add_bot_bot, LowerSet.Iio_bot, Icc_isBoundaryPoint_bot, Subfield.splits_bot, Filter.HasBasis.eq_bot_iff, Polynomial.roots_eq_zero_iff_isRoot_eq_bot, LieAlgebra.IsKilling.ker_traceForm_eq_bot_of_isCartanSubalgebra, LieSubalgebra.mem_bot, SimpleGraph.bot_not_preconnected, Algebra.toSubring_bot, isCyclic, partialSups_add_one', PrincipalSeg.map_bot, EReal.image_coe_Iio, Filter.lift'_bot, Ideal.jacobson_bot, BooleanSubalgebra.coe_bot, Filter.bot_coprod_bot, Subalgebra.LinearDisjoint.inf_eq_bot_of_commute, Ideal.bot_pow, rank_bot, CategoryTheory.Functor.WellOrderInductionData.sectionsMk_val_op_bot, sSup_empty, SimpleGraph.UnitDistEmbedding.bot_p, TwoSidedIdeal.bot_asIdeal, IntermediateField.adjoin_zero, CategoryTheory.ObjectProperty.isCodetecting_bot_of_isGroupoid, Finpartition.parts_bot, Submodule.dualAnnihilator_eq_top_iff, Submodule.orthogonal_eq_bot_iff, IsBot.eq_bot, Ordnode.Bounded.weak_left, nhdsSet_empty, linearIndependent_iff_ker, IsAtomic.eq_bot_or_exists_atom_le, Filter.tendsto_Ioc_pure_bot, Subsemiring.map_bot, Subalgebra.algebra_isAlgebraic_bot_right, Matrix.SpecialLinearGroup.center_eq_bot_of_subsingleton, AddMonoidHom.ker_eq_bot_iff, LinearMap.iInf_ker_proj, isFiniteLength_iff_exists_compositionSeries, CategoryTheory.TransfiniteCompositionOfShape.iic_isoBot, BoxIntegral.Prepartition.IsPartition.compl_eq_bot, Subalgebra.comm_trans_rTensorBot, AffineSubspace.not_wSameSide_bot, AlgebraicGeometry.Scheme.bot_mem_precoverage, Finset.sup_erase_bot, Complementeds.mk_bot, Subgroup.card_eq_one, Subalgebra.algebra_isAlgebraic_bot_left_iff, ContinuousMap.concatCM_left, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isoBot, LinearGrowth.linearGrowthSup_bot, LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_lt, LieModule.iSup_ucs_le_genWeightSpace_zero, AddCon.toSetoid_bot, Ideal.jacobson_bot_polynomial_le_sInf_map_maximal, Filter.div_eq_bot_iff, Finset.Iio_eq_Ico, SimpleGraph.Subgraph.edgeSet_bot, AddSubgroup.map_zero_eq_bot, TopologicalSpace.Closeds.coe_eq_empty, HomogeneousIdeal.eq_bot_iff, NonUnitalSubring.closure_empty, SimpleGraph.cycleGraph_one_eq_bot, IsPrecomplete.bot, Submonoid.mk_eq_bot, max_bot_left, SupBotHomClass.map_bot, Submodule.botEquivPUnit_apply, AlgebraicGeometry.eq_bot_of_comp_quotientMk_eq_sigmaSpec, AddSubmonoid.smul_bot, LieSubmodule.lie_bot, Finsupp.iInf_ker_lapply_le_bot, LowerSet.coe_eq_empty, Filter.vsub_bot, Submodule.ker_subtype, Geometry.SimplicialComplex.faces_bot, disjoint_bot_right, Submodule.orthogonalProjection_bot, lowerClosure_eq_bot_iff, LinearMap.ker_eq_bot, bot_covBy_top, inf_sdiff_inf, Subgroup.card_bot, ProperCone.coe_bot, Subgroup.bot_or_nontrivial, Ideal.prod_bot_bot, Ideal.isIdempotentElem_iff_eq_bot_or_top, Ideal.mul_bot, Submonoid.prod_bot_sup_bot_prod, SimpleGraph.edgeDisjointTriangles_bot, Order.Ideal.principal_bot, AlgEquiv.quotientBot_mk, AddSubsemigroup.notMem_bot, sSupHom.coe_bot, LinearMap.ker_id, Filter.mem_bot, NonUnitalSubsemiring.closure_empty, RingEquiv.quotientBot_symm_mk, isBot_iff_eq_bot, IsIntegrallyClosedIn.integralClosure_eq_bot, CategoryTheory.Subobject.bot_eq_initial_to, LinearMap.BilinForm.span_singleton_inf_orthogonal_eq_bot, integralClosure_idem, groupCohomology.coboundaries₁_eq_bot_of_isTrivial, LinearMap.range_le_bot_iff, Submodule.closedComplemented_bot, Submodule.mem_bot, SimpleGraph.emptyGraph_eq_bot, Filter.vsub_eq_bot_iff, ClosedSubmodule.mem_bot, LieSubmodule.lowerCentralSeries_eq_bot_iff_lcs_eq_bot, Sum.Lex.inl_bot, instIsAbelianGaloisSubtypeMemIntermediateFieldBot, SimpleGraph.singletonSubgraph_adj, CategoryTheory.Sieve.functorPullback_bot, AddSubmonoid.unop_eq_bot, Submonoid.coe_bot, Algebra.mem_bot, Ideal.isPrime_int_iff, SimpleGraph.center_bot, Submodule.smul_bot', is_bot_adic_iff, Asymptotics.isLittleO_bot, CategoryTheory.Sieve.generate_bot, AddSubsemigroup.coe_bot, EReal.bot_div_of_neg_ne_bot, SimpleGraph.deleteEdges_univ, induced_topology_pure, FirstOrder.Language.Substructure.small_bot, ofBoolAlg_bot, EReal.bot_add, LieAlgebra.abelian_of_solvable_ideal_eq_bot_iff, Multiplicative.ofAdd_eq_bot, disjoint_top, InitialSeg.map_bot, Filter.totallyBounded_bot, Submonoid.eq_bot_of_card_eq, DoubleCoset.left_bot_eq_left_quot, WellFoundedGT.finite_ne_bot_of_iSupIndep, SimpleGraph.girth_bot, WithBot.add_coe_eq_bot_iff, EReal.nhds_bot_basis, equivShrink_symm_bot, Order.IsNormal.ext, BooleanSubalgebra.map_bot, LinearMap.IsRefl.ker_eq_bot_iff_ker_flip_eq_bot, Submonoid.eq_bot_of_card_le, PseudoMetric.IsUltra.bot, GradeMinOrder.exists_nat_orderEmbedding_of_forall_covby_finite, LinearMap.range_zero, GrpCat.mono_iff_ker_eq_bot, StarSubalgebra.mem_bot, MeasureTheory.ae_zero, inf_sdiff_self_left, AddSubgroup.Normal.eq_bot_or_eq_top, IntermediateField.fixingSubgroup_top, ENNReal.bot_eq_zero, Subsemiring.smul_bot, WithBot.Ioc_bot_coe, IntermediateField.bot_toSubalgebra, Submonoid.op_eq_bot, TopologicalSpace.CompactOpens.coe_bot, Subgroup.normal_bot, Algebra.toSubmodule_bot, OrthogonalFamily.isInternal_iff_of_isComplete, MeasurableSet.subtype_bot_eq, Algebra.map_bot, Subfield.mem_bot_iff_pow_eq_self, rootsOfUnity_one, List.max_le_of_forall_le, Subfield.isTotallyReal_bot, AddSubsemigroup.op_eq_bot, Subring.closure_singleton_natCast, IsAtom.bot_covBy, countable_setOf_isolated_right, Fin.rev_top, LieSubmodule.subsingleton_of_bot, ContinuousLinearMap.iInf_ker_proj, TwoSidedIdeal.matrix_bot, Subsemigroup.closure_empty, AlgebraicGeometry.Scheme.IdealSheafData.zero_eq_bot, EReal.canLift, PEquiv.toMatrix_bot, HomogeneousIdeal.coe_bot, Finset.Icc_bot_top, Algebra.adjoin_singleton_zero, LieSubmodule.bot_coe, EReal.bot_lt_coe, Prop.bot_eq_false, Submodule.ker_inl, FirstOrder.Language.BoundedFormula.isQF_bot, IsLocalRing.maximalIdeal_eq_bot, CategoryTheory.ObjectProperty.isDetecting_bot_of_isGroupoid, Algebra.coe_bot, Setoid.injective_iff_ker_bot, Filter.bot_vadd, MeasureTheory.condLExp_bot, HomogeneousIdeal.toIdeal_bot, LinearMap.isUnit_iff_ker_eq_bot, Module.Basis.flag_zero, sSupHom.bot_apply, CategoryTheory.HasLiftingProperty.transfiniteComposition.hasLiftingProperty_ι_app_bot, Submodule.annihilator_mul, upperCentralSeries_zero, DoubleCoset.right_bot_eq_right_quot, Multiset.sup_coe, LinearMap.bot_lt_ker_of_det_eq_zero, Filter.OrderBot.atBot_eq, Submonoid.eq_bot_iff_forall, Subsemigroup.notMem_bot, Ideal.eq_bot_or_top, LieSubmodule.isNilpotent_iff_exists_self_le_ucs, SSet.Subcomplex.instSubsingletonHomToSSetBot, Fintype.IsSimpleOrder.univ, FirstOrder.Language.Theory.bot_imp, Submodule.FG.eq_bot_of_le_jacobson_smul, BooleanSubalgebra.bot_mem', Subgroup.eq_bot_iff_card, Nimber.bot_eq_zero, PrimeSpectrum.isIdempotentElemEquivClopens_symm_bot, AddSubmonoid.neg_bot, Submodule.traceDual_top', Filter.prod_bot, Order.succ_eq_zero, AlgebraicGeometry.isSchemeTheoreticallyDominant_iff, AddSubsemigroup.unop_eq_bot, Finpartition.ofErase_parts, BotHom.map_bot', EReal.bot_lt_add_iff, MonoidHom.range_one, bot_symmDiff, Ideal.bot_mul, NatOrdinal.bot_eq_zero, Flag.bot_mem, SimpleGraph.free_bot, AddSubmonoid.unop_bot, MeasureTheory.Measure.haar.prehaar_empty, Subsemigroup.unop_eq_bot, sdiff_self, IsDedekindDomain.integer_empty, toBoolAlg_zero, AddSubmonoid.pi_eq_bot_iff, AffineSubspace.not_sSameSide_bot, eq_bot_of_isCompl_top, WithBot.Ico_bot_coe, SSet.nonDegenerate_eq_bot_of_hasDimensionLT, EReal.tendsto_toReal_atBot, Submodule.span_eq_bot, intervalIntegral.FTCFilter.pure, Associates.bot_eq_one, Submodule.mem_annihilator', Digraph.default_def, Ideal.IsHomogeneous.bot, Equiv.withBotSubtypeNe_symm_apply_coe, Ordinal.bot_eq_zero, Subalgebra.eq_bot_of_finrank_one, LinearMap.BilinForm.orthogonal_eq_bot_iff, Ideal.map_mk_eq_bot_of_le, Submodule.map_bot, intervalIntegral.FTCFilter.nhdsWithinSingleton, Filter.add_eq_bot_iff, IsPredArchimedean.pred_findAtom, MonoidHom.mker_inl, Digraph.bot_adj, MeasureTheory.hittingBtwn_bot_le_iff, WithTop.ofDual_apply_top, WithBot.map₂_eq_bot_iff, continuous_bot, AddSubgroup.isComplement'_top_bot, LieSubmodule.comap_incl_eq_bot, WithBot.unbotD_bot, IntermediateField.LinearDisjoint.bot_left, LieHom.ker_eq_bot, FirstOrder.Language.Substructure.cg_bot, IntermediateField.isTotallyReal_bot, EReal.mem_nhds_bot_iff, SimpleGraph.edgeSet_bot, WithBot.strictAnti_iff, AddMonoidHom.ker_id, LieSubmodule.ucs_comap_incl, Filter.inf_principal_eq_bot, EReal.add_bot, DiscreteQuotient.proj_bot_bijective, Finpartition.bot_isUniform, Subgroup.isComplement'_bot_right, WithBot.bot_add, MeasureTheory.lowerCrossingTime_zero, compl_inf_eq_bot, BoxIntegral.Prepartition.compl_top, SupBotHom.bot_apply, Subalgebra.lTensorBot_one_tmul, WithBot.succ_eq_bot, Pairwise.disjoint_extend_bot, ofAdd_bot, Matrix.ker_mulVecLin_eq_bot_iff, Projectivization.Subspace.span_empty, LieModule.isNilpotent_iff, AddSubmonoid.op_eq_bot, Submonoid.mrange_inr, EReal.top_sub_bot, Dynamics.netEntropyEntourage_empty, vectorSpan_empty, IsHausdorff.iInf_pow_smul, limsup_eq_bot, SimpleGraph.Subgraph.induce_empty, Submodule.botEquivPUnit_symm_apply, IsLocalization.coeSubmodule_bot, lowerClosure_empty, LinearMap.ker_eq_bot_iff_range_eq_top_of_finrank_eq_finrank, Subalgebra.mulMap_bot_left_eq, Finset.truncatedInf_union_of_notMem, Filter.lift'_closure_eq_bot, SimpleGraph.edge_self_eq_bot, Submodule.LinearDisjoint.linearIndependent_right_of_flat, ConvexCone.notMem_bot, AffineSubspace.bot_coe, AddSubsemigroup.map_bot, SimpleGraph.cliqueFree_bot, IntermediateField.instFiniteSubtypeMemBot, MonoidHom.range_eq_bot_iff, RingEquiv.quotientBot_mk, not_lt_bot, EReal.range_coe_eq_Ioo, AffineSubspace.parallel_bot_iff_eq_bot, FractionalIdeal.absNorm_bot, Submodule.eq_bot_of_subsingleton, LieSubmodule.lieSpan_eq_bot_iff, CategoryTheory.TransfiniteCompositionOfShape.iic_isColimit, Module.Flat.torsion_eq_bot, alternatingGroup.center_eq_bot, bot_sup_eq, EReal.image_coe_Iic, ClosedSubmodule.bot_orthogonal_eq_top, MeasureTheory.ae_restrict_eq_bot, essSup_const_bot, IsAdicComplete.bot, AlgebraicGeometry.Scheme.ker_toSpecΓ, Submodule.snd_map_fst, AlgebraicGeometry.Scheme.IdealSheafData.ideal_bot, isCancelSMul_iff_stabilizer_eq_bot, Topology.IsQuotientMap.isCoveringMapOn_of_properlyDiscontinuousVAdd, WellFoundedLT.induction_bot, IsPredArchimedean.findAtom_eq_bot, LieModule.isNilpotent_iff_int, Filter.Iic_pure, Order.bot_lt_krullDim, CategoryTheory.Subobject.bot_factors_iff_zero, AddSubgroup.isComplement'_top_left, disjoint_iff, MonomialOrder.bot_eq_zero, CompleteSublattice.bot_mem, AddSubmonoid.pi_bot, Directed.extend_bot, LieModule.IsNilpotent.nilpotent, List.le_max_of_le, ConvexCone.isGenerating_bot, SimpleGraph.Subgraph.spanningCoe_bot, Subring.op_bot, Filter.coLindelof_eq_bot, LieModule.finite_genWeightSpaceOf_ne_bot, WithBot.map_bot, MeasureTheory.cofinite_eq_bot, IntermediateField.finrank_eq_one_iff, ArchimedeanClass.ballAddSubgroup_top, LinearMap.ker_toSpanSingleton, GrpCat.ker_eq_bot_of_mono, Ideal.span_singleton_zero, Finpartition.parts_eq_empty_iff, AddMonoidAlgebra.supDegree_zero, BoxIntegral.Prepartition.bot_boxes, TopologicalSpace.Compacts.coe_bot, Module.End.eigenspace_restrict_eq_bot, least_descending_central_series_length_eq_nilpotencyClass, TwoSidedIdeal.ker_eq_bot, IntermediateField.eq_bot_of_isAlgClosed_of_isAlgebraic, disjoint_bot_left, AddSubmonoid.closure_zero_prod, LinearMap.range_eq_bot, Sublattice.map_bot, IntermediateField.insepDegree_bot', Submonoid.inv_bot, MeasurableSet.coe_bot, Submodule.fst_inf_snd, Submodule.bot_smul, Ideal.isMaximal_iff_of_bijective, ClosedSubmodule.top_orthogonal_eq_bot, Submodule.map₂_bot_left, LieIdeal.subsingleton_of_bot, Set.Ico.coe_bot, isCoatom_bot, AddSubmonoid.eq_bot_of_card_eq, CommGroup.isMulTorsionFree_iff_torsion_eq_bot, Ideal.primesOver_bot, LieAlgebra.isSolvable_iff, Submonoid.card_bot, SimpleGraph.Subgraph.isAcyclic_coe_bot, WithBot.toDual_bot, Module.Basis.toDual_ker, Ideal.ramificationIdx_bot, LieSubalgebra.subsingleton_of_bot, Irreducible.isRoot_eq_bot_of_natDegree_ne_one, Finset.fold_max_add, Sym2.fromRel_bot_iff, Subgroup.ker_subtype, IsDiscreteValuationRing.toWithBotNat_zero, Interval.bot_mul, Ideal.isRadical_bot, IsNoetherianRing.exists_relSeries_isQuotientEquivQuotientPrime, ValuativeRel.ValueGroupWithZero.bot_eq_zero, Ideal.radical_bot_of_noZeroDivisors, ringKrullDim_eq_bot_of_subsingleton, NonUnitalSubsemiring.coe_bot, PrimeSpectrum.basicOpen_zero, Filter.nhds_bot, Set.Icc_bot_top, CategoryTheory.GrothendieckTopology.bot_covers, AddMonoidHom.ker_eq_bot_of_cancel, AffineSubspace.smul_bot, isDenseEmbedding_pure, TopologicalSpace.Opens.coe_eq_empty, FractionalIdeal.coeToSubmodule_eq_bot, EReal.mul_top_of_neg, NonUnitalAlgebra.toSubmodule_bot, not_supIrred_bot, WithBot.add_bot, FirstOrder.Language.BoundedFormula.realize_foldr_sup, CategoryTheory.SmallObject.SuccStruct.Iteration.obj_bot, Submodule.localized₀_bot, Submodule.bot_toAddSubmonoid, PrimeSpectrum.iInf_localization_eq_bot, IntermediateField.bot_eq_top_of_finrank_adjoin_eq_one, Finset.sup_empty, AddSubgroup.op_bot, Submodule.isOrtho_top_left, IntermediateField.botContinuousSMul, Subgroup.closure_empty, Subalgebra.unop_bot, isComplemented_bot, Subgroup.prod_eq_bot_iff, OrthogonalFamily.isInternal_iff, AffineSubspace.parallel_iff_direction_eq_and_eq_bot_iff_eq_bot, Sublattice.pi_univ_bot, SimpleGraph.preconnected_bot, ProperCone.dual_univ, NumberField.mixedEmbedding.fundamentalCone.integerSetTorsionSMul_stabilizer, AddSubmonoid.map_inl, Submodule.prod_eq_bot_iff, Submonoid.mem_bot, EReal.bot_sub, exists_compositionSeries_of_isNoetherian_isArtinian, iSupIndep.subtype_ne_bot_le_finrank, Submodule.annihilator_smul, StrictMono.apply_eq_bot_iff, AlgHom.ker_coe_equiv, EReal.bot_mul_bot, NumberField.RingOfIntegers.ker_algebraMap_eq_bot, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.image_preimage_is_empty, Filter.isCountablyGenerated_bot, AddSubmonoid.addUnits_bot, Algebra.bijective_algebraMap_iff, coe_set_eq_zero, BooleanAlgebra.inf_compl_le_bot, Pi.bot_comp, Ideal.Quotient.mk_bijective_iff_eq_bot, Set.Iic.complementedLattice_iff, hnot_top, Submodule.dualCoannihilator_bot, Finset.max_mem_insert_bot_image_coe, bot_lt_iff_ne_bot, Subgroup.subgroupOf_eq_bot, SimpleGraph.egirth_bot, WithBot.exists, SimpleGraph.support_eq_bot_iff, Subsemiring.closure_singleton_one, Ideal.instIsTwoSidedBot, SSet.instHasDimensionLTToSSetBotSubcomplex, Interval.dual_bot, CategoryTheory.MorphismProperty.bot_mem_precoverage, Submodule.dualCoannihilator_top, IntermediateField.rank_adjoin_eq_one_iff, LinearMap.separatingRight_iff_flip_ker_eq_bot, CategoryTheory.TransfiniteCompositionOfShape.map_isoBot, Filter.frequently_bot, Filter.smul_eq_bot_iff, WithBot.Iio_coe, List.maximum_nil, IsLocalization.bot_lt_comap_prime, sSup_diff_singleton_bot, nilpotent_iff_lowerCentralSeries, Submodule.ker_liftQ_eq_bot', Pi.bot_apply, Finset.Iic_bot, Filter.principal_eq_bot_iff, AddSubgroup.coe_topologicalClosure_bot, WithBot.bot_lt_add, TopologicalSpace.Closeds.coe_bot, Order.not_isSuccLimit_bot, IntermediateField.adjoin_one, CategoryTheory.sheafBotEquivalence_inverse_map_val, Subgroup.pi_eq_bot_iff, OrdinalApprox.lfpApprox_ord_eq_lfp, LinearEquiv.eq_bot_of_equiv, ClosedSubmodule.coe_bot, inf_sdiff_self_right, WithBot.unbotD_eq_iff, Submodule.annihilator_bot, AlgebraicGeometry.Scheme.IdealSheafData.support_eq_top_iff, Subgroup.isComplement'_top_right, WithBot.eq_bot_iff_forall_le, Submodule.span_singleton_eq_bot, LowerSet.Iio_eq_bot, CategoryTheory.TransfiniteCompositionOfShape.fac, Filter.map_inl_inf_map_inr, IsDomain.minimalPrimes_eq_singleton_bot, Setoid.bot_def, CategoryTheory.Subfunctor.Subpresheaf.bot_obj, Subfield.bot_eq_of_zMod_algebra, Subgroup.ker_inclusion, NNReal.bot_eq_zero, LT.lt.eq_bot, LieSubmodule.trivial_lie_oper_zero, CategoryTheory.Limits.imageSubobject_zero, SimpleGraph.isVertexCover_bot, Order.pred_bot, Finset.Iic_eq_Icc, Ideal.map_eq_bot_iff_of_injective, MeasurableSpace.measurableSet_bot_iff, Filter.subsingleton_iff_bot_or_pure, Subfield.map_bot, IsDiscreteValuationRing.bot_lt_toWithBotNat_iff, LieModule.posFittingCompOf_eq_bot_of_isNilpotent, LinearMap.ker_toSpanSingleton_eq_bot_iff, Submodule.baseChange_bot, CategoryTheory.isSeparating_empty_of_thin, Submodule.comm_trans_rTensorOne, LieAlgebra.abelian_iff_derived_one_eq_bot, AddSubgroup.pi_eq_bot_iff, CategoryTheory.Subobject.map_bot, Disjoint.out, Filter.eventually_false_iff_eq_bot, WithBot.image_coe_Iio, symmDiff_eq_right, AddMonoidHom.ker_snd, CategoryTheory.sheafBotEquivalence_unitIso, BoxIntegral.Prepartition.iUnion_eq_empty, Ideal.dvd_bot, WithBot.Iic_coe, SimpleGraph.maxDegree_bot_eq_zero, Subgroup.bot_or_exists_ne_one, CategoryTheory.MonoOver.bot_left, Subgroup.closure_singleton_one, AddMonoidHom.range_eq_bot_iff, MeasureTheory.Content.innerContent_bot, SimpleGraph.Finsubgraph.coe_bot, IntermediateField.extendScalars_self, WithBot.map₂_bot_left, CategoryTheory.MonoOver.bot_arrow, Subsemiring.closure_singleton_natCast, Ideal.comap_bot_of_injective, UpperSet.coe_eq_univ, AddSubgroup.zmultiples_zero_eq_bot, Subring.mem_bot, Finpartition.default_eq_empty, hnot_bot, WithBot.toDual_apply_bot, CategoryTheory.Subobject.mk_eq_bot_iff_zero, Submodule.top_orthogonal_eq_bot, AlgebraicGeometry.Scheme.IdealSheafData.bot_mul, EReal.eq_bot_iff_forall_lt, MonoidHom.comap_bot', IsLocalRing.isField_iff_maximalIdeal_eq, LieModuleHom.le_ker_iff_map, isAtomic_iff, isSMulRegular_iff_torsionBy_eq_bot, CovBy.nhdsGT, le_compl_self, IsAtom.le_iff, csSup_empty, GaloisConnection.l_eq_bot, Finset.inf_eq_bot_iff, isSimpleRing_iff_isTwoSided_imp, EReal.range_coe, LieModule.exists₂_genWeightSpace_smul_add_eq_bot, DiscreteUniformity.eq_bot, Matrix.ker_toLin_eq_bot, Interval.canLift, ModuleCat.ker_eq_bot_of_mono, CategoryTheory.sheafBotEquivalence_inverse_obj_val, LinearMapClass.ker_eq_bot, Subfield.roots_X_pow_char_sub_X_bot, EReal.continuousAt_add_bot_coe, AddMonoidHom.comap_bot', SimpleGraph.vertexCoverNum_eq_zero, LieModule.genWeightSpace_chainBotCoeff_sub_one_zsmul_sub, AddSubgroup.map_eq_bot_iff, Ideal.isRadical_bot_iff, Filter.comap_const_of_notMem, Submodule.lTensorOne'_tmul, LieSubmodule.ker_incl, LieSubalgebra.span_empty, Subring.smul_bot, Disjoint.eq_bot_of_self, AddMonoidHom.mker_fst, Submodule.rTensorOne'_tmul_one, Filter.coprodᵢ_bot, IsGaloisGroup.fixedPoints_bot, FirstOrder.Language.BoundedFormula.relabel_bot, Cubic.degree_of_d_eq_zero, Subgroup.relIndex_bot_left, Submonoid.eq_bot_of_subsingleton, Con.toSetoid_eq_bot, Sublattice.prod_eq_bot, MeasureTheory.condExp_bot, Submodule.rTensorOne'_tmul, WithBot.bot_neg, ofBoolRing_zero, TopologicalSpace.Opens.mem_bot, FirstOrder.Language.DefinableSet.coe_bot, nhdsSet_eq_bot_iff, iSupIndep.injOn, Subgroup.map_eq_bot_iff, Seminorm.sSup_empty, Finset.truncatedInf_empty, LinearMap.ker_eq_bot', eq_bot_of_generator_maximal_submoduleImage_eq_zero, Heyting.Regular.coe_bot, Submodule.exists_dual_map_eq_bot_of_lt_top, Subring.map_bot, MeasurableSpace.generateFrom_singleton_univ, Ideal.map_quotient_self, Quantale.mul_bot, Submodule.bot_pow, Submonoid.bot_or_exists_ne_one, SimpleGraph.not_connected_bot, WithBot.monotone_iff, IsLprojection.coe_bot, bot_isPrincipal, Set.setOf_bot, WithBot.range_eq, iSupIndep.subtype_ne_bot_le_rank, SimpleGraph.default_def, LinearMap.BilinForm.nondegenerate_iff_ker_eq_bot, Submodule.ker_inclusion, Set.bot_eq_empty, AddSubgroup.map_eq_bot_iff_of_injective, LieSubmodule.mem_bot, EReal.continuousOn_toReal, CompleteLinearOrder.himp_bot, ArchimedeanClass.addSubgroup_eq_bot, CategoryTheory.MonoOver.bot_arrow_eq_zero, ExpGrowth.expGrowthSup_zero, sup_eq_bot_iff, Multiset.bot_eq_zero, iSupIndep_ne_bot, AddSubgroup.isSimpleAddGroup_iff, WithBot.bot_lt_natCast, AlgebraicGeometry.LocallyRingedSpace.basicOpen_zero, FractionalIdeal.bot_eq_zero, RootPairing.invtRootSubmodule.eq_bot_iff, Set.Ioi_bot, eq_bot_or_bot_lt, DoubleCoset.rel_bot_eq_right_group_rel, Submonoid.closure_prod_one, ULift.down_bot, AddSubgroup.card_le_one_iff_eq_bot, WithBot.lt_def, StarSubalgebra.coe_bot, Interval.neg_bot, Asymptotics.isBigOWith_bot, IsHausdorff.bot, Subring.prod_bot_sup_bot_prod, WithBot.bot_mul_bot, Digraph.toSimpleGraphInclusive_bot, DFinsupp.bot_eq_zero, UniformSpace.toTopologicalSpace_bot, CompHausLike.LocallyConstant.locallyConstantIsoContinuousMap_hom, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot', AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot, IntermediateField.finrank_adjoin_eq_one_iff, FractionalIdeal.coeIdeal_eq_zero', Nonneg.bot_eq, sdiff_eq_right, LieAlgebra.IsKilling.rootSpace_one_div_two_smul, Bornology.cobounded_eq_bot, IntermediateField.bot_eq_top_of_rank_adjoin_eq_one, DihedralGroup.center_eq_bot_of_odd_ne_one, Filter.pi_inf_principal_pi_eq_bot, Submodule.starProjection_bot, Subalgebra.LinearDisjoint.mulRightMap_ker_eq_bot_iff_linearIndependent, sSup_eq_bot', bot_eq_one', Multiplicative.toAdd_eq_bot, AlgebraicGeometry.Scheme.instSubsingletonCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensBot, Subgroup.commutator_eq_bot_iff_le_centralizer, Ideal.isRadical_bot_of_noZeroDivisors, Ideal.isPrime_bot, Finset.Ici_bot, Subgroup.map_bot, Sylow.commutator_eq_bot_or_commutator_eq_self, MvPolynomial.zeroLocus_bot, Partition.bot_notMem', AddSubmonoid.bot_or_exists_ne_zero, IntermediateField.finrank_bot, symmDiff_self, sdiff_sdiff_self, EReal.preimage_coe_Ioi_bot, AddSubsemigroup.bot_prod_bot, Order.isSuccPrelimit_bot, isCoatom_iff_eq_bot, Filter.bot_sets_eq, Coheyting.boundary_eq_bot, IsIntegrallyClosed.integralClosure_eq_bot, Polynomial.degree_zero, WithTop.toDual_apply_top, Ideal.zero_eq_bot, NonUnitalSubring.mem_bot, IsIntegrallyClosed.integralClosure_eq_bot_iff, IsPGroup.bot_lt_center, WithTop.coe_eq_bot, IntermediateField.sepDegree_bot, AlgebraicGeometry.Scheme.Hom.ker_eq_bot_of_isIso, WithBot.image_coe_Iic, AddQuantale.add_bot, Submodule.finrank_eq_zero, NonUnitalSubring.coe_bot, Module.length_bot, Submodule.rTensorOne_tmul, StrictAnti.apply_eq_bot_iff, Subgroup.IsSubnormal.eq_bot_or_top_of_isSimpleGroup, EReal.bot_lt_zero, Nat.WithBot.lt_zero_iff, IntermediateField.finInsepDegree_bot', Interval.sub_bot, Finset.fold_sup_bot_singleton, List.maximum_eq_bot, AddSubmonoid.eq_bot_iff_card, AddSubgroup.isComplement'_top_right, LieAlgebra.hasTrivialRadical_iff_no_solvable_ideals, MeasureTheory.ae_eq_bot, IsSimpleAddGroup.eq_bot_or_eq_top_of_normal, IntermediateField.restrictScalars_bot_eq_self, pNilradical_eq_bot, Interval.add_bot, Disjoint.eq_bot_of_le, sup_bot_eq, BotHom.coe_bot, WithBot.bot_covBy_coe, Module.End.injOn_genEigenspace, Subgroup.index_bot, AddSubgroup.ker_subtype, Additive.toMul_bot, Prod.snd_bot, IsSimpleModule.jacobson_eq_bot, IntermediateField.fg_bot, NonUnitalSubring.map_bot, IccLeftChart_extend_bot, Filter.limsInf_top, AlgebraicGeometry.Scheme.nilradical_eq_bot, Subgroup.commutator_bot_right, AlgebraicGeometry.Scheme.IdealSheafData.support_eq_bot_iff, Filter.comap_inl_map_inr, AddSubmonoid.mrange_inr', SimpleGraph.IsContained.bot, WithBot.preimage_coe_bot, GroupTopology.toTopologicalSpace_bot, SimpleGraph.edist_bot, Order.krullDim_le_one_iff_of_boundedOrder, Algebra.adjoin_singleton_one, LinearMap.hasEigenvalue_zero_tfae, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot, EReal.sign_bot, Associates.isUnit_iff_eq_bot, Submonoid.prod_eq_bot_iff, LieAlgebra.IsExtension.ker_eq_bot, transfiniteIterate_bot, CategoryTheory.TransfiniteCompositionOfShape.ici_isoBot, CompleteSublattice.coe_bot, EReal.bot_lt_inv, RingHom.ker_eq_bot_iff_eq_zero, IntermediateField.adjoin_empty, Ideal.relNorm_eq_bot_iff, IsAdicComplete.le_jacobson_bot, AddSubgroup.mem_bot, PartENat.ne_zero_iff, Ideal.map_bot, AddSubmonoid.FG.bot, Module.Flat.flat_iff_torsion_eq_bot_of_valuationRing_localization_isMaximal, BoxIntegral.Prepartition.iUnion_bot, ciSup_of_empty, LieAlgebra.IsSolvable.solvable_int, OrderHom.bot_def, IsUpperSet.bot_mem, Fin.bot_eq_zero, IsPGroup.commutator_eq_bot_or_commutator_eq_self, Field.Emb.Cardinal.eq_bot_of_not_nonempty, SimpleGraph.bot_isContained_iff_card_le, isSimpleAddGroup_iff, FirstOrder.Language.BoundedFormula.realize_bot, IntermediateField.rank_bot, Submodule.map_inr, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, CategoryTheory.TransfiniteCompositionOfShape.iic_F, IsAtom.bot_lt, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w, Interval.mul_bot, iSup_eq_dif, Module.End.injOn_maxGenEigenspace, Seminorm.coe_bot, separableClosure_inf_perfectClosure, Multiplicative.ofAdd_bot, Module.stabilizer_units_eq_bot_of_ne_zero, inf_compl_self, Submodule.rank_eq_zero, Submonoid.bot_prod_bot, MeasureTheory.cofinite_eq_bot_iff, Subalgebra.rTensorBot_tmul_one, SimpleGraph.dist_bot, sdiff_eq_bot_iff, SimpleGraph.Subgraph.not_bot_adj, Matrix.ker_toLin'_eq_bot_iff, inf_nhds_atTop, LieModule.ideal_oper_maxTrivSubmodule_eq_bot, Nucleus.coe_bot, Polynomial.jacobson_bot_of_integral_localization, Filter.mul_eq_bot_iff, Filter.smallSets_bot, WithBot.orderSucc_bot, Interval.forall, WithBot.map_eq_bot_iff, MeasureTheory.hitting_bot_le_iff, LieModule.genWeightSpace_chainTopCoeff_add_one_zsmul_add, Submonoid.card_le_one_iff_eq_bot, Filter.comap_inr_map_inl, Sublattice.prod_bot, WithBot.coe_add_eq_bot_iff, BoundedLatticeHom.map_bot', Subfield.bot_eq_of_charZero, WithBot.bot_mul', Subsemigroup.mk_eq_bot, IsIntegrallyClosedIn.integralClosure_eq_bot_iff, Interval.bot_div, transcendental_iff_ker_eq_bot, Order.krullDim_eq_bot_iff, Finset.truncatedInf_singleton, WithBot.sSup_empty, Subring.op_eq_bot, IsCompl.inf_eq_bot, inf_compl_eq_bot', AddSubgroup.map_bot, SimpleGraph.diam_bot, PrimeSpectrum.zeroLocus_bot, GeneralizedBooleanAlgebra.inf_inf_sdiff, Subgroup.map_eq_bot_iff_of_injective, EReal.bot_lt_coe_ennreal, IntermediateField.bot_eq_top_iff_finrank_eq_one, Submodule.neg_bot, WithTop.coe_bot, TwoSidedIdeal.coe_bot, Filter.smul_filter_eq_bot_iff, IntermediateField.adjoin_eq_bot_iff, MeasureTheory.SimpleFunc.simpleFunc_bot', Submodule.rTensorOne_tmul_one, WithBot.recBotCoe_bot, Finset.truncatedInf_sups_of_notMem, Submodule.ker_liftQ_eq_bot, CategoryTheory.GrothendieckTopology.trivial_eq_bot, Filter.map_eq_bot_iff, FirstOrder.Language.Substructure.closure_empty, BoxIntegral.Box.splitLower_eq_bot, Filter.limsup_bot, LieSubmodule.Quotient.map_mk'_eq_bot_le, IntermediateField.lift_sepDegree_bot', Set.pairwise_bot_iff, WithZero.toMulBot_zero, Finpartition.mem_bot_iff, Polynomial.Chebyshev.degree_U_neg_one, WithBot.strictMono_iff, instLiesOverResidueFieldBotIdeal, AddSubgroup.unop_eq_bot, WithBot.forall, BoxIntegral.Box.mk'_eq_bot, OrderBot.bot_le, EReal.toReal_image_Ioo_bot_zero, PEquiv.single_trans_single_of_ne, AddSubgroup.coe_bot, Submodule.map_eq_bot_iff, EReal.neg_eq_bot_iff, ArchimedeanClass.ball_top, inf_sdiff_eq_bot_iff, WithBot.toDualTopEquiv_symm_bot, Filter.nhds_pure, AffineSubspace.coe_eq_bot_iff, Finset.Nonempty.inf_eq_bot_iff, iSup₂_eq_bot, essSup_measure_zero, Algebra.adjoin_singleton_natCast, EReal.zero_lt_exp_iff, Submonoid.unop_eq_bot, Finset.min_eq_bot, IntermediateField.LinearDisjoint.inf_eq_bot, isUniformEmbedding_of_spaced_out, EReal.tendsto_exp_nhds_bot_nhds_zero, LieModule.isNilpotent_iff_exists_ucs_eq_top, Subgroup.isComplement'_bot_left, Ideal.ramificationIdx_bot', Filter.nsmul_bot, AddSubgroup.IsSubnormal.bot, Filter.vadd_filter_bot, FirstOrder.Language.Substructure.map_bot, Subring.closure_empty, AddSubmonoid.eq_bot_of_card_le, BotHomClass.map_bot, Ideal.Filtration.bot_N, Submodule.empty_set_smul, Subalgebra.bot_eq_top_iff_finrank_eq_one, Ideal.comap_map_of_surjective, Subalgebra.mulMap_bot_right_eq, LieModule.exists_genWeightSpace_smul_add_eq_bot, Submodule.bot_colon', Subgroup.bot_toSubmonoid, AddSubmonoid.mem_bot, EReal.preimage_coe_Ioo_bot, ProjectiveSpectrum.zeroLocus_bot, AddSubgroup.coe_eq_singleton, AddSubgroup.unop_bot, CategoryTheory.Subfunctor.bot_obj, Set.dissipate_bot, maximal_orthonormal_iff_orthogonalComplement_eq_bot, Finset.max_eq_bot, LieSubalgebra.toSubmodule_eq_bot, LieModule.finite_genWeightSpace_ne_bot, SimpleGraph.support_bot, SimpleGraph.fromEdgeSet_empty, IsMin.eq_bot, Submodule.isOrtho_top_right, SimpleGraph.connected_bot_iff, ULift.up_bot, Subsemigroup.op_bot, CommGrpCat.mono_iff_ker_eq_bot, LieIdeal.derivedSeries_eq_bot_iff, Ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot, EReal.bot_mul_top, lowerCentralSeries_eq_bot_iff_nilpotencyClass_le, Bornology.cobounded_eq_bot_iff, MonoidHom.mker_inr, Subalgebra.lTensorBot_symm_apply, MeasureTheory.upperCrossingTime_zero, Subring.unop_eq_bot, Topology.IsQuotientMap.isCoveringMapOn_of_smul_disjoint, bot_covBy_iff, bot_codisjoint, LinearMap.ker_eq_bot_of_cancel, FractionalIdeal.coeIdeal_bot, isSolvable_def, Pi.isAtom_iff_eq_single, Con.toSetoid_bot, max_eq_bot, ClosedSubmodule.orthogonal_eq_top_iff, MeasureTheory.sigmaFinite_bot_iff, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_isoBot, iSup_neg, Subgroup.eq_bot_or_eq_top_of_prime_card, discreteUniformity_iff_eq_bot, Module.eval_ker, IntermediateField.lift_bot, LieAlgebra.center_eq_bot, Order.height_bot, IsSimpleOrder.equivBool_symm_apply, Submodule.finite_ne_bot_of_iSupIndep, IsGalois.fixedField_top, InfHom.withBot'_toFun, AddSubgroup.eq_bot_or_eq_top_of_prime_card, TopologicalSpace.Opens.eq_bot_or_top, isSimpleOrder_iff, MulAction.BlockMem.coe_bot, LieModule.isFaithful_iff_ker_eq_bot, associated_norm_prod_smith, AddSubmonoid.mrange_inr, LocallyConstant.ker_comapₗ, OrderBot.ext_bot, Filter.coprodᵢ_eq_bot_iff, WithBot.not_lt_bot, MeasureTheory.hittingAfter_eq_sInf, MeasureTheory.condLExp_bot_ae_eq, Subring.unop_bot, Topology.IsQuotientMap.isCoveringMapOn_of_properlyDiscontinuousSMul, SuccOrder.nhdsGT, Filter.subsingleton_bot, CategoryTheory.GrothendieckTopology.bot_covering, SupHom.withBot'_toFun, Submodule.mulMap_one_left_eq, EReal.tendsto_coe_nhds_bot_iff, OrderDual.toDual_top, AffineSubspace.isEmpty_bot, EReal.tendsto_coe_atBot, upperClosure_univ, WithBot.ofDual_bot, Asymptotics.isBigO_bot, Ideal.iInf_pow_eq_bot_of_isLocalRing, IntermediateField.adjoin_simple_eq_bot_iff, isCancelVAdd_iff_stabilizer_eq_bot, IntermediateField.relfinrank_bot_left, Finset.max_empty, LT.lt.bot_lt, Finsupp.supported_empty, AddSubgroup.addSubgroupOf_bot_eq_top, Filter.eq_or_neBot, Filter.div_bot, Module.Flat.flat_iff_torsion_eq_bot_of_isBezout, UniformSpace.uniformSpace_eq_bot, Filter.coprodᵢ_bot', EReal.exists, EReal.toReal_bot, WithBot.ciSup_empty, CategoryTheory.MorphismProperty.IsStableUnderTransfiniteCompositionOfShape.of_isStableUnderColimitsOfShape.mem_map_bot_le, SpecialLinearGroup.center_eq_bot_of_finrank_le_one, AlgebraicGeometry.Scheme.Hom.ker_eq_bot, AddSubgroup.bot_addSubgroupOf, RingCon.matrix_bot, Submodule.ker_subtypeL, Submodule.bot_mul, MeasureTheory.OuterMeasure.coe_bot, bot_lt_top, AlgebraicGeometry.Scheme.default_asIdeal, Valuation.leIdeal_zero, QuotientAddGroup.quotientBot_apply, PredOrder.nhdsLT, Ideal.eq_bot_of_prime, AddSubsemigroup.unop_bot, LieModule.chainTopCoeff_add_one, EReal.top_mul_bot, HeytingHomClass.map_bot, Submodule.fst_map_snd, Filter.comap_eq_bot_iff_compl_range, AlgebraicGeometry.Scheme.instIsIsoSubschemeιBotIdealSheafData, TopologicalSpace.Opens.mk_empty, EReal.sub_bot, Ideal.jacobson_eq_iff_jacobson_quotient_eq_bot, nhdsSetWithin_empty', upperClosure_eq_bot_iff, Sym2.fromRel_bot, iSup_ne_bot_subtype, IsLocalRing.Ring.KrullDimLE.eq_bot_or_eq_top, IntermediateField.adjoin_intCast, Submodule.isQuotientEquivQuotientPrime_iff, MonoidHom.ker_eq_bot_of_cancel, Pi.isAtom_iff, Monoid.Coprod.mker_swap, Subsemigroup.map_bot, MonoidHom.mker_fst, isDiscrete_iff_nhdsNE, Filter.smul_bot, Algebra.surjective_algebraMap_iff, RingHom.injective_iff_ker_eq_bot, SimpleGraph.lineGraph_bot, IntermediateField.sepDegree_bot', SupBotHom.map_bot', ProperCone.toPointedCone_bot, CategoryTheory.Presheaf.isSheaf_bot, Asymptotics.IsLittleOTVS.bot, IntermediateField.LinearDisjoint.bot_right, Filter.limsSup_bot, SimpleGraph.reachable_bot, Subgroup.eq_bot_iff_forall, Finset.sup_eq_bot_of_isEmpty, BoxIntegral.Prepartition.distortion_bot, Ideal.isPrime_nat_iff, AffineSubspace.pointwise_vadd_bot, EReal.bot_mul_of_pos, Equiv.withBotSubtypeNe_apply, CategoryTheory.Subobject.bot_arrow, LieModule.le_max_triv_iff_bracket_eq_bot, Polynomial.contentIdeal_eq_bot_iff, Ordnode.Bounded.weak, IsAtom.Iic_eq, iSup_emptyset, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isoBot_inv, Submodule.mkQ_map_self, Ideal.bot_isMaximal, MonoidHom.ker_fst, discreteTopology_bot, AlgebraicGeometry.Scheme.Hom.ker_toNormalization, WithBot.succ_bot, IsArtinianRing.isNilpotent_jacobson_bot, Filter.map_inr_inf_map_inl, compl_bihimp_self, RingCon.coe_bot, Filter.principal_empty, top_disjoint, IntermediateField.rank_eq_one_iff, BoxIntegral.norm_volume_sub_integral_face_upper_sub_lower_smul_le, Submodule.map_zero, bot_himp, ContDiffMapSupportedIn.seminorm_eq_bot_of_gt, CategoryTheory.ObjectProperty.isSeparating_bot_of_isThin, Filter.cofinite_eq_bot_iff, Filter.isMeasurablyGenerated_bot, Subalgebra.fg_bot, disjoint_of_le_iff_left_eq_bot, vectorSpan_singleton, Descriptive.Tree.tree_eq_bot, nilpotent_iff_finite_descending_central_series, Subgroup.bot_subgroupOf, Polynomial.degree_of_subsingleton, Module.annihilator_eq_bot, IntermediateField.eq_bot_of_isPurelyInseparable_of_isSeparable, ClosedSubmodule.inf_orthogonal_eq_bot, Subgroup.coe_topologicalClosure_bot, Equiv.Perm.support_prod_le, AddSubgroup.card_bot, dividedPowersBot_dpow_eq, SimpleGraph.bot_preconnected_iff_subsingleton, Subsemigroup.coe_bot, ProjectiveSpectrum.basicOpen_zero, Polynomial.contentIdeal_zero, PerfectRing.pNilradical_eq_bot, AddSubgroup.relIndex_bot_right, map_eq_bot_iff, AffineSubspace.not_sOppSide_bot, MulAction.stabilizer_image_coe_quotient, Ideal.instLiesOverBotOfIsPrime, SimpleGraph.bot_adj, isSimpleOrder_iff_isCoatom_bot, coe_set_eq_one, IsMaxChain.bot_mem, Submodule.map_inl, LatticeHom.withBot'_toFun, nhdsWithin_empty, AddSubmonoid.closure_prod_zero, AddSubgroup.eq_bot_iff_forall, Filter.empty_mem_iff_bot, Additive.ofMul_eq_bot, TopologicalSpace.Compacts.coe_eq_empty, Subgroup.isComplement'_top_bot, SimpleGraph.isClique_bot_iff, WithBot.lt_def_aux, Filter.neg_eq_bot_iff, EReal.preimage_coe_Ioo_bot_top, Submonoid.pi_bot, LieAlgebra.IsKilling.ideal_eq_bot_of_isLieAbelian, Ideal.isPrime_iff_of_isPrincipalIdealRing_of_noZeroDivisors, EReal.toENNReal_bot, Filter.cofinite_eq_bot, CategoryTheory.Subobject.bot_eq_zero, notMem_closure_iff_nhdsWithin_eq_bot, isDenseInducing_pure, Submodule.topologicalClosure_eq_top_iff, symmDiff_eq_bot, RingHom.ker_eq_comap_bot, PEquiv.trans_single_of_eq_none, AddSubmonoid.mrange_inl, Interval.coe_bot, LieSubmodule.ucs_le_of_normalizer_eq_self, eq_bot_of_top_isCompl, IntermediateField.isScalarTower_over_bot, ProbabilityTheory.condVar_bot', Filter.mul_bot, MvPolynomial.ker_evalₗ, LowerSet.prod_eq_bot, Subgroup.zpowers_eq_bot, max_bot_right, Submodule.reflection_bot, WithBot.mul_eq_bot_iff, Metric.isUniformEmbedding_bot_of_pairwise_le_dist, LieModule.eventually_genWeightSpace_smul_add_eq_bot, LieAlgebra.HasTrivialRadical.radical_eq_bot, bot_mem_lowerBounds, SimpleGraph.eq_bot_iff_forall_not_adj, IntermediateField.bot_toSubfield, Submodule.span_zero_singleton, compl_inf_self, AffineSubspace.span_empty, WithBot.lt_coe_bot, Filter.vadd_bot, IsSimpleGroup.eq_bot_or_eq_top_of_normal, NonUnitalStarAlgebra.map_bot, AffineSubspace.map_bot, Subalgebra.lTensorBot_tmul, FirstOrder.Language.BoundedFormula.inf_not_iff_bot, SimpleGraph.edgeFinset_bot, Filter.bot_div, AddSubgroup.isComplement'_bot_left, NonUnitalAlgebra.adjoin_empty, AddSubgroup.bot_or_nontrivial, nhdsSetWithin_empty, TopCat.Presheaf.isSheaf_on_punit_iff_isTerminal, EReal.bot_div_of_pos_ne_top, Filter.vadd_eq_bot_iff, Sublattice.pi_bot, MonoidHom.ker_eq_bot_iff, EReal.mul_bot_of_pos, discreteTopology_subtype_iff, CategoryTheory.Sieve.functorPushforward_bot, WithBot.bot_lt_iff_ne_bot, WithBot.pred_coe_of_isMin, nhdsWithin_subtype_eq_bot_iff, ProbabilityTheory.condIndep_bot_right, Order.Frame.himp_bot, CategoryTheory.projectiveDimension_eq_bot_iff, mem_bot_iff_intCast, WithBot.canLift, WithTop.bot_eq_coe, EReal.mul_eq_bot, Filter.map₂_eq_bot_iff, IntermediateField.adjoin_natCast, LowerSet.notMem_bot, TopologicalSpace.Opens.coe_bot, Submodule.torsionBy_one, Submodule.dualAnnihilator_top, WithBot.subtypeOrderIso_apply_coe, Submodule.IsPrincipal.eq_bot_iff_generator_eq_zero, LieSubalgebra.normalizer_eq_self_iff, Filter.sub_bot, AddMonoid.Coprod.mker_swap, Complementeds.coe_bot, Set.Iic_bot, AlgebraicGeometry.Scheme.IdealSheafData.comap_bot, TopologicalSpace.Closeds.isClopen_singleton_bot, IsCyclotomicExtension.singleton_one, MeasureTheory.hittingBtwn_eq_sInf, Sublattice.bot_prod, EReal.top_mul_of_neg, isMin_iff_eq_bot, AddSubmonoid.closure_singleton_zero, Subgroup.isSimpleGroup_iff, LinearIndependent.repr_ker, Filter.inv_eq_bot_iff, Pi.bot_def, Finpartition.card_bot, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_isoBot, LieSubmodule.mk_eq_bot_iff, LieAlgebra.IsKilling.killingCompl_top_eq_bot, AddSubgroup.botCharacteristic, IntermediateField.isPurelyInseparable_bot, LowerSet.prod_le_prod_iff, AddQuantale.bot_add, EReal.nhds_bot', Submonoid.closure_empty, Ideal.span_eq_bot, WithBot.le_def_aux, Filter.coprod_bot, Submodule.cardQuot_bot, Subsemiring.closure_empty, Order.le_pred_iff_eq_bot, Ideal.smul_bot, Submonoid.unop_bot, NumberField.InfinitePlace.isUnramified_iff_stabilizer_eq_bot, CategoryTheory.TransfiniteCompositionOfShape.iic_incl_app, EReal.inv_bot, inf_bot_eq, isCoveringMapOn_quotientMk_of_properlyDiscontinuousVAdd, Ideal.span_zero, Module.length_eq_coheight, AlgEquiv.quotientBot_symm_mk, Ideal.ofList_nil, Filter.bot_coprod, LinearMap.IsProj.submodule_eq_bot_iff, IsDiscreteValuationRing.TFAE, AffineSubspace.map_eq_bot_iff, Cubic.degree_of_d_eq_zero', AddSubsemigroup.op_bot, isOpen_singleton_iff_punctured_nhds, Interval.inv_bot, Submodule.prod_bot, ENNReal.log_zero, IsDiscreteValuationRing.toWithBotNat_eq_bot_iff, lowerCentralSeries_nilpotencyClass, AddSubmonoid.bot_mul, MulArchimedeanClass.ballSubgroup_top, AddAction.BlockMem.coe_bot, Subalgebra.rTensorBot_symm_apply, FractionalIdeal.coeIdeal_eq_zero, RootPairing.coe_bot, IsAtom.ne_iff_eq_bot, Ideal.inertiaDeg_bot, WithBot.bot_lt_coe, ProbabilityTheory.indep_bot_right, LaurentPolynomial.degree_C_ite, Module.Basis.eq_bot_of_rank_eq_zero, Submodule.set_smul_bot, WithBot.toDualTopEquiv_bot, EReal.nhds_bot, MeasureTheory.Content.empty, Set.Icc.coe_bot, ProbabilityTheory.condVar_bot_ae_eq, Submodule.zero_eq_bot, AffineSubspace.direction_bot, FractionalIdeal.bot_lt_mul_inv, OrderDual.toDual_eq_top, LinearMap.span_singleton_inf_orthogonal_eq_bot, Submodule.basisOfPid_bot, LieAlgebra.hasTrivialRadical_iff_no_abelian_ideals, WithBot.le_def', SimpleGraph.completeEquipartiteGraph_eq_bot_iff, MeasureTheory.upperCrossingTime_zero', WithBot.sum_lt_bot, MaximalSpectrum.iInf_localization_eq_bot, LieAlgebra.isFaithful_self_iff, Finset.Icc_bot, IsDiscreteValuationRing.iff_pid_with_one_nonzero_prime, Algebra.IsCentral.center_eq_bot, IsGaloisGroup.fixingSubgroup_bot, Multiplicative.toAdd_bot, Ideal.iInf_pow_eq_bot_of_isDomain, ProperCone.mem_bot, SimpleGraph.not_isHamiltonian_bot_of_card_ne_one, nhdsWithin_pi_eq_bot, Filter.tendsto_atBot_pure, ProbabilityTheory.indep_bot_left, QuotientAddGroup.quotientBot_symm_apply, GaloisConnection.l_bot, Submodule.traceDual_bot, Ideal.spanNorm_bot, RingHom.ker_coe_equiv, nhdsLT_eq_bot_iff, PseudoMetric.bot_apply, Finpartition.nonUniforms_bot, Subring.closure_singleton_zero, CategoryTheory.injectiveDimension_eq_bot_iff, Nat.Subtype.coe_bot, Seminorm.closedBall_bot, Submodule.lTensorOne_symm_apply, countable_setOf_isolated_left_within, Finset.Iio_bot, IntermediateField.finInsepDegree_bot, MvPolynomial.supported_empty, Submodule.isOrtho_bot_right, ClosedSubmodule.toSubmodule_bot, Subsemigroup.unop_bot, WithBot.mul_bot, LinearOrder.bot_topologicalSpace_eq_generateFrom, nilradical_eq_bot_iff, MeasureTheory.SimpleFunc.simpleFunc_bot, MeasureTheory.Measure.haar.chaar_empty, Set.Ico_bot, LowerSet.prod_bot, affineSpan_eq_bot, ProbabilityTheory.condVar_bot, fixedPoints.lfp_eq_sSup_iterate, MvPolynomial.weightedTotalDegree'_zero, Interval.bot_sub, Filter.limsup_const_bot, compl_eq_bot, CommGrpCat.ker_eq_bot_of_mono, JacobsonNoether.exists_separable_and_not_isCentral', IsPGroup.of_bot, IsPredArchimedean.findAtom_bot, Subgroup.isComplement'_bot_top, AddSubmonoid.bot_or_nontrivial, Filter.ker_bot, Filter.coprodᵢ_eq_bot_iff', Fin.rev_last_eq_bot, Submodule.lTensorOne'_one_tmul, Subsemiring.prod_bot_sup_bot_prod, WithBot.lt_def', LieModule.iSup_ucs_eq_genWeightSpace_zero, AlgebraicGeometry.Proj.basicOpen_zero, Subgroup.botCharacteristic, Dynamics.netEntropyInfEntourage_empty, Submonoid.mrange_inl, IntermediateField.finrank_bot', AddSubgroup.addSubgroupOf_bot_eq_bot, sdiff_top, finiteDimensional_bot, isCoveringMapOn_quotientMk_of_properlyDiscontinuousSMul, AddSubmonoid.map_inr, Quantale.bot_mul, Prod.fst_bot, CategoryTheory.Pretopology.toGrothendieck_bot, nhdsGT_eq_bot_iff, Ideal.prod_eq_bot_iff, LinearMap.IsProj.bot, Partition.bot_lt_of_mem, Submodule.isTorsionFree_iff_torsion_eq_bot, FiniteMulArchimedeanClass.subgroup_eq_bot, Filter.liminf_bot, Submodule.orthogonal_eq_top_iff, Module.End.ker_aeval_ring_hom'_unit_polynomial, Setoid.mk_eq_bot, Valuation.leAddSubgroup_zero, LinearMap.BilinForm.orthogonal_bot, Subgroup.eq_bot_of_card_eq, Dynamics.coverEntropyInf_empty, symmDiff_eq_left, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces, Filter.bot_add, Ideal.span_empty, Filter.limsInf_bot, MeasureTheory.Measure.finiteAtBot, Subalgebra.rank_eq_one_iff, Module.ker_algebraMap_end, Submodule.torsionBySet_univ, sdiff_bot, CategoryTheory.HasLiftingProperty.transfiniteComposition.hasLiftingPropertyFixedBot_ι_app_bot, DiscreteTopology.eq_bot, Submodule.inf_orthogonal_eq_bot, MulArchimedeanClass.closedBallSubgroup_top, CovBy.nhdsLT, LieModule.IsNilpotent.nilpotent_int, Subsemiring.unop_bot, EReal.coe_mul_bot_of_neg, WithBot.le_bot_iff, Order.Ideal.bot_mem, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w_assoc, IntermediateField.botEquiv_def, LinearMap.ker_eq_bot_of_injective, Subgroup.eq_bot_of_card_le, Pi.eq_bot_iff, OrderDual.toDual_bot, bot_lt_isotypicComponents, Additive.toMul_eq_bot, Valuation.Integers.integralClosure, IntermediateField.finSepDegree_bot', eq_bot_of_generator_maximal_map_eq_zero, AddSubmonoid.mrange_inl', IsCoercive.ker_eq_bot, HeytingHom.map_bot', LieAlgebra.derivedSeries_of_bot_eq_bot, Subgroup.unop_bot, stronglyMeasurable_bot_iff, ENNReal.bot_lt_log_iff, ContinuousMap.concatCM_right, compl_top, IntermediateField.eq_bot_of_isSepClosed_of_isSeparable, IsSimpleOrder.lt_top_iff_eq_bot, SimpleGraph.edgeFinset_eq_empty, Submonoid.pi_eq_bot_iff, WellFoundedLT.finite_ne_bot_of_iSupIndep, iSup_eq_if, SimpleGraph.Subgraph.subgraphInhabited_default, Multiset.max_le_of_forall_le, MvPolynomial.zeroLocus_top, LieAlgebra.IsKilling.invtSubmoduleToLieIdeal_apply_eq_bot_iff, ConditionallyCompleteLinearOrderBot.csSup_empty, FirstOrder.Language.Substructure.elementarySkolem₁Reduct.instSmall, Finset.Colex.toColex_empty, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, bot_bihimp, Set.Icc_bot, Subalgebra.eq_bot_of_rank_le_one, Submodule.spanFinrank_eq_zero_iff_eq_bot, LieAlgebra.abelian_iff_derived_succ_eq_bot, SimpleGraph.bot_degree, Submonoid.map_bot, EReal.toReal_eq_zero_iff, isGLB_univ, IntermediateField.bot_eq_top_of_finrank_adjoin_le_one, isBot_bot, Submodule.lTensorOne_tmul, AlgebraicGeometry.IsSchemeTheoreticallyDominant.ker_eq_bot, AddCon.toSetoid_eq_bot, IntermediateField.relrank_bot_right, Filter.not_neBot, LieSubmodule.map_bot, SimpleGraph.bot_isCompleteMultipartite, IsSemisimpleRing.jacobson_eq_bot, AlgebraicGeometry.Scheme.IdealSheafData.support_top, Subalgebra.comm_trans_lTensorBot, SimpleGraph.Subgraph.eq_bot_iff_verts_eq_empty, OrderType.bot_eq_zero, InfiniteGalois.fixedField_bot, CompletelyDistribLattice.himp_bot, IsCompl.inf_right_eq_bot_iff, NonUnitalAlgebra.map_bot, Module.Finite.bot, Order.krullDim_eq_bot, ContinuousMap.idealOfEmpty_eq_bot, WithBot.map₂_bot_right, UpperSet.compl_bot, IsSepClosed.separableClosure_eq_bot_iff, RestrictedProduct.topologicalSpace_eq_of_bot, Subfield.closure_empty, EReal.preimage_coe_Ioc_bot, HeytingAlgebra.himp_bot, Order.coheight_bot_eq_krullDim, Subalgebra.bot_eq_top_of_finrank_eq_one, AddAction.stabilizer_image_coe_quotient, Polynomial.roots_eq_zero_iff_eq_zero_or_isRoot_eq_bot, AddSubgroup.inf_eq_bot_of_coprime, Filter.cocompact_eq_bot, DiscreteQuotient.proj_bot_eq, OrderDual.toDual_eq_bot, AddMonoidHom.comap_bot, Ideal.bot_lt_annihilator_of_disjoint_nonZeroDivisors, isCompl_bot_top, AlgebraicGeometry.Scheme.basicOpen_zero, IsArtinian.isSemisimpleModule_iff_jacobson, OpenPartialHomeomorph.MDifferentiable.ker_mfderiv_eq_bot, IsSimpleOrder.eq_bot_of_lt, AlgebraicGeometry.Scheme.IdealSheafData.map_bot, Submodule.spanFinrank_bot, Submodule.bot_orthogonal_eq_top, iInf_eq_bot, Filter.lt_pure_iff, Submodule.span_empty, pNilradical_one, eq_bot_of_singletons_open, AddMonoidHom.range_zero, Subsemigroup.op_eq_bot, Digraph.toSimpleGraphStrict_bot, Filter.bot_prod, LieModule.genWeightSpace_chainTopCoeff_add_one_nsmul_add, BooleanSubalgebra.bot_mem, LinearMap.ker_eq_bot_iff_range_eq_top, Sublattice.notMem_bot, Filter.Realizer.bot_F, Subalgebra.isAlgebraic_bot_iff, Ideal.spanNorm_eq_bot_iff, disjointed_bot, TwoSidedIdeal.bot_ringCon, Subgroup.eq_bot_of_subsingleton, AddSubmonoid.map_bot, Submodule.dualAnnihilator_bot, Ideal.absNorm_eq_zero_iff, Asymptotics.isTheta_bot, AlgebraicGeometry.isAffineOpen_bot, List.foldr_sup_eq_sup_toFinset, Submodule.spanRank_eq_zero_iff_eq_bot, nhds_bot_order, iInf₂_eq_bot, ciSup_false, SupBotHom.coe_bot, perfectClosure.eq_bot_of_isSeparable, Order.IsSuccLimit.bot_lt, SimpleGraph.minDegree_bot_eq_zero, UpperSet.bot_prod_bot, subsingleton_iff_bot_eq_top, QuotientGroup.quotientBot_apply, AddCommGroup.isAddTorsionFree_iff_torsion_eq_bot, LaurentPolynomial.degree_eq_bot_iff, ProbabilityTheory.Kernel.indep_bot_left, Finpartition.bot_notMem, Subsemigroup.bot_prod_bot, LinearMap.BilinForm.orthogonal_eq_top_iff, Submodule.eq_zero_of_bot_submodule, SimpleGraph.preconnected_bot_iff_subsingleton, IntermediateField.fixedField_bot, AddSubgroup.FG.bot, WithBot.bot_lt_sum_iff, EReal.coe_sub_bot, LinearMap.injective_domRestrict_iff, Order.le_succ_bot_iff, Subring.coe_bot, Subgroup.card_le_one_iff_eq_bot, MeasureTheory.sigmaFinite_trim_bot_iff, OrdinalApprox.lfp_mem_range_lfpApprox, WithBot.Ioo_bot_coe, partialSups_bot, Ideal.torsionOf_eq_bot_iff_of_noZeroSMulDivisors, SimpleGraph.radius_bot, Submodule.coe_torsion_eq_annihilator_ne_bot, Filter.comap_surjective_eq_bot, FaithfulSMul.ker_algebraMap_eq_bot, Partition.coe_removeBot, IsSemisimpleModule.eq_bot_or_exists_simple_le, Submonoid.closure_singleton_one, WithBot.bot_mul, not_bot_lt_iff, Heyting.isRegular_bot, LieAlgebra.IsKilling.rootSpace_two_smul, ConvexCone.isGenerating_bot_iff, RestrictedProduct.isEmbedding_coe_of_bot, Submodule.eq_bot_iff, AddSubsemigroup.mk_eq_bot, LieAlgebra.IsKilling.ker_restrict_eq_bot_of_isCartanSubalgebra, Ne.bot_lt', BoundedLatticeHomClass.map_bot, AddSubmonoid.coe_bot, compl_eq_top, MvPolynomial.weightedTotalDegree'_eq_bot_iff, subsingleton_iff_top_eq_bot, LowerSet.compl_bot, WithBot.preimage_coe_Ioc_bot, PseudoMetric.coe_bot, EReal.coe_mul_bot_of_pos, QuotientAddGroup.map_mk'_self, AddSubmonoid.card_le_one_iff_eq_bot, QuotientGroup.map_mk'_self, Geometry.SimplicialComplex.facets_bot, LinearMap.BilinForm.orthogonal_top_eq_bot, Ideal.absNorm_bot, Submodule.isOrtho_self, FirstOrder.Language.Substructure.instIsEmptySubtypeMemBotOfConstants, Filter.isCobounded_bot, EReal.exp_eq_zero_iff, IntermediateField.insepDegree_bot, CategoryTheory.isDetecting_empty_of_groupoid, bot_eq_zero'', DoubleCoset.bot_rel_eq_leftRel, IsAlgClosed.algebraicClosure_eq_bot_iff, ModuleCat.mono_iff_ker_eq_bot, IntermediateField.rank_bot', disjoint_iff_inf_le, IsAntichain.bot_mem_iff, Finset.sup_bot, WithBot.preimage_coe_Ioi_bot, Disjoint.eq_iff, Submodule.fg_bot, Submodule.exists_dual_map_eq_bot_of_notMem, LinearMap.separatingLeft_iff_ker_eq_bot, Ring.isField_iff_maximal_bot, WithBot.none_eq_bot, AlgebraicGeometry.genericPoint_eq_bot_of_affine, Ideal.isIdempotentElem_iff_eq_bot_or_top_of_isLocalRing, InfHom.coe_bot, AddSubgroup.card_eq_one, AddSubgroup.eq_bot_iff_card, Subsemiring.unop_eq_bot, LinearMap.BilinForm.Nondegenerate.ker_eq_bot, Order.lt_succ_bot_iff, AddSubgroup.op_eq_bot, DualNumber.ideal_trichotomy, Filter.blimsup_false, Submonoid.map_inl, eq_bot_iff, EReal.abs_bot, EReal.mul_bot_of_neg, MeasureTheory.condExp_bot', PEquiv.symm_bot, IsGalois.tfae, Subfield.card_bot, AlgebraicGeometry.basicOpen_eq_bot_iff, LinearMap.trace_eq_sum_trace_restrict', AddMonoidHom.mker_inr, finrank_bot, Ideal.iInf_pow_smul_eq_bot_of_isTorsionFree, EReal.bot_mul_of_neg, nhds_bot_basis_Iic, Ideal.matrix_bot, LieAlgebra.HasTrivialRadical.eq_bot_of_isSolvable, AddSubgroup.bot_or_exists_ne_zero, Ideal.multiset_prod_eq_bot, IntermediateField.LinearDisjoint.eq_bot_of_self, UpperSet.Ici_bot, Submodule.ker_inr, Filter.le_iff_forall_inf_principal_compl, inf_nhds_atBot, SubRootedTree.bot_mem_iff, ProbabilityTheory.Kernel.indep_bot_right, LinearMap.not_hasEigenvalue_zero_tfae, separableClosure.separableClosure_eq_bot, FiniteField.sum_subgroup_units, Interval.exists, Ideal.relNorm_bot, ExpGrowth.expGrowthInf_zero, PEquiv.bot_trans, SimpleGraph.edgeSet_eq_empty, Filter.bot_pow, AlgebraicGeometry.LocallyRingedSpace.basicOpen_eq_bot_of_isNilpotent, NonUnitalAlgebra.mem_bot, not_isMax_bot, AlgebraicGeometry.Scheme.IdealSheafData.support_bot, IsSemisimpleModule.jacobson_eq_bot, Submodule.lTensorOne_one_tmul, Subsemiring.closure_singleton_zero, BoxIntegral.Prepartition.notMem_bot, Filter.generate_univ, WithBot.unbotD_eq_unbotD_iff, iSup_of_empty, isIsotypic_iff_isFullyInvariant_imp_bot_or_top, AddGrpCat.ker_eq_bot_of_mono, Submodule.dualAnnihilator_eq_bot_iff, Subgroup.subgroupOf_bot_eq_top, CategoryTheory.sheafBotEquivalence_counitIso, LieAlgebra.ad_ker_eq_bot_of_hasTrivialRadical, discreteTopology_iff_nhds_ne, Interval.bot_pow, Subgroup.op_eq_bot, SimpleGraph.not_preconnected_bot, Submodule.bot_eq_top_of_rank_eq_zero, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₁, isLUB_empty, AddSubmonoid.card_bot, LieSubalgebra.bot_toSubmodule, AddSubgroup.addSubgroupOf_eq_bot, Subgroup.relIndex_bot_right, disjoint_self, LieModule.iInf_lowerCentralSeries_eq_bot_of_isNilpotent, BooleanAlgebra.bot_le, AffineSubspace.not_wOppSide_bot, Representation.invtSubmodule.coe_bot, LieSubmodule.toSubmodule_eq_bot, isSMulRegular_iff_ker_lsmul_eq_bot, Digraph.emptyDigraph_eq_bot, isLeast_bot_iff, countable_setOf_isolated_left, pNilradical_eq_bot_of_frobenius_inj, AddSubmonoid.eq_bot_iff_forall, LinearEquiv.ker, isCompl_top_bot, Valuation.leSubmodule_zero, Subfield.extendScalars_self, iSup_eq_bot, NonUnitalSubsemiring.map_bot, AddSubmonoid.addSubmonoid_smul_bot, Finsupp.ker_lsingle, Submodule.dualAnnihilator_eq_bot_iff', Subgroup.zpowers_one_eq_bot, LinearMap.ker_lsmul, csInf_univ, WithTop.ofDual_top, IntermediateField.relrank_bot_left, Filter.filter_eq_bot_of_isEmpty, CompleteBooleanAlgebra.inf_compl_le_bot, Subalgebra.LinearDisjoint.eq_bot_of_commute_of_self, RingPreordering.supportAddSubgroup_eq_bot, Sublattice.coe_eq_empty, AlgebraicGeometry.Scheme.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, AddSubgroup.eq_bot_of_card_le, Subalgebra.finrank_bot, SimpleGraph.killCopies_def, Topology.IsQuotientMap.isCoveringMapOn_of_vadd_disjoint, Filter.vadd_filter_eq_bot_iff, Dynamics.coverEntropyEntourage_empty, bot_eq_zero, Module.End.invtSubmodule.mk_eq_bot_iff, CategoryTheory.ObjectProperty.isCoseparating_bot_of_isThin, ZMod.fieldRange_castHom_eq_bot, MeasureTheory.Measure.haar.addCHaar_empty, OrderBot.lowerBounds_univ, IsSimpleOrder.bot_lt_iff_eq_top, MonoidHom.ker_id, AlgebraicGeometry.Scheme.IdealSheafData.mul_bot, Subgroup.bot_prod_bot, Dynamics.coverEntropy_empty, Submodule.QuotientTorsion.torsion_eq_bot, isSimpleGroup_iff, Submonoid.FG.bot, SimpleGraph.isAcyclic_bot, bihimp_hnot_self, AddSubsemigroup.closure_empty, Dynamics.coverEntropyInfEntourage_empty, MeasureTheory.exists_upperSemicontinuous_lt_integral_gt, Finset.fold_inf_univ, AffineSubspace.eq_bot_or_nonempty, Module.End.genEigenspace_zero, Polynomial.annIdealGenerator_eq_zero_iff, Subgroup.closure_eq_bot_iff, GaloisConnection.l_u_bot, Submodule.span_zero, Subgroup.smul_bot, SimpleGraph.isNClique_bot_iff, MeasureTheory.hitting_eq_sInf, SimpleGraph.bot_preconnected, LinearMap.ker_eq_bot_range_liftQ_iff, Finset.sup_eq_bot_iff, Ideal.bot_quotient_isMaximal_iff, ConvexCone.coe_bot, IntermediateField.mem_bot, Ideal.height_bot, Submodule.LinearDisjoint.linearIndependent_left_of_flat, LieAlgebra.isSolvableBot, OrderIso.map_bot, IsArtinianRing.isSemisimpleRing_iff_jacobson, DiscreteUniformity.inst, MulArchimedeanClass.subgroup_eq_bot, LieAlgebra.IsKilling.ker_killingForm_eq_bot, Algebra.IsCentral.out, IsSimpleOrder.eq_bot_or_eq_top, Ideal.iInf_pow_smul_eq_bot_of_noZeroSMulDivisors, Subgroup.Normal.eq_bot_or_eq_top, AddSubmonoid.prod_bot_sup_bot_prod, LinearMap.ker_single, GaloisCoinsertion.u_bot, Filter.mem_iff_inf_principal_compl, MonoidHom.ker_snd, SimpleGraph.ediam_bot, Ideal.bot_liesOver_bot, AddSubmonoid.mul_bot, FirstOrder.Language.DefinableSet.notMem_bot, Interval.bot_nsmul, LinearMap.le_ker_iff_map, AddSubgroup.prod_eq_bot_iff, TopologicalSpace.Opens.not_nonempty_iff_eq_bot, AddSubgroup.isComplement'_bot_top, Module.End.invtSubmodule.bot_mem, EReal.add_eq_bot_iff, lowerCentralSeries_length_eq_nilpotencyClass, Ideal.bot_prime, bot_le, Filter.Germ.const_bot, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isoBot_hom, AddCommGrpCat.ker_eq_bot_of_mono, LieModule.injOn_genWeightSpace, Subgroup.inf_eq_bot_of_coprime, Subalgebra.LinearDisjoint.mulLeftMap_ker_eq_bot_iff_linearIndependent_op, LinearMap.ker_eq_bot_of_inverse, Filter.comap_bot, Module.jacobson_quotient_jacobson, IntermediateField.fixingSubgroup_bot, Submodule.localized'_bot, OrderDual.ofDual_eq_top, Subgroup.IsSubnormal.bot, symmDiff_bot, MeasureTheory.upcrossingsBefore_bot, QuotientGroup.quotientBot_symm_apply, AddMonoidHom.mker_inl, Filter.sub_eq_bot_iff, Subalgebra.bot_eq_top_iff_rank_eq_one, HenselianRing.jac, LieAlgebra.IsSolvable.solvable, LieModule.posFittingComp_eq_bot_of_isNilpotent, WithTop.sub_top, FiniteArchimedeanClass.addSubgroup_eq_bot, Ideal.cotangentIdeal_square, isGalois_bot, Subalgebra.rTensorBot_tmul, Submodule.eq_bot_of_eq_pointwise_smul_of_mem_jacobson_annihilator, PEquiv.trans_bot, EReal.mul_eq_top, Submodule.isOrtho_bot_left, pNilradical_eq_bot', Submonoid.bot_or_nontrivial, Filter.prod_eq_bot, lowerCentralSeries_succ_eq_bot, iSup_extend_bot, LieSubmodule.ucs_bot_one, AddCommGrpCat.mono_iff_ker_eq_bot, Set.Iio_bot, Ideal.mul_eq_bot, iSup_bot, Submodule.comap_bot, AddSubgroup.isComplement'_bot_right, isGalois_iff_isGalois_bot, Booleanisation.lift_bot, Fin.rev_bot, isMin_bot, Disjoint.eq_bot, PEquiv.bot_apply, boundary_Icc, Polynomial.leadingCoeff_eq_zero_iff_deg_eq_bot, AffineSubspace.bot_parallel_iff_eq_bot, Submodule.bot_colon, Cubic.degree_of_zero, Module.Finite.iff_cofg_bot, Submodule.LinearDisjoint.bot_left, FirstOrder.Language.Substructure.fg_bot, Submodule.annihilator_eq_top_iff, MvPolynomial.weightedTotalDegree_zero, SimpleGraph.cycleGraph_zero_eq_bot, Submonoid.op_bot, SimpleGraph.chromaticNumber_eq_one_iff, Submodule.traceDual_top, Ring.jacobson_quotient_jacobson, AddSubmonoid.closure_empty, Subgroup.FG.bot, WithZero.toMulBot_symm_bot, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₁_assoc, Metric.uniformSpace_eq_bot, bihimp_bot, Set.Iic.coe_bot, WithBot.bot_lt_one, sdiff_inf_sdiff, RestrictedProduct.continuous_rng_of_bot, SetLike.isAtom_iff, LieAlgebra.IsKilling.corootSpace_zero_eq_bot, EReal.neg_top, EReal.nhdsWithin_bot, LieSubmodule.span_empty, min_bot_right, LieSubmodule.lie_eq_bot_iff, Set.Ici_bot, IntermediateField.finrank_adjoin_simple_eq_one_iff, LieModule.genWeightSpace_neg_add_chainBot, CompleteLattice.ωScottContinuous.bot, Submodule.colon_bot, Module.supportDim_eq_bot_of_subsingleton, Submodule.eq_bot_of_eq_ideal_smul_of_le_jacobson_annihilator, LowerSet.coe_bot, WithBot.unbotD_eq_self_iff, Subgroup.commutator_bot_left, IsCancelVAdd.stabilizer_eq_bot, Submodule.eq_bot_of_set_smul_eq_of_subset_jacobson_annihilator, boundary_product, UpperSet.coe_bot, Nat.bot_eq_zero, Subalgebra.LinearDisjoint.eq_bot_of_self, LieSubmodule.eq_bot_iff, Submodule.toConvexCone_bot, sInf_eq_bot, Order.bot_lt_krullDim_iff, inf_compl_eq_bot, Submodule.bot_toAddSubgroup, AddSubgroup.eq_bot_of_subsingleton, WithBot.le_def, Subgroup.mem_bot, separableClosure.eq_bot_iff, Subalgebra.LinearDisjoint.bot_left, LieIdeal.ker_incl, Subalgebra.rank_bot, Module.Basis.eval_ker, eq_bot_of_minimal, EReal.coe_mul_top_of_neg, WithBot.preimage_coe_Ioo_bot, toBoolRing_bot, CompleteSublattice.notMem_bot, Coheyting.boundary_bot, BooleanSubalgebra.mk_bot, Subalgebra.LinearDisjoint.bot_right, LieSubmodule.normalizer_bot_eq_maxTrivSubmodule, IntermediateField.rank_adjoin_simple_eq_one_iff, LieModule.genWeightSpace_add_chainTop, Concept.extent_bot, SimpleGraph.bot_strongly_regular, RingPreordering.support_eq_bot, LaurentPolynomial.degree_zero, AddSubgroup.zmultiples_eq_bot, EReal.div_bot, Subgroup.coe_eq_singleton, notMem_iff_exists_ne_and_isConjRoot, Polynomial.degree_eq_bot, IsCancelSMul.stabilizer_eq_bot, commutator_eq_bot_iff_center_eq_top, Ne.bot_lt, TopCat.Presheaf.isSheaf_iff_isTerminal_of_indiscrete, Order.bot_lt_succ, LieIdeal.comap_incl_eq_bot, MeasureTheory.Measure.haar.addPrehaar_empty, Submonoid.eq_bot_iff_card, compl_bot, AlgebraicGeometry.IsClosedImmersion.isIso_iff_ker_eq_bot, LieIdeal.map_eq_bot_iff, Finpartition.bot_isEquipartition, Algebra.adjoin_empty, Subalgebra.fg_bot_toSubmodule, Algebra.botEquiv_symm_apply, MeasurableSpace.generateFrom_singleton_empty, NonUnitalStarAlgebra.toNonUnitalSubalgebra_bot, IccLeftChart_extend_bot_mem_frontier, BoundedOrderHom.map_bot', AffineSubspace.notMem_bot, Filter.pi_eq_bot, bot_inf_eq, Submodule.isPrimary_iff_zero_divisor_quotient_imp_nilpotent_smul, WithBot.bot_mem_insertBot, not_supPrime_bot, UniformSpace.inseparableSetoid_ring, WithBot.Icc_bot_coe, EReal.neg_bot, Subgroup.coe_bot, TopologicalSpace.NonemptyCompacts.range_toCompacts, countable_setOf_isolated_right_within, equivShrink_bot, Submodule.disjoint_iff_comap_eq_bot, ext_iff, Submonoid.smul_bot, isLeast_univ, MeasureTheory.condExp_bot_ae_eq, exists_orderEmbedding_covby_of_forall_covby_finite_of_bot, TwoSidedIdeal.mem_bot, AddSubgroup.index_bot, Finset.Colex.ofColex_bot, Nucleus.bot_apply, AddSubgroup.IsSubnormal.eq_bot_or_top_of_isSimpleAddGroup, DiscreteQuotient.proj_bot_injective, SimpleGraph.Subgraph.verts_bot, Seminorm.ball_bot, Filter.HasBasis.uniformSpace_eq_bot, Subalgebra.bot_eq_top_of_rank_eq_one, RingCon.toCon_bot, LieSubalgebra.eq_bot_iff, Set.Intersecting.bot_notMem, linearIndepOn_iff_linearCombinationOn, CategoryTheory.Functor.WellOrderInductionData.Extension.zero_val, ArchimedeanClass.closedBall_top, SimpleGraph.isVertexCover_empty, IsGalois.mem_bot_iff_fixed, UpperSet.mem_bot, Subalgebra.finrank_eq_one_iff, bot_notMem_iff, BooleanSubalgebra.mem_bot, IsSolvable.solvable, IntermediateField.map_bot, bihimp_eq_bot, PrimeSpectrum.basicOpen_eq_bot_iff, SimpleGraph.edist_bot_of_ne, WithBot.bot_wcovBy_coe, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_bot, Finpartition.parts_inf, Ideal.map_eq_bot_iff_le_ker, Subgroup.subgroupOf_bot_eq_bot, AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot_of_isCompact, bot_eq_one, countableInterFilter_bot, AddMonoidHom.mker_snd, Ideal.mem_jacobson_bot, YoungDiagram.notMem_bot, LieAlgebra.IsSimple.eq_bot_or_eq_top, Filter.add_bot, LieModule.ker_eq_bot, Ring.not_isField_iff_exists_ideal_bot_lt_and_lt_top, FractionalIdeal.coe_zero, iSupIndep.subtype_ne_bot_le_finrank_aux, bot_eq_zero', EReal.tendsto_nhds_bot_iff_real, AddSubgroup.relIndex_bot_left, WithTop.eq_bot_iff_forall_le, Finpartition.avoid_parts_val, upperClosure_eq_bot, Representation.invtSubmodule.bot_mem, Ideal.eq_bot_of_liesOver_bot, Submonoid.closure_one_prod, Submodule.mul_bot, separableClosure.eq_bot_of_isPurelyInseparable, Subalgebra.eq_bot_of_isPurelyInseparable_of_isSeparable, AddGrpCat.mono_iff_ker_eq_bot, Filter.smul_filter_bot, SimpleGraph.chromaticNumber_bot, WithBot.orderIsoPUnitSumLex_bot, Subalgebra.finite_bot, IntermediateField.finSepDegree_bot, AddSubgroup.ker_inclusion, OrderDual.ofDual_top, Filter.eventually_bot, Pi.isAtom_single, Subsemiring.coe_bot, Submodule.spanRank_bot, Module.End.injOn_iInf_maxGenEigenspace, AddSubmonoid.mk_eq_bot, AddSubmonoid.op_bot, AddGroupTopology.toTopologicalSpace_bot, WithBot.add_eq_bot, WithBot.ofDual_apply_bot, IsGaloisGroup.fixedPoints_eq_bot, Filter.inf_eq_bot_iff, ENNReal.log_ofReal, EReal.top_mul_coe_of_neg, IsLowerSet.bot_notMem, Finset.truncatedInf_of_notMem, Subsemiring.op_bot, vectorSpan_of_subsingleton, OrderDual.ofDual_eq_bot, LieSubmodule.baseChange_bot, IsDedekindDomain.flat_iff_torsion_eq_bot, Filter.le_pure_iff', SSet.skeleton_zero, SimpleGraph.Subgraph.coe_bot, isAddCyclic bridge: bot_eq_false

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
ext 📖	—	bot	—	—	—
ext_iff 📖	mathematical	—	bot	—	ext

Compl

Definitions

Name	Category	Theorems
compl 📖	CompOp	1306 math math: PredOrder.nhdsGT_eq_nhdsNE, absorbent_iff_eventually_nhdsNE_zero, mem_coLindelof', Metric.hasBasis_cobounded_compl_closedBall, snd_compl, tendsto_zero_iff_meromorphicOrderAt_pos, ModelWithCorners.compl_boundary, Finset.insert_compl_self, Set.Countable.measure_restrict_compl, OnePoint.isOpen_def, codisjoint_iff_compl_le_right, MeasureTheory.mem_generateSetAlgebra_elim, Set.indicator_self_add_compl, FirstOrder.Language.Theory.CompleteType.compl_setOf_mem, completelyRegularSpace_iff_isOpen, SetTheory.PGame.grundyValue_eq_sInf_moveLeft, MeasureTheory.setIntegral_compl₀, AlgebraicGeometry.Scheme.zeroLocus_iInf, fst_compl, ENNReal.iUnion_Iio_coe_nat, compl_symmDiff_self, Set.compl_iInter₂, Set.compl_range_inr, tendsto_norm_sub_self_nhdsNE, isConnected_compl_of_one_lt_codim, Cardinal.compl_nonempty_of_mk_lt_mk, Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsGE, Ordinal.sInf_compl_lt_lift_ord_succ, Real.contDiffOn_log, Topology.IsClosedEmbedding.continuousOn_comap_finiteMeasure, Set.even_ncard_compl_iff, Set.eqOn_piecewise, Finset.compl_ssubset_compl, Subalgebra.spectrum_sUnion_connectedComponentIn, ContDiff.dense_compl_range_of_finrank_lt_finrank, nhds_ne_subtype_neBot_iff, Set.disjoint_compl_left_iff_subset, MeasureTheory.GridLines.T_lmarginal_antitone, MeasureTheory.unifTight_iff_real, Convex.nhdsWithin_diff_eq_nhdsNE, IsIdempotentElem.coe_compl, Filter.compl_mem_cocardinal_of_card_lt, Set.compl_subset_compl_of_subset, SSet.horn₃₁.desc.multicofork_π_two, Topology.IsUpper.isOpen_iff_generate_Iic_compl, Summable.sum_add_tsum_compl, frontier_compl, OpenPartialHomeomorph.eventually_ne_nhdsWithin, Topology.IsConstructible.compl, MeasureTheory.restrict_compl_singleton, Finset.Ioi_disjUnion_Iio, compl_le, punctured_nhds_smul, lt_compl_self, TopologicalSpace.Closeds.coe_compl, nhds_ne_subtype_eq_bot_iff, Metric.hasAntitoneBasis_cobounded_compl_ball, ProbabilityTheory.Kernel.borelMarkovFromReal_apply', SubMulAction.ofStabilizer_carrier, Set.compl_union, Finset.compl_inter, isCompact_setOf_finiteMeasure_le_of_isCompact, MeasureTheory.probReal_compl_eq_one_sub₀, tendsto_cobounded_iff_meromorphicOrderAt_neg, Metric.mem_cocompact_iff_closedBall_compl_subset, SSet.horn.faceSingletonComplIso_inv_ι_assoc, symmDiff_eq', mem_codiscreteWithin_iff_forall_mem_nhdsNE, IsAntichain.image_compl, Filter.inv_nhdsWithin_ne_zero, MeasureTheory.measure_compl_sigmaFiniteSet, HasFPowerSeriesAt.locally_ne_zero, Function.Periodic.tendsto_nhds_zero, Set.compl_def, isClopen_compl_iff, isAntichain_union, tendsto_zpow_nhdsNE_zero_cobounded, BaireMeasurableSet.compl, sup_inf_inf_compl, Set.preimage_boolIndicator, Set.compl_compl_image, Finset.compl_eq_univ_sdiff, nhdsWithin_uIoo_right_le_nhdsNE, frontier_union_subset, CompleteBooleanAlgebra.himp_eq, sup_compl_le_himp, isConnected_compl_singleton_of_one_lt_rank, Set.iUnion_eq_compl_iInter_compl, Set.mulIndicator_self_mul_compl_apply, Filter.mem_cofinite, PrimeSpectrum.isRetrocompact_zeroLocus_compl_of_fg, MeasureTheory.ae_eq_set_compl, Function.Periodic.cuspFunction_zero_eq_limUnder_nhds_ne, compl_frontier_eq_union_interior, MeasureTheory.Measure.toSphere_apply_aux, Finset.card_compl_add_card, eqOn_dslope_sub_smul, Set.compl_iInter, Set.Finite.multipliable_compl_iff, Fin.image_succ_univ, Set.compl_sInter, Fin.range_succ, SimpleGraph.isNClique_compl, ContinuousLinearMap.image_rayleigh_eq_image_rayleigh_sphere, OnePoint.continuousAt_infty, MeasureTheory.IsSetAlgebra.compl_mem, Polynomial.isCoveringMapOn_eval, tangentConeAt_nonempty_of_properSpace, compl_inf, MeromorphicOn.toMeromorphicNFOn_eq_self_on_nhdsNE, TopologicalSpace.Opens.CompleteCopy.dist_eq, IsUpperSet.compl, ContinuousMap.notMem_idealOfSet, Affine.Simplex.mongePointVSubFaceCentroidWeightsWithCircumcenter_eq_sub, symmDiff_compl_self, compl_sInf, Set.compl_image, MvPolynomial.image_comap_C_basicOpen, tendsto_norm_nhdsNE_one, SimpleGraph.toTopEdgeLabeling_labelGraph_compl, instNeBotNhdsWithinComplSetSingletonOfNontrivial, Set.toFinset_compl, Set.subset_compl_singleton_iff, SimpleGraph.edgeFinset_top, Real.differentiableOn_log, Set.compl_inv, Bornology.IsCobounded.closedBall_compl_subset, Set.image_union_image_compl_eq_range, nhds_basis_closeds, MeasureTheory.measure_compl, MeasureTheory.measure_compl_sigmaFiniteSetWRT, Real.differentiableOn_arcsin, MeasureTheory.restrict_compl_sigmaFiniteSet, PeriodPair.eqOn_deriv_weierstrassPExcept_derivWeierstrassPExcept, PrimitiveSpectrum.isTopologicalBasis_relativeLower, MeasureTheory.SignedMeasure.exists_compl_positive_negative, Function.update_eventuallyEq_nhdsNE, Filter.compl_mem_kernMap, Set.inter_eq_compl_compl_union_compl, OnePoint.isOpen_iff_of_mem, Order.Ideal.isPrime_iff, IsSemilinearSet.compl, Finset.insert_compl_insert, Order.PFilter.IsPrime.compl_ideal, Finset.compl_inf, OnePoint.isOpen_iff_of_mem', compl_sdiff, Order.Ideal.IsProper.notMem_or_compl_notMem, ProbabilityTheory.Kernel.withDensity_rnDeriv_eq_zero_iff_measure_eq_zero, Set.vadd_set_compl, MeasureTheory.average_mem_openSegment_compl_self, symmDiff_top, MeasureTheory.measurableSet_generateFrom_singleton_iff, compl_iff_not, SSet.horn₃₂.desc.multicofork_π_one, CategoryTheory.Limits.kernelForkBiproductToSubtype_cone, compl_compl, MeasureTheory.eLpNorm_top_piecewise, Real.punctured_nhds_module_neBot, AlgebraicIndependent.iff_adjoin_image_compl, Order.Ideal.IsPrime.compl_mem_of_notMem, himp_bot, MeasureTheory.measure_compl_le_add_of_le_add, Pi.compl_def, Finset.isGδ_compl, IsClosed.isOpen_compl, Std.Irrefl.compl, MeasureTheory.prob_compl_eq_one_iff₀, Finset.union_compl, Matrix.adjp_apply, Bool.compl_eq_bnot, BooleanAlgebra.sdiff_eq, Filter.disjoint_principal_left, Set.Definable.compl, MeromorphicAt.eq_nhdsNE_toMeromorphicNFAt, Set.subset_union_compl_iff_inter_subset, Finset.card_add_card_compl, map_compl', exists_nhds_ne_inf_principal_neBot, Set.Iio_top, CategoryTheory.Limits.cokernelCoforkBiproductFromSubtype_isColimit, MeasureTheory.aedisjoint_compl_right, Summable.summable_compl_iff, MeasureTheory.Measure.restrict_add_restrict_compl, Finset.compl_erase, Filter.inv_nhdsNE_zero, stereographic'_source, Prop.compl_singleton, OnePoint.compl_infty, MeasureTheory.IsHahnDecomposition.compl, Finset.compl_sup, Finset.inclusion_exclusion_card_inf_compl, SimpleGraph.card_interedges_add_card_interedges_compl, comap_norm_nhdsGT_zero, subset_closure_inter_union_closure_compl_left, Heyting.IsRegular.eq, HasDerivAt.eventually_ne, MulAction.smul_zpow_movedBy_eq_of_commute, SimpleGraph.neighborSet_subset_between_union, continuousWithinAt_compl_self, Set.odd_ncard_compl_iff, IsIdempotentElem.one_compl, MeasureTheory.NullMeasurableSet.compl_toMeasurable_compl_ae_eq, biUnion_associatedPrimes_eq_compl_regular, Set.iInter_eq_compl_iUnion_compl, tendsto_norm_inv_nhdsNE_zero_atTop, dslope_eventuallyEq_slope_nhdsNE, PrimeSpectrum.isCompact_isOpen_iff, Absorbs.eventually_nhdsNE_zero, Set.mulIndicator_mul_compl_eq_piecewise, Filter.limsup_compl, compl_mem_codiscrete_iff, Filter.le_cofinite_iff_compl_singleton_mem, Topology.IsUpper.isTopologicalBasis_insert_univ_subbasis, disjoint_compl_right_iff, Set.SurjOn.mapsTo_compl, Disjoint.subset_compl_right, codisjoint_iff_compl_le_left, MeasureTheory.measure_univ_le_add_compl, Metric.ball_infDist_compl_subset, IsAntichain.preimage_compl, Finset.compl_union, AnalyticAt.frequently_zero_iff_eventually_zero, AlgebraicGeometry.Scheme.zeroLocus_biInf, orbit_fixingAddSubgroup_compl_subset, Filter.diff_mem_inf_principal_compl, Real.continuousOn_log, Heyting.IsRegular.disjoint_compl_right_iff, ofDual_hnot, AddAction.movedBy_mem_fixedBy_of_addCommute, Ordinal.cof_type, PFun.core_eq, contDiffWithinAt_compl_self, MeasureTheory.setIntegral_compl, meromorphicOrderAt_ne_top_iff, top_symmDiff, IsLindelof.compl_mem_coLindelof, Ordinal.card_sInf_range_compl_le_lift, Set.kernImage_preimage_eq_iff, contMDiffOn_inv₀, CompleteBooleanAlgebra.sdiff_eq, compl_le_compl, Set.Finite.compl_mem_hyperfilter, SimpleGraph.cliqueNum_compl, meromorphicOrderAt_eq_top_iff, Set.preimage_invFun_of_mem, Set.compl_cIoo, FirstOrder.Field.ACF_zero_realize_iff_finite_ACF_prime_not_realize, nhdsNE_le_cofinite, Homeomorph.map_punctured_nhds_eq, OnePoint.nhdsNE_infty_neBot, compl_compl_compl, MeasureTheory.ae_eq_set_compl_compl, Finset.card_compl, isCoatom_compl, disjointed_eq_inter_compl, Set.subset_compl_comm, himp_eq, MeasureTheory.probReal_add_probReal_compl, Finset.insert_inj_on, mem_codiscrete', Set.subset_compl_iff_disjoint_right, MeasureTheory.compl_cylinder, Finset.compl_singleton, AlgebraicGeometry.Scheme.zeroLocus_singleton, Std.Refl.compl, MeasureTheory.Measure.sum_add_sum_compl, SimpleGraph.edgeSet_top, Filter.HasBasis.disjoint_iff_right, Affine.Simplex.altitudeFoot_mem_affineSpan_image_compl, compl_sSup', ite_inter_closure_compl_eq_of_inter_frontier_eq, Finset.compl_mem_compls, PeriodPair.compl_lattice_diff_singleton_mem_nhds, Set.offDiag_univ, SimpleGraph.neighborFinset_completeEquipartiteGraph, Filter.hasBasis_cofinite, SimpleGraph.reachable_or_reachable_compl, MeasureTheory.Measure.mem_cofinite, ENNReal.range_coe, Module.punctured_nhds_neBot, OpenPartialHomeomorph.IsImage.compl, tendsto_cobounded_of_meromorphicOrderAt_neg, compl_symmDiff, Affine.Simplex.inner_mongePoint_vsub_face_centroid_vsub, CofiniteTopology.mem_nhds_iff, SSet.horn₃₁.desc.multicofork_pt, MeasurableSet.compl_iff, SimpleGraph.IsRegularOfDegree.compl, compl_sup_compl_le, SimpleGraph.neighborFinset_compl, compl_anti, Filter.mem_coclosedCompact_iff, Metric.ball_infDist_subset_compl, Filter.inv_cobounded₀, Heyting.Regular.coe_sdiff, isPathConnected_compl_singleton_of_one_lt_rank, coborder_eq_compl_frontier_iff, IsCompact.compl_mem_cocompact, IsLprojection.coe_compl, hasDerivAtFilter_iff_tendsto_slope, starConvex_compl_Ici, MeasureTheory.NullMeasurableSet.compl, extChartAt_target_union_compl_range_mem_nhds_of_mem, himp_compl, PeriodPair.analyticOnNhd_derivWeierstrassPExcept, Ordinal.card_sInf_range_compl_le, Complex.differentiableOn_update_limUnder_of_bddAbove, SSet.horn.faceSingletonComplIso_inv_ι, SimpleGraph.isMaximalIndepSet_compl, compl_lt_self, OnePoint.tendsto_nhds_infty, Finset.inter_compl, MeasurableSpace.DynkinSystem.generateHas_compl, HasSubset.Subset.disjoint_compl_right, Filter.compl_mem_coprodᵢ, disjoint_compl_compl_left_iff, range_stereographic_symm, ENNReal.iUnion_Iic_coe_nat, PreErgodic.measure_self_or_compl_eq_zero, Nimber.add_def, mem_closure_isSwap, stabilizer_compl, Filter.map_add_left_nhdsNE, Filter.mem_cocardinal, Real.differentiableOn_rpow_const, SimpleGraph.neighborSet_union_compl_neighborSet_eq, Topology.IsLower.isOpen_iff_generate_Ici_compl, Meromorphic.MeromorphicOn.countable_compl_analyticAt, EReal.tendsto_toReal_atTop, Set.range_diff_image, Set.nonempty_compl_of_nontrivial, compl_singleton_mem_nhds_iff, EReal.tendsto_toReal_atBot, compl_sSup, tendsto_norm_div_self_nhdsNE, Filter.mem_comk, Set.image_compl_eq, hasBasis_coLindelof, SubMulAction.ofFixingSubgroup_carrier, OnePoint.compl_range_coe, Convex.radon_partition, mem_codiscrete, FirstOrder.Language.DefinableSet.mem_compl, MeasureTheory.prob_compl_eq_one_sub₀, compl_bijective, Function.Periodic.boundedAtFilter_cuspFunction, Filter.inf_principal_eq_bot, lowerHemicontinuous_iff_isOpen_compl_preimage_Iic_compl, SSet.stdSimplex.range_δ, MeasureTheory.prob_compl_eq_one_iff, Dense.interior_compl, PrimeSpectrum.isIdempotentElemEquivClopens_one_sub, Topology.IsUpper.isTopologicalSpace_basis, compl_inf_eq_bot, Language.IsRegular_compl, PrimeSpectrum.mem_compl_zeroLocus_iff_notMem, exists_isClopen_of_totally_separated, Polynomial.exists_image_comap_of_monic, SimpleGraph.neighborFinset_subset_between_union, multipliable_subtype_and_compl, Set.indicator_compl_add_self_apply, absorbs_iff_eventually_nhdsNE_zero, Function.Embedding.optionEmbeddingEquiv_apply_snd_coe, CategoryTheory.Limits.kernelBiproductToSubtypeIso_hom, Cardinal.mk_compl_finset_of_infinite, Set.indicator_compl', tendsto_riemannZeta_sub_one_div, NumberField.InfinitePlace.card_eq_card_isUnramifiedIn, SimpleGraph.neighborSet_compl, ZetaAsymptotics.tendsto_Gamma_term_aux, Set.ncard_compl, mem_fixingAddSubgroup_compl_iff_movedBy_subset, Fintype.prod_add, nhdsWithin_compl_singleton_le, Symmetric.compl, compl_sdiff_compl, ContDiffOn.dense_compl_image_of_dimH_lt_finrank, MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt, finite_compl_fixedBy_swap, compl_eq_sSup_disjoint, Set.union_inter_compl_right_subset, Metric.subset_compl_thickening_compl_thickening_self, isClosed_and_discrete_iff, Set.diff_eq_compl_inter, MeasureTheory.norm_integral_sub_setIntegral_le, IsSelfAdjoint.isConnected_spectrum_compl, MeasureTheory.setLIntegral_compl, AlgebraicGeometry.ExistsHomHomCompEqCompAux.exists_index, MeasureTheory.measure_compl_le_add_iff, Set.isCoatom_iff, HasLineDerivAt.tendsto_slope_zero, AlgebraicGeometry.Scheme.zeroLocus_def, Finset.subset_compl_singleton, Filter.map_add_right_nhdsNE, MeasureTheory.prob_compl_lt_one_sub_of_lt_prob, Metric.closedBall_compl_subset_of_mem_cocompact, Filter.inv_nhdsNE, Finset.piecewise_compl, Topology.reorderRestrictProd_restrict_compl, Finset.inclusion_exclusion_sum_inf_compl, Set.compl_inter, IsIdempotentElem.zero_compl, ContDiffMapSupportedIn.zero_on_compl', Set.kernImage_compl, Order.Ideal.IsPrime.compl_filter, MeasureTheory.aedisjoint_compl_left, compl_image_latticeClosure, SSet.horn₃₁.desc.multicofork_π_two_assoc, Set.compl_neg, Complex.comap_exp_nhdsNE, mem_closure_ne_iff_frequently_within, Ultrafilter.mem_or_compl_mem, Affine.Simplex.mongePlane_def, SSet.horn₃₁.desc.multicofork_π_zero_assoc, BooleanSubalgebra.compl_mem_iff, Bool.compl_singleton, Finset.prod_mul_prod_compl, AlgebraicGeometry.Polynomial.imageOfDf_eq_comap_C_compl_zeroLocus, MeasurableSpace.DynkinSystem.has_compl, Affine.Simplex.ExcenterExists.excenterWeights_eq_excenterWeights_iff, SetTheory.PGame.grundyValue_eq_sInf_moveRight, Fintype.prod_eq_prod_compl_mul, SimpleGraph.fromEdgeSet_not_isDiag, Order.Ideal.PrimePair.compl_I_eq_F, ContinuousMap.ideal_isMaximal_iff, Complex.isOpen_compl_range_intCast, ContDiffMapSupportedIn.zero_on_compl, HurwitzZeta.completedHurwitzZetaEven_residue_one, IsClopen.compl, disjoint_compl_left, Finset.isCoatom_compl_singleton, codiscreteWithin_iff_locallyEmptyComplementWithin, Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhds, RelIso.compl_apply, Affine.Simplex.vectorSpan_isOrtho_altitude_direction, MeasureTheory.compl_mem_measurableCylinders, Topology.isConstructible_compl, PeriodPair.differentiableOn_derivWeierstrassP, tendsto_nhds_iff_meromorphicOrderAt_nonneg, Meromorphic.countable_compl_analyticAt, disjoint_compl_compl_right_iff, Set.subset_image_compl, Filter.hasBasis_coclosedCompact, Function.locallyFinsuppWithin.restrict_eqOn_compl, Set.Countable.isPathConnected_compl_of_one_lt_rank, isOpen_compl_singleton, MeasureTheory.limsup_measure_compl_le_of_le_liminf_measure, Topology.reorderRestrictProd_mem_preimage_image_restrict, comap_norm_nhdsGT_zero', Set.preimage_boolIndicator_eq_union, ZetaAsymptotics.tendsto_riemannZeta_sub_one_div_Gammaℝ, Complex.tendsto_norm_tan_atTop, BooleanAlgebra.inf_compl_le_bot, SimpleGraph.Connected.exists_preconnected_induce_compl_singleton_of_finite, Set.diff_eq, Bornology.isBounded_def, SimpleGraph.compl_isIndContained_compl, Equiv.Perm.IsSwap.finite_compl_fixedBy, Complex.tendsto_self_mul_Gamma_nhds_zero, isClosed_isNowhereDense_iff_compl, TopologicalSpace.CompactOpens.coe_compl, Set.ite_compl, Set.compl_subset_comm, antisymmRel_compl_apply, sdiff_eq, Real.differentiableOn_mul_log, MeasureTheory.JordanDecomposition.exists_compl_positive_negative, compl_lt_compl_iff_lt, Concept.compl_intent, NormedField.nhdsNE_neBot, Set.compl_image_set_of, Complex.map_exp_comap_re_atBot, compl_mul_closure_one_eq, HasDerivAt.tendsto_nhdsNE, piecewise_ae_eq_restrict_compl, exists_sum_eq_one_iff_pairwise_coprime', SimpleGraph.connected_or_connected_compl, Order.Ideal.isPrime_iff_mem_or_compl_mem, ENNReal.essSup_piecewise, ProjectiveSpectrum.isOpen_iff, toDual_compl, Bornology.isCobounded_ofBounded_iff, tendsto_abs_nhdsNE_zero, GaloisConnection.compl, mem_interior_iff_not_clusterPt_compl, SimpleGraph.IsSRGWith.matrix_eq, IsLowerSet.compl, Equiv.image_compl, Set.compl_cIcc, deriv.lhopital_zero_nhds, MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt, Filter.mem_comap_iff_compl, Real.continuousOn_logb, Equiv.Set.sumCompl_symm_apply_of_mem, Function.update_eventuallyEq, meromorphicOrderAt_eq_int_iff, FirstOrder.Language.DefinableSet.coe_compl, Algebra.unramifiedLocus_eq_compl_support, Equiv.Set.sumCompl_symm_apply, MeasureTheory.measureReal_add_measureReal_compl₀, compl_ge, MeromorphicAt.eventuallyEq_zero_nhdsNE_of_eventuallyEq_zero_codiscreteWithin, Finset.compl_insert, BooleanSubalgebra.compl_mem', Set.eqOn_mulIndicator', Fintype.prod_eq_mul_prod_compl, compl_sup_le_himp, symmDiff_eq, tendsto_zero_of_meromorphicOrderAt_pos, Metric.hasBasis_cobounded_compl_ball, Topology.reorderRestrictProd_of_mem, MeasureTheory.measure_compl_sigmaFiniteSet_eq_zero_iff_sigmaFinite, Set.kernImage_empty, MeasureTheory.restrict_compl_sigmaFiniteSet_eq_zero_or_top, UpperSet.coe_compl, coborder_eq_union_frontier_compl, MeasureTheory.eLpNormEssSup_piecewise, SimpleGraph.isIndepSet_compl, mem_codiscrete_accPt, continuousOn_inv₀, AnalyticOnNhd.preimage_zero_mem_codiscrete, le_compl_self, accPt_iff_frequently_nhdsNE, Booleanisation.compl_comp, eqOn_dslope_slope, Homeomorph.image_compl, MeasureTheory.integral_add_compl, Set.union_compl_self, OrderIso.compl_symm_apply, AlgebraicGeometry.Scheme.zeroLocus_map, EReal.range_coe, MeasureTheory.lintegral_add_compl, hnot_eq_compl, schnirelmannDensity_eq_one_iff, PartialEquiv.IsImage.compl, compl_injective, Set.indicator_const_preimage, Metric.hasAntitoneBasis_cobounded_compl_closedBall, SimpleGraph.compl_adj, DirSupClosed.compl, Finset.sum_compl_add_sum, mem_coLindelof, Set.compl_range_some, Finset.preimage_compl, ofDual_compl, Ne.nhdsWithin_compl_singleton, Affine.Simplex.exsphere_compl, PrimeSpectrum.isOpen_iff, Set.mulIndicator_const_preimage, coborder_eq_union_closure_compl, Set.compl_ne_eq_singleton, Disjoint.le_compl_right, SimpleGraph.Connected.induce_compl_singleton_of_degree_eq_one, Set.compl_Ioi, MeasureTheory.measure_add_measure_compl, Finset.compl_filter, Cardinal.mk_sum_compl, SSet.stdSimplex.faceSingletonComplIso_hom_ι, image_subset_closure_compl_image_compl_of_isOpen, Absorbent.eventually_nhdsNE_zero, bihimp_eq, NumberField.InfinitePlace.card_isUnramified_compl, Set.ncard_add_ncard_compl, MeromorphicAt.eventually_continuousAt, HurwitzZeta.hurwitzZeta_residue_one, LinearIndependent.notMem_span, le_compl_iff_le_compl, Set.compl_iUnion₂, Sym2.diagSet_compl_eq_fromRel_ne, MeasureTheory.mem_map_restrict_ae_iff, Finset.mem_compl, EReal.continuousOn_toReal, IsGδ.compl_singleton, CompleteLinearOrder.himp_bot, Set.union_inter_compl_left_subset, Set.piecewise_compl, Set.Ioi_bot, Set.Intersecting.disjoint_map_compl, Set.indicator_self_add_compl_apply, compl_singleton_mem_nhds, Finset.coe_compl, MeasureTheory.Measure.inf_apply, stableUnderGeneralization_compl_iff, compl_iSup, Affine.Simplex.exradius_compl, toDual_hnot, Filter.principal_coprod_principal, compl_iInf, exists_nhds_ne_neBot, Finset.compl_univ, homeomorphUnitSphereProd_symm_apply_coe, MeasurableSpace.DynkinSystem.has_compl_iff, Set.compl_univ, nonunits.subset_compl_ball, Booleanisation.compl_lift, Relation.cutExpand_le_invImage_lex, tendsto_ne_zero_of_meromorphicOrderAt_eq_zero, IsCompl.compl_eq, Set.range_extend_subset, Set.nonempty_inter_compl_of_ncard_add_ncard_lt, ModelWithCorners.compl_interior, mem_fixingSubgroup_compl_iff_movedBy_subset, Set.compl_prod_eq_union, Equiv.Perm.card_compl_support_modEq, top_sdiff, MeasureTheory.prob_compl_eq_zero_iff, MeasureTheory.tendstoUniformlyOn_of_ae_tendsto', BooleanSubalgebra.val_compl, Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsLE, MeasurableSet.compl, Topology.continuous_reorderRestrictProd, MeasureTheory.Measure.compl_support_eq_sUnion, Set.Countable.isConnected_compl_of_one_lt_rank, nhdsGT_le_nhdsNE, PolishSpace.IsClopenable.compl, HurwitzZeta.completedCosZeta_residue_zero, CategoryTheory.Limits.cokernelBiproductFromSubtypeIso_hom, tendsto_ne_zero_iff_meromorphicOrderAt_eq_zero, Filter.liminf_compl, spectrum.subset_singleton_zero_compl, compl_le_self, Affine.Simplex.instNonemptyElemComplSetSingletonOfNontrivial, HasFDerivAt.eventually_notMem, MeasureTheory.measure_compl₀, Set.disjoint_compl_right_iff_subset, Filter.tendsto_inv₀_nhdsWithin_ne_zero, HasFDerivWithinAt.tendsto_nhdsWithin_nhdsNE, Finset.compl_empty, PrimeSpectrum.exists_mul_eq_zero_add_eq_one_basicOpen_eq_of_isClopen, Set.Countable.dense_compl, Cardinal.mk_compl_eq_mk_compl_infinite, hasDerivAt_iff_tendsto_slope_zero, IsCompact.compl_mem_coclosedCompact_of_isClosed, Set.compl_Iic, LocallyFinite.iInter_compl_mem_nhds, IsClosed.compl_mem_nhds, MeasureTheory.Measure.measure_compl_support, Nat.smoothNumbers_compl, eq_compl_iff_isCompl, Set.compl_iUnion, MeromorphicAt.eventually_analyticAt, Set.compl_subset_compl, Subalgebra.spectrum_isBounded_connectedComponentIn, SimpleGraph.compl_neighborSet_disjoint, Finset.prod_prod_Ioi_mul_eq_prod_prod_off_diag, Set.isCoatom_singleton_compl, SimpleGraph.degree_le_between_add, BooleanSubalgebra.compl_mk, MeasureTheory.IsHahnDecomposition.ge_on_compl, inf_compl_self, IsOpen.measure_eq_biSup_integral_continuous, Topology.image_snd_preimageImageRestrict, dense_compl_singleton_iff_not_open, MvPolynomial.aeval_toPolynomialAdjoinImageCompl_eq_zero, hasBasis_coclosedLindelof, aeSeq.measure_compl_aeSeqSet_eq_zero, Real.tendsto_logb_nhdsNE_zero_of_base_lt_one, compl_singleton_mem_nhdsSet_iff, SSet.face_le_horn, Filter.mem_kernMap_iff_compl, dirSupInacc_compl, Filter.mem_ofCardinalUnion, Real.differentiableOn_negMulLog, Digraph.compl_adj, Order.PFilter.isPrime_iff, IsOpen.isClosed_compl, inf_compl_eq_bot', homeomorphSphereProd_symm_apply_coe, MeasureTheory.OuterMeasure.isCaratheodory_compl, Finset.orderEmbOfFin_compl_singleton_eq_succAboveOrderEmb, Set.compl_star, Set.smul_set_compl, compl_beattySeq', DFA.compl_def, ProbabilityTheory.cond_add_cond_compl_eq, AffineIndependent.exists_affineCombination_eq_smul_eq_of_fintype, Set.subset_compl_iff_disjoint_left, Set.image_compl_subset, Metric.thickening_compl_thickening_self_subset_compl, Set.range_diff_image_subset, NormedField.tendsto_norm_inv_nhdsNE_zero_atTop, Heyting.isRegular_compl, compl_surjective, MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd, Sym2.card_diagSet_compl, Summable.tsum_subtype_add_tsum_subtype_compl, Filter.Tendsto.countable_compl_preimage_ker, Set.restrict_ite_compl, AddAction.vadd_zsmul_movedBy_eq_of_addCommute, ConnectedSpace.neBot_nhdsWithin_compl_of_nontrivial_of_t1space, DFA.accepts_compl, Set.compl_empty_iff, PrimitiveSpectrum.preimage_upperClosure_compl_finset, isCoveringMapOn_npow, homeomorphUnitSphereProd_apply_fst_coe, MeasureTheory.unifTight_iff_ennreal, Filter.neg_nhdsNE, Set.powersetCard.coe_compl, disjoint_compl_left_iff, Set.mem_compl_singleton_iff, Matrix.IsAdjMatrix.toGraph_compl_eq, SimpleGraph.IsSRGWith.compl_is_regular, SimpleGraph.isMaximalClique_compl, SSet.horn.faceι_ι, Set.restrict_dite_compl, Complex.isCoveringMapOn_exp, SimpleGraph.IsIndContained.compl, Nimber.not_bddAbove_compl_of_small, Finset.forall_mem_compls, HasSubset.Subset.disjoint_compl_left, contDiffOn_inv, compl_comp_compl, compl_himp, compl_symmDiff_compl, MeasureTheory.integral_add_compl₀, eventually_nhdsNE_eventually_nhds_iff, Real.tendsto_abs_tan_of_cos_eq_zero, MeasureTheory.prob_compl_le_one_sub_of_le_prob, PeriodPair.isOpen_compl_lattice_diff, MeromorphicOn.countable_compl_analyticAt_inter, Fin.image_castSucc, Set.indicator_one_preimage, SimpleGraph.isClique_compl, RelIso.compl_symm_apply, Sym2.fromRel_subset_compl_diagSet, map_compl, Bornology.isBounded_compl_iff, mem_coclosedLindelof, MeasurableSet.coe_compl, Set.univ_pi_piecewise, compl_compl_himp_distrib, compl_le_himp, Filter.hasBasis_cocardinal, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow_of_adjoin_eq_top, Heyting.Regular.coe_toRegular, compl_compl_inf_distrib, Set.compl_range_inl, Filter.mem_cocountable, compl_sup_distrib, Set.Iio_union_Ioi, Tactic.ComputeAsymptotics.tendsto_nhdsNE_of_tendsto_atTop, ContDiffMapSupportedIn.iteratedFDeriv_zero_on_compl, continuousAt_iff_punctured_nhds, SSet.horn_eq_iSup, sup_compl_eq_top, HasDerivAt.lhopital_zero_nhds, MeromorphicAt.frequently_eq_iff_eventuallyEq, ProbabilityTheory.uniformOn_add_compl_eq, ContinuousMap.setOfIdeal_eq_compl_singleton, Rat.dense_compl_compact, MeasurableSpace.measurableSet_compl, Bornology.IsBounded.compl, Set.mem_compl_image, Function.compl_mulSupport, Ultrafilter.compl_notMem_iff, HasDerivAt.tendsto_slope, compl_involutive, MeasureTheory.Measure.compl_mem_cofinite, Equiv.Perm.isPretransitive_of_isCycle_mem, MeromorphicAt.eventually_eq_zero_or_eventually_ne_zero, isGreatest_compl, Set.mulIndicator_compl', SimpleGraph.sdiff_compl_neighborFinset_inter_eq, Set.compl_subset_iff_union, indicator_ae_eq_restrict_compl, Set.restrict_extend_compl_range, Complex.tendsto_norm_tan_of_cos_eq_zero, TopologicalSpace.Clopens.coe_compl, Filter.comap_eq_bot_iff_compl_range, Set.injective_piecewise_iff, Function.Periodic.invQParam_tendsto, isLowerSet_compl, HasProd.hasProd_iff_compl, mem_codiscreteWithin, Real.differentiableOn_arccos, MeromorphicAt.eqOn_compl_singleton_toMeromorphicNFAt, isDiscrete_iff_nhdsNE, Set.BijOn.compl, SSet.horn₃₂.desc.multicofork_π_zero_assoc, Finset.sum_sum_Ioi_add_eq_sum_sum_off_diag, Set.piecewise_eqOn_compl, nhdsLT_le_nhdsNE, Set.indicator_add_compl_eq_piecewise, Metric.AreSeparated.subset_compl_right, ConjClasses.mk_bijOn, Finset.compl_eq_univ_iff, toMeromorphicNFOn_eq_self_on_compl, Sym2.diagSet_compl_eq_setOf_not_isDiag, MeasureTheory.tendstoUniformlyOn_of_ae_tendsto_of_measurable_edist', Fintype.sum_eq_sum_compl_add, Set.notMem_compl_iff, MeasureTheory.isTightMeasureSet_iff_exists_isCompact_measure_compl_le, Polynomial.image_comap_C_basicOpen, OnePoint.compl_image_coe, Set.inter_subset, Disjoint.subset_compl_left, Set.indicator_const_preimage_eq_union, MeasureTheory.AEFinStronglyMeasurable.ae_eq_zero_compl, ProbabilityTheory.condIndep_biSup_compl, SimpleGraph.isNIndepSet_compl, OnePoint.nhdsNE_infty_eq, Bornology.IsCobounded.compl, Real.contDiffOn_arccos, compl_bihimp_self, SSet.horn.faceι_ι_assoc, himp_compl_comm, Filter.mem_ofCountableUnion, MeromorphicOn.eventually_analyticAt_or_mem_compl, PrimitiveSpectrum.isOpen_iff, stereographic_source, PrimeSpectrum.isRetrocompact_zeroLocus_compl, Filter.compl_mem_coclosedCompact, Set.Finite.isGδ_compl, Set.sUnion_eq_compl_sInter_compl, nhdsWithin_uIoo_left_le_nhdsNE, Set.indicator_compl, frontier_eq_inter_compl_interior, hasLineDerivAt_iff_tendsto_slope_zero, HasSum.hasSum_iff_compl, Set.univ_pi_update, ProjectiveSpectrum.basicOpen_eq_zeroLocus_compl, compl_sup, MeasureTheory.Measure.subset_compl_support_of_isOpen, SubAddAction.compl_def, isOpen_setOf_eventually_nhdsWithin, IsClosed.nhdsSet_le_sup, Set.compl_sUnion, MeromorphicNFAt.eventuallyEq_nhdsNE_iff_eventuallyEq_nhds, IsClosed.nhdsSet_le_sup', compl_antitone, IsLindeof.compl_mem_coclosedLindelof_of_isClosed, BooleanAlgebra.himp_eq, compl_strictAnti, finite_compl_fixedBy_closure_iff, Set.Subsingleton.isGδ_compl, StableUnderSpecialization.compl, ProbabilityTheory.Kernel.withDensity_rnDeriv_eq_zero_iff_apply_eq_zero, ENNReal.sum_add_tsum_compl, sdiff_compl, incompRel_compl_apply, stableUnderSpecialization_compl_iff, Function.Periodic.qParam_tendsto, Set.Finite.compl_mem_cofinite, PeriodPair.analyticOnNhd_derivWeierstrassP, Fin.range_succAbove, Complex.Gammaℝ_residue_zero, Language.IsRegular.compl, Set.image_val_compl, Ordinal.lift_card_sInf_compl_le, Filter.hnot_def, compl_inf_self, SSet.horn.multicoequalizerDiagram, Multipliable.prod_mul_tprod_compl, compl_himp_compl, OnePoint.hasBasis_nhds_infty, punctured_nhds_eq_nhdsWithin_sup_nhdsWithin, summable_subtype_and_compl, IsOpen.coborder_eq, Filter.HasBasis.disjoint_iff_left, MeasureTheory.measureReal_compl₀, Set.eqOn_indicator', Function.Periodic.eventually_differentiableAt_cuspFunction_nhds_ne_zero, isUpperSet_compl, HasDerivAt.eventually_notMem, Function.Embedding.optionEmbeddingEquiv_symm_apply, Algebra.SubmersivePresentation.basisKaehler_apply, HasDerivWithinAt.tendsto_nhdsWithin_nhdsNE, mem_closure_isSwap', DFA.acceptsFrom_compl, SSet.horn₃₁.desc.multicofork_π_three_assoc, discreteTopology_subtype_iff, Finset.subset_compl_comm, Set.inter_union_compl, MeasureTheory.NullMeasurableSet.compl_iff, TopologicalSpace.Opens.coe_compl, regularSpace_generateFrom, Order.Frame.himp_bot, Finset.card_compl_lt_iff_nonempty, le_compl_iff_disjoint_left, closure_compl, SimpleGraph.degree_compl, Filter.notMem_iff_inf_principal_compl, disjointed_eq_inf_compl, SSet.horn₃₁.desc.multicofork_π_zero, IsIdempotentElem.compl_compl, AnalyticAt.eventually_eq_or_eventually_ne, measurable_compl, Set.ite_inter_compl_self, NormedField.tendsto_norm_zpow_nhdsNE_zero_atTop, MeasureTheory.laverage_mem_openSegment_compl_self, Language.compl_compl, SubMulAction.compl_def, AnalyticAt.eventually_eq_zero_or_eventually_ne_zero, StableUnderGeneralization.compl, Ordinal.nonempty_compl_range, eventuallyConst_nhdsNE_iff_meromorphicOrderAt_sub_eq_top, Nimber.mul_def, MvPolynomial.irreducible_toPolynomialAdjoinImageCompl, SimpleGraph.isIndepSet_compl_iff_isVertexCover, Disjoint.le_compl_left, BoundedContinuousFunction.dist_extend_extend, Filter.countable_compl_ker, biUnion_associatedPrimes_eq_compl_nonZeroDivisors, isOpen_singleton_iff_punctured_nhds, SSet.stdSimplex.ofSimplex_yonedaEquiv_δ, ProbabilityTheory.Kernel.borelMarkovFromReal_apply, frontier_eq_closure_inter_closure, dense_compl_singleton, Set.subset_inter_union_compl_left, LE.le.disjoint_compl_right, Topology.IsScott.isOpen_iff_Iic_compl_or_univ, Set.Finite.infinite_compl, MeasureTheory.IsTightMeasureSet_iff_exists_isCompact_measure_compl_le, Set.inter_compl_self, CompleteBooleanAlgebra.top_le_sup_compl, Set.compl_empty, Metric.isCobounded_iff_closedBall_compl_subset, Set.compl_eq_univ_diff, MeasureTheory.Measure.isOpen_compl_support, SimpleGraph.edgeSet_subset_setOf_not_isDiag, symmDiff_symmDiff_right', Finset.mem_compls, Filter.map_mul_right_nhdsNE, MeasureTheory.UnifTight.exists_measurableSet_indicator, SSet.horn₃₂.desc.multicofork_π_three, SimpleGraph.cliqueFreeOn_two, MeasureTheory.Measure.MutuallySingular.measure_compl_nullSet, LowerSet.coe_compl, MeasureTheory.measureReal_compl, punctured_nhds_smul₀, closure_sUnion_irreducibleComponents_diff_singleton, Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter, Set.biUnion_compl_eq_of_pairwise_disjoint_of_iUnion_eq_univ, antisymmRel_compl, MeasureTheory.Measure.support_eq_sInter, ULift.up_compl, Set.Intersecting.compl_notMem, Bornology.isCobounded_compl_iff, disjoint_compl_right, interior_union_inter_interior_compl_left_subset, Set.pi_inter_compl, compl_le_compl_iff_le, Finset.exists_compls_iff, Filter.hasBasis_cocompact, IsCompl.compl_eq_iff, OrderIso.compl_apply, Set.compl_Iio, le_compl_comm, compl_eq_bot, Function.Injective.compl_image_eq, BooleanAlgebra.top_le_sup_compl, Set.compl_range_subset_kernImage, Finset.coe_compls, SubAddAction.ofFixingAddSubgroup_carrier, PrimeSpectrum.basicOpen_eq_zeroLocus_compl, compl_le_hnot, diff_mem_nhdsWithin_compl, ProbabilityTheory.indep_biSup_compl, SSet.stdSimplex.faceSingletonComplIso_hom_ι_assoc, subset_closure_inter_union_closure_compl_right, compl_beattySeq, compl_add_closure_zero_eq_iff, Set.Finite.summable_compl_iff, dirSupClosed_compl, Filter.compl_mem_coprod, Set.compl_singleton_eq, Equiv.Set.sumCompl_apply_inr, Complex.compl_Iic_zero, MeasureTheory.exists_setLIntegral_compl_lt, MeasureTheory.le_measure_compl_liminf_of_limsup_measure_le, Set.range_piecewise, PrimeSpectrum.range_comap_algebraMap_localization_compl_eq_range_comap_quotientMk, ProbabilityTheory.Kernel.singularPart_compl_mutuallySingularSetSlice, le_compl_compl, Filter.compl_mem_hyperfilter_of_finite, SimpleGraph.isMaximumClique_compl, HasSum.hasSum_compl_iff, Tactic.ComputeAsymptotics.tendsto_nhdsNE_of_tendsto_atTop_nhds_of_eq, Filter.compl_mem_comap, Ordinal.sInf_compl_lt_ord_succ, OnePoint.nhdsNE_coe_neBot, Set.preimage_compl_eq_image_compl, Filter.EventuallyEq.compl, compl_eq_iff_isCompl, HasDerivAt.tendsto_slope_zero, IsAtom.compl, MeasureTheory.mem_ae_iff, homeomorphSphereProd_apply_snd_coe, ProjectiveSpectrum.mem_compl_zeroLocus_iff_notMem, interior_union_inter_interior_compl_right_subset, NNReal.continuousOn_rpow_const_compl_zero, PFun.compl_dom_subset_core, interior_eq_compl_closure_compl, MeasureTheory.Measure.nullMeasurableSet_compl_support, isPathConnected_compl_of_one_lt_codim, SSet.boundary_eq_iSup, le_compl_iff_disjoint_right, compl_top, Set.preimage_boolIndicator_false, Set.compl_union_self, PeriodPair.differentiableOn_weierstrassPExcept, isCompl_compl, Ultrafilter.compl_mem_iff_notMem, bot_bihimp, Set.compl_Ici, Set.insert_image_compl_eq_range, Heyting.Regular.coe_sup, PeriodPair.differentiableOn_weierstrassP, Set.mulIndicator_compl_mul_self_apply, Set.powersetCard.coe_mulActionHom_compl, CompletelyDistribLattice.himp_bot, closure_eq_compl_interior_compl, HeytingAlgebra.himp_bot, Real.tendsto_abs_tan_atTop, Finset.isCoatom_iff, tendsto_norm_nhdsNE_zero, perfectSpace_iff_forall_not_isolated, MeasureTheory.Measure.MutuallySingular.restrict_compl_nullSet, SSet.horn₃₂.desc.multicofork_pt, Set.kernImage_eq_compl, MeasureTheory.tendsto_measure_compl_closedBall_of_isTightMeasureSet, exists_convex_convex_compl_subset, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow, interior_compl, MeasureTheory.measure_add_measure_compl₀, ProbabilityTheory.uniformOn_compl, Finset.compl_truncatedInf, Filter.EventuallyLE.compl, homeomorphUnitSphereProd_apply_snd_coe, DirichletCharacter.LFunctionTrivChar_residue_one, MeasureTheory.restrict_compl_sigmaFiniteSetWRT, AlgebraicIndependent.iff_adjoin_image, IsCompact.exists_mem_frontier_infDist_compl_eq_dist, pure_sup_nhdsNE, Multipliable.tprod_subtype_mul_tprod_subtype_compl, MeasureTheory.VectorMeasure.restrict_add_restrict_compl, SimpleGraph.IsSRGWith.compl, Metric.closedBall_infDist_compl_subset_closure, Subtype.preimage_coe_compl', Equiv.Set.sumCompl_apply_inl, Affine.Simplex.excenterExists_compl, completedRiemannZeta_residue_one, Sym2.irreflexive_iff_fromRel_subset_diagSet_compl, Set.indicator_compl_add_self, Multipliable.multipliable_compl_iff, SimpleGraph.connected_or_preconnected_compl, IsLprojection.distrib_lattice_lemma, homeomorphSphereProd_apply_fst_coe, SimpleGraph.compl_neighborFinset_sdiff_inter_eq, MeromorphicAt.eventuallyEq_nhdsNE_of_eventuallyEq_codiscreteWithin, Set.compl_inter_self, Complex.range_exp, compl_le_iff_compl_le, MeasureTheory.prob_compl_eq_one_sub, Filter.compl_diagonal_mem_prod, Topology.IsLower.isTopologicalBasis_insert_univ_subbasis, starConvex_compl_Iic, MeasureTheory.Measure.exists_null_set_measure_lt_of_disjoint, HallMarriageTheorem.hall_cond_of_compl, Set.MapsTo.surjOn_compl, SimpleGraph.reachable_or_compl_adj, Cardinal.mk_compl_eq_mk_compl_finite_lift, PrimeSpectrum.exists_image_comap_of_finite_of_free, Function.compl_support, Filter.comap_neBot_iff_compl_range, Set.encard_add_encard_compl, compl_eq_top, Set.mulIndicator_const_preimage_eq_union, Set.preimage_subtype_coe_eq_compl, insert_mem_nhds_iff, HasFDerivAt.tendsto_nhdsNE, Ne.instIsEquiv_compl, SubAddAction.ofStabilizer_carrier, Set.preimage_compl, upperHemicontinuous_iff_isClosed_compl_preimage_Iic_compl, Set.union_eq_compl_compl_inter_compl, ContinuousMap.mem_idealOfSet_compl_singleton, ZMod.LFunction_residue_one, MeasurableSpace.compl_mem_generateMeasurableRec, PUnit.compl_eq, Filter.map_mul_left_nhdsNE, MeasureTheory.ae_eq_univ, closure_compl_singleton, Set.subset_inter_union_compl_right, Filter.compl_mem_comk, riemannZeta_residue_one, Set.mulIndicator_compl, dense_compl_of_dimH_lt_finrank, compl_bihimp_compl, Topology.IsLower.isTopologicalSpace_basis, Filter.le_iff_forall_inf_principal_compl, BooleanSubalgebra.compl_mem, compl_mul_closure_one_eq_iff, Function.insert_injOn, PeriodPair.analyticOnNhd_weierstrassPExcept, totallySeparatedSpace_iff_exists_isClopen, isCoveringMapOn_zpow, HurwitzZeta.completedHurwitzZetaEven_residue_zero, compl_lt, continuousOn_zpow₀, disjoint_nhdsWithin_of_mem_discrete, Ordinal.not_bddAbove_compl_of_small, IsLprojection.mul_compl_self, AnalyticOnNhd.preimage_zero_mem_codiscreteWithin, compl_sInf', compl_inj_iff, discreteTopology_iff_nhds_ne, Pi.compl_apply, ContinuousMap.idealOf_compl_singleton_isMaximal, SimpleGraph.Connected.exists_connected_induce_compl_singleton_of_finite_nontrivial, bihimp_eq', Filter.tendsto_inv₀_nhdsNE_zero, SimpleGraph.edgeDensity_add_edgeDensity_compl, ContinuousAt.eventuallyEq_nhds_iff_eventuallyEq_nhdsNE, DirSupInacc.compl, interior_eq_empty_iff_dense_compl, MeasureTheory.prob_add_prob_compl, Set.diff_subset_compl, SimpleGraph.card_neighborSet_union_compl_neighborSet, Fintype.card_compl_set, Set.Finite.compl_mem_cocardinal, MeromorphicOn.countable_compl_analyticAt, SimpleGraph.IsIndepSet.nonempty_mem_compl_mem_edge, Fintype.sum_eq_add_sum_compl, Real.tendsto_log_nhdsNE_zero, Heyting.IsRegular.disjoint_compl_left_iff, Algebra.smoothLocus_eq_compl_support_inter, OnePoint.isOpen_compl_image_coe, AmpleSet.of_one_lt_codim, OnePoint.le_nhds_infty, hasDerivAt_iff_tendsto_slope, Fin.image_succAbove_univ, CompleteBooleanAlgebra.inf_compl_le_bot, Finset.prod_compl_mul_prod, Finset.subset_compl_iff_disjoint_left, CategoryTheory.Limits.cokernelCoforkBiproductFromSubtype_cocone, Cardinal.mk_compl_eq_mk_compl_finite, Function.support_eq_preimage, AnalyticAt.map_nhdsNE, Set.Countable.isGδ_compl, incompRel_compl, PFun.core_res, FirstOrder.Language.Theory.CompleteType.typesWith_not, nhdsLT_sup_nhdsGT, AlgebraicGeometry.Scheme.zeroLocus_univ, AnalyticAt.frequently_eq_iff_eventually_eq, bihimp_hnot_self, SimpleGraph.edgeSet_subset_compl_diagSet, MeasureTheory.isTightMeasureSet_iff_tendsto_measure_compl_closedBall, Filter.mem_inf_principal', SimpleGraph.Finsubgraph.coe_compl, Affine.Simplex.excenterWeightsUnnorm_compl, EReal.nhdsWithin_top, SimpleGraph.indepSetFree_compl, SimpleGraph.isVertexCover_compl, compl_eq_comm, compl_bihimp, Function.mulSupport_eq_preimage, accPt_iff_clusterPt, Cardinal.mk_compl_of_infinite, SSet.horn₃₂.desc.multicofork_π_zero, ProbabilityTheory.Kernel.indep_biSup_compl, MvPolynomial.isAlgebraic_of_mem_vars_of_forall_totalDegree_le, SSet.horn₃₂.desc.multicofork_π_three_assoc, SimpleGraph.isMaximumIndepSet_compl, Filter.mem_iff_inf_principal_compl, Set.compl_Ioc, Set.compl_diff, SSet.horn₃₂.desc.multicofork_π_one_assoc, punctured_nhds_vadd, mem_coclosed_Lindelof', PeriodPair.analyticOnNhd_weierstrassP, Submodule.connectedComponentIn_eq_self_of_one_lt_codim, SuccOrder.nhdsLT_eq_nhdsNE, Set.inter_compl_nonempty_iff, compl_sup_eq_top, Topology.reorderRestrictProd_of_compl, MeasureTheory.lintegral_piecewise, Set.sInter_eq_compl_sUnion_compl, MeasureTheory.OuterMeasure.isCaratheodory_compl_iff, SimpleGraph.cliqueFree_compl, CategoryTheory.Limits.cokernelBiproductFromSubtypeIso_inv, Affine.Simplex.affineSpan_pair_eq_altitude_iff, tendsto_nhds_of_meromorphicOrderAt_nonneg, Affine.Simplex.direction_altitude, Set.nonempty_compl, IsCompl.eq_compl, Set.prod_subset_compl_diagonal_iff_disjoint, Filter.mem_cocompact', WeakFEPair.Λ_residue_zero, SimpleGraph.neighborSet_completeEquipartiteGraph, Subtype.preimage_coe_compl, compl_gt, AlgebraicIndependent.iff_transcendental_adjoin_image, Real.contDiffOn_arcsin, Equiv.Set.sumCompl_symm_apply_compl, Concept.compl_extent, PrimeSpectrum.isCompact_isOpen_iff_ideal, Fintype.not_linearIndependent_iffₒₛ, Affine.Simplex.excenter_compl, Finset.sum_add_sum_compl, MeasureTheory.Measure.restrict_compl_add_restrict, MeasureTheory.measureReal_add_measureReal_compl, MeromorphicAt.frequently_zero_iff_eventuallyEq_zero, LocallyConstant.ofIsClopen_fiber_one, Finset.image_compl, Affine.Simplex.range_faceOpposite_points, CofiniteTopology.isOpen_iff, CofiniteTopology.isOpen_iff', bihimp_bot, MeasureTheory.prob_compl_eq_zero_iff₀, Set.image_compl_eq_range_diff_image, isOpen_compl_iff, CategoryTheory.Limits.kernelForkBiproductToSubtype_isLimit, SSet.horn₃₁.desc.multicofork_π_three, meromorphicOrderAt_ne_top_iff_eventually_ne_zero, EReal.nhdsWithin_bot, Cardinal.mk_compl_eq_mk_compl_finite_same, ULift.down_compl, Affine.Simplex.ExcenterExists.excenter_eq_excenter_iff, Finset.compl_subset_compl, WeakFEPair.Λ_residue_k, PrimeSpectrum.isIdempotentElemEquivClopens_symm_compl, CategoryTheory.Limits.kernelBiproductToSubtypeIso_inv, Set.inl_compl_union_inr_compl, Set.Finite.cofinite_inf_principal_compl, Order.Ideal.PrimePair.compl_F_eq_I, compl_add_closure_zero_eq, Finset.sdiff_eq_inter_compl, continuousAt_update_same, inf_compl_eq_bot, Set.Finite.compl_mem_codiscrete, Real.tendsto_logb_nhdsNE_zero, MeasureTheory.exists_isCompact_closure_measure_compl_lt, AlgebraicGeometry.RingedSpace.zeroLocus_singleton, Set.compl_univ_iff, Affine.Simplex.faceOppositeCentroid_eq_affineCombination, Topology.restrict_compl_reorderRestrictProd, Set.mem_compl_iff, IsCoatom.compl, Filter.isCompl_principal, compl_unique, Set.range_extend, Filter.mem_cocompact, Set.mem_compl, Nat.coe_maximalIdeal, MeasureTheory.SignedMeasure.toJordanDecomposition_spec, Set.mulIndicator_self_mul_compl, compl_bot, Affine.Simplex.excenterWeights_compl, ofBoolAlg_compl, isAtom_compl, Set.compl_setOf, Equiv.Set.sumCompl_symm_apply_of_notMem, MeasureTheory.probReal_compl_eq_one_sub, AddCircle.openPartialHomeomorphCoe_target, mem_map_indicator_ae_iff_of_zero_notMem, MeasureTheory.AEFinStronglyMeasurable.exists_set_sigmaFinite, Finset.compls_singleton, orbit_fixingSubgroup_compl_subset, SSet.stdSimplex.face_singleton_compl, TopologicalSpace.NonemptyCompacts.range_toCompacts, tendsto_mabs_nhdsNE_one, Finset.compl_eq_empty_iff, Finset.compl_truncatedSup, Filter.tendsto_inv₀_cobounded', eq_compl_comm, nhdsNE_sup_pure, HasFDerivAt.eventually_ne, Finset.subset_compl_iff_disjoint_right, Algebra.etaleLocus_eq_compl_support, Order.Ideal.IsPrime.mem_or_compl_mem, Set.diff_compl, MeasureTheory.VectorMeasure.of_compl, LE.le.disjoint_compl_left, Set.image_compl_preimage, CompletelyRegularSpace.completely_regular_isOpen, Affine.Simplex.altitude_def, MeasureTheory.MemLp.exists_eLpNorm_indicator_compl_lt, MeasureTheory.compl_mem_ae_iff, ContDiffMapSupportedInClass.map_zero_on_compl, Finset.notMem_compl, Nat.factoredNumbers_compl, Set.mulIndicator_compl_mul_self, PerfectSpace.not_isolated, Finset.insert_inj_on', Complex.tendsto_exp_comap_re_atBot_nhdsNE, Filter.disjoint_principal_right, MulAction.movedBy_mem_fixedBy_of_commute, Matroid.setOf_dep_eq, MeasureTheory.stoppedValue_piecewise_const', Asymptotics.isBigO_one_nhds_ne_iff, SimpleGraph.indepNum_compl, Heyting.Regular.coe_compl, Set.Finite.toFinset_compl, IsLprojection.compl_mul, HurwitzZeta.hurwitzZetaEven_residue_one, Set.restrict_piecewise_compl, Function.Embedding.optionEmbeddingEquiv_apply_fst, Filter.compl_notMem, SimpleGraph.card_edgeFinset_induce_compl_singleton, PeriodPair.differentiableOn_derivWeierstrassPExcept, isClosed_compl_iff, exists_mem_frontier_infDist_compl_eq_dist, HasProd.hasProd_compl_iff

HImp

Definitions

Name	Category	Theorems
himp 📖	CompOp	115 math math: HeytingHomClass.map_himp, himp_inf_distrib, sup_himp_self_right, Nucleus.himp_apply, Nucleus.map_himp_apply, CompleteBooleanAlgebra.himp_eq, sup_compl_le_himp, himp_triangle, inf_himp_bihimp, IsClopen.himp, compl_sdiff, himp_inf_le, himp_bot, Codisjoint.himp_eq_left, Pi.himp_apply, le_himp_comm, Nucleus.map_himp_le, le_himp_himp, bihimp_himp_left, himp_top, himp_eq, bihimp_himp_eq_inf, Heyting.Regular.coe_himp, toDual_sdiff, himp_iff_imp, ofDual_himp, himp_compl, le_himp_iff_left, himp_bihimp_left, Finset.inf_himp_right, Topology.IsConstructible.himp, snd_himp, Codisjoint.himp_le_of_right_le, himp_le_himp_right, isGreatest_himp, himp_himp, Pi.himp_def, himp_le, himp_eq_top_iff, himp_inf_himp_cancel, himp_inf_himp_inf_le, compl_sup_le_himp, fst_himp, Order.Frame.le_himp_iff, himp_le_left, Codisjoint.himp_eq_right, le_himp_iff', CompleteLinearOrder.himp_bot, himp_eq_himp_iff, Sublocale.himp_mem', himp_eq_left, CompleteLinearOrder.le_himp_iff, MeasurableSet.himp, Set.Definable.himp, inf_himp, MeasurableSet.coe_himp, bihimp_eq_sup_himp_inf, bihimp_of_le, HeytingHom.map_himp', CompletelyDistribLattice.le_himp_iff, Sublocale.coe_himp, GeneralizedHeytingAlgebra.le_himp_iff, compl_himp, le_himp_iff, himp_bihimp_right, Sublocale.himp_mem, compl_compl_himp_distrib, compl_le_himp, bihimp_of_ge, himp_le_himp_himp_himp, Codisjoint.himp_inf_cancel_right, gc_inf_himp, bot_himp, himp_compl_comm, BooleanAlgebra.himp_eq, TopologicalSpace.Clopens.coe_himp, BiheytingHom.map_himp', compl_himp_compl, himp_inf_self, Order.Frame.himp_bot, himp_iInf_eq, bihimp_def, himp_le_iff, iSup_himp_eq, PUnit.himp_eq, himp_left_comm, himp_le_himp_left, sup_himp_self_left, himp_bihimp_eq_inf, Codisjoint.himp_inf_cancel_left, himp_self, BooleanSubalgebra.mk_himp_mk, Finset.sup_himp_right, SimpleGraph.Finsubgraph.coe_himp, himp_bihimp, CompletelyDistribLattice.himp_bot, HeytingAlgebra.himp_bot, FirstOrder.Language.DefinableSet.coe_himp, codisjoint_himp_self_left, sup_himp_bihimp, BooleanSubalgebra.val_himp, top_himp, le_himp, BooleanSubalgebra.himp_mem, sup_himp_distrib, himp_le_himp, codisjoint_himp_self_right, Finset.sup_himp_left, inf_himp_le, bihimp_himp_right, TopologicalSpace.CompactOpens.coe_himp, Heyting.IsRegular.himp, BiheytingHomClass.map_himp, himp_idem, himp_eq_sSup

HNot

Definitions

Name	Category	Theorems
hnot 📖	CompOp	63 math math: Pi.hnot_def, SimpleGraph.Finsubgraph.coe_hnot, hnot_le_iff_codisjoint_left, Coheyting.boundary_le_hnot, snd_hnot, Coheyting.hnot_boundary, hnot_symmDiff_self, Coheyting.hnot_eq_top_iff_exists_boundary, hnot_hnot_le, symmDiff_top', ofDual_hnot, codisjoint_hnot_right, le_hnot_inf_hnot, sdiff_le_hnot, Codisjoint.hnot_le_left, CompleteLinearOrder.top_sdiff, map_hnot, Coheyting.hnot_hnot_sup_boundary, Pi.hnot_apply, fst_hnot, sup_hnot_self, hnot_top, CompleteDistribLattice.top_sdiff, hnot_sdiff_comm, toDual_compl, hnot_bot, hnot_eq_compl, PUnit.hnot_eq, ofDual_compl, Codisjoint.hnot_le_right, toDual_hnot, Coheyting.boundary_hnot_hnot, IsCompl.hnot_eq, sdiff_le_inf_hnot, hnot_eq_sInf_codisjoint, Coheyting.inf_hnot_self, Order.Coframe.top_sdiff, hnot_inf_distrib, LE.le.codisjoint_hnot_right, codisjoint_hnot_left, IsCompl.eq_hnot, CompletelyDistribLattice.top_sdiff, Coheyting.boundary_hnot_le, hnot_hnot_sdiff_distrib, hnot_hnot_hnot, isLeast_hnot, Filter.hnot_def, LE.le.codisjoint_hnot_left, codisjoint_hnot_hnot_left_iff, hnot_sdiff, symmDiff_hnot_self, compl_le_hnot, hnot_sup_self, hnot_le_hnot, hnot_anti, hnot_le_comm, BiheytingAlgebra.top_sdiff, top_symmDiff', top_sdiff', hnot_hnot_sup_distrib, hnot_le_iff_codisjoint_right, codisjoint_hnot_hnot_right_iff, CoheytingAlgebra.top_sdiff

HasCompl

Definitions

Name	Category	Theorems
compl 📖	CompOp	—

Mathlib.Meta

Definitions

Name	Category	Theorems
delabInf 📖	CompOp	—
delabSup 📖	CompOp	—

Max

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
ext 📖	—	—	—	—	—
ext_iff 📖	—	—	—	—	ext

Min

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
ext 📖	—	—	—	—	—
ext_iff 📖	—	—	—	—	ext

Top

Definitions

Name	Category	Theorems
top 📖	CompOp	4071 math, 6 bridge math: ContinuousMap.dense_setOf_contDiff, Submonoid.inv_top, TangentBundle.continuousLinearMapAt_model_space, tendstoUniformly_iff_tendstoUniformlyOnFilter, AlgebraicGeometry.Scheme.toSpecΓ_apply, EReal.nhds_top_basis, Subring.range_snd, MeasureTheory.exists_lt_lowerSemicontinuous_integral_gt_nnreal, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen, LinearGrowth.linearGrowthSup_top, AlgebraicGeometry.Γ_map_morphismRestrict, MeasureTheory.Integrable.measure_norm_gt_lt_top_enorm, Matroid.eRk_lt_top_iff, Ideal.isPrime_ideal_prod_top, PartENat.top_add, MeasureTheory.hasFiniteIntegral_count_iff_enorm, AlgebraicGeometry.Scheme.Hom.smoothLocus_eq_top_iff, Filter.top_add_top, IsCyclotomicExtension.adjoin_primitive_root_eq_top, FractionalIdeal.coeIdeal_top, ENat.add_lt_top, Cardinal.ofENat_top, NonUnitalSubalgebra.center_eq_top, isMax_iff_eq_top, ENNReal.div_top, AddMonoidHom.mrange_eq_top_of_surjective, ContinuousLinearMap.hasFPowerSeriesOnBall, Ideal.maximal_of_no_maximal, AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality_assoc, Subsemiring.mem_top, FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_changeOrigin, Submodule.colon_empty, WithTop.recTopCoe_top, WithTop.lt_def, ENat.toENNReal_lt_top, AlgebraicGeometry.Scheme.Hom.toPartialMap_hom, AlgebraicGeometry.Scheme.map_PrimeSpectrum_basicOpen_of_affine, AddSubmonoid.comap_top, IntermediateField.finInsepDegree_top, TopologicalSpace.NonemptyCompacts.coe_top, Submodule.topEquiv_symm_apply_coe, AdicCompletion.val_sub_apply, HahnEmbedding.IsPartial.baseEmbedding_le, MeromorphicOn.codiscrete_setOf_meromorphicOrderAt_eq_zero_or_top, IsDiscreteValuationRing.addVal_zero, InfHom.top_apply, SSet.Subcomplex.preimage_eq_top_iff, StieltjesFunction.measure_univ_of_tendsto_atBot_atBot, IsCoatom.ne_iff_eq_top, LieSubalgebra.top_toSubmodule, ofBoolRing_one, SmoothBumpCovering.toSmoothPartitionOfUnity_eq_mul_prod, HahnSeries.untop_orderTop_of_ne_zero, measurable_from_top, LowerSet.coe_eq_univ, LeftInvariantDerivation.lift_zero, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_appTop, ofDual_toAdd_zero, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo, Subsemigroup.srange_snd, LinearOrderedAddCommGroupWithTop.neg_eq_top, Finset.Icc_top, NonUnitalSubring.coe_top, NonUnitalSubring.toNonUnitalSubsemiring_eq_top, LinearPMap.zero_domain, Int.zmultiples_one, IntermediateField.adjoin_eq_top_iff_of_isAlgebraic, MonoidHom.mker_snd, EReal.continuousAt_add_coe_top, ENat.top_pos, ENNReal.iUnion_Iio_coe_nat, EReal.bot_mul_coe_of_neg, Submodule.comap_zero, Ideal.eq_jacobson_iff_sInf_maximal, compl_symmDiff_self, ENNReal.HolderConjugate.instOneInfty, MvPowerSeries.weightedOrder_monomial, AddSubgroup.addSubgroupOf_eq_top, Algebra.Extension.Cotangent.span_eq_top_of_span_eq_ker, Subgroup.isComplement'_top_left, SimplexCategoryGenRel.multiplicativeClosure_isGenerator_eq_top, lp.isLUB_norm, Heyting.isRegular_top, LinearMap.eqLocus_same, LinearOrderedAddCommGroupWithTop.sub_pos, IsTop.eq_top, Topology.RelCWComplex.skeleton_top, Module.support_quotient, SimpleGraph.Subgraph.deleteVerts_mono', IsCompl.sup_eq_top, AnalyticOn.exists_hasFTaylorSeriesUpToOn, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app, Subsemiring.eq_top_iff', instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, Submodule.range_snd, ENat.sSup_eq_top_of_infinite, LeftInvariantDerivation.leibniz, AlgebraicGeometry.Scheme.IsQuasiAffine.toIsImmersion, AlgebraicGeometry.StructureSheaf.globalSectionsIso_inv, isGreatest_univ, MulAction.IwasawaStructure.is_generator, Set.Ioc_top, zpowers_eq_top_of_prime_card, TopologicalSpace.Opens.mem_top, AlgebraicGeometry.iSup_affineOpens_eq_top, AlgebraicGeometry.isAffineOpen_top, smooth_barycentric_coord, ENNReal.rpow_lt_top_iff_of_pos, Order.krullDim_of_noMaxOrder, LocalSubring.range_toSubring, MeasureTheory.Integrable.measure_enorm_ge_lt_top, WithTop.sub_eq_top_iff, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv, CategoryTheory.MorphismProperty.comp_eq_top_iff, CommRingCat.closure_range_union_range_eq_top_of_isPushout, ENNReal.toNNReal_top_mul, SimpleGraph.TopEdgeLabeling.labelGraph_adj, AlgebraicTopology.NormalizedMooreComplex.obj_d, MeasureTheory.Measure.sub_top, AlgebraicGeometry.Scheme.support_nilradical, ENNReal.canLift, LieIdeal.comap_incl_eq_top, ENNReal.top_sub_coe, Submodule.top_mul_eq_top_of_mul_eq_one, AdicCompletion.AdicCauchySequence.mk_eq_mk, LinearMap.range_id, meromorphicOrderAt_const_ofNat, BoundedOrderHomClass.map_top, FiniteArchimedeanClass.mem_addSubgroup_iff, LinearMap.ker_eq_top, Ideal.map_eq_top_iff_of_ker_le, NumberField.IsCMField.zpowers_complexConj_eq_top, RingTheory.Sequence.isWeaklyRegular_cons_iff', ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, ENat.ceil_eq_top, MeasureTheory.memLp_top_of_bound, IsAddFoelner.eventually_meas_ne_top, Ideal.iInf_pow_smul_eq_bot_of_isLocalRing, Additive.ofMul_eq_top, MeasureTheory.SimpleFunc.measure_support_lt_top_of_integrable, TopologicalSpace.PositiveCompacts.coe_top, LieModule.lowerCentralSeries_zero, AddSubgroup.closure_preimage_eq_top, Algebra.GrothendieckGroup.instFG, ENNReal.toNNReal_eq_zero_iff, Submodule.isInternal_prime_power_torsion_of_pid, ENNReal.toNNReal_top, Submonoid.unop_eq_top, contMDiffWithinAt_vectorSpace_iff_contDiffWithinAt, WithTop.continuousOn_untopD, WithTop.toDual_top, SSet.degenerate_eq_top_of_hasDimensionLT, MulArchimedeanClass.subgroup_strictAntiOn, IsCofinal.singleton_top, smoothSheafCommRing.nonunits_stalk, Sublattice.pi_top, ZMod.rootsOfUnity_eq_top, AdicCompletion.map_val_apply, Submodule.top_toAddSubmonoid, ValuationSubring.mem_top, EReal.sub_top, SimpleGraph.Finsubgraph.coe_top, Matrix.iSup_eigenspace_toLin'_diagonal_eq_top, ENNReal.toReal_pos_iff, Subalgebra.pi_top, Ideal.height_of_subsingleton, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top, Finset.truncatedSup_union_of_notMem, Filter.top_prod, AlgebraicGeometry.LocallyRingedSpace.notMem_prime_iff_unit_in_stalk, sSup_univ, Monoid.Coprod.range_inl_sup_range_inr, ContDiffMapSupportedIn.iteratedFDerivLM_apply, AlgebraicGeometry.Scheme.restrictFunctorΓ_inv_app, MeasureTheory.MemLp.toLp_val, RingHom.ker_eq_top_of_subsingleton, Ideal.smul_top_eq_map, Submodule.localized₀_top, Metric.eball_top_eq_univ, TwoSidedIdeal.one_mem_iff, Multiplicative.ofAdd_eq_top, AlgebraicGeometry.instIsDomainCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTopOfIsIntegral, bihimp_eq_left, tendstoUniformly_iff_tendsto, Subgroup.eq_top_of_card_eq, MeasureTheory.OuterMeasure.mkMetric_top, codisjoint_bot, GradedAlgebra.exists_finset_adjoin_eq_top_and_homogeneous_ne_zero, ENNReal.rpow_eq_zero_iff, RingTheory.Sequence.isWeaklyRegular_cons_iff, Module.Relations.Solution.surjective_π_iff_span_eq_top, EReal.toENNReal_top, AffineBasis.tot, SimpleGraph.spanningCoe_induce_top, SimpleGraph.eccent_bot, meromorphicOrderAt_const, ValueDistribution.characteristic_mul_top_le, Algebra.mem_top, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_symm_apply, Module.isTorsionBySet_quotient_set_smul, span_fourier_closure_eq_top, Filter.liminf_const_top, MeasureTheory.NullMeasurableSet.exists_isOpen_symmDiff_lt, RingHom.range_eq_top_of_surjective, CategoryTheory.MorphismProperty.DescendsAlong.top, Finset.Colex.toColex_univ, Polynomial.Sequence.span, MeasureTheory.extend_eq_top, AlgebraicGeometry.Scheme.fromSpecStalk_toSpecΓ_assoc, ordinaryHypergeometric_radius_top_of_neg_nat₃, ENat.card_lt_top, FirstOrder.Language.Structure.fg_def, WithLp.prod_nnnorm_ofLp, AlgebraicGeometry.AffineSpace.SpecIso_hom_appTop, ArchimedeanClass.closedBallAddSubgroup_top, Module.Finite.fg_top, AddSubgroup.pi_top, AlgebraicGeometry.Scheme.IdealSheafData.one_eq_top, IsOpen.exists_subset_affineIndependent_span_eq_top, SSet.iSup_subcomplexOfSimplex_prod_eq_top, Subring.centralizer_eq_top_iff_subset, Submodule.dense_iff_topologicalClosure_eq_top, MeasureTheory.measure_eq_top_of_subset_compl_sigmaFiniteSetWRT'_of_measurableSet, isSimpleOrder_iff_isAtom_top, PiLp.norm_ofLp, OrdinalApprox.gfp_mem_range_gfpApprox, StieltjesFunction.measure_Ioi_of_tendsto_atTop_atTop, ContDiffBumpBase.smooth, LipschitzWith.memLp_lineDeriv, MeasureTheory.measure_eq_top_iff_of_symmDiff, SmoothPartitionOfUnity.contMDiffAt_finsum, CategoryTheory.MorphismProperty.Over.hasPullbacks, Submodule.span_setOf_mem_eq_top, LinearMap.range_eq_top_of_surjective, Ideal.one_eq_top, Associates.prod_top, AlgebraicGeometry.Scheme.zeroLocus_eq_univ_iff_subset_nilradical, Submodule.closedComplemented_top, ContinuousLinearEquiv.symm_toDiffeomorph, ContDiffMapSupportedIn.structureMapCLM_apply, Profinite.NobelingProof.Products.span_nil_eq_top, AlgebraicGeometry.Scheme.Opens.topIso_inv, WithTop.top_mul', Booleanisation.comp_bot, Submonoid.pi_top, RingHom.rangeS_eq_top, Submonoid.prod_top, isCyclic_iff_exists_zpowers_eq_top, CategoryTheory.Sieve.mem_iff_pullback_eq_top, NonUnitalRingHom.srange_eq_map, NonUnitalSubsemiring.top_prod, Ideal.under_top, LeftInvariantDerivation.coe_derivation, Ideal.height_top, SmoothPartitionOfUnity.locallyFinite, FormalMultilinearSeries.radius_eq_top_of_summable_norm, Finset.inf_eq_top_iff, Ideal.natCast_eq_top, HahnEmbedding.Partial.orderTop_eq_archimedeanClassMk, SimpleGraph.turanGraph_eq_top, AddSubgroup.coe_top, LSeries_injOn, AddSubmonoid.prod_top, tsum_geometric_encode_lt_top, AddSubsemigroup.center_eq_top, ENNReal.top_div_of_ne_top, CategoryTheory.MorphismProperty.Over.instHasTerminalTopOfContainsIdentities, MeasureTheory.SimpleFunc.measure_support_lt_top_of_memLp, MeasureTheory.Integrable.measure_norm_ge_lt_top, Polynomial.contentIdeal_one, LSeries_eventually_eq_zero_iff', SimpleGraph.diam_eq_zero_iff_ediam_eq_top, TensorProduct.span_tmul_eq_top, iInf_of_empty, normalClosure_of_stabilizer_eq_top, AddValuation.top_iff, EReal.forall, inseparable_top, Submodule.fst_sup_snd, BoxIntegral.IntegrationParams.tendsto_embedBox_toFilteriUnion_top, WithTop.Ico_coe_top, Subgroup.card_top, SmoothPartitionOfUnity.nonneg, TensorAlgebra.adjoin_range_ι, ENat.ceil_top, LeftInvariantDerivation.left_invariant', AddSubgroup.top_addSubgroupOf, NonUnitalStarAlgebra.mem_top, lowerClosure_eq_top_iff, MeasureTheory.MemLp.evariance_lt_top, IsCofinal.top_mem, AddMonoid.fg_iff, Module.isTorsionBySet_quotient_ideal_smul, AlgHom.equalizer_eq_top, OrderDual.ofDual_bot, QuotSMulTop.equivTensorQuot_naturality, MeasureTheory.Measure.isTopologicalBasis_isOpen_lt_top, NonUnitalSubring.prod_top, Group.isNilpotent_iff, SimpleGraph.isExtremal_top_free_iff_isTuranMaximal, Ideal.height_lt_top, iInf_false, EMetric.hausdorffEdist_empty, AlgebraicGeometry.Scheme.Hom.id_appTop, CategoryTheory.Presheaf.imageSieve_app, EReal.top_div_of_neg_ne_bot, Continuous.exists_contDiff_dist_le_of_forall_mem_ball_dist_le, DividedPowers.SubDPIdeal.sInf_carrier_def, Submodule.top_eq_ofList_cons_smul_iff, MeasureTheory.eLpNorm_const_lt_top_iff_enorm, AddSubsemigroup.closure_univ, SimpleGraph.Subgraph.Connected.adj_union, Set.einfsep_lt_top_iff, symmDiff_compl_self, SmoothBumpCovering.exists_immersion_euclidean, iInf_eq_top, AddSubsemigroup.prod_eq_top_iff, Filter.mem_top_iff_forall, SetLike.isCoatom_iff, IsGaloisGroup.fixingSubgroup_top, Submonoid.mem_top, LeftInvariantDerivation.left_invariant, Cardinal.toENatAux_eq_top, SmoothPartitionOfUnity.locallyFinite', LieModule.iSup_genWeightSpaceOf_eq_top, MeasureTheory.hasFiniteIntegral_iff_ofNNReal, WithTop.coe_lt_top, WithTop.Ici_coe, Submodule.unique_quotient_iff_eq_top, AdicCompletion.val_smul, SimpleGraph.toTopEdgeLabeling_labelGraph_compl, tsum_geometric_lt_top, RootPairing.span_orbit_eq_top, AddSubgroup.instNontrivialSubtypeMemTop, Dynamics.coverMincard_finite_of_isCompact_invariant, Real.dimH_lt_top, Equiv.Perm.closure_isSwap, CategoryTheory.ObjectProperty.topEquivalence_counitIso, groupHomology.comap_coinvariantsKer_pOpcycles_range_subtype_pOpcycles_eq_top, IsGaloisGroup.fixedPoints_top, ENNReal.natCast_lt_top, ENat.canLift, FirstOrder.Language.Hom.range_le_iff_comap, TwoSidedIdeal.coe_top, SimpleGraph.edgeFinset_top, WithTop.iInf_empty, MeasureTheory.Lp.eLpNorm_exponent_top_lim_le_liminf_eLpNorm_exponent_top, StieltjesFunction.measure_Ici_of_tendsto_atTop_atTop, AddSubsemigroup.op_eq_top, AlgebraicGeometry.Scheme.ideal_ker_le_ker_ΓSpecIso_inv_comp, AdicCompletion.incl_apply, Subsemiring.op_eq_top, FiniteArchimedeanClass.mk_lt_mk, Algebra.toSubsemiring_eq_top, SimpleGraph.isClique_iff_induce_eq, AddSubmonoid.closure_addIrreducible, NonUnitalSubsemiring.toAddSubmonoid_top, smoothSheafCommRing.eval_germ, WithTop.preimage_coe_Iio_top, ContinuousLinearEquiv.coe_toDiffeomorph_symm, CategoryTheory.MorphismProperty.Over.map_obj_left, MeasureTheory.OuterMeasure.trim_top, Subfield.mem_top, MeasureTheory.measure_eq_top_of_setLIntegral_ne_top, WithTop.lt_def', Subsemiring.center_eq_top, RootPairing.invtRootSubmodule.eq_top_iff, ENat.coe_top_add_one, IsLocalRing.closedPoint_mem_iff, Ideal.iInf_pow_smul_eq_bot_of_le_jacobson, fixingSubgroup_empty, AdicCompletion.val_smul_eq_evalₐ_smul, MeasureTheory.eLpNorm_exponent_top, Submodule.eq_top_iff', AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ, QuotientAddGroup.leftRel_eq_top, SimpleGraph.ediam_eq_top, WithTop.le_def, LieSubalgebra.span_univ, MeasureTheory.restrict_compl_sigmaFiniteSet, PrimeSpectrum.primeSpectrumProd_symm_inr_asIdeal, Finset.Nonempty.sup_eq_top_iff, NonUnitalSubring.eq_top_iff', RingCon.matrix_top, SSet.Subcomplex.range_eq_top, AlgHom.fieldRange_eq_map, Field.exists_primitive_element, Module.supportDim_add_length_eq_supportDim_of_isRegular, isGalois_iff_isGalois_top, CategoryTheory.MorphismProperty.Over.pullbackComp_hom_app_left, EReal.top_sub, AlgebraicGeometry.isIso_ΓSpec_adjunction_unit_app_basicOpen, List.foldr_inf_eq_inf_toFinset, AlgebraicGeometry.isNoetherian_iff_of_finite_affine_openCover, ENNReal.zero_lt_top, Coheyting.boundary_top, AlgebraicGeometry.Scheme.ι_toIso_inv, UpperSet.Ici_lt_top, LTSeries.exists_relSeries_covBy_and_head_eq_bot_and_last_eq_bot, LowerSet.Iic_top, Subgroup.subgroupOf_eq_top, AlgebraicGeometry.Scheme.locallyCoverDense_of_le, MeasureTheory.measure_support_eapprox_lt_top, BooleanSubalgebra.top_mem, Subfield.relfinrank_top_left, Group.fg_def, CategoryTheory.Subfunctor.range_toRange, UnitAddTorus.mFourierSubalgebra_closure_eq_top, LieModule.isNilpotent_of_top_iff, eq_top_iff, SimpleGraph.eccent_eq_top_of_not_connected, MeasureTheory.norm_indicatorConstLp_top, BoxIntegral.Prepartition.top_boxes, Algebra.toSubring_eq_top, FreeGroup.closure_range_of, ValueDistribution.logCounting_pow_top, AddCon.toSetoid_top, TensorProduct.quotTensorEquivQuotSMul_comp_mkQ_rTensor, LinearMap.isUnit_iff_range_eq_top, equivShrink_top, CategoryTheory.MorphismProperty.Under.mk_hom, CStarAlgebra.span_nonneg_inter_unitBall, LinearOrderedAddCommGroupWithTop.add_eq_top, AddSubgroup.addSubgroupOf_self, ENNReal.iInf_ennreal, Module.Basis.flag_last, symmDiff_top, NumberField.adjoin_eq_top_of_infinitePlace_lt, MeasureTheory.measure_eq_top_of_subset_compl_sigmaFiniteSetWRT', derivedSeries_zero, Subring.top_prod, Ideal.minimalPrimes_top, Subfield.coe_top, DirectSum.isInternal_submodule_iff_iSupIndep_and_iSup_eq_top, Polynomial.IsSplittingField.splits_iff, AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine_apply, MeasureTheory.eLpNorm_top_piecewise, SSet.Subcomplex.topIso_inv_app_coe, WithTop.not_top_lt, AlgebraicGeometry.instIsOpenImmersionLeftSchemeDiscretePUnitMapWalkingSpanOverTopMorphismPropertySpan, isotypicComponent_eq_top_iff, MeasureTheory.eLpNorm_add_lt_top, CategoryTheory.Subobject.top_arrow_isIso, MeasureTheory.eLpNorm_le_eLpNorm_mul_eLpNorm_top, Submodule.neg_top, IndiscreteTopology.nhds_eq, QuotientAddGroup.subsingleton_quotient_top, Module.jacobson_lt_top, Filter.Subsingleton.atTop_eq, polynomialFunctions.starClosure_topologicalClosure, Coheyting.hnot_boundary, WithTop.eq_top_iff_forall_gt, Subgroup.IsSubnormal.iff_eq_top_or_exists, CommGroup.center_eq_top, AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine_symm_apply, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.exists_ordinal, AddSubgroup.card_eq_iff_eq_top, CategoryTheory.GrothendieckTopology.trivial_covering, hnot_symmDiff_self, EReal.neg_eq_top_iff, AffineEquiv.span_eq_top_iff, Ideal.ideal_prod_prime, AddMonoidHom.ker_fst, AlgebraicGeometry.Scheme.SpecΓIdentity_hom_app, LinearMap.iSup_range_single, smoothSheafCommRing.instLocalRing_stalk, ENNReal.tendsto_rpow_atTop_of_one_lt_base, AffineSubspace.direction_eq_top_iff_of_nonempty, Additive.ofMul_top, AddSubgroup.eq_top_of_card_eq, RootPairing.span_coroot'_eq_top, memℓp_infty, Filter.iSup_pure_eq_top, WithTop.Ioo_coe_top, nhds_false, IsCompl.symmDiff_eq_top, ENNReal.add_eq_top, isLocalRing_top, Nat.Partition.tendsto_order_genFun_term_atTop_nhds_top, Set.Iio_top, BooleanSubalgebra.mem_top, Submodule.comap_fst, ProbabilityTheory.evariance_lt_top_iff_memLp, Metric.ediam_univ_of_noncompact, add_top, WithTop.top_mul, induced_const, Ideal.map_eq_top_or_isMaximal_of_surjective, Submonoid.centralizer_eq_top_iff_subset, LieModule.iSup_genWeightSpace_eq_top', SimpleGraph.Copy.topEmbedding_apply, Ideal.Quotient.subsingleton_iff, RingTheory.Sequence.isRegular_cons_iff, isMax_top, BoxIntegral.HasIntegral.tendsto, QuotSMulTop.equivTensorQuot_naturality_mk, integralClosure_eq_top_iff, ENNReal.pow_lt_top_iff, WithTop.map_eq_top_iff, OrderHom.top_def, interior_convexHull_nonempty_iff_affineSpan_eq_top, contMDiff_infty, CompleteSublattice.top_mem, WithTop.sInf_empty, AlgebraicGeometry.Scheme.isoSpec_inv_preimage_zeroLocus, BooleanSubalgebra.coe_bot, AddAction.aestabilizer_empty, TopHom.coe_top, AddSubgroup.IsSubnormal.lt_normal, thickenedIndicatorAux_lt_top, Coheyting.hnot_eq_top_iff_exists_boundary, Submodule.restrictScalars_top, WithTop.one_lt_top, TopologicalSpace.eq_top_iff_forall_inseparable, Submonoid.topOrderMonoidIso_symm_apply_coe, MulArchimedeanClass.top_eq_mk_iff, CategoryTheory.MorphismProperty.Over.mapCongr_inv_app_left, MeasureTheory.measure_spanningSets_lt_top, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app_assoc, AlgebraicGeometry.PresheafedSpace.Γ_obj_op, EReal.coe_ennreal_mul_top, Submodule.dualAnnihilator_eq_top_iff, compactlySupported_eq_top_of_isCompact, Submodule.orthogonal_eq_bot_iff, MeasureTheory.ae_measure_preimage_mul_right_lt_top, ENNReal.nhds_top', Subgroup.subgroupOf_self, CategoryTheory.Subobject.map_top, Ring.jacobson_smul_top_le, NonUnitalSubsemiring.mem_top, IntermediateField.adjoin_univ, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app, TopCat.GlueData.MkCore.V_id, AffineSubspace.linear_topEquiv, UniformSpace.toTopologicalSpace_top, MeasureTheory.MemLp.meas_ge_lt_top, BoxIntegral.integrable_of_continuousOn, TwoSidedIdeal.matrix_top, MeasureTheory.isFiniteMeasure_iff, ENNReal.toNNReal_mul_top, SimpleGraph.Subgraph.top_induce_pair_connected_of_adj, Equiv.Perm.mclosure_swap_castSucc_succ, isFiniteLength_iff_exists_compositionSeries, ENNReal.tendsto_nhds_top_iff_nnreal, HahnEmbedding.Partial.archimedeanClassMk_eq_iff, OpenSubgroup.toSubgroup_top, ValuationSubring.toSubring_top, Sylow.normalizer_sup_eq_top', Ideal.primeHeight_lt_top, Submodule.pow_smul_top_le, AddGroup.fg_iff', MeasureTheory.MemLp.exist_eLpNorm_sub_le, CategoryTheory.Subfunctor.Subpresheaf.preimage_eq_top_iff, groupHomology.cycles₁_eq_top_of_isTrivial, Submodule.biSup_comap_subtype_eq_top, NumberField.isTotallyReal_top_iff, not_lt_top_iff, symmDiff_top', lt_top_of_lt, CategoryTheory.Sieve.top_apply, WithTop.untopD_top, UpperSet.coe_eq_empty, ValueDistribution.logCounting_add_top_le, QuotSMulTop.map_comp_mkQ, Dynamics.netMaxcard_infinite_iff, ContinuousMap.concatCM_left, MulAction.BlockMem.coe_top, ENNReal.top_div_coe, LinearMap.range_domRestrict_eq_range_iff, Algebra.EssFiniteType.adjoin_mem_finset, SimpleGraph.induce_eq_coe_induce_top, ENat.sub_ne_top_iff, CategoryTheory.MorphismProperty.IsMultiplicative.instTop, Submonoid.top_prod, ENNReal.zpow_lt_top, EReal.top_mul_coe_of_pos, AlgebraicGeometry.Scheme.Hom.preimage_top, Polynomial.IsSplittingField.adjoin_rootSet, MeasureTheory.SimpleFunc.measure_preimage_lt_top_of_integrable, TensorProduct.tensorQuotEquivQuotSMul_comp_mkQ_lTensor, CategoryTheory.MorphismProperty.Over.pullbackMapHomPullback_app, AlgebraicGeometry.Scheme.isoSpec_hom, AlgebraicGeometry.Scheme.ι_toIso_inv_assoc, LieIdeal.coe_killingCompl_top, Ideal.relNorm_top, LinearMap.span_singleton_sup_orthogonal_eq_top, Submodule.span_range_inclusion_restrictScalars_eq_top, analyticOrderAt_eq_top, NonemptyInterval.dual_top, Polynomial.IsDistinguishedAt.degree_eq_coe_lift_order_map, SimpleGraph.Subgraph.le_induce_top_verts, Monoid.FG.fg_top, SchwartzMap.eLpNorm_lt_top, BooleanSubalgebra.coe_eq_univ, HahnEmbedding.Seed.baseEmbedding_strictMono, AlgebraicGeometry.IsAffineOpen.self_le_iSup_basicOpen_iff, EReal.add_lt_top, BooleanSubalgebra.coe_top, AlgebraicGeometry.Proj.basicOpenToSpec_app_top, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, NonUnitalSubalgebra.prod_top, ringKrullDim_quotSMulTop_succ_eq_ringKrullDim_of_mem_jacobson, ImplicitFunctionData.range_leftDeriv, NormedSpace.exp_hasFPowerSeriesOnBall, WithLp.prod_norm_toLp, AlgebraicGeometry.Scheme.Hom.image_top_eq_opensRange, WithTop.preimage_coe_top, ext_iff, lp.inftyCStarRing, AddSubmonoid.coe_top, CategoryTheory.MorphismProperty.Over.mk_hom, EReal.top_mul_coe_ennreal, CategoryTheory.MorphismProperty.Over.pullback_obj_left, Ne.lt_top', CategoryTheory.MorphismProperty.Over.map_map_left, BoxIntegral.unitPartition.integralSum_eq_tsum_div, Submonoid.mrange_inl_sup_mrange_inr, PowerSeries.order_finite_iff_ne_zero, Matroid.eRank_eq_top, FiniteArchimedeanClass.val_mk, ValueDistribution.logCounting_top, MeasurableSpace.map_const, bot_covBy_top, MeasureTheory.Integrable.measure_ge_lt_top, LeftInvariantDerivation.lift_add, ExteriorAlgebra.ιMulti_span, Ideal.isIdempotentElem_iff_eq_bot_or_top, top_symmDiff, MonoidHom.ker_eq_top_iff, NonUnitalStarAlgebra.coe_top, AlgebraicGeometry.Scheme.toSpecΓ_naturality_assoc, ContDiffMapSupportedIn.iteratedFDerivLM_eq_withOrder, Ideal.sup_eq_top_iff_isCoprime, Filter.instNeBotTop, SSet.Subcomplex.degenerate_eq_top_iff, AdicCompletion.pi_apply_coe, SSet.Truncated.HomotopyCategory.multiplicativeClosure_morphismPropertyHomMk, MeasureTheory.measure_eq_top_of_subset_compl_sigmaFiniteSetWRT, IsCompact.exists_open_superset_measure_lt_top', Filter.Germ.const_top, Set.Icc_top, Sublocale.top_mem, Metric.ediam_eq_top_iff_unbounded, AlgebraicGeometry.SurjectiveOnStalks.iff_of_isAffine, NonUnitalSubring.comap_top, contDiffOn_infty, AlgebraicGeometry.SpecMap_ΓSpecIso_hom, MeasureTheory.measure_lt_top, Filter.limsup_top_eq_ciSup, Subalgebra.center_eq_top, EMetric.isClosed_ball_top, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isComplex, FiniteArchimedeanClass.mem_ballAddSubgroup_iff, Ideal.isPrime_ideal_prod_top', RingTheory.Sequence.isWeaklyRegular_iff_Fin, ENat.floor_top, InformationTheory.klDiv_eq_top_iff, SSet.iSup_skeleton, Subfield.relrank_top_left, Subring.center_eq_top, RingHom.rangeS_toSubmonoid, ENNReal.top_rpow_def, tangentBundle_model_space_coe_chartAt, meromorphicOrderAt_eq_top_iff, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap, Submodule.span_singleton_eq_top_iff, alternatingGroup.normalClosure_swap_mul_swap_five, PrimeSpectrum.iSup_basicOpen_eq_top_iff, AdicCompletion.val_add_apply, IsNormalClosure.adjoin_rootSet, SimpleGraph.chromaticNumber_top, PartENat.ofNat_lt_top, Filter.nhds_top, ENNReal.iSup_ne_top, AffineBasis.tot', ENNReal.continuousOn_sub, Filter.map_top, Order.krullDim_eq_top, IsBoundedBilinearMap.isBigO', ENNReal.iInter_Ici_coe_nat, MonoidHom.mrange_eq_map, himp_top, FirstOrder.Language.BoundedFormula.IsQF.top, AdicCompletion.smul_eval, CategoryTheory.Localization.Construction.morphismProperty_eq_top', EReal.tendsto_coe_atTop, ModuleCat.smulShortComplex_X₃_isAddCommGroup, TopologicalSpace.Opens.isOpenEmbedding_obj_top, AlgebraicGeometry.LocallyRingedSpace.Γ_obj_op, LeftInvariantDerivation.lift_smul, Subgroup.pi_top, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_appTop_coord, Fin.top_eq_last, NonUnitalSubsemiring.center_eq_top, MulAction.isBlock_top, AddSubsemigroup.coe_top, Monoid.Coprod.mrange_swap, MeasureTheory.eLpNormEssSup_lt_top_of_ae_enorm_bound, ENNReal.log_top, SmoothPartitionOfUnity.sum_finsupport', UpperSet.Ioi_top, MeasureTheory.Integrable.measure_lt_lt_top, ValueDistribution.logCounting_mul_top_eventuallyLE, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over_assoc, Ideal.toCotangent_range, NonUnitalSubring.mem_top, AddMonoidHom.range_eq_map, Subgroup.op_top, WithTop.tendsto_untop, Monoid.Coprod.closure_range_inl_union_inr, RootPairing.IsIrreducible.eq_top_of_invtSubmodule_coreflection, Submodule.rank_le_spanRank, ValueDistribution.proximity_inv, bihimp_eq_right, SSet.Subcomplex.eq_top_iff_of_hasDimensionLT, EReal.bot_div_of_neg_ne_bot, AddAction.aestabilizer_univ, AlgebraicGeometry.Scheme.isoSpec_hom_naturality, CategoryTheory.MorphismProperty.Over.Hom.ext_iff, AddHom.srange_eq_top_of_surjective, BoxIntegral.IntegrationParams.eventually_isPartition, SimpleGraph.edgeSet_top, SimpleGraph.completeMultipartiteGraph.topEmbedding_apply_fst, ValuationSubring.eq_top_iff, Subsemiring.prod_top, iInf₂_eq_top, Group.IsNilpotent.nilpotent', AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv_assoc, disjoint_top, Ideal.adic_module_basis, MeasureTheory.hasFiniteIntegral_def, MeasureTheory.measure_inter_lt_top_of_right_ne_top, lowerClosure_univ, Sym2.fromRel_top, SimpleGraph.edist_eq_top_of_not_reachable, CategoryTheory.Functor.isLeftAdjoint_iff_rightAdjointObjIsDefined_eq_top, HahnSeries.orderTop_of_subsingleton, essInf_measure_zero, MeasureTheory.Measure.exists_subset_measure_lt_top, HahnEmbedding.Partial.toOrderAddMonoidHom_apply, Polynomial.SplittingFieldAux.adjoin_rootSet, MeasureTheory.memLp_const_iff, Algebra.GrothendieckAddGroup.neg_mk, SimpleGraph.Subgraph.verts_top, WithTop.mul_top, Polynomial.isPrimitive_iff_contentIdeal_eq_top, RingCon.subsingleton_quotient, MeasureTheory.ae_eq_top, Finsupp.supported_univ, LinearOrderedAddCommGroup.negGen_eq_of_top, EReal.top_mul_of_pos, Ideal.jacobson_eq_top_iff, AddSubsemigroup.topEquiv_apply, EMetric.infEdist_empty, SimpleGraph.support_top_of_nontrivial, CategoryTheory.Sieve.generate_top, WithBot.coe_eq_top, SimpleGraph.neighborFinset_completeEquipartiteGraph, ringKrullDim_quotSMulTop_succ_eq_ringKrullDim, Submonoid.topEquiv_symm_apply_coe, Submodule.topEquiv_apply, SSet.Subcomplex.topIso_inv_ι, AlgebraicGeometry.Scheme.toSpecΓ_naturality, ENNReal.tsum_const_eq_top_of_ne_zero, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst, AlgebraicGeometry.Scheme.Hom.quasiFiniteLocus_eq_top, MeasureTheory.Measure.mem_cofinite, KaehlerDifferential.span_range_map_derivation_of_isLocalization, sSup_isotypicComponents, AddSubgroup.Normal.eq_bot_or_eq_top, IntermediateField.fixingSubgroup_top, ENNReal.range_coe, AddSubsemigroup.op_top, AffineSubspace.coe_eq_univ_iff, Filter.top_add_of_nonneg, CategoryTheory.Sieve.equalizer_self, WithBot.eq_top_iff_forall_ge, Profinite.NobelingProof.GoodProducts.spanFin, TopologicalSpace.Opens.mk_univ, WithTop.forall, AddAction.stabilizer_finset_univ, SimpleGraph.toTopEdgeLabeling_get, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_counit_app, top_bihimp, SimpleGraph.cycleGraph_two_eq_top, hasFPowerSeriesOnBall_const, CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mk, HahnSeries.orderTop_of_Subsingleton, ContDiffMapSupportedIn.seminorm_le_iff, Submodule.map_top, least_ascending_central_series_length_eq_nilpotencyClass, Cardinal.ofENat_lt_aleph0, AlgebraicGeometry.LocallyRingedSpace.Γ_Spec_left_triangle, ENNReal.not_top_le_coe, SimpleGraph.preconnected_iff_reachable_eq_top, inf_top_eq, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp_f, AddSubmonoid.closure_univ, AddSubmonoid.subPairs_comap, LatticeHom.withTopWithBot'_toFun, LieSubmodule.map_incl_top, Codisjoint.top_le, Finset.Ici_eq_Icc, AlgebraicGeometry.RingedSpace.mem_top_basicOpen, IsCoatom.sup_eq_top_of_ne, MeasureTheory.lintegral_eq_top_of_measure_eq_top_ne_zero, MeasureTheory.Measure.count_apply_eq_top, Submodule.range_mkQ, PMF.toOuterMeasure_caratheodory, IsSolvable.commutator_lt_top_of_nontrivial, not_top_lt, BoxIntegral.Prepartition.isPartitionTop, Filter.Eventually.lt_top_iff_ne_top, EReal.nhds_top', Fin.rev_top, IntermediateField.relfinrank_top_right, Nat.addSubmonoidClosure_one, Subgroup.top_prod, PartENat.top_eq_none, AddSubgroup.topCharacteristic, NonUnitalSubring.topEquiv_symm_apply_coe, Submodule.spanRank_range_le, NonUnitalRingHom.eqLocus_same, EReal.canLift, Order.succ_top, Order.coheight_eq_coe_add_one_iff, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone_pt, IndiscreteTopology.eq_top, MeasureTheory.setLIntegral_lt_top_of_le_nnreal, QuotSMulTop.map_surjective, Finset.Icc_bot_top, AddAction.stabilizer_univ, ENNReal.csupr_ne_top, Differentiable.hasFPowerSeriesOnBall, liminf_eq_top, FiniteMulArchimedeanClass.withTopOrderIso_apply_coe, Set.Ioi_top, UpperSet.prod_le_prod_iff, CategoryTheory.MorphismProperty.instRespectsIsoTop, LeftInvariantDerivation.comp_L, AlgebraicGeometry.Scheme.Hom.toPartialMap_domain, WithTop.LinearOrderedAddCommGroup.sub_top, egauge_zero_left, CompleteLinearOrder.top_sdiff, HahnEmbedding.Partial.isWF_support_evalCoeff, Submodule.toConvexCone_top, ENNReal.Ioo_zero_top_eq_iUnion_Ico_zpow, FirstOrder.Language.DefinableSet.mem_top, HahnEmbedding.Partial.orderTop_eq_iff, Submodule.localized'_top, ENat.map_top, fixingAddSubgroup_empty, Mathlib.Tactic.ENatToNat.not_lt_top, LinearIndependent.span_eq_top_of_card_eq_finrank', CategoryTheory.MorphismProperty.instFaithfulOverTopOverForget, LinearGrowth.linearGrowthInf_top, AlgebraicGeometry.IsAffineOpen.isoSpec_inv, ENat.top_epow, AddMonoidHom.mrange_eq_top, ArchimedeanClass.top_eq_mk_iff, ENNReal.toNNReal_eq_toNNReal_iff, CategoryTheory.MorphismProperty.IsLocalAtSource.top, AlgebraicGeometry.Scheme.Γ_obj, CategoryTheory.Presieve.isSheafFor_top_sieve, LieSubmodule.span_univ, AlgebraicGeometry.isLocallyNoetherian_iff_of_affine_openCover, Matroid.eRank_eq_top_iff, Subgroup.map_top_of_surjective, compl_lt_self, SimpleGraph.IsSRGWith.top, AlgebraicGeometry.Scheme.IdealSheafData.instIsEmptyCarrierCarrierCommRingCatSubschemeTop, Ideal.eq_bot_or_top, Submodule.eq_top_of_nonempty_interior', SSet.hasDimensionLT_subcomplex_top_iff, Monoid.IsTorsion.torsionMulEquiv_apply, AddSubmonoid.op_eq_top, MeasureTheory.measure_eq_zero_or_top_of_subset_compl_sigmaFiniteSet, StieltjesFunction.measure_Iic_of_tendsto_atBot_atBot, Subgroup.IsSubnormal.exists_normal_and_le_and_lt_top_of_ne, IntermediateField.restrictScalars_top, SimpleGraph.degree_completeEquipartiteGraph, nhds_top_basis_Ici, Fintype.IsSimpleOrder.univ, MeasureTheory.Content.lt_top, LieSubmodule.mk_eq_top_iff, Subgroup.map_equiv_top, BoundedContinuousFunction.lintegral_lt_top_of_nnreal, finite_integral_rpow_sub_one_pow_aux, CStarAlgebra.span_nonneg, EuclideanGeometry.Sphere.orthRadius_center, MonoidHom.range_eq_map, Representation.invtSubmodule.coe_top, EReal.preimage_coe_Ioo_top, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_id, Finset.top_eq_univ, instIsManifoldRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, SmoothBumpCovering.toSmoothPartitionOfUnity_apply, TopologicalSpace.isOpen_top_iff, OpenSubgroup.mem_top, Function.hasTemperateGrowth_iff_isBigO, Hausdorffification.instIsHausdorff, AlgebraicGeometry.IsLocallyArtinian.isArtinianRing_of_isAffine, ENNReal.iUnion_Iic_coe_nat, AlgebraicGeometry.StructureSheaf.toPushforwardStalkAlgHom_apply, CommRing.relPic_eq_top, minSmoothness_eq_infty, AlgebraicGeometry.Scheme.preimage_basicOpen_top, Fin.top_eq_zero, MvPolynomial.adjoin_range_X, Submodule.traceDual_top', sup_top_eq, ProbabilityTheory.Kernel.rnDeriv_eq_top_iff', Subring.eq_top_iff', AlgebraicGeometry.Scheme.ΓSpecIso_inv, Subsemigroup.topEquiv_symm_apply_coe, MeasureTheory.condExpIndSMul_empty, SmoothPartitionOfUnity.contDiffAt_finsum, Order.krullDim_int, NonUnitalAlgebra.range_id, CategoryTheory.MorphismProperty.Over.map_comp, Set.Finite.encard_lt_top, PrimeSpectrum.vanishingIdeal_eq_top_iff, LieSubmodule.comap_incl_eq_top, MeasureTheory.measure_union_lt_top_iff, IntermediateField.mem_top, ENat.card_lt_top_of_finite, Submonoid.comap_top, CategoryTheory.MorphismProperty.Comma.instFullTopCommaForget, AddGroup.fg_iff, AlgebraicGeometry.Scheme.isoSpec_hom_naturality_assoc, Subring.card_top, AddAction.stabilizer_empty, AdicCompletion.mkₐ_apply_coe, AlgebraicGeometry.Scheme.isoSpec_inv_image_zeroLocus, Ideal.span_singleton_one, Equiv.Perm.closure_isCycle, Filter.HasBasis.prod_top, Submodule.torsionBy_torsionBy_eq_top, EReal.tendsto_toReal_atTop, EReal.top_add_of_ne_bot, Field.primitive_element_iff_algHom_eq_of_eval', Ideal.span_eq_top_iff_finite, Ideal.eq_top_of_isUnit_mem, Algebra.GrothendieckAddGroup.instFG, Module.End.genEigenspace_top_eq_maxUnifEigenspaceIndex, Filter.HasBasis.eq_top_iff, codisjoint_iff, BoxIntegral.Box.measure_coe_lt_top, AddSubgroup.map_top_of_surjective, CategoryTheory.GrothendieckTopology.top_mem, UpperSet.notMem_top, ENNReal.iSup_coe_lt_top, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app', Flag.top_mem, StieltjesFunction.measure_univ_of_tendsto_atTop_atTop, LieIdeal.le_killingCompl_top_of_isLieAbelian, eHolderNorm_lt_top, Ideal.span_single_eq_top, Ideal.Quotient.span_singleton_one, WithTop.untop₀_top, NonUnitalSubring.closure_univ, MeasureTheory.Integrable.measure_gt_lt_top, Subgroup.closure_closure_coe_preimage, Submodule.starProjection_top', AdicCompletion.isAdicCauchy_iff, Monoid.CoprodI.mclosure_iUnion_range_of, PresentedMonoid.closure_range_of, LinearMap.BilinForm.orthogonal_eq_bot_iff, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen_topIso_inv, BoxIntegral.IntegrationParams.hasBasis_toFilteriUnion_top, IntermediateField.relrank_top_right, IsCoercive.range_eq_top, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ, alternatingGroup.normalClosure_finRotate_five, LinearMap.range_eq_top_of_cancel, UpperSet.prod_top, AffineBasis.affineSpan_eq_top_of_toMatrix_left_inv, ValueDistribution.isBigO_characteristic_sub_characteristic_shift, ProbabilityTheory.Kernel.ae_lt_top_of_comp_ne_top, CategoryTheory.ObjectProperty.topEquivalence_unitIso, LieAlgebra.radical_eq_top_of_isSolvable, AlgebraicGeometry.Scheme.toSpecΓ_preimage_zeroLocus, LieAlgebra.IsKilling.invtSubmoduleToLieIdeal_top, CategoryTheory.MorphismProperty.Over.instPreservesFiniteLimitsTopPullback, WithTop.ofDual_apply_top, BoxIntegral.Box.measure_Icc_lt_top, Finset.truncatedSup_empty, IsLocalRing.map_tensorProduct_mk_eq_top, AddSubgroup.pi_empty, AdicCompletion.val_sum, AddSubgroup.isComplement'_top_bot, Algebra.coe_top, MeasureTheory.Measure.rnDeriv_lt_top, SimpleGraph.edist_top, Ideal.eq_jacobson_iff_sInf_maximal', TopologicalSpace.Opens.inclusion'_top_functor, CongruenceSubgroup.Gamma_one_top, SimpleGraph.cycleGraph_three_eq_top, ENat.iInf_coe_lt_top, MeasureTheory.Measure.mkMetric_top, Set.instNonemptyTop, contDiffOn_omega_iff_analyticOn, Subsemiring.unop_eq_top, ENat.ceil_lt_top, Ideal.comap_eq_top_iff, UpperSet.top_prod, Set.Ici_top, ENNReal.iSup_natCast, SSet.Subcomplex.eq_top_iff_contains_nonDegenerate, max_top_right, Subgroup.top_toSubmonoid, AlgebraicGeometry.Scheme.fromSpecStalk_appTop, MonoidHom.mrange_eq_top, MeasureTheory.AEContinuous.hasBoxIntegral, Submonoid.LocalizationMap.top_injective_iff, Subgroup.isComplement'_bot_right, MeasureTheory.Lp.boundedContinuousFunction_topologicalClosure, MeasureTheory.measure_univ_of_isMulLeftInvariant, Subalgebra.unop_top, ENNReal.smul_top, LinearMap.range_rangeRestrict, isJacobsonRing_iff_sInf_maximal, BoxIntegral.Prepartition.compl_top, ProperCone.innerDual_zero, top_fixedByFinite, ENNReal.top_mul_top, Finpartition.top_isEquipartition, AlgebraicGeometry.PresheafedSpace.Γ_map_op, InformationTheory.klDiv_zero_right, LieAlgebra.IsSimple.eq_top_of_isAtom, NonUnitalSubsemiring.eq_top_iff', Metric.emetric_ball_top, InfTopHomClass.map_top, CategoryTheory.Cat.FreeRefl.multiplicativeClosure_morphismPropertyHomMk, ValueDistribution.characteristic_sub_characteristic_eq_proximity_sub_proximity, Ideal.FiniteHeight.eq_top_or_height_ne_top, Order.Ideal.IsProper.top_notMem, ENNReal.one_lt_top, IsFoelner.eventually_meas_ne_top, instLieGroupRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, Order.pred_top_le_iff, Submodule.torsion_torsion_eq_top, BoxIntegral.Prepartition.biUnion_top, AddHom.srange_eq_top_iff_surjective, Convex.span_tangentConeAt, Submonoid.mrange_inr, EReal.top_sub_bot, Polynomial.trailingDegree_zero, Asymptotics.isBigO_top, Algebra.GrothendieckGroup.lift_symm_apply, IsHausdorff.iInf_pow_smul, Finpartition.parts_top_subset, AlgebraicGeometry.Scheme.id_appTop, contDiffOn_infty_iff_fderivWithin, Module.isTorsionBySet_iff_torsionBySet_eq_top, LieAlgebra.instIsSolvableSubtypeMemLieSubalgebraTop, NumberField.instIsTotallyRealSubtypeMemSubfieldTop, LinearMap.ker_eq_bot_iff_range_eq_top_of_finrank_eq_finrank, sSup_compact_eq_top, Module.length_top, SymmetricPower.span_tprod_eq_top, Associates.factors_zero, MeasureTheory.laverage_lt_top, NonUnitalSubring.center_eq_top, Submodule.span_range_inclusion_eq_top, LinearOrderedAddCommGroupWithTop.sub_top, isGLB_empty, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop_assoc, Submodule.prod_top, LeftInvariantDerivation.evalAt_coe, MeasureTheory.measure_singleton_lt_top, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_unit_app, Codisjoint.eq_top_of_le, ClusterPt.top, ENNReal.ofReal_lt_top, Subgroup.pi_empty, Convex.interior_nonempty_iff_affineSpan_eq_top, AddSubgroup.normalizer_eq_top_iff, Submodule.map_mkQ_eq_top, MeasureTheory.Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_group, ValueDistribution.logCounting_sub_const, Filter.eventually_top, EReal.range_coe_eq_Ioo, Polynomial.adjoin_rootSet_eq_range, Submodule.eq_top_of_disjoint, CategoryTheory.Presheaf.equalizerSieve_self_eq_top, ENNReal.toReal_mul_top, ProbabilityTheory.IsFiniteKernel.bound_lt_top, CategoryTheory.TransfiniteCompositionOfShape.iic_isColimit, HahnEmbedding.IsPartial.strictMono, AddSubgroup.closure_univ, WithTop.eq_top_iff_forall_ne, Multiset.inf_zero, ClosedSubmodule.bot_orthogonal_eq_top, Subring.unop_top, AlgebraicGeometry.Scheme.fromSpecStalk_toSpecΓ, Module.supportDim_quotSMulTop_succ_eq_of_notMem_minimalPrimes_of_mem_maximalIdeal, Submodule.map_eq_top_iff, LieSubmodule.map_incl_lt_iff_lt_top, AlgebraicGeometry.Scheme.ker_toSpecΓ, ValueDistribution.characteristic_sub_characteristic_inv_of_ne_zero, TopCat.Presheaf.map_germ_eq_Γgerm, SimpleGraph.ConnectedComponent.odd_matches_node_outside, Algebra.top_toSubmodule, AddSubmonoid.map_equiv_top, Set.eq_empty_or_encard_eq_top_or_encard_diff_singleton_lt, Subgroup.centralizer_eq_top_iff_subset, Set.encard_eq_top_iff, BoxIntegral.integrable_of_bounded_and_ae_continuous, meromorphicOrderAt_const_natCast, SSet.Subcomplex.preimage_range, AlgebraicGeometry.Scheme.ker_of_isAffine, Submodule.isTorsion'_iff_torsion'_eq_top, AlgebraicGeometry.IsAffineOpen.algebraMap_Spec_obj, AlgebraicGeometry.isBasis_basicOpen, Digraph.toSimpleGraphStrict_top, ENat.toENNReal_top, Filter.add_top_of_nonneg, SmoothPartitionOfUnity.le_one, instContMDiffVectorBundleTopWithTopENatTangentSpaceOfIsManifold, Filter.tendsto_atTop_pure, ENat.eq_top_iff_forall_gt, Polynomial.contentIdeal_eq_top_iff_forall_gaussNorm_eq_one, MeasureTheory.eLpNorm_le_eLpNorm_top_mul_eLpNorm, AddSubgroup.isComplement'_top_left, MeasureTheory.Measure.lintegral_rnDeriv_lt_top, map_eq_top_iff, AddSubsemigroup.srange_snd, AddSubgroup.map_equiv_top, KaehlerDifferential.span_range_derivation, ModuleCat.range_eq_top_of_epi, SimpleGraph.Subgraph.edgeSet_top, AlgebraicGeometry.Scheme.Γevaluation_naturality_apply, Submonoid.closure_univ, WithLp.prod_edist_eq_sup, ProbabilityTheory.tsum_prob_mem_Ioi_lt_top, FiniteMulArchimedeanClass.mem_ballSubgroup_iff, exists_spanning_measurableSet_le, MulHom.srange_eq_top_iff_surjective, CliffordAlgebra.adjoin_range_ι, AlgebraicGeometry.Flat.flat_and_surjective_iff_faithfullyFlat_of_isAffine, AddSubmonoid.unop_top, WithTop.add_lt_top, Dynamics.coverMincard_finite_of_isCompact_uniformContinuous, ProbabilityTheory.Kernel.ae_kernel_lt_top, MeasureTheory.lintegral_edist_lt_top, ContinuousMultilinearMap.hasFTaylorSeriesUpTo_iteratedFDeriv, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top_assoc, BoxIntegral.BoxAdditiveMap.volume_apply, LieModule.lowerCentralSeries_succ, PointedContMDiffMap.smul_def, AlgebraicGeometry.LocallyRingedSpace.coe_toΓSpecSheafedSpace_hom_base_hom_apply_asIdeal, compactlySupported_eq_top, Sylow.orbit_eq_top, AdicCompletion.range_eval, Subgroup.normal_top, Ideal.Quotient.smul_top, Codisjoint.eq_top_of_self, ProbabilityTheory.Kernel.rnDeriv_ne_top, EReal.abs_top, Polynomial.Splits.adjoin_rootSet_eq_range, CategoryTheory.MorphismProperty.Over.mapId_inv_app_left, BoxIntegral.integral_nonneg, ArchimedeanClass.ballAddSubgroup_top, Setoid.top_def, MeromorphicOn.isClopen_setOf_meromorphicOrderAt_eq_top, codisjoint_self, AlgebraicGeometry.isIntegral_appTop_of_universallyClosed, IntermediateField.lift_top, LieAlgebra.cartan_sup_iSup_rootSpace_eq_top, ENat.map_eq_top_iff, min_top_left, SSet.Truncated.liftOfStrictSegal.naturalityProperty_eq_top, memℓp_infty_iff, AddSubgroup.op_top, ENNReal.isOpen_ne_top, WithTop.sub_ne_top_iff, AdicCompletion.val_neg_apply, WithTop.LinearOrderedAddCommGroup.sub_eq_top_iff, iSup_eq_top, CStarAlgebra.span_nonneg_inter_unitClosedBall, Interval.dual_top, smoothSheafCommRing.isUnit_stalk_iff, Ideal.eq_bot_of_minimalPrimes_eq_empty, contMDiff_vectorSpace_iff_contDiff, FiniteArchimedeanClass.liftOrderHom_mk, MeasureTheory.hasFiniteIntegral_iff_edist, Real.volume_Iio, LinearIsometryEquiv.reflections_generate, List.min_le_of_le, AlgebraicGeometry.ΓSpec.adjunction_counit_app, MeasureTheory.Measure.InnerRegularWRT.of_sigmaFinite, ContractingWith.edist_efixedPoint_lt_top', WithLp.prod_isometry_ofLp_infty, isCoatomic_iff, AlgebraicGeometry.tilde.isoTop_hom, CategoryTheory.Subfunctor.range_eq_top, borel_eq_top_of_discrete, SSet.hasDimensionLT_iff, Module.Quotient.mk_smul_mk, FiniteMulArchimedeanClass.mem_closedBallSubgroup_iff, ClosedSubmodule.top_orthogonal_eq_bot, SimpleGraph.preconnected_top, Sublattice.top_prod_top, MeasureTheory.SimpleFunc.exists_lt_lintegral_simpleFunc_of_lt_lintegral, OrderTop.le_top, ValueDistribution.characteristic_sub_characteristic_inv_at_zero, Associates.factors_subsingleton, AntitoneOn.memLp_top, RestrictedProduct.continuous_rng_of_top, contDiff_bernoulliFun, ProbabilityTheory.Kernel.rnDeriv_eq_top_iff, Submodule.top_toAddSubgroup, BoundedContinuousFunction.memLp_top, WithBot.toDual_bot, AlgebraicGeometry.instHasOfPostcompPropertySchemeQuasiSeparatedTopMorphismProperty, CoheytingHomClass.map_top, LeftInvariantDerivation.map_zero, EuclideanSpace.instIsManifoldSphere, Filter.isMeasurablyGenerated_top, PowerSeries.order_monomial, Filter.principal_univ, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop, HahnSeries.orderTop_eq_top_iff, ENat.top_sub_one, HahnEmbedding.ArchimedeanStrata.archimedeanClassMk_of_mem_stratum, LinearMap.IsSymmetric.iSup_iInf_eq_top_of_commute, IsNoetherianRing.exists_relSeries_isQuotientEquivQuotientPrime, EReal.toENNReal_eq_top_iff, CategoryTheory.Subfunctor.Subpresheaf.image_top, top_isPrincipal, Ideal.Filtration.top_N, ENNReal.mul_rpow_eq_ite, TangentBundle.coordChange_model_space, MeasureTheory.hittingAfter_def, MvPolynomial.restrictSupport_univ, ValueDistribution.proximity_sum_top_le, AddSubsemigroup.topEquiv_symm_apply_coe, WithTop.toDualBotEquiv_symm_top, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec_assoc, PointedCone.dual_empty, LowerSet.mem_top, GradedAlgebra.exists_finset_adjoin_eq_top_and_homogeneous, AlgebraicGeometry.Γ_restrict_isLocalization, fdifferential_apply, PartENat.not_dom_iff_eq_top, IntermediateField.restrictScalars_eq_top_iff, Matrix.toBlock_mul_eq_mul, Set.Icc_bot_top, not_infPrime_top, coe_ringEquiv_lpBCF, HahnEmbedding.IsPartial.truncLT_mem_range, Subsemigroup.topEquiv_toMulHom, IsUpperSet.top_mem, Complementeds.coe_top, SupHom.coe_top, WithTop.iInf_coe_eq_top, WithLp.prod_norm_ofLp, ENNReal.tsum_top, Module.length_eq_top_iff_infiniteDimensionalOrder, SmoothBumpFunction.contMDiffAt, CategoryTheory.top_apply, NonUnitalSubring.topEquiv_apply, FirstOrder.Language.Substructure.realize_formula_top, EReal.mul_top_of_neg, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec, upperCentralSeries_nilpotencyClass, WithLp.prod_norm_eq_idemFst_sup_idemSnd, ENNReal.tendsto_rpow_at_top, LieModule.IsTriangularizable.maxGenEigenspace_eq_top, SimpleGraph.egirth_eq_top, CategoryTheory.MorphismProperty.Over.mapCongr_hom_app_left, LieSubmodule.Quotient.range_mk', MeasureTheory.lpMeasToLpTrimLie_symm_indicator, CategoryTheory.MorphismProperty.IsLocalAtTarget.top, AlgebraicGeometry.ΓSpecIso_obj_hom, LinearOrderedAddCommGroupWithTop.neg_pos, DFinsupp.iSup_range_lsingle, Subring.toSubsemiring_top, AdicCompletion.transitionMap_comp_eval, CategoryTheory.GrothendieckTopology.Cover.preOneHypercover_sieve₁, sup_hnot_self, SimpleGraph.fromEdgeSet_not_isDiag, SSet.skeleton_obj_eq_top, Set.Ioc.coe_top, Set.encard_eq_top, AlgebraicGeometry.Spec.germ_stalkMapIso_hom_assoc, ModuleCat.smulShortComplex_g, WithBot.top_eq_coe, ENNReal.eq_top_of_forall_nnreal_le, Function.Surjective.filter_map_top, AlgebraicGeometry.Scheme.Hom.preimage_basicOpen_top, PartENat.add_top, LowerSet.coe_top, ENNReal.tendsto_pow_atTop_nhds_top_iff, IntermediateField.bot_eq_top_of_finrank_adjoin_eq_one, SimpleGraph.ConnectedComponent.top_supp_eq_univ, CoxeterSystem.subgroup_closure_range_simple, AddSubmonoid.exponent_top, QuotientGroup.subgroup_eq_top_of_subsingleton, stabilizer_empty_eq_top, Setoid.mk_eq_top, MeasureTheory.OuterMeasure.comap_top, SmoothBumpCovering.sum_toSmoothPartitionOfUnity_eq, CategoryTheory.Sieve.overEquiv_top, Submodule.isOrtho_top_left, Submonoid.exists_minimal_closure_eq_top, ProbabilityTheory.iIndep_comap_mem_iff, Subgroup.normalizer_eq_top, Field.exists_primitive_element_of_finite_bot, Polynomial.sup_aeval_range_eq_top_of_isCoprime, PiLp.dist_eq_iSup, Set.encard_lt_top_iff, CategoryTheory.GrothendieckTopology.close_eq_top_iff_mem, TopologicalSpace.Opens.functor_obj_map_obj, smoothSheafCommRing.evalHom_germ, WithTop.coe_covBy_top, CategoryTheory.Sieve.arrows_eq_top_iff, coe_lpBCFₗᵢ, MulAction.stabilizer_finset_univ, MvPolynomial.map_restrict_dom_evalₗ, MeasureTheory.ae_measure_preimage_mul_right_lt_top_of_ne_zero, Submodule.subsingleton_quotient_iff_eq_top, MeasureTheory.SimpleFunc.memLp_iff, Submodule.snd_map_snd, AddSubsemigroup.top_prod_top, L_mul, Subgroup.coe_top, TopHom.map_top', FreeMonoid.closure_range_of, LeftInvariantDerivation.coe_sub, LieSubmodule.top_toSubmodule, AlgebraicGeometry.IsAffineOpen.self_le_basicOpen_union_iff, AlgebraicGeometry.exists_appTop_π_eq_of_isAffine_of_isLimit, ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall, CategoryTheory.ObjectProperty.instIsSerreClassTop, Finset.Iic_top, exists_compositionSeries_of_isNoetherian_isArtinian, Equiv.Perm.closure_cycle_coprime_swap, lp.infty_coeFn_mul, ENNReal.sub_eq_top_iff, CategoryTheory.Sieve.arrows_top, AddGroup.rank_spec, Submodule.jacobson_smul_lt_top, Filter.top_pow, QuotientAddGroup.subsingleton_iff, QuotientAddGroup.rightRel_eq_top, EReal.bot_mul_bot, LieAlgebra.IsSemisimple.sSup_atoms_eq_top, AlgebraicGeometry.Scheme.OpenCover.iSup_opensRange, MeasureTheory.Measure.MeasureDense.indicatorConstLp_subset_closure, IsCoatom.Ici_eq, NonUnitalSubring.toAddSubgroup_eq_top, AddSubmonoid.mem_top, AddCommGrpCat.range_eq_top_of_epi, MeasureTheory.memLp_const_iff_enorm, AffineSubspace.mem_top, ProbabilityTheory.evariance_eq_top_iff, Algebra.bijective_algebraMap_iff, Subalgebra.topEquiv_apply, SimpleGraph.chromaticNumber_eq_card_iff, CategoryTheory.topologyOfClosureOperator_sieves, Set.einfsep_eq_top_iff, hnot_top, MeasureTheory.levyProkhorovEDist_lt_top, Field.exists_primitive_element_of_finite_top, CategoryTheory.Subobject.isIso_top_arrow, Submodule.dualCoannihilator_bot, SSet.stdSimplex.face_obj, Group.rank_spec, AddSubmonoid.exists_minimal_closure_eq_top, Submodule.pi_empty, SimpleGraph.egirth_bot, IntermediateField.adjoin_simple_eq_top_iff_of_isAlgebraic, continuous_top, AlgebraicGeometry.Scheme.Γevaluation_naturality_assoc, AdicCompletion.coe_eval, essInf_const_top, ENat.card_eq_top, AddSubsemigroup.closure_closure_coe_preimage, Monoid.Coprod.range_swap, AlgebraicGeometry.Scheme.IdealSheafData.coe_support_ofIdealTop, NonUnitalSubring.range_snd, LinearOrderedAddCommGroupWithTop.top_pos, RootPairing.invtRootSubmodule.top_mem, LeftInvariantDerivation.left_invariant'', Subring.topEquiv_apply, Matroid.IsRkFinite.eRk_lt_top, TopologicalSpace.Compacts.coe_top, himp_eq_top_iff, Submodule.dualCoannihilator_top, LieAlgebra.IsSimple.isAtom_top, CategoryTheory.ObjectProperty.instIsClosedUnderExtensionsTop, ArchimedeanClass.mk_zero, InformationTheory.klDiv_def, AffineIndependent.vectorSpan_eq_top_of_card_eq_finrank_add_one, LatticeHom.withTop'_toFun, CategoryTheory.MorphismProperty.instIsStableUnderCobaseChangeTop, InformationTheory.klDiv_eq_lintegral_klFun, AddMonoid.FG.fg_top, Filter.Subsingleton.atBot_eq, AlgebraicGeometry.Scheme.AffineZariskiSite.generate_presieveOfSections_mem_grothendieckTopology, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, AddGroupTopology.toTopologicalSpace_top, ENat.sub_eq_top_iff, top_inf_eq, Subsemiring.top_prod_top, ExistsContDiffBumpBase.u_exists, LinearMap.sup_range_inl_inr, Subring.op_top, NonUnitalSubsemiring.toAddSubmonoid_eq_top, TensorProduct.tensorQuotEquivQuotSMul_tmul_mk, IsLocalizedModule.subsingleton_iff_ker_eq_top, AlgebraicGeometry.Scheme.Opens.toSpecΓ_top, MeasureTheory.LpAddConst_lt_top, fact_one_le_top_ennreal, CategoryTheory.MorphismProperty.Over.forget_comp_forget_map, Submodule.comap_subtype_self, IntermediateField.rank_top, WithLp.prod_dist_eq_sup, CompleteDistribLattice.top_sdiff, RieszExtension.exists_top, MeasureTheory.Measure.eventually_cofinite, NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_top, LinearMap.span_singleton_sup_ker_eq_top, SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux, LinearMap.IsPerfectCompl.left_top_iff, Module.Basis.eval_range, CategoryTheory.Sieve.generate_of_singleton_isSplitEpi, Group.fg_iff, AlgebraicGeometry.AffineSpace.SpecIso_inv_appTop_coord, CategoryTheory.Sieve.functorPullback_top, compactlySupported_eq_top_iff, max_eq_top, Subring.mem_top, Matroid.eRank_lt_top_iff, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall, Finset.truncatedSup_singleton, AdicCompletion.val_mul, Subsemiring.comap_top, MeasureTheory.measure_lt_top_of_isCompact_of_isMulLeftInvariant, AlgebraicGeometry.germ_stalkClosedPointIso_hom_assoc, CategoryTheory.MorphismProperty.Over.pullbackComp_inv_app_left, AddMonoid.IsTorsion.torsionAddEquiv_symm_apply_coe, Submodule.annihilator_bot, ValueDistribution.proximity_add_top_le, AlgebraicGeometry.Scheme.IdealSheafData.support_eq_top_iff, RootPairing.isIrreducible_iff, RootPairing.GeckConstruction.span_range_h'_eq_top, WithTop.pred_eq_top, Subgroup.isComplement'_top_right, AddMonoidHom.range_eq_top, NonUnitalAlgebra.top_toNonUnitalSubsemiring, List.minimum_nil, SimpleGraph.extremalNumber_top, Quotient.subsingleton_iff, IsUpperSet.top_notMem, Submodule.span_univ, ENat.top_epow_top, emultiplicity_eq_top, smul_top_inf_eq_smul_of_isSMulRegular_on_quot, SmoothPartitionOfUnity.sum_eq_one', MeasureTheory.Measure.count_apply_lt_top, PowerBasis.adjoin_gen_eq_top, MeasureTheory.IntegrableOn.setLIntegral_lt_top, EReal.abs_coe_lt_top, SimpleGraph.Subgraph.map_hom_top, BoundedLatticeHom.map_top', MeasureTheory.hittingAfter_eq_top_iff, Order.height_of_noMinOrder, Set.infsep_zero, StarSubalgebra.eq_top_iff, Finset.min_empty, AddCon.mrange_mk', Finset.Colex.ofColex_top, UpperSet.Ioi_eq_top, PartENat.one_lt_top, IntermediateField.adjoin_root_eq_top, ValueDistribution.logCounting_add_analyticOn, ENNReal.sum_lt_top, codisjoint_iff_le_sup, Submonoid.unop_top, FiniteMulArchimedeanClass.withTopOrderIso_symm_apply, AddGroup.FG.out, FiniteArchimedeanClass.mem_closedBallAddSubgroup_iff, AffineSubspace.smul_top, ConvexCone.toPointedCone_top, AdicCompletion.mk_smul_mk, HahnSeries.leadingCoeff_of_ne, Submodule.top_colon, SimpleGraph.dist_top_of_ne, CategoryTheory.MorphismProperty.instHasPullbackHomDiscretePUnitOfHasPullbacksAlong, LocalizedModule.subsingleton_iff_ker_eq_top, SimpleGraph.top_adj, Order.pred_lt_top, iInf_ne_top_subtype, CategoryTheory.GrothendieckTopology.discrete_eq_top, TopCat.Presheaf.map_germ_eq_Γgerm_assoc, Ideal.span_singleton_eq_top, Subgroup.instFiniteIndexTop, AddSubgroup.prod_top, FiniteArchimedeanClass.mem_ball_iff, NonUnitalStarAlgebra.top_toNonUnitalSubalgebra, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, Subring.top_prod_top, MulAction.stabilizer_finset_empty, Set.addCentralizer_empty, ENNReal.rpow_eq_top_iff, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone_ι_app, Sublattice.comap_top, CoheytingHom.map_top', Finset.Ioi_eq_Ioc, SmoothPartitionOfUnity.mem_finsupport, Module.FaithfullyFlat.iff_flat_and_ideal_smul_eq_top, equivShrink_symm_top, MeasureTheory.OuterMeasure.zero_caratheodory, FirstOrder.Language.Substructure.coe_top, PowerSeries.order_zero, Finset.fold_sup_univ, ConvexCone.mem_top, IsLprojection.coe_top, LocalSubring.map_maximalIdeal_eq_top_of_isMax, AddMonoidHom.ker_snd, span_range_eq_top_iff_surjective_fintypeLinearCombination, emultiplicity_zero, ENNReal.continuousOn_sub_left, LinearOrderedAddCommGroupWithTop.add_lt_top, ENNReal.top_rpow_of_pos, FiniteMulArchimedeanClass.liftOrderHom_mk, Submonoid.units_top, IsFractionRing.closure_range_algebraMap, Order.coheight_int, WithTop.eq_top_iff_forall_ge, EReal.top_sub_coe, IsMax.eq_top, TopologicalSpace.Clopens.coe_top, MeasureTheory.OuterMeasure.top_caratheodory, Multiset.inf_coe, AlgebraicGeometry.StructureSheaf.globalSectionsIso_hom, Submodule.isCoatom_comap_or_eq_top, Module.End.invtSubmodule.one, IntermediateField.finrank_top, Filter.top_mul_top, ENat.iInf_eq_top_of_isEmpty, MeasureTheory.restrict_compl_sigmaFiniteSet_eq_zero_or_top, Finset.sup_eq_top_iff, hnot_bot, WithBot.toDual_apply_bot, WithTop.orderIsoSumLexPUnit_top, WithTop.subtypeOrderIso_symm_apply, Submodule.top_orthogonal_eq_bot, ENNReal.mul_top', Filter.lift_top, HilbertBasis.dense_span, Set.einfsep_top, MeasureTheory.measure_lt_top_of_subset, contDiffWithinAt_omega_iff_analyticWithinAt, MeasureTheory.Measure.MeasureDense.fin_meas, smoothRightMul_one, contMDiff_smul, Multiplicative.toAdd_eq_top, Ideal.finiteHeight_iff, trivializationAt_model_space_apply, Module.Basis.toDual_range, NonUnitalStarAlgebra.range_eq_top, SimplexCategory.Truncated.morphismProperty_eq_top, separableClosure.eq_top_iff, Equiv.withTopSubtypeNe_symm_apply_coe, isSimpleRing_iff_isTwoSided_imp, ProbabilityTheory.iIndepSet.iIndep_comap_mem, LinearMap.IsPerfectCompl.right_top_iff, EReal.range_coe, ENat.iInf_coe_eq_top, WithTop.iSup_coe_lt_top, Algebra.top_toSubring, Real.isBigO_logb_log, SimpleGraph.card_edgeFinset_top_eq_card_choose_two, MeasurableSet.exists_isOpen_diff_lt, AlgebraicGeometry.Scheme.ker_eq_top_of_isEmpty, MeasureTheory.Measure.WeaklyRegular.innerRegular_measurable, ConvexCone.IsGenerating.top_le_span, AlgebraicGeometry.ΓSpec.left_triangle, CategoryTheory.Subfunctor.eq_top_iff_isIso, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app_assoc, isAddCyclic_iff_exists_zmultiples_eq_top, AlgebraicGeometry.AffineSpace.comp_homOfVector, IntermediateField.top_toSubalgebra, ENNReal.tendsto_nat_nhds_top, mem_lowerCentralSeries_succ_iff, HahnSeries.orderTop_lt_top, EReal.top_add_iff_ne_bot, SimpleGraph.fromEdgeSet_univ, ENat.floor_lt_top, ValueDistribution.characteristic_sub_characteristic_inv_le, Submonoid.center_eq_top, SimpleGraph.isExtremal_top_free_turanGraph, IntermediateField.relrank_top_left, AddValuation.map_zero, eHolderNorm_eq_top, SimpleGraph.ediam_top, RingTheory.Sequence.IsWeaklyRegular.regular_mod_prev, NonUnitalRingHom.range_eq_top, AlgebraicGeometry.Scheme.instIsOpenImmersionToSpecΓOfIsQuasiAffine, ENNReal.inv_zero, AlgebraicGeometry.Scheme.homOfLE_appTop, AddMonoidHom.mker_fst, Module.annihilator_eq_top_iff, CategoryTheory.MorphismProperty.instHasOfPrecompPropertyTop, FirstOrder.Language.Hom.range_eq_map, Subfield.relfinrank_top_right, Subsemigroup.op_eq_top, Monoid.IsTorsion.torsionMulEquiv_symm_apply_coe, GaloisConnection.u_eq_top, IsGaloisGroup.fixedPoints_bot, TwoSidedIdeal.eq_top, AlgebraicGeometry.Scheme.isoSpec_inv_naturality_assoc, Pi.top_def, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self, one_memℓp_infty, SimpleGraph.Subgraph.connected_induce_top_sup, NormedAddGroupHom.range_comp_incl_top, nhds_top, ordinaryHypergeometric_radius_top_of_neg_nat₂, Submodule.pi_top, LipschitzWith.coordinate, QuotSMulTop.equivQuotTensor_naturality, AffineSpace.asymptoticNhds_zero, egauge_empty, ValueDistribution.characteristic_add_top_eventuallyLE, AddMonoidHom.range_eq_top_of_surjective, Equiv.Perm.eq_top_of_isPreprimitive_of_isSwap_mem, AlgebraicGeometry.PresheafedSpace.restrictTopIso_hom, HahnEmbedding.Partial.eval_smul, NumberField.maximalRealSubfield_eq_top_iff_isTotallyReal, himp_le_left, IsCoatomic.eq_top_or_exists_le_coatom, Finsupp.linearCombinationOn_range, Subsemigroup.centralizer_eq_top_iff_subset, exists_root_adjoin_eq_top_of_isCyclic, grade_top, AlgebraicGeometry.AffineSpace.hom_ext_iff, Submonoid.top_prod_top, Metric.hausdorffEDist_empty, MeasureTheory.exists_lt_lintegral_simpleFunc_of_lt_lintegral, AdicCompletion.transitionMap_comp_reduceModIdeal, AlgebraicGeometry.ΓSpec.unop_locallyRingedSpaceAdjunction_counit_app', FractionalIdeal.coe_one_eq_coeSubmodule_top, Ideal.torsionOf_zero, MeasureTheory.StronglyMeasurable.exists_spanning_measurableSet_norm_le, WithTop.add_eq_top, ENNReal.HolderConjugate.eq_top_iff_eq_one, ENat.mul_top', Algebra.GrothendieckGroup.inv_mk, MeasureTheory.Measure.rnDeriv_ne_top, AdicCompletion.instIsScalarTowerQuotientIdealHSMulTopSubmodule, OrderTop.upperBounds_univ, isLUB_univ, FiniteArchimedeanClass.subsemigroup_eq_addSubgroup, egauge_zero_left_eq_top, Subsemigroup.strictMono_topEquiv, Order.coheight_of_noMaxOrder, Submodule.comap_snd, Ideal.ofNat_eq_top, Filter.lift'_top, AddSubmonoid.op_top, AlgebraicGeometry.Scheme.isoSpec_Spec_hom, LinearMap.exact_smul_id_smul_top_mkQ, Filter.Eventually.ne_top_of_lt, sSup_atoms_eq_top, NonemptyInterval.coe_top_interval, IntermediateField.finrank_eq_one_iff_eq_top, SSet.Subcomplex.iSup_ofSimplex_nonDegenerate_eq_top, MeasureTheory.SimpleFunc.FinMeasSupp.meas_preimage_singleton_ne_zero, IsSemisimpleModule.finite_tfae, FractionalIdeal.coe_inv_of_ne_zero, MeasureTheory.measure_inter_lt_top_of_left_ne_top, Subgroup.topEquiv_symm_apply_coe, MonoidHom.mrange_id, Order.height_eq_coe_add_one_iff, MeasureTheory.SimpleFunc.memLp_top, ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, AlgebraicGeometry.tilde.isIso_toOpen_top, upperClosure_eq_top_iff, SupHom.withTop'_toFun, EReal.continuousOn_toReal, UpperSet.compl_top, LowerSet.top_prod_top, ArchimedeanClass.addSubgroup_eq_bot, AddSubmonoid.pi_empty, Submodule.comap_subtype_eq_top, codisjoint_top_left, EReal.exp_eq_top_iff, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp'_X, instIsNilpotentSubtypeMemLieSubalgebraTop, Subsemigroup.prod_top, HahnSeries.orderTop_eq_top, lt_top_iff_ne_top, Subfield.extendScalars_top, AlgebraicGeometry.HasRingHomProperty.appTop, Matroid.eRk_eq_top_iff, ENNReal.nnreal_smul_lt_top_iff, CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.essentiallyLarge_top, AffineSubspace.mk'_top, NormedSpace.equicontinuous_TFAE, SpecialLinearGroup.SL2Z_generators, Profinite.NobelingProof.GoodProducts.span, Order.krullDim_enat, Algebra.zariskisMainProperty_iff_exists_saturation_eq_top, NumberField.is_primitive_element_of_infinitePlace_lt, NonUnitalSubring.top_prod, WithTop.add_top, MulAction.stabilizer_univ, TwoSidedIdeal.mem_top, PiLp.nnnorm_eq_ciSup, MeasureTheory.setLIntegral_eq_top_of_measure_eq_top_ne_zero, lp.infty_coeFn_pow, MeasureTheory.SimpleFunc.integrable_iff, MeasureTheory.ae_bdd_liminf_atTop_rpow_of_eLpNorm_bdd, AddSubgroup.IsSubnormal.exists_normal_and_le_and_lt_top_of_ne, LieAlgebra.zero_rootSpace_eq_top_of_nilpotent, NormedSpace.expSeries_radius_eq_top, Subring.unop_eq_top, AddSubsemigroup.strictMono_topEquiv, Matrix.range_toLin_eq_top, StrictAnti.apply_eq_top_iff, AdicCompletion.smul_mk, Order.height_eq_coe_iff, CategoryTheory.Presheaf.isLocallySurjective_iff_range_sheafify_eq_top, SimpleGraph.top_isIndContained_iff_top_isContained, lp.infty_smulCommClass, himp_eq_left, MonoidAlgebra.exists_finset_adjoin_eq_top, AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot, CategoryTheory.ObjectProperty.instContainsZeroTopOfHasZeroObject, SmoothBumpCovering.embeddingPiTangent_injective_mfderiv, EReal.mul_top_of_pos, BoxIntegral.norm_integral_le_of_le_const, AddHom.srange_eq_map, SimpleGraph.ediam_eq_one, IntermediateField.bot_eq_top_of_rank_adjoin_eq_one, NumberField.IsTotallyReal.maximalRealSubfield_eq_top, ENNReal.iSup_ennreal, LinearGrowth.tendsto_atTop_of_linearGrowthInf_pos, ENNReal.nhds_top_basis, SeparationQuotient.inseparableSetoid_eq_top_iff, AddGroup.fg_def, AlgebraicGeometry.Scheme.isPullback_toSpecΓ_toSpecΓ, AlgebraicGeometry.Scheme.IdealSheafData.mul_top, ValueDistribution.logCounting_add_top_eventuallyLE, AlgebraicGeometry.Scheme.ΓSpecIso_naturality, MeasureTheory.stoppedValue_stoppedProcess, Filter.OrderTop.atTop_eq, SimpleGraph.diam_eq_one, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp'_f, GromovHausdorff.ghDist_eq_hausdorffDist, MvPolynomial.zeroLocus_bot, AlgebraicGeometry.Scheme.restrictFunctorΓ_hom_app, WithTop.coe_add_eq_top_iff, NonUnitalRingHom.srange_eq_top_iff_surjective, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_snd, CategoryTheory.ObjectProperty.IsStrongGenerator.subobject_eq_top, Real.volume_Iic, Ideal.matrix_top, Prod.snd_top, EReal.tendsto_exp_nhds_top_nhds_top, ValueDistribution.logCounting_mul_top_le, MeasureTheory.Measure.hausdorffMeasure_zero_or_top, Ordnode.Bounded.weak_right, Filter.top_smul_nhds_zero, SimpleGraph.toTopEdgeLabeling_labelGraph, Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality, LinearMap.IsProj.top, PowerBasis.adjoin_eq_top_of_gen_mem_adjoin, WithTop.iInf_coe_lt_top, NonUnitalAlgebra.eq_top_iff, AlgebraicGeometry.SheafedSpace.Γ_map, hasFiniteFPowerSeriesOnBall_const, tangentBundle_model_space_coe_chartAt_symm, WithTop.toDual_apply_top, SmoothPartitionOfUnity.coe_finsupport, MulAction.stabilizer_empty, ContinuousMap.sublattice_closure_eq_top, isFoelner_iff, LieHom.range_eq_top, finite_integral_one_add_norm, tangentBundleModelSpaceHomeomorph_coe, top_sdiff, LowerSet.compl_top, Polynomial.IsSplittingField.adjoin_rootSet', Subsemigroup.mem_top, RootPairing.IsRootSystem.span_root_eq_top, AlgebraicGeometry.germ_stalkClosedPointIso_hom, Subring.topEquiv_symm_apply_coe, Set.einfsep_singleton, contDiffOn_infty_iff_fderiv_of_isOpen, ProbabilityTheory.Kernel.iIndep_comap_mem_iff, AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv, algebraMap_memℓp_infty, ValueDistribution.proximity_mul_top_le, AlgebraicGeometry.IsFinite.instHasAffinePropertyAndIsAffineFiniteCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTopHomAppTop, BoxIntegral.Prepartition.iUnion_top, BoxIntegral.Prepartition.distortion_top, ProperCone.dual_zero, Submodule.annihilator_top_inter_nonZeroDivisors, R_mul, Submonoid.coe_top, AddSubgroup.topEquiv_symm_apply_coe, AddMonoidHom.mker_zero, AlgebraicGeometry.Scheme.smallGrothendieckTopologyOfLE_eq_toGrothendieck_smallPretopology, Subgroup.IsSubnormal.eq_bot_or_top_of_isSimpleGroup, AlgebraicGeometry.IsAffineOpen.instIsAffineToSchemeBasicOpen, Subsemigroup.srange_fst, ENNReal.mul_eq_top, Ideal.fg_top, OrdinalApprox.gfpApprox_ord_eq_gfp, CategoryTheory.Coverage.eq_top_pullback, NumberField.Units.closure_fundSystem_sup_torsion_eq_top, Algebra.GrothendieckGroup.mk_div_mk, AddMonoid.fG_iff, Set.Infinite.meas_eq_top, AddSubgroup.isComplement'_top_right, ProbabilityTheory.bayesRisk_of_isEmpty', SimpleGraph.Subgraph.comap_equiv_top, WithTop.image_coe_Ici, Subgroup.top_prod_top, IsSimpleAddGroup.eq_bot_or_eq_top_of_normal, AddSubgroup.top_prod_top, RingHom.rangeS_eq_map, CategoryTheory.MorphismProperty.instFullUnderTopUnderForget, CategoryTheory.Paths.morphismProperty_eq_top', MvPowerSeries.lexOrder_zero, Digraph.top_adj, Module.End.mem_genEigenspace_top, Submodule.prod_eq_top_iff, smoothLeftMul_one, RingTheory.Sequence.isWeaklyRegular_append_iff', PartENat.find_eq_top_iff, tangentConeAt_def, Subsemiring.range_fst, emultiplicity_one_left, ENNReal.mul_lt_top_iff, EReal.image_coe_Ici, AddSubmonoid.mem_subPairs, RootPairing.isSimpleModule_weylGroupRootRep_iff, tangentBundleCore_coordChange_model_space, EReal.toReal_top, AlgebraicGeometry.Scheme.toIso_inv_ι_assoc, ValueDistribution.characteristic_top_mul_le, Stream'.Seq.length'_of_not_terminates, Metric.eball_top, Filter.isCobounded_top, AlgebraicGeometry.SheafedSpace.restrictTopIso_inv, CommGrpCat.range_eq_top_of_epi, CategoryTheory.Localization.Construction.morphismProperty_is_top', IsCoprime.sup_eq, AlgebraicGeometry.Scheme.toSpecΓ_appTop, Order.Ideal.top_toLowerSet, LinearMap.range_eq_top, LeftInvariantDerivation.map_add, CategoryTheory.MorphismProperty.instIsLeftAdjointOverTopMapOfHasPullbacksAlongOfIsStableUnderBaseChangeAlong, RingHom.rangeS_top_iff_surjective, compl_le_self, AnalyticOnNhd.codiscreteWithin_setOf_analyticOrderAt_eq_zero_or_top, Ideal.ker_tensorProductMk_quotient, Order.Coframe.top_sdiff, binomialSeries_radius_eq_top_of_nat, CategoryTheory.MorphismProperty.Over.mapComp_hom_app_left, ENat.card_eq_top_of_infinite, Filter.limsInf_top, PointedCone.dual_zero, Ideal.span_one, AlgebraicGeometry.Scheme.IdealSheafData.support_eq_bot_iff, Dynamics.coverEntropyEntourage_finite_of_isCompact_invariant, ValueDistribution.logCounting_top_mul_eventually_le, PMF.apply_lt_top, CategoryTheory.Presheaf.isLocallySurjective_iff_range_sheafify_eq_top', ENat.LEInfty.out, span_selfAdjoint, smoothSheaf.obj_eq, SmoothPartitionOfUnity.finsum_smul_mem_convex, MeasureTheory.Measure.finiteAt_principal, Submodule.colon_eq_top_iff_subset, Equiv.Perm.subgroup_eq_top_of_isPreprimitive_of_isSwap_mem, SimpleGraph.edist_bot, Order.krullDim_le_one_iff_of_boundedOrder, AlgHom.range_eq_top, MeasureTheory.upcrossings_eq_top_of_frequently_lt, CategoryTheory.Subfunctor.Subpresheaf.epi_iff_range_eq_top, ZSpan.span_top, NonUnitalAlgebra.mem_top, Set.top_eq_univ, Submodule.IsLattice.span_eq_top, PiLp.norm_eq_ciSup, AddSubgroup.card_top, KuratowskiEmbedding.embeddingOfSubset_isometry, LeftInvariantDerivation.coe_add, WithTop.image_coe_Ioi, NonUnitalStarAlgebra.toNonUnitalSubalgebra_eq_top, AlgebraicGeometry.IsAffineOpen.iSup_basicOpen_eq_self_iff, SSet.Subcomplex.image_top, Subgroup.exponent_top, isLUB_atoms_top, ENNReal.iUnion_Icc_coe_nat, Set.Ici.coe_top, Subspace.exists_eq_top_of_iUnion_eq_univ, Ideal.iSup_iInf_eq_top_iff_pairwise, Submodule.colon_singleton_zero, Ideal.isCoprime_tfae, ENat.iSup_natCast, SmoothPartitionOfUnity.sum_le_one', FirstOrder.Language.DefinableSet.coe_top, ValueDistribution.characteristic_sub_characteristic_inv, LinearOrderedAddCommGroupWithTop.neg_top, LieSubmodule.ucs_eq_top_iff, WithTop.not_top_le_coe, LieSubmodule.top_lie_le_iff_le_normalizer, LieIdeal.topEquiv_apply, AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonempty, MulArchimedeanClass.mk_one, Interval.coe_top, Asymptotics.isBigOWith_top, LieHom.range_eq_map, IsCoatom.lt_iff, AffineSubspace.topEquiv_symm_apply_coe, InformationTheory.klDiv_eq_integral_klFun, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap_assoc, Subsemigroup.unop_eq_top, MeasureTheory.hasFiniteIntegral_iff_ofReal, ProbabilityTheory.measure_eq_zero_or_one_or_top_of_indepSet_self, CategoryTheory.MorphismProperty.instIsStableUnderBaseChangeTop, LieModule.maxNilpotentSubmodule_eq_top_of_isNilpotent, AlgebraicGeometry.StructureSheaf.algebraMap_obj_top_bijective, Submodule.rank_eq_spanRank_of_free, AddSubsemigroup.map_equiv_top, Module.End.invtSubmodule.mk_eq_top_iff, MeasureTheory.measure_univ_of_isAddLeftInvariant, TopologicalSpace.Opens.inclusion'_map_eq_top, InfHom.withTop'_toFun, GromovHausdorff.eq_toGHSpace, isSimpleAddGroup_iff, Subalgebra.centralizer_eq_top_iff_subset, PiLp.edist_eq_iSup, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, MeasureTheory.measure_lt_top_of_isCompact_of_isAddLeftInvariant, ENNReal.top_mul, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_self, SmoothPartitionOfUnity.sum_nonneg, EReal.add_top_of_ne_bot, AlgebraicGeometry.Scheme.Hom.ker_eq_top_iff_isEmpty, CategoryTheory.MorphismProperty.Over.w_assoc, tendsto_prod_top_iff, NonUnitalSubsemiring.closure_univ, ENNReal.lt_top_of_mul_ne_top_left, Set.Iic_top, MeasureTheory.Measure.add_top, Heyting.Regular.coe_top, AddMonoidHom.mrange_eq_map, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_apply, Algebra.top_toSubsemiring, Algebra.Smooth.exists_span_eq_top_isStandardSmooth, Subgroup.eq_top_iff', PointedContMDiffMap.instIsScalarTowerSomeENatTop, RootPairing.GeckConstruction.ωConjLieSubmodule_eq_top_iff, AlgebraicGeometry.Scheme.IdealSheafData.map_top, IsLocalRing.PrimeSpectrum.asIdeal_top, QuotSMulTop.map_exact, ValueDistribution.isBigO_characteristic_sub_characteristic_inv, MeasureTheory.measure_union_eq_top_iff, AddSubmonoid.topEquiv_symm_apply_coe, EReal.coe_mul_top_of_pos, ProbabilityTheory.bayesRisk_lt_top, MeasureTheory.Measure.FiniteSpanningSetsIn.finite, CategoryTheory.Localization.Construction.morphismProperty_eq_top, Submonoid.exponent_top, AlgebraicGeometry.Spec_zeroLocus_eq_zeroLocus, NonUnitalSubring.top_prod_top, LieAlgebra.derivedSeries_def, WithTop.orderPred_top, AlgebraicGeometry.Scheme.Opens.ι_appTop, CategoryTheory.MorphismProperty.instHasOfPostcompPropertyTop, AddSubgroup.relIndex_top_right, Quot.subsingleton_iff, MeasureTheory.setLIntegral_lt_top_of_bddAbove, TensorProduct.tensorQuotEquivQuotSMul_symm_mk, Filter.prod_top, LinearMap.reduceModIdeal_apply, WithTop.pow_lt_top_iff, RingTheory.Sequence.isWeaklyRegular_append_iff, IsArtinian.disjoint_partial_infs_eventually_top, alternatingGroup.subgroup_eq_top_of_isPreprimitive, IsCoatom.covBy_top, Finset.min_eq_top, ENat.add_one_eq_coe_top_iff, EReal.top_add_coe, AddSubmonoid.mrange_inl_sup_mrange_inr, MulHom.srange_eq_top_of_surjective, PartENat.eq_top_iff_forall_le, SimpleGraph.Subgraph.map_iso_top, WithTop.coe_wcovBy_top, AffineMap.map_top_of_surjective, ENNReal.iSup_coe_eq_top, WithTop.map₂_top_left, AlgebraicGeometry.Scheme.map_basicOpen, ValueDistribution.characteristic_sum_top_le, CategoryTheory.Subfunctor.Subpresheaf.top_obj, ENNReal.toReal_eq_toReal_iff, fdifferential_comp, Module.supportDim_quotSMulTop_succ_eq_supportDim, PrimeSpectrum.vanishingIdeal_empty, WithTop.map₂_top_right, PartENat.natCast_lt_top, CategoryTheory.exists_equivalence_iff_of_locallySmall, SymmetricPower.range_mk, Ideal.prod_eq_top_iff, Subfield.comap_top, HomogeneousIdeal.toIdeal_top, MeasureTheory.setLIntegral_const_lt_top, NonUnitalAlgebra.adjoin_univ, CongruenceSubgroup.finiteIndex_conjGL, QuotientGroup.range_mk', MeasureTheory.memLp_top_const_enorm, LeftInvariantDerivation.coe_injective, AlgebraicGeometry.isRetrocompact_basicOpen, Order.pred_top_lt_iff, MonoidHom.range_eq_top, MeasureTheory.Integrable.measure_norm_gt_lt_top, AlgebraicGeometry.Scheme.isoSpec_inv_naturality, OpenPartialHomeomorph.MDifferentiable.range_mfderiv_eq_top, IntermediateField.bot_eq_top_iff_finrank_eq_one, NonUnitalSubring.toNonUnitalSubsemiring_top, ENat.top_sub_coe, MeasureTheory.L2.eLpNorm_inner_lt_top, Submodule.torsionBySet_torsionBySet_eq_top, LieSubmodule.eq_top_of_isIrreducible, SimpleGraph.nonempty_dart_top, AlgebraicGeometry.Scheme.Hom.quasiFiniteLocus_eq_top_iff, SmoothBumpCovering.exists_finset_toSmoothPartitionOfUnity_eventuallyEq, LieAlgebra.IsKilling.invtSubmoduleToLieIdeal_apply_eq_top_iff, ArchimedeanClass.out_top, ValueDistribution.characteristic_add_top_le, AlgebraicGeometry.instQuasiSeparatedToSpecΓOfQuasiSeparatedSpaceCarrierCarrierCommRingCat, LieAlgebra.IsKilling.biSup_corootSpace_eq_top, AddSubgroup.unop_eq_top, CategoryTheory.Sieve.pullback_eq_top_of_mem, ProbabilityTheory.Kernel.bound_lt_top, ExistsContDiffBumpBase.u_smooth, CategoryTheory.ObjectProperty.instEssentiallySmallTopOfEssentiallySmall, AntilipschitzWith.edist_lt_top, AlgebraicGeometry.Scheme.comp_appTop_assoc, ENNReal.zero_rpow_def, PartENat.eq_top_iff_forall_lt, Ideal.top_liesOver_top, SimpleGraph.turanGraph_zero, LeftInvariantDerivation.coe_neg, AlgebraicGeometry.Proj.basicOpen_one, span_lt_top_of_card_lt_finrank, GaloisConnection.u_top, FiniteMulArchimedeanClass.mk_le_mk, DFinsupp.add_closure_iUnion_range_single, AlgebraicGeometry.Scheme.IdealSheafData.ideal_top, Monoid.IsTorsion.torsion_eq_top, List.minimum_eq_top, Ideal.map_eq_top_iff, Set.Infinite.encard_eq, CategoryTheory.MorphismProperty.instFaithfulCostructuredArrowTopOverToOver, Order.coheight_top, contDiffWithinAt_infty, PiLp.nnnorm_toLp, AddSubmonoid.closure_closure_coe_preimage, nhds_top_order, tangentBundle_model_space_chartAt, Subgroup.op_eq_top, NNRat.addSubmonoid_closure_range_pow, MeasureTheory.Measure.InnerRegularCompactLTTop.innerRegular, Submodule.biSup_comap_eq_top_of_range_eq_biSup, QuotientAddGroup.addSubgroup_eq_top_of_subsingleton, ContinuousLinearMap.fpowerSeries_radius, CompletelyDistribLattice.top_sdiff, isGreatest_top_iff, RestrictedProduct.isEmbedding_inclusion_top, IsDiscreteValuationRing.map_algebraMap_eq_valuationSubring, PartENat.toWithTop_top, Module.Relations.Solution.isPresentation_iff, InformationTheory.klDiv_of_not_integrable, EReal.neg_eq_bot_iff, Subalgebra.op_top, Filter.ker_eq_univ, AlgebraicGeometry.Scheme.isoSpec_Spec, ArchimedeanClass.ball_top, CategoryTheory.Subfunctor.Subpresheaf.range_id, ENNReal.iUnion_Ico_coe_nat, LieModule.coe_genWeightSpace_of_top, FirstOrder.Language.BoundedFormula.realize_foldr_inf, measure_Icc_lt_top, IsPrecomplete.top, upperClosure_empty, Order.isPredPrelimit_top, WithTop.mul_top', FreeAddGroup.closure_range_of, Order.PFilter.top_mem, LieModuleHom.range_eq_top, Ideal.toCotangent_apply, Subsemigroup.top_prod, Pi.top_apply, FiniteArchimedeanClass.mk_le_mk, LieModule.isNilpotent_iff_exists_ucs_eq_top, Field.exists_primitive_element_iff_finite_intermediateField, Subgroup.isComplement'_bot_left, Subsemigroup.closure_closure_coe_preimage, AddSubgroup.top_toAddSubmonoid, Order.coheight_eq_top_iff, AddCommGrpCat.epi_iff_range_eq_top, RingHom.rangeS_top_of_surjective, ENNReal.div_eq_zero_iff, CategoryTheory.ExtremalEpi.subobject_eq_top, AlgebraicGeometry.IsClosedImmersion.hasAffineProperty, Field.Emb.Cardinal.filtration_apply, CategoryTheory.MorphismProperty.CostructuredArrow.toOver_map, Associates.mem_factorSet_top, AlgebraicGeometry.Scheme.preimage_opensRange_toSpecΓ, AlgebraicGeometry.instHasCoproductsOfShapeOverSchemeTopMorphismPropertyOfSmall, ENNReal.sub_ne_top_iff, BoxIntegral.Prepartition.splitMany_empty, indiscreteTopology_iff, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv, Subalgebra.bot_eq_top_iff_finrank_eq_one, countableInterFilter_top, WithTop.prod_eq_top_iff, AddSubgroup.eq_top_of_le_card, AddAction.isBlock_top, ContMDiffMap.mdifferentiable, Ideal.eq_top_iff_one, IsSemisimpleModule.sSup_simples_eq_top, Ideal.absNorm_top, UpperSet.coe_top, Order.height_top_eq_krullDim, ENNReal.tendsto_ofReal_atTop, ENNReal.log_lt_top_iff, Metric.infEdist_eq_top_iff, AlgebraicGeometry.Scheme.eq_zeroLocus_of_isClosed_of_isAffine, AddMonoidAlgebra.exists_finset_adjoin_eq_top, Finsupp.linearCombination_range, AddSubsemigroup.mem_top, AlgebraicGeometry.Scheme.Opens.ι_preimage_self, CategoryTheory.Subfunctor.instIsIsoFunctorTypeιTop, ValuationSubring.top_coe_div, WithLp.prod_norm_eq_sup, LinearIndependent.span_eq_top_of_card_eq_finrank, AlgebraicGeometry.Scheme.toSpecΓ_image_zeroLocus, ProbabilityTheory.evariance_eq_top, AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c, locallyFinsuppWithin.logCounting_divisor, Monoid.fg_iff, FreeAddMonoid.closure_range_of, Ordinal.enum_succ_eq_top, Submodule.top_le_span_range_iff_forall_exists_fun, AddMonoid.fg_def, LieSubalgebra.top_coe, Ideal.eq_top_of_unit_mem, WithTop.LinearOrderedAddCommGroup.top_sub, Submodule.isOrtho_top_right, IsLowerSet.top_mem, MulHom.srange_eq_map, Subring.coe_top, CategoryTheory.MorphismProperty.CostructuredArrow.toOver_obj, PartENat.withTopEquiv_top, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv_assoc, CategoryTheory.MorphismProperty.Under.w, AlgebraicGeometry.SheafedSpace.Γ_obj_op, ENNReal.toReal_top_mul, EReal.bot_mul_top, Algebra.isAlgebraic_iff, enorm_lt_top, TopologicalSpace.Closeds.coe_top, LieAlgebra.IsKilling.span_weight_isNonZero_eq_top, MeasureTheory.exists_lt_lowerSemicontinuous_integral_lt, Algebra.GrothendieckAddGroup.of_injective, BoundedContinuousFunction.lintegral_of_real_lt_top, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self_apply, NonUnitalStarAlgebra.comap_top, Subsemiring.coe_top, CategoryTheory.Dial.tensorUnit_rel, Diffeology.isPlot_iff_contDiff, Submodule.fst_map_fst, bot_codisjoint, Filter.smallSets_top, Filter.comap_top, PartENat.toWithTop_top', MeasureTheory.memLp_top_of_bound_enorm, FreeAlgebra.adjoin_range_ι, ENNReal.top_pow, ContinuousMap.subalgebra_topologicalClosure_eq_top_of_separatesPoints, MulAction.aestabilizer_empty, ENat.pow_lt_top_iff, MeasureTheory.ContinuousOn.hasBoxIntegral, max_top_left, WithTop.pred_top, multiples_eq_top_of_prime_card, Profinite.NobelingProof.spanFinBasis.span, RootPairing.span_root'_eq_top, min_top_right, ClosedSubmodule.orthogonal_eq_top_iff, Subsemiring.unop_top, FiniteMulArchimedeanClass.mem_subgroup_iff, SSet.Subcomplex.topIso_inv_ι_assoc, AlgebraicGeometry.Scheme.inv_appTop, Subsemiring.range_snd, IntermediateField.finrank_top', AddSubgroup.top_prod, AlgebraicGeometry.isLocalization_away_of_isAffine, ENNReal.range_coe', CategoryTheory.SemilatticeInf.tensorUnit, lp.infty_coeFn_one, Ideal.adic_basis, AlgebraicGeometry.IsAffineOpen.ι_basicOpen_preimage, coe_addEquiv_lpBCF_symm, Subsemigroup.eq_top_iff', AddSubsemigroup.unop_top, LeftInvariantDerivation.map_smul, Subgroup.closure_univ, FormalMultilinearSeries.zero_radius, EReal.coe_add_top, WithTop.Ioi_coe, MvPowerSeries.order_eq_top_iff, AffineSubspace.direction_top, ENat.toENNReal_eq_top, Bornology.IsBounded.measure_lt_top, Subgroup.eq_bot_or_eq_top_of_prime_card, Subring.prod_top, Affine.Simplex.span_eq_top, SimpleGraph.Subgraph.isInduced_iff_exists_eq_induce_top, IsZGroup.commutator_lt, MeasureTheory.Integrable.lintegral_lt_top, Set.einfsep_lt_top, IsSimpleOrder.equivBool_symm_apply, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isReal, Module.finite_def, IccRightChart_extend_top_mem_frontier, IsGalois.fixedField_top, finrank_top, WithBot.sInf_empty, SimpleGraph.induce_singleton_eq_top, AddSubgroup.eq_bot_or_eq_top_of_prime_card, TopologicalSpace.Opens.eq_bot_or_top, SimpleGraph.pathGraph_two_eq_top, lowerCentralSeries_succ, LinearIndependent.repr_range, AlgebraicGeometry.morphismRestrict_appTop, isSimpleOrder_iff, IsLocalRing.closed_point_mem_iff, AlgebraicGeometry.Scheme.IdealSheafData.ofIdealTop_ideal, QuotientGroup.subsingleton_quotient_top, sup_compl_eq_top, ENat.eq_top_iff_forall_ne, AddSubmonoid.mrange_inr, SmoothPartitionOfUnity.sum_eq_one, EReal.preimage_coe_Ico_top, MeasureTheory.eLpNorm_lt_top_of_finite, Algebra.IsAlgebraic.isNormalClosure_iff, TensorProduct.map₂_mk_top_top_eq_top, Set.eq_top_of_card_le_of_finite, iInf_top, Module.isTorsionBySet_annihilator_top, AddSubmonoid.prod_eq_top_iff, MeasureTheory.hittingAfter_eq_sInf, ENNReal.div_lt_top, FirstOrder.Language.Structure.cg_def, AlgebraicGeometry.Scheme.Hom.preimage_opensRange, StarSubalgebra.toSubalgebra_eq_top, Padic.AddValuation.map_zero, SimpleGraph.Subgraph.neighborSet_top, CategoryTheory.MorphismProperty.Over.mk_left, Cardinal.continuum_toENat, AlgebraicGeometry.ΓSpecIso_hom_stalkClosedPointIso_inv, LieModule.isNilpotent_of_top_iff', LieAlgebra.isLieAbelian_iff_center_eq_top, List.le_min_of_forall_le, StarSubalgebra.mem_top, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_apply, CategoryTheory.GrothendieckTopology.bot_covering, normalizerCondition_iff_only_full_group_self_normalizing, SimpleGraph.cycleGraph_one_eq_top, NonUnitalSubsemiring.range_fst, TensorProduct.quotTensorEquivQuotSMul_symm_mk, OrderDual.toDual_top, LinearMap.range_le_iff_comap, Submodule.cardQuot_eq_one_iff, MeasureTheory.SimpleFunc.measure_support_lt_top_of_lintegral_ne_top, ProbabilityTheory.Kernel.rnDeriv_lt_top, AddSubsemigroup.centralizer_eq_top_iff_subset, WithBot.ofDual_bot, AddSubmonoid.topEquiv_apply, AlgebraicGeometry.LocallyRingedSpace.Γ_map, MeasureTheory.Measure.count_apply_infinite, Finset.max_eq_top, MeasureTheory.Measure.compl_mem_cofinite, AlgebraicGeometry.isCompactOpen_iff_eq_basicOpen_union, AddSubmonoid.top_prod, LipschitzOnWith.coordinate, AddSubgroup.addSubgroupOf_bot_eq_top, covBy_top_iff, BoxIntegral.hasIntegral_const, exists_subset_affineIndependent_affineSpan_eq_top, CategoryTheory.MorphismProperty.CostructuredArrow.mk_left, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv, AddSubmonoid.neg_top, WithTop.map₂_eq_top_iff, smoothSheaf.eval_germ, FiniteMulArchimedeanClass.congrOrderIso_symm, EReal.exists, Subgroup.prod_top, EReal.inv_top, WithTop.strictAnti_iff, Subring.comap_top, Module.Baer.extensionOfMax_to_submodule_eq_top, AddSubgroup.normalizer_eq_top, AddMonoid.Coprod.range_swap, Additive.toMul_top, Associates.factors_eq_top_iff_zero, bot_lt_top, Algebra.adjoin_adjoin_coe_preimage, SmoothBumpCovering.embeddingPiTangent_injOn, ValueDistribution.characteristic_pow_top, EReal.top_mul_bot, ClassGroup.equivPic_symm_apply, ENNReal.continuousOn_toNNReal, LinearMap.IsSymmetric.iSup_iSup_eigenspace_inf_eigenspace_eq_top_of_commute, Equiv.Perm.eq_top_of_isMultiplyPretransitive, AlgebraicGeometry.eq_top_of_sigmaSpec_subset_of_isCompact, ENNReal.zero_rpow_of_neg, AddSubsemigroup.eq_top_iff', Algebra.adjoin_top, EReal.sub_bot, nhdsSet_univ, FirstOrder.Language.Hom.range_id, WithTop.natCast_lt_top, contMDiffAt_vectorSpace_iff_contDiffAt, bihimp_self, ENNReal.div_zero, commutator_alternatingGroup_eq_top, WithTop.top_sub_coe, HahnEmbedding.ArchimedeanStrata.isInternal_stratum', AdicCompletion.val_add, Absorbent.submodule_eq_top, TopHomClass.map_top, AlgebraicGeometry.PresheafedSpace.Γ_obj, IsLocalRing.Ring.KrullDimLE.eq_bot_or_eq_top, Function.locallyFinsuppWithin.logCounting_divisor_eq_circleAverage_sub_const, AffineSubspace.perpBisector_eq_top, Ideal.not_isPrime_iff, MeasureTheory.condExpIndL1Fin_disjoint_union, SimpleGraph.preconnected_induce_iff, Algebra.adjoin_root_eq_top_of_isSplittingField, PointedContMDiffMap.instIsScalarTowerSomeENatTopContMDiffMapModelWithCornersSelf, not_isMin_top, HasFPowerSeriesOnBall.r_eq_top_of_exists, PartENat.add_eq_top_iff, ENNReal.iInf_ne_top, Filter.nsmul_top, TendstoUniformly.tendstoUniformlyOnFilter, MonoidHom.mker_fst, EReal.top_div_of_pos_ne_top, LeftInvariantDerivation.coe_smul, AlgebraicGeometry.PresheafedSpace.toRestrictTop_c, AddSubgroup.centralizer_eq_top_iff_subset, Algebra.surjective_algebraMap_iff, LaurentSeries.powerSeriesEquivSubring_apply, AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ_assoc, SimpleGraph.Walk.toSubgraph_le_induce_support, SimpleGraph.isIndepSet_induce, WithTop.sum_eq_top, CategoryTheory.ObjectProperty.ι_map_top, NumberField.mixedEmbedding.minkowskiBound_lt_top, IsCoatom.le_iff, Module.supportDim_le_supportDim_quotSMulTop_succ, QuotSMulTop.equivQuotTensor_naturality_mk, Module.exists_isPrincipal_quotient_of_finite, Equiv.Perm.subgroup_eq_top_of_swap_mem, EReal.continuousAt_add_top_coe, MeasureTheory.ae_measure_preimage_add_right_lt_top_of_ne_zero, AddSubmonoid.isLocalizationMap_top_nat_int, span_fourierLp_closure_eq_top, Field.primitive_element_iff_minpoly_degree_eq, FiniteMulArchimedeanClass.min_le_mk_mul, LieHom.idealRange_eq_map, Algebra.toSubmodule_eq_top, DirectSum.IsInternal.addSubmonoid_iSup_eq_top, WithLp.prod_nndist_eq_sup, ENNReal.top_mul', AddSubmonoid.mrange_fst, LieModule.le_max_triv_iff_bracket_eq_bot, AlgHom.fieldRange_eq_top, Ordnode.Bounded.weak, Submonoid.prod_eq_top_iff, AdicCompletion.mk_smul_top_ofAlgEquiv_symm, Ne.lt_top, TwoSidedIdeal.top_asIdeal, AddSubmonoid.mrange_snd, Continuous.memLp_top_of_hasCompactSupport, AdicCompletion.val_one, MonoidHom.range_eq_top_of_surjective, WithCStarModule.map_top_submodule, Module.supportDim_quotSMulTop_succ_eq_supportDim_mem_jacobson, RingHom.fieldRange_eq_map, WithLp.prod_nnnorm_eq_sup, NonUnitalRingHom.range_eq_top_of_surjective, ValueDistribution.logCounting_sum_top_eventuallyLE, CategoryTheory.MorphismProperty.Under.Hom.ext_iff, L_apply, MonoidHom.ker_fst, measure_eq_measure_preimage_add_measure_tsum_Ico_zpow, Submodule.mem_smul_top_iff, EReal.sign_top, SimpleGraph.connected_induce_iff, lp.infty_coeFn_intCast, Module.support_quotSMulTop, OpenSubgroup.coe_top, IsCompact.measure_lt_top, Finset.inf_empty, DualNumber.range_inlAlgHom_sup_adjoin_eps, edist_lt_top, AlgebraicGeometry.Scheme.toOpen_eq, ContinuousMap.setOfTop_eq_univ, RingCon.range_mk', AnalyticOnNhd.isClopen_setOf_analyticOrderAt_eq_top, SimpleGraph.isNClique_map_copy_top, contDiffAt_infty, isPurelyInseparable_iff_perfectClosure_eq_top, Fin.cast_top, Int.addSubgroupClosure_one, FirstOrder.Language.Structure.cg_iff, CategoryTheory.ObjectProperty.IsLocal.top, Module.End.genEigenspace_top, top_disjoint, LieAlgebra.maxNilpotentIdeal_eq_top_of_isNilpotent, VectorField.contMDiffWithinAt_mpullbackWithin_extChartAt_symm, BoundedLatticeHomClass.map_top, TangentBundle.symmL_model_space, HahnEmbedding.Partial.orderTop_eq_finiteArchimedeanClassMk, AddSubmonoid.centralizer_eq_top_iff_subset, bot_himp, ENNReal.coe_rpow_def, CategoryTheory.MonoOver.top_arrow, ENat.pow_eq_top_iff, ImplicitFunctionData.range_rightDeriv, ringKrullDim_lt_top, CStarAlgebra.span_nonneg_inter_closedBall, OpenAddSubgroup.coe_top, Sublattice.top_prod, SimpleGraph.Subgraph.IsPerfectMatching.symmDiff_of_isAlternating, Diffeology.IsContDiffCompatible.isPlot_iff, AddSubgroup.eq_top_iff', WithTop.canLift, CategoryTheory.MorphismProperty.Under.mk_left, Submonoid.eq_top_iff', FirstOrder.Language.BoundedFormula.realize_top, AddSubsemigroup.comap_top, Monoid.CoprodI.iSup_mrange_of, inf_eq_top_iff, Algebra.adjoin_univ, AlgHom.equalizer_same, InfTopHom.map_top', coe_lpBCFₗᵢ_symm, closure_of_isSwap_of_isPretransitive, IsLocalRing.quotient_span_eq_top_iff_span_eq_top, CategoryTheory.Subobject.mk_eq_top_of_isIso, CategoryTheory.Subfunctor.image_top, BooleanSubalgebra.mk_top, PUnit.top_eq, AddMonoidHom.eqLocusM_same, TopologicalSpace.Closeds.coe_eq_univ, Tropical.trop_top, MeasureTheory.not_isFiniteMeasure_iff, Metric.isClosed_eball_top, hahnEmbedding_isOrderedModule_rat, LinearMap.ker_zero, Ideal.isCompactElement_top, LieModuleEquiv.ofTop_apply, Subfield.relrank_top_right, FiniteArchimedeanClass.congrOrderIso_symm, AffineIndependent.affineSpan_eq_top_iff_card_eq_finrank_add_one, IntermediateField.adjoin_root_eq_top_of_isSplittingField, AlgebraicGeometry.ΓSpecIso_inv_ΓSpec_adjunction_homEquiv, AnalyticOnNhd.codiscrete_setOf_analyticOrderAt_eq_zero_or_top, TopHom.top_apply, algebraicClosure.eq_top_iff, NonUnitalRingHom.srange_eq_top_of_surjective, CategoryTheory.ObjectProperty.instIsClosedUnderQuotientsTop, WithTop.top_add, IsZLattice.span_top, Submonoid.mem_divPairs, MeasureTheory.SimpleFunc.measure_preimage_lt_top_of_memLp, Subgroup.isComplement'_top_bot, RingHom.eqLocus_same, ENat.floor_eq_top, AddAction.BlockMem.coe_top, coe_addEquiv_lpBCF, ENNReal.log_eq_top_iff, intCast_memℓp_infty, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, IsOpen.exists_between_affineIndependent_span_eq_top, Setoid.eq_top_iff, Ideal.mem_iInf_smul_pow_eq_bot_iff, SSet.horn_obj_zero, MonoidHom.range_eq_top_of_cancel, ENNReal.mul_top, EReal.preimage_coe_Ioo_bot_top, AffineSubspace.top_coe, emultiplicity_lt_top, MeasureTheory.ae_lt_top', ProbabilityTheory.evariance_lt_top, ENat.iSup_coe_eq_top, Hausdorffification.lift_comp_of, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv, ClosureOperator.closure_top, SimpleGraph.diam_top, Field.primitive_element_iff_minpoly_natDegree_eq, ENat.recTopCoe_top, CategoryTheory.MorphismProperty.Over.instPreservesFiniteLimitsTopOverForget, LieSubalgebra.engel_zero, sInfHom.coe_top, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓUnitOpensCarrierCarrierCommRingCatRingCatSheaf, MeasureTheory.LocallyIntegrable.exists_contDiff_dist_le_of_forall_mem_ball_dist_le, Subalgebra.fg_top, MeasureTheory.eLpNorm'_measure_zero_of_neg, le_top, Cardinal.toENat_eq_top, NonUnitalAlgebra.toSubmodule_eq_top, WithTop.untopD_eq_iff, Submodule.topologicalClosure_eq_top_iff, CategoryTheory.Subobject.top_eq_id, Finsupp.add_closure_setOf_eq_single, AlgebraicGeometry.Scheme.Hom.inv_appTop, Filter.top_mul_of_one_le, SSet.iSup_skeletonOfMono, AddSubmonoid.mrange_inl, Subgroup.unop_eq_top, affineSpan_coe_preimage_eq_top, ENNReal.div_eq_top, AffineSubspace.pointwise_vadd_top, Module.FinitePresentation.out, ExistsContDiffBumpBase.y_smooth, ofBoolAlg_top, SimpleGraph.isClique_range_copy_top, Complementeds.mk_top, ValueDistribution.abs_characteristic_sub_characteristic_shift_eqO, TwoSidedIdeal.top_ringCon, Equiv.Perm.IsThreeCycle.alternating_normalClosure, ContractingWith.edist_efixedPoint_lt_top, Order.coheight_nat, EReal.tendsto_coe_nhds_top_iff, AffineSubspace.perpBisector_self, LieModule.zero_genWeightSpace_eq_top_of_nilpotent, EMetric.closedBall_top, SimpleGraph.ediam_eq_top_of_not_connected, codisjoint_top_right, CategoryTheory.MorphismProperty.Under.forget_comp_forget_map, HahnEmbedding.Seed.truncLT_mem_range_baseEmbedding, GaloisConnection.u_l_top, FractionalIdeal.coe_inv_of_nonzero, FirstOrder.Language.ElementarySubstructure.coe_top, Subgroup.normalizer_eq_top_iff, AlgebraicGeometry.Spec_zeroLocus, Subsemigroup.center_eq_top, ProperCone.innerDual_empty, ENat.top_sub_ofNat, PiCountable.edist_lt_top, AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp_X, Real.volume_Ici, CategoryTheory.MorphismProperty.instFullOverTopOverForget, IntermediateField.topEquiv_symm_apply_coe, SSet.skeletonOfMono_obj_eq_top, top_sup_eq, MvPolynomial.vanishingIdeal_empty, Ideal.torsionOf_eq_top_iff, LieIdeal.comap_incl_self, Filter.tendsto_top, IsSimpleGroup.eq_bot_or_eq_top_of_normal, EReal.div_top, IsLocalRing.span_eq_top_of_tmul_eq_basis, AddMonoid.minOrder_eq_top_iff, affineSpan_eq_top_of_nonempty_interior, OrderIso.map_top, AddSubgroup.isComplement'_bot_left, Submodule.sup_orthogonal_of_hasOrthogonalProjection, AddMonoid.Coprod.mrange_mk, FiniteArchimedeanClass.withTopOrderIso_symm_apply, Equiv.Perm.subgroup_eq_top_of_nontrivial, PreTilt.exists_smodEq_untiltAux, CategoryTheory.Limits.equalizerSubobject_of_self, LieSubalgebra.topEquiv_apply, ValueDistribution.proximity_const, CategoryTheory.MorphismProperty.Comma.hasColimitsOfShape_of_closedUnderColimitsOfShape, LieDerivation.IsKilling.range_ad_eq_top, SSet.iSup_range_eq_top_of_isColimit, SmoothPartitionOfUnity.exists_pos_of_mem, ENNReal.iUnion_Ioo_coe_nat, Ideal.absNorm_eq_one_iff, HomogeneousIdeal.coe_top, IntermediateField.rank_top', SimpleGraph.eq_top_iff_forall_eccent_eq_one, SimpleGraph.Subgraph.singletonSubgraph_eq_induce, CategoryTheory.MorphismProperty.Over.w, AdicCompletion.transitionMap_map_pow, Subalgebra.topEquiv_symm_apply_coe, MeasureTheory.ae_bdd_liminf_atTop_of_eLpNorm_bdd, HahnEmbedding.Partial.mem_domain, AlgebraicGeometry.Scheme.SpecΓIdentity_inv_app, MeasureTheory.OuterMeasure.boundedBy_top, AlgebraicGeometry.Scheme.Pullback.diagonalCoverDiagonalRange_eq_top_of_injective, iInf_eq_dif, WithTop.pow_eq_top_iff, ofDual_toAdd_eq_top_iff, AddMonoid.Coprod.mrange_inl_sup_mrange_inr, CompleteSublattice.coe_top, Submodule.eq_top_iff_forall_basis_mem, Monoid.Coprod.mrange_mk, Representation.invtSubmodule.top_mem, IsAssociatedPrime.annihilator_le, IntermediateField.topEquiv_apply, AddMonoid.IsTorsion.torsion_eq_top, MeasureTheory.MemLp.meas_ge_lt_top', AlgebraicGeometry.Scheme.Cover.ColimitGluingData.trans_app_left, LieModule.iSup_genWeightSpace_eq_top, AddMonoid.Coprod.mclosure_range_inl_union_inr, MulArchimedeanClass.out_top, Submodule.starProjection_top, Ideal.instIsTwoSidedTop, zmultiples_eq_top_of_prime_card, AddSubsemigroup.top_prod, WithTop.top_mul_top, lp.infty_coeFn_natCast, Submodule.submoduleOf_eq_top, HahnEmbedding.Seed.mem_domain_baseEmbedding, MvPowerSeries.lexOrder_eq_top_iff_eq_zero, AddSubsemigroup.mk_eq_top, Digraph.completeDigraph_eq_top, CategoryTheory.Subobject.top_factors, EReal.mul_eq_bot, FirstOrder.Language.Equiv.toHom_range, AlgebraicGeometry.basicOpen_eq_of_affine', Diffeology.IsPlot.contDiff, LowerAdjoint.closure_top, FormalMultilinearSeries.radius_eq_top_of_forall_image_add_eq_zero, tangentBundleModelSpaceHomeomorph_coe_symm, OpenAddSubgroup.mem_top, CategoryTheory.Subgroupoid.full_univ, AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom_appTop, Subsemigroup.topEquiv_apply, Module.rank_le_one_iff_top_isPrincipal, Submodule.dualAnnihilator_top, ENNReal.not_lt_top, Dynamics.netMaxcard_finite_iff, AlgebraicGeometry.Scheme.instLocallyCoverDenseOverTopMorphismPropertyOverForgetOverGrothendieckTopology, Group.isNilpotent_top, CategoryTheory.MorphismProperty.CodescendsAlong.top, AddSubmonoid.mk_eq_top, AffineSubspace.topEquiv_apply, SmoothBumpCovering.embeddingPiTangent_injective, AddSubgroup.normal_top, AlgebraicGeometry.instIsDominantToSpecΓOfCompactSpaceCarrierCarrierCommRingCat, AlgebraicGeometry.Scheme.preimage_eq_top_of_closedPoint_mem, RingHom.range_eq_map, Sublattice.mem_top, LinearOrderedCommGroup.genLTOne_eq_of_top, BoxIntegral.integralSum_sub_partitions, iInf_extend_top, AddSubgroup.closure_closure_coe_preimage, Diffeomorph.instContinuousMapClassSomeENatTop, IsCyclotomicExtension.singleton_one, MeasureTheory.hittingBtwn_eq_sInf, InfTopHom.coe_top, SSet.finite_subcomplex_top_iff, NonUnitalSubsemiring.top_prod_top, CategoryTheory.Subobject.eq_top_of_isIso_arrow, EReal.top_mul_of_neg, AlgebraicGeometry.Scheme.isoSpec_Spec_inv, ConvexCone.IsGenerating.span_eq_top, ContinuousLinearMap.range_eq_map_coprodSubtypeLEquivOfIsCompl, Pi.top_comp, Algebra.adjoin_restrictScalars, Submonoid.op_eq_top, EReal.preimage_coe_Iio_top, AddMonoid.IsTorsion.torsionAddEquiv_apply, measure_Ioo_lt_top, WithTop.LinearOrderedAddCommGroup.neg_top, MeasureTheory.innerRegularWRT_isCompact_isClosed_measure_ne_top_of_group, ENNReal.inv_eq_top, top_add, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_comp, NonUnitalAlgebra.coe_top, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.top_mem_range, LieAlgebra.IsKilling.killingCompl_top_eq_bot, QuotientGroup.rightRel_eq_top, NonUnitalAlgebra.map_top, LeftInvariantDerivation.map_sub, AdicCompletion.val_sub, IsHausdorff.eq_iff_smodEq, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_assoc, AlgebraicGeometry.Scheme.topIso_hom, AddSubmonoid.top_prod_top, SimpleGraph.TopEdgeLabeling.labelGraph_toTopEdgeLabeling, SmoothPartitionOfUnity.sum_finsupport_smul_eq_finsum, ENNReal.iInf_coe_lt_top, ENNReal.cinfi_ne_top, MeasurableSpace.generateFrom_singleton, AlgebraicGeometry.finite_appTop_of_universallyClosed, AffineSubspace.span_univ, IsCompact.exists_open_superset_measure_lt_top, eventuallyConst_nhdsNE_iff_meromorphicOrderAt_sub_eq_top, IsSimpleModule.span_singleton_eq_top, IntermediateField.top_toSubfield, AddSubmonoid.unop_eq_top, ENNReal.none_eq_top, ValueDistribution.logCounting_add_const, TopologicalSpace.IsOpenCover.iSup_eq_top, LeftInvariantDerivation.map_neg, Algebra.FormallyUnramified.range_eq_top_of_isPurelyInseparable, PartENat.zero_lt_top, Group.fg_iff', IsDiscreteValuationRing.addVal_eq_top_iff, Subgroup.coe_eq_univ, MeasureTheory.Lp.mem_Lp_iff_eLpNorm_lt_top, QuotSMulTop.map_first_exact_on_four_term_exact_of_isSMulRegular_last, MeasureTheory.AddContent.extend_eq_top, CompleteSublattice.mem_top, Module.Finite.top, LinearOrderedAddCommMonoidWithTop.top_add', WithTop.iSup_coe_eq_top, ENat.sub_top, NonUnitalAlgebra.to_subring_eq_top, eq_top_of_bot_isCompl, contDiff_omega_iff_analyticOnNhd, RingOfIntegers.exponent_eq_one_iff, Codisjoint.out, MeasureTheory.Measure.FiniteAtFilter.eventually, sSup_eq_top, BoxIntegral.integrable_iff_cauchy, CategoryTheory.Cat.FreeRefl.morphismProperty_eq_top, AlgebraicGeometry.specTargetImageFactorization_app_injective, Ideal.IsMaximal.coprime_of_ne, MeasureTheory.Measure.toBoxAdditive_apply, MulArchimedeanClass.ballSubgroup_top, CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsTop, R_apply, Metric.infEDist_empty, LieSubmodule.top_coe, Algebra.comap_top, Filter.mem_prod_top, Ideal.top_mul, Finset.inf_erase_top, SmoothPartitionOfUnity.contMDiff_finsum_smul, CategoryTheory.Subobject.underlyingIso_inv_top_arrow_assoc, Subsemiring.closure_univ, AlgebraicGeometry.PresheafedSpace.Γ_map, Module.End.invtSubmodule.top_mem, NonUnitalAlgebra.toNonUnitalSubring_eq_top, ENNReal.ofNat_lt_top, SmoothPartitionOfUnity.sum_finsupport, top_le_iff, Order.coheight_coe_enat, AdicCompletion.val_neg, BooleanSubalgebra.map_top, EReal.tendsto_nhds_top_iff_real, CategoryTheory.Paths.morphismProperty_eq_top_of_isMultiplicative, Ideal.isUnit_iff, PrimeSpectrum.isIdempotentElemEquivClopens_symm_top, Subsemigroup.comap_top, LieSubalgebra.toSubmodule_eq_top, FiniteArchimedeanClass.addSubgroup_strictAnti, IsLocalRing.CotangentSpace.map_eq_top_iff, AlgebraicGeometry.StructureSheaf.toOpenₗ_top_bijective, MeasureTheory.Measure.ae_measure_lt_top, LieIdeal.normalizer_eq_top, OrderDual.toDual_eq_top, CategoryTheory.Subobject.isIso_arrow_iff_eq_top, Codisjoint.eq_iff, SimpleGraph.completeGraph_eq_top, ClosedSubmodule.mem_top, ContinuousLinearMap.fpowerSeriesBilinear_radius, AddSubgroup.instFiniteIndexTop, AddSubgroup.topEquiv_apply, ENNReal.tsum_coe_eq_top_iff_not_summable_coe, SSet.HasDimensionLT.degenerate_eq_top, CategoryTheory.Subgroupoid.top_isNormal, CategoryTheory.Sieve.functorInclusion_top_isIso, LinearMap.BilinForm.orthogonal_top_eq_ker, SimpleGraph.center_top, SchwartzMap.memLp_top, MeasurableSet.coe_top, SimpleGraph.ediam_eq_top_of_not_preconnected, CompleteBooleanAlgebra.top_le_sup_compl, WithTop.tendsto_coe_atTop, Submodule.isInternal_prime_power_torsion, PresentedGroup.closure_range_of, Submodule.annihilator_top, AlgebraicGeometry.instHasOfPostcompPropertySchemeIsSeparatedTopMorphismProperty, Sublattice.map_top, AffineBasis.isUnit_toMatrix_iff, ContinuousLinearEquiv.coe_toDiffeomorph, FiniteMulArchimedeanClass.ballSubgroup_strictAnti, IsGaloisGroup.fixingSubgroup_bot, CategoryTheory.MorphismProperty.Comma.hasColimit_of_closedUnderColimitsOfShape, Set.exists_seq_iSup_eq_top_iff_countable, WithLp.prod_nnnorm_toLp, ProbabilityTheory.gaussianPDF_lt_top, Fin.rev_zero_eq_top, AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom, CategoryTheory.IsCardinalFilteredGenerator.of_isDense, TopologicalSpace.CompactOpens.coe_top, Order.not_isPredLimit_top, LieAlgebra.top_isCartanSubalgebra_of_nilpotent, AffineSubspace.instNonemptySubtypeMemTop, AddSubmonoid.pi_top, AdicCompletion.transitionMap_ideal_mk, MeasureTheory.hittingAfter_empty, Metric.infEDist_eq_top_iff, MeasureTheory.UnifTight.exists_measurableSet_indicator, Subgroup.mem_top, WithBotTop.rec_top, MeasureTheory.Lp.eLpNorm_lt_top, Algebra.GrothendieckAddGroup.lift_apply, Submonoid.mrange_snd, Submodule.sup_eq_top_iff, EReal.toReal_image_Ioo_zero_top, SimpleGraph.Subgraph.subgraphOfAdj_eq_induce, AlgebraicGeometry.affineAnd_apply, Submodule.traceDual_bot, WithTop.add_coe_eq_top_iff, AdicCompletion.transitionMap_map_mul, CategoryTheory.MorphismProperty.CostructuredArrow.Hom.ext_iff, Concept.intent_top, EReal.inv_lt_top, WithTop.top_mem_insertTop, OpenAddSubgroup.toAddSubgroup_top, AlgebraicGeometry.IsImmersion.instHasOfPostcompPropertySchemeTopMorphismProperty, RingHom.range_eq_top, IntermediateField.fg_top, isTop_iff_eq_top, instDiscreteMeasurableSpace, MeasureTheory.OuterMeasure.top_apply', Submodule.fg_top, AlgebraicGeometry.AffineSpace.reindex_appTop_coord, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv_assoc, Profinite.NobelingProof.GoodProducts.span_iff_products, LieIdeal.lcs_zero, List.foldr_min_of_ne_nil, IsCyclotomicExtension.iff_adjoin_eq_top, lp.infty_isScalarTower, CategoryTheory.Subobject.underlyingIso_inv_top_arrow, Subspace.top_mem_of_biUnion_eq_univ, MeasureTheory.measure_ball_lt_top, LinearMap.eqLocus_eq_top, ValueDistribution.logCounting_top_mul_le, NonUnitalSubsemiring.centralizer_eq_top_iff_subset, LinearMap.IsProj.submodule_eq_top_iff, FormalMultilinearSeries.radius_eq_top_of_forall_nnreal_isBigO, AlgEquiv.fieldRange_eq_top, Field.Emb.Cardinal.iSup_adjoin_eq_top, ValueDistribution.proximity_pow_top, WithBot.coe_top, AlgebraicGeometry.ΓSpec.toSpecΓ_of, FiniteArchimedeanClass.coe_congrOrderIso_apply, SimpleGraph.completeMultipartiteGraph.topEmbedding_apply_snd, Sylow.normalizer_sup_eq_top, CliffordAlgebra.iSup_ι_range_eq_top, Equiv.Perm.closure_cycle_adjacent_swap, upperCentralSeries_eq_top_iff_nilpotencyClass_le, AlgebraicGeometry.Scheme.smallGrothendieckTopology_eq_toGrothendieck_smallPretopology, DiscreteQuotient.instSubsingletonQuotientTop, LieModule.isTrivial_iff_max_triv_eq_top, Filter.cardinalInterFilter_top, CategoryTheory.MorphismProperty.Over.pullback_map_left, SimpleGraph.chromaticNumber_top_eq_top_of_infinite, PresentedAddMonoid.closure_range_of, symmDiff_hnot_self, compl_eq_bot, Finset.Ioi_top, sInf_diff_singleton_top, FirstOrder.Language.BoundedFormula.sup_not_iff_top, QuotientAddGroup.range_mk', top_mem_upperBounds, OrderTop.tendsto_atTop_nhds, Set.centralizer_empty, BooleanAlgebra.top_le_sup_compl, contMDiffWithinAt_infty, Module.supportDim_le_supportDim_quotSMulTop_succ_of_mem_jacobson, SmoothBumpCovering.support_toSmoothPartitionOfUnity_subset, span_flip_eq_top_iff_linearIndependent, AlgebraicGeometry.exists_appTop_π_eq_of_isLimit, MvPowerSeries.order_monomial, Subgroup.isComplement'_bot_top, WithTop.top_pow, SimpleGraph.Subgraph.IsInduced.top, Submodule.CoFG.top, CategoryTheory.Subobject.underlyingIso_top_hom, Subgroup.index_eq_one, BooleanSubalgebra.val_top, LieModule.zero_genWeightSpace_eq_top_of_nilpotent', StrictMono.apply_eq_top_iff, AlgebraicGeometry.IsAffine.affine, StarSubalgebra.coe_top, AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal.to_basicOpen, ContMDiffMap.mdifferentiableAt, AlgebraicGeometry.SheafedSpace.Γ_obj, ProperCone.dual_empty, ProbabilityTheory.Kernel.measure_eq_zero_or_one_or_top_of_indepSet_self, EReal.top_mul_top, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_top, Subsemiring.topEquiv_symm_apply_coe, MeasureTheory.Submartingale.upcrossings_ae_lt_top', MeasureTheory.eLpNormEssSup_lt_top_iff_isBoundedUnder, ENat.toNat_eq_zero, ENNReal.trichotomy, ArchimedeanClass.mk_eq_top_iff, ENNReal.inv_eq_zero, lowerCentralSeries_zero, Submonoid.mrange_inl, PiLp.isometry_ofLp_infty, AlgebraicGeometry.Scheme.mem_basicOpen_top, sdiff_top, PowerSeries.IsWeierstrassFactorization.degree_eq_coe_lift_order_map, ConvexCone.isGenerating_top, MonoidHom.mrange_eq_top_of_surjective, measure_Ico_lt_top, LieModule.maxGenEigenSpace_toEnd_eq_top, ValuationSubring.le_top, Ideal.jacobson_top, BoxIntegral.integral_const, FirstOrder.Language.Substructure.coe_topEquiv, AddGrpCat.epi_iff_range_eq_top, Ideal.sup_height_eq_ringKrullDim, AlgebraicTopology.NormalizedMooreComplex.objX_zero, Submodule.toAddSubgroup_eq_top, Metric.ediam_of_unbounded, ProbabilityTheory.cond_eq_zero, Set.Iic.coe_top, Ideal.IsHomogeneous.top, WellFoundedGT.induction_top, ENNReal.rpow_eq_top_iff_of_pos, LieIdeal.top_toLieSubalgebra, IsBoundedBilinearMap.isBigO, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen', AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_assoc, Hausdorffification.lift_of, FiniteMulArchimedeanClass.subgroup_eq_bot, Algebra.eq_top_iff, ExpGrowth.expGrowthSup_top, Filter.liminf_bot, SimpleGraph.top_preconnected, MeasureTheory.exists_setLIntegral_compl_lt, SmoothBumpFunction.contMDiff, Submodule.orthogonal_eq_top_iff, Submodule.map_subtype_top, ValueDistribution.logCounting_sum_top_le, CategoryTheory.Functor.isRightAdjoint_iff_leftAdjointObjIsDefined_eq_top, AffineSubspace.comap_top, RestrictedProduct.isEmbedding_coe_of_top, LinearMap.BilinForm.orthogonal_bot, Metric.closedEBall_top, fourierSubalgebra_closure_eq_top, QuotSMulTop.map_comp, MonoidHom.eqLocus_same, SimpleGraph.card_commonNeighbors_top, top_notMem_iff, AddMonoidHom.eqLocus_same, MeasureTheory.SimpleFunc.measure_lt_top_of_memLp_indicator, AlgebraicGeometry.instIsLocallyDirectedCompSchemeOverOverTopMorphismPropertyForgetForgetForget, AddSubgroup.exponent_top, himp_self, Filter.limsInf_bot, LieSubmodule.iSup_toSubmodule_eq_top, AddMonoid.Coprod.mrange_swap, AlgebraicGeometry.AffineSpace.homOverEquiv_apply, NonUnitalStarAlgebra.range_id, Ideal.finiteHeight_iff_lt, Order.height_int, Submodule.span_span_coe_preimage, eventuallyConst_iff_analyticOrderAt_sub_eq_top, Subalgebra.prod_top, CategoryTheory.Sieve.overEquiv_symm_top, MulArchimedeanClass.closedBallSubgroup_top, MeasureTheory.eLpNormEssSup_lt_top_of_ae_bound, MeasureTheory.Measure.MeasureDense.nonempty', BoxIntegral.Box.volume_apply, AddSubgroup.comap_top, SmoothPartitionOfUnity.finite_tsupport, Submonoid.mrange_fst, NonUnitalAlgebra.comap_top, Submodule.mul_top_eq_top_of_mul_eq_one, MeasureTheory.Measure.toOuterMeasure_top, hnot_sup_self, NonUnitalStarAlgebra.map_top, span_range_eq_top_iff_surjective_finsuppLinearCombination, AlgebraicGeometry.Scheme.comp_appTop, Polynomial.addSubmonoid_closure_setOf_eq_monomial, EReal.coe_mul_bot_of_neg, LieAlgebra.derivedSeries_lt_top_of_solvable, MeasureTheory.IsStoppingTime.measurableSet_eq_top, FirstOrder.Language.Substructure.comap_top, Order.coheight_eq_coe_iff, CategoryTheory.Subgroupoid.mem_top_objs, symmDiff_eq_top, AlgebraicGeometry.IsClosedImmersion.isAffine_surjective_of_isAffine, CategoryTheory.sieve₁'_toPreOneHypercover_eq_top, LieSubmodule.mem_top, SModEq.top, subalgebra_top_finrank_eq_submodule_top_finrank, PowerSeries.IsWeierstrassFactorizationAt.degree_eq_coe_lift_order_map_of_ne_top, IntermediateField.adjoin_eq_top_iff, OrderDual.toDual_bot, LieIdeal.derivedSeries_succ_eq_top_iff, MeasureTheory.Measure.HasTemperateGrowth.exists_eLpNorm_lt_top, Fin.range_natAdd_eq_Ioi, SimpleGraph.eq_top_iff_forall_ne_adj, MeasureTheory.Lp.eLpNorm_exponent_top_lim_eq_essSup_liminf, ENat.top_pow, BoxIntegral.Prepartition.split_of_notMem_Ioo, IsCyclotomicExtension.Rat.adjoin_singleton_eq_top, AlgebraicGeometry.Scheme.fromSpecStalk_app, Filter.generate_empty, MulArchimedeanClass.mk_eq_top_iff, WithTop.subtypeOrderIso_apply_coe, smoothSheaf.contMDiff_section, LeftInvariantDerivation.coe_zero, contDiff_infty_iff_deriv, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_comp, Algebra.IsUnramifiedAt.exists_notMem_forall_ne_mem_and_adjoin_eq_top, CategoryTheory.Subobject.pullback_top, Subsemiring.centralizer_eq_top_iff_subset, IsLocalRing.CotangentSpace.span_image_eq_top_iff, EReal.exp_lt_top_iff, isPrecomplete_iff, AlgebraicGeometry.isField_of_universallyClosed, polynomialFunctions.topologicalClosure, ENat.one_lt_top, ENNReal.image_coe_Ici, Subgroup.index_top, sInf_empty, RingCon.range_mkₐ, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_eq_zero_iff_notMem_basicOpen, WithTop.monotone_iff, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_fst, ContinuousMap.concatCM_right, UpperHalfPlane.instIsManifoldComplexModelWithCornersSelfTopWithTopENat, IsCompact.measure_lt_top_of_nhdsWithin, FiniteArchimedeanClass.ballAddSubgroup_strictAnti, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv_assoc, lp.instNormOneClassSubtypePreLpMemAddSubgroupTopENNRealOfNonempty, compl_top, ENat.top_mul, IsSimpleOrder.lt_top_iff_eq_bot, CategoryTheory.MorphismProperty.Over.pullback_obj_hom, MeasurableSpace.map_top, CategoryTheory.Subobject.epi_iff_mk_eq_top, exists_embedding_euclidean_of_compact, MeasureTheory.Integrable.measure_le_lt_top, EReal.continuousAt_add_top_top, LeftInvariantDerivation.toDerivation_injective, MvPolynomial.zeroLocus_top, RootPairing.coe_top, ArchimedeanClass.addSubgroup_strictAntiOn, ContractingWith.eq_or_edist_eq_top_of_fixedPoints, Digraph.toSimpleGraphInclusive_top, WithTop.map_top, Ideal.eq_top_of_norm_lt_one, Algebra.map_top, Concept.extent_top, CategoryTheory.Subfunctor.top_obj, CategoryTheory.FreeGroupoid.instIsLocalizationOfTopMorphismProperty, LeftInvariantDerivation.evalAt_mul, ENNReal.top_div, CategoryTheory.MorphismProperty.instHasTwoOutOfThreePropertyTop, ENNReal.sub_top, AlgebraicGeometry.Scheme.Hom.smoothLocus_eq_top, FiniteArchimedeanClass.submodule_strictAnti, CategoryTheory.Sieve.functorPushforward_top, ValueDistribution.logCounting_zero_sub_logCounting_top_eq_circleAverage_sub_const, IsSemisimpleModule.exists_sSupIndep_sSup_simples_eq_top, RingCon.rangeS_mk', ENNReal.image_coe_Ioi, NumberField.IsCMField.indexRealUnits_eq_two_iff, EReal.toReal_eq_zero_iff, CategoryTheory.MorphismProperty.Over.mapComp_inv_app_left, Module.AEval.annihilator_top_eq_ker_aeval, NonUnitalSubsemiring.comap_top, FirstOrder.Language.Hom.range_eq_top, Ideal.eq_prime_pow_mul_coprime, NonUnitalStarSubalgebra.center_eq_top, AlgebraicGeometry.IsAffineOpen.fromSpec_top, IntermediateField.bot_eq_top_of_finrank_adjoin_le_one, CategoryTheory.Presieve.isSeparatedFor_top, WithTop.orderIsoSumLexPUnit_symm_inr, Complex.subfield_eq_of_closed, Ideal.radical_top, Subgroup.comap_top, MeasureTheory.IsFiniteMeasureOnCompacts.lt_top_of_isCompact, LinearMap.range_eq_map, AlgebraicGeometry.Scheme.IdealSheafData.support_top, SimpleGraph.radius_eq_top_of_not_connected, Filter.HasBasis.top_prod, UnitAddTorus.span_mFourier_closure_eq_top, Ideal.comap_top, CategoryTheory.Subobject.isIso_iff_mk_eq_top, CategoryTheory.Localization.morphismProperty_eq_top, InfiniteGalois.fixedField_bot, SimpleGraph.Subgraph.top_adj, AlgebraicGeometry.Scheme.map_basicOpen_map, ClosedSubmodule.coe_top, CompleteLattice.ωScottContinuous.top, CategoryTheory.Subobject.pullback_self, VitaliFamily.measure_limRatioMeas_top, SimpleGraph.radius_top, AddMonoidHom.ker_eq_top_iff, ENNReal.inv_top, StarAlgHom.range_eq_map_top, Monoid.Coprod.mclosure_range_inl_union_inr, Filter.isCountablyGenerated_top, Ideal.prod_top_top, AlgebraicGeometry.Scheme.Hom.comp_appTop, MeasureTheory.integrableAtFilter_top, NonUnitalStarAlgebra.eq_top_iff, DirectSum.IsInternal.submodule_iSup_eq_top, Ideal.map_top, WithTop.succ_coe_of_isMax, Submodule.top_smul, Ideal.eq_top_iff_of_liesOver, WithTop.top_le_iff, IsSMulRegular.isSMulRegular_on_quot_iff_smul_top_inf_eq_smul, Ideal.minimalPrimes_eq_empty_iff, Subalgebra.bot_eq_top_of_finrank_eq_one, AlgebraicGeometry.IsIntegralHom.hasAffineProperty, CategoryTheory.MorphismProperty.Under.w_assoc, AddValuation.mem_supp_iff, CategoryTheory.MonoOver.top_left, MeasureTheory.MemLp.eLpNorm_lt_top, MeasureTheory.lintegral_const_lt_top, ENNReal.iUnion_Ioc_coe_nat, RingCon.toCon_eq_top, OrderDual.toDual_eq_bot, CategoryTheory.MorphismProperty.instFullCostructuredArrowTopOverToOver, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec, MeasureTheory.OuterMeasure.map_top_of_surjective, isAtom_iff_eq_top, SimpleGraph.isNIndepSet_induce, SemidirectProduct.mulEquivSubgroup_apply, MeasureTheory.Measure.count_apply_eq_top', Finpartition.parts_top_subsingleton, Real.volume_univ, FiniteMulArchimedeanClass.subsemigroup_eq_subgroup, isCompl_bot_top, ENNReal.dichotomy, Subsemigroup.map_equiv_top, KuratowskiEmbedding.embeddingOfSubset_dist_le, Subring.range_fst, LieAlgebra.IsExtension.range_eq_top, Submodule.span_eq_top_of_ne_zero, SimpleGraph.Subgraph.IsInduced.induce_top_verts, MeasureTheory.AddQuotientMeasureEqMeasurePreimage.covolume_ne_top, AddMonoid.Coprod.closure_range_inl_union_inr, Dynamics.coverMincard_finite_iff, Module.length_eq_height, AlgebraicGeometry.Scheme.IdealSheafData.top_mul, WithTop.top_pos, Submodule.bot_orthogonal_eq_top, Set.infsep_pos, AlgebraicGeometry.Scheme.mem_smallGrothendieckTopology, Subring.toAddSubgroup_eq_top, AddMonoid.minOrder_eq_top, AlgebraicGeometry.instHasAffinePropertyIsomorphismsSchemeAndIsAffineIsIsoCommRingCatAppTop, MeasureTheory.eLpNormEssSup_lt_top_of_ae_nnnorm_bound, AddSubsemigroup.topEquiv_toAddHom, ExpGrowth.expGrowthInf_top, AlgebraicGeometry.IsAffineOpen.basicOpen_union_eq_self_iff, MvPolynomial.supported_univ, Subgroup.closure_preimage_eq_top, conductor_eq_top_iff_adjoin_eq_top, Codisjoint.eq_top_of_ge, CategoryTheory.MorphismProperty.map_top_eq_top_of_essSurj_of_full, LinearMap.ker_eq_bot_iff_range_eq_top, SimpleGraph.commonNeighbors_top_eq, contDiff_infty, fixedPoints.gfp_eq_sInf_iterate, ordinaryHypergeometric_radius_top_of_neg_nat₁, MeasureTheory.restrict_compl_sigmaFiniteSetWRT, contMDiff_tangentBundleModelSpaceHomeomorph, IsMaxChain.top_mem, Subring.closure_univ, isAtom_top, Submonoid.map_equiv_top, QuotSMulTop.map_apply_mk, CategoryTheory.MorphismProperty.instHasPullbackSndHomDiscretePUnitOfHasPullbacksAlongOfIsStableUnderBaseChangeAlong, Submodule.dualAnnihilator_bot, ArchimedeanClass.eq_zero_or_top_of_archimedean, AdjoinRoot.adjoinRoot_eq_top, AlgebraicGeometry.Scheme.IsLocallyDirected.V_self, Nucleus.coe_top, borel_eq_top_of_countable, MvPowerSeries.weightedOrder_zero, MeasureTheory.measure_lt_top_of_isCompact_of_isAddLeftInvariant', CategoryTheory.GrothendieckTopology.top_mem', TopCat.Presheaf.Γgerm_res_apply, IntermediateField.extendScalars_top, Filter.liminf_top_eq_iInf, Subsemigroup.coe_top, AdicCompletion.eval_of, NonUnitalSubsemiring.prod_top, coe_ringEquiv_lpBCF_symm, SmoothPartitionOfUnity.mem_fintsupport_iff, Ideal.span_univ, ProbabilityTheory.IsFiniteKernel.exists_univ_le, subsingleton_iff_bot_eq_top, EReal.nhds_top, Sublattice.prod_eq_top, ConvexCone.coe_top, Prod.fst_top, MeasurableSpace.measurableSet_top, UniformContinuous.exists_contDiff_dist_le, CategoryTheory.Subgroupoid.mem_top, CategoryTheory.Presheaf.equalizerSieve_eq_top_iff, PowerSeries.order_eq_top, Submodule.map_range_rTensor_subtype_lid, Filter.Realizer.top_F, LinearMap.BilinForm.orthogonal_eq_top_iff, FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_of_finite, IntermediateField.fixedField_bot, EReal.coe_sub_bot, SimpleGraph.Subgraph.spanningCoe_top, MeasureTheory.eLpNorm_const_lt_top_iff, NonUnitalAlgebra.range_eq_top, measure_Ioc_lt_top, BooleanAlgebra.le_top, SemidirectProduct.mulEquivSubgroup_symm_apply, RingHom.fieldRange_eq_top_iff, IsCoatom.lt_top, AddSubgroup.unop_top, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_ne_zero_iff_mem_basicOpen, LinearMap.BilinForm.toLin_restrict_ker_eq_inf_orthogonal, AlgebraicGeometry.basicOpen_eq_of_affine, AlgebraicGeometry.LocallyRingedSpace.Γ_map_op, ProbabilityTheory.minimaxRisk_of_isEmpty', IsLocalization.span_invSubmonoid, MonoidHom.mker_one, SimpleGraph.card_edgeFinset_completeEquipartiteGraph, FiniteMulArchimedeanClass.val_mk, FiniteArchimedeanClass.ball_strictAnti, WithTop.Ioc_coe_top, FormalMultilinearSeries.radius_eq_top_iff_summable_norm, MonotoneOn.memLp_top, ArchimedeanClass.orderHom_top, powers_eq_top_of_prime_card, AlgebraicGeometry.Scheme.ΓSpecIso_naturality_assoc, top_himp, LT.lt.lt_top, Submodule.top_coe, Subsemigroup.mk_eq_top, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ_assoc, Complex.adjoin_I, Asymptotics.isLittleO_top, HahnEmbedding.Partial.eval_zero, SimpleGraph.radius_bot, SSet.Subcomplex.range_eq_top_iff, RootPairing.span_root_image_eq_top_of_forall_orthogonal, LieSubmodule.lcs_succ, Con.toSetoid_top, ENNReal.continuousOn_toReal, Equiv.withTopSubtypeNe_apply, Submodule.linearProjOfIsCompl_range, AlgebraicGeometry.PresheafedSpace.toRestrictTop_base, AlgebraicGeometry.LocallyRingedSpace.isUnit_res_toΓSpecMapBasicOpen, PiTensorProduct.span_tprod_eq_top, finrank_eq_one_iff_of_nonzero, PrimeSpectrum.primeSpectrumProd_symm_inl_asIdeal, ENNReal.lt_top_of_tsum_ne_top, Module.End.iSup_maxGenEigenspace_eq_top, Submodule.Quotient.subsingleton_iff, conductor_eq_top_of_powerBasis, AlgebraicGeometry.ΓSpec_adjunction_homEquiv_eq, Filter.liminf_top_eq_ciInf, ContinuousMap.elemental_id_eq_top, EReal.top_add_top, contMDiffAt_infty, MeasureTheory.Measure.count_apply_lt_top', HahnSeries.finiteArchimedeanClassOrderIso_apply, MeasureTheory.OuterMeasure.map_top, WithTop.tendsto_nhds_top_iff, compl_eq_top, AddMonoidHom.mrange_id, commutator_def, Algebra.FiniteType.out, subsingleton_iff_top_eq_bot, Metric.ediam_univ_eq_top_iff_noncompact, NNRat.addSubmonoid_closure_range_mul_self, ENNReal.HolderConjugate.lt_top_iff_one_lt, TensorProduct.tensorQuotEquivQuotSMul_comp_mk, Cardinal.aleph_toENat, AddSubgroup.IsSubnormal.iff_eq_top_or_exists, polynomialFunctions_closure_eq_top', Subgroup.top_subgroupOf, Submodule.cardQuot_top, Submodule.restrictScalars_eq_top_iff, WithTop.le_def', AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial, Filter.eventuallyEq_top, ENNReal.tendsto_nhds_top_iff_nat, Subsemiring.top_prod, Ideal.ideal_prod_prime_aux, Projectivization.Subspace.span_univ, LinearMap.BilinForm.orthogonal_top_eq_bot, FirstOrder.Language.DirectLimit.iSup_range_of_eq_top, Set.Nontrivial.einfsep_lt_top, AlgebraicGeometry.Scheme.toIso_inv_ι, FirstOrder.Language.Theory.CompleteType.toList_foldr_inf_mem, ValueDistribution.proximity_top_mul_le, contMDiff_tangentBundleModelSpaceHomeomorph_symm, WithTop.coe_top_lt, Filter.mul_top_of_one_le, IsSimpleOrder.eq_top_of_lt, Equiv.Perm.eq_top_if_isMultiplyPretransitive, FiniteArchimedeanClass.min_le_mk_add, Submodule.span_range_subtype_eq_top_iff, lowerClosure_eq_top, Submodule.spanRank_top, Filter.hasBasis_top, Subsemiring.op_top, Ideal.top_pow, Filter.eq_top_of_neBot, ClosedSubmodule.toSubmodule_top, Submodule.baseChange_top, OpenSubgroup.toOpens_top, egauge_eq_top, Module.Flat.top_mul_submoduleAlgebra, AdicCompletion.val_zero, eq_top_of_isCompl_bot, ENNReal.sum_eq_top, AddAction.stabilizer_finset_empty, ENNReal.nhds_top, isJacobsonRing_iff_sInf_maximal', iInf_eq_if, TopologicalSpace.Opens.map_top, meromorphicOrderAt_const_intCast, HasCompactSupport.exist_eLpNorm_sub_le_of_continuous, ENNReal.toReal_top, Equiv.Perm.closure_prime_cycle_swap, CategoryTheory.Functor.imageSieve_map, sSup_simples_eq_top_iff_isSemisimpleModule, Submonoid.divPairs_comap, Subgroup.topCharacteristic, Group.FG.out, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_zeroLocus_eq, Subsemigroup.prod_eq_top_iff, Real.deriv_arcsin_aux, MeasureTheory.FinStronglyMeasurable.fin_support_approx, Ideal.mul_top, lp.norm_eq_ciSup, Ideal.isIdempotentElem_iff_eq_bot_or_top_of_isLocalRing, PartENat.ofENat_top, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_hom_app, MeasureTheory.Measure.sigmaFinite_iff_measure_singleton_lt_top, Ideal.pow_eq_top_iff, AdicCompletion.mk_apply_coe, CategoryTheory.Sieve.pullback_top, Set.not_top_subset, IntermediateField.insepDegree_top, isNoetherian_top_iff, ENNReal.HolderConjugate.top_one, FiniteMulArchimedeanClass.mk_lt_mk, DualNumber.ideal_trichotomy, ProjectiveSpectrum.basicOpen_one, FirstOrder.Language.Substructure.realize_boundedFormula_top, MeasureTheory.SimpleFunc.eapprox_lt_top, EReal.abs_bot, AlgebraicGeometry.Scheme.Γevaluation_naturality, IsLocalRing.map_mkQ_eq_top, EReal.mul_bot_of_neg, ENNReal.add_lt_top, IsGalois.tfae, RingCon.coe_top, OpenAddSubgroup.toOpens_top, Ideal.iInf_pow_smul_eq_bot_of_isTorsionFree, EReal.bot_mul_of_neg, AlgebraicGeometry.Scheme.IdealSheafData.ker_glueDataObjι_appTop, WithTop.untop₀_eq_zero, CategoryTheory.Sieve.uliftFunctorInclusion_top_isIso, AlgebraicGeometry.Spec.germ_stalkMapIso_hom, ContMDiffSection.mdifferentiableAt, EReal.zero_lt_top, SimpleGraph.eq_top_of_chromaticNumber_eq_card, LieSubmodule.toSubmodule_eq_top, Ideal.radical_eq_top, IsFiniteMeasure.lintegral_lt_top_of_bounded_to_ennreal, Module.End.invtSubmodule.zero, IsUltraUniformity.top, WithTop.continuousOn_untopA, ENNReal.iInter_Ioi_coe_nat, minSmoothness_def, nhds_top_basis, Valuation.valuationSubring_eq_top_iff, WithTop.preimage_coe_Ioo_top, MeasureTheory.extend_top, AddSubmonoid.eq_top_iff', RootPairing.rootSpan_eq_top_iff, NonUnitalStarSubalgebra.prod_top, OrderTop.ext_top, Finset.inf_top, contDiffOn_infty_iff_deriv_of_isOpen, EReal.add_top_iff_ne_bot, SimpleGraph.diam_eq_zero, InformationTheory.klDiv_of_not_ac, CoxeterSystem.submonoid_closure_range_simple, KuratowskiEmbedding.exists_isometric_embedding, RingTheory.Sequence.map_first_exact_on_four_term_right_exact_of_isSMulRegular_last, Submodule.mk_eq_top, CStarAlgebra.span_nonneg_inter_ball, LinearOrderedAddCommGroupWithTop.top_add', RingTheory.Sequence.isWeaklyRegular_iff, ENat.toNat_top, Sum.Lex.inr_top, LeftInvariantDerivation.commutator_apply, AlgebraicGeometry.Spec.fromSpecStalk_eq, NonUnitalAlgebra.top_toSubring, essentiallySmall_of_le, AddMonoid.Coprod.range_inl_sup_range_inr, ContinuousMapZero.elemental_eq_top, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over, Subring.op_eq_top, IntermediateField.fg_top_iff, Submonoid.closure_closure_coe_preimage, LeftInvariantDerivation.commutator_coe_derivation, Module.End.invtSubmodule.id, Equiv.Perm.mclosure_isSwap, LinearMap.range_eq_of_proj, ENat.tendsto_nhds_top_iff_natCast_lt, Module.Basis.span_eq, Submodule.instHasOrthogonalProjectionTop, CategoryTheory.GrothendieckTopology.top_covers, PresheafOfModules.pullbackObjIsDefined_eq_top, BoxIntegral.integrable_of_bounded_and_ae_continuousWithinAt, CategoryTheory.Presieve.factorsThru_top, LinearMap.BilinForm.eq_top_of_restrict_nondegenerate_of_orthogonal_eq_bot, MeasureTheory.hasFiniteIntegral_iff_norm, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality, Filter.mem_top, FormalMultilinearSeries.ofScalars_radius_eq_top_of_tendsto, Algebra.GrothendieckGroup.lift_apply, AlgebraicGeometry.Proj.iSup_basicOpen_eq_top, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen', KuratowskiEmbedding.embeddingOfSubset_coe, induced_top, AlgebraicGeometry.Scheme.IdealSheafData.support_bot, AlgebraicGeometry.Scheme.Hom.opensRange_of_isIso, AlgebraicGeometry.LocallyRingedSpace.toΓSpecMapBasicOpen_eq, SchwartzMap.smooth', Submonoid.topEquiv_toMonoidHom, Filter.ker_top, IntermediateField.relfinrank_top_left, AdicCompletion.transitionMap_comp_eval_apply, FirstOrder.Language.Formula.realize_top, WithTop.strictMono_iff, ModuleCat.smulShortComplex_X₃_isModule, NonUnitalRingHom.range_eq_map, FirstOrder.Language.Structure.CG.out, AlgebraicGeometry.instMonoObjWalkingSpanCompOverSchemeTopMorphismPropertySpanOverForgetForgetForgetNoneWalkingPairSomeMapInitOfIsOpenImmersionLeftDiscretePUnit, AlgebraicGeometry.Scheme.Opens.instIsIsoCommRingCatAppLEιTopToScheme, Module.surjective_piEquiv_apply_iff, isIsotypic_iff_isFullyInvariant_imp_bot_or_top, Filter.coprod_eq_prod_top_sup_top_prod, RestrictedProduct.topologicalSpace_eq_of_top, MulAction.aestabilizer_of_aeconst, sInf_eq_top, iInf_neg, Submodule.span_range_eq_top_of_injective_of_rank_le, AlgebraicGeometry.IsAffineOpen.ΓSpecIso_hom_fromSpec_app, Submodule.dualAnnihilator_eq_bot_iff, Subgroup.subgroupOf_bot_eq_top, TensorProduct.quotTensorEquivQuotSMul_comp_mk, Finset.truncatedSup_infs_of_notMem, GroupTopology.toTopologicalSpace_top, ContMDiffSection.mdifferentiable, Fin.val_top, Matrix.iSup_eigenspace_toLin_diagonal_eq_top, iInf_lt_top, Con.toSetoid_eq_top, ENat.mul_top, MeasureTheory.OuterMeasure.dirac_caratheodory, rank_top, Submodule.bot_eq_top_of_rank_eq_zero, MeasureTheory.Lp.dense_hasCompactSupport_contDiff, LieAlgebra.IsKilling.span_weight_eq_top, Real.volume_Ioi, WithTop.untopD_eq_untopD_iff, SmoothPartitionOfUnity.toPartitionOfUnity_toFun, IntermediateField.finSepDegree_top, EReal.coe_nnreal_lt_top, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.largerSubobject_top, SSet.N.iSup_subcomplex_eq_top, AddSubgroup.index_top, Nucleus.top_apply, IsOpen.affineSpan_eq_top, WithTop.none_eq_top, CategoryTheory.Sieve.id_mem_iff_eq_top, SimpleGraph.radius_eq_top_of_isEmpty, IsLocalFrameOn.generating, SmoothPartitionOfUnity.contMDiff_smul, contDiff_infty_iff_fderiv, coe_algEquiv_lpBCF_symm, AlgebraicGeometry.instQuasiCompactToSpecΓOfCompactSpaceCarrierCarrierCommRingCat, Topology.RelCWComplex.skeletonLT_top, FormalMultilinearSeries.radius_eq_top_of_eventually_eq_zero, ENat.eq_top_iff_forall_ge, IsAdjoinRoot.primitive_element_root, Set.Icc.coe_top, AlgebraicGeometry.AffineSpace.comp_homOfVector_assoc, ValueDistribution.characteristic_top_mul_eventually_le, Order.IsPredLimit.lt_top, GrpCat.epi_iff_range_eq_top, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor_map, ENNReal.zero_zpow_def, AddSubsemigroup.srange_fst, MonoidHom.ker_one, PiLp.norm_toLp, AlgebraicGeometry.Scheme.Opens.ι_image_top, CategoryTheory.ObjectProperty.instIsClosedUnderSubobjectsTop, Filter.isBounded_top, LeftInvariantDerivation.ext_iff, AdicCompletion.val_zero_apply, Module.supportDim_quotSMulTop_succ_eq_of_notMem_minimalPrimes_of_mem_jacobson, LinearMap.BilinForm.finrank_add_finrank_orthogonal, isCompl_top_bot, ENNReal.rpow_lt_top_of_nonneg, HomogeneousIdeal.eq_top_iff, Field.Emb.Cardinal.adjoin_basis_eq_top, Filter.comap_const_of_mem, NonUnitalAlgebra.top_toSubmodule, AddCommGroup.smul_top_eq_top_of_divisibleBy_int, VectorField.eventually_contMDiffWithinAt_mpullbackWithin_extChartAt_symm, ENNReal.inv_lt_top, Algebra.TensorProduct.adjoin_tmul_eq_top, MeasurableSet.exists_isOpen_symmDiff_lt, RootPairing.EmbeddedG2.span_eq_top, AlgebraicGeometry.Scheme.Γ_obj_op, Set.pairwise_top, ContinuousMap.starSubalgebra_topologicalClosure_eq_top_of_separatesPoints, BiheytingAlgebra.top_sdiff, Algebra.GrothendieckGroup.of_injective, LipschitzWith.edist_lt_top, Subsemiring.topEquiv_apply, WithTop.ofDual_top, Submonoid.topOrderMonoidIso_apply, SSet.Subcomplex.topIso_hom, Submonoid.closure_irreducible, WithTop.Icc_coe_top, MvPowerSeries.order_zero, CategoryTheory.Sieve.pullback_ofObjects_eq_top, VitaliFamily.eventually_measure_lt_top, HahnEmbedding.Partial.exists_domain_eq_top, ENNReal.tendsto_ofReal_nhds_top, QuotSMulTop.map_id, AlgebraicGeometry.HasRingHomProperty.iff_of_source_openCover, FiniteMulArchimedeanClass.subgroup_strictAnti, PrimeSpectrum.zeroLocus_empty_iff_eq_top, ValuationSubring.top_coe_inv, MvPowerSeries.weightedOrder_eq_top_iff, Module.isPrincipal_def, AlgebraicGeometry.Scheme.IdealSheafData.radical_top, CategoryTheory.ObjectProperty.topEquivalence_inverse, AlgebraicGeometry.Scheme.Opens.topIso_hom, MeasureTheory.SimpleFunc.finMeasSupp_iff, AddSubgroup.relIndex_top_left, MeasureTheory.OuterMeasure.top_apply, Order.Ideal.coe_top, RootPairing.IsRootSystem.span_coroot_eq_top, NonUnitalSubsemiring.coe_top, Submodule.smul_top_le_comap_smul_top, Diffeology.DSmooth.contDiff, Submodule.set_smul_top_eq_span, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, SimpleGraph.IsRegularOfDegree.top, CategoryTheory.presheafIsGeneratedBy_of_isFinite, Subgroup.IsSubnormal.lt_normal, Submonoid.pi_empty, ENNReal.top_sub, IsSimpleOrder.bot_lt_iff_eq_top, Subalgebra.restrictScalars_top, QuotientGroup.leftRel_eq_top, CompactSpace.elim_nhds_subcover, ValueDistribution.characteristic_sum_top_eventuallyLE, CategoryTheory.ObjectProperty.topEquivalence_functor, WithTop.continuous_untop, PrimeSpectrum.basicOpen_one, Real.subfield_eq_of_closed, Subfield.closure_univ, isSimpleGroup_iff, Filter.principal_eq_map_coe_top, SimpleGraph.IsAcyclic.egirth_eq_top, contMDiffOn_vectorSpace_iff_contDiffOn, Ideal.isCoprime_iff_sup_eq, SimpleGraph.Hom.injective_of_top_hom, AlgebraicGeometry.Scheme.Hom.comp_appTop_assoc, AlgebraicGeometry.IsAffineOpen.fromSpec_app_of_le, toBoolRing_top, MeasureTheory.Measure.top_add, AlgebraicGeometry.AffineSpace.map_appTop_coord, top_symmDiff', AlgebraicGeometry.Scheme.toSpecΓ_preimage_basicOpen, isCofinal_iff_top_mem, PrimeSpectrum.iSup_basicOpen_eq_top_iff', ValueDistribution.log_counting_zero_sub_logCounting_top, Filter.bliminf_false, MeasureTheory.Measure.FiniteAtFilter.exists_mem_basis, HahnSeries.orderTop_zero, Set.Subsingleton.einfsep, MeasureTheory.eLpNorm_lt_top_iff_lintegral_rpow_enorm_lt_top, NormedAddGroupHom.ker_zero, CommGrpCat.epi_iff_range_eq_top, MeasureTheory.hitting_eq_sInf, EReal.nhdsWithin_top, AlgebraicGeometry.isIso_fromTildeΓ_iff, top_sdiff', MeasureTheory.Content.outerMeasure_lt_top_of_isCompact, UniformFun.gc, Sublattice.coe_top, MeasureTheory.innerRegularWRT_isCompact_isClosed_measure_ne_top_of_addGroup, LeftInvariantDerivation.toFun_eq_coe, ENNReal.tendsto_rpow_atBot_of_base_lt_one, AdicCompletion.eval_surjective, Subsemigroup.top_prod_top, MulArchimedeanClass.subgroup_eq_bot, AlgebraicGeometry.PresheafedSpace.restrictTopIso_inv, Module.Basis.mk_eq_spanRank, Con.mrange_mk', Set.einfsep_empty, polynomialFunctions_closure_eq_top, MeasureTheory.measure_eq_top_of_lintegral_ne_top, AlgebraicGeometry.Scheme.openCoverBasicOpenTop_f, exteriorPower.ιMulti_span, IsSimpleOrder.eq_bot_or_eq_top, Ideal.iInf_pow_smul_eq_bot_of_noZeroSMulDivisors, BooleanSubalgebra.comap_top, IsDedekindDomain.integer_univ, EReal.image_coe_Ioi, Subgroup.Normal.eq_bot_or_eq_top, InfTopHom.top_apply, bihimp_top, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_hom_c_app, LT.lt.eq_top, AlgebraicGeometry.Scheme.IdealSheafData.comap_top, MonoidHom.ker_snd, IsAdjoinRoot.adjoin_root_eq_top, IsLocalization.coeSubmodule_top, AddMonoidHom.range_eq_top_of_cancel, NonUnitalAlgebra.toNonUnitalSubring_top, iInf_emptyset, dimH_def, SimpleGraph.ediam_bot, Ideal.eq_top_of_mk_tensor_eq_one, Submodule.spanRank_eq_of_equiv, SmoothBumpCovering.embeddingPiTangent_coe, LieSubalgebra.mem_top, Subgroup.IsComplement'.sup_eq_top, SimpleGraph.card_edgeFinset_eq_extremalNumber_top_iff_nonempty_iso_turanGraph, Module.Finite.exists_fin, AlgebraicGeometry.isField_of_isIntegral_of_subsingleton, Order.krullDim_of_noMinOrder, contDiffOn_infty_iff_derivWithin, MeasureTheory.upcrossings_lt_top_iff, ENNReal.tendsto_nhds_top, SmoothPartitionOfUnity.nonneg', MeasureTheory.Measure.exists_isOpen_measure_lt_top, Submodule.torsion'_torsion'_eq_top, ENNReal.tendsto_coe_nhds_top, AddSubgroup.isComplement'_bot_top, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app, ValueDistribution.abs_characteristic_sub_characteristic_shift_le, SmoothPartitionOfUnity.IsSubordinate.contMDiff_finsum_smul, UnitAddTorus.span_mFourierLp_closure_eq_top, Algebra.GrothendieckAddGroup.lift_symm_apply, MeasureTheory.setLAverage_lt_top, MeasureTheory.Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_addGroup, Subgroup.instNontrivialSubtypeMemTop, ULift.down_top, RootPairing.eq_top_of_mem_invtSubmodule_of_forall_eq_univ, FirstOrder.Language.Structure.FG.out, Submodule.mem_top, CategoryTheory.PreOneHypercover.sieve₀_trivial, toBoolAlg_one, inTangentCoordinates_model_space, ENat.zero_epow_top, SimpleGraph.edist_top_of_ne, ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz, ENNReal.HolderConjugate.one_top, CategoryTheory.Subfunctor.preimage_eq_top_iff, AdicCompletion.transitionMap_map_one, IntermediateField.fixingSubgroup_bot, Sublattice.pi_empty, compl_sup_eq_top, CategoryTheory.Subfunctor.Subpresheaf.eq_top_iff_isIso, iSup₂_eq_top, Submonoid.op_top, ModuleCat.epi_iff_range_eq_top, ENNReal.toNNReal_pos_iff, CategoryTheory.Dial.tensorUnitImpl_rel, ofAdd_toDual_eq_zero_iff, OrderDual.ofDual_eq_top, Finset.Ioc_top, Submodule.height_lt_top, Ideal.spanNorm_top, CategoryTheory.Presieve.isSheafFor_top, Order.succ_le_iff_eq_top, MeasureTheory.Measure.lintegral_rnDeriv_lt_top_of_measure_ne_top, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ, Subalgebra.bot_eq_top_iff_rank_eq_one, LinearMap.ker_tensorProductMk, LieSubmodule.baseChange_top, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor_obj, ringKrullDim_le_ringKrullDim_quotSMulTop_succ, Module.supportDim_quotSMulTop_succ_le_of_notMem_minimalPrimes, Module.isTorsionBy_iff_torsionBy_eq_top, WithTop.sub_top, IntermediateField.coe_top, Representation.invariants_eq_top, FiniteArchimedeanClass.addSubgroup_eq_bot, AlgebraicGeometry.AffineSpace.homOfVector_appTop_coord, PMF.support_uniformOfFintype, min_eq_top, Order.height_eq_top_iff, Subring.toSubsemiring_eq_top, Monoid.Coprod.mrange_inl_sup_mrange_inr, AlgebraicGeometry.Scheme.IsQuasiAffine.isBasis_basicOpen, Submodule.comap_top, ENNReal.trichotomy₂, Submodule.coe_eq_univ, HahnEmbedding.Partial.exists_isMax, ENNReal.top_rpow_of_neg, SmoothPartitionOfUnity.sum_le_one, Fin.zero_eq_top, eq_top_or_lt_top, EReal.mul_eq_top, AlgebraicGeometry.Scheme.isoSpec_image_zeroLocus, WithTop.sum_lt_top, ENat.epow_top, AddSubgroup.coe_eq_univ, FirstOrder.Language.Theory.CompleteType.typesWith_top, NonUnitalSubsemiring.range_snd, IccRightChart_extend_top, Algebra.range_id, Polynomial.trailingDegree_eq_top, Subsemigroup.unop_top, Subsemigroup.op_top, Algebra.GrothendieckAddGroup.mk_sub_mk, AdicCompletion.eval_apply, Polynomial.SplittingField.adjoin_rootSet, AlgebraicGeometry.isCompact_and_isOpen_iff_finite_and_eq_biUnion_basicOpen, isSplittingField_iff_intermediateField, ValueDistribution.logCounting_inv, AddMonoidHom.ker_zero, AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf, AddSubgroup.isComplement'_bot_right, Finset.truncatedSup_of_notMem, Fin.rev_bot, AlgebraicGeometry.Scheme.mem_toGrothendieck_smallPretopology, ClosureOperator.isClosed_top, NonemptyInterval.coe_top, boundary_Icc, ULift.up_top, TrivSqZeroExt.range_inlAlgHom_sup_adjoin_range_inr, Subgroup.topEquiv_apply, Subgroup.relIndex_top_right, CategoryTheory.MorphismProperty.Over.mapId_hom_app_left, Polynomial.adjoin_X, AddSubgroup.op_eq_top, LieAlgebra.IsSimple.isAtom_iff_eq_top, FormalMultilinearSeries.constFormalMultilinearSeries_radius, ENNReal.pow_eq_top_iff, bihimp_eq_top, WithTop.lt_top_iff_ne_top, TensorProduct.quotTensorEquivQuotSMul_symm_comp_mkQ, AddSubmonoid.addUnits_top, ENNReal.toReal_eq_zero_iff, Submodule.annihilator_eq_top_iff, CategoryTheory.MorphismProperty.Over.pullbackComp_left_fst_fst, MeasureTheory.hasFiniteIntegral_iff_enorm, StieltjesFunction.measure_Iio_of_tendsto_atBot_atBot, SimpleGraph.cliqueFree_iff_top_free, Submonoid.mk_eq_top, Ring.jacobson_lt_top, RCLike.span_one_I, Submodule.traceDual_top, LieModuleHom.map_top, WithTop.preimage_coe_Ico_top, NonUnitalSubring.toAddSubgroup_top, ENNReal.top_zpow_def, LSeries_eq_zero_iff, CategoryTheory.MorphismProperty.Comma.hasLimitsOfShape_of_closedUnderLimitsOfShape, TopologicalSpace.Opens.coe_top, Group.IsNilpotent.nilpotent, ValueDistribution.proximity_top, PartENat.withTopEquiv_symm_top, EReal.eq_top_iff_forall_lt, isAddFoelner_iff, EReal.neg_top, MeasureTheory.measure_closedBall_lt_top, RingTheory.Sequence.isRegular_cons_iff', CategoryTheory.Subfunctor.epi_iff_range_eq_top, Filter.Realizer.top_σ, Function.HasTemperateGrowth.isBigO_uniform, Sym2.fromRel_top_iff, QuotientGroup.subsingleton_iff, smooth_functions_tower, Submodule.colon_bot, CategoryTheory.PreOneHypercover.sieve₁_trivial, StarSubalgebra.top_toSubalgebra, BoxIntegral.Prepartition.mem_top, Module.Basis.is_basis_iff_det, BoundedOrderHom.map_top', coe_algEquiv_lpBCF, nilpotent_iff_finite_ascending_central_series, CategoryTheory.isGroupoid_iff_isomorphisms_eq_top, MemHolder.eHolderNorm_lt_top, instContMDiffVectorBundleSomeENatTopTangentSpaceOfIsManifold, IsSimpleOrder.equivBool_apply, CategoryTheory.Localization.instIsGroupoidLocalizationTopMorphismProperty, CategoryTheory.Subfunctor.Subpresheaf.range_eq_top, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_basicOpen_eq, Ideal.Quotient.zero_eq_one_iff, boundary_product, instIndiscreteTopology, LieSubmodule.comap_incl_self, UpperSet.prod_eq_top, GromovHausdorff.eq_toGHSpace_iff, NonUnitalAlgebra.toNonUnitalSubsemiring_eq_top, Subgroup.IsSubnormal.isSubnormal_iff, irreducibleSpace_def, TopologicalSpace.Opens.coe_eq_univ, Submodule.IsPrincipal.isPrimitive_iff_contentIdeal_eq_top, HahnEmbedding.Seed.domain_baseEmbedding, AlgebraicGeometry.Scheme.AffineZariskiSite.mem_grothendieckTopology_iff_sectionsOfPresieve, Field.primitive_element_iff_algHom_eq_of_eval, ENNReal.iInf_coe_eq_top, MeasureTheory.L2.eLpNorm_rpow_two_norm_lt_top, inCoordinates_tangent_bundle_core_model_space, Subring.toAddSubgroup_top, Sublattice.prod_top, FirstOrder.Language.Substructure.mem_top, Set.setOf_top, Algebra.Extension.Cotangent.ker_mk, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_appTop, Submodule.IsPrimary.mem_or_mem, Additive.toMul_eq_top, Associates.out_top, AdicCompletion.val_sum_apply, FiniteArchimedeanClass.withTopOrderIso_apply_coe, Filter.le_comap_top, EReal.coe_ennreal_eq_top_iff, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓFreeOpensCarrierCarrierCommRingCat, RootPairing.IsIrreducible.eq_top_of_invtSubmodule_reflection, CategoryTheory.Subfunctor.range_id, MulAction.aestabilizer_univ, CategoryTheory.MorphismProperty.top_apply, LieIdeal.lcs_top, AlgebraicGeometry.instHasFiniteCoproductsOverSchemeTopMorphismProperty, EReal.coe_mul_top_of_neg, MeasureTheory.MemLp.meas_ge_lt_top_enorm, ContDiffMapSupportedIn.structureMapLM_apply, CStarAlgebra.span_unitary, MonoidHom.eqLocusM_same, ENNReal.lt_top_of_mul_ne_top_right, CategoryTheory.Localization.Construction.morphismProperty_is_top, FiniteMulArchimedeanClass.coe_congrOrderIso_apply, WithTop.range_coe, Submonoid.topEquiv_apply, LeftInvariantDerivation.instLinearMapClassContMDiffMapModelWithCornersSelfSomeENatTop, separableClosure.adjoin_eq_of_isAlgebraic_of_isSeparable, Tropical.untrop_zero, LeftInvariantDerivation.coeFnAddMonoidHom_apply, AddSubmonoid.topEquiv_toAddMonoidHom, SupHom.top_apply, AddCon.toSetoid_eq_top, Set.Iic.eq_top_iff, AddSubgroup.mem_top, Monoid.minOrder_eq_top, contMDiff_snd_tangentBundle_modelSpace, Monoid.minOrder_eq_top_iff, Summable.tsum_ofReal_lt_top, ENNReal.mul_self_lt_top_iff, Filter.frequently_top, SimpleGraph.card_topEdgeLabeling, Module.erange_coe, ValueDistribution.proximity_sub_proximity_inv_eq_circleAverage, EReal.coe_ennreal_top, commutator_eq_bot_iff_center_eq_top, MeasureTheory.ae_measure_preimage_add_right_lt_top, Cardinal.toENat_lt_top, MvPolynomial.range_evalᵢ, AlgebraicGeometry.instIsAffineHomιBasicOpen, SimpleGraph.cycleGraph_zero_eq_top, ENNReal.lt_top_of_sum_ne_top, Codisjoint.eq_top, contDiff_sigmoid, compl_bot, Submodule.submoduleOf_self, AddSubgroup.index_eq_one, Submodule.lt_top_of_finrank_lt_finrank, HahnSeries.leadingCoeff_of_ne_zero, Finsupp.range_restrictDom, SSet.Truncated.HomotopyCategory.morphismProperty_eq_top, MeasureTheory.IsFiniteMeasure.measure_univ_lt_top, AddSubmonoid.LocalizationMap.top_injective_iff, CategoryTheory.MorphismProperty.top_eq, Derivation.evalAt_apply, Submodule.isPrimary_iff_zero_divisor_quotient_imp_nilpotent_smul, Associates.FactorSet.prod_eq_zero_iff, top_uniformity, Finset.Ici_top, rootsOfUnity_zero, ENNReal.coe_lt_top, not_infIrred_top, EReal.neg_bot, Icc_isBoundaryPoint_top, MeasureTheory.SimpleFunc.finMeasSupp_iff_support, AdicCompletion.of_apply, LinearMap.exists_map_addHaar_eq_smul_addHaar', MeasureTheory.eLpNorm_smul_le_eLpNorm_top_mul_eLpNorm, Subgroup.card_eq_iff_eq_top, EReal.exp_top, ENat.iSup_coe_lt_top, ENNReal.exists_countable_dense_no_zero_top, ENNReal.HolderTriple.instInfty, EReal.mem_nhds_top_iff, Function.HasTemperateGrowth.isBigO, ENat.range_natCast, PiLp.nnnorm_ofLp, ValueDistribution.characteristic_mul_top_eventuallyLE, FiniteArchimedeanClass.mem_closedBall_iff, NonUnitalSubring.range_fst, WithTop.exists, AddSubgroup.IsSubnormal.eq_bot_or_top_of_isSimpleAddGroup, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst_assoc, CategoryTheory.Sieve.generate_of_contains_isSplitEpi, Subalgebra.rank_top, Monoid.fg_def, Module.isTorsionBy_quotient_element_smul, contMDiffOn_infty, AlgebraicGeometry.HasRingHomProperty.iff_of_isAffine, Subalgebra.bot_eq_top_of_rank_eq_one, LinearEquiv.range, MulArchimedeanClass.orderHom_top, EReal.coe_lt_top, sInfHom.top_apply, ContDiffMapSupportedIn.structureMapLM_eq, ArchimedeanClass.closedBall_top, CategoryTheory.Subfunctor.Subpresheaf.range_toRange, AlgebraicGeometry.SheafedSpace.restrictTopIso_hom, InfHom.coe_top, MeasureTheory.setLIntegral_lt_top_of_isCompact, Ideal.IsOka.top, WithTop.toDualBotEquiv_top, Submodule.range_fst, Order.krullDim_nat, MeasureTheory.ae_lt_top, BooleanSubalgebra.mem_bot, AlgebraicGeometry.ΓSpec.toSpecΓ_unop, RingHom.eqLocusS_same, hausdorffMeasure_of_lt_dimH, MeasureTheory.measure_lt_top_of_isCompact_of_isMulLeftInvariant', LieModuleEquiv.range_coe, Ideal.exists_pow_inf_eq_pow_smul, MeasureTheory.OuterMeasure.toMeasure_top, hahnEmbedding_isOrderedAddMonoid, Prop.top_eq_true, FirstOrder.Language.ElementarySubstructure.mem_top, Multiplicative.toAdd_top, MeasureTheory.Measure.InnerRegularWRT.measurableSet_of_isOpen, subalgebra_top_rank_eq_submodule_top_rank, Filter.limsup_top_eq_iSup, isComplemented_top, Sublattice.coe_eq_univ, AdicCompletion.eval_comp_of, CategoryTheory.MorphismProperty.CostructuredArrow.mk_hom, MeasureTheory.MemLp.eLpNorm_mk_lt_top, SmoothBumpCovering.toSmoothPartitionOfUnity_zero_of_zero, SimpleGraph.edist_bot_of_ne, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_bot, AlgebraicGeometry.SheafedSpace.Γ_map_op, SmoothPartitionOfUnity.contMDiff_sum, AdicCompletion.val_smul_apply, FirstOrder.Language.Theory.imp_top, AddMonoidHom.mker_snd, MeasureTheory.memLp_top_const, CategoryTheory.Paths.morphismProperty_eq_top, MeasureTheory.MemLp.exists_eLpNorm_indicator_compl_lt, LieAlgebra.IsSimple.eq_bot_or_eq_top, AddSubsemigroup.prod_top, ENNReal.forall_ennreal, SimpleGraph.dist_top, Module.Dual.range_eq_top_of_ne_zero, FirstOrder.Language.Substructure.closure_univ, NonUnitalSubsemiring.topEquiv_symm_apply_coe, PiLp.nndist_eq_iSup, RingCon.toCon_top, Ring.not_isField_iff_exists_ideal_bot_lt_and_lt_top, Subgroup.eq_top_of_le_card, Submodule.span_range_inclusionSpan, LinearMap.surjective_domRestrict_iff, SimpleGraph.eccent_top, TensorProduct.quotTensorEquivQuotSMul_mk_tmul, WithTop.range_eq, ClopenUpperSet.coe_top, Subsemigroup.closure_univ, AddSubgroup.IsSubnormal.isSubnormal_iff, Submodule.map_le_smul_top, Multiplicative.ofAdd_top, CategoryTheory.MorphismProperty.Comma.hasLimit_of_closedUnderLimitsOfShape, TensorProduct.tensorQuotEquivQuotSMul_symm_comp_mkQ, ProjectiveSpectrum.vanishingIdeal_univ, kuratowskiEmbedding.isometry, ENat.top_mul', Finsupp.iSup_lsingle_range, Subgroup.IsSubnormal.exists_chain, isCyclic_tfae, Order.krullDim_eq_top_iff, MeasureTheory.eLpNorm_smul_le_eLpNorm_mul_eLpNorm_top, Finset.min_mem_insert_top_image_coe, CategoryTheory.MorphismProperty.Over.map_obj_hom, LieHom.idealRange_eq_top_of_surjective, MeasureTheory.QuotientMeasureEqMeasurePreimage.covolume_ne_top, isTop_top, affineSpan_eq_top_iff_nonempty_of_subsingleton, Module.finrank_le_one_iff_top_isPrincipal, LieSubmodule.gc_top_lie_normalizer, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ_assoc, GaloisInsertion.l_top, OrderDual.ofDual_top, MeasureTheory.pdf.ae_lt_top, NonUnitalSubsemiring.topEquiv_apply, ENat.coe_lt_top, CategoryTheory.MorphismProperty.instFaithfulUnderTopUnderForget, CategoryTheory.GrothendieckTopology.top_covering, Filter.limsSup_top, hahnEmbedding_isOrderedModule, Fin.succ_top, AlgebraicGeometry.LocallyRingedSpace.Γ_obj, LinearMap.range_lt_top_of_det_eq_zero, stabilizer_univ_eq_top, CoheytingAlgebra.top_sdiff, AlgebraicGeometry.Scheme.Spec_fromSpecStalk, IntermediateField.sepDegree_top, WithTop.mul_eq_top_iff, WithBot.ofDual_apply_bot, EReal.top_mul_coe_of_neg, natCast_memℓp_infty, Submodule.eq_top_of_finrank_eq, Set.chainHeight_eq_top_iff, AddSubsemigroup.unop_eq_top, OrderDual.ofDual_eq_bot, Diffeology.dSmooth_iff_contDiff, LinearMap.BilinForm.span_singleton_sup_orthogonal_eq_top, IsAntichain.top_mem_iff, LeftInvariantDerivation.evalAt_apply, Algebra.TensorProduct.closure_range_union_range_eq_top, Order.Ideal.principal_top, WithTop.untopD_eq_self_iff, Subgroup.relIndex_top_left, FirstOrder.Language.Structure.fg_iff, HilbertBasis.finite_spans_dense, SimplexCategory.morphismProperty_eq_top, Subgroup.unop_top, CategoryTheory.Limits.kernelSubobject_zero, AlgebraicGeometry.Scheme.toSpecΓ_base, HahnEmbedding.Partial.toOrderAddMonoidHom_injective bridge: BoxIntegral.hasIntegralIndicatorConst, MeasureTheory.SimpleFunc.hasBoxIntegral, MeasureTheory.IntegrableOn.hasBoxIntegral, BoxIntegral.HasIntegral.of_aeEq_zero, MeasureTheory.SimpleFunc.box_integral_eq_integral, top_eq_true

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
ext 📖	—	top	—	—	—
ext_iff 📖	mathematical	—	top	—	ext

(root)

Definitions

Name	Category	Theorems
Bot 📖	CompData	—
Compl 📖	CompData	—
HImp 📖	CompData	—
HNot 📖	CompData	—
HasCompl 📖	CompData	—
Top 📖	CompData	—
«term_ᶜ» 📖	CompOp	—
«term_⇨_» 📖	CompOp	—
«term_⊓_» 📖	CompOp	—
«term_⊔_» 📖	CompOp	—
«term⊤» 📖	CompOp	—
«term⊥» 📖	CompOp	—
«term￢_» 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
bot_nonempty 📖	—	—	—	—	—
top_nonempty 📖	—	—	—	—	—

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