Real

📁 Source: MathlibTest/Real.lean

Statistics

Metric	Count
Definitions Real	1
Theorems	0
Total	1

(root)

Definitions

Name	Category	Theorems
Real 📖	CompData	11476 math, 2 bridge math: AddGroupNorm.add_apply, ContinuousMap.dense_setOf_contDiff, List.norm_prod_le, Real.cos_add_nat_mul_pi, ArithmeticFunction.vonMangoldt.residueClass_eq, Padic.eq_ratNorm, MeasureTheory.Measure.exists_innerRegular_eq_of_isCompact, Measurable.ereal_toReal, Unitary.openPartialHomeomorph_source, withSeminorms_iff_mem_nhds_isVonNBounded, SchwartzMap.norm_toLp_le_seminorm, range_cfcₙ_nnreal, IsUnit.cfcRpow, MeasureTheory.tendstoInMeasure_iff_measureReal_norm, CircleDeg1Lift.units_inv_apply_apply, Orientation.rightAngleRotationAux₁_rightAngleRotationAux₁, Behrend.roth_lower_bound, ValueDistribution.logCounting_zero, MeasureTheory.exists_pos_preimage_ball, CFC.rpow_inv_rpow, Polynomial.logMahlerMeasure_one, comap_dist_left_atTop_eq_cocompact, norm_eq_zero, CuspFormClass.qExpansion_isBigO, AddCircle.measure_univ, MeasureTheory.Measure.integral_comp_inv_smul, EReal.nhds_top_basis, Real.Angle.abs_toReal_neg_coe_eq_self_iff, Real.pi_div_four_le_arcsin, Metric.hausdorffDist_empty', ProbabilityTheory.Kernel.measurable_rnDerivAux, ZLattice.summable_norm_zpow, ENNReal.one_rpow, Real.rpow_eq_pow, BoundingSieve.nu_lt_one_of_dvd_prodPrimes, Real.differentiableOn_arcosh, Affine.Simplex.isTangentAt_insphere_iff_eq_touchpoint, isEquivalent_descFactorial, NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symm, Real.hasDerivAt_arccos, PiLp.lipschitzWith_toLp, HurwitzZeta.isBigO_atTop_evenKernel_sub, CStarAlgebra.preimage_inr_Icc_zero_one, Metric.hasBasis_cobounded_compl_closedBall, RCLike.map_from_real, RCLike.conj_re, norm_sub_sq_real, ArithmeticFunction.vonMangoldt.summable_residueClass_non_primes_div, HurwitzZeta.expZeta_zero, Real.range_sin, TemperedDistribution.lineDerivOpCLM_eq, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', continuousSMul_sphere_ball, CircleDeg1Lift.instOrderHomClassReal, BoundedContinuousFunction.tietze_extension_step, NumberField.mixedEmbedding.fundamentalDomain_integerLattice, Complex.log_conj_eq_ite, Complex.verticalSegment_eq, Orientation.oangle_sign_smul_add_right, MeasureTheory.Lp.toTemperedDistributionCLM_apply, InformationTheory.integrable_klFun_rnDeriv_iff, RCLike.sqrt_eq_ite, ContinuousMap.HomotopyRel.prod_apply, Complex.im_qsmul, Asymptotics.isBigO_norm_norm, MeasureTheory.setIntegral_tilted, Real.isFiniteMeasure_restrict_Ioc, Circle.periodic_exp, Orientation.oangle_eq_zero_or_eq_pi_iff_right_eq_smul, TemperedDistribution.fourierInv_toTemperedDistributionCLM_eq, MeasureTheory.Integrable.integral_norm_prod_right, norm_smul_le, Real.smoothTransition.eq_one_iff_one_le, TendstoUniformly.im, Seminorm.isBounded_const, MeasureTheory.L1.SimpleFunc.norm_Integral_le_one, isConformalMap_conj, PiLp.norm_toLp_const', MeasureTheory.eLpNorm'_norm, NNReal.orderIsoIccZeroCoe_apply_coe_coe, lp.norm_apply_le_norm, NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingOfIsReal, Real.tan_pi_div_four, RCLike.im_le_neg_norm_iff_eq_neg_I_mul_norm, Real.ofDigits_const_last_eq_one, MeasureTheory.mulEquivHaarChar_smul_integral_map, RCLike.measurable_ofReal, EuclideanGeometry.dist_smul_vadd_sq, SemiNormedGrp.explicitCokernelDesc_norm_le, Bundle.ContMDiffRiemannianMetric.isVonNBounded, ProbabilityTheory.tendsto_defaultRatCDF_atBot, SchwartzMap.lineDerivOpCLM_eq, NumberField.InfinitePlace.isNontrivial, Subgroup.isRegularAtInfty_iff, ProbabilityTheory.stieltjesOfMeasurableRat_ae_eq, Irrational.instNoMaxOrderSubtypeReal, IsUltrametricDist.isNonarchimedean_norm, Real.cos_pi_div_five, dist_le_range_sum_dist, NNReal.summable_coe, real_inner_div_norm_mul_norm_eq_neg_one_iff, NumberField.InfinitePlace.eq_iff_isEquiv, dist_triangle, Real.isBigO_log_mul_const_log_atTop, Metric.cauchySeq_iff, ConformalAt.differentiableAt, AddGroupNorm.coe_le_coe, Orientation.oangle_ne_zero_and_ne_pi_iff_linearIndependent, isCompact_stdSimplex, Polynomial.mahlerMeasure_def_of_ne_zero, ProbabilityTheory.Kernel.tendsto_m_density, exists_continuous_sum_one_of_isOpen_isCompact, Real.one_le_sqrt, EulerSine.integral_cos_mul_cos_pow, Height.logHeight₁_pow, MeasureTheory.condExpInd_of_measurable, WithLp.norm_fst_le, SpectrumRestricts.nnreal_of_nonneg, Complex.mul_im, MeasureTheory.Lp.mul_meas_ge_le_pow_enorm', PiLp.nndist_eq_sum, gold_sq, AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound, ModularGroup.SLOnGLPos_smul_apply, RCLike.pos_iff_exists_ofReal, MeasureTheory.llr_self, norm_lt_of_mem_ball', PadicInt.coe_sub, RCLike.one_re, HasDerivAt.le_of_lipschitz, Real.sin_add_sin, Real.logb_zero_left, Bundle.ContMDiffRiemannianMetric.contMDiff, continuousOn_stereoToFun, Real.exists_floor, SmoothBumpCovering.toSmoothPartitionOfUnity_eq_mul_prod, ModularForm.smul_slash, completelyRegularSpace_iff_isOpen, Complex.re_mul_ofReal, ValueDistribution.characteristic_even, LiouvilleWith.nat_sub_iff, Finset.Nonempty.norm_sum_le_sup'_norm, ContinuousAlternatingMap.opNorm_prod, Complex.div_ofReal_re, Real.expNear_succ, Real.Angle.sign_two_zsmul_eq_sign_iff, Real.goldenConj_mul_fib_succ_add_fib, ProbabilityTheory.condIndepFun_iff_condExp_inter_preimage_eq_mul, ProbabilityTheory.condCDF_ae_eq, ProbabilityTheory.isGaussian_iff_gaussian_charFun, GroupSeminorm.apply_one, CircleDeg1Lift.translationNumber_mul_of_commute, NormedAddGroupHom.norm_id_of_nontrivial_seminorm, Real.Angle.neg_coe_abs_toReal_of_sign_nonpos, NNReal.rpow_sub_intCast, Real.differentiable_arctan, MeasureTheory.SimpleFunc.posPart_sub_negPart, ProbabilityTheory.gaussianReal_map_const_mul, ProperCone.innerDual_le_innerDual, EReal.coe_le_coe_iff, Real.map_exp_nhds, NormedCommGroup.tendsto_nhds_nhds, Seminorm.mem_ball_zero, RCLike.map_apply, exists_contMDiffMap_zero_one_of_isClosed, Real.arcosh_bijOn, IsUltrametricDist.isNonarchimedean_invariantExtension, CStarMatrix.norm_entry_le_norm, Real.differentiableAt_mulExpNegMulSq, Path.subpath_self, EReal.image_coe_Icc, Real.sinh_eq, Complex.restrictScalars_one_smulRight', MeasureTheory.eval_integral, MeasureTheory.aestronglyMeasurable_condExpInd, MeasureTheory.eLpNorm_condExp_le, BoundedContinuousMapClass.map_bounded, MeasureTheory.setIntegral_nonpos_ae, Real.one_le_cosh, Real.not_continuousAt_inv_log_neg_one, HasCompactSupport.convolution_integrand_bound_left, Real.Angle.toReal_add_of_sign_eq_neg_sign, IsPathConnected.exists_path_through_family', Real.iInf_of_isEmpty, ProbabilityTheory.lintegral_condCDF, MeasureTheory.Martingale.smul, Real.isLittleO_logb_id_atTop, Complex.coe_realPart, Real.toNNReal_lt_natCast', ContDiffBump.nonneg_normed, IsSelfAdjoint.quasispectrumRestricts, LinearMap.coe_toSeminorm, eventually_residual_irrational, NumberField.mixedEmbedding.logMap_one, EisensteinSeries.linear_inv_isBigO_left, mellin_eq_fourier, Real.sSup_smul_of_nonpos, Real.HolderTriple.inv_add_inv_eq_inv, ENNReal.toReal_min, SchwartzMap.instLineDerivLeftSMulReal, Real.hasMeasurablePow, lp.isLUB_norm, BumpCovering.eventuallyEq_one, bernsteinApproximation.apply_zero, Quaternion.coeComplex_re, LipschitzOnWith.norm_sub_le, unitInterval.sigmoid_le_iff, ContinuousLinearMap.norm_inr_le_one, EuclideanGeometry.abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq, taylorWithin_succ, NumberField.mixedEmbedding.lintegral_comp_polarCoord_symm, Complex.UnitDisc.normSq_lt_one, Real.sin_arctan, MeasureTheory.Measure.addHaar_image_continuousLinearMap, Real.sin_eq_zero_iff_cos_eq, ofDigits_zero_two_sequence_mem_cantorSet, Matrix.IsHermitian.isClosedEmbedding_cfcAux, BoxIntegral.Prepartition.measure_iUnion_toReal, Stirling.log_stirlingSeq_bounded_aux, BoundedContinuousFunction.dist_eq_iSup, IsUltrametricDist.algNormOfAlgEquiv_extends, integral_cos, RCLike.ofRealCLM_apply, RCLike.normSq_to_real, MeasureTheory.norm_indicatorConstLp_le, SchwartzMap.integral_sesq_fourier_fourier, tendsto_norm_sub_self_nhdsNE, Real.pi_le_four, NumberField.InfinitePlace.norm_embedding_of_isReal, ProbabilityTheory.condDistrib_ae_eq_condExp, Real.volume_real_Ioc, Real.dimH_of_mem_nhds, WithSeminorms.image_isVonNBounded_iff_seminorm_bounded, Real.iteratedDeriv_odd_cos, MeasureTheory.charFun_eq_fourierIntegral', norm_of_subsingleton', Real.hasFDerivAt_fourierChar_neg_bilinear_left, Real.tan_pi_sub, isApproximateAddSubgroup_zero, instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, Real.differentiableAt_arcsin, geometric_hahn_banach_point_point, NumberField.mixedEmbedding.fundamentalCone.interior_paramSet, segment_subset_closedBall_right, Complex.linearEquiv_det_conjLIE, NumberField.mixedEmbedding.measurable_polarCoordReal_symm, NormedRing.inverse_one_sub_norm, Real.arcsin_eq_pi_div_two_sub_arccos, MeasureTheory.condExpInd_ae_eq_condExpIndSMul, Real.range_log, Real.instIsOrderedRing, Complex.normSq_pos, MeasureTheory.levyProkhorovDist_triangle, Function.hasTemperateGrowth_inner_right, Isometry.preimage_perpBisector, norm_zsmul, ProbabilityTheory.condCDF_nonneg, RCLike.reCLM_apply, PadicInt.norm_int_lt_one_iff_dvd, gauge_def', CircleDeg1Lift.translate_inv_apply, bernoulliFun_eval_one_sub, NumberField.Units.finrank_eq_rank, unitInterval.symmHomeomorph_apply, MeasureTheory.hausdorffMeasure_segment, Real.abs_sinc_le_one, MeasureTheory.integrable_withDensity_iff_integrable_coe_smul, Irrational.ratCast_sub, ValueDistribution.proximity_zero, CircleDeg1Lift.map_sub_int, Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_face, RCLike.div_re_ofReal, Affine.Simplex.smul_mongePoint_vsub_circumcenter_eq_sum_vsub, dist_midpoint_right, Real.sqrt_eq_cases, AddDissociated.randomisation, Complex.reProdIm_nonempty, TsirelsonInequality.sqrt_two_inv_mul_self, CFC.abs_eq_cfc_norm, ZLattice.summable_norm_sub_inv_pow, Orientation.inner_rotation_pi_div_two_right_smul, intervalIntegral.intervalIntegrable_one_div_one_add_sq, Complex.lim_conj, Real.contDiffOn_log, Orientation.oangle_add_left_smul_rotation_pi_div_two, ContinuousLinearMap.exists_preimage_norm_le, GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I, CFC.monotoneOn_one_sub_one_add_inv, ProbabilityTheory.tendsto_defaultRatCDF_atTop, Real.fourierIntegral_comp_linearIsometry, ProbabilityTheory.IsCondKernelCDF.toKernel_Iic, Path.continuousMapClass, ODE.FunSpace.next_apply, Affine.Simplex.sSameSide_excenter_singleton_point, ProbabilityTheory.IsMeasurableRatCDF.iInf_rat_gt_eq, MeasureTheory.integral_smul_nnreal_measure, ExistsContDiffBumpBase.u_support, CFC.sqrt_eq_one_iff', CFC.posPart_one, Real.smul_map_volume_mul_right, NumberField.mixedEmbedding.norm_eq_sup'_normAtPlace, gauge_le_one_of_mem, ContinuousMap.abs_mem_subalgebra_closure, Seminorm.le_finset_sup_apply, unitInterval.volume_Ioo, AddGroupNorm.ext_iff, Affine.Simplex.neg_mul_lt_inner_vsub_altitudeFoot, unitInterval.volume_Iic, EuclideanGeometry.Sphere.isExtTangent_iff_dist_center, GroupSeminorm.coe_sup, ContinuousMap.HomotopyWith.coe_toContinuousMap, hasDerivAt_sqrt_mul_log, NumberField.Units.logEmbedding_fundSystem, Manifold.pathELength_eq_lintegral_mfderiv_Ioo, LinearMap.IsSymmetric.restrictScalars, Seminorm.norm_sub_map_le_sub, NNReal.rpow_rpow_inv, MeasureTheory.MeasuredSets.real_sub_real_le_dist, Complex.isOpenMap_im, IsometryEquiv.toRealLinearIsometryEquiv_symm_apply, Real.cos_add_pi, SmoothBumpFunction.support_eq_symm_image, Filter.hasBasis_cobounded_norm', ProbabilityTheory.Kernel.densityProcess_antitone_kernel_right, SchwartzMap.norm_le_seminorm, Int.cast_complex_isTheta_cast_real, ZSpan.volume_real_fundamentalDomain, InnerProductGeometry.angle_add_angle_sub_add_angle_sub_eq_pi, realPart_idem, NumberField.mixedEmbedding.convexBodyLT'_mem, Real.arctan_eq_arcsin, Complex.ofRealCLM_coe, ContractingWith.dist_fixedPoint_le, Complex.kahler, Complex.norm_polarCoord_symm, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left, spectrum.norm_le_norm_of_mem, Complex.norm_sub_eq, Real.exp_sub_sinh, ContinuousMap.integral_apply, PadicInt.mem_subring_iff, NumberField.prod_nonarchAbsVal_eq, ProbabilityTheory.eqOn_complexMGF_of_mgf', MeasureTheory.Measure.integral_comp_mul_right, ProbabilityTheory.IsCondKernelCDF.le_one, SimpleGraph.det_lapMatrix_eq_zero, Real.sin_pi_div_two, RightDerivMeasurableAux.D_subset_differentiable_set, MeasureTheory.upperCrossingTime_succ_eq, ContinuousLinearMap.sSup_unit_ball_eq_norm, SchwartzMap.inner_fourier_toL2_eq, Real.arsinh_surjective, Complex.areaForm, NNReal.rpowMonoidHom_apply, Function.locallyFinsuppWithin.toClosedBall_support_subset_closedBall, SchwartzMap.toLp_fourierTransformInv_eq, ZSpan.fundamentalDomain_measurableSet, intervalIntegral.inv_smul_integral_comp_div_add, ContinuousAlternatingMap.norm_ofSubsingleton_id_le, unitInterval.volume_def, CliffordAlgebraComplex.ofComplex_conj, finrank_real_complex_fact', ProbabilityTheory.covariance_neg_left, ProbabilityTheory.betaPDF_eq, Metric.exists_continuous_real_forall_closedEBall_subset, Complex.instIsComplete, GaussianInt.intCast_im, Chebyshev.theta_eq_theta_coe_floor, GroupNorm.le_def, Real.deriv_negMulLog, EuclideanGeometry.eq_zero_or_angle_eq_zero_or_pi_of_sign_oangle_eq_zero, Real.hasDerivAt_sigmoid, ContDiffMapSupportedInClass.map_contDiff, Metric.uniformContinuous_iff_le, UnitAddCircle.lintegral_preimage, Real.analyticOn_cos, ProbabilityTheory.lintegral_toKernel_univ, NonarchAddGroupSeminorm.coe_iSup_apply, EuclideanGeometry.Sphere.isDiameter_iff_right_mem_and_midpoint_eq_center, gold_add_goldConj, ProbabilityTheory.analyticOn_mgf, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, Complex.ofReal_eq_one, Metric.unitSphere.coe_one, Complex.normSq_natCast, Real.fourierIntegralInv_eq', Asymptotics.isBigO_abs_abs, MeasureTheory.eLpNorm'_const', Real.Angle.two_zsmul_eq_pi_iff, IntervalIntegrable.sum, PositiveLinearMap.apply_le_of_isSelfAdjoint, CircleDeg1Lift.map_add_nat, Mathlib.Tactic.Rify.ratCast_le, Matrix.IsHermitian.det_abs, volume_iUnion_setOf_liouvilleWith, Real.tan_inv_eq_cot, Real.ringHom_apply, RCLike.ofRealLI_apply, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, Complex.comap_exp_cobounded, Metric.continuousWithinAt_iff', RightDerivMeasurableAux.measurableSet_B, Metric.diam_mono, GroupNorm.toGroupSeminorm_eq_coe, PadicInt.coe_zero, ModularForm.mul_slash, Real.sin_add_two_pi, Height.mulHeight₁_eq, Padic.norm_intCast_eq_one_iff, Real.strictMonoOn_sqrt, ProbabilityTheory.condIndep_iff, deriv_abs, integral_sin_mul_cos₂, Asymptotics.isLittleO_const_left, EuclideanGeometry.dist_inversion_inversion, curveIntegrable_segment, ZMod.LFunction_stdAddChar_eq_expZeta, Padic.eq_padicNorm, Affine.Simplex.finiteDimensional_direction_altitude, MeasureTheory.SimpleFunc.posPart_map_norm, Real.Angle.sin_add_pi_div_two, MeasureTheory.sum_measureReal_singleton, LiouvilleWith.sub_rat, Stirling.factorial_isEquivalent_stirling, NumberField.FinitePlace.mk_apply, Complex.norm_le_abs_re_add_abs_im, StieltjesFunction.rightLim_eq, AkraBazziRecurrence.tendsto_zero_sumCoeffsExp, ProbabilityTheory.covarianceBilinDual_apply', Real.sinh_add, Real.measurable_sinh, Circle.exp_arg, Complex.exists_mem_frontier_isMaxOn_norm, covBySMul_zero, Real.abs_cos_le_one, ContinuousLinearMap.sSup_unitClosedBall_eq_nnnorm, spectrum.subset_closedBall_norm_mul, Circle.injective_arg, continuousSMul_sphere_sphere, Real.logb_one, Real.deriv_binEntropy, MeasureTheory.upcrossingStrat_nonneg, CFC.monotone_nnrpow, AffineSubspace.mem_perpBisector_iff_inner_eq_zero', lebesgue_number_lemma_of_metric_sUnion, ProbabilityTheory.mgf_const_add, LiouvilleWith.rat_sub_iff, Metric.closedBall_eq_bInter_ball, RCLike.re_add_im, CFC.posPart_natCast, MeasureTheory.charFunDual_apply, InnerProductSpace.Core.inner_mul_inner_self_le, Real.cos_sub_pi, gauge_lt_one_of_mem_of_isOpen, Polynomial.Chebyshev.complex_ofReal_eval_S, uniqueDiffWithinAt_Iic, Real.cos_eq_zero_iff, Real.Angle.cos_add, SmoothBumpCovering.mem_support_ind, BoundedContinuousFunction.norm_compContinuous_le, MeasureTheory.Measure.hausdorffMeasure_zero_singleton, BoxIntegral.Box.splitUpper_eq_bot, Complex.ofRealLI_apply, ProbabilityTheory.Kernel.densityProcess_mono_set, CuspFormClass.zero_at_infty_comp_ofComplex, Affine.Simplex.circumcenter_map, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, Complex.GammaIntegral_eq_mellin, ProbabilityTheory.variance_fun_id_gaussianReal, NNReal.coe_indicator, Polynomial.mahlerMeasure_eq_leadingCoeff_mul_prod_roots, Metric.hasAntitoneBasis_cobounded_compl_ball, IsSelfAdjoint.norm_mul_self, BoundedContinuousFunction.integral_eq_integral_nnrealPart_sub, ProbabilityTheory.hasGaussianLaw_iff_charFunDual_map_eq, Real.young_inequality, norm_jacobiTheta₂_term_fderiv_ge, unitInterval.zero_mem, UpperHalfPlane.normSq_pos, norm_add_eq_iff_real, NormedAddGroupHom.norm_comp_le, ENNReal.toReal_pos_iff, Complex.integral_comp_pi_polarCoord_symm, ProbabilityTheory.Kernel.borelMarkovFromReal_apply', Real.summable_ofDigitsTerm, ContinuousLinearMap.norm_inl_le_one, CFC.tendsto_cfc_rpow_sub_one_log, MeasureTheory.lpNorm_fun_div_natCast, MeasureTheory.norm_condExpL2_le, contDiffAt_norm_smul_iff, AkraBazziRecurrence.T_gt_zero', ProbabilityTheory.IsGaussian.integrable_dual, Complex.norm_mul_self_eq_normSq, UnitAddCircle.intervalIntegral_preimage, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne, SchwartzMap.pairing_apply_apply, intervalIntegral.mul_integral_comp_mul_sub, BoxIntegral.unitPartition.mem_box_iff', norm_iteratedFDerivWithin_smul_le, ProbabilityTheory.Kernel.density_fst_univ, BumpCovering.toPartitionOfUnity_apply, ENNReal.rpow_mul, ContDiffMapSupportedIn.iteratedFDerivLM_apply, Real.tan_int_mul_pi, Real.real_sqrt_le_nat_sqrt_succ, IsLprojection.Lnorm, Real.sSup_empty, Complex.real_smul, MeasureTheory.weightedSMul_apply, ContinuousMultilinearMap.norm_map_snoc_le, NumberField.InfinitePlace.le_iff_le, ProbabilityTheory.HasSubgaussianMGF.integrable_exp_mul, ContinuousLinearMap.comp_condExp_comm, MeasureTheory.probReal_compl_eq_one_sub₀, Complex.real_algHom_eq_id_or_conj, Padic.withValUniformEquiv_norm_le_one_iff, SmoothBumpFunction.rOut_pos, Real.analyticOnNhd_sin, Commute.cfcₙ_nnreal, NumberField.norm_norm_le_norm_mul_house_pow, inseparable_one_iff_norm, Valued.toNormedField.norm_le_one_iff, ProbabilityTheory.setLIntegral_preCDF_fst, Orthonormal.norm_eq_one, countingFunction_finsum_eq_finsum_add, Polynomial.card_rootSet_le_derivative, AddCircle.homeomorphCircle'_apply_mk, Real.hasStrictDerivAt_rpow_const_of_ne, SmoothBumpCovering.IsSubordinate.support_subset, Matrix.IsHermitian.cfc_eq, Complex.add_im, HolderOnWith.interpolate, UpperHalfPlane.image_coe_sphere, realPart_ofReal, MeasureTheory.SignedMeasure.rnDeriv_def, Real.neg_pi_div_two_eq_arcsin, Real.log2_le_logb, intervalIntegrable_iff, NormedCommGroup.cauchySeq_iff, Real.sign_one, dist_smul_le, norm_natCast_eq_mul_norm_one, Orientation.linearEquiv_det_rotation, MeasureTheory.measureReal_symmDiff_le, Real.mapsTo_cos, ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, unitInterval.strictAnti_symm, Orientation.tan_oangle_add_left_smul_rotation_pi_div_two, ENNReal.rpow_eq_zero_iff, Affine.Simplex.inv_height_eq_sum_mul_inv_dist, GroupSeminorm.coe_iSup_apply, CFC.sq_sqrt, ContinuousMap.attachBound_apply_coe, Real.sinh_nonneg_iff, Complex.reProdIm_subset_iff', Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_faceOpposite, SeminormedGroup.disjoint_nhds, Real.mapsTo_cos_Ioo, Complex.equivRealProdAddHom_symm_apply, Matrix.l2_opNorm_mulVec, MeasureTheory.fst_integral_withLp, Cardinal.mk_Iio_real, frontier_halfSpace, range_circleMap, Real.sin_periodic, NumberField.mixedEmbedding.convexBodySumFun_add_le, Metric.infDist_le_dist_of_mem, Real.binEntropy_continuous, EuclideanGeometry.Cospherical.affineIndependent_of_mem_of_ne, Metric.PiNatEmbed.continuous_distDenseSeq_inv, UpperHalfPlane.im_div_exp_dist_le, UpperHalfPlane.re_smul, Seminorm.finset_sup_apply, ProbabilityTheory.unitInterval.cdf_eq_real, Real.ofCauchy_sup, Rat.continuous_coe_real, NNReal.zero_rpow, MeasureTheory.Measure.toJordanDecomposition_toSignedMeasure_sub, span_fourier_closure_eq_top, Real.fourierIntegral_eq, PeriodPair.basis_one, ENNReal.rpow_intCast_mul, ProbabilityTheory.gaussianReal_map_neg, norm_pos_iff, NonarchAddGroupSeminormClass.toNonarchimedeanHomClass, AddSubgroup.norm_normedMk_le, isBounded_iff_forall_norm_le', Real.Angle.cos_zero, Submodule.re_inner_starProjection_eq_normSq, RCLike.conjCLE_norm, AffineSpace.cobounded_eq_iSup_sphere_asymptoticNhds, ProperCone.innerDual_univ, Affine.Simplex.sign_excenterWeights_singleton_pos, Affine.Simplex.circumcenter_mem_affineSpan, GenLoop.fromLoop_apply, EuclideanGeometry.angle_le_pi, HasDerivWithinAt.complexToReal_fderiv', CStarAlgebra.inr_mem_Icc_iff_norm_le, Affine.Simplex.affineSpan_pair_altitudeFoot_eq_altitude, Orientation.kahler_comp_rightAngleRotation', integral_const_on_unit_interval, InformationTheory.mul_log_le_klDiv, circleIntegral_def_Icc, setOf_riemmanianEDist_lt_subset_nhds, Urysohns.CU.approx_of_mem_C, Complex.natCast_re, StrictConvexSpace.of_norm_add_ne_two, isMIntegralCurve_comp_add, MeasureTheory.integral_unique, Orientation.rotation_eq_self_iff, setIntegral_withDensity_eq_setIntegral_smul₀, WithSeminorms.toLocallyConvexSpace, Nat.isUniformEmbedding_coe_real, Affine.Simplex.excenter_singleton_mem_affineSpan_range, NumberField.isInfinitePlace_iff, ContDiffBump.integrable, CircleDeg1Lift.commute_nat_add, EuclideanGeometry.law_sin, Real.arctan_nonneg, intervalIntegral.intervalIntegral_eq_integral_uIoc, not_bounded_iff_exists_ne_zero_mem_asymptoticCone, ENNReal.rpow_left_injective, AddCircle.volume_eq_smul_haarAddCircle, ZLattice.covolume_eq_det_inv, Seminorm.ball_smul_closedBall, ProbabilityTheory.lintegral_gaussianPDF_eq_one, ContinuousLinearMap.integral_apply, RCLike.algebraMap_eq_ofReal, NumberField.IsCMField.equivInfinitePlace_symm_apply, ENNReal.rpow_add, ProbabilityTheory.mgf_nonneg, Orientation.two_zsmul_oangle_smul_left_of_ne_zero, Complex.arg_neg_I, Real.Gamma_nat_add_half, ODE.FunSpace.isUniformInducing_toContinuousMap, QuotientGroup.norm_mk_eq_zero, ContDiffBump.support_normed_eq, circleIntegrable_iff, LinearMap.polar_eq_iInter, ProbabilityTheory.covarianceBilinDual_apply, Real.posLog_norm_add_le, Real.sinh_surjective, CFC.exists_pos_algebraMap_le_iff, HolderWith.edist_le_of_le, InnerProductGeometry.angle_normalize_left, hasFDerivAt_stereoInvFunAux, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, Complex.exp_re, instTrivialStarReal, ProbabilityTheory.IsGaussian.map_eq_gaussianReal, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_one_of_monotone, ProbabilityTheory.Kernel.densityProcess_mono_kernel_left, IsOpen.exists_subset_affineIndependent_span_eq_top, NNReal.coe_toRealHom, not_integrableOn_Ioi_cpow, NormedCommGroup.nhds_one_basis_norm_lt, Real.instStarOrderedRing, MeasureTheory.integral_fintype_prod_volume_eq_pow, LiouvilleWith.sub_nat, Real.fderiv_fourierChar_neg_bilinear_right_apply, LiouvilleWith.int_sub, CircleDeg1Lift.iterate_pos_le_iff, NumberField.InfinitePlace.isometry_embedding, WithSeminorms.mem_nhds_iff, Real.eulerMascheroniConstant_lt_two_thirds, LipschitzWith.dist_le_mul, PiLp.norm_toLp_one, Metric.diam_triple, LinearMap.IsPositive.re_inner_nonneg_right, eventually_cobounded_le_norm, stdSimplexHomeomorphUnitInterval_symm_apply_coe, Nat.dist_cast_real, LiouvilleWith.rat_add_iff, PMF.bernoulli_expectation, real_inner_smul_self_left, norm_iteratedFDeriv_mul_le, Real.toNNReal_le_toNNReal_iff', Units.val_cfcRpow, flip_innerSL_real, ContDiffBumpBase.smooth, goldConj_sq, Orientation.volumeForm_robust_neg, Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq, EReal.image_coe_Ioc, NormedSpace.isBounded_iff_subset_smul_ball, Irrational.ratCast_mul, dist_triangle4_right, NumberField.mixedEmbedding.normAtAllPlaces_apply, HolderWith.of_le, Real.analyticOn_cosh, WeakFEPair.hf_modif_int, Quaternion.continuous_imI, Metric.hausdorffDist_triangle, intervalIntegrable_bernoulliFun, RCLike.norm_I_of_ne_zero, LinearMap.IsSymmetric.im_inner_self_apply, imaginaryPart_I_smul, Real.exp_mul, Disjoint.exists_cthickenings, ContinuousLinearMap.norm_compLp_le, Asymptotics.IsBigOWith.pow, PseudoMetricSpace.dist_self, measurable_norm, Affine.Simplex.dist_point_faceOppositeCentroid, Quaternion.coeComplex_mul, Real.geom_goldenRatio_isSol_fibRec, Polynomial.Chebyshev.zero_lt_prod_node_sub_node, ContDiffBump.eventuallyEq_one, Stirling.log_stirlingSeq_sub_log_stirlingSeq_succ, ContDiffMapSupportedIn.structureMapCLM_apply, RCLike.sub_conj, Complex.uniformlyContinuous_im, lp.norm_eq_zero_iff, RCLike.re_sqrt_ofReal, eventually_enorm_mfderivWithin_symm_extChartAt_lt, bernoulliFun_eval_half_eq_zero, Circle.exp_natCast_mul, MeasureTheory.lpNorm_add_le', Real.cos_int_mul_two_pi, AkraBazziRecurrence.exists_eventually_const_mul_le_r, Real.natFloor_logb_natCast, ProbabilityTheory.tendsto_condCDF_atBot, ProbabilityTheory.integrable_preCDF, nnnorm_norm', SchwartzMap.lineDerivOp_fourier_eq, Polynomial.logMahlerMeasure_C_mul, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, ProbabilityTheory.mgf_neg, SeparationQuotient.norm_liftNormedAddGroupHom_apply_le, Orientation.areaForm_le, Seminorm.ext_iff, RCLike.pos_iff, MeasureTheory.isTightMeasureSet_iff_inner_tendsto, diam_smul₀, Real.log_neg_natCast_nonneg, Asymptotics.IsBigO.norm_left, Seminorm.uniformContinuous_of_forall, ENNReal.toReal_mono', schnirelmannDensity_le_one, PadicInt.norm_intCast_lt_one_iff, det_fderivPolarCoordSymm, NumberField.dedekindZeta_residue_def, setIntegral_withDensity_eq_setIntegral_toReal_smul, AddCircle.coe_real_preimage_closedBall_eq_iUnion, Complex.not_le_iff, Real.nat_floor_real_sqrt_eq_nat_sqrt, CircleDeg1Lift.iterate_pos_lt_iff, Metric.equicontinuousAt_iff_pair, RCLike.norm_expect_le, MeasureTheory.integral_mul_norm_le_Lp_mul_Lq, ProbabilityTheory.rnDeriv_gaussianReal, ProbabilityTheory.condVar_const, EuclideanGeometry.Sphere.IsExtTangent.dist_center, Real.Ioo_eq_ball, Complex.measurable_arg, SmoothPartitionOfUnity.locallyFinite, InnerProductGeometry.sin_angle, MeasureTheory.lpNorm_nonneg, ContinuousLinearEquiv.subsingleton_or_norm_symm_pos, Topology.RelCWComplex.continuousOn_symm, Real.Angle.sin_eq_zero_iff, ProbabilityTheory.Kernel.densityProcess_le_one, Real.isBoundedUnder_le_exp_comp, SeminormFamily.filter_eq_iInf, MeasureTheory.Integrable.norm_integral_condExpKernel, EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_right, BoxIntegral.Box.measurableSet_Icc, Affine.Simplex.incenter_map, SchwartzMap.integral_bilin_fourierInv_eq, isMIntegralCurve_comp_sub, TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars, exists_smooth_one_nhds_of_subset_interior, Real.differentiable_sinh, MeasureTheory.mem_L1_toReal_of_lintegral_ne_top, Asymptotics.isLittleO_abs_abs, MeasureTheory.norm_indicatorConstLp, norm_iteratedFDerivWithin_clm_apply, circleMap_neg_pi_div_two, CongruenceSubgroup.exists_Gamma_le_conj', MeasureTheory.Measure.toSphere_apply_aux, Orientation.neg_rotation, Metric.eventually_prod_nhds_iff, AkraBazziRecurrence.isLittleO_deriv_one_add_smoothingFn, ENNReal.toReal_add, NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm_apply_fst, unitInterval.toNNReal_continuous, EReal.coe_coe_eq_natCast, Metric.tendsto_atTop, RCLike.map_same_eq_id, Topology.CWComplex.continuousOn, ProbabilityTheory.covarianceBilin_apply_eq_cov, Complex.div_ofNat_im, Complex.arg_div_self, LSeries_eventually_eq_zero_iff', Real.isBoundedUnder_ge_exp_comp, ProbabilityTheory.covarianceBilin_self, NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isComplex, Real.range_sin_infinite, closure_one_eq, unitInterval.measurePreserving_coe, DiffeologicalSpace.CorePlotsOn.isOpen_iff_preimages_plots, expNegInvGlue.not_analyticAt_zero, dist_left_midpoint, Seminorm.bddAbove_range_iff, AffineSubspace.left_mem_perpBisector, Complex.continuousOn_arg, Real.tendsto_toNNReal_atTop_iff, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, Complex.lipschitz_equivRealProd, Real.sqrt_div_self, NormedSpace.image_isVonNBounded_iff, EuclideanGeometry.preimage_inversion_perpBisector_inversion, Asymptotics.isBigOWith_norm_right, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, EuclideanSpace.norm_sq_eq, Affine.Triangle.sSameSide_affineSpan_pair_point_incenter, UpperHalfPlane.dist_le_iff_dist_coe_center_le, Complex.angle_exp_one, gauge_smul_of_nonneg, SmoothPartitionOfUnity.nonneg, ContinuousMap.Homotopy.apply_zero_path, WithLp.prod_norm_eq_idemFst_of_L1, selfAdjoint.expUnitaryPathToOne_apply, FormalMultilinearSeries.norm_le_div_pow_of_pos_of_lt_radius, UpperHalfPlane.subset_verticalStrip_of_isCompact, AkraBazziRecurrence.tendsto_atTop_sumCoeffsExp, NormedRing.inverse_add_norm_diff_nth_order, Orientation.eq_rotation_self_iff_angle_eq_zero, hasDerivAt_bernoulliFun, Unitary.continuousOn_argSelfAdjoint, Real.norm_two, bernoulliFun_two, ContinuousLinearMap.norm_compContinuousMultilinearMap_le, Orientation.volumeForm_neg_orientation, BoxIntegral.Box.isBounded, ValueDistribution.proximity_zero_mul_le, QuasispectrumRestricts.nnreal_iff, HomotopyGroup.symmAt_indep, UpperHalfPlane.im_pos, Real.continuous_mul_log, NumberField.mixedEmbedding.norm_unit_smul, Real.log_prod, Complex.nndist_self_conj, Real.sin_arctan_nonneg, Real.log_abs, AddCircle.toCircle_add, IsUltrametricDist.norm_intCast_le_one, CFC.nnnorm_sqrt, BoxIntegral.unitPartition.box_upper, norm_abs_sub_abs, ContinuousMap.dist_le_two_norm, NumberField.mixedEmbedding.norm_eq_norm, covByVAdd_zero, Set.instTietzeExtensionUnitBall, IsometryEquiv.toRealLinearIsometryEquiv_apply, MeasureTheory.pdf.integral_mul_eq_integral, MeasureTheory.condExpIndL1Fin_smul, MeasureTheory.measureReal_le_measureReal_union_left, NormedAddGroupHom.NormNoninc.normNoninc_iff_norm_le_one, AbsolutelyContinuousOnInterval.add, Tactic.ComputeAsymptotics.Seq.dist_cons_nil, ContDiffBump.integrable_normed, NormedAddGroupHom.norm_id_le, NNReal.canLift, Metric.exists_forall_closedEBall_subset_aux₂, NumberField.mixedEmbedding.norm_le_convexBodySumFun, SlashInvariantForm.quotientFunc_mk, Real.instArchimedean, ProbabilityTheory.uncenteredCovarianceBilin_apply, MeasureTheory.exp_llr_of_ac', Real.cosh_abs, Complex.UnitDisc.instSMulCommClass_closedBall_circle, HolderOnWith.comp, TemperedDistribution.lineDerivOp_fourier_eq, Complex.frontier_setOf_re_le, MeasureTheory.charFun_neg, ContDiffPointwiseHolderAt.isBigO, Real.deriv_log, ModularForm.SL_slash, CStarAlgebra.norm_or_neg_norm_mem_spectrum, CongruenceSubgroup.conjGL_coe, Real.arctan_pos, SchwartzMap.decay', Real.rpow_neg_one, Complex.mul_re, Metric.sphere_zero, intervalIntegral.integral_comp_sub_div, MeasureTheory.measurableEmbedding_embeddingReal, Isometry.coe_affineIsometryOfStrictConvexSpace, Complex.ofRealCLM_norm, Behrend.roth_lower_bound_explicit, Complex.UnitDisc.instSMulCommClass_closedBall_left, MulAlgebraNorm.extends_norm', contMDiff_neg_sphere, PiCountable.min_dist_le_dist_pi, HasDerivAt.comp_ofReal, OrderedFinpartition.norm_compAlongOrderedFinpartition_le, dense_liouville, CircleDeg1Lift.tendsto_translationNumber_aux, not_differentiableAt_norm_zero, Complex.reLm_coe, Real.goldenRatio_mul_goldenConj, ContinuousLinearMap.opNorm_lsmul_apply_le, intervalIntegral.integral_comp_mul_left, uniqueDiffOn_Iic, Real.continuous_arcsin, IsUltrametricDist.norm_add_one_le_max_norm_one, BumpCovering.point_finite, Besicovitch.SatelliteConfig.centerAndRescale_radius, rotation_injective, Metric.comap_dist_left_atTop, ContinuousMap.norm_coe_le_norm, NNReal.coe_sSup, Besicovitch.ae_tendsto_measure_inter_div_of_measurableSet, NumberField.mixedEmbedding.mem_idealLattice, Polynomial.one_le_prod_max_one_norm_roots, Complex.re_balance, UpperHalfPlane.im_smul_eq_div_normSq, NormedAddGroupHom.opNorm_le_of_lipschitz, BoxIntegral.unitPartition.mem_smul_span_iff, LinearMap.IsPositive.nonneg_eigenvalues, deltaGenerated_eq_coinduced, intervalIntegral.integral_comp_mul_sub, ContinuousMap.HomotopyWith.prop', cauchySeq_iff_tendsto_dist_atTop_0, SchwartzMap.bilinLeftCLM_apply, TopologicalSpace.Opens.CompleteCopy.dist_eq, ContDiffBump.integral_normed, ODE.FunSpace.range_toContinuousMap, Real.HolderTriple.holderConjugate_div_div, Real.tendsto_cos_pi_div_two, Complex.norm_eq_one_iff', MeasureTheory.integral_fintype_prod_eq_prod, Affine.Simplex.mongePointVSubFaceCentroidWeightsWithCircumcenter_eq_sub, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, NumberField.Units.regOfFamily_eq_det, CocompactMapClass.norm_le, Probability.cauchyMeasure_of_scale_ne_zero, SmoothBumpCovering.exists_immersion_euclidean, Affine.Simplex.circumradius_nonneg, IsOpen.exists_msmooth_support_eq, Affine.Triangle.sbtw_touchpoint_singleton, Affine.Triangle.dist_point_faceOppositeCentroid, OrderedFinpartition.norm_applyOrderedFinpartition_le, Complex.equivRealProd_apply, IsCompact.exists_bound_of_continuousOn', UpperHalfPlane.specialLinearGroup_apply, ArchimedeanClass.stdPart_zero, BoxIntegral.Box.le_TFAE, Submodule.starProjection_singleton, EuclideanHalfSpace.ext_iff, IsOpen.exists_smooth_support_eq, HasSolidNorm.solid, ContinuousLinearMap.comp_condExp_add_const_comm, SmoothPartitionOfUnity.locallyFinite', isUltrametricDist_iff_forall_norm_natCast_le_one, MeasureTheory.Lp.nnnorm_le_of_ae_bound, ProbabilityTheory.integrable_toReal_condExpKernel, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_le_one, CFC.rpow_eq_pow, Real.isIntegral_two_mul_sin_rat_mul_pi, instSMulCommClass_sphere_sphere_sphere, interval_average_eq_div, Bundle.RiemannianMetric.isVonNBounded, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, MeasureTheory.hasFiniteIntegral_iff_ofNNReal, RingSeminorm.ringSeminormClass, Orientation.tan_oangle_add_right_smul_rotation_pi_div_two, BoundedContinuousFunction.indicator_apply, Affine.Simplex.mem_circumsphere, ProbabilityTheory.setIntegral_condCDF, PadicInt.nonarchimedean, MeasureTheory.le_eLpNorm_of_bddBelow, NumberField.FinitePlace.mulSupport_finite, Complex.convexHull_reProdIm, tendsto_norm_nhdsNE_one, Complex.conjLIE_apply, ENNReal.rpow_inv_rpow, one_mem_posTangentConeAt_iff_frequently, Real.hasDerivAt_sin, Seminorm.continuous_of_forall', Circle.starRingEnd_addChar, CircleDeg1Lift.isUnit_iff_bijective, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, unitInterval.pos_iff_ne_zero, QuotientAddGroup.le_norm_iff, Path.Homotopy.map_apply, curveIntegralFun_smul, LiouvilleWith.mul_int_iff, ProbabilityTheory.mgf_zero_fun, EisensteinSeries.abs_le_right_of_norm, Module.Basis.exists_opNorm_le, ProbabilityTheory.IsCondKernelCDF.tendsto_atTop_one, Complex.closure_preimage_im, CFC.sqrt_rpow, Path.pi_coe, RCLike.ofReal_re, integral_pow, Quaternion.imI_coeComplex, Real.summable_one_div_nat_add_rpow, ProbabilityTheory.integral_gaussianReal_eq_integral_smul, Matrix.linfty_opNorm_replicateRow, MeasureTheory.charFun_toDual_symm_eq_charFunDual, Height.logHeight₁_sum_le, UpperHalfPlane.canLift, QuotientAddGroup.norm_mk_eq_zero_iff_mem_closure, MeasureTheory.Measure.jordanDecompositionOfToSignedMeasureSub_toSignedMeasure, EuclideanGeometry.Sphere.mem_commonExtTangents_iff, not_IntegrableOn_Ioi_inv, unitInterval.coe_symmMeasurableEquiv, variationOnFromTo.eq_of_ge, Height.logHeight₁_add_le, NNReal.tendsto_dist_agmSequences_atTop_zero, Complex.sqrt_I, Diffeology.isPlot_id', intervalIntegral.integral_comp_sub_left, NumberField.FinitePlace.prod_eq_inv_abs_norm, Real.continuousAt_tan, CircleDeg1Lift.commute_iff_commute, PadicInt.norm_p_pow, Real.round_exp_one_eq_three, Urysohns.CU.approx_le_succ, InnerProductSpace.canonicalCovariantTensor_eq_sum, RCLike.re_add_im_ax, MeasureTheory.charFun_eq_fourierIntegral, mem_ball_iff_norm'', Real.strictAntiOn_arccos, Matrix.PosSemidef.sqrt_eq_zero_iff, Real.differentiableOn_log, ProbabilityTheory.integral_continuousLinearMap_gaussianReal, Real.abs_tanh_lt_one, Behrend.sphere_subset_preimage_metric_sphere, integral_log_sin_zero_pi_div_two, lintegral_fderiv_lineMap_eq_edist, EuclideanGeometry.oangle_sign_eq_zero_iff_collinear, NumberField.InfiniteAdeleRing.algebraMap_apply, RCLike.normSq_neg, Complex.IsExpCmpFilter.isBigO_im_pow_re, Real.toNNReal_le_ofNat, UnitAddTorus.mFourierSubalgebra_coe, mulRight_bound, Subgroup.widthInfty_pos, Complex.range_re, Real.volume_closedEBall, Path.ofLine_extend, NumberField.Units.dirichletUnitTheorem.seq_decreasing, CStarAlgebra.mem_Icc_iff_norm_le_one, Real.exp_nsmul, Path.range_subpathAux, unitInterval.volume_Ico, LiouvilleNumber.partialSum_eq_rat, MeasureTheory.integral_const_mul, OrthonormalBasis.det_eq_neg_det_of_opposite_orientation, MeasureTheory.isAddHaarMeasure_hausdorffMeasure, Real.iteratedDeriv_even_cosh, EReal.image_coe_Ico, Real.sin_two_pi, schnirelmannDensity_le_iff_forall, IntervalIntegrable.neg, norm_add_pow_two_real, intervalIntegral.integral_ofReal, EuclideanGeometry.dist_eq_add_dist_iff_angle_eq_pi, Complex.reProdIm_subset_iff, Besicovitch.SatelliteConfig.hlast, PadicInt.coe_eq_zero, sum_geometric_two_le, ProbabilityTheory.hasGaussianLaw_iff_charFun_map_eq, InnerProductSpace.gramSchmidtNormed_unit_length_coe, MeasureTheory.Measure.toSignedMeasure_le_toSignedMeasure_iff, IsUnifLocDoublingMeasure.eventually_measure_mul_le_scalingConstantOf_mul, instStarModuleNNRealOfReal, RCLike.is_real_TFAE, PadicInt.padic_norm_e_of_padicInt, enorm_norm', Seminorm.continuous', BoundedContinuousFunction.coe_normComp, mem_ball_one_iff, OrthonormalBasis.det_to_matrix_orthonormalBasis_of_opposite_orientation, Affine.Triangle.prod_dist_div_dist_eq_one_of_mem_line_of_mem_line, ContinuousMap.toNNReal_neg_algebraMap, Real.tan_sub', NNReal.rpow_intCast_mul, NNReal.coe_le_one, PNat.dist_eq, Path.ext_iff, Complex.im_expect, Real.summable_one_div_int_pow, Real.differentiableOn_arcsin, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunctionAux_eq, ContinuousMap.HomotopyLike.map_zero_left, norm_cexp_neg_mul_sq, ContinuousMap.Homotopy.evalAt_eq, UpperHalfPlane.num_neg, Polynomial.Chebyshev.eval_T_real_node, norm_smul, ENNReal.ofReal_iInf, Polynomial.Chebyshev.complex_ofReal_eval_T, norm_nonneg', conformal_const_smul, ENNReal.ofReal_eq_zero, MeasureTheory.SignedMeasure.exists_compl_positive_negative, MeasureTheory.MemLp.integrable_norm_rpow', le_schnirelmannDensity_iff, LiouvilleWith.neg_iff, UniformSpace.Completion.mem_uniformity_dist, Complex.hasStrictFDerivAt_exp_real, integral_exp, Set.infsep_zero_iff_subsingleton_of_finite, measurable_ereal_toReal, UpperHalfPlane.moebius_im, ContinuousMultilinearMap.opNorm_zero_iff, RCLike.abs_im_div_norm_le_one, ModularForm.prod_slash, Real.one_le_exp_iff, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_sub_smoothingFn, comap_norm_atTop', EReal.nhds_coe, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, ProbabilityTheory.HasSubgaussianMGF.mgf_le, norm_sub_mul_self, Topology.RelCWComplex.pairwiseDisjoint', Seminorm.coe_le_coe, NumberField.abs_discr_ge', WithCStarModule.prod_norm_sq, uniqueDiffOn_Ioc, Module.Basis.parallelepiped_basisFun, NumberField.mixedEmbedding.instIsAddHaarMeasureMixedSpaceVolume, ProbabilityTheory.covariance_mul_right, Height.fun_mulHeight_zero, log_add_one_le_harmonic, SchwartzMap.laplacianCLM_eq, NNReal.pow_rpow_inv_natCast, LiouvilleWith.sub_int, ProbabilityTheory.Kernel.HasSubgaussianMGF.add_compProd, monomial_has_deriv_aux, Real.Angle.toReal_coe_eq_self_iff_mem_Ioc, Real.norm_exp_I_mul_ofReal_sub_one_le, Cardinal.Real.Ioc_countable_iff, StieltjesFunction.measure_Ioo, Real.HolderTriple.inv_nonneg', MeasureTheory.hasFiniteIntegral_prod_iff', Real.vector_fourierIntegral_eq_integral_exp_smul, Archimedean.embedRealFun_add, HasFDerivAt.le_of_lipschitzOn, NumberField.mixedEmbedding.fundamentalCone.compactSet_eq_union_aux₁, PiTensorProduct.projectiveSeminormAux_smul, MeasureTheory.integral_div, ContinuousMap.coeNNRealReal_apply, MeasureTheory.lpNorm_fun_zero, HurwitzZeta.evenKernel_def, Matrix.IsHermitian.eigenvalues_eq, MeasureTheory.MemLp.norm_rpow, cfc_complex_eq_real, Real.contDiffAt_tan, Real.range_arctan, UnitAddTorus.mFourierSubalgebra_closure_eq_top, Real.hasDerivAt_mul_log, ModularGroup.one_lt_normSq_T_zpow_smul, Real.fourier_real_eq_integral_exp_smul, Dilation.mapsTo_sphere, EuclideanGeometry.Sphere.mem_tangentsFrom_iff, Real.pi_nonneg, NumberField.abs_discr_ge, Real.rpowIntegrand₀₁_zero_right, NNReal.enorm_eq, ENNReal.rpow_left_surjective, Filter.tendsto_ofReal_iff', ProbabilityTheory.covarianceOperator_apply, WithLp.prod_nnnorm_eq_add, NumberField.mixedEmbedding.polarCoordReal_apply, setOf_liouvilleWith_subset_aux, ValueDistribution.logCounting_pow_top, InnerProductGeometry.angle_normalize_right, differentiableWithinAt_abs, PadicInt.coe_sum, Metric.dist_lt_add_of_nonempty_ball_inter_ball, MeasureTheory.integral_tilted, MeasureTheory.eLpNorm_smul_measure_of_ne_top', inner_lt_norm_mul_iff_real, Asymptotics.isLittleO_const_id_atTop, UpperHalfPlane.isometry_real_vadd, Complex.instFiniteDimensionalReal, Mathlib.Tactic.Rify.ratCast_lt, EuclideanGeometry.Sphere.IsDiameter.dist_left_right, Real.tendsto_sigmoid_atTop, CStarAlgebra.span_nonneg_inter_unitBall, Complex.nnnorm_ratCast, SimpleGraph.card_connectedComponent_eq_finrank_ker_toLin'_lapMatrix, Real.continuous_sinc, Real.deriv_arccos, Complex.arg_le_pi, IntervalIntegrable.zero, smul_unitClosedBall, im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat_rat, MeasureTheory.average_mem_openSegment_compl_self, Real.hasStrictDerivAt_sinh, AddCircle.homeomorphCircle'_symm_apply, TestFunction.continuous_iff_continuous_comp, CongruenceSubgroup.strictPeriods_Gamma0, Polynomial.Chebyshev.eval_T_real_eq_neg_one_iff, isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts, Real.tendsto_exp_atTop, UpperHalfPlane.center_zero, Complex.normSq_ratCast, entry_norm_bound_of_unitary, integral_sin_pow_three, MeasureTheory.Measure.toSphere_real_apply_univ, Real.Gamma_strictAntiOn_Ioc, dist_le_norm_add_norm, Real.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_quasispectrum, Matrix.PosDef.eigenvalues_pos, integrableOn_exp_Iic, Real.log_mul_self_monotoneOn, unitInterval.volume_apply, RCLike.hasSum_ofReal, CStarAlgebra.norm_le_natCast_iff_of_nonneg, CFC.negPart_algebraMap, torusIntegral_succ, Real.analyticWithinAt_sinh, cfcₙHom_nnreal_eq_restrict, NonUnitalIsometricContinuousFunctionalCalculus.norm_quasispectrum_le, ContDiffMapSupportedIn.contDiff, Height.logHeight₁_sub_le, CircleDeg1Lift.dist_map_zero_translationNumber_le, instIsManifoldRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc, norm_iteratedFDeriv_clm_apply, TestFunction.toBoundedContinuousFunctionCLM_apply, Metric.unitBall.instContinuousMul, IsCompact.exists_thickening_image_subset, Real.sin_le_one, RCLike.continuous_normSq, Conformal.const_smul, ProbabilityTheory.IsCondKernelCDF.nonneg, ContinuousAlternatingMap.norm_def, ContinuousLinearEquiv.hasTemperateGrowth, AntilipschitzWith.mul_le_dist, ValueDistribution.logCounting_eval_zero, SmoothBumpFunction.le_one, NNReal.rpow_natCast, stronglyMeasurable_derivWithin_Ioi, variationOnFromTo.antitoneOn, PadicInt.norm_units, SchwartzMap.fderivCLM_apply, CStarRing.norm_of_mem_unitary, deriv_sqrt_mul_log, Complex.norm_cos_add_sin_mul_I, ProbabilityTheory.gaussianReal_zero_var, Real.volume_closedBall, AkraBazziRecurrence.T_pos, Real.Wallis.W_le, Submodule.norm_starProjection_apply_le, ContDiffBump.pos_of_mem_ball, ContinuousLinearMap.norm_extendTo𝕜, Probability.measurable_cauchyPDFReal, ModularForm.norm_eq_zero_iff, MeasureTheory.Measure.sub_toSignedMeasure_eq_toSignedMeasure_sub, Real.mulExpNegSq_apply, Seminorm.continuousAt_zero_of_forall', Rat.dist_eq, Real.sin_pi_sub, Metric.tendsto_nhds_nhds, EuclideanGeometry.Sphere.mem_commonTangents_iff, ENNReal.ofReal_eq_ofNat, tendsto_norm_div_self, CircleDeg1Lift.map_lt_add_floor_translationNumber_add_one, Real.artanh_bijOn, Circle.isAddQuotientCoveringMap_exp, ProbabilityTheory.IsRatCondKernelCDF.setIntegral, ProbabilityTheory.covariance_mul_left, Real.one_sub_sq_div_two_le_cos, RCLike.ofNat_re, Complex.norm_pow, CircleDeg1Lift.tendsto_atBot, analyticOnNhd_circleMap, IsUltrametricDist.exists_norm_multiset_prod_le, tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support, EReal.preimage_coe_Ioi, antideriv_bernoulliFun, NumberField.mixedEmbedding.commMap_apply_of_isComplex, AddCircle.integral_haarAddCircle, Real.sin_pi, Complex.arg_one, Real.arcsin_nonpos, InnerProductSpace.HarmonicAt.const_smul, differentiableAt_sigmoid, NumberField.Units.pos_at_place, AEMeasurable.norm, Affine.Simplex.excenterWeightsUnnorm_reindex, mem_closedBall_iff_norm'', BumpCovering.support_toPOUFun_subset, NumberField.InfinitePlace.Completion.norm_coe, PointwiseConvergenceCLM.tendsto_nhds, RCLike.ofReal_balance, MeasureTheory.eLpNorm_le_of_ae_nnnorm_bound, ProbabilityTheory.Kernel.densityProcess_empty, NNReal.coe_add, norm_pow, SpectrumRestricts.nnreal_iff, GroupSeminorm.lt_def, Asymptotics.IsBigOWith_def, IsometryEquiv.midpoint_fixed, ProbabilityTheory.Kernel.density_le_one, ProbabilityTheory.IsCondKernelCDF.integral, ENNReal.tendsto_rpow_atTop_of_one_lt_base, Real.integrable_prod_sub, Seminorm.mem_closedBall_zero, Real.analyticAt_cos, OrthogonalFamily.norm_sq_diff_sum, MeasureTheory.mul_meas_ge_le_pow_eLpNorm', circleMap_zero_inv, Real.smul_map_diagonal_volume_pi, NNReal.coe_iSup, Irrational.ratCast_div, PadicAlgCl.isNonarchimedean, Real.goldenRatio_lt_two, norm_smul_inv_norm, Real.HolderTriple.one_div_eq, unitInterval.sigmoid_strictMono, BoxIntegral.Box.measurableSet_coe, NumberField.InfinitePlace.comap_apply, MeasureTheory.L2.inner_def, CliffordAlgebraComplex.ofComplex_toComplex, Real.logb_inv, Orientation.volumeForm_map, SimpleGraph.antitoneOn_extremalNumber_div_choose_two, rotation_apply, toMatrix_rotation, Polynomial.supNorm_zero, NumberField.mixedEmbedding.instNoAtomsMixedSpaceVolume, RCLike.nonpos_iff, Complex.normSq_mk, convexHull_union_neg_eq_absConvexHull, WeakFEPair.hf_zero', RCLike.smul_re, Icc_isBoundaryPoint_bot, RCLike.nonpos_iff_exists_ofReal, Real.one_sub_le_exp_neg, Real.sigmoid_neg, dist_birkhoffSum_birkhoffSum_le, GaussianInt.toComplex_def₂, OrthonormalBasis.sum_sq_inner_right, Real.volume_val, Polynomial.Chebyshev.integral_T_real_mul_self_measureT_of_ne_zero, Real.borel_eq_generateFrom_Iio_rat, ProbabilityTheory.moment_one, HurwitzKernelBounds.isBigO_atTop_F_int_one, Asymptotics.isBigOWith_refl, Seminorm.lt_def, ValueDistribution.proximity_pow_zero, PartitionOfUnity.nonneg', OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, Real.differentiableWithinAt_arccos_Ici, MeasureTheory.BorelCantelli.martingalePart_process_ae_eq, Complex.toBasis_orthonormalBasisOneI, RCLike.realRingEquiv_symm_apply, Homeomorph.contDiff_unitBall, CliffordAlgebraComplex.toComplex_comp_ofComplex, Real.sinc_eq_dslope, Real.Angle.abs_toReal_eq_pi_div_two_iff, LinearMap.polar_singleton, Real.arcosh_zero, HurwitzZeta.hurwitzZetaEven_zero, OrthonormalBasis.toBasis_adjustToOrientation, ModularForm.prod_slash_sum_weights, Matrix.IsHermitian.rank_eq_rank_diagonal, NumberField.prod_abs_eq_one, Complex.isCauSeq_conj, norm_div_le, Stirling.log_stirlingSeq_formula, Real.summable_nat_rpow_inv, Asymptotics.isBigO_iff_div_isBoundedUnder, Real.ball_eq_Ioo, Tactic.ComputeAsymptotics.WellFormedBasis.head_eventually_pos, ENNReal.hasMeasurablePow, irrational_sqrt_ratCast_iff, ProbabilityTheory.Kernel.notMem_mutuallySingularSetSlice, AddGroupNorm.coe_add, Real.iUnion_Iic_rat, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_dvd_norm_le, Complex.neg_pi_div_two_lt_arg_iff, Real.cos_add_int_mul_two_pi, Polynomial.Chebyshev.integral_measureT, Real.log_neg_eq_log, SchwartzMap.compCLMOfContinuousLinearEquiv_apply, intervalIntegral.integral_div, AffineIsometryEquiv.pointReflection_midpoint_left, MeasureTheory.tilted_zero, ProbabilityTheory.stronglyMeasurable_geometricPMFReal, Multipliable.norm, HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principal, stereographic'_source, interior_convexHull_nonempty_iff_affineSpan_eq_top, MeasureTheory.Measure.iInf_IicSnd_gt, Real.monotone_arcsin, IsCompact.uniform_oscillation, EReal.image_coe_Iio, Real.tendsto_exp_div_pow_atTop, Real.log_div_log, Behrend.bound_aux', BoxIntegral.Box.upper_sub_lower_splitCenterBox, integral_sin_pow_pos, Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter, AmpleSet.preimage_iff, unitInterval.symm_le_symm, Besicovitch.BallPackage.r_le, Real.Angle.abs_toReal_le_pi, Affine.Simplex.sign_touchpointWeights_empty, EuclideanGeometry.inversion_mem_perpBisector_inversion_iff', NonarchAddGroupSeminorm.coe_sup, ProbabilityTheory.centralMoment_one, Affine.Simplex.sum_mongePointWeightsWithCircumcenter, ProbabilityTheory.HasSubgaussianMGF.const_mul, MeasureTheory.weightedSMul_nonneg, NumberField.mixedEmbedding.convexBodyLT_volume, ModularGroup.coe_apply_complex, Real.artanh_zero, instStarModuleNNRealReal, ContinuousMap.toLp_norm_le, Chebyshev.psi_eq_psi_coe_floor, jacobiTheta_T_sq_smul, Real.nnnorm_exp_I_mul_ofReal_sub_one_le, InformationTheory.tendsto_klFun_atTop, parallelogram_law_with_norm, stdSimplexHomeomorphUnitInterval_zero, ContinuousMultilinearMap.norm_smulRightL_le, Affine.Simplex.ExcenterExists.touchpoint_map, comap_norm_nhdsGT_zero, StieltjesFunction.mono', NNReal.coe_div, ENNReal.lintegral_mul_rpow_le_lintegral_rpow_mul_lintegral_rpow, norm_le_norm_add_norm_sub', List.norm_prod_le', Seminorm.closedBall_smul_ball, Orientation.inner_rightAngleRotation_swap', spectralAlgNorm_def, EuclideanGeometry.angle_eq_iff_oangle_eq_or_wbtw, InformationTheory.klFun_apply, ProbabilityTheory.variance_fun_neg, ContDiffMapSupportedIn.contDiff', MeasureTheory.Measure.haar.prehaar_le_index, NNReal.sqrt_eq_rpow, MeasureTheory.Measure.addHaar_preimage_smul, setIntegral_withDensity_eq_setIntegral_toReal_smul', Real.sign_inv, QuadraticForm.equivalent_signType_weighted_sum_squared, Asymptotics.isBigO_norm_right, OrthonormalBasis.measurePreserving_repr, Complex.exp_def, InformationTheory.leftDeriv_klFun_one, IsBoundedBilinearMap.isBigO_comp, Module.Basis.parallelepiped_reindex, RCLike.ofReal_comp_balance, Real.sin_pi_div_three, Real.abs_sinh, Complex.arg_mul_eq_add_arg_iff, RCLike.abs_re_le_norm, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars, IsClosed.mem_iff_infDist_zero, ZMod.completedLFunction_def_even, Behrend.log_two_mul_two_le_sqrt_log_eight, SchwartzMap.integral_fourierInv_smul_eq, ContinuousMultilinearMap.norm_mkPiAlgebra_le, ball_zero_eq, Real.logb_mul, exists_smooth_tsupport_subset, strictConvexOn_pow, Circle.exp_eq_exp, RCLike.reCLM_norm, HolderOnWith.ediam_image_le_of_subset_of_le, GenLoop.homotopyTo_apply, signedDist_triangle, IsUltrametricDist.invariantExtension_apply, Similar.exists_pos_dist_eq, AEMeasurable.im, Real.inv_logb_div_base, Besicovitch.SatelliteConfig.h, Real.arctan_eq_zero_iff, SchwartzMap.inner_toL2_toL2_eq, ProbabilityTheory.Kernel.isCondKernelCDF_condKernelCDF, Complex.UnitDisc.im_neg, Irrational.natCast_add, Real.sinh_zero, Real.inv_goldenConj, PartitionOfUnity.locallyFinite, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, integral_bernoulliFun, MeasureTheory.SignedMeasure.toComplexMeasure_apply, Asymptotics.isBigO_abs_left, ModularForm.levelOne_neg_weight_rank_zero, Path.Homotopy.continuous_transAssocReparamAux, Complex.UnitDisc.im_star, dist_inv_inv₀, Metric.iUnion_ball_nat_succ, UniformSpace.Completion.uniformContinuous_dist, AkraBazziRecurrence.GrowsPolynomially.const_mul, Subgroup.IsArithmetic.is_commensurable, Complex.coe_orthonormalBasisOneI, Subgroup.IsArithmetic.inter, Polynomial.Chebyshev.isLocalMin_T_real, Real.expPartialHomeomorph_apply, Height.logHeight₁_one, Metric.equicontinuousAt_iff, Complex.integral_circleTransform, tendsto_norm_inv_nhdsNE_zero_atTop, Real.sigmoid_nonneg, AddGroupSeminorm.ext_iff, schnirelmannDensity_setOf_prime, formalMultilinearSeries_geometric_apply_norm_le, NormedField.norm_mul, convexOn_univ_dist, ModularGroup.sl_moeb, RCLike.ofReal_sub, norm_le_add_norm_add, Padic.norm_int_le_one, Path.extend_symm_apply, ENNReal.inv_rpow, norm_pow_le_mul_norm, Archimedean.embedReal_apply, Polynomial.toAddCircle_X_pow_eq_fourier, Real.arsinh_zero, Real.Angle.abs_cos_eq_abs_sin_of_two_zsmul_add_two_zsmul_eq_pi, irrational_sqrt_intCast_iff, dist_sub_sub_le, NumberField.InfinitePlace.smul_apply, MeasureTheory.AEStronglyMeasurable.ae_integrable_condKernel_iff, Irrational.intCast_add, Complex.arg_le_pi_div_two_iff, NNReal.rpow_mul_intCast, Real.instZeroLEOneClass, NormedSpace.isBounded_iff_subset_smul_closedBall, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform_aux, MeasureTheory.Measure.hausdorffMeasure_le_liminf_sum, one_sub_gold, Path.Homotopy.target, Real.Angle.toReal_coe, Real.cos_arcsin, RCLike.norm_sq_eq_def_ax, InnerProductGeometry.sin_angle_div_norm_eq_sin_angle_div_norm, Orientation.abs_volumeForm_apply_of_orthonormal, ContDiffBump.normed_def, signedDist_linear_apply_apply, HurwitzZeta.oddKernel_def', MeromorphicOn.extract_zeros_poles_log, aemeasurable_coe_nnreal_real_iff, Affine.Simplex.sSameSide_incenter_point, IsApproximateAddSubgroup.one_le, spectrum.spectralRadius_le_liminf_pow_nnnorm_pow_one_div, Circle.exp_two_pi_mul_int, SemilinearMapClass.bound_of_continuous, Real.arctan_mem_Ioo, EuclideanGeometry.collinear_iff_of_two_zsmul_oangle_eq, setIntegral_withDensity_eq_setIntegral_toReal_smul₀, setIntegral_Ioi_zero_rpow, SchwartzMap.integral_bilin_fourierIntegral_eq, MeasureTheory.SignedMeasure.bddBelow_measureOfNegatives, Matrix.norm_entry_le_entrywise_sup_norm, ProbabilityTheory.Kernel.measurable_singularPart_fun_right, AddGroupNorm.coe_sup, EuclideanGeometry.oangle_midpoint_right, Real.Angle.two_zsmul_coe_div_two, Affine.Simplex.ExcenterExists.excenter_map, Metric.tendsto_nhds, EReal.coe_nonpos, Real.ofCauchy_zero, analyticAt_rexp, NumberField.mixedEmbedding.polarSpaceCoord_target, AddCircle.scaled_exp_map_periodic, PiNat.dist_triangle_nonarch, SchwartzMap.toLp_fourierInv_eq, Topology.RelCWComplex.source_eq, InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two, norm_add₃_le, NumberField.mixedEmbedding.negAt_apply_snd, CircleDeg1Lift.translationNumber_one, GaussianInt.toComplex_div_re, Real.logb_eq_zero, CStarRing.norm_mul_self_le, Real.tan_arccos, nnnorm_algebraMap_nnreal, MeasureTheory.setIntegral_prod_mul, Orientation.neg_rotation_neg_pi_div_two, EReal.isOpenEmbedding_coe, Real.borel_eq_generateFrom_Ioo_rat, NNReal.young_inequality, MeasureTheory.measureReal_mono, Real.hasSum_sinh, Complex.im_nnqsmul, CFC.rpow_def, Real.tendsto_eulerMascheroniSeq', NNReal.map_coe_atTop, Real.one_add_rpow_hasFPowerSeriesOnBall_zero, ProbabilityTheory.monotone_cdf, Real.arccos_pos, ContinuousLinearMap.sSup_sphere_eq_nnnorm, VectorFourier.fourierPowSMulRight_eq_comp, RCLike.intCast_re, Complex.measurableEquivPi_apply, ENNReal.toReal_max, Height.one_le_mulHeight, LiouvilleWith.int_sub_iff, Polynomial.cyclotomic.eval_apply_ofReal, Real.monotoneOn_posLog, MeasureTheory.charFunDual_eq_charFun_map_one, Circle.argPartialEquiv_source, Real.volume_real_Ioo, Quaternion.instCStarRingReal, WithSeminorms.tendsto_nhds', norm_multiset_sum_le, RCLike.im_eq_zero_iff_isSelfAdjoint, Complex.tendsto_exp_nhds_zero_iff, fourier_norm, EuclideanGeometry.angle_self_of_ne, Real.isLittleO_log_id_atTop, ContinuousLinearMap.opNorm_mul, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw, Metric.continuousAt_inv_infDist_pt, VitaliFamily.eventually_filterAt_iff, AlgebraNormClass.map_smul_eq_mul, Complex.uniformContinuous_im, MeasureTheory.integral_fintype_prod_eq_pow, Real.sin_add_int_mul_pi, MeasureTheory.charFun_apply, UpperHalfPlane.isometry_vertical_line, MeasureTheory.memLp_two_iff_integrable_sq_norm, RCLike.norm_ofReal, unitInterval.symmMeasurableEquiv_apply, StieltjesFunction.measure_singleton, InnerProductSpace.harmonicOnNhd_comp_CLE_iff, NumberField.Units.dirichletUnitTheorem.seq_next, sameRay_iff_inv_norm_smul_eq_of_ne, Complex.frontier_preimage_re, CuspForm.coe_trace, antilipschitzWith_iff_le_mul_dist, Real.Polynomial.isRoot_cos_pi_div_five, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_add_compProd, indicator_thickening_eventually_eq_indicator_closure, Real.surjOn_log', comap_norm_nhds_zero, SmoothBumpFunction.continuous, image_circleMap_Ioc, NumberField.mixedEmbedding.convexBodyLT_mem, NumberField.InfinitePlace.coe_apply, Set.OrdConnected.nullMeasurableSet, ENNReal.toReal_one, inner_mul_inner_self_le, Real.strictMonoOn_artanh, MulRingSeminorm.apply_one, Real.exp_one_lt_three, gold_mul_goldConj, Real.sInf_smul_of_nonneg, integral_cos_pow, Complex.cosh_ofReal_im, Real.neg_pi_div_two_lt_arctan, Metric.inseparable_iff, Orientation.oangle_sign_sub_smul_left, MeasureTheory.SimpleFunc.integral_eq_sum_filter, Real.cos_nat_mul_two_pi_sub_pi, Real.comap_exp_nhds_zero, Real.cosPartialEquiv_target, Height.mulHeight₁_zpow, Real.analyticAt_sinh, instHasSolidNormReal, HomotopyGroup.isUnital_auxGroup, Real.hasStrictDerivAt_arccos, Complex.sub_im, RCLike.conjCLE_apply, Real.cauSeq_converges, NumberField.mixedEmbedding.convexBodySumFun_apply', ContinuousLinearMap.norm_fst_le, CStarModule.norm_nonneg, MeasureTheory.integrable_norm_rpow_iff, Stirling.log_stirlingSeq_diff_hasSum, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_norm_eq_mul_torsion, AntilipschitzWith.le_mul_norm, IsUltrametricDist.norm_tsum_le, AnalyticAt.harmonicAt_im, ProbabilityTheory.integral_stieltjesOfMeasurableRat, ENNReal.liminf_toReal_eq, Real.inv_goldenRatio, MeasureTheory.Measure.quasiMeasurePreserving_smul, MeasureTheory.measureReal_symmDiff_eq, Affine.Simplex.ExcenterExists.touchpoint_notMem_affineSpan_of_ne, unitInterval.mem_unitIntervalSubmonoid, Real.sin_antiperiodic, Path.delayReflRight_zero, MeasureTheory.dominatedFinMeasAdditive_condExpInd, CovBySMul.nonneg, Complex.reCLM_nnnorm, Real.log_list_prod, Real.arsinh_neg, Polynomial.logMahlerMeasure_of_degree_eq_one, norm_sub_pow_two_real, Affine.Simplex.abs_inner_vsub_altitudeFoot_div_lt_one, intervalIntegral.integral_comp_sub_right, Complex.nndist_of_im_eq, NumberField.InfinitePlace.comp_of_comap_eq, UpperHalfPlane.coe_pos_real_smul, Rat.dist_cast, UpperHalfPlane.J_sq, IsUnit.cfcSqrt, Real.HolderConjugate.two_two, MeasureTheory.integral_norm_eq_lintegral_enorm, CFC.continuousOn_log, isScalarTower_closedBall_closedBall_closedBall, Orientation.rightAngleRotation_def, EuclideanGeometry.angle_eq_zero_iff_eq_and_ne_or_sbtw, ContinuousLinearMap.le_opNorm, IsUltrametricDist.invariantExtension_extends, CFC.rpow_algebraMap, MeasureTheory.SignedMeasure.toJordanDecomposition_zero, RCLike.mul_im_ax, Real.Gamma_two, Function.locallyFinsuppWithin.logCounting_eval_zero, intervalIntegral.intervalIntegrable_inv_one_add_sq, RCLike.ofReal_injective, ModularGroup.coe_T_zpow_smul_eq, SingularManifold.isManifold, ProbabilityTheory.IndepFun.integral_comp_mul_comp, QuotientGroup.norm_mk_eq_zero_iff_mem_closure, ENNReal.hasSum_toReal, ProbabilityTheory.IsRatCondKernelCDFAux.measurable, Topology.RelCWComplex.continuousOn, Function.HasTemperateGrowth.toTemperedDistribution_apply, Euclidean.closedBall_eq_image, Affine.Simplex.touchpoint_singleton_mem_interior_faceOpposite, NumberField.mixedEmbedding.fundamentalCone.expMap_target, Real.continuousOn_log, CircleDeg1Lift.strictMono_iff_injective, NumberField.mixedEmbedding.convexBodySum_neg_mem, intervalIntegral.FTCFilter.finiteAt_inner, Real.sin_sub_pi_div_two, NumberField.FinitePlace.prod_eq_inv_abs_norm_int, NumberField.mixedEmbedding.negAt_preimage, ENNReal.pow_rpow_inv_natCast, Height.mulHeight₁_pow, InformationTheory.not_differentiableWithinAt_klFun_Iio_zero, InnerProductSpace.Core.norm_eq_sqrt_re_inner, Real.sigmoid_lt_iff, isScalarTower_sphere_closedBall_closedBall, ProbabilityTheory.Kernel.HasSubgaussianMGF.memLp_exp_mul, ContDiffPointwiseHolderAt.differentiableAt, PadicInt.norm_lt_one_iff_dvd, Complex.deriv_ofReal_cpow_const, exists_continuous_zero_one_of_isClosed, Real.arsinh_injective, Real.tan_int_mul_pi_div_two, Affine.Simplex.excenterExists_reindex, Real.Wallis.tendsto_W_nhds_pi_div_two, Chebyshev.psi_sub_theta_eq_sum_not_prime, Real.isOpenEmbedding_exp, Real.Angle.sign_two_nsmul_eq_neg_sign_iff, SchwartzMap.integral_sesq_fourier_eq, Real.cos_add_two_pi, norm_le_norm_add_norm_sub, Real.ofCauchy_mul, AbsolutelyContinuousOnInterval.boundedVariationOn, NumberField.mixedEmbedding.fundamentalCone.volume_frontier_normLeOne, MeasureTheory.L1.SimpleFunc.setToL1S_add_left, EuclideanGeometry.Sphere.secondInter_collinear, Pi.sum_norm_apply_le_norm', ContinuousMap.HomotopyWith.apply_one, NNReal.eventually_pow_one_div_le, Real.isIntegral_two_mul_cos_rat_mul_pi, MeasureTheory.norm_setIntegral_le_of_norm_le_const_ae', MeasureTheory.charFunDual_pi', RCLike.toIsStrictOrderedModule, stdSimplex_subset_closedBall, ValueDistribution.logCounting_const_zero, NumberField.house_intCast, Rat.isDenseEmbedding_coe_real, RCLike.abs_re_div_norm_le_one, MeasureTheory.eLpNorm_norm, NNReal.rpow_zero_pos, BoxIntegral.unitPartition.integralSum_eq_tsum_div, MeasureTheory.hasFiniteIntegral_toReal_of_lintegral_ne_top, InformationTheory.toReal_klDiv_eq_integral_klFun, ProbabilityTheory.Kernel.HasSubgaussianMGF.add_comp, ValueDistribution.logCounting_mul_zero_eventuallyLE, Real.instPathConnectedSpace, norm_sub_sq, ValueDistribution.logCounting_top, Quaternion.linearIsometryEquivTuple_symm_apply, trapezoidal_error_eq, EuclideanGeometry.Sphere.dist_div_sin_oangle_div_two_eq_radius, PiLp.dist_eq_card, Affine.Simplex.ninePointCircle_eq_circumsphere_medial, Probability.integral_cauchyPDFReal, ContinuousMap.norm_le_of_nonempty, MeasureTheory.SignedMeasure.singularPart_smul, uniformContinuous_norm, WithLp.prod_dist_eq_of_L2, PowerSeries.gaussNorm_zero, WithLp.prod_norm_eq_of_nat, NumberField.mixedEmbedding.normAtPlace_apply_of_isReal, RCLike.I_re_ax, MeasureTheory.condExpInd_nonneg, MeasureTheory.charFun_apply_real, balancedHull_subset_convexHull_union_neg, Topology.RelCWComplex.union', MeasureTheory.measureReal_empty, Orientation.areaForm_to_volumeForm, Path.Homotopy.eval_zero, stereoInvFunAux_apply, fourierCoeff_bernoulli_eq, irrational_mul_natCast_iff, Complex.norm_dslope_le_div_of_mapsTo_ball, Polynomial.card_roots_le_derivative, PiTensorProduct.projectiveSeminorm_apply, PadicInt.algebraMap_apply, Real.sqrt_inv, ENNReal.rpow_sub, ArchimedeanClass.stdPart_of_mk_ne_zero, Complex.log_exp_eq_re_add_toIocMod, Real.cosh_surjOn, UpperHalfPlane.denom_cocycle_σ, ContinuousAffineMap.norm_def, circleAverage_log_norm_sub_const_eq_log_radius_add_posLog, signedDist_le_dist, Real.not_continuousAt_deriv_mul_log_zero, ProbabilityTheory.integrable_condCDF, NNReal.algebraMap_eq_coe, ContinuousLinearMap.norm_iteratedFDerivWithin_comp_left, Real.Gamma_mul_Gamma_add_half, Complex.log_inv_eq_ite, RCLike.re_nonneg_of_nonneg, CovByVAdd.trans, EuclideanGeometry.Sphere.IsTangentAt.mem_space, Complex.continuousAt_arg, Subgroup.instIsArithmeticRangeSpecialLinearGroupFinOfNatNatIntGeneralLinearGroupRealMapGL, EReal.preimage_coe_Ioo, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isComplex, ContDiffBump.one_lt_rOut_div_rIn, NormedAddGroupHom.IsQuotient.norm_le, strictConvexOn_exp, Affine.Simplex.circumcenter_reindex, spectrum.norm_le_norm_mul_of_mem, OpenPartialHomeomorph.contDiff_univUnitBall, AddGroupNorm.le_def, ZMod.LFunction_def_odd, LinearMap.IsSymmetric.coe_re_inner_self_apply, LiouvilleWith.rat_sub, Real.two_mul_arctan_inv_2_sub_arctan_inv_7, Finsupp.logb_prod, HolderOnWith.nndist_le_of_le, InformationTheory.klDiv_eq_top_iff, torusMap_zero_radius, EulerSine.integral_cos_mul_cos_pow_aux, Affine.Simplex.ninePointCircle_radius, IsPowMul.map_one_le_one, AntilipschitzWith.le_mul_dist, SchwartzMap.fourier_lineDerivOp_eq, Complex.equivRealProd_symm_apply, Real.Angle.toReal_mem_Ioc, Complex.starConvex_one_slitPlane, Real.antitoneOn_cos, Real.sSup_smul_of_nonneg, Affine.Simplex.inv_height_lt_sum_inv_height, Real.arccos_one, Real.Angle.toReal_neg_pi_div_two, ENNReal.top_rpow_def, EuclideanGeometry.affineSpan_of_orthocentricSystem, Polynomial.logMahlerMeasure_mul_eq_add_logMahelerMeasure, TemperedDistribution.instLineDerivLeftSMulReal, entrywise_sup_norm_bound_of_unitary, LindemannWeierstrass.exp_polynomial_approx, Real.norm_natCast, DirichletCharacter.norm_le_one, NNReal.image_coe_uIoc, Cardinal.cantorFunctionAux_false, norm_iteratedFDerivWithin_clm_apply_const, Polynomial.Chebyshev.complex_ofReal_eval_C, Real.pi_lt_d6, AffineSubspace.mem_perpBisector_iff_inner_eq_zero, CircleDeg1Lift.floor_sub_le_translationNumber, Orientation.areaForm_neg_orientation, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_atBot_zero, NNReal.image_coe_Ico, NumberField.FinitePlace.norm_embedding_eq, Complex.tan_arg, Real.cos_two_neg, Complex.normSq_mul, RCLike.ofReal_nonneg, Real.closedBall_eq_Icc, schnirelmannDensity_finite, Real.sin_add_nat_mul_pi, Real.hasSum_cosh, AffineBasis.interior_convexHull, Real.cos_nat_mul_pi, NNReal.coe_rpow, Real.infinite_rat_abs_sub_lt_one_div_den_sq_of_irrational, EuclideanGeometry.inversion_vsub_center, NNReal.rpow_add_intCast', Complex.interior_setOf_le_re, Real.singleton_eq_inter_Icc, MeasureTheory.Measure.haar.prehaar_sup_le, InnerProductGeometry.angle_le_pi, set_smul_sphere_zero, EuclideanGeometry.oangle_eq_zero_iff_angle_eq_zero, Orientation.rightAngleRotation_trans_rightAngleRotation, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, IsBoundedBilinearMap.isBigO', ENNReal.tendsto_toReal, Irrational.mul_intCast, MeasureTheory.pdf.integral_pdf_smul, Real.one_lt_goldenRatio, Filter.tendsto_ofReal_iff, ValueDistribution.proximity_nonneg, IsUltrametricDist.norm_tprod_le, NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd, CFC.continuousOn_sqrt, ProbabilityTheory.mgf_const, AddSubgroup.norm_trivial_quotient_mk, Metric.mem_closure_iff_infDist_zero, Irrational.intCast_mul, Real.log_two_near_10, Real.coe_toNNReal_le, InnerProductGeometry.norm_add_eq_norm_sub_iff_angle_eq_pi_div_two, ProbabilityTheory.iCondIndep_iff, MeasureTheory.integral_fin_nat_prod_volume_eq_prod, ExistsContDiffBumpBase.u_continuous, TemperedDistribution.fourierInv_lineDerivOp_eq, Polynomial.mahlerMeasure_nonneg, norm_algebraMap_nnreal, MeasureTheory.condExpL2_indicator_ae_eq_smul, Affine.Simplex.excenter_eq_affineCombination, LipschitzWith.norm_div_le, similar_iff_exists_dist_eq, mfderivWithin_comp_projIcc_one, Real.enorm_natCast, EReal.tendsto_coe_atTop, ProbabilityTheory.iCondIndepFun_iff_condExp_inter_preimage_eq_mul, conformalAt_const_smul, Affine.Triangle.dist_div_sin_angle_eq_two_mul_circumradius, NumberField.mixedEmbedding.fundamentalCone.isCompact_compactSet, PartitionOfUnity.sum_eq_one', Metric.Sum.one_le_dist_inr_inl, Metric.hausdorffDist_self_closure, MeasureTheory.Measure.integral_toReal_rnDeriv', ENNReal.rpow_pos, CircleDeg1Lift.map_one_add, AddCircle.intervalIntegral_preimage, Real.pi_div_two_le_two, EReal.coe_neg, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_reachable, Asymptotics.isLittleO_iff_nat_mul_le, NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, NNReal.dist_agmSequences_fst_snd, EuclideanGeometry.Sphere.nonempty_iff, ContinuousMap.HomotopyRel.refl_apply, NumberField.mixedEmbedding.fundamentalCone.volume_interior_eq_volume_closure, re_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, LiouvilleWith.mul_nat, SmoothPartitionOfUnity.sum_finsupport', AddCircle.norm_div_natCast, EReal.toReal_nonpos, Stirling.le_log_factorial_stirling, abs_real_inner_le_norm, Real.dimH_univ_eq_finrank, EuclideanGeometry.Sphere.commonIntTangents_union_commonExtTangents, analyticOnNhd_rexp, Finset.infsep_pos_iff_nontrivial, MeasureTheory.Measure.integral_comp_inv_mul_left, ValueDistribution.logCounting_mul_top_eventuallyLE, Metric.comap_dist_right_atTop, Orientation.kahler_eq_zero_iff, Real.tanh_eq_sinh_div_cosh, Real.sqrt_monotone, MeasureTheory.probReal_add_probReal_compl, Real.tan_neg, curveIntegralFun_trans_aeeq_right, norm_indicator_eq_indicator_norm, TestFunction.contDiff, Real.not_summable_indicator_one_div_natCast, unitInterval.qRight_one_left, Metric.uniformEquicontinuous_iff, ModularGroup.tendsto_abs_re_smul, BoundedContinuousFunction.integral_const_sub, MeasureTheory.measure_smul_average, Metric.tendsto_atTop', ProbabilityTheory.support_gaussianPDF, MeasureTheory.condExpL1CLM_of_aestronglyMeasurable', ContinuousMap.Homotopy.ulift_apply, UpperHalfPlane.dist_eq_iff_eq_sinh, spectralValueTerms_bddAbove, InnerProductSpace.HarmonicOnNhd.comp_CLM, Orientation.oangle_sign_sub_smul_right, Real.continuous_tan, IsUltrametricDist.isUltrametricDist_iff_isNonarchimedean_norm, ProperCone.innerDual_sUnion, AffineSubspace.perpBisector_nonempty, Complex.integral_comp_polarCoord_symm, smul_closedBall', Complex.uniformContinuous_re, signedDist_apply_apply, InformationTheory.measurable_klFun, Complex.liftAux_apply, mem_closedBall_iff_norm', GenLoop.loopHomeo_apply, integral_sin_sq, SchwartzMap.integral_norm_sq_fourier, norm_add_eq_sqrt_iff_real_inner_eq_zero, Complex.reProdIm_eq_empty, Real.differentiableAt_rpow_const_of_ne, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_intCast_le_one, Real.arcsin_eq_pi_div_two, strictConcaveOn_log_Iio, Affine.Simplex.altitudeFoot_mem_affineSpan_image_compl, UnitAddTorus.mFourierCoeff_toLp, ProbabilityTheory.gaussianReal_map_continuousLinearMap, Real.logb_prod, Manifold.pathELength_def, ODE.FunSpace.continuousOn_comp_compProj, HolderWith.holderWith_zero_of_bounded, Real.exp_sub_sum_range_succ_isLittleO_pow, EuclideanSpace.volume_closedBall_fin_three, BoxIntegral.Box.isCompact_Icc, NumberField.exists_conjugate_one_le_norm, Metric.unitSphere.coe_mul, Real.isTheta_exp_comp_one, Congruent.pairwise_dist_eq, Real.hasDerivAt_arsinh, MeasureTheory.SignedMeasure.mutuallySingular_ennreal_iff, Complex.ratCast_im, NumberField.InfinitePlace.norm_embedding_eq, norm_lineDeriv_le_of_lipschitz, re_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, SchwartzMap.differentiable, NormedField.exists_norm_lt_one, LinearMap.extendTo𝕜'_apply, Real.cauchy_sub, pow_mem_closedBall, Orientation.areaForm_swap, hasSum_zeta_four, NumberField.mixedEmbedding.fundamentalCone.smul_mem_of_mem, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, Real.dimH_univ, real_inner_mul_inner_self_le, Mathlib.Tactic.Rify.ofNat_rat_real, Polynomial.Chebyshev.T_real_cos, Real.cos_pi_div_four, Real.Angle.cos_sq_add_sin_sq, MeasureTheory.SignedMeasure.exists_isCompl_positive_negative, ProbabilityTheory.Kernel.instIsMarkovKernelCondKernelUnitReal, Real.uniformContinuous_const_mul, ArithmeticFunction.vonMangoldt.support_residueClass_prime_div, ProbabilityTheory.covarianceOperator_zero, HasFDerivAt.curveIntegral_segment_source, Polynomial.supNorm_X, EReal.nhds_bot_basis, Bundle.ContinuousRiemannianMetric.symm, Real.volume_preimage_mul_left, InnerProductGeometry.sin_angle_mul_norm_eq_sin_angle_mul_norm, Path.delayReflLeft_one, norm_indicator_le_of_subset, LinearIsometryEquiv.measurePreserving, ProbabilityTheory.cgf_zero_fun, setIntegral_Ioi_zero_cpow, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, Function.locallyFinsuppWithin.logCounting_eventually_le, Subgroup.instIsArithmeticMapSpecialLinearGroupFinOfNatNatIntGeneralLinearGroupRealMapGLOfFiniteIndex, Complex.ofNat_arg, CircleDeg1Lift.map_le_of_map_zero, dist_pair_smul, ProbabilityTheory.Kernel.tendsto_density_atTop_ae_of_antitone, MulRingSeminorm.map_mul', Affine.Simplex.finrank_direction_altitude, Real.volume_pi_Ico, InformationTheory.tendsto_rightDeriv_klFun_atTop, norm_sub_le, Real.mk_one, Complex.natCast_im, TemperedDistribution.instFourierAdd, Metric.le_glueDist_inr_inl, Real.arccos_eq_zero, Asymptotics.isBigO_iff, Complex.sameRay_of_arg_eq, MeasureTheory.Integrable.integral_norm_condDistrib_map, ProbabilityTheory.setBernoulli_one, Real.contDiffAt_sqrt, CircleDeg1Lift.le_map_of_map_zero, HurwitzZeta.completedSinZeta_neg, SlashInvariantForm.coe_translate, MulRingNorm.ext_iff, NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm, NNReal.rpow_eq_pow, gronwallBound_of_K_ne_0, Complex.ofReal_zpow, Real.exp_list_sum, Metric.biInter_gt_ball, MeasureTheory.Lp.norm_zero, NonUnitalSeminormedRing.norm_mul_le, Complex.measurableEquivRealProd_apply, MeasureTheory.ComplexMeasure.singularPart_add_withDensity_rnDeriv_eq, Path.truncate_self, Real.sin_sq_arctan, EuclideanGeometry.Sphere.IsDiameter.wbtw, Metric.measure_closedBall_pos_iff, Affine.Simplex.mongePoint_mem_mongePlane, Orientation.kahler_swap, BoxIntegral.Prepartition.mem_split_iff', Orientation.det_rotation, IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul'', strongConcaveOn_zero, Metric.PiNatEmbed.dist_def, Orientation.rotation_pi_apply, integral_withDensity_eq_integral_smul, MeasureTheory.L1.dist_eq_integral_dist, NumberField.tendsto_sub_one_mul_dedekindZeta_nhdsGT, intervalIntegral.integral_comp_add_div, volume_setOf_liouville, StieltjesFunction.id_leftLim, Real.deriv_sqrt_aux, PiLp.nnnorm_toLp_one, norm_one', gauge_zero', norm_sub_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zero, CircleDeg1Lift.ext_iff, UpperHalfPlane.dist_log_im_le, Affine.Simplex.isTangentAt_insphere_touchpoint, InnerProductGeometry.norm_add_eq_add_norm_iff_angle_eq_zero, Real.smoothTransition.one, Complex.frontier_setOf_im_lt, Orientation.rotation_rotation, ContinuousMap.HomotopyRel.trans_apply, convexHull_diam, Real.Angle.two_nsmul_toReal_eq_two_mul_sub_two_pi, curveIntegralFun_symm_apply, MeasureTheory.SignedMeasure.mutuallySingular_singularPart, Real.tan_nat_mul_pi_sub, ModularGroup.exists_max_im, Polynomial.logMahlerMeasure_mul_eq_add_logMahlerMeasure, SeparationQuotient.norm_normedMk_eq_one, Affine.Simplex.excenterWeightsUnnorm_map, Real.range_cos, uniformContinuous_dist, EuclideanGeometry.Sphere.IsExtTangentAt.wbtw, inner_re_zero_right, HasStrictDerivAt.real_of_complex, norm_le_of_mem_closedBall, LinearEquiv.toSpanNonzeroSingleton_homothety, NumberField.house_mul_le, SeparationQuotient.norm_normedMk_le, AddCircle.instIsAddHaarMeasureRealVolume, Matrix.PosSemidef.det_sqrt, Real.arccos_eq_pi_div_two_sub_arcsin, norm_circleMap_zero, ProbabilityTheory.cdf_eq_real, ProbabilityTheory.cgf_zero, Real.cos_add_cos, BoxIntegral.HasIntegral.smul, Real.deriv_rpow_const, Real.sqrt_sq_eq_abs, TemperedDistribution.instFourierSMul, instIsContinuousRiemannianBundleTrivial, Metric.hausdorffDist_zero_iff_closure_eq_closure, Nat.closedBall_eq_Icc, integral_smul_const, IsSelfAdjoint.coe_mem_spectrum_complex, Real.comap_exp_nhds_exp, Complex.ofReal_mul', tendsto_norm_sub_self, ContinuousMap.dist_apply_le_dist, CStarModule.inner_smul_right_real, Real.map_matrix_volume_pi_eq_smul_volume_pi, Set.Finite.infsep_of_nontrivial, Metric.continuous_iff, Path.Homotopy.reflTransSymmAux_mem_I, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff', Real.tendsto_exp_neg_atTop_nhds_zero, NormedField.denselyOrdered_range_norm, hasDerivWithinAt_abs, Path.continuous_extend, contDiff_circleMap, ContDiffBump.nonneg, ProbabilityTheory.covariance_mul_const_left, ProbabilityTheory.covariance_fun_neg_right, IsUltrametricDist.dist_triangle_max, Subgroup.IsArithmetic.isCusp_iff_isCusp_SL2Z, Affine.Simplex.ExcenterExists.affineSpan_faceOpposite_eq_orthRadius, Real.Angle.sin_add_pi, ContinuousLinearEquiv.one_le_norm_mul_norm_symm, Real.Angle.toReal_coe_eq_self_iff, HurwitzZeta.evenKernel_eq_cosKernel_of_zero, PartitionOfUnity.exists_finset_nhds, eventually_norm_mfderivWithin_symm_extChartAt_lt, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_integral_of_antitone, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, Affine.Simplex.inner_mongePoint_vsub_face_centroid_vsub, Hyperreal.tendsto_iff_forall, AkraBazziRecurrence.sumTransform_def, ContinuousMultilinearMap.norm_compContinuous_linearIsometry_le, norm_pow_le, instPathConnectedSpaceElemForallRealStdSimplexOfNonempty, UpperHalfPlane.im_le_im_mul_exp_dist, dist_div_div_le, Real.Gamma_mul_Gamma_one_sub, Orientation.volumeForm_def, AkraBazziRecurrence.eventually_deriv_one_add_smoothingFn, CircleDeg1Lift.dist_map_map_zero_lt, ProbabilityTheory.Kernel.setIntegral_densityProcess_of_mem, MeasureTheory.tendstoInMeasure_iff_norm, AbsolutelyContinuousOnInterval.tendsto_volume_totalLengthFilter_nhds_zero, Complex.tendsto_exp_comap_re_atTop, measurable_circleMap, convex_halfSpace_re_le, Complex.reCLM_coe, MeasureTheory.Measure.haar.prehaar_pos, BoundedContinuousFunction.exists_extension_norm_eq_of_isClosedEmbedding, norm_pos_iff', Real.Angle.sin_neg, FiniteDimensional.complexToReal, AntilipschitzWith.le_mul_norm', HurwitzZeta.hurwitzZetaEven_apply_zero, MeasureTheory.Measure.addHaar_unitClosedBall_eq_addHaar_unitBall, NNReal.coe_eq_zero, Real.neg_one_lt_goldenConj, Seminorm.ball_norm_mul_subset, DirichletCharacter.unit_norm_eq_one, EReal.nhds_top', Padic.norm_eq_zpow_log_mulValuation, Real.arcsin_le_pi_div_two, Complex.continuous_re, Valued.integer.exists_norm_lt_one, Real.sin_sub, Real.deriv_sinh, UpperHalfPlane.isBoundedAtImInfty_iff, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding, ContinuousMap.norm_eq_iSup_norm, ContinuousMultilinearMap.opNorm_smul_le, Asymptotics.div_isBoundedUnder_of_isBigO, Real.cos_three_mul, ENNReal.prod_rpow_of_ne_top, Real.cos_two_pi, MeasureTheory.upcrossingStrat_le_one, PartitionOfUnity.IsSubordinate.continuous_finsum_smul, MeasureTheory.convolution_precompR_apply, Irrational.neg, AlgebraNorm.ext_iff, ProbabilityTheory.IsMeasurableRatCDF.instIsProbabilityMeasure_stieltjesFunction, EReal.canLift, Metric.isBounded_iff_eventually, orthonormal_fourier, Set.Finite.isCompact_convexHull, ProbabilityTheory.condIndepSets_singleton_iff, irrational_intCast_sub_iff, isCusp_SL2Z_iff', InnerProductGeometry.angle_neg_right, ModularGroup.lcRow0Extend_symm_apply, Real.volume_Icc_pi, ProbabilityTheory.Kernel.rnDeriv_def', ContinuousMap.Homotopy.cast_apply, norm_injOn_ray_right, Metric.diam_eq_zero_of_unbounded, InformationTheory.hasDerivAt_klFun, MeasureTheory.setIntegral_condExpL2_indicator, ContinuousMap.toNNReal_algebraMap, Path.toHomotopyConst_apply, NumberField.IsCMField.regulator_div_regulator_eq_two_pow_mul_indexRealUnits_inv, contMDiff_coe_sphere, integral_cos_pow_aux, HurwitzZeta.expZeta_one_sub, CircleDeg1Lift.inf_apply, unitInterval.measurePreserving_symm, ContinuousMultilinearMap.norm_restr, Real.tan_two_mul, antilipschitzWith_iff_exists_mul_le_norm', ContinuousMultilinearMap.norm_image_sub_le, Seminorm.closedBall_zero_eq_preimage_closedBall, EisensteinSeries.r_pos, Metric.mem_thickening_iff, ProbabilityTheory.isPosSemidef_covarianceBilin, diam_stdSimplex, NNReal.image_coe_uIcc, Real.negMulLog_mul, EisensteinSeries.r1_pos, MeasureTheory.L1.SimpleFunc.integral_eq_norm_posPart_sub, intervalIntegral.intervalIntegrable_sin, stereographic_apply_neg, LinearIsometry.norm_toContinuousLinearMap, intervalIntegral.abs_intervalIntegral_eq, StarAlgHom.continuous_realContinuousMapOfNNReal, ModularGroup.denom_apply, Orientation.kahler_comp_rightAngleRotation, Polynomial.card_eq_of_natDegree_le_of_coeff_le, Seminorm.ball_smul, Even.strictConvexOn_pow, TemperedDistribution.instFourierPairInv, Real.Gamma_one, InnerProductGeometry.sin_angle_nonneg, MeasureTheory.SimpleFunc.setToSimpleFunc_add_left, Complex.norm_natCast, EuclideanGeometry.oangle_eq_pi_iff_sbtw, TemperedDistribution.instFourierPair, NNReal.isGreatest_Lp, UpperHalfPlane.vadd_re, ae_differentiableAt_norm, Real.hasSum_cos, IsOpen.exists_contMDiff_support_eq_aux, ENNReal.le_toReal_sub, ArithmeticFunction.vonMangoldt.residueClass_apply, Real.one_lt_toNNReal, MeasureTheory.lpNorm_add_le, Real.sinhHomeomorph_symm_apply, Complex.lift_apply, ENNReal.rpow_one, IsApproximateSubgroup.subgroup, Real.arccos_image_Icc, Commute.cfc_real, dist_triangle4, TemperedDistribution.delta_apply, torusMap_eq_center_iff, Urysohns.CU.approx_nonneg, isTheta_choose, MeasureTheory.memLp_haarAddCircle_iff, ProbabilityTheory.gaussianReal_of_var_ne_zero, ContinuousLinearMap.contDiffPointwiseHolderAt, NumberField.Units.instZLattice_unitLattice, Manifold.pathELength_eq_lintegral_mfderivWithin_Icc, Real.continuous_log, ENNReal.rpow_natCast, NNReal.rpow_inv_rpow, curveIntegralFun_refl, Affine.Simplex.circumcenter_eq_affineCombination_of_pointsWithCircumcenter, Submodule.norm_eq_iInf_iff_inner_eq_zero, mem_closure_one_iff_norm, InnerProductGeometry.angle_zero_right, MeasureTheory.BorelCantelli.predictablePart_process_ae_eq, AddCircle.ergodic_nsmul_add, Finset.coe_infsep_of_offDiag_nonempty, Real.ediam_Ioc, ProbabilityTheory.iIndepSet.condExp_indicator_filtrationOfSet_ae_eq, MeasureTheory.integral_singleton', NumberField.InfiniteAdeleRing.mixedEmbedding_eq_algebraMap_comp, MeasureTheory.measureReal_union_null_iff, MeasureTheory.lpNorm_mul_natCast, lp.summable_mul, NumberField.mulHeight_eq, ProbabilityTheory.noAtoms_gaussianReal, MeasureTheory.integral_exp_tilted, NNReal.isCoboundedUnder_le_toReal, NumberField.mixedEmbedding.convexBodySum_compact, Unitary.norm_sub_one_lt_two_iff, ContinuousMap.continuous_toNNReal, Orientation.volumeForm_zero_pos, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_mgf', Real.continuous_sqrt, NNReal.coe_prod, Metric.exists_forall_closedEBall_subset_aux₁, ContinuousMap.Homotopy.pathExtend_evalAt, Set.Nontrivial.infsep_of_fintype, Real.HolderConjugate.one_sub_inv, Real.cos_pi_div_sixteen, Real.Angle.cos_add_pi, selfAdjoint.imaginaryPart_coe, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply, AddCircle.dense_addSubgroup_iff_ne_zmultiples, Bundle.ContinuousRiemannianMetric.continuous, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_adicAbv, AddSubgroup.tendsto_zmultiples_subtype_cofinite, Real.ofCauchy_nnratCast, Affine.Simplex.affineSpan_faceOpposite_eq_orthRadius_insphere, ModularGroup.im_T_smul, indiscreteTopology_iff_forall_norm_eq_zero, Matrix.IsHermitian.charpoly_cfc_eq, Nat.preimage_closedBall, NormedSpace.norm_expSeries_summable, Real.coe_toNNReal', CFC.rpow_one, IsGreatest.norm_cfcₙ, Real.one_add_tan_sq_mul_cos_sq_eq_one, CFC.rpow_neg, SchwartzMap.laplacianCLM_eq', CircleDeg1Lift.coe_toOrderIso_symm, PseudoMetricSpace.le_two_mul_dist_ofPreNNDist, BoxIntegral.Box.le_iff_bounds, norm_inner_eq_norm_iff, Real.volume_eq_stieltjes_id, RCLike.re_monotone, Real.logb_neg_base_eq_logb, LSeries.summable_real_of_abscissaOfAbsConv_lt, Complex.norm_exp_I_mul_ofReal_sub_one, integral_exp_mul_complex, Polynomial.exists_eq_gaussNorm, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, Real.measurable_sinc, CuspFormClass.petersson_bounded_left, MeasureTheory.AEStronglyMeasurable.dist, CircleDeg1Lift.translate_iterate, Quaternion.nnnorm_star, VitaliFamily.filterAt_basis_closedBall, Real.Angle.cos_add_pi_div_two, MeasureTheory.charFunDual_prod, add_mem_ball_iff_norm, Real.smul_map_volume_mul_left, Real.GammaSeq_tendsto_Gamma, ProbabilityTheory.Kernel.integrable_densityProcess, norm_zero, RCLike.im_ofReal_pow, Real.holderTriple_iff, Real.cos_two_pi_sub, EuclideanGeometry.Sphere.orthRadius_center, NumberField.Units.span_basisOfIsMaxRank, EReal.preimage_coe_Ioo_top, ENNReal.measurable_toReal, Complex.ofReal_comp_sub, nnnorm_cfcₙ_nnreal_lt, NumberField.mixedEmbedding.fundamentalCone.norm_pos_of_mem, CFC.sqrt_eq_rpow, ProbabilityTheory.covariance_zero_right, Real.arsinh_nonpos_iff, instIsManifoldRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, SmoothBumpCovering.toSmoothPartitionOfUnity_apply, LipschitzWith.dist_left, ProbabilityTheory.Kernel.HasSubgaussianMGF.const_mul, ProbabilityTheory.covariance_smul_left, Irrational.mul_natCast, MeasureTheory.tendstoInMeasure_iff_measureReal_dist, InnerProductGeometry.sin_eq_one_iff_angle_eq_pi_div_two, Complex.arg_cos_add_sin_mul_I_sub, ProbabilityTheory.Kernel.martingale_densityProcess, EReal.toReal_zero, normHom_apply, Complex.sub_re, Real.Angle.coe_add, Function.hasTemperateGrowth_iff_isBigO, FiniteDimensional.rclike_to_real, Complex.sq_norm_sub_sq_re, Complex.comap_exp_nhds_zero, Complex.equivRealProdCLM_symm_apply, ProbabilityTheory.monotone_defaultRatCDF, Seminorm.convexOn, Real.sin_sq, Complex.abs_re_eq_norm, Real.Angle.cos_nonneg_iff_abs_toReal_le_pi_div_two, Complex.GammaIntegral_ofReal, TemperedDistribution.instContinuousFourier, gronwallBound_ε0_δ0, CircleDeg1Lift.map_int_of_map_zero, CStarAlgebra.nnnorm_le_iff_of_nonneg, ProbabilityTheory.strong_law_ae, zero_eq_dist, Real.HolderTriple.inv_nonneg, Complex.norm_add_eq, Real.Gamma_one_half_eq, NumberField.Units.logEmbeddingQuot_apply, strictConcaveOn_sqrt_mul_log_Ioi, Set.Finite.infsep, NumberField.InfinitePlace.pos_iff, Real.Angle.abs_toReal_neg, Module.Basis.prod_addHaar, NNReal.continuous_coe, PiLp.volume_preserving_toLp, Real.smoothTransition.zero, Real.pi_div_two_eq_arcsin, CompactlySupportedContinuousMap.coe_toRealLinearMap, Complex.norm_cpow_of_ne_zero, Complex.interior_preimage_re, dist_nonneg, InnerProductGeometry.norm_toLp_symm_crossProduct, QuotientAddGroup.norm_lt_iff, ContractingWith.aposteriori_dist_iterate_fixedPoint_le, NNReal.bddBelow_coe, ZSpan.measureReal_fundamentalDomain, Real.two_le_pi, fourier_one, Affine.Simplex.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, Chebyshev.integral_one_div_log_sq_isBigO, Complex.natCast_log, MeasureTheory.charFun_eq_prod_iff, ENNReal.lintegral_rpow_add_le_add_eLpNorm_mul_lintegral_rpow_add, Module.Basis.norm_smul, Similar.exists_dist_eq, ContinuousLinearMap.bounds_nonempty, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, Polynomial.ofReal_eval, Real.inv_one_add_tan_sq, PadicInt.norm_natCast_zmodRepr_eq_one_iff_ne, Seminorm.coe_restrictScalars, LiouvilleWith.nat_mul, CovByVAdd.of_subset, NumberField.Units.basisOfIsMaxRank_apply, coe_normGroupNorm, MeasureTheory.measureReal_nonneg, Complex.im_le_norm, Real.totallyBounded_ball, Complex.norm_ofReal_cpow_eventually_eq_atTop, SmoothBumpFunction.support_mem_nhds, Asymptotics.bound_of_isBigO_cofinite, MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar, Real.differentiableOn_rpow_const, EuclideanGeometry.Sphere.coe_secondInter, Path.uniformContinuous_extend_left, MeasureTheory.MemLp.integrable_norm_pow, continuousMap_mem_polynomialFunctions_closure, AkraBazziRecurrence.isBigO_symm_asympBound, Orientation.measure_eq_volume, ProbabilityTheory.abs_truncation_le_bound, BoxIntegral.Box.nndist_le_distortion_mul, ContinuousLinearMapWOT.instLocallyConvexSpace, inner_self_im, measurableEmbedding_sigmoid, Asymptotics.isLittleO_norm_right, lintegral_comp_pi_polarCoord_symm, MeasureTheory.lpNorm_smul_measure_of_ne_zero, BoundingSieve.one_le_y, SimplexCategory.toTop_obj, irrational_sqrt_natCast_iff, Real.HolderTriple.left_pos, NumberField.mixedEmbedding.fundamentalCone.subset_interior_normLeOne, bernoulliFun_eval_one, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_sub_two_mul_dist_mul_dist_mul_cos_angle, polarCoord_target, Complex.norm_mul_cos_arg, ProbabilityTheory.variance_map_equiv, NonarchAddGroupSeminorm.coe_zero, BoxIntegral.TaggedPrepartition.isSubordinate_single, Complex.sq_norm, MeasureTheory.SimpleFunc.exists_forall_norm_le, Polynomial.gaussNorm_zero, NNReal.rpow_sub_natCast, Real.arsinh_nonneg_iff, EReal.coe_natCast, Real.volume_singleton, HomotopyGroup.transAt_indep, PiTensorProduct.projectiveSeminorm_tprod_le, EReal.tendsto_toReal_atTop, MeasureTheory.Measure.haar.prehaar_empty, Real.smoothTransition.contDiffAt, Complex.measurable_re, NNReal.isEmbedding_coe, mem_closedBall_iff_norm, MeasureTheory.SignedMeasure.absolutelyContinuous_iff_withDensityᵥ_rnDeriv_eq, AddCircle.denseRange_zsmul_iff, UpperHalfPlane.σ_mul, ENNReal.exists_frequently_lt_of_liminf_ne_top', unitInterval.toNNReal_zero, CFC.sqrt_map_prod, NonarchAddGroupSeminormClass.map_neg_eq_map', PeriodPair.basis_zero, UpperHalfPlane.image_coe_ball, LiouvilleWith.int_add, MeasureTheory.Integrable.norm_integral_condDistrib, ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_pos_eq_zero_of_hasSubGaussianMGF_zero, BoxIntegral.Box.measure_coe_lt_top, Complex.exists_norm_eq_mul_self, RCLike.ofReal_natCast, has_fderiv_at_filter_real_equiv, Metric.mem_nhdsWithin_iff, NumberField.mixedEmbedding.negAt_signSet_apply_isReal, one_sub_goldConj, NumberField.Units.regulator_eq_det, Matrix.PosSemidef.posSemidef_sqrt, orthonormalBasis_one_dim, ContDiffBump.contDiff, Complex.closure_setOf_lt_im, Real.hasDerivWithinAt_arccos_Ici, RightDerivMeasurableAux.differentiable_set_subset_D, MeasureTheory.posConvolution_eq_convolution_indicator, unitInterval.symm_projIcc, MeasureTheory.setIntegral_condExpInd, ContinuousLinearMap.isPositive_def, indicator_norm_le_norm_self, MeasureTheory.Measure.haar.addCHaar_nonneg, continuous_dist, ContinuousMap.Homotopy.compContinuousMap_apply, Seminorm.gaugeSeminorm_ball, Metric.eventually_nhds_iff, EuclideanGeometry.oangle_midpoint_rev_left, EReal.tendsto_toReal_atBot, ENNReal.mul_rpow_of_ne_zero, Real.toNNReal_le_one, InformationTheory.leftDeriv_klFun, Real.exp_monotone, Real.lt_cauchy, integral_bernoulliFun_eq_zero, Path.cast_coe, tendsto_integral_exp_smul_cocompact, ENNReal.ofNat_le_ofReal, ContinuousMap.Homotopy.comp_apply, Real.logb_zero_left_eq_zero, Real.pi_div_two_pos, Complex.dist_self_conj, Affine.Triangle.touchpoint_singleton_sbtw, ProbabilityTheory.eqOn_complexMGF_of_mgf, Real.le_exp_log, intervalIntegral.FTCFilter.pure, StarAlgHom.realContinuousMapOfNNReal_apply, curveIntegral_segment, TestFunction.postcompCLM_apply, irrational_sqrt_ratCast_iff_of_nonneg, InnerProductSpace.Core.normSq_eq_zero_of_eq_zero, tendsto_norm_div_self_nhdsNE, Complex.ofReal_neg, ProbabilityTheory.Kernel.measurable_density, LiouvilleWith.add_rat, AddCircle.exists_norm_nsmul_le, Real.arctan_eq_neg_pi_div_four, isEquivalent_choose, MeasureTheory.SignedMeasure.totalVariation_zero, Real.sqrt_le_iff, NNReal.lt_iff_exists_rat_btwn, PadicInt.mk_coe, NNReal.rpow_sub, ExistsContDiffBumpBase.u_le_one, CircleDeg1Lift.coe_toOrderIso_inv, Orientation.rotation_symm, MeasureTheory.Measure.haar.prehaar_sup_eq, ProbabilityTheory.IsMeasurableRatCDF.tendsto_atBot_zero, Homeomorph.coe_unitBall_apply_zero, EuclideanGeometry.Sphere.isTangent_iff_isTangentAt_orthogonalProjection, eventually_riemmanianEDist_lt, NNReal.rpow_sub', IsGreatest.norm_cfc, inner_re_zero_left, IsSelfAdjoint.neg_algebraMap_norm_le_self, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, Real.exists_isMinOn_Gamma_Ioi, Affine.Simplex.exradius_map, Hyperreal.isSt_sSup, Polynomial.card_roots_toFinset_le_card_roots_derivative_diff_roots_succ, gauge_norm_smul, ENNReal.toReal_lt_of_lt_ofReal, MeasureTheory.Integrable.integral_norm_comp, ENNReal.ofReal_le_iff_le_toReal, Complex.div_ofNat, intervalIntegral.FTCFilter.nhdsWithinSingleton, InnerProductSpace.Core.cauchy_schwarz_aux, ODE.FunSpace.dist_iterate_iterate_next_le_of_lipschitzWith, Set.OrdConnected.image_ennreal_ofReal, Real.tendsto_exp_comp_nhds_zero, Complex.smul_re, circleMap_pi_div_two, Real.volume_pi_Ioc, inner_self_ofReal_re, AkraBazziRecurrence.strictMonoOn_one_sub_smoothingFn, Asymptotics.IsBigOWith.const_smul_left, ValueDistribution.isBigO_characteristic_sub_characteristic_shift, Orientation.oangle_eq_zero_iff_sameRay, RCLike.conjLIE_apply, Real.measurable_cos, unitSphereToUnits_apply_coe, Complex.uniformlyContinuous_re, Complex.map_exp_comap_re_atTop, Real.continuousAt_const_rpow', Real.isPiSystem_Iic_rat, ProbabilityTheory.moment_zero, convexOn_univ_norm, BoxIntegral.Box.measure_Icc_lt_top, RCLike.summable_ofReal, edist_lt_ofReal, Polynomial.mahlerMeasure_eq_zero_iff, Real.exists_rat_abs_sub_lt_and_lt_of_irrational, tendsto_norm_div_self_nhdsGE, Complex.orthonormalBasisOneI_repr_apply, RCLike.ofReal_le_ofReal, WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminorm, MeasureTheory.lpNorm_one_eq_integral_norm, Valued.integer.norm_irreducible_lt_one, ContinuousMapZero.integral_apply, SimplexCategory.toTop_map, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_eq, EisensteinSeries.summable_norm_eisSummand, Real.Angle.neg_pi_lt_toReal, Quaternion.coeComplex_add, Real.volume_emetric_closedBall, analyticOn_log, MeasureTheory.Measure.haar.mem_prehaar_empty, Affine.Triangle.dist_circumcenter_reflection_orthocenter, MeasureTheory.norm_condExpL2_coe_le, LipschitzWith.mapsTo_ball, Seminorm.ball_zero_eq_preimage_ball, IsometryEquiv.coe_toRealAffineIsometryEquiv, lp.norm_const_smul, MeasureTheory.lpNorm_measure_zero, AkraBazziRecurrence.GrowsPolynomially.norm, NormedAlgebra.exists_isMinOn_norm_sub_smul, tendsto_sub_mul_tsum_nat_cpow, Polynomial.toAddCircle.integrable, IsApproximateAddSubgroup.nsmul_inter_nsmul, intervalIntegral.FTCFilter.le_nhds, AddCircle.instHasAddFundamentalDomainSubtypeAddOppositeRealMemAddSubgroupOpZmultiples, Besicovitch.ae_tendsto_rnDeriv, fourier_zero, ContDiffBump.hasCompactSupport, WithCStarModule.prod_norm_le_norm_add, Real.arcosh_injOn, Complex.normSq_I, RCLike.imLm_coe, Metric.ball_eq_ball, ContinuousLinearMap.exists_approx_preimage_norm_le, Real.sqrt_two_lt_three_halves, BoundedContinuousFunction.bddAbove_range_norm_comp, fourier_neg', openSegment_subset_ball_of_ne, ValueDistribution.logCounting_const, NormedSpace.normalize_smul, analyticOnNhd_log, ProbabilityTheory.condVar_smul, NNReal.coe_multiset_prod, Real.toNNReal_monotone, MeasureTheory.integrable_withDensity_iff_integrable_smul', MeasureTheory.MemLp.integrable_enorm_rpow', Real.cosPartialEquiv_apply, Real.differentiable_cos, Orientation.angle_eq_iff_oangle_eq_or_sameRay, NNReal.rpow_neg_one, IsMIntegralCurveOn.comp_mul, Real.fourierIntegralInv_comp_linearIsometry, Real.coe_expOrderIso_apply, Complex.norm_cpow_of_imp, ContinuousMultilinearMap.le_opNorm, approxOrderOf.image_pow_subset_of_coprime, ConvexBody.coe_smul, PartitionOfUnity.coe_finsupport, Real.sigmoid_def, BoxIntegral.Box.splitUpper_eq_self, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, cauchySeq_finset_iff_vanishing_norm, UpperHalfPlane.dist_triangle, Asymptotics.isBigOWith_norm_norm, Path.subpathAux_one, SchwartzMap.delta_apply, InnerProductGeometry.angle_eq_zero_iff, Path.continuous_delayReflRight, Affine.Simplex.abs_inner_vsub_altitudeFoot_lt_mul, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_mgf, SchwartzMap.norm_fourier_toL2_eq, norm_cauchyPowerSeries_le, Orientation.rotation_map, Real.log_nat_eq_sum_factorization, Real.qaryEntropy_continuous, IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul, RCLike.div_im, norm_le_add_norm_add', ProbabilityTheory.Kernel.setIntegral_densityProcess_of_le, Orientation.oangle_rotation_left, Real.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, abs_dist_sub_le, unitInterval.lt_one_iff_ne_one, AddGroupNormClass.toNormedAddGroup_norm_eq, SchwartzMap.instFourierPair, measurableEmbedding_sigmoid_comp_embeddingReal, Real.ofDigitsTerm_le, lebesgue_number_lemma_of_metric, Complex.re_comp_balance, MulAlgebraNormClass.toMulRingNormClass, dist_birkhoffAverage_apply_birkhoffAverage, ProbabilityTheory.cdf_nonneg, isMIntegralCurveOn_comp_add, MeasureTheory.lowerCrossingTime_zero, MeasureTheory.exists_subset_real_measurableEquiv, unitInterval.lt_symm_comm, curveIntegral_def, Real.volume_ball, ENNReal.eventually_pow_one_div_le, Real.Angle.coe_abs_toReal_of_sign_nonneg, GenLoop.instContinuousEval, CFC.rpow_rpow_inv, MeasureTheory.Measure.addHaar_preimage_continuousLinearMap, NormSMulClass.norm_smul, Euclidean.nhds_basis_closedBall, Path.Homotopy.hcomp_half, HasFPowerSeriesOnBall.uniform_geometric_approx, Stirling.stirlingSeq_one, ProperCone.innerDual_zero, Real.logb_div, BoundedContinuousFunction.dist_eq, Matrix.eigenvalues_conjTranspose_mul_self_nonneg, summable_jacobiTheta₂_term_fderiv_iff, ProbabilityTheory.covariance_const_left, Affine.Simplex.excenterWeights_reindex, MeasureTheory.lpNorm_le_add_lpNorm_add, ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, StieltjesFunction.iInf_rat_gt_eq, sameRay_iff_of_norm_eq, ball_eq, ProbabilityTheory.IsMeasurableRatCDF.stronglyMeasurable_stieltjesFunction, Metric.tendsto_nhdsWithin_nhds, Metric.exists_smooth_forall_closedBall_subset, QuotientGroup.nhds_one_hasBasis, Complex.abs_arg_le_pi, SmoothBumpFunction.support_eq_inter_preimage, Real.isBigO_one_exp_comp, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, ValueDistribution.characteristic_sub_characteristic_eq_proximity_sub_proximity, AddCircle.norm_coe_mul, ZMod.toAddCircle_inj, Set.Icc.convexCombo_one, Real.arccos_le_pi, GroupSeminorm.ext_iff, CompactlySupportedContinuousMap.nnrealPart_add_le_add_nnrealPart, RCLike.ofReal_mul, instLieGroupRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, Path.Homotopy.hcomp_apply, ProbabilityTheory.isRatCondKernelCDF_preCDF, Complex.norm_eq_one_iff, TrivSqZeroExt.norm_def, NNReal.comap_coe_atTop, UpperHalfPlane.dist_of_re_eq, NumberField.Units.finrank_mul_regOfFamily_eq_det, dist_le_zero, InnerProductGeometry.cos_angle, Affine.Simplex.sum_mongePointVSubFaceCentroidWeightsWithCircumcenter, Filter.IsIncreasingApproximateUnit.eventually_norm, Real.expNear_sub, Real.sinh_sub_id_strictMono, Complex.re_le_re, Real.dimH_univ_pi_fin, Set.Nontrivial.infsep_eq_iInf, dist_lineMap_left, PartitionOfUnity.exists_finset_nhds_support_subset, ZMod.completedLFunction_def_odd, Real.instIsCompleteAbs, OrthonormalBasis.norm_eq_one, Urysohns.CU.approx_mono, MeasureTheory.SignedMeasure.toJordanDecomposition_smul_real, PadicInt.norm_eq_zpow_neg_valuation, RCLike.im_to_real, fib_golden_exp', Real.fourier_real_eq, ContinuousAlternatingMap.le_opNorm, ProbabilityTheory.ofReal_condCDF_ae_eq, norm_natCast, Asymptotics.isBigO_top, Path.continuous_delayReflLeft, geom_gold_isSol_fibRec, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_univ, Real.cot_eq_cos_div_sin, eq_zero_or_norm_pos, Affine.Simplex.ExcenterExists.isTangentAt_touchpoint, Subgroup.instIsArithmeticAdjoinNegOne, quarters_mem_preCantorSet, OnePoint.isZeroAt_infty_iff, Path.Homotopy.symm_apply, ProbabilityTheory.defaultRatCDF_le_one, IsPicardLindelof.continuousOn, MeasureTheory.L1.integral_def, Stirling.stirlingSeq'_antitone, Real.cos_one_le, spectralValueTerms_finite_range, Asymptotics.isBigOWith_abs_left, Subgroup.strictWidthInfty_eq_one_of_T_mem, Affine.Simplex.inradius_reindex, BoundedContinuousFunction.Lp_nnnorm_le, Real.Angle.coe_eq_zero_iff, Tactic.ComputeAsymptotics.Seq.dist_cons_cons_eq_one, EuclideanGeometry.preimage_inversion_perpBisector, hasSum_fourier_series_L2, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, MeasureTheory.integrable_comp_div_iff, isMIntegralCurveOn_comp_sub, Complex.div_ratCast_re, unitInterval.volume_uIcc, IsSelfAdjoint.val_re_map_spectrum, norm_commutator_sub_one_le, realPart.norm_le, ZSpan.volume_fundamentalDomain, Path.instContinuousEvalElemRealUnitInterval, NNReal.eq_rpow_inv_iff, Complex.tendsto_normSq_cocompact_atTop, Real.isBigO_exp_comp_one, ProbabilityTheory.covarianceBilin_zero, dist_le_coe, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIdealLattice, CFC.posPart_algebraMap_nnreal, NumberField.mixedEmbedding.convexBodySumFun_apply, RCLike.conjCLE_coe, Path.Homotopy.transAssocReparamAux_mem_I, Irrational.add_natCast, Height.mulHeight_pow, Real.tendsto_integral_gaussian_smul', EReal.toReal_neg, ContinuousAlternatingMap.bounds_bddBelow, contDiffOn_stereoToFun, MeasureTheory.Measure.haar.add_prehaar_le_addIndex, Affine.Simplex.incenter_mem_interior, ENNReal.ofReal_add_le, Real.finrank_eq_int_finrank_of_discrete, Affine.Simplex.mongePoint_eq_affineCombination_of_pointsWithCircumcenter, Hyperreal.coe_eq_one, exists_seq_norm_le_one_le_norm_sub, unitInterval.volume_Ici, Rat.AbsoluteValue.exists_nat_rpow_iff_isEquiv, Real.analyticAt_sin, AddCircle.ergodic_add_left, RCLike.ext_iff, abs_dist_sub_le_dist_mul_mul, Affine.Simplex.altitudeFoot_map, smul_sphere', AddCircle.norm_half_period_eq, Diffeology.IsPlot.dSmooth, Polynomial.Chebyshev.isLocalMax_T_real, analyticOnNhd_sigmoid, LiouvilleWith.add_rat_iff, ContinuousOn.norm', map_pow_le_pow, Metric.hausdorffDist_triangle', Real.Angle.coe_coeHom, ZSpan.measure_fundamentalDomain, convex_halfSpace_im_gt, Real.tendsto_cos_neg_pi_div_two, Real.measurable_arctan, norm_jacobiTheta₂_term, Real.logb_abs_base, Path.Homotopy.eval_apply, dist_midpoint_midpoint_le, CircleDeg1Lift.units_apply_inv_apply, RCLike.normSq_inv, Padic.norm_natCast_lt_one_iff, Matrix.PosSemidef.sqrt_eq_one_iff, Real.Angle.toReal_neg_eq_neg_toReal_iff, ProbabilityTheory.condExpKernel_ae_eq_condExp', Real.deriv_Gamma_nat, trapezoidal_integral_ext, coe_mem_spectrum_real_of_nonneg, Rat.AbsoluteValue.equiv_on_nat_iff_equiv, real_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, Path.Homotopy.transAssocReparamAux_zero, eq_one_or_norm_pos, ENNReal.rpow_zero_pos, Real.iInf_const_zero, EuclideanGeometry.angle_le_angle_add_angle, BoxIntegral.unitPartition.mem_box_iff, Real.LogDeriv_exp, AkraBazziRecurrence.isTheta_smoothingFn_sub_self, MeasureTheory.Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_group, Isometry.mapsTo_perpBisector, CStarRing.norm_star_mul_self', NumberField.InfinitePlace.Completion.locallyCompactSpace, CircleDeg1Lift.map_map_zero_lt, MeasureTheory.Measure.HasTemperateGrowth.exists_integrable, EuclideanGeometry.Cospherical.affineIndependent_of_ne, HurwitzZeta.sinKernel_neg, NormedAddCommGroup.cauchySeq_iff, EReal.range_coe_eq_Ioo, Real.tan_pi_div_two, ProbabilityTheory.isGaussian_map_equiv_iff, Circle.exp_two_pi, Complex.polarCoord_apply, HurwitzZeta.continuousOn_cosKernel, Affine.Simplex.circumcenter_eq_point, Real.fourierIntegral_convergent_iff', ENNReal.toReal_mul_top, EuclideanGeometry.dist_eq_add_dist_of_angle_eq_pi, NNReal.rpow_mul, Matrix.PosSemidef.sqrt_sq, MeasureTheory.measureReal_zero, Seminorm.continuous, instIsTopologicalDivisionRingReal, PiLp.nnnorm_toLp_const', MeasureTheory.SignedMeasure.absolutelyContinuous_ennreal_iff, Seminorm.coe_smul, EReal.image_coe_Iic, IsUltrametricDist.exists_norm_finset_prod_le, Complex.normSq_add, NormOneClass.norm_one, Polynomial.Chebyshev.S_two_mul_real_cos, IsPathConnected.exists_path_through_family, ContinuousMap.Homotopy.apply_one_path, MeasureTheory.tendstoInMeasure_iff_dist, UpperHalfPlane.center_im, Irrational.inv, InnerProductGeometry.cos_angle_mul_norm_mul_norm, Inseparable.dist_eq_zero, Real.analyticOnNhd_cosh, ContractingWith.apriori_dist_iterate_fixedPoint_le, Complex.ofReal_balance, MeasureTheory.integral_indicatorConstLp, MeasureTheory.Measure.toSphere_apply_univ, Real.hasDerivAt_binEntropy, Submodule.norm_sq_eq_add_norm_sq_starProjection, hasDerivAt_gronwallBound_shift, SeminormedAddGroup.disjoint_nhds_zero, RCLike.re_eq_norm_of_mul_conj, PartitionOfUnity.sum_le_one', MeasureTheory.norm_integral_le_integral_norm, Height.mulHeight_pos, Bundle.ContMDiffRiemannianMetric.symm, Real.rpow_zero, MeasureTheory.hausdorffMeasure_pi_real, Real.arccos_le_pi_div_two, MeasureTheory.charFunDual_eq_prod_iff, ValueDistribution.characteristic_sub_characteristic_inv_of_ne_zero, SchwartzMap.pairing_apply, Complex.abs_im_le_norm, Real.nnnorm_nnratCast, Real.exp_one_mul_le_exp, Real.continuous_cosh, Real.fourier_comp_linearIsometry, MeasureTheory.Measure.integral_comp_smul, variationOnFromTo.eq_zero_iff_of_le, ContinuousMultilinearMap.isLeast_opNorm, unitInterval.volume_uIoo, NNReal.rpow_add_natCast', Affine.Simplex.touchpointWeights_empty_pos, zero_mem_cantorSet, UnitAddTorus.mFourier_add, continuous_polarCoord_symm, MeasureTheory.integral_comap_eq_addEquivAddHaarChar_smul, setIntegral_withDensity_eq_setIntegral_smul₀', Set.Finite.infsep_pos_iff_nontrivial, WithLp.prod_edist_eq_of_L2, Real.hasDerivAt_qaryEntropy, TorusIntegrable.torusIntegrable_zero_radius, AkraBazziRecurrence.T_nonneg, Metric.iUnion_ball_nat, IsCoveringMap.liftPath_const, GroupNorm.coe_sup, Complex.cpow_ofReal_re, IsUltrametricDist.exists_norm_finset_prod_le_of_nonempty, Real.artanh_surjOn, Metric.uniformity_basis_dist, WithSeminorms.isVonNBounded_iff_seminorm_bddAbove, spectralAlgNorm_mul, NNReal.one_le_coe, intervalIntegral.FTCFilter.nhdsUIcc, spectralNorm_eq_invariantExtension, UpperHalfPlane.cosh_dist, WithCStarModule.norm_apply_le_norm, ContDiffBumpBase.mem_Icc, ProbabilityTheory.analyticOnNhd_cgf, Padic.norm_p_pow, MultilinearMap.exists_bound_of_continuous, real_inner_div_norm_mul_norm_eq_one_iff, SmoothBumpFunction.tsupport_subset_symm_image_closedBall, UpperHalfPlane.image_coe_closedBall, Real.goldenRatio_pow_sub_goldenRatio_pow, MeasureTheory.lintegral_nnnorm_condExpL2_le, EisensteinSeries.G2_S_transform, Asymptotics.isBigO_nat_atTop_iff, SmoothPartitionOfUnity.le_one, Padic.norm_p_lt_one, ContDiffPointwiseHolderAt.snd, PadicInt.norm_ascPochhammer_le, Behrend.lower_bound_le_one, EuclideanGeometry.oangle_eq_zero_iff_wbtw, RCLike.conj_eq_iff_re, WeakFEPair.hk, Tactic.ComputeAsymptotics.Seq.dist_eq_one_of_head, Real.HolderTriple.pos, MeasureTheory.measureReal_union_le, Complex.re_sq_le_normSq, CircleDeg1Lift.le_floor_map_map_zero, HurwitzZeta.oddKernel_def, Hyperreal.st_mul, irrational_ratCast_mul_iff, StrongFEPair.hf_zero', SimplexCategory.toTop₀_map, NonarchAddGroupSeminorm.coe_smul, Polynomial.contentIdeal_eq_top_iff_forall_gaussNorm_eq_one, ProbabilityTheory.IsCondKernelCDF.setIntegral, MeasureTheory.integrable_withDensity_iff_integrable_smul₀', IntervalIntegrable.aestronglyMeasurable', Real.borel_eq_generateFrom_Ioi_rat, norm_mul₃_le, one_mem_posTangentConeAt_iff_mem_closure, Asymptotics.isBigO_one_iff, BumpCovering.le_one, Complex.div_im, Complex.im_nnratCast, unitSphereToUnits_injective, SchwartzMap.norm_fourierTransformCLM_toL2_eq, Real.integrable_sinc, Continuous.dist, Real.sigmoid_mul_rexp_neg, MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_tendsto, Real.coe_tanPartialHomeomorph, EuclideanSpace.volume_closedBall_fin_two, ModularGroup.SL_to_GL_tower, NormedCommGroup.uniformity_basis_dist, ContDiffMapSupportedIn.uniformSpace_eq_iInf, Real.sq_cos_pi_div_six, NormedSpace.norm_expSeries_summable_of_mem_ball', MeasureTheory.Measure.haar.chaar_mono, ContinuousMap.HomotopyRel.compContinuousMap_apply, Function.locallyFinsuppWithin.logCounting_eventuallyLE, spectrum.gelfand_formula, tendsto_pow_atTop_nhds_zero_iff_norm_lt_one, MeasureTheory.enorm_indicatorConstLp_le, PseudoMetricSpace.dist_triangle, Real.sign_zero, NNReal.coe_zero, Cardinal.cantorFunctionAux_succ, ProbabilityTheory.stronglyMeasurable_poissonPMFReal, ModularFormClass.one_mem_strictPeriods_SL2Z, Continuous.norm', Int.ball_eq_Ioo, Complex.norm_nnratCast, MeasureTheory.stoppedValue_lowerCrossingTime, NumberField.mixedEmbedding.polarCoordReal_source, NormedSpace.inclusionInDoubleDual_norm_le, Real.Angle.two_zsmul_toReal_eq_two_mul_sub_two_pi, not_IntegrableOn_Ici_inv, AkraBazziRecurrence.tendsto_atTop_r_real, LinearIsometryEquiv.coe_toMeasurableEquiv, stereographic'_target, RCLike.rank_le_two, Real.abs_cos_int_mul_pi, curveIntegral_segment_const, ProbabilityTheory.measurable_gaussianPDF, Real.real_sqrt_lt_nat_sqrt_succ, Irrational.instOrderTopologySubtypeReal, Real.ofCauchy_sub, Complex.tan_ofReal_im, PiNat.dist_triangle, NumberField.mixedEmbedding.fundamentalCone.mem_normLeOne, Complex.norm_add_eq_iff, Metric.hausdorffDist_empty, MeasureTheory.L1.integral_eq_setToL1, Real.self_lt_sinh_iff, ArchimedeanClass.stdPart_eq_sInf, Real.mk_lt, NumberField.InfinitePlace.map_ratCast, Affine.Simplex.signedInfDist_apply_self, BoxIntegral.BoxAdditiveMap.volume_apply, Quaternion.continuous_imJ, CircleDeg1Lift.mul_apply, Real.abs_iteratedDeriv_cos_le_one, norm_le_insert', Real.HolderTriple.nonneg', Real.differentiableAt_rpow_of_ne, exists_contMDiffMap_zero_one_nhds_of_isClosed, Circle.exp_sub, CFC.sqrt_eq_one_iff, ProbabilityTheory.HasCondSubgaussianMGF.ae_condExp_le, SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux, Behrend.norm_of_mem_sphere, Real.one_div_one_sub_hasFPowerSeriesOnBall_zero, Metric.uniformity_basis_dist_rat, MeasureTheory.measureReal_union₀', RCLike.reCLM_coe, MulAlgebraNorm.toFun_eq_coe, Irrational.intCast_div, ContDiffBump.normed_convolution_eq_right, continuousSMul_closedBall_ball, UpperHalfPlane.dist_coe_center, ProbabilityTheory.gaussianReal_map_linearMap, Int.dist_eq', PiTensorProduct.bddBelow_projectiveSemiNormAux, Metric.uniformContinuous_infDist_Hausdorff_dist, AddCircle.ergodic_add_right, realPart_add_I_smul_imaginaryPart, Real.strictMono_eulerMascheroniSeq, projIcc_eq_one, RCLike.ofNat_mul_re, Real.differentiableAt_log, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, CStarAlgebra.norm_posPart_le, ContDiffMapSupportedIn.continuous_iff_comp_withOrder, norm_sub_eq_sqrt_iff_real_inner_eq_zero, ball_one_eq, Subgroup.two_mul_withInfty_mem_strictPeriods, EuclideanGeometry.Sphere.dist_div_sin_oangle_eq_two_mul_radius, PiLp.dist_eq_of_L1, Real.exists_seq_rat_strictAnti_tendsto, Real.tendsto_sin_neg_pi_div_two, bernoulliFun_endpoints_eq_of_ne_one, ConvexBody.convex, Path.mul_apply, intervalIntegral.intervalIntegrable_cos, NNReal.range_coe, Polynomial.gaussNorm_intAdicAbv_le_one, tendsto_measure_Icc, exists_mem_interior_convexHull_affineBasis, Real.sqrtTwoAddSeries_two, Real.Angle.cos_sub_pi, Stirling.le_factorial_stirling, Polynomial.Chebyshev.strictAntiOn_node, EuclideanGeometry.angle_self_right, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, MeasureTheory.Measure.integral_toReal_rnDeriv, dist_right_midpoint, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, Complex.equivRealProd_apply_le', AkraBazziRecurrence.eventually_asympBound_pos, Real.coe_fib_eq, EisensteinSeries.div_linear_zpow_differentiableOn, Seminorm.comp_smul, UnitAddTorus.mFourier_zero, memℓp_infty_iff, ContinuousMap.HomotopyLike.toContinuousMapClass, norm_le_norm_add_norm_div', Int.norm_natCast, Real.tendsto_exp_nhds_zero_nhds_one, BoxIntegral.Box.coe_ae_eq_Icc, Subgroup.widthInfty_nonneg, intervalIntegral.smul_integral_comp_mul_sub, Urysohns.CU.lim_le_one, Real.fourierInv_comp_linearIsometry, isScalarTower_sphere_sphere_sphere, Polynomial.gaussNorm_lt_one_iff_contentIdeal_le, MeasureTheory.hasFDerivAt_convolution_right_with_param, Complex.sq_norm_sub_sq_im, NumberField.InfinitePlace.ext_iff, CStarAlgebra.span_nonneg_inter_unitClosedBall, ProbabilityTheory.IsGaussian.charFun_eq', Real.deriv_inv_log, Real.Gamma_strictMonoOn_Ici, ProbabilityTheory.covarianceBilinDual_eq_covariance, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, Real.iteratedDeriv_add_one_cosh, InnerProductSpace.Core.inner_im_symm, OrthonormalBasis.sum_sq_norm_inner_right, Real.sin_zero, signedDist_zero, EReal.coe_sub, MeasureTheory.condExpL1CLM_indicatorConstLp, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_mul, EMetric.exists_forall_closedBall_subset_aux₂, Real.sinh_lt_self_iff, Orientation.oangle_eq_zero_iff_angle_eq_zero, Real.volume_Iio, LSeriesSummable.le_const_mul_rpow, LinearIsometryEquiv.reflections_generate, Real.exp_one_gt_d9, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, EulerSine.sin_pi_mul_eq, ContinuousLinearMap.ratio_le_opNorm, Complex.arg_neg_eq_arg_add_pi_iff, CircleDeg1Lift.transnumAuxSeq_dist_lt, spectralMulAlgNorm_def, integral_exp_Iic, UnitAddCircle.measure_univ, RCLike.isUniformEmbedding_ofReal, dist_center_homothety, CompactlySupportedContinuousMap.toRealLinearMap_apply, Seminorm.smul', AddGroupSeminorm.toFun_eq_coe, Real.zero_eq_arcsin_iff, jacobiTheta_S_smul, aestronglyMeasurable_derivWithin_Ioi, MeasureTheory.integrable_comp, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, norm_sub_norm_le', not_irrational_zero, PartitionOfUnity.sum_eq_one, Complex.normSq_eq_norm_sq, ArchimedeanClass.stdPart_add, exists_bounded_zero_one_of_closed, MeasureTheory.Integrable.integral_norm_prod_left, Real.exp_eq_one_iff, HasCompactSupport.hasFDerivAt_convolution_right, frontier_range_modelWithCornersEuclideanHalfSpace, BoundedContinuousFunction.norm_eq, irrational_mul_ratCast_iff, ProbabilityTheory.exponentialPDF_eq, SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv, ContDiffMapSupportedIn.structureMapCLM_zero_apply, NNReal.map_coe_nhdsGT, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn, Real.posLog_sub_posLog_inv, Real.sigmoid_pos, Metric.uniformity_basis_dist_inv_nat_succ, ValueDistribution.characteristic_sub_characteristic_inv_at_zero, SchwartzMap.integral_bilinear_deriv_right_eq_neg_left, Real.iteratedDeriv_add_one_sinh, Real.circleAverage_zero, Quaternion.coeComplex_zero, AddCircle.instIsUnifLocDoublingMeasureRealVolume, SchwartzMap.norm_iteratedFDeriv_le_seminorm, ProbabilityTheory.covarianceBilinDual_zero, Complex.inv_cpow_eq_ite', ContDiffBump.rIn_lt_rOut, AlgHom.norm_apply_le_self, Irrational.eventually_forall_le_dist_cast_div_of_denom_le, Submodule.norm_orthogonalProjection_apply_le, ContinuousLinearMap.bounds_bddBelow, ProbabilityTheory.IsRatCondKernelCDFAux.mono, Affine.Simplex.ExcenterExists.sOppSide_excenter_point_iff, contDiff_bernoulliFun, Affine.Simplex.incenter_notMem_affineSpan_face, RealRMK.integral_rieszMeasure, Complex.antilipschitz_equivRealProd, Hyperreal.coe_nonneg, dense_irrational, CFC.continuous_abs, ModularForm.levelOne_weight_zero_rank_one, ofDigits_bool_to_fin_three_mem_cantorSet, bernstein.variance, Real.continuous_probChar, ModularGroup.re_T_smul, ENNReal.prod_coe_rpow, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, EuclideanSpace.instIsManifoldSphere, Complex.abs_im_eq_norm, Affine.Triangle.affineSpan_pair_eq_orthRadius, Metric.isUniformInducing_iff, CongruenceSubgroup.strictWidthInfty_Gamma0, MeasureTheory.SimpleFunc.integral_eq_sum, Complex.ratCast_re, BoxIntegral.Box.Ioo_ae_eq_Icc, RCLike.I_eq_zero_or_im_I_eq_one, lp.norm_nonneg', Asymptotics.IsBigOWith.norm_left, SmoothBumpCovering.locallyFinite', Real.arcsin_neg_one, LiouvilleWith.add_int, bernstein_apply, Complex.isometry_ofReal, Real.logb_nat_eq_sum_factorization, norm_fderiv_le_of_lipschitz, Complex.norm_cpow_real, Real.isEquivalent_sin, Real.tendsto_sigmoid_atBot, Metric.dist_le_infDist_add_diam, Quaternion.instCompleteSpaceReal, UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_left, Prod.dist_eq, NNReal.image_coe_Iio, CFC.posPart_smul, Complex.isTheta_ofReal, enorm'_le_iff_norm_le, ENNReal.toReal_inv, MeasureTheory.L1.SimpleFunc.coe_negPart, RCLike.normSq_nonneg, contraction_of_isPowMul, NumberField.mixedEmbedding.convexBodySumFun_smul, HolderWith.ediam_image_le, Complex.interior_preimage_im, NNReal.isBoundedUnder_ge_toReal, Orthonormal.inner_products_summable, Real.tendsto_harmonic_sub_log, Asymptotics.IsBigOWith.norm_norm, NumberField.InfinitePlace.instMonoidWithZeroHomClassReal, Height.logHeight_one, continuousOn_cfc_nnreal, ProbabilityTheory.integrableExpSet_id_gaussianReal, IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul', Height.logHeight_zero, Height.mulHeight₁_add_le, Real.sin_nat_mul_two_pi_sub, ENNReal.mul_rpow_eq_ite, Real.differentiable_exp, intervalIntegral.integral_cases, NumberField.mixedEmbedding.logMap_real_smul, Complex.isBigO_re_sub_re, measurable_real_toNNReal, MeasureTheory.condExpInd_disjoint_union, ValueDistribution.proximity_sum_top_le, Orientation.oangle_rotation_oangle_right, CongruenceSubgroup.IsArithmetic.conj, Metric.infDist_zero_of_mem, lipschitzWith_one_norm', irrational_mul_intCast_iff, ProbabilityTheory.condIndepSet_iff, Metric.boundedSpace_iff, ENNReal.rpow_two, ProbabilityTheory.differentiableOn_mgf, Complex.comap_exp_nhdsNE, norm_eq_zero', contDiffOn_abs, AkraBazziRecurrence.eventually_one_sub_smoothingFn_pos, Metric.tendsto_dist_left_atTop_iff, ArchimedeanClass.stdPart_map_real, ContinuousMultilinearMap.opNorm_nonneg, Nat.realSqrt_mem_Ico, HurwitzZeta.hurwitzEvenFEPair_zero_symm, Int.isClosedEmbedding_coe_real, RCLike.le_iff_re_im, CliffordAlgebraComplex.ofComplex_I, LinearMap.extendTo𝕜_apply, Real.coe_nnabs, Complex.log_exp_eq_sub_toIocDiv, UnitAddTorus.coeFn_mFourierLp, Dilation.mapsTo_closedBall, MeasureTheory.Integrable.integral_norm_condExpKernel, norm_sum_neg_one_pow_le, Matrix.l2_opNorm_conjTranspose_mul_self, EReal.coe_zsmul, InnerProductGeometry.angle_self, Asymptotics.IsBigOWith.pow', ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, CircleDeg1Lift.transnumAuxSeq_zero, Real.isAlgebraic_tan_rat_mul_pi, UpperHalfPlane.denom_cocycle, Real.differentiableAt_cos, MeasureTheory.Measure.instIsFiniteMeasureElemSphereOfNatRealToSphere, Real.isBigO_log_const_mul_log_atTop, Complex.norm_exp_sub_sum_le_norm_mul_exp, isClosed_preCantorSet, CompactlySupportedContinuousMap.nnrealPart_neg_toReal_eq, ContinuousWithinAt.norm, EuclideanGeometry.image_inversion_perpBisector, ProbabilityTheory.Kernel.HasSubgaussianMGF.neg, CircleDeg1Lift.iterate_mono, MeasureTheory.SimpleFunc.norm_approxOn_y₀_le, Polynomial.le_supNorm, innerₗ_apply, GenLoop.ext_iff, SmoothBumpFunction.contMDiffAt, CircleDeg1Lift.tendsto_translation_number', MeasureTheory.setIntegral_condExpIndSMul, StieltjesFunction.length_subadditive_Icc_Ioo, Orientation.rightAngleRotation_symm, MeasureTheory.weightedSMul_empty, norm_snd_le, totallyBounded_absConvexHull, Set.infsep_eq_iInf, lipschitz_with_lipschitz_const_mul, Besicovitch.SatelliteConfig.rpos, MeasureTheory.measureReal_biUnion_finset, NumberField.mixedEmbedding.polarCoord_symm_apply, MeasureTheory.integrable_withDensity_iff_integrable_smul₀, inv_norm_smul_mem_unitClosedBall, NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_coe, Affine.Simplex.mongePlane_def, Affine.Triangle.acuteAngled_iff_angle_lt, ContinuousMap.dist_lt_iff_of_nonempty, SmoothBumpFunction.hasCompactSupport, ProbabilityTheory.complexMGF_id_mul_I, AddGroupSeminorm.coe_lt_coe, Polynomial.intervalIntegrable_mahlerMeasure, ProbabilityTheory.Kernel.measurable_densityProcess, WithLp.prod_norm_eq_idemFst_sup_idemSnd, exists_continuous_one_zero_of_isCompact, ModularGroup.lcRow0Extend_apply, irrational_natCast_mul_iff, lipschitzOnWith_iff_norm_div_le, MeasureTheory.ProbabilityMeasure.continuous_iff_forall_continuousMap_continuous_integral, Real.deriv_log', Circle.exp_neg, ProbabilityTheory.IsCondKernelCDF.setLIntegral, cfc_nnreal_eq_real, Seminorm.coe_sup, ENNReal.rpow_mul_natCast, unitInterval.measurable_symm, Real.sin_pi_div_two_sub, BumpCovering.toPartitionOfUnity_eq_mul_prod, BoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homothetic, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, Real.exp_one_rpow, Filter.Tendsto.norm, ProbabilityTheory.instIsProbabilityMeasureGaussianReal, intervalIntegrable_sub_inv_iff, Real.one_div_sub_hasFPowerSeriesOnBall_zero, FormalMultilinearSeries.compAlongComposition_bound, ProbabilityTheory.integrable_condVar, AlternatingMap.exists_bound_of_continuous, Complex.liftAux_neg_I, Metric.PiNatEmbed.separation, Real.log_zpow, UpperHalfPlane.lt_dist_iff_lt_dist_coe_center, Real.isLittleO_pow_exp_atTop, unitInterval.continuous_sigmoid, Metric.infDist_empty, norm_sub_eq_zero_iff, HasCompactSupport.exists_bound_of_continuous, measurableSet_pi_polarCoord_target, cfcₙ_real_eq_complex, WithLp.dist_snd_le, MeasureTheory.lpMeasToLpTrimLie_symm_indicator, intervalIntegral.integral_comp_add_mul, NumberField.InfinitePlace.isInfinitePlace, ContinuousMap.HomotopyWith.coeFn_injective, Real.two_mul_le_exp, ProbabilityTheory.integrableExpSet_fun_id_gaussianReal, Complex.ofReal_intCast, Complex.ofReal_add, Real.exp_one_near_20, ConvexBody.ext_iff, HasBesicovitchCovering.no_satelliteConfig, NumberField.Units.dirichletUnitTheorem.map_logEmbedding_sup_torsion, MeasureTheory.setIntegral_rnDeriv_smul, instIsTopologicalRingReal, PseudoMetricSpace.dist_ofPreNNDist_le, isMIntegralCurveAt_iff, norm_le_pi_norm, irrational_div_natCast_iff, Metric.cthickening_zero, Complex.UnitDisc.coe_closedBall_smul, Height.zero_le_logHeight₁, Path.truncate_zero_zero, Bundle.ContMDiffRiemannianMetric.pos, Real.arccos_eq_pi_div_two, Metric.unitClosedBall.coe_mul, HasDerivWithinAt.complexToReal_fderiv, signedDist_triangle_left, Real.Gamma_eq_zero_iff, Real.tendsto_comp_exp_atTop, ProbabilityTheory.measurable_paretoPDFReal, ProbabilityTheory.centralMoment_zero, Real.arcsin_mem_Icc, AlgebraNorm.smul', Real.log_two_gt_d9, InnerProductGeometry.sin_eq_zero_iff_angle_eq_zero_or_angle_eq_pi, TemperedDistribution.fourier_toTemperedDistributionCLM_eq, MeasureTheory.Measure.haar.addCHaar_sup_le, IsContMDiffRiemannianBundle.exists_contMDiff, Affine.Simplex.excenterExists_map, IsUltrametricDist.exists_norm_multiset_sum_le, Complex.add_re, integral_sin_pow_mul_cos_pow_odd, MeasureTheory.Lp.norm_const_le, Seminorm.coe_add, AnalyticAt.exists_ball_analyticOnNhd, MeasureTheory.SignedMeasure.singularPart_add, Real.toNNReal_le_natCast, Real.arccos_neg, integral_conj, Complex.hasSum_ofReal, Real.ofDigits_eq_sum_add_ofDigits, IsClosed.exists_wbtw_isVisible, dist_triangle_right, Affine.Simplex.exradius_nonneg, Height.fun_logHeight_zero, Real.natCeil_logb_natCast, isBounded_iff_asymptoticCone_subset_singleton, Path.Homotopy.transAssocReparamAux_one, ProbabilityTheory.instIsGaussianMapHSub, NumberField.FinitePlace.norm_lt_one_iff_mem, MeasureTheory.measureReal_add_apply, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_intAdicAbv, Real.isAlgebraic_cos_rat_mul_pi, MeasureTheory.tendsto_indicator_ge, Complex.ofRealCLM_nnnorm, Complex.imCLM_norm, Real.deriv2_binEntropy, Real.cos_pi_div_two, SeminormedSpace.Core.norm_triangle, MeasureTheory.SimpleFunc.ennrealRatEmbed_encode, isClosed_stdSimplex, Complex.dist_le_dist_of_mapsTo_ball, EuclideanGeometry.Sphere.IsDiameter.left_ne_right_iff_radius_pos, MeasureTheory.MemLp.eLpNormEssSup_indicator_norm_ge_eq_zero, Real.convergent_succ, Quaternion.norm_coe, CFC.nnrpow_def, SmoothBumpCovering.sum_toSmoothPartitionOfUnity_eq, NormMulClass.isAbsoluteValue_norm, UnitAddTorus.mFourier_neg, interior_halfSpace, LiouvilleWith.mul_rat, gronwallBound_K0, gauge_closure_zero, NumberField.mixedEmbedding.unit_smul_eq_iff_mul_eq, SimplexCategory.toTop₀_obj, PiLp.dist_eq_iSup, Metric.tendsto_dist_left_cobounded_atTop, NumberField.InfinitePlace.Completion.bijective_extensionEmbedding_of_isReal, ProbabilityTheory.integral_gaussianPDFReal_eq_one, Height.one_le_mulHeight₁, ProbabilityTheory.HasSubgaussianMGF.fun_zero, CircleDeg1Lift.map_nat_add, Matrix.PosSemidef.eigenvalues_nonneg, RCLike.exists_norm_eq_mul_self, EReal.preimage_coe_Icc, Affine.Simplex.vectorSpan_isOrtho_altitude_direction, exists_continuous_nonneg_pos, Hyperreal.coe_pos, Real.posLog_neg, Matrix.frobenius_norm_def, integral_exp_mul_I_eq_sinc, ContinuousMap.sup_mem_closed_subalgebra, MulAlgebraNorm.ext_iff, contMDiff_subtype_coe_Icc, Real.hasDerivAt_arcsin, RCLike.real_smul_eq_coe_smul, Real.circleAverage_neg_radius, MeasureTheory.Lp.coeFn_negPart_eq_max, Orientation.inner_rotation_pi_div_two_right, integral_comp_polarCoord_symm, Affine.Simplex.exsphere_reindex, gold_sub_goldConj, EuclideanGeometry.sin_eq_zero_iff_angle_eq_zero_or_angle_eq_pi, ContinuousAffineMap.norm_contLinear_le, Polynomial.Chebyshev.node_eq_neg_one, Complex.normSq_sub, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, Function.Periodic.im_invQParam, HurwitzZeta.cosZeta_eq, RCLike.measurable_re, Metric.nonempty_ball, ENNReal.ofReal_le_ofNat, Real.volume_Ico, Matrix.SpecialLinearGroup.isClosedEmbedding_mapGLInt, GaussianInt.toComplex_im_div, ProperCone.innerDual_singleton, LiouvilleWith.mul_int, Real.eulerMascheroniSeq_zero, CircleDeg1Lift.commute_add_int, real_inner_eq_re_inner, AbsolutelyContinuousOnInterval.neg, CurveIntegrable.intervalIntegrable_curveIntegralFun_trans_left, RCLike.add_conj, Path.Homotopy.transReflReparamAux_one, spectralNorm.spectralNorm_pow_natDegree_eq_prod_roots, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_eq, RCLike.ofReal_re_ax, differentiable_inner, InnerProductSpace.Core.inner_self_eq_norm_mul_norm, MeasureTheory.Measure.haar.prehaar_nonneg, ProbabilityTheory.Kernel.rnDeriv_toReal_pos, CFC.abs_natCast, VitaliFamily.ae_tendsto_average_norm_sub, interior_subset_gauge_lt_one, Urysohns.CU.bddAbove_range_approx, Subgroup.IsArithmetic.isFiniteRelIndexSL, MeasureTheory.Measure.haar.addPrehaar_sup_eq, UpperHalfPlane.norm_exp_two_pi_I_lt_one, NumberField.InfinitePlace.smul_coe_apply, ENNReal.toReal_natCast, spectralNorm_mul, CStarAlgebra.isStrictlyPositive_iff_isStrictlyPositive_sqrt_and_eq_sqrt_mul_sqrt, RCLike.im_eq_conj_sub, OrthonormalBasis.volume_parallelepiped, Real.hasDerivAt_tan, Real.logb_pow, Real.Angle.toReal_mem_Ioo_iff_sign_pos, MeasureTheory.eLpNorm_smul_measure_of_ne_top, Matrix.IsHermitian.posSemidef_iff_eigenvalues_nonneg, intervalIntegral.FTCFilter.nhdsIcc, Complex.inv_re, integral_id, Affine.Simplex.altitudeFoot_mem_affineSpan, Behrend.bound, Complex.arg_exp_mul_I, Behrend.four_zero_nine_six_lt_exp_sixteen, Icc_chartedSpaceChartAt, LiouvilleWith.add_int_iff, Real.arctan_neg, NonarchAddGroupSeminorm.lt_def, Orientation.oangle_rotation, Real.deriv_tan_sub_id, ExistsContDiffBumpBase.u_int_pos, Real.instIsOrderBornology, RCLike.conj_im_ax, PadicInt.continuousAddCharEquiv_of_norm_mul_apply, AddCircle.volume_closedBall, Real.contDiffAt_log, mul_gauge_le_norm, norm_add_le, ArchimedeanClass.stdPart_ofNat, Real.leftDeriv_mul_log, Complex.preimage_equivRealProd_prod, SchwartzMap.integral_mul_laplacian_right_eq_left, Finset.norm_prod_one_add_sub_one_le, circleIntegrable_log_norm_factorizedRational, Real.tan_sub_pi, ENNReal.rpow_natCast_mul, UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_ne_zero, Complex.isCauSeq_norm_exp, Real.Angle.toReal_nonneg_iff_sign_nonneg, PiTensorProduct.norm_eval_le_injectiveSeminorm, MeasureTheory.charFun_pi, MeasureTheory.weightedSMul_null, stereoToFun_apply, SchwartzMap.convolution_apply, NumberField.mixedEmbedding.realSpace.volume_eq_zero, Bornology.IsBounded.exists_pos_norm_lt', ArchimedeanClass.mk_sub_stdPart_pos, MeasureTheory.lpNorm_fun_mul_natCast, unitInterval.one_minus_le_one, Real.differentiableAt_Gamma, Real.exists_nat_abs_mul_sub_round_le, UpperHalfPlane.modular_S_smul, ProbabilityTheory.preCDF_le_one, Module.Basis.addHaar_reindex, orthogonalBilin_innerₗ, comap_norm_nhdsGT_zero', Real.Angle.toReal_pi_div_two, ContinuousLinearMap.norm_smulRight_apply, ContinuousMap.Homotopy.extend_apply_coe, Real.hasStrictDerivAt_cosh, LiouvilleWith.int_add_iff, AlgebraNorm.toFun_eq_coe, Set.Icc.coe_convexCombo, Metric.thickening_eq_empty_iff, Real.pi_pos, norm_deriv_le_of_lipschitzOn, similar_iff_exists_pairwise_dist_eq, dist_birkhoffAverage_birkhoffAverage, NumberField.mixedEmbedding.mem_span_latticeBasis, irrational_sqrt_intCast_iff_of_nonneg, Polynomial.mahlerMeasure_C_mul_X_add_C, PadicInt.coe_one, Complex.tendsto_norm_tan_atTop, AddGroupSeminorm.add_bddBelow_range_add, AkraBazziRecurrence.asympBound_def, ProbabilityTheory.evariance_eq_lintegral_ofReal, TemperedDistribution.fourierTransformInv_toTemperedDistributionCLM_eq, CFC.rpow_rpow, TopologicalSpace.Opens.CompleteCopy.dist_val_le_dist, Real.sinhEquiv_symm_apply, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', ContinuousMap.Homotopy.evalAt_apply, Real.log_one, CircleDeg1Lift.continuous_iff_surjective, Function.hasTemperateGrowth_norm_sq, BoundedContinuousFunction.innerProbChar_apply, ProbabilityTheory.analyticOn_cgf, IsometryEquiv.map_midpoint, Complex.ofReal_prod, norm_multiset_prod_le, BoundedContinuousFunction.exists_norm_eq_restrict_eq_of_closed, Complex.IsExpCmpFilter.tendsto_re, ProbabilityTheory.Kernel.HasSubgaussianMGF.add, Real.strictConvexOn_mul_log, UniformSpace.Completion.norm_toComplL, Real.zero_at_infty_fourierIntegral, interval_average_symm, diam_stdSimplex_of_subsingleton, IsUltrametricDist.norm_mul_eq_max_of_norm_ne_norm, ProbabilityTheory.covarianceBilin_comm, ProbabilityTheory.Kernel.tendsto_integral_density_of_monotone, EReal.sign_coe, instSMulCommClass_sphere_closedBall_closedBall, Orientation.inner_rotation_pi_div_two_left, ProbabilityTheory.centralMoment_zero_measure, ProbabilityTheory.Kernel.measurable_densityProcess_left, AmpleSet.preimage, ProbabilityTheory.Kernel.memL1_limitProcess_densityProcess, UniformConcaveOn.sub, gauge_empty, Affine.Simplex.sign_excenterWeights_singleton_neg, ProbabilityTheory.cdf_le_one, Probability.cauchyPDF_pos, Real.ofDigits_SurjOn, Subgroup.strictPeriods_eq_zmultiples_one_of_T_mem, Hyperreal.IsSt.add, MeasureTheory.integral_indicator_one, BoundedContinuousFunction.neg_norm_le_apply, SchwartzMap.integral_bilin_fourier_eq, ValueDistribution.proximity_mul_zero_le, Real.isTopologicalBasis_Ioo_rat, Complex.det_conjAe, Metric.ball_zero, gradient_eq_deriv', Orientation.oangle_rotation_self_left, Complex.sub_conj, Real.strictAnti_eulerMascheroniSeq', RCLike.ofReal_add, ZetaAsymptotics.continuousOn_term, ProbabilityTheory.covariance_neg_right, ContinuousLinearEquiv.contDiffPointwiseHolderAt, QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared, ModularGroup.re_T_inv_smul, Metric.nonneg_of_mem_sphere, Affine.Simplex.excenterWeights_empty_lt_inv_two, Real.map_sqrt_atTop, Chebyshev.integrableOn_theta_div_id_mul_log_sq, IsApproximateSubgroup.pow_inter_pow, MeasureTheory.lpNorm_sub_le, summable_iff_vanishing_norm, Real.logb_self_eq_one_iff, Orientation.kahler_neg_orientation, FormalMultilinearSeries.radius_inv_eq_limsup, Real.hasStrictDerivAt_log, IsSelfAdjoint.cfc_arg, MeasureTheory.L2.integral_inner_eq_sq_eLpNorm, Real.iteratedDeriv_add_one_cos, SmoothBumpFunction.tsupport_subset_chartAt_source, Real.sinhEquiv_apply, Complex.conj_im, convex_eball, real_inner_self_nonneg, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, NumberField.mixedEmbedding.fundamentalCone.existsUnique_preimage_of_mem_integerSet, Real.sin_eq_tsum, ContinuousMap.Homotopy.symm_apply, Real.sin_arctan_pos, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, unitInterval.volume_Icc, tendsto_rpow_div_mul_add, Real.exp_abs_le, Real.arccos_le_pi_div_four, ArithmeticFunction.convolution_vonMangoldt_const_one, Seminorm.bddAbove_iff, indiscreteTopology_iff_forall_norm_eq_zero', AffineIsometryEquiv.dist_pointReflection_self, NonarchAddGroupSeminormClass.toAddGroupSeminormClass, BoxIntegral.Box.dist_le_distortion_mul, Real.cos_int_mul_pi_sub, ContinuousMultilinearMap.norm_map_init_le, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, schnirelmannDensity_setOf_even, IsApproximateSubgroup.card_mul_self_le, ArithmeticFunction.vonMangoldt.not_summable_residueClass_prime_div, spectrum.pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius, ProbabilityTheory.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero, AffineIsometryEquiv.dist_pointReflection_self_real, Padic.norm_eq_zpow_neg_valuation, SmoothBumpFunction.ball_subset, Cardinal.mk_real, ProbabilityTheory.variance_zero_measure, SchwartzMap.fourierInv_apply_eq, SchwartzMap.smulRightCLM_apply_apply, Real.differentiableOn_Gamma_Ioi, ProbabilityTheory.measurable_gammaPDFReal, NormedSpace.norm_expSeries_summable_of_mem_ball, Real.differentiableOn_mul_log, UpperHalfPlane.dist_lt_iff_dist_coe_center_lt, Real.arsinh_pos_iff, SlashInvariantForm.exists_one_half_le_im_and_norm_le, unitInterval.range_sigmoid, Complex.arg_lt_pi_div_two_iff, InformationTheory.klDiv_def, HasDerivAt.complexToReal_fderiv', PartitionOfUnity.exists_isSubordinate_of_locallyFinite_t2space, Filter.hasBasis_cobounded_norm, MeasureTheory.L2.inner_indicatorConstLp_one, Nat.dist_eq, MeasureTheory.Integrable.norm_integral_condKernel, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin, RCLike.ofReal_neg, BoxIntegral.Box.mem_splitCenterBox, IsStrictlyPositive.rpow, MeasureTheory.L2.inner_indicatorConstLp_indicatorConstLp, ProbabilityTheory.Kernel.tendsto_densityProcess_atTop_empty_of_antitone, CongruenceSubgroup.isArithmetic_conj_SL2Z, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf', Real.sin_sq_eq_half_sub, Complex.arg_mem_Ioc, NNReal.inv_rpow, Path.source', PiNat.lipschitz_with_one_iff_forall_dist_image_le_of_mem_cylinder, EuclideanGeometry.image_inversion_sphere_dist_center, Real.sin_add, InnerProductSpace.volume_ball, RCLike.ofReal_zpow, Real.Angle.sin_two_nsmul, NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, MeasureTheory.JordanDecomposition.exists_compl_positive_negative, ProbabilityTheory.IsRatCondKernelCDF.tendsto_atTop_one, ProbabilityTheory.memLp_id_gaussianReal', RCLike.im_mul_ofReal, Real.cosh_sq, lipschitzWith_circleMap, SchwartzMap.toTemperedDistributionCLM_apply_apply, EisensteinSeries.q_expansion_riemannZeta, Seminorm.continuousAt_zero', HasDerivAt.complexToReal_fderiv, Real.continuousOn_cos, LiouvilleWith.sub_int_iff, ExistsContDiffBumpBase.u_exists, Real.sigmoid_injective, BoundedContinuousFunction.dist_lt_iff_of_nonempty_compact, Affine.Simplex.sum_excenterWeightsUnnorm_singleton_pos, CompactlySupportedContinuousMap.toReal_apply, NumberField.house_sum_le_sum_house, PositiveLinearMap.exists_norm_apply_le, MeasureTheory.measureReal_inter_add_diff₀, Real.fourierIntegral_real_eq_integral_exp_smul, Complex.map_exp_comap_re_atBot, Complex.intCast_re, Real.deriv_mulExpNegMulSq, EuclideanHalfSpace.convex, Real.sin_neg, norm_le_norm_of_abs_le_abs, fourier_coe_apply, NormedStarGroup.norm_star_le, Real.cos_pi_div_eight, Complex.liftAux_I, Complex.interior_setOf_le_im, unitInterval.coe_unitIntervalSubmonoid, dist_right_pointReflection, Polynomial.supNorm_nonneg, integral_exp_mul_I_eq_sin, InnerProductGeometry.inner_eq_neg_mul_norm_of_angle_eq_pi, EisensteinSeries.norm_eq_max_natAbs, Real.tan_sq_div_one_add_tan_sq, RCLike.geometric_hahn_banach_point_point, ProbabilityTheory.covariance_fun_neg_left, norm_cfcₙ_lt_iff, Nat.Primes.not_summable_one_div, CircleDeg1Lift.iterate_monotone, WithLp.prod_dist_eq_sup, Orientation.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero, Metric.uniformContinuousOn_iff, GromovHausdorff.ghDist_le_hausdorffDist, unitInterval.mul_le_left, periodizedBernoulli.continuous, NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_top, Real.goldenConj_mul_goldenRatio, GenLoop.continuous_fromLoop, PiNat.mem_cylinder_iff_dist_le, quotient_norm_add_le, SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux, inner_smul_real_right, Affine.Triangle.sOppSide_affineSpan_pair_excenter_singleton_point, fourierSubalgebra_separatesPoints, IndiscreteTopology.norm_eq_zero, enorm_le_iff_norm_le, NonarchAddGroupSeminorm.coe_lt_coe, ProbabilityTheory.cgf_const, ContinuousMultilinearMap.opNorm_zero, AddGroupNormClass.toNormedAddCommGroup_norm_eq, MeasureTheory.Measure.haar.addPrehaar_mono, Metric.exists_lt_mem_ball_of_mem_ball, ArithmeticFunction.convolution_vonMangoldt_zeta, dense_differentiableAt_norm, Orientation.inner_eq_norm_mul_norm_mul_cos_oangle, Metric.unitBall.coe_eq_zero, MeasureTheory.SignedMeasure.re_toComplexMeasure, snd_integral, NNReal.val_eq_coe, CStarAlgebra.instNonnegSpectrumClass, FormalMultilinearSeries.ofScalars_norm_le, ContDiffBump.support_eq, preCantorSet_subset_unitInterval, SmoothBumpFunction.eqOn_source, ModularGroup.denom_S, Hyperreal.Infinite.st_eq, Set.Nontrivial.infsep_lt_iff, NumberField.mixedEmbedding.covolume_idealLattice, HurwitzZeta.continuousOn_evenKernel, Real.lipschitzWith_sin, Complex.zero_im, Real.one_rpow, Real.injOn_tan, ValueDistribution.proximity_add_top_le, NumberField.place_apply, Submodule.norm_subtypeL, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_eq, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos, fourierCoeff.const_smul, MeasureTheory.SignedMeasure.mutuallySingular_iff, ContractingWith.dist_le_mul, NumberField.mixedEmbedding.volume_preserving_negAt, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, StarAlgHom.realContinuousMapOfNNReal_apply_comp_toReal, cantorSet_eq_zero_two_ofDigits, NumberField.mixedEmbedding.normAtPlace_add_le, setIntegral_withDensity_eq_setIntegral_toReal_smul₀', Real.deriv_qaryEntropy, Asymptotics.isLittleO_sum_range_of_tendsto_zero, closure_of_rat_image_lt, IsSelfAdjoint.spectrum_nonempty, Real.Angle.toReal_coe_eq_self_sub_two_mul_int_mul_pi_iff, IsUltrametricDist.norm_fwdDiff_iter_apply_le, contDiffPointwiseHolderAt_iff, mem_closure_zero_iff_norm, CircleDeg1Lift.commute_sub_int, Real.deriv_arctan, Urysohns.CU.lim_of_mem_C, AffineSubspace.isPreconnected_setOf_wOppSide, continuousSMul_sphere_closedBall, HurwitzZeta.completedHurwitzZetaEven_eq, monotoneOn_deriv_descPochhammer_eval, NNReal.rpow_ofNat, RingNorm.apply_one, Real.toNNReal_inv, AddCircle.instIsProbabilityMeasureRealHaarAddCircle, SchwartzMap.smulLeftCLM_const, ProbabilityTheory.IsAEKolmogorovProcess.kolmogorovCondition, NumberField.house_pow_le, Metric.closure_eq_iInter_cthickening, ProbabilityTheory.HasSubgaussianMGF.memLp_exp_mul, MeasureTheory.integral_fintype, Metric.tendsto_dist_right_cobounded_atTop, Asymptotics.isLittleO_pow_sub_pow_sub, GroupSeminorm.inf_apply, SmoothPartitionOfUnity.sum_eq_one', OrthonormalBasis.sum_sq_inner_left, Circle.exp_inj, Tactic.ComputeAsymptotics.Seq.dist_cons_cons, Real.sinh_eq_tsum, Real.sign_eq_zero_iff, Real.mk_mul, Irrational.sub_ratCast, RCLike.sqrt_real, BumpCovering.locallyFinite, Path.reparam_id, Complex.arg_eq_zero_iff_zero_le, CStarModule.norm_triangle, Real.arctan_strictMono, NormedDivisionRing.norm_eq_one_iff_ne_zero_of_discrete, UpperHalfPlane.dist_self_center, Set.infsep_pos_iff_nontrivial_of_finite, Complex.angle_eq_abs_arg, Irrational.div_intCast, integral_sin_mul_cos₁, intervalIntegral.smul_integral_comp_sub_mul, Matrix.permMatrix_l2_opNorm_le, Real.cos_eq_tsum, Metric.exists_ball_inter_eq_singleton_of_mem_discrete, MeasureTheory.Lp.norm_const', Function.locallyFinsuppWithin.toClosedBall_divisor, HasFPowerSeriesAt.isBigO_image_sub_norm_mul_norm_sub, MeasureTheory.norm_condExpIndL1_le, BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg, MeasureTheory.Measure.withDensityᵥ_absolutelyContinuous, Real.sinh_neg, Real.continuous_sin, SmoothBumpFunction.mem_Icc, Set.infsep_zero, Real.Angle.two_zsmul_neg_pi_div_two, Orientation.rightAngleRotation_map', NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_pow, EuclideanGeometry.oangle_midpoint_left, RCLike.wInner_one_eq_inner, StieltjesFunction.countable_leftLim_ne, ProbabilityTheory.iCondIndepSets_singleton_iff, NumberField.mixedEmbedding.negAt_apply_isComplex, ProbabilityTheory.hasFiniteIntegral_compProd_iff', AkraBazziRecurrence.p_def, Real.continuousOn_logb, CFC.rpow_natCast, MeasureTheory.Measure.haar.prehaar_mono, ProbabilityTheory.isGaussian_iff_charFun_eq, Matrix.eigenvalues_self_mul_conjTranspose_nonneg, Orientation.inner_rotation_pi_div_two_left_smul, MeasureTheory.Measure.toSignedMeasure_toMeasureOfZeroLE, Nonneg.instNonUnitalIsometricContinuousFunctionalCalculus, Submodule.norm_sq_eq_add_norm_sq_projection, EuclideanGeometry.Sphere.abs_oangle_center_left_toReal_lt_pi_div_two, GroupSeminorm.coe_comp, ProbabilityTheory.mgf_zero, LinearMap.extendTo𝕜'_apply_re, Complex.ofReal_one, ProbabilityTheory.mgf_zero_measure, Int.norm_eq_abs, ENNReal.toReal_nonneg, Filter.Tendsto.norm', NumberField.mixedEmbedding.fundamentalCone.expMapBasis_closure_subset_compactSet, Real.sqrtTwoAddSeries_zero_nonneg, Asymptotics.IsBigO.norm_norm, MeasureTheory.Measure.toSignedMeasure_smul, irrational_div_intCast_iff, InnerProductGeometry.inner_eq_neg_mul_norm_iff_angle_eq_pi, Complex.arg_zero, Real.goldenRatio_mul_fib_succ_add_fib, InnerProductGeometry.cos_eq_zero_iff_angle_eq_pi_div_two, Real.exp_arsinh, fourierIntegral_eq_half_sub_half_period_translate, RCLike.re_to_real, ProbabilityTheory.tilted_mul_apply_mgf', MeasureTheory.norm_integral_le_lintegral_norm, AbsolutelyContinuousOnInterval.exists_bound, Affine.Simplex.circumsphere_unique_dist_eq, Complex.algHom_ext_iff, Real.artanh_eq_zero_iff, swap_integral, Topology.CWComplex.union', Path.uniformContinuous, Real.ofNat_lt_toNNReal, Quaternion.re_exp, ContinuousLinearMap.norm_precompR_le, PadicInt.coe_natCast, dist_lineMap_right, NumberField.mixedEmbedding.fundamentalCone.continuous_expMap, ContDiffMapSupportedIn.structureMapLM_apply_withOrder, continuous_circleMap, MeasureTheory.lpNorm_fun_natCast_mul, Real.summable_nat_pow_inv, intervalIntegral.FTCFilter.nhdsRight, not_integrableOn_Ioi_rpow, Complex.equivRealProdAddHom_symm_apply_re, BoundingSieve.nu_lt_one_of_prime, AbsolutelyContinuousOnInterval.uniformContinuousOn, RCLike.neg_iff, isScalarTower_closedBall_ball_ball, PowerSeries.IsRestricted.isRestricted_iff, MeasureTheory.Measure.haar.chaar_nonneg, integral_sin_pow_aux, RingSeminorm.mul_le', ProbabilityTheory.instIsGaussianDirac, ProbabilityTheory.Kernel.measurable_countableFiltration_densityProcess, NormedSpace.ofReal_exp_ℝ_ℝ, integral_comp_abs, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat, MeasureTheory.hausdorffMeasure_prod_real, Complex.sq_nonneg_iff, dist_triangle_left, Circle.exp_add_two_pi, ContinuousMap.HomotopyWith.trans_apply, harmonic_le_one_add_log, AkraBazziRecurrence.min_bi_le, convex_halfSpace_im_lt, RCLike.sqrt_eq_real_add_ite, Real.sinh_eq_zero, PadicInt.norm_int_le_pow_iff_dvd, Real.isBigO_logb_mul_const_log_atTop, integral_div_sq_add_sq, MeasureTheory.lpNorm_le_lpNorm_add_lpNorm_sub', Padic.padicNormE.is_rat, ENNReal.rpow_eq_top_iff, MeasureTheory.Measure.addHaar_parallelepiped, MeasureTheory.L1.SimpleFunc.norm_eq_sum_mul, NormedSpace.isVonNBounded_iff', Polynomial.rootSet_derivative_subset_convexHull_rootSet, LipschitzWith.dist_iterate_succ_le_geometric, LineDeriv.laplacianCLM_eq_sum, ProbabilityTheory.mgf_fun_id_gaussianReal, Polynomial.Chebyshev.S_two_mul_real_cosh, PadicInt.valuation_coe_nonneg, SmoothPartitionOfUnity.mem_finsupport, Real.binEntropy_zero, ProbabilityTheory.IsKolmogorovProcess.kolmogorovCondition, Continuous.inner_bundle, RCLike.inv_im, IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus, Real.Wallis.W_eq_integral_sin_pow_div_integral_sin_pow, Real.convergent_of_zero, Metric.isBounded_iff, MeasureTheory.measureReal_add_measureReal_compl₀, Real.continuous_negMulLog, EuclideanGeometry.preimage_inversion_sphere_dist_center, NormedAddGroupHom.bound', MeasureTheory.Measure.integrable_measure_prodMk_left, MeasureTheory.norm_condExpInd_apply_le, ArchimedeanClass.stdPart_one, regionBetween_subset, has_antideriv_at_fourier_neg, IsMIntegralCurve.comp_add, OpenPartialHomeomorph.univUnitBall_target, Real.differentiableAt_log_iff, Complex.ofReal_nnratCast, norm_iteratedFDerivWithin_prod_le, SmoothBumpFunction.tsupport_mem_nhds, EReal.coe_zero, IsOpen.exists_contMDiff_support_eq, Real.uniformContinuous_neg, Real.convexOn_log_Gamma, UnitAddTorus.mFourier_norm, CStarModule.norm_inner_le, Orientation.rotation_neg_orientation_eq_neg, Real.posLog_eq_zero_iff, ProbabilityTheory.IndepFun.integral_fun_mul_eq_mul_integral, Matrix.IsHermitian.eigenvalues₀_antitone, ContinuousLinearMap.rayleighQuotient_add, Matrix.instNonnegSpectrumClass, IsPicardLindelof.continuousOn_uncurry, Complex.UnitDisc.instCanLiftCoeLtRealNormOfNat, WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup, hasFDerivAt_iff_tendsto, Complex.equivRealProdAddHom_symm_apply_im, Orientation.eq_rotation_self_iff, GenLoop.toLoop_apply, Bornology.IsBounded.subset_ball_lt, LiouvilleWith.rat_mul_iff, Height.mulHeight_zero, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, AddGroupSeminorm.coe_add, Complex.selfAdjointEquiv_apply, norm_sub_le_norm_mul, Real.isPiSystem_Iio_rat, BoundedContinuousFunction.nnrealPart_coeFn_eq, UpperHalfPlane.im_smul, RCLike.ofReal_prod, tsum_geometric_two, FormalMultilinearSeries.not_summable_norm_of_radius_lt_nnnorm, Real.Angle.two_zsmul_toReal_eq_two_mul, MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_sum_opNorm, MeasureTheory.lintegral_ofReal_le_lintegral_enorm, MeasureTheory.tendsto_measure_norm_gt_of_isTightMeasureSet, Complex.range_liftAux, Orientation.areaForm'_apply, Padic.padicNormE.is_norm, NumberField.mixedEmbedding.fundamentalCone.expMap_smul, Real.continuous_const_rpow, Asymptotics.isBigO_const_iff, IsApproximateAddSubgroup.card_nsmul_le, ENNReal.rpow_rpow_inv, IsGδ.setOf_irrational, inner_eq_norm_sq_left_iff, SzemerediRegularity.biUnion_star_subset_nonuniformWitness, MeasureTheory.hausdorffMeasure_lineMap_image, Real.log_eq_zero, Set.infsep_of_fintype, UpperHalfPlane.normSq_denom_pos, Metric.mem_closure_iff, ENNReal.continuous_ofReal, Real.antitone_arccos, Real.cauchy_inv, MeasureTheory.BorelCantelli.process_zero, UniformContinuousOn.cexp, Complex.neg_pi_lt_arg, ENNReal.ofReal_le_ofReal_iff', PiCountable.dist_summable, Polynomial.one_le_mahlerMeasure_of_ne_zero, RCLike.ofReal_mul_pos_iff, Real.summable_exp_neg_nat, Real.sin_nat_mul_pi, Real.abs_sin_sub_sin_le, unitInterval.one_mem, Real.Angle.abs_cos_eq_abs_sin_of_two_nsmul_add_two_nsmul_eq_pi, Affine.Triangle.dist_orthocenter_reflection_circumcenter, ODE.FunSpace.toContinuousMap_apply_eq_apply, Complex.neg_iff, Complex.inv_cpow_eq_ite, ArithmeticFunction.log_apply, Complex.liftAux_apply_I, BoxIntegral.Box.volume_face_mul, RCLike.ofReal_finsupp_sum, Asymptotics.IsTheta.norm_left, intervalIntegral.integral_smul_measure, ContDiffPointwiseHolderAt.prodMk, Asymptotics.IsTheta.isBoundedUnder_le_iff, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_lt_one_iff, Metric.hasBasis_cobounded_compl_ball, MeasureTheory.BorelCantelli.integrable_process, Distribution.mapCLM_apply, OnePoint.IsZeroAt.smul_iff, unitInterval.fract_mem, CFC.rpow_map_prod, FormalMultilinearSeries.norm_compContinuousLinearMap_le, intervalIntegral.FTCFilter.meas_gen, Quaternion.normSq_eq_norm_mul_self, MeasureTheory.SignedMeasure.singularPart_zero, tendsto_real_toNNReal_atTop, AkraBazziRecurrence.GrowsPolynomially.div, AkraBazziRecurrence.GrowsPolynomially.neg, NNReal.nnrpow_def, spectralValueTerms_nonneg, Besicovitch.TauPackage.one_lt_tau, UpperHalfPlane.σ_neg, mem_nullAddSubgroup_iff, Metric.diam_nonneg, IsContinuousRiemannianBundle.exists_continuous, norm_zsmul_le, Set.OrdConnected.null_frontier, InnerProductSpaceable.inner_.norm_sq, ProbabilityTheory.gaussianReal_apply, ArithmeticFunction.vonMangoldt_pos_iff, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn, Besicovitch.SatelliteConfig.inter', Real.contDiff_arsinh, ProbabilityTheory.Kernel.densityProcess_fst_univ_ae, Seminorm.ball_add_ball_subset, Complex.frontier_preimage_im, MeasureTheory.MemLp.integrable_norm_rpow, ENNReal.lt_iff_exists_real_btwn, EuclideanGeometry.angle_eq_zero_of_angle_eq_pi_left, NNReal.rpow_two, CircleDeg1Lift.commute_add_nat, Irrational.natCast_sub, Real.comap_toNNReal_atTop, gauge_of_subset_zero, Polynomial.mahlerMeasure_pos_of_ne_zero, MeasureTheory.tilted_apply_eq_ofReal_integral, Real.exp_strictMono, Set.Finite.isClosed_convexHull, ModularFormClass.exists_petersson_le, Affine.Simplex.exradius_reindex, Submodule.smul_starProjection_singleton, NumberField.Units.mem_torsion, Metric.tendsto_nhdsWithin_nhdsWithin, Affine.Simplex.ninePointCircle_reindex, norm_of_subsingleton, SMulCommClass.complexToReal, Real.arctan_injective, Circle.invOn_arg_exp, ContinuousLinearMap.opNorm_comp_le, ProbabilityTheory.condExp_set_generateFrom_singleton, Chebyshev.primeCounting_sub_theta_div_log_isBigO, NNReal.sub_def, Real.two_pi_pos, norm_mul, Path.Homotopy.trans_assoc_reparam, RCLike.one_im, UpperHalfPlane.coe_smul, ProbabilityTheory.gaussianPDFReal_def, Complex.inv_def, Complex.equivRealProdLm_apply, Orientation.inner_comp_rightAngleRotation, Complex.div_intCast, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_natCast_le_one, Real.contDiffAt_arcsin_iff, Real.isPiSystem_Ioi_rat, CStarAlgebra.linear_combination_nonneg, RCLike.natCast_re, ProbabilityTheory.HasCondSubgaussianMGF.zero, Real.tendsto_comp_exp_atBot, Complex.IsExpCmpFilter.tendsto_norm, HasFPowerSeriesWithinOnBall.image_sub_sub_deriv_le, NNReal.coe_lt_one, instSeparatingDualRealOfIsTopologicalAddGroupOfContinuousSMulOfLocallyConvexSpaceOfT1Space, Asymptotics.isBigOWith_self_const_mul, EReal.range_coe, MeasureTheory.Lp.norm_smul_le, Valued.integer.norm_le_one, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, Urysohns.CU.approx_mem_Icc_right_left, Real.cos_eq_cos_iff, intervalIntegral.intervalIntegrable_id, Real.sinh_sq, Bornology.IsBounded.exists_norm_le', signedDist_lineMap_lineMap, Real.isBigO_logb_log, Complex.ofRealCLM_apply, MeasureTheory.IntegrableAtFilter.norm, Real.cauchy_nnratCast, ModularGroup.exists_row_one_eq_and_min_re, AkraBazziRecurrence.differentiableOn_one_add_smoothingFn, ENNReal.ofReal_eq_natCast, Real.arsinh_lt_arsinh, Asymptotics.IsLittleO.isBigOWith, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform, InnerProductSpace.Core.inner_self_nonneg, RCLike.ofReal_finsuppProd, BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_isClosedEmbedding, differentiableAt_complex_iff_differentiableAt_real, mfderiv_coe_sphere_injective, exists_continuous_zero_one_of_isCompact', cfcHom_real_eq_restrict, intervalIntegral.inv_smul_integral_comp_sub_div, SeparationQuotient.normedMk_eq_zero_iff, Real.volume_pi_le_prod_diam, inner_re_symm, schnirelmannDensity_eq_one_iff, MeasureTheory.SimpleFunc.negPart_map_norm, Seminorm.iSup_apply, Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius, lipschitzWith_iff_norm_div_le, NumberField.Units.regOfFamily_of_isMaxRank, MeasureTheory.Measure.setIntegral_toReal_rnDeriv', circleIntegral.integral_radius_zero, ArithmeticFunction.vonMangoldt_sum, IsUnifLocDoublingMeasure.eventually_measure_le_doublingConstant_mul, dist_triangle_max, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, SmoothBumpFunction.nhds_basis_support, InnerProductGeometry.angle_zero_left, ProbabilityTheory.gaussianReal_conv_gaussianReal, AkraBazziRecurrence.strictAnti_sumCoeffsExp, WithSeminorms.tendsto_nhds, intervalIntegral.inv_mul_integral_comp_add_div, AkraBazziRecurrence.strictAntiOn_one_add_smoothingFn, star_mul_self_add_self_mul_star, nonneg_iff_isSelfAdjoint_and_spectrumRestricts, Complex.arg_conj, inner_map_complex, analyticAt_sigmoid, Real.sinh_sub, Real.toNNReal_pos, NNReal.ContinuousMap.canLift, Filter.Tendsto.dist, Metric.hasAntitoneBasis_cobounded_compl_closedBall, HomotopyGroup.mul_spec, Metric.hausdorffDist_self_zero, Rat.AbsoluteValue.padic_eq_padicNorm, HurwitzZeta.completedCosZeta₀_neg, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_norm_quasispectrum, InnerProductGeometry.angle_add_angle_eq_pi_of_angle_eq_pi, BoundedContinuousFunction.probCharDual_zero, ValueDistribution.characteristic_sub_characteristic_inv_le, BoundedContinuousFunction.norm_le_of_nonempty, contDiffAt_norm, Submodule.starProjection_norm_le, UniformConvexOn.add, MeasureTheory.pdf.IsUniform.pdf_toReal_ae_eq, MeasureTheory.charFun_conv, RCLike.norm_le_re_iff_eq_norm, NumberField.Units.regOfFamily_div_regulator, PadicComplex.isNonarchimedean, expNegInvGlue.tendsto_polynomial_inv_mul_zero, WithSeminorms.isOpen_iff_mem_balls, EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radius, PiLp.volume_preserving_ofLp, Probability.cauchyPDF_scale_zero, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbeddingOfIsReal, BoundedContinuousFunction.norm_integral_le_norm, exists_lt_subset_ball, MeasureTheory.lpNorm_sub_le_lpNorm_sub_add_lpNorm_sub, EuclideanGeometry.sin_eq_one_iff_angle_eq_pi_div_two, integral_sin_pow_even_mul_cos_pow_even, Real.arctan_zero, ProbabilityTheory.variance_zero, EuclideanGeometry.dist_eq_abs_sub_dist_iff_angle_eq_zero, Real.sin_two_pi_sub, sameRay_iff_norm_add, Real.mk_add, SimpleGraph.UnitDistEmbedding.unit_dist, Complex.dist_le_dist_of_mapsTo_ball_self, ProbabilityTheory.Kernel.setIntegral_density_of_measurableSet, NormedAddGroupHom.opNorm_add_le, Complex.tendsto_exp_comap_re_atBot, continuous_bernoulliFun, EuclideanGeometry.sin_angle_div_dist_eq_sin_angle_div_dist, measurableSet_of_differentiableWithinAt_Ici_of_isComplete, Complex.normSq_ofNat, signedDist_vadd_left_swap, IsSelfAdjoint.spectrumRestricts, Real.sInf_neg, Complex.UnitDisc.re_neg, Real.qaryEntropy_strictAntiOn, diam_stdSimplex_le, gronwallBound_x0, SeparationQuotient.mk_eq_zero_iff, HurwitzZeta.continuousOn_oddKernel, Metric.dist_lt_add_of_nonempty_closedBall_inter_ball, NumberField.mixedEmbedding.fundamentalCone.closure_normLeOne_subset, Real.borel_eq_generateFrom_Ici_rat, StieltjesFunction.zero_apply, Polynomial.logMahlerMeasure_eq_log_leadingCoeff_add_sum_log_roots, intervalIntegral.FTCFilter.nhdsUniv, imaginaryPart.norm_le, Seminorm.const_isBounded, OpenPartialHomeomorph.contDiffOn_univUnitBall_symm, Seminorm.preimage_metric_closedBall, Real.sinOrderIso_apply, MeasureTheory.integrable_prod_iff, Polynomial.eq_centerMass_of_eval_derivative_eq_zero, Tactic.ComputeAsymptotics.WellFormedBasis.tendsto_atTop, ProbabilityTheory.IsMeasurableRatCDF.le_one, ValueDistribution.characteristic_eventually_nonneg, abs_norm', instCStarRingReal, AddGroupSeminorm.coe_iSup_apply, Real.exp_sub_cosh, CFC.abs_algebraMap, preCantorSet_antitone, MeasureTheory.norm_weightedSMul_le, NumberField.mixedEmbedding.convexBodySumFun_neg, Complex.restrictScalars_one_smulRight, Tactic.ComputeAsymptotics.Seq.dist_eq_two_inv_pow, LipschitzWith.coordinate, PartitionOfUnity.nonneg, GroupSeminorm.smul_apply, Real.isPiSystem_Ici_rat, real_inner_self_abs, Complex.summable_ofReal, Orientation.oangle_eq_iff_eq_pos_smul_rotation_or_eq_zero, BoundedContinuousFunction.apply_le_norm, hasDerivAt_fourier_neg, Orientation.rotation_zero, ValueDistribution.characteristic_add_top_eventuallyLE, NNReal.mk_one, ProbabilityTheory.isGaussian_gaussianReal, Real.Angle.cos_eq_zero_iff, ArchimedeanClass.stdPart_intCast, Tactic.ComputeAsymptotics.Seq.Stream'.dist_le_one, Real.floor_real_sqrt_eq_nat_sqrt, IsPrimitiveRoot.arg_eq_zero_iff, integral_inner, NumberField.FinitePlace.add_le, schnirelmannDensity_eq_zero_of_one_notMem, Complex.nonpos_iff, Metric.continuous_iff', Real.leTotal_R, deriv_abs_zero, AnalyticAt.harmonicAt_conj, RCLike.ofReal_im, NumberField.FinitePlace.instNonnegHomClassReal, Real.Angle.angle_eq_iff_two_pi_dvd_sub, CircleDeg1Lift.semiconj_of_isUnit_of_translationNumber_eq, bounded_stdSimplex, InnerProductGeometry.cos_eq_neg_one_iff_angle_eq_pi, expNegInvGlue.nonneg, irrational_inv_iff, Algebra.norm_complex_eq, Real.sin_two_mul, realPart_comp_subtype_selfAdjoint, Real.convergent_zero, ProbabilityTheory.gaussianPDFReal_sub, Metric.exists_continuous_real_forall_closedBall_subset, Real.doublingGamma_log_convex_Ioi, InnerProductGeometry.norm_ofLp_crossProduct, hasStrictDerivAt_abs, BoundingSieve.siftedSum_eq_sum_support_mul_ite, fourier_eval_zero, Asymptotics.isBigOWith_iff, Matrix.IsHermitian.roots_charpoly_eq_eigenvalues, ContinuousAlternatingMap.isLeast_opNorm, EuclideanGeometry.OrthocentricSystem.affineIndependent, Irrational.natCast_div, Complex.arg_lt_pi_iff, Matrix.IsHermitian.cfcAux_apply, SchwartzMap.fourierInv_lineDerivOp_eq, Affine.Simplex.touchpointWeights_reindex, RCLike.abs_im_le_norm, RCLike.finrank_le_two, MeasureTheory.StronglyMeasurable.exists_spanning_measurableSet_norm_le, Real.cos_int_mul_two_pi_add_pi, EuclideanGeometry.Sphere.secondInter_smul, ProbabilityTheory.monotone_preCDF, InnerProductSpace.harmonicAt_comp_CLE_iff, smoothingFun_le, Bundle.RiemannianMetric.symm, EReal.preimage_coe_Ici, dist_homothety_self, BoundedContinuousFunction.dist_coe_le_dist, MeasureTheory.stoppedValue_upperCrossingTime, OneHomClass.bound_of_antilipschitz, real_inner_add_sub_eq_zero_iff, strongConcaveOn_iff_convex, Real.iteratedDeriv_odd_sinh, Affine.Simplex.height_map, Complex.dist_le_div_mul_dist_of_mapsTo_ball, Asymptotics.isLittleO_const_id_atBot, Real.smul_iInf_of_nonpos, NNReal.rpow_natCast_mul, ContinuousMap.toNNReal_one, ProbabilityTheory.Kernel.tendsto_integral_density_of_antitone, EReal.image_coe_Ioo, MeasureTheory.Lp.lipschitzWith_pos_part, linear_isometry_complex, closure_open_halfSpace, MeasureTheory.condExpIndL1_smul, ModularGroup.re_T_zpow_smul, Path.extend_range, Real.Angle.toCircle_coe, eventually_norm_pow_le, ProbabilityTheory.Fernique.normThreshold_eq, Complex.dist_of_im_eq, MeasureTheory.measureReal_diff, Unitization.norm_eq_sup, RCLike.nonneg_iff, unitInterval.symm_one, ProbabilityTheory.isGaussian_map, instIsZLatticeRealSpan, Affine.Simplex.orthogonalProjection_circumcenter, Real.Angle.tan_eq_inv_of_two_nsmul_add_two_nsmul_eq_pi, Real.hasDerivAt_cos, GenLoop.fromLoop_symm_toLoop, ENNReal.truncateToReal_le, Topology.CWComplex.source_eq, RCLike.ofReal_zero, NumberField.mixedEmbedding.convexBodySumFun_continuous, Topology.CWComplex.pairwiseDisjoint', Real.toNNReal_one, coe_comp_nnnorm', summable_pow_div_add, ProbabilityTheory.IsMeasurableRatCDF.nonneg, Real.sin_eq_sin_iff, HurwitzZeta.continuousOn_sinKernel, intervalIntegral.norm_intervalIntegral_eq, ProbabilityTheory.HasSubgaussianMGF.integrable, IsStrictlyPositive.nnrpow, GroupSeminorm.zero_apply, Affine.Triangle.prod_dist_eq_prod_dist_of_mem_line_of_mem_line, NNReal.geom_mean_le_arith_mean4_weighted, BoundedContinuousFunction.norm_eq_zero_of_empty, BoxIntegral.Box.volume_apply', CStarModule.norm_pos, Complex.arg_eq_pi_div_two_iff, MeasureTheory.measureReal_iUnion_fintype, PiNat.isOpen_iff_dist, intervalIntegral.inv_mul_integral_comp_sub_div, Real.iSup_const_zero, PadicInt.coe_adicCompletionIntegersEquiv_apply, ENNReal.coe_rpow_of_ne_zero, CircleDeg1Lift.le_map_map_zero, CircleDeg1Lift.map_sub_nat, Real.measurable_cosh, ZMod.toAddCircle_natCast, UpperHalfPlane.dist_eq, EulerSine.integral_sin_mul_sin_mul_cos_pow_eq, Submodule.norm_starProjection, Real.disjoint_residual_ae, Circle.star_addChar, IsSelfAdjoint.norm_pow_two_pow, Path.delayReflLeft_zero, Real.sqrt_div_self', Real.comap_sqrt_atTop, Asymptotics.IsBigOWith.triangle, FormalMultilinearSeries.isLittleO_one_of_lt_radius, ContinuousMap.sup_mem_subalgebra_closure, RCLike.continuous_re, isBigO_at_im_infty_jacobiTheta_sub_one, Asymptotics.IsBigO.exists_mem_basis, Bornology.IsBounded.exists_pos_norm_lt, Real.log_div_self, MeasureTheory.weightedSMul_add_measure, NormedAddGroupHom.ratio_le_opNorm, nhds_comap_dist, MeasureTheory.Measure.NullMeasurableSet.const_smul, Tactic.ComputeAsymptotics.Seq.dist_nil_cons, MDifferentiable.slash, Real.zero_rpow_eq_iff, MeasureTheory.Measure.map_conv_continuousLinearMap, Polynomial.mahlerMeasure_X_add_C, AkraBazziRecurrence.bi_min_div_two_pos, exists_dual_vector, CStarModule.norm_zero, norm_nsmul_le, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, Real.sign_mul_nonneg, NumberField.mixedEmbedding.logMap_eq_logEmbedding, ContDiffMapSupportedIn.locallyConvexSpace, Probability.cauchyPDFReal_scale_zero, Complex.conjAe_coe, ContinuousMultilinearMap.bounds_bddBelow, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, OnePoint.isBoundedAt_infty_iff, fourierCoeff_toLp, Orientation.oangle_rotation_oangle_left, nsmul_mem_closedBall, ContinuousLinearMap.rayleighQuotient_le_norm, OrthonormalBasis.det_to_matrix_orthonormalBasis, CircleDeg1Lift.transnumAuxSeq_def, mem_balancedHull_iff, Real.continuous_logb, EReal.continuousOn_toReal, gauge_smul_left_of_nonneg, RingSeminorm.eq_zero_iff, Real.eq_zero_rpow_iff, map_real_smul, MeasureTheory.DominatedFinMeasAdditive.of_smul_measure, ContinuousLinearMap.norm_def, ProbabilityTheory.IsGaussian.charFunDual_eq, Real.arcsin_neg, Padic.norm_natCast_eq_one_iff, coe_fourierBasis, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, tendsto_measure_Icc_nhdsWithin_right, Asymptotics.IsBigOWith.smul, Real.Angle.sin_coe_pi, ENNReal.monotone_truncateToReal, lipschitzWith_iff_norm_sub_le, Real.differentiableWithinAt_arcsin_Ici, mem_closedBall_iff_norm''', Height.mulHeight₁_sum_le, Complex.ofReal_comp_add, NNReal.rpow_inv_eq_iff, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, norm_inner_eq_norm_tfae, Real.circleAverage_def, mem_ball_iff_norm, BoxIntegral.Box.coe_mk', abs_norm_sub_norm_le, ProbabilityTheory.Kernel.density_ae_eq_limitProcess, irrational_add_intCast_iff, BumpCovering.continuous_toPOUFun, BoxIntegral.Prepartition.upper_le_upper, intervalIntegral.FTCFilter.toTendstoIxxClass, Set.infsep_nonneg, Polynomial.mahlerMeasure_mul, CuspForm.coe_translate, InformationTheory.klDiv_ne_top_iff, Complex.norm_real, Real.toNNReal_eq_natCast, Chebyshev.theta_eq_log_primorial, CuspFormClass.petersson_bounded_right, MeasureTheory.integrable_conv_iff, Polynomial.exists_forall_norm_le, Stirling.sqrt_pi_le_stirlingSeq, ProbabilityTheory.Kernel.IsFiniteKernel.integrable, Real.hasDerivWithinAt_arcsin_Ici, Seminorm.add_apply, UpperHalfPlane.norm_qParam_lt_one, signedDist_vadd_right, ProbabilityTheory.Kernel.compProd_fst_condKernelReal, unitInterval.coe_symm_eq, NumberField.Ideal.tendsto_norm_le_div_atTop₀, NumberField.isFinitePlace_iff, GroupNorm.coe_le_coe, InnerProductSpace.instIsContPerfPairRealInnerₗOfCompleteSpace, Complex.range_arg, RCLike.zero_re, Real.smoothTransition.le_one, cfcₙ_tsub, ProbabilityTheory.IsRatCondKernelCDFAux.mono', Real.neg_one_lt_tanh, Matrix.instFiniteElemRealSpectrum, unitInterval.symmMeasurableEquiv_symm_apply, Archimedean.embedReal_injective, InnerProductSpace.Core.inner_re_symm, EuclideanGeometry.Sphere.isExtTangentAt_center_iff, unitInterval.qRight_zero_right, rotationOf_rotation, not_sameRay_iff_of_norm_eq, Irrational.natCast_mul, MeasureTheory.DominatedFinMeasAdditive.smul, CFC.rpow_neg_one_eq_cfc_inv, CStarModule.norm_zero_iff, NormedSpace.equicontinuous_TFAE, hasDerivAt_taylorWithinEval_succ, CFC.monotoneOn_one_sub_one_add_inv_real, convexOn_descPochhammer_eval, unitInterval.sigmoid_neg, IsMIntegralCurveAt.hasMFDerivAt, RCLike.smul_im, dist_single_single, MeasureTheory.tendsto_sum_indicator_atTop_iff', ProbabilityTheory.Kernel.rnDerivAux_le_one, polarCoord_symm_apply, Real.Gamma_add_one, NNReal.rpow_add_natCast, skewAdjoint.negISMul_apply_coe, isNonarchimedean_spectralNorm, Besicovitch.exists_goodδ, PMF.integral_eq_tsum, SpectrumRestricts.real_iff, Complex.log_mul_eq_add_log_iff, dist_self_homothety, hasSum_geometric_two, GaussianInt.to_real_re, ContinuousAt.norm', Probability.stronglyMeasurable_cauchyPDF, NNReal.coe_natCast, ProbabilityTheory.condVar_zero, Affine.Simplex.exradius_singleton_pos, LSeries.norm_term_eq, MeasureTheory.ae_bdd_liminf_atTop_rpow_of_eLpNorm_bdd, Asymptotics.isLittleO_one_left_iff, RCLike.tendsto_ofReal_cobounded_cobounded, ProbabilityTheory.norm_complexMGF_le_mgf, Complex.UnitDisc.im_conj, EReal.toReal_neg_eq, Real.injOn_arcsin, Pi.sum_norm_apply_le_norm, Real.cosh_zero, ModularFormClass.exists_bound, Metric.le_infDist, NumberField.mixedEmbedding.volume_preserving_mixedSpaceToRealMixedSpace_symm, unitary.spectrum_subset_circle, ProbabilityTheory.Kernel.measurable_singularPart_fun, MeasureTheory.integral_prod_mul, intervalIntegral.integral_comp_div, norm_div_sub_norm_div_le_norm_div, Complex.rank_real_complex', contDiff_norm_sq, Real.concaveOn_negMulLog, ContinuousLinearMap.opNorm_add_le, Valued.toNormedField.norm_le_iff, AddCircle.ergodic_nsmul, AddCircle.injective_toCircle, Real.range_exp, tendsto_integral_mulExpNegMulSq_comp, NNReal.geom_mean_le_arith_mean2_weighted, ContinuousLinearMap.sSup_sphere_eq_norm, SmoothBumpCovering.embeddingPiTangent_injective_mfderiv, MeasureTheory.tilted_apply, Real.Angle.coe_sub, Polynomial.logMahlerMeasure_def, Real.pi_gt_d2, aestronglyMeasurable_derivWithin_Ici, MeasureTheory.lpNorm_nnreal_eq_integral_norm_rpow, NNReal.image_coe_Ioc, Complex.frontier_setOf_lt_im, Polynomial.logMahlerMeasure_X, MulRingNorm.mulRingNormClass, Real.continuous_logb', Orientation.oangle_sign_smul_left, HurwitzZeta.sinKernel_zero, StieltjesFunction.add_apply, Complex.exp_ofReal_im, ContDiffPointwiseHolderAt.continuousLinearMap_comp, Height.mulHeight₁_pos, SmoothBumpCovering.point_finite, unitInterval.mul_le_right, padic_polynomial_dist, Height.mulHeight₁_sub_le, Quaternion.coeComplex_imK, PartitionOfUnity.locallyFinite', Polynomial.aeval_conj, InnerProductGeometry.angle_le_angle_add_angle, ContinuousLinearMap.NonlinearRightInverse.bound, ContinuousLinearMap.norm_inr, EReal.ENNReal.rpow_eq_exp_mul_log, Metric.closedBall_zero, lp.norm_eq_card_dsupport, MeasureTheory.setAverage_eq, ConvexBody.isBounded, Real.Angle.intCast_mul_eq_zsmul, PiLp.norm_sq_eq_of_L2, RCLike.re_eq_add_conj, Complex.slitPlane_eq_union, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMap, ZSpan.isAddFundamentalDomain', MeasureTheory.Measure.integrable_compProd_iff, Polynomial.prod_mahlerMeasure_eq_mahlerMeasure_prod, Real.abs_sin_half, Complex.interior_reProdIm, Affine.Simplex.touchpoint_mem_affineSpan, HurwitzZeta.completedCosZeta₀_zero, HurwitzZeta.oddKernel_zero, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, ValueDistribution.logCounting_add_top_eventuallyLE, Path.isUniformEmbedding_coe, ContinuousMap.inf_mem_subalgebra_closure, Real.two_mul_cos_mul_cos, unitInterval.symmHomeomorph_symm_apply, Complex.ofReal_sum, Conformal.differentiable, Real.tendsto_mul_log_one_add_div_atTop, AkraBazziRecurrence.GrowsPolynomially.mul, Real.sqrtTwoAddSeries_succ, Real.differentiableAt_cosh, Complex.mul_I_re, Path.range_subpath, EuclideanGeometry.oangle_eq_zero_or_eq_pi_iff_collinear, MeasureTheory.Measure.toSignedMeasure_apply, homeomorphUnitSphereProd_symm_apply_coe, WithLp.prod_nndist_eq_add, ProbabilityTheory.covarianceBilin_self_nonneg, Orientation.rightAngleRotation_rightAngleRotation, add_mem_closedBall_iff_norm, PiLp.norm_eq_of_L1, taylorWithinEval_succ, NNReal.coe_sum, QuotientAddGroup.nhds_zero_hasBasis, Real.mul_logb, WeakBilin.locallyConvexSpace, GromovHausdorff.ghDist_eq_hausdorffDist, Complex.I_re, unitInterval.continuous_qRight, ProbabilityTheory.integral_linearMap_gaussianReal, MeasureTheory.Measure.haar.mem_addPrehaar_empty, MeasureTheory.SignedMeasure.toJordanDecomposition_neg, UniformConcaveOn.neg, MeasureTheory.Measure.exists_integral_isMulLeftInvariant_eq_smul_of_hasCompactSupport, Real.abs_sin_eq_sqrt_one_sub_cos_sq, conformalAt_iff_isConformalMap_fderiv, exists_msmooth_support_eq_eq_one_iff, EuclideanGeometry.Sphere.abs_oangle_center_right_toReal_lt_pi_div_two, nonunits.subset_compl_ball, Real.fourier_eq, ProbabilityTheory.HasSubgaussianMGF.aemeasurable, EuclideanQuadrant.convex, instOrderTopologyReal, Real.volume_Iic, AkraBazziRecurrence.GrowsPolynomially.abs, Complex.closure_preimage_re, Path.symm_apply, ContinuousOn.isBigOWith_rev_principal, FormalMultilinearSeries.le_mul_pow_of_radius_pos, ZSpan.norm_fract_le, Asymptotics.IsBigO_def, InnerProductSpace.Core.norm_inner_le_norm, ContinuousMap.inf_mem_closed_subalgebra, Complex.nndist_of_re_eq, HasFPowerSeriesOnBall.isBigO_image_sub_image_sub_deriv_principal, Real.continuousAt_arcsin, Polynomial.Chebyshev.integral_eval_T_real_measureT_zero, ZetaAsymptotics.term_one, MeasureTheory.MemLp.eLpNorm_eq_integral_rpow_norm, norm_norm, unitInterval.nonneg', Real.closedBall_zero_eq_Icc, NormedAddGroupHom.SurjectiveOnWith.exists_pos, Real.dimH_of_nonempty_interior, Real.log_div, MeasureTheory.L2.real_inner_indicatorConstLp_one_indicatorConstLp_one, ProbabilityTheory.condIndepSets_iff, CFC.continuousOn_nnrpow, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, EReal.coe_coe_sign, instFactIsCuspInftyRealOfIsArithmetic, Polynomial.hermite_eq_deriv_gaussian', inner_vsub_vsub_right_eq_dist_sq_left_iff, ProbabilityTheory.condVar_of_not_le, AkraBazziRecurrence.growsPolynomially_pow, ContinuousLinearMap.reApplyInnerSelf_apply, imaginaryPart_realPart, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, Orientation.oangle_sign_smul_add_smul_smul_add_smul, EReal.preimage_coe_Ioi_bot, ProbabilityTheory.indepFun_iff_charFunDual_prod', ProbabilityTheory.setLIntegral_toKernel_univ, AddCircle.toCircle_zero, norm_sup_le_add, Affine.Simplex.direction_mongePlane, AntilipschitzWith.le_mul_norm_div, AddCircle.continuous_toCircle, MeasureTheory.integrable_norm_iff, Real.analyticOnNhd_arsinh, BoxIntegral.unitPartition.box_lower, Complex.normSq_zero, MeasureTheory.integrable_toReal_of_lintegral_ne_top, Real.abs_rpow_le_abs_rpow, MeasureTheory.Measure.integral_comp_mul_left, Cardinal.cantorFunctionAux_true, unitInterval.le_one', MeasureTheory.eLpNormLESNormFDerivOneConst_def, RCLike.wInner_const_left, Hyperreal.IsSt.mul, ProbabilityTheory.covarianceBilinDual_self_eq_variance, ENNReal.natCast_le_ofReal, Real.ofReal_le_enorm, NormedAddGroupHom.bounds_nonempty, ProperCone.innerDual_union, CompactlySupportedContinuousMap.integralLinearMap_apply, ProbabilityTheory.iCondIndepSet_iff, Affine.Simplex.dist_point_centroid, Circle.exp_add, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, Path.Homotopy.trans_apply, ContDiffAt.real_of_complex, CircleDeg1Lift.coe_mul, MeasureTheory.eLpNorm_indicator_const_le, Asymptotics.isBigOWith_abs_abs, inner_self_eq_norm_mul_norm, HurwitzZeta.oddKernel_functional_equation, hasStrictFDerivAt_norm_sq, ProbabilityTheory.Kernel.withDensity_one_sub_rnDerivAux, Affine.Simplex.altitudeFoot_reindex, Height.fun_logHeight_one, SmoothPartitionOfUnity.coe_finsupport, SchwartzMap.fourier_evalCLM_eq, RingNorm.toFun_eq_coe, NumberField.one_le_house_of_isIntegral, unitInterval.symm_le_comm, Mathlib.Tactic.Rify.ratCast_eq, Matrix.IsHermitian.sort_roots_charpoly_eq_eigenvalues₀, Real.toNNReal_add_le, WeakFEPair.hg_top, ENNReal.ofReal_le_one, Real.tan_pi_div_two_sub, Complex.interior_setOf_im_le, Finset.coe_infsep, Real.tendsto_log_nhdsGT_zero, Real.cos_add, RCLike.norm_nsmul, Emetric.exists_contMDiffMap_forall_closedBall_subset, SchwartzMap.contDiffAt, CovBySMul.trans, GroupSeminorm.coe_zero, Complex.ofReal_comp_mul, ContinuousMultilinearMap.norm_mkPiAlgebra, Subgroup.isArithmetic_iff_finiteIndex, MeasureTheory.exists_pos_ball, ENNReal.toReal_pow, Metric.PiNatEmbed.exists_closed_embedding_to_hilbert_cube, Real.cos_arcsin_nonneg, EisensteinSeries.norm_le_tsum_norm, Real.isFiniteMeasure_restrict_Ioo, NumberField.mixedEmbedding.convexBodySumFun_nonneg, StieltjesFunction.mono, BumpCovering.nonneg', Real.deriv_exp, IsMIntegralCurveAt.continuousAt, norm_add_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zero, NumberField.FinitePlace.mulSupport_finite_int, ENNReal.continuousAt_toReal, ValueDistribution.proximity_mul_top_le, Orientation.oangle_sign_smul_sub_left, Liouville.frequently_exists_num, Hyperreal.IsSt.inv, Real.contDiff_sin, NormedAddGroupHom.opNorm_zero_iff, AlgebraNormClass.toRingNormClass, CircleDeg1Lift.translate_apply, SchwartzMap.hasFDerivAt, Affine.Simplex.excenterWeightsUnnorm_empty_apply, ContinuousMultilinearMap.opNorm_add_le, Complex.norm_ratCast, Real.cos_one_pos, QuasispectrumRestricts.real_iff, MeasureTheory.memL1_smul_of_L1_withDensity, unitInterval.instTietzeExtension, Real.cos_pi_sub, imaginaryPart_eq_neg_I_smul_skewAdjointPart, Submodule.reflection_sub, Real.sin_int_mul_two_pi_sub, TemperedDistribution.instLineDerivSMulReal, MeasureTheory.MemLp.condExp, eventually_cobounded_le_norm', Real.ball_zero_eq_Ioo, NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero, PadicInt.one_le_norm_iff, ProbabilityTheory.gaussianPDF_zero_var, range_cfcₙ_nnreal_eq_image_cfcₙ_real, SchwartzMap.evalCLM_apply_apply, Real.volume_Icc, Affine.Simplex.altitudeFoot_mem_altitude, Real.tan_eq_one_sub_tan_half_sq_div_one_add_tan_half_sq, HurwitzZeta.isBigO_atTop_oddKernel, unitary.two_mul_one_sub_le_norm_sub_one_sq, Real.ofCauchy_natCast, Topology.CWComplex.mapsTo', NNReal.list_prod_map_rpow', Complex.conj_cpow_eq_ite, Orientation.rotation_eq_self_iff_angle_eq_zero, Complex.abs_im_lt_norm, isClosed_cantorSet, Int.toNat_add_toNat_neg_eq_norm, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, SmoothBumpCovering.eventuallyEq_one, Real.cos_pi_div_six, NormedRing.inverse_add_norm, UpperHalfPlane.ofComplex_apply_eq_ite, IsSelfAdjoint.sq_spectrumRestricts, Multipliable.norm_tprod, Height.mulHeight_eq, ENNReal.one_le_ofReal, SingularManifold.boundaryless, Nat.pairwise_one_le_dist, PadicInt.norm_natCast_zmodRepr_eq_one_iff, NumberField.FinitePlace.coe_apply, dist_mono_left_pi, Metric.unitBall.instIsLeftCancelMulZero, Real.sqrt_le_one, Affine.Simplex.inradius_eq_abs_inv_sum, ENNReal.ofReal_lt_natCast, isBounded_convexHull, MeasureTheory.Measure.toTemperedDistribution_apply, Real.range_arcsin, EReal.preimage_coe_Ioc, tendsto_integral_exp_smul_cocompact_of_inner_product, ProbabilityTheory.withDensity_preCDF, Real.nnnorm_two, CircleDeg1Lift.translationNumber_le_ceil_sub, ProbabilityTheory.Kernel.setIntegral_densityProcess, BoxIntegral.Box.Icc_def, PUnit.norm_eq_zero, SchwartzMap.instContinuousFourierInv, LinearMap.re_inner_adjoint_mul_self_nonneg, range_euclideanHalfSpace, NNReal.isBoundedUnder_le_toReal, mem_parallelepiped_iff, Asymptotics.isBigOWith_norm_left, MeasureTheory.integral_biUnion_eq_sum_powerset, EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_affineIndependent, DirichletCharacter.convolution_twist_vonMangoldt, ModularGroup.im_T_zpow_smul, Orientation.oangle_rotation_right, Complex.neg_pi_lt_log_im, Complex.ofReal_comp_balance, rothNumberNat_isLittleO_id, ValueDistribution.characteristic_mul_zero_eventuallyLE, real_inner_le_norm, Real.tendsto_log_nhdsLT_zero, Affine.Triangle.affineSpan_orthocenter_point_le_altitude, MeasureTheory.Integrable.re_im_iff, one_lt_gold, Path.Homotopy.continuous_reflTransSymmAux, Real.arccos_eq_pi, RCLike.normSq_mul, InnerProductGeometry.norm_sub_eq_add_norm_iff_angle_eq_pi, EisensteinSeries.isBoundedAtImInfty_eisensteinSeries_SIF, ValueDistribution.characteristic_pow_zero, Path.inv_apply, differentiableAt_norm_smul, Real.zero_rpow, MeasureTheory.measurableEquiv_range_coe_nat_of_infinite_of_countable, AbsolutelyContinuousOnInterval.tendsto_volume_restrict_totalLengthFilter_disjWithin_nhds_zero, Asymptotics.isTheta_norm_right, NNReal.image_coe_Ici, Real.coe_intFib_eq, MeasureTheory.SignedMeasure.singularPart_neg, ContinuousLinearMap.norm_map_tail_le, Complex.I_im, ProbabilityTheory.measurable_preCDF', continuous_coe_real_ereal, NonarchAddGroupNorm.le_def, Real.circleAverage_eq_integral_add, Asymptotics.isBigO_atTop_iff_eventually_exists, MeasureTheory.HasFiniteIntegral.norm, MeasureTheory.setIntegral_abs_condExp_le, MeasureTheory.integrable_enorm_rpow_iff, MeasureTheory.AEStronglyMeasurable.norm, EReal.image_coe_Ici, Real.iter_deriv_exp, intervalIntegral.inv_smul_integral_comp_div_sub, EReal.toReal_top, Module.Basis.prod_parallelepiped, ProbabilityTheory.measurable_poissonPMFReal, Metric.exists_contMDiffMap_forall_closedBall_subset, ProbabilityTheory.IndepFun.integral_fun_comp_mul_comp, Real.convexOn_Gamma, NumberField.mixedEmbedding.norm_nonneg, EMetric.exists_forall_closedBall_subset_aux₁, Real.differentiable_iteratedDeriv_cos, parallelepiped_basis_eq, EuclideanGeometry.Cospherical.affineIndependent, ProbabilityTheory.gaussianPDFReal_pos, NumberField.mixedEmbedding.mixedEmbedding_apply_isReal, Complex.ofReal_nsmul, Real.Gamma_nat_add_one_add_half, EReal.coe_neg', Seminorm.convex_ball, ContinuousMap.Homotopy.trans_apply, Real.rpow_one, Hyperreal.coe_inv, ContinuousMap.HomotopyRel.symm_apply, IsUnit.cfcNNRpow, exists_dual_vector'', exists_msmooth_zero_iff_one_iff_of_isClosed, PiTensorProduct.injectiveSeminorm_apply, Metric.infDist_le_infDist_of_subset, Homeomorph.unitBall_apply_coe, PartitionOfUnity.sum_finsupport_smul_eq_finsum, Real.continuous_sinh, BoundedContinuousFunction.Lp_norm_le, ProbabilityTheory.IsGaussian.memLp_dual, Asymptotics.isBigO_atTop_iff_eventually_exists_pos, Units.val_inv_cfcRpow, Complex.normSq_conj, Set.OrdConnected.image_coe_nnreal_real, schnirelmannDensity_univ, Path.refl_apply, IsCompact.extremePoints_nonempty, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul_real, isConnected_setOf_sameRay_and_ne_zero, curveIntegralFun_neg, Real.continuousOn_exp, ZetaAsymptotics.term_tsum_one, ENNReal.rpow_intCast, WithLp.prod_lipschitzWith_toLp, UpperHalfPlane.dist_eq_iff_dist_coe_center_eq, ENNReal.toNNReal_natCast_eq_toNNReal, Complex.continuous_normSq, Chebyshev.theta_mono, Real.pi_lt_four, MeasureTheory.Lp.norm_constL_le, NNReal.rpow_eq_zero, Polynomial.Chebyshev.rootMultiplicity_T_real, Real.tan_periodic, isTheta_deriv_rpow_const_atTop, ProbabilityTheory.covarianceBilinDual_self_nonneg, periodic_circleMap, IccLeftChart_extend_bot, NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst, BoxIntegral.Box.isBounded_Icc, ball_eq', Path.range_segment, Metric.mem_closedBall', ContDiffBump.measure_closedBall_le_integral, Real.iSup_of_isEmpty, Metric.Sum.one_le_dist_inl_inr, TemperedDistribution.fourier_lineDerivOp_eq, isCusp_SL2Z_iff, NumberField.mixedEmbedding.fundamentalCone.continuous_expMapBasis, Complex.equivRealProdLm_symm_apply, PadicInt.isUnit_iff, Irrational.sub_intCast, ValueDistribution.logCounting_top_mul_eventually_le, Complex.norm_zpow, Real.log_div_self_antitoneOn, ENNReal.ofReal_one, isOpen_deltaGenerated_iff, NonarchAddGroupSeminorm.smul_apply, ProbabilityTheory.Kernel.integral_densityProcess, MeasureTheory.charFunDual_map_const_add, Metric.mem_closure_range_iff, Real.Angle.sign_two_nsmul_eq_sign_iff, norm_prod_le_iff, MeasureTheory.charFunDual_map_add_const, Real.logb_one_left, Continuous.norm, TemperedDistribution.fourier_delta_zero, intervalIntegral.mul_integral_comp_add_mul, ProbabilityTheory.condCDF_eq_stieltjesOfMeasurableRat_unit_prod, NNReal.rpow_add', Measurable.im, Cardinal.Real.Icc_countable_iff, Complex.equivRealProdLm_symm_apply_im, Hyperreal.IsSt.le, AddCircle.toCircle_zsmul, ProbabilityTheory.setBernoulli_zero, IsPicardLindelof.exists_eq_forall_mem_Icc_eq_picard, Complex.add_conj, IntervalIntegrable.aestronglyMeasurable, Complex.coe_basisOneI_repr, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, realPart_I_smul, ProbabilityTheory.evariance_zero, Orientation.rotation_trans, NormedAddCommGroup.tendsto_nhds_nhds, ProbabilityTheory.IsRatCondKernelCDFAux.le_one', NNReal.isCoboundedUnder_ge_toReal, uniqueDiffWithinAt_Ioi, RCLike.norm_im_le_norm, Seminorm.exists_apply_eq_finset_sup, ENNReal.toNNReal_rpow, Path.continuous_uncurry_iff, PiLp.norm_eq_ciSup, ProbabilityTheory.Kernel.densityProcess_nonneg, Metric.hausdorffDist_le_diam, MeasureTheory.Measure.toSignedMeasure_add, KuratowskiEmbedding.embeddingOfSubset_isometry, NNReal.coe_min, CFC.rpow_neg_one_eq_inv, signedDist_lineMap_left, MeasureTheory.ae_le_lpNorm_exponent_top, gauge_def, ProbabilityTheory.variance_mul_const, dist_add_add_le, ModularGroup.tendsto_normSq_coprime_pair, WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded, ProbabilityTheory.covarianceBilin_real_self, Real.enorm_eq_ofReal_abs, Real.toNNReal_lt_one, MeasureTheory.Measure.IicSnd_apply, MeasureTheory.setIntegral_condExpL1CLM_of_measure_ne_top, BoundingSieve.siftedSum_le_sum_of_upperMoebius, Real.tendsto_rightDeriv_mul_log_atTop, Metric.mem_ball, NumberField.mixedEmbedding.norm_smul, Real.hasStrictDerivAt_arsinh, ModularForm.slash_action_eq'_iff, circleMap_preimage_codiscrete, Rat.norm_cast_real, NNReal.coe_nnqsmul, Complex.abs_arg_inv, MeasureTheory.lpNorm_norm, Complex.normSq_intCast, unitInterval.qRight_zero_left, MeasureTheory.integral_comp_rpow_Ioi, EuclideanGeometry.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, bernsteinApproximation.apply_one, convex_closedEBall, LiouvilleWith.add_nat, MeasureTheory.condExp_ae_eq_condExpL1CLM, integral_univ_inv_one_add_sq, Real.sin_int_mul_pi_sub, ProbabilityTheory.covariance_const_mul_right, Real.posLog_abs, Real.posLog_def, ProbabilityTheory.cgf_neg, GaussianInt.to_real_im, PseudoMetricSpace.uniformity_dist, norm_inv, MeasureTheory.Integrable.integral_norm_compProd, Complex.lintegral_comp_polarCoord_symm, LinearMap.norm_extendTo𝕜'_apply_sq, NumberField.mixedEmbedding.fundamentalDomain_stdBasis, SmoothPartitionOfUnity.sum_le_one', Int.tendsto_zmultiplesHom_cofinite, Real.logb_one_left_eq_zero, ValueDistribution.characteristic_sub_characteristic_inv, MeasureTheory.Lp.eLpNorm'_lim_eq_lintegral_liminf, trapezoidal_error_symm, RCLike.sqrt_of_nonneg, Real.HolderConjugate.mul_eq_add, surjective_cosetToCuspOrbit, NumberField.mixedEmbedding.span_latticeBasis, tsum_geometric_two', Height.AdmissibleAbsValues.mulSupport_finite, Real.arcsin_le_neg_pi_div_two, ProbabilityTheory.indepFun_iff_charFun_prod, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, ProbabilityTheory.IsRatStieltjesPoint.mono, WeakFEPair.hf_zero, RCLike.realLinearIsometryEquiv_symm_apply, convex_ball, ProbabilityTheory.Kernel.rnDerivAux_nonneg, Polynomial.Chebyshev.U_real_cos, real_inner_smul_right, HolderOnWith.holderOnWith_zero_of_bounded, Metric.continuousAt_iff', WithLp.prod_norm_eq_of_L1, Real.inv_sqrt_two_sub_one, ProbabilityTheory.IsCondKernelCDF.measurable, Asymptotics.isBigOWith_top, Circle.leftInverse_exp_arg, ContinuousLinearMap.hasTemperateGrowth, Complex.measurable_im, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, Seminorm.uniformContinuous, ProbabilityTheory.HasSubgaussianMGF.neg, HolderWith.comp_holderOnWith, UpperHalfPlane.pos_real_smul_injective, MeasureTheory.eLpNorm_le_of_ae_enorm_bound, infDist_smul₀, InformationTheory.klDiv_eq_integral_klFun, Orientation.oangle_sub_right_smul_rotation_pi_div_two, Real.toNNReal_eq_zero, ProbabilityTheory.IsKolmogorovProcess.q_pos, OrthonormalBasis.sum_sq_norm_inner_left, NNReal.rpow_add, CircleDeg1Lift.dist_pow_map_zero_mul_translationNumber_le, ArchimedeanClass.stdPart_monotoneOn, norm_mul₄_le', EuclideanGeometry.continuousAt_angle, EisensteinSeries.linear_inv_isBigO_right_add, Path.prod_coe, Urysohns.CU.approx_le_one, abs_real_inner_div_norm_mul_norm_le_one, LinearMap.isPositive_iff_complex, GaussianInt.toComplex_re_div, Real.Angle.sin_pi_div_two_sub, Real.sin_add_pi_div_two, bernstein_nonneg, VectorFourier.fourierSMulRight_apply, Real.contDiff_cos, inner_self_eq_norm_sq, tendsto_fib_div_fib_succ_atTop, Real.cosh_pos, Real.volume_pi_Ioo, MeasureTheory.measureReal_union_add_inter₀, CStarAlgebra.mem_Icc_algebraMap_iff_nnnorm_le, Real.rpow_neg_eq_inv_rpow, RCLike.continuous_ofReal, RCLike.exists_norm_mul_eq_self, Real.rpow_add_one, stereographic_neg_apply, Real.geom_goldConj_isSol_fibRec, Probability.cauchyMeasure_zero_scale, Metric.hasBasis_nhdsSet_cthickening, Real.sq_lt, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, NormedRing.inverse_add_norm_diff_second_order, MeasureTheory.Measure.addHaar_image_linearMap, continuousAt_gauge_zero, NumberField.mixedEmbedding.measurableSet_fundamentalCone, MeasureTheory.tendsto_ae_condExp, PiLp.dist_apply_le, Real.cos_sub_nat_mul_two_pi, BumpCovering.exists_finset_toPartitionOfUnity_eventuallyEq, Affine.Simplex.sOppSide_excenter_singleton_point, MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, Real.Angle.sin_add, RCLike.lipschitzWith_re, NumberField.mixedEmbedding.fundamentalCone.expMap_symm_apply, GromovHausdorff.eq_toGHSpace, ContinuousOn.isBigOWith_principal, Real.HolderConjugate.conjugate_eq, Real.binEntropy_one, CongruenceSubgroup.strictWidthInfty_Gamma1, NonarchAddGroupSeminorm.ext_iff, Seminorm.closedBall_smul, instIsRiemannianManifoldModelWithCornersSelfReal, PartitionOfUnity.locallyFinite_tsupport, Measurable.re, MeasureTheory.eLpNorm_const', RCLike.ofReal_pow, Real.stronglyMeasurable_sinc, OrthonormalBasis.det_adjustToOrientation, Cardinal.mk_Iic_real, NumberField.Units.dirichletUnitTheorem.unitLattice_inter_ball_finite, NumberField.mixedEmbedding.polarCoord_source, MeasureTheory.condExpL1CLM_indicatorConst, nnnorm_cfc_nnreal_lt, NormedAddGroupHom.bound, Real.isScalarTower, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, UpperHalfPlane.J_smul, Real.circleAverage_eq_circleAverage_zero_one, Asymptotics.isLittleO_norm_pow_norm_pow, Real.continuous_log', variationOnFromTo.eq_zero_iff_of_ge, Complex.orthonormalBasisOneI_repr_symm_apply, SmoothPartitionOfUnity.sum_nonneg, ProbabilityTheory.Kernel.tendsto_densityProcess_fst_atTop_univ_of_monotone, MeasureTheory.L1.nnnorm_Integral_le_one, irrational_sqrt_of_multiplicity_odd, Manifold.riemannianEDist_def, MeasureTheory.norm_charFun_le_one, Measurable.coe_nnreal_real, UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_center, NNReal.coe_two, Seminorm.coe_bot, hasDerivAt_circleMap, NNReal.coe_nsmul, unitInterval.le_one, Subgroup.instHasDetPlusMinusOneFinOfNatNatRealOfIsArithmetic, spectralNorm_one, curveIntegralFun_fun_zero, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_zero_of_antitone, Real.one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, EuclideanGeometry.oangle_homothety, Real.Angle.toReal_injective, GaussianInt.toComplex_re, MeasureTheory.ProbabilityMeasure.continuous_integral_boundedContinuousFunction, RCLike.ofReal_alg, MeasureTheory.integral_fun_norm_addHaar, Affine.Simplex.ExcenterExists.sOppSide_point_excenter_iff, MeasureTheory.setIntegral_ge_of_const_le, isScalarTower_sphere_sphere_closedBall, MeasureTheory.L1.integral_eq_norm_posPart_sub, signedDist_anticomm, Irrational.instDenselyOrderedSubtypeReal, ENNReal.ofReal_max, imaginaryPart_apply_coe, BumpCovering.locallyFinite_tsupport, Affine.Simplex.height_pos, Complex.UnitDisc.instSMulCommClass_closedBall_right, IsOpen.measure_eq_biSup_integral_continuous, real_inner_self_eq_norm_sq, PartitionOfUnity.continuous_finsum_smul, AkraBazziRecurrence.eventually_one_sub_smoothingFn_pos_real, Nat.realSqrt_lt_ratSqrt_add_inv_prec, PseudoMetricSpace.cobounded_sets, Real.ratCast_lt, Real.iteratedDeriv_even_cos, MeasureTheory.weightedSMul_smul, ContinuousLinearEquiv.norm_symm_pos, MeasureTheory.integral_continuousLinearMap_prod, EisensteinSeries.eisensteinSeries_SIF_apply, Metric.closedBall_zero', norm_deriv_le_of_lipschitz, Real.goldenConj_neg, segment_subset_closedBall_left, Real.continuousAt_rpow_of_ne, MeasureTheory.Lp.norm_const, ProbabilityTheory.Kernel.HasSubgaussianMGF.of_map, ProbabilityTheory.mgf_add_const, Real.zero_lt_one, TemperedDistribution.laplacian_eq_sum, tendsto_uniformity_iff_dist_tendsto_zero, Affine.Simplex.dist_circumcenter_eq_circumradius, curveIntegralFun_def', NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, Real.sinh_two_mul, Orientation.areaForm_comp_rightAngleRotation, NumberField.mixedEmbedding.continuous_norm, Real.sinhOrderIso_apply, IsMIntegralCurve.continuous, uniqueDiffOn_Icc_zero_one, MeasureTheory.SimpleFunc.norm_integral_le_integral_norm, Complex.cpow_inv_two_re, ValueDistribution.isBigO_characteristic_sub_characteristic_inv, totallyBounded_convexHull, MeasureTheory.lpNorm_nsmul, Real.one_le_pi_div_two, Real.ofDigits_nonneg, Real.cauchy_natCast, unitInterval.instIsProbabilityMeasureElemRealVolume, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, MeasureTheory.Measure.haar.chaar_self, modelWithCornersEuclideanHalfSpace_zero, IsStrictlyPositive.sqrt, NumberField.Units.dirichletUnitTheorem.logEmbedding_eq_zero_iff, ENNReal.lt_ofReal_iff_toReal_lt, UnitAddCircle.mem_approxAddOrderOf_iff, instProperSpaceReal, dist_self, IsUltrametricDist.norm_zsmul_le, ContinuousMultilinearMap.ratio_le_opNorm, ZSpan.fundamentalDomain_subset_parallelepiped, ContinuousLinearMap.norm_extendTo𝕜'_bound, Real.pi_gt_sqrtTwoAddSeries, CStarRing.norm_star_mul_self, SmoothBumpFunction.isClosed_symm_image_closedBall, Real.tendsto_exp_comp_atTop, Quaternion.normSq_exp, ProbabilityTheory.Fernique.logRatio_mul_normThreshold_add_one_le, MeasureTheory.AEStronglyMeasurable.re, Real.differentiableAt_arctan, comap_norm_atTop, isBounded_iff_forall_norm_le, ContinuousMultilinearMap.integral_apply, Matrix.PosSemidef.isUnit_sqrt_iff, ENNReal.toReal_pos, pi_norm_const_le', uniqueDiffWithinAt_Iio, NNReal.rpow_inv_rpow_self, spectralNorm_smul, Real.cosh_le_exp_half_sq, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, Real.measurable_arccos, Complex.im_balance, ArchimedeanClass.stdPart_neg, LinearIsometryEquiv.contDiffPointwiseHolderAt_left_comp, Complex.ofReal_expect, IsSelfAdjoint.im_eq_zero_of_mem_spectrum, EuclideanGeometry.cos_eq_neg_one_iff_angle_eq_pi, MeasureTheory.integral_comp, Affine.Simplex.sum_circumcenterWeightsWithCircumcenter, TemperedDistribution.instContinuousLineDeriv, RCLike.I_im, GroupNorm.groupNormClass, EisensteinSeries.r1_eq, NormedField.exists_lt_norm, MeasureTheory.GridLines.T_empty, AddGroupSeminorm.sup_apply, tsirelson_inequality, UpperHalfPlane.instIsIsometricSMulSpecialLinearGroupFinOfNatNatReal, Real.differentiableOn_negMulLog, MeasureTheory.average_union_mem_segment, Real.Gamma_ofNat_eq_factorial, UpperHalfPlane.denom_neg, Submonoid.coe_unitSphere, Complex.div_re, Real.convex_iff_isPreconnected, Complex.abs_arg_le_pi_div_two_iff, ProbabilityTheory.integrable_exp_mul_gaussianReal, hasGradientAt_iff_tendsto, unitInterval.symm_eq_zero, MulRingNorm.mulRingNormEquivAbsoluteValue_symm_apply, InformationTheory.convexOn_klFun, hasDerivAt_fourier, Real.logb_inv_base, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup, UniformConcaveOn.add, BoxIntegral.Box.monotone_upper, Real.arcsin_eq_zero_iff, Real.inv_logb_mul_base, NumberField.Units.regOfFamily_div_regOfFamily, OpenPartialHomeomorph.contDiff_univBall, AddGroupSeminorm.coe_le_coe, ProbabilityTheory.measurable_geometricPMFReal, closure_zero_eq, ProbabilityTheory.instIsProbabilityMeasureCondCDF, Circle.norm_coe, imaginaryPart_comp_subtype_selfAdjoint, NumberField.mixedEmbedding.polarSpaceCoord_symm_apply, spectrum.limsup_pow_nnnorm_pow_one_div_le_spectralRadius, stdSimplexHomeomorphUnitInterval_apply_coe, AddGroupSeminorm.coe_sSup_apply, SeparationQuotient.norm_liftNormedAddGroupHom_le, Complex.measurableEquivRealProd_symm_polarCoord_symm_apply, HurwitzZeta.completedHurwitzZetaOdd_neg, Besicovitch.ae_tendsto_measure_inter_div, SmoothBumpFunction.c_mem_support, Complex.UnitDisc.instIsScalarTower_closedBall, ArchimedeanClass.stdPart_sub_eq_right, Real.isFiniteMeasure_restrict_Icc, Hyperreal.IsSt.sub, Complex.volume_preserving_equiv_real_prod, Real.summable_one_div_nat_rpow, Real.ceil_exp_one_eq_three, Real.rpow_sub_one, EuclideanGeometry.Sphere.direction_orthRadius_le_iff, NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, MeasureTheory.integrable_comp_mul_left_iff, ProbabilityTheory.gaussianReal_map_mul_const, Metric.continuousWithinAt_iff, ContinuousLinearMap.IsPositive.re_inner_nonneg_left, Metric.thickening_ball, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_rclike_tendsto, Real.ofDigitsTerm_nonneg, Metric.sphere.instContinuousMul, Real.rightDeriv_mul_log, dist_add_dist_eq_iff, ProbabilityTheory.Kernel.integrable_density, nnnorm_cfc_nnreal_le, ZLattice.summable_norm_pow_inv, AkraBazziRecurrence.asympBound_def', Metric.mem_thickening_iff_infDist_lt, ZMod.LFunction_def_even, Metric.uniformity_basis_dist_le, IndiscreteTopology.norm_eq_zero', MeasureTheory.Measure.one_le_hausdorffMeasure_zero_of_nonempty, BoxIntegral.BoxAdditiveMap.toSMul_apply, ProbabilityTheory.IsGaussian.map_rotation_eq_self, AddGroupSeminormClass.toSeminormedAddGroup_norm_eq, LinearMap.toSpanSingleton_homothety, ProbabilityTheory.hasFiniteIntegral_prodMk_left, UpperHalfPlane.le_dist_coe, IsSelfAdjoint.norm_eq_max_norm_posPart_negPart, Real.ofCauchy_ratCast, Prod.norm_def, Real.continuousOn_sin, EuclideanGeometry.Sphere.IsTangentAt.mem_and_mem_iff_eq, ContinuousMap.HomotopyWith.extendProp, Real.isLittleO_const_log_atTop, Polynomial.gaussNorm_monomial, fourier_apply, ContinuousLinearMap.le_opNorm₂, Nat.roughNumbersUpTo_card_le', quotient_norm_mk_eq, Polynomial.Chebyshev.isMinOn_T_real, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, EuclideanGeometry.collinear_iff_eq_or_eq_or_sin_eq_zero, ProbabilityTheory.hasFiniteIntegral_comp_iff', circleMap_neg_radius, irrational_ratCast_div_iff, schnirelmannDensity_le_div, ContinuousLinearMap.norm_iteratedFDeriv_comp_left, Real.Angle.two_nsmul_toReal_eq_two_mul_add_two_pi, RCLike.wInner_const_right, ProbabilityTheory.covarianceOperator_inner, real_inner_self_nonpos, Real.goldenRatio_add_goldenConj, CongruenceSubgroup.finiteIndex_conjGL, WithLp.unitization_norm_def, Complex.HadamardThreeLines.diffContOnCl_interpStrip, ContinuousLinearMap.opNorm_mul_le, HasCompactMulSupport.exists_bound_of_continuous, Real.tan_nat_mul_pi, ContinuousMap.Homotopy.curry_apply, EuclideanGeometry.Sphere.IsDiameter.sbtw, Real.log_div_sqrt_antitoneOn, EuclideanSpace.norm_eq, irrational_natCast_sub_iff, ContinuousLinearMap.opNorm_subsingleton, mellin_eq_fourierIntegral, Asymptotics.IsBigO.exists_nonneg, DeltaGeneratedSpace.isOpen_iff, unitInterval.sigmoid_injective, Orientation.inner_rightAngleRotation_left, MeasureTheory.AEStronglyMeasurable.fourierPowSMulRight, WithSeminorms.continuous_seminorm, Height.mulHeight₁_nonneg, AffineSubspace.mem_perpBisector_iff_inner_eq_inner, Real.HolderTriple.inv_pos, CliffordAlgebraComplex.equiv_symm_apply, Real.cosh_add_sinh, ProbabilityTheory.iIndepFun_iff_charFunDual_pi, InnerProductGeometry.angle_eq_angle_add_angle_iff, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding_of_isReal, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, NormedField.tendsto_norm_inv_nhdsNE_zero_atTop, Topology.RelCWComplex.map_zero_mem_openCell, integral_cos_pow_three, MeasureTheory.SignedMeasure.measurable_rnDeriv, VitaliFamily.mem_filterAt_iff, MeasureTheory.stronglyMeasurable_llr, isScalarTower_sphere_sphere_ball, Real.isLittleO_exp_comp_exp_comp, IsUltrametricDist.algNormOfAlgEquiv_apply, ProbabilityTheory.variance_mul, Real.abs_cos_sub_cos_le, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_le_one, ProbabilityTheory.Kernel.condKernelUnitReal.instIsCondKernel, Complex.zero_lt_real, Complex.tanh_ofReal_im, EuclideanGeometry.Sphere.IsTangent.infDist_eq_radius, SchwartzMap.integral_sesq_fourierIntegral_eq, bernoulliFun_eval_zero, NNReal.coe_ofScientific, zero_mem_preCantorSet, AddGroupSeminorm.apply_one, Real.fourierIntegral_eq', EisensteinSeries.isBigO_linear_add_const_vec, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, AddCircle.norm_coe_eq_abs_iff, EReal.toReal_add, HurwitzZeta.oddKernel_neg, WithAbs.norm_eq_abv, Complex.frontier_setOf_le_re, ModularGroup.exists_one_half_le_im_smul, DirichletCharacter.LSeriesSummable_iff, MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd, Seminorm.le_def, MeasureTheory.integrable_withDensity_iff_integrable_smul, MeasureTheory.Measure.instSigmaFiniteElemRealIoiOfNatVolumeIoiPow, CStarModule.norm_sq_eq, Real.self_le_sinh_iff, isPathConnected_stdSimplex, Polynomial.Chebyshev.isLocalExtr_T_real_iff, InnerProductGeometry.angle_nonneg, norm_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, RCLike.ofNat_mul_im, Quaternion.im_exp, Complex.norm_natCast_cpow_of_pos, HasCompactSupport.exists_pos_le_norm, LiouvilleWith.int_mul, PiLp.antilipschitzWith_ofLp, MeasureTheory.condExpL1CLM_lpMeas, Module.Basis.coe_parallelepiped, ProbabilityTheory.IsRatCondKernelCDF.tendsto_atBot_zero, MeasureTheory.L1.SimpleFunc.negPart_toSimpleFunc, Real.arctan_inv_2_add_arctan_inv_3, NumberField.InfinitePlace.embedding_of_isReal_apply, HurwitzZeta.evenKernel_neg, Real.hasPDF_iff, Real.arctan_one, CFC.sqrt_sq, SmoothBumpCovering.exists_finset_toSmoothPartitionOfUnity_eventuallyEq, convex_halfSpace_re_ge, EuclideanGeometry.inversion_def, deriv_circleMap, CircleDeg1Lift.semiconj_of_group_action_of_forall_translationNumber_eq, InnerProductSpaceable.parallelogram_identity, Algebra.leftMulMatrix_complex, Affine.Simplex.inner_vsub_altitudeFoot_vsub_altitudeFoot_eq_zero, Real.analyticWithinAt_cos, MeasureTheory.Measure.haar.chaar_sup_eq, norm_le_norm_sub_add, Affine.Simplex.sum_excenterWeights_eq_one_iff, GromovHausdorff.ghDist_le_nonemptyCompacts_dist, self_subset_gauge_le_one, SchwartzMap.integral_bilinear_laplacian_right_eq_left, ExistsContDiffBumpBase.u_smooth, AddGroupSeminorm.add_le', CauSeq.tendsto_limit, Seminorm.comp_apply, ZLattice.covolume_eq_det_mul_measureReal, FormalMultilinearSeries.compAlongComposition_norm, Path.Homotopy.transReflReparamAux_zero, NonarchAddGroupSeminorm.apply_one, Complex.norm_div, Matrix.IsHermitian.spectrum_eq_image_range, isLittleO_rpow_exp_atTop, ExistsContDiffBumpBase.y_nonneg, AddCircle.measurePreserving_equivIoc, intervalIntegral.integral_comp_sub_mul, Quaternion.re_coeComplex, MeasureTheory.hasFiniteIntegral_norm_iff, Circle.argEquiv_symm_apply, BoundingSieve.weights_nonneg, MeasureTheory.Integrable.norm_integral_condDistrib_map, Metric.iUnion_inter_closedBall_nat, NumberField.mixedEmbedding.normAtAllPlaces_mixedEmbedding, ENNReal.zero_rpow_def, Real.tendsto_exp_atBot, ProbabilityTheory.condExpKernel_ae_eq_condExp, BoundedContinuousFunction.dist_zero_of_empty, AddCircle.toCircle_apply_mk, spectralNorm_nonneg, Real.binEntropy_eq_negMulLog_add_negMulLog_one_sub', HurwitzZeta.cosZeta_zero, homeomorphUnitSphereProd_apply_fst_coe, CFC.rpow_sqrt_nnreal, ProbabilityTheory.Kernel.isRatCondKernelCDF_density_Iic, RCLike.isCauSeq_im, Asymptotics.isBigO_norm_left, Real.Angle.two_nsmul_eq_pi_iff, InnerProductSpace.norm_sq_eq_re_inner, BoxIntegral.Box.splitLower_eq_bot, NumberField.mixedEmbedding.covolume_integerLattice, LipschitzWith.ae_differentiableAt, Real.nnnorm_abs, realPart_surjective, Orientation.kahler_apply_self, Complex.frontier_setOf_re_lt, MeasureTheory.MemLp.enorm_rpow, Metric.nonempty_closedBall, Affine.Simplex.dist_circumcenter_eq_circumradius', Real.differentiableWithinAt_arcsin_Iic, Metric.mem_of_closed', NNReal.rpow_sub_one, signedDist_triangle_right, Polynomial.hermite_eq_deriv_gaussian, isCompact_closedAbsConvexHull_of_totallyBounded, Asymptotics.isBigOWith_zero', Real.one_half_lt_eulerMascheroniSeq_six, Real.exp_half, Real.negMulLog_one, Orientation.inner_smul_rotation_pi_div_two_right, formalMultilinearSeries_geometric_apply_norm, ProbabilityTheory.hasFiniteIntegral_comp_iff, ZSpan.instDiscreteTopologySubtypeMemSubmoduleIntSpanRangeCoeBasisRealOfFinite, NonarchAddGroupSeminorm.zero_apply, Real.neg_one_le_sinc, SingularManifold.instBoundarylessManifoldRealM, EuclideanGeometry.Sphere.IsIntTangentAt.wbtw, EReal.tendsto_coe, Unitary.spectrum_subset_slitPlane_iff_norm_lt_two, Complex.conjCLE_nnorm, Path.Homotopy.cast_apply, HasStrictDerivAt.complexToReal_fderiv', contMDiffWithinAt_comp_projIcc_iff, Orientation.inner_mul_areaForm_sub', hasFDerivAt_polarCoord_symm, NormedSpace.norm_expSeries_summable', continuous_norm', Metric.isBounded_image_iff, Real.sin_pi_over_two_pow_succ, Real.continuous_exp, trapezoidal_integral_one, Asymptotics.isLittleO_const_left_of_ne, EuclideanGeometry.Sphere.IsTangentAt.le_orthRadius, Asymptotics.isLittleO_norm_left, Dilation.mapsTo_ball, IsBoundedSMul.dist_pair_smul', MeasureTheory.eLpNorm_nnreal_eq_lintegral, NumberField.mixedEmbedding.mixedSpaceToRealMixedSpace_apply, MeasureTheory.measureReal_ennreal_smul_apply, IsometryEquiv.coe_toRealLinearIsometryEquivOfMapZero, ProbabilityTheory.variance_nonneg, Real.bijOn_sin, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, Real.toNNReal_lt_ofNat, Polynomial.supNorm_def', ZSpan.isAddFundamentalDomain, CircleDeg1Lift.coe_toOrderIso, BoxIntegral.Box.mk'_eq_bot, CircleDeg1Lift.translate_zpow, EReal.coe_nonneg, Real.cosh_bijOn, NormedSpace.norm_expSeries_div_summable_of_mem_ball, RCLike.I_to_real, RingSeminorm.toFun_eq_coe, dist_homothety_center, EuclideanGeometry.sin_angle_mul_dist_eq_sin_angle_mul_dist, EReal.toReal_image_Ioo_bot_zero, intervalIntegral.intervalIntegrable_exp, IntervalIntegrable.norm, Real.sign_neg, Complex.hasSum_re, MeasureTheory.SignedMeasure.toComplexMeasure_apply_re, MeasureTheory.weightedSMul_union, MeasureTheory.average_pair, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, Real.deriv_arcsin, irrational_ratCast_add_iff, Complex.isBigO_im_sub_im, Metric.exists_isCompact_closedBall, gronwallBound_continuous_ε, Real.div_sqrt, BoxIntegral.Box.coe_splitLower, Metric.unitSphere.coe_inv, abs_signedDist_eq_dist_iff_vsub_mem_span, InnerProductSpace.innerSL_norm, MeasureTheory.uniformIntegrable_average, Quaternion.coeComplex_coe, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_densityProcess_limitProcess, BumpCovering.toFun_eq_coe, NNReal.rpow_one_sub', SchwartzMap.le_seminorm, NNReal.rpow_intCast, ContinuousMap.toNNReal_mul_add_neg_mul_add_mul_neg_eq, LipschitzWith.norm_sub_le, Real.bijOn_cos, AbsolutelyContinuousOnInterval.biUnion_uIoc_subset_of_mem_disjWithin, circleMap_zero_mul, Real.cos_sq', Real.tan_add_int_mul_pi, GenLoop.toLoop_apply_coe, tendsto_gauge_nhds_zero_nhdsGE, UniformConvexSpace.toStrictConvexSpace, AmpleSet.image_iff, SchwartzMap.eLpNorm_le_seminorm, EuclideanGeometry.Concyclic.Coplanar, Affine.Simplex.ExcenterExists.isTangentAt_exsphere_iff_eq_touchpoint, Real.qaryEntropy_strictMonoOn, NumberField.Units.instDiscrete_unitLattice, UpperHalfPlane.petersson_slash_SL, Real.tan_pi_div_six, Finset.norm_prod_le', ENNReal.toReal_le_coe_of_le_coe, Orientation.kahler_rotation_left', MeasureTheory.Measure.addHaar_affineSubspace, NumberField.mixedEmbedding.fundamentalCone.closure_paramSet, Irrational.ratCast_add, Real.differentiable_sin, MeasureTheory.setIntegral_rnDeriv_smul', NNReal.rpow_left_injective, RCLike.hasSum_re, ContinuousMultilinearMap.norm_ofSubsingleton_id_le, norm_prod, ArchimedeanClass.stdPart_natCast, Real.volume_Ioc, NumberField.mixedEmbedding.euclidean.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, ProbabilityTheory.Kernel.integral_density, CliffordAlgebraComplex.toComplex_ι, LipschitzOnWith.norm_div_le, Stirling.stirlingSeq'_bounded_by_pos_constant, irrational_sub_intCast_iff, Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_pair, WithLp.prod_dist_eq_of_L1, Affine.Simplex.pointsWithCircumcenter_point, convex_halfSpace_im_ge, ContinuousLinearMap.sSup_unit_ball_eq_nnnorm, NormedAddGroupHom.le_opNorm, Real.strictMonoOn_arcsin, WithLp.prod_dist_eq_card, HasFPowerSeriesOnBall.uniform_geometric_approx', tendsto_dist_left_cocompact_atTop, Real.one_sub_lt_exp_neg, intervalIntegral.smul_integral_comp_mul_left, Real.arccos_lt_pi, Orientation.oangle_eq_zero_or_eq_pi_iff_not_linearIndependent, IsBoundedLinearMap.bound, Real.continuous_arctan, Hyperreal.coe_eq_zero, ContinuousLinearMap.extendTo𝕜_apply, AkraBazziRecurrence.isEquivalent_one_sub_smoothingFn_one, Real.natLog_le_logb, Complex.ofReal_eq_zero, rotation_trans, CStarAlgebra.rpow_neg_one_le_rpow_neg_one, Valued.toNormedField.one_lt_norm_iff, Real.Angle.sign_two_zsmul_eq_neg_sign_iff, Real.eulerMascheroniConstant_eq_neg_deriv, MeasureTheory.MeasuredSets.lipschitzWith_measureReal, Metric.PiNatEmbed.continuous_distDenseSeq, Real.arsinh_neg_iff, not_sameRay_iff_abs_lt_norm_sub, EuclideanSpace.volume_ball_fin_three, Real.not_differentiableAt_inv_log_zero, Real.sigmoid_monotone, ProbabilityTheory.IsGaussian.integral_dual, NumberField.mixedEmbedding.convexBodyLT_neg_mem, Affine.Simplex.mongePoint_reindex, UpperHalfPlane.le_dist_iff_le_dist_coe_center, Real.arctan_inv_sqrt_three, irrational_sub_ratCast_iff, LipschitzWith.norm_le_mul, uniformConcaveOn_zero, Affine.Triangle.affineSpan_pair_eq_orthRadius_insphere, instNoncompactSpaceReal, Complex.linearEquiv_det_conjAe, Real.goldenRatio_pos, Orientation.abs_areaForm_le, EuclideanGeometry.cospherical_or_collinear_of_two_zsmul_oangle_eq, Complex.ofReal_zero, Affine.Simplex.ExcenterExists.sign_touchpointWeights, Real.deriv_mul_log, ZLattice.exists_forall_abs_repr_le_norm, intervalIntegrable_const_iff, ArithmeticFunction.log_mul_moebius_eq_vonMangoldt, Metric.le_glueDist_inl_inr, BoxIntegral.Prepartition.splitMany_empty, IsOpen.exists_msmooth_support_eq_aux, SeminormedAddCommGroup.mem_closure_iff, NumberField.mixedEmbedding.polarCoord_target, Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter, PadicInt.norm_le_pow_iff_norm_lt_pow_add_one, EuclideanGeometry.Sphere.dist_div_cos_oangle_center_eq_two_mul_radius, Complex.continuousAt_arg_coe_angle, EuclideanGeometry.angle_homothety, AddCircle.denseRange_zsmul_coe_iff, isScalarTower_sphere_closedBall_ball, EuclideanGeometry.Sphere.IsDiameter.left_eq_right_iff, MeasureTheory.Measure.addHaar_image_continuousLinearEquiv, Set.Nontrivial.infsep_anti, ContinuousLinearMap.norm_single, CauSeq.cauchySeq, ContinuousMapZero.toNNReal_mul_add_neg_mul_add_mul_neg_eq, MeasureTheory.integral_rnDeriv_mul_log, EisensteinSeries.r_mul_max_le, Real.cos_sub_int_mul_pi, Real.logDeriv_exp, bernstein.z_zero, SmoothBumpFunction.eventuallyEq_of_mem_source, ContinuousLinearMap.norm_extendTo𝕜', Int.dist_cast_real, InnerProductGeometry.angle_smul_smul, integral_log_sin_zero_pi, MeasureTheory.Measure.hausdorffMeasure_le_liminf_tsum, Valued.norm_add_le, GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I', Cardinal.mk_univ_real, Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT, Asymptotics.bound_of_isBigO_nat_atTop, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMapBasis, ContinuousMapZero.toContinuousMapHom_toNNReal, ModularForm.SL_slash_def, AddChar.norm_apply, Path.Homotopy.coeFn_injective, cauchySeq_iff_le_tendsto_0, IsUltrametricDist.norm_pow_le, Valued.isNonarchimedean_norm, Asymptotics.IsBigO.bound, NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isReal, Complex.div_ofReal, convex_halfSpace_re_lt, NumberField.count_multisetInfinitePlace_eq_mult, Affine.Simplex.sign_touchpointWeights_singleton_pos, EReal.preimage_coe_Ioo_bot, Affine.Simplex.altitude_reindex, MeasureTheory.L2.inner_indicatorConstLp_eq_setIntegral_inner, ModelWithCorners.convex_range, Quaternion.summable_coe, Complex.instStarModuleReal, MeasureTheory.Integrable.integral_norm_condDistrib, ENNReal.tendsto_ofReal_atTop, PadicInt.norm_intCast_eq_one_iff, NumberField.mixedEmbedding.euclidean.instIsZLatticeRealMixedSpaceIntegerLattice, IsUltrametricDist.exists_norm_finset_sum_le, NNReal.coe_inv, signedDist_neg, CStarAlgebra.mul_star_le_algebraMap_norm_sq, norm_lineDeriv_le_of_lipschitzOn, Delone.DeloneSet.packingRadius_lt_dist_of_mem_ne, ContDiffBump.integral_normed_smul, ProbabilityTheory.IsRatCondKernelCDFAux.integrable, exists_contMDiff_zero_iff_one_iff_of_isClosed, hasSum_geometric_two', Complex.ball_one_subset_slitPlane, ProbabilityTheory.instIsGaussianMapHAdd_1, Real.arsinh_eq_zero_iff, Complex.restrictScalars_toSpanSingleton, ProbabilityTheory.measure_cdf, Orientation.oangle_sign_smul_right, Orientation.normSq_kahler, Real.Angle.toReal_neg_iff_sign_neg, AddGroupSeminorm.coe_sSup_apply', ProbabilityTheory.IsCondKernelCDF.integrable, Complex.tendsto_one_add_div_cpow_exp, Padic.isAbsoluteValue, tendsto_norm_one, LipschitzWith.dist_right, norm_le_mul_norm_add', Real.log_natCast_nonneg, NormedDivisionRing.unitClosedBall_eq_univ_of_discrete, ENNReal.coe_mul_rpow, AkraBazziRecurrence.eventually_one_sub_smoothingFn_nonneg, unitInterval.image_coe_preimage_symm, Complex.closure_setOf_re_lt, Real.Angle.abs_cos_eq_of_two_zsmul_eq, Real.arcsin_lt_zero, ENNReal.mul_rpow_of_ne_top, WithLp.prod_norm_eq_sup, ProbabilityTheory.condExpKernel_ae_eq_trim_condExp, integral_inv_sq_add_sq, Real.rpow_two, Real.sigmoid_le_one, Complex.normSq_inv, ProbabilityTheory.IndepFun.charFunDual_map_add_eq_mul, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, QuotientAddGroup.norm_lift_apply_le, tendsto_iff_norm_div_tendsto_zero, ProbabilityTheory.HasCondSubgaussianMGF.memLp_exp_mul, ENNReal.orderIsoUnitIntervalBirational_apply_coe, Real.sigmoid_le_iff, NNReal.smul_def, Real.sinh_lt_sinh, MeasureTheory.nnnorm_indicatorConstLp_le, locallyFinsuppWithin.logCounting_divisor, Height.logHeight_nonneg, ProbabilityTheory.paretoPDF_eq, gauge_unit_ball, eventually_ball_subset, ProbabilityTheory.setIntegral_preCDF_fst, EReal.coe_injective, isMIntegralCurve_iff_isMIntegralCurveOn, ENNReal.ofNat_lt_ofReal, Real.pi_lt_d2, Real.differentiableAt_tan, Real.sin_div_le_inv_abs, CFC.rpow_nonneg, ContinuousAlternatingMap.norm_image_sub_le', Real.differentiable_cosh, PiNat.dist_eq_of_ne, norm_le_pi_norm', GromovHausdorff.hausdorffDist_optimal_le_HD, NumberField.InfinitePlace.Completion.extensionEmbedding_coe, NumberField.mixedEmbedding.negAt_symm, IsSelfAdjoint.instIsometricContinuousFunctionalCalculus, Stirling.log_stirlingSeq_bounded_by_constant, Real.isFiniteMeasure_restrict_Ico, MeasureTheory.setLIntegral_tilted, PadicInt.norm_le_pow_iff_le_valuation, irrational_div_ratCast_iff, Real.fromBinary_surjective, Real.sqrt_pos, EuclideanGeometry.mul_dist_add_mul_dist_eq_mul_dist_of_cospherical, MeasureTheory.count_real_singleton', fourierSubalgebra_coe, NumberField.InfinitePlace.denseRange_algebraMap_pi, Complex.norm_ofNat, MeasureTheory.lpNorm_le_lpNorm_add_lpNorm_sub, AddGroupNorm.apply_one, Irrational.instNoMinOrderSubtypeReal, ODE.FunSpace.exists_forall_closedBall_funSpace_dist_le_mul, Real.eulerMascheroniSeq_lt_eulerMascheroniSeq', ProbabilityTheory.integrable_compProd_iff, CircleDeg1Lift.map_add_int, Polynomial.toAddCircle_monomial_eq_smul_fourier, Metric.dist_le_diam_of_mem, Complex.inner, sameRay_iff_inv_norm_smul_eq, RCLike.instStarModuleReal, imaginaryPart_surjective, Set.Finite.infsep_zero_iff_subsingleton, Real.Angle.abs_toReal_add_abs_toReal_eq_pi_of_two_zsmul_add_eq_zero_of_sign_eq, CompletelyRegularSpace.completely_regular, ENNReal.ofReal_pos, NumberField.mixedEmbedding.fundamentalCone.mixedEmbedding_preimageOfMemIntegerSet, preCantorSet_succ, cfcHom_nnreal_eq_restrict, Real.one_lt_cosh, Finset.coe_infsep_of_offDiag_empty, ENNReal.toReal_top_mul, mellin_comp_inv, BoxIntegral.integral_smul, GenLoop.loopHomeo_symm_apply, Matrix.IsHermitian.spectral_theorem, ContractingWith.dist_inequality, Real.sin_sub_int_mul_pi, norm_sub_sub_norm_sub_le_norm_sub, NumberField.mixedEmbedding.fundamentalCone.normAtPlace_pos_of_mem, Complex.isTheta_ofReal_right, Complex.polarCoord_source, Module.Basis.norm_nonneg, Polynomial.sum_sq_norm_coeff_eq_circleAverage, Metric.isOpen_iff, Real.one_sub_goldenConj, ProbabilityTheory.IdentDistrib.norm, ContDiffBump.contDiff_normed, Euclidean.nhds_basis_ball, ENNReal.toReal_pos_iff_ne_top, ProbabilityTheory.integral_tilted_mul_eq_mgf, Real.ofCauchy_intCast, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_paramSet_exp, MeasureTheory.integral_simpleFunc_larger_space, Complex.coe_imAddGroupHom, CircleDeg1Lift.le_ceil_map_map_zero, ValueDistribution.logCounting_zero_mul_eventually_le, Tactic.ComputeAsymptotics.Majorized.smul, AnalyticAt.harmonicAt_re, Polynomial.mahlerMeasure_X_sub_C, RCLike.mul_im_I_ax, ContDiffBump.apply, isProperMap_dist, EMetric.exists_continuous_real_forall_closedBall_subset, CircleDeg1Lift.coe_one, BoundedContinuousFunction.lintegral_of_real_lt_top, MeasureTheory.L1.SimpleFunc.posPart_toSimpleFunc, intervalIntegral.intervalIntegrable_const, Orientation.oangle_sign_add_smul_left, MeasureTheory.MemLp.norm_rpow_div, NNReal.rpow_add_intCast, NumberField.mixedEmbedding.polarCoord_symm_eq, NormedAddGroupHom.bounds_bddBelow, ProbabilityTheory.iCondIndepSets_iff, MeasureTheory.Measure.IicSnd_le_fst, tsum_geometric_inv_two_ge, Real.tendsto_tan_pi_div_two, upperHemicontinuous_spectrum_nnreal, Diffeology.isPlot_iff_contDiff, Matrix.PosSemidef.sq_sqrt, Real.one_le_toNNReal, signedDist_vsub_self_rev, BumpCovering.ind_apply, InformationTheory.toReal_klDiv_of_measure_eq, Real.probChar_apply', Real.rpow_inv_log_le_exp_one, norm_algebraMap, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangent, UpperHalfPlane.coe_J_smul, Orientation.neg_rotation_pi_div_two, approxAddOrderOf.image_nsmul_subset, EReal.coe_strictMono, Real.exists_rat_abs_sub_le_and_den_le, BoundedContinuousFunction.dist_le_iff_of_nonempty, RCLike.norm_natCast, Tactic.ComputeAsymptotics.Majorized.zero, coord_norm', ProperCone.relative_hyperplane_separation, PadicInt.norm_le_pow_iff_mem_span_pow, Real.tendsto_log_comp_add_sub_log, contDiffAt_inner, Int.Matrix.one_le_norm_A_of_ne_zero, Complex.normSq_div, InnerProductGeometry.norm_sub_eq_add_norm_of_angle_eq_pi, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, BoxIntegral.Box.exists_seq_mono_tendsto, AddGroupSeminorm.comp_apply, OrthonormalBasis.measurePreserving_repr_symm, Real.measurable_arcsin, Diffeology.isPlot_iff_dSmooth, BoxIntegral.IntegrationParams.RCond.min, ZLattice.normBound_pos, bernoulliFun_zero, ContinuousMap.HomotopyWith.ext_iff, Hyperreal.coe_zero, Real.sSup_univ, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIntegerLattice, Real.abs_sin_lt_abs, Measurable.infDist, MeasureTheory.JordanDecomposition.coe_smul, MeasureTheory.ofReal_integral_norm_eq_lintegral_enorm, eventually_enorm_mfderiv_extChartAt_lt, MeasureTheory.exp_neg_llr, enorm_tangentSpace_vectorSpace, Hyperreal.coe_min, integral_exp_neg_Ioi, NNReal.rpow_eq_rpow_iff, Real.volume_eball, Real.ceil_pi_eq_four, FormalMultilinearSeries.norm_mul_pow_le_mul_pow_of_lt_radius, ProbabilityTheory.IsKolmogorovProcess.p_pos, Tactic.ComputeAsymptotics.WellFormedBasis.eventually_pos, ContinuousMap.norm_lt_iff_of_nonempty, UpperHalfPlane.dist_center_dist, Asymptotics.IsBigOWith.add, Real.surjOn_log, NNReal.coe_sub_def, Complex.normSq_ofReal, signedDist_linear_apply, PreInnerProductSpace.Core.re_inner_nonneg, Complex.isBigO_ofReal_left, UpperHalfPlane.isZeroAtImInfty_iff, Real.cos_pi_div_thirty_two, UnitAddCircle.measurePreserving_mk, Prod.norm_mk, Real.isBoundedSMul, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, Real.binEntropy_one_sub, Orientation.rotation_eq_matrix_toLin, MeasureTheory.AEStronglyMeasurable.fourierSMulRight, Real.hasDerivAt_log, MeasureTheory.addHaarMeasure_eq_volume_pi, oneTangentSpaceIcc_def, smul_unitBall, Padic.norm_le_one_iff_val_nonneg, intervalIntegral.integral_const_of_cdf, Padic.norm_intCast_lt_one_iff, RCLike.ofReal_intCast, Complex.isHomeomorphicTrivialFiberBundle_re, Affine.Simplex.circumradius_pos, Real.cosh_lt_cosh, EuclideanGeometry.mul_dist_le_mul_dist_add_mul_dist, Real.cosh_sub, bernoulliFun_one, Metric.closedBall_eq_empty, Orientation.inner_rightAngleRotation_swap, MulRingNorm.toFun_eq_coe, NumberField.Units.abs_det_eq_abs_det, Real.continuous_inv, Path.continuous, MeasureTheory.tendstoInMeasure_iff_measureReal_enorm, NumberField.mixedEmbedding.polarSpaceCoord_target', MeasureTheory.exp_neg_llr', intervalIntegral.integral_const', Real.volume_le_diam, Complex.im_comp_balance, ProbabilityTheory.cgf_zero', EuclideanQuadrant.ext_iff, Real.abs_circleAverage_le_circleAverage_abs, RCLike.normSq_eq_def', AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_zero_or_pos_or_neg, Stirling.log_stirlingSeq'_antitone, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isReal, MulRingNorm.mulRingNormEquivAbsoluteValue_apply, RCLike.ofReal_eq_zero, CircleDeg1Lift.commute_int_add, IccRightChart_extend_top_mem_frontier, Metric.unitSphere.coe_zpow, integral_comp_neg_Iic, MeasureTheory.ofReal_setIntegral_one, CongruenceSubgroup.strictPeriods_Gamma1, BoxIntegral.unitPartition.index_apply, Asymptotics.IsTheta.tendsto_norm_atTop_iff, rotationOf_coe, Real.nndist_eq, CompactlySupportedContinuousMap.toReal_add, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_eq, cantorSet_subset_unitInterval, Algebra.norm_complex_apply, Real.neg_one_le_cos, NumberField.mixedEmbedding.convexBodyLT'_volume, Real.sin_sq_le_sq, PadicInt.norm_natCast_zmodRepr_eq, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_Iic, Real.goldenConj_sq, ProbabilityTheory.moment_zero_measure, StrongDual.norm_toLpₗ_le, ContDiffMapSupportedIn.iteratedFDeriv_zero_on_compl, Path.source_mem_range, Orientation.oangle_sub_left_smul_rotation_pi_div_two, Real.sin_sq_le_one, tangentConeAt_real_subset_isRCLikeNormedField, ProperCone.innerDual_insert, ProbabilityTheory.IsCondKernelCDF.tendsto_atBot_zero, ENNReal.toReal_prod, Module.Basis.parallelepiped_eq_map, selfAdjoint.realPart_coe, ContinuousMap.HomotopyLike.map_one_left, range_cfc_nnreal, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_eq_one_iff, Real.sinh_sub_cosh, ContDiffMapSupportedIn.norm_apply_le_seminorm, InnerProductSpace.gramSchmidtNormed_unit_length, ProbabilityTheory.Kernel.HasSubgaussianMGF.zero, Complex.norm_def, integral_withDensity_eq_integral_toReal_smul, Real.volume_real_interval, Real.Angle.two_zsmul_toReal_eq_two_mul_add_two_pi, ProbabilityTheory.HasSubgaussianMGF.cgf_le, AEMeasurable.carg, ZLattice.covolume.tendsto_card_div_pow', Real.binEntropy_eq_log_two, RCLike.re_mul_ofReal, Path.neg_apply, SmoothPartitionOfUnity.sum_eq_one, Complex.UnitDisc.im_zero, ProbabilityTheory.cgf_const', NumberField.InfinitePlace.isometry_embedding_of_isReal, Complex.isBigO_comp_ofReal_nhds_ne, Real.HolderConjugate.inv_add_inv_eq_one, isCauSeq_iff_cauchySeq, Path.target_mem_range, SchwartzMap.hasDerivAt, EReal.preimage_coe_Ico_top, MeasureTheory.toReal_laverage, Real.exp_multiset_sum, UpperHalfPlane.dist_le_dist_coe_div_sqrt, MeasureTheory.tendsto_eLpNorm_condExp, AkraBazziRecurrence.growsPolynomially_one_add_smoothingFn, OnePoint.IsBoundedAt.smul_iff, exists_continuous_zero_one_of_isCompact, GroupNorm.coe_add, Seminorm.inf_apply, Asymptotics.isBigO_one_nat_atTop_iff, PiLp.dist_sq_eq_of_L2, ContDiffBump.continuous, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_or_eq_zero, Polynomial.Chebyshev.isMaxOn_T_real, ContinuousLinearMap.instNonnegSpectrumClassRealId, MeasureTheory.eLpNorm_one_condExp_le_eLpNorm, NumberField.ComplexEmbedding.IsReal.coe_embedding_apply, Affine.Simplex.incenter_eq_affineCombination, LiouvilleWith.mul_rat_iff, Complex.abs_im_div_norm_le_one, NNReal.mk_zero, Complex.norm_int_of_nonneg, LinearMap.mem_polar_singleton, integral_log, Real.exp_le_exp, tendsto_norm_comp_cofinite_atTop_of_isClosedEmbedding', signedDist_self, MeasureTheory.MemLp.norm, comap_norm_nhds_one, circleMap_zero_div, QuotientAddGroup.norm_mk_eq_zero, CuspFormClass.exists_bound, Real.ofCauchy_div, CFC.rpow_add, Real.volume_real_Icc, MeasureTheory.L1.norm_integral_le, Unitization.nnreal_cfcₙ_eq_cfc_inr, hasDerivAtFilter_iff_tendsto, ProperCone.dual_flip_dual, RCLike.ofRealCLM_norm, integral_sqrt_one_sub_sq, NonarchAddGroupSeminorm.add_bddBelow_range_add, unitInterval.tendsto_sigmoid_atTop, integrable_inv_one_add_sq, Complex.IsExpCmpFilter.isLittleO_log_norm_re, Real.strictMonoOn_arcosh, CStarModule.inner_smul_left_real, Real.rank_rat_real, ENNReal.tsum_coe_ne_top_iff_summable_coe, Set.infsep_singleton, InnerProductSpace.HarmonicOnNhd.const_smul, circleAverage_log_norm_add_const_eq_posLog, Complex.UnitDisc.coe_smul_closedBall, Complex.norm_natCast_cpow_pos_of_pos, ProbabilityTheory.gaussianReal_map_sub_const, MeasureTheory.setIntegral_indicatorConstLp, signedDist_vsub_self, Archimedean.ratLt'_nonempty, Real.Gamma_zero, isBoundedLinearMap_iff, spectralAlgNorm_one, irrational_ratCast_sub_iff, EuclideanGeometry.inversion_mul, Complex.re_le_norm, EReal.tendsto_coe_nhds_bot_iff, Real.cos_nat_mul_pi_sub, lp.norm_zero, UpperHalfPlane.pos_real_re, Subgroup.strictWidthInfty_nonneg, PathConnectedSpace.exists_path_through_family, MeasureTheory.SignedMeasure.rnDeriv_smul, ContDiffBump.contDiffAt, UpperHalfPlane.IsZeroAtImInfty.zero_at_infty_comp_ofComplex, ContinuousMap.realToNNReal_apply, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, ProbabilityTheory.isGaussian_conv, MeasureTheory.sum_measureReal_preimage_singleton, Metric.unitClosedBall.coe_eq_zero, Complex.norm_add_mul_I, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_continuousOn, Polynomial.Chebyshev.rootMultiplicity_U_real, MeasureTheory.hausdorffMeasure_smul_right_image, NNReal.convex_iff, instIsUniformAddGroupReal, signedDist_smul, EReal.tendsto_coe_atBot, ENNReal.tendsto_toReal_zero_iff, Metric.diam_singleton, RCLike.im_tsum, ENNReal.ofReal_le_coe, TemperedDistribution.fourierTransform_apply, ContinuousLinearMap.opNorm_zero, Orientation.oangle_add_right_smul_rotation_pi_div_two, ProbabilityTheory.gaussianPDFReal_inv_mul, variationOnFromTo.add, not_sameRay_iff_norm_add_lt, StieltjesFunction.measure_Icc, Real.continuous_cos, NNReal.coe_expect, Complex.equivRealProdAddHom_apply, Real.hasStrictDerivAt_arctan, one_le_norm_one, ContinuousMultilinearMap.norm_iteratedFDeriv_le, ENNReal.lintegral_mul_le_Lp_mul_Lq, Complex.interior_setOf_re_le, LipschitzOnWith.coordinate, Quaternion.tsum_coe, Complex.abs_re_le_norm, Orientation.inner_smul_rotation_pi_div_two_left, InformationTheory.klFun_zero, Real.surjOn_sin, CFC.abs_ofNat, unitInterval.symm_zero, Real.dimH_univ_pi, ProbabilityTheory.compProd_toKernel, BoxIntegral.hasIntegral_const, ZLattice.volume_image_eq_volume_div_covolume, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, Real.rpow_left_injOn, Real.sin_pi_div_thirty_two, Real.map_linearMap_volume_pi_eq_smul_volume_pi, Circle.exp_zero, NNReal.rpow_add_one, LipschitzOnWith.iff_le_add_mul, Height.logHeight₁_zpow, CStarModule.norm_eq_csSup, Complex.arg_neg_iff, Int.dist_eq, CFC.negPart_one, intervalIntegral.inv_mul_integral_comp_div_sub, RCLike.norm_re_le_norm, BoxIntegral.Box.diam_Icc_le_of_distortion_le, setIntegral_withDensity_eq_setIntegral_smul, Real.sqrtTwoAddSeries_one, Affine.Simplex.sOppSide_point_excenter_singleton, ProbabilityTheory.poissonPMFReal_pos, SlashInvariantForm.coe_trace, GroupNorm.apply_one, isConformalMap_complex_linear_conj, Real.arctan_le_arctan_iff, TendstoUniformlyOn.im, Real.neg_pi_div_two_lt_arcsin, ProbabilityTheory.HasSubgaussianMGF.integrableExpSet_eq_univ, lipschitzWith_iff_dist_le_mul, Euclidean.closedBall_eq_preimage, integral_pair, mellin_comp_rpow, tendsto_norm', re_inner_self_pos, Quaternion.continuous_im, GroupNorm.add_apply, EReal.toReal_bot, ArithmeticFunction.vonMangoldt.residueClass_nonneg, AffineSubspace.mem_perpBisector_iff_dist_eq', Matrix.PosSemidef.inv_sqrt, ContinuousMultilinearMap.norm_iteratedFDeriv_le', uniqueDiffOn_Iio, MeasureTheory.Measure.haar.chaar_sup_le, MulAlgebraNormClass.map_smul_eq_mul, Rat.not_irrational, AffineSubspace.isPreconnected_setOf_wSameSide, ProbabilityTheory.IsMeasurableRatCDF.measurable_stieltjesFunction, NumberField.mixedEmbedding.logMap_unit_smul, convex_RCLike_iff_convex_real, spectralAlgNorm_extends, Chebyshev.theta_eq_sum_Icc, Metric.frontier_thickening_disjoint, Complex.div_ofNat_re, Mathlib.Meta.Positivity.nnreal_coe_pos, ProbabilityTheory.memLp_id_gaussianReal, Valued.integer.norm_unit, Real.le_toNNReal_iff_coe_le', Set.infsep_pair_le_toReal_inf, Real.cos_eq_two_mul_tan_half_div_one_sub_tan_half_sq, Asymptotics.isBigO_cofinite_iff, Matrix.linfty_opNorm_mulVec, intervalIntegral.smul_integral_comp_mul_add, ProbabilityTheory.Fernique.logRatio_pos, Real.iteratedDeriv_odd_cosh, Matrix.finite_real_spectrum, Complex.tendsto_norm_tan_of_cos_eq_zero, InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_fst_ofIsReal, Affine.Simplex.ninePointCircle_center_mem_affineSpan, dist_lt_coe, AddCircle.norm_neg_period, SmoothBumpCovering.embeddingPiTangent_injOn, MeasureTheory.memLp_norm_rpow_iff, Real.Angle.continuous_coe, Complex.measurableEquivPi_symm_apply, AddCircle.compactSpace, ContinuousAffineMap.norm_image_zero_le, ValueDistribution.characteristic_pow_top, WithLp.prod_norm_eq_card, Real.sin_pi_div_six, EulerSine.integral_cos_pow_eq, Real.abs_mulExpNegMulSq_one_le_one, exists_dual_vector', MeasureTheory.SignedMeasure.totalVariation_neg, BoxIntegral.Prepartition.splitMany_insert, IsCompact.exists_bound_of_continuousOn, ENNReal.natCast_lt_ofReal, ContinuousMapZero.toNNReal_add_add_neg_add_neg_eq, AddCircle.ergodic_zsmul, Orientation.kahler_rightAngleRotation_left, Real.analyticOn_sin, NumberField.InfinitePlace.Completion.bijective_extensionEmbeddingOfIsReal, NormedAddGroupHom.ofLipschitz_norm_le, Real.hasDerivAt_mulExpNegMulSq, LSeriesSummable_one_iff, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, Real.tendstoLocallyUniformlyOn_rpow_sub_one_log, GroupNorm.ext_iff, Real.sqrt_zero, SchwartzMap.tsupport_smulLeftCLM_subset, MeasureTheory.integral_condExp_indicator, AkraBazziRecurrence.eventually_deriv_one_sub_smoothingFn, Real.image_tan_Ioo, eventually_norm_symmL_trivializationAt_lt, AkraBazziRecurrence.eventually_atTop_sumTransform_le, cfcₙHom_real_eq_restrict, Real.posLog_zero, CFC.abs_algebraMap_nnreal, Function.FactorizedRational.log_norm_meromorphicTrailingCoeffAt, Asymptotics.IsBigOWith.norm_right, Real.Angle.toReal_eq_zero_iff, Complex.equivRealProdLm_symm_apply_re, ContDiffMapSupportedIn.structureMapCLM_apply_withOrder, MeasureTheory.lpNorm_zero, MeasureTheory.ComplexMeasure.im_apply, ProbabilityTheory.covariance_map_equiv, PowerSeries.IsRestricted.convergenceSet_BddAbove, Real.sin_sub_pi, mem_closedBall_one_iff, Metric.infDist_lt_iff, LiouvilleWith.int_mul_iff, Function.locallyFinsuppWithin.logCounting_divisor_eq_circleAverage_sub_const, AffineSubspace.perpBisector_eq_top, Real.smoothTransition.continuousAt, Complex.im_nsmul, Complex.closure_setOf_lt_re, UnitAddTorus.mFourierSubalgebra_separatesPoints, NNReal.rpow_add_one', ENNReal.toReal_nsmul, Probability.cauchyPDFReal_def', dist_pointReflection_right, RCLike.nonneg_iff_exists_ofReal, NumberField.mixedEmbedding.normAtPlace_neg, NormedDivisionRing.norm_mul, RCLike.ofReal_expect, Real.differentiableOn_arccos, EisensteinSeries.linear_isTheta_left, Metric.mem_nhds_iff, tendsto_zero_iff_norm_tendsto_zero, Seminorm.ball_smul_ball, CStarRing.norm_self_mul_star, Complex.coe_algebraMap, Real.fourierIntegral_convergent_iff, smoothingFun_le_self, Real.lipschitzWith_toNNReal, ZeroHomClass.bound_of_antilipschitz, Real.hasDerivAt_cosh, Real.tendsto_deriv_mul_log_atTop, Real.dist_eq, BoundedContinuousFunction.norm_lt_iff_of_nonempty_compact, Isometry.affineIsometryOfStrictConvexSpace_apply, ProbabilityTheory.Kernel.tendsto_setIntegral_densityProcess, Real.one_lt_exp_iff, MeasureTheory.AEStronglyMeasurable.ae_integrable_condDistrib_map_iff, UnitAddCircle.norm_eq, WithLp.prod_norm_sq_eq_of_L2, upperHemicontinuous_quasispectrum_nnreal, SmoothBumpCovering.mem_extChartAt_ind_source, integral_sin, ENNReal.ofReal_nsmul, SlashInvariantForm.slash_action_eqn_SL'', innerₗ_apply_apply, indicator_cthickening_eventually_eq_indicator_closure, Affine.Simplex.sign_touchpointWeights_singleton_neg, Complex.ofReal_comp_pow, ProbabilityTheory.Kernel.stronglyMeasurable_countableFiltration_densityProcess, Real.sin_sq_add_cos_sq, Set.infsep_triple, LinearMap.polar_eq_biInter_preimage, IsUltrametricDist.norm_add_le_max, ProbabilityTheory.HasSubgaussianMGF.add, NNReal.iInf_real_pos_eq_iInf_nnreal_pos, Seminorm.coe_sSup_eq, tendsto_gauge_nhds_zero, Metric.cauchy_iff, ConvexBody.nonempty, Function.hasTemperateGrowth_inner_left, CongruenceSubgroup.strictWidthInfty_Gamma, MeasureTheory.integral_rnDeriv_smul, IsUltrametricDist.norm_add_eq_max_of_norm_ne_norm, Real.pi_gt_d4, gauge_nonneg, ProbabilityTheory.mgf_smul_left, Path.subpathAux_continuous, NumberField.mixedEmbedding.unitSMul_smul, fourierCoeff_eq_intervalIntegral, Continuous.bounded_above_of_compact_support, Seminorm.bddBelow_range_add, MeasureTheory.Measure.setIntegral_toReal_rnDeriv_eq_withDensity', Real.map_exp_atBot, CStarAlgebra.conjugate_le_norm_smul', RCLike.ofReal_nonpos, NumberField.mixedEmbedding.continuous_normAtPlace, uniformContinuous_norm', SchwartzMap.tsupport_fderivCLM_subset, irrational_add_natCast_iff, Metric.mem_uniformity_dist, unitInterval.subtype_Ici_eq_Icc, Real.doublingGamma_add_one, UpperHalfPlane.continuous_im, Bornology.IsBounded.subset_closedBall_lt, tendsto_mod_div_atTop_nhds_zero_nat, EuclideanGeometry.abs_oangle_left_toReal_lt_pi_div_two_of_dist_eq, AffineSubspace.midpoint_mem_perpBisector, EuclideanGeometry.Sphere.radius_nonneg_of_mem, dist_pos, Complex.closure_reProdIm, Polynomial.sum_derivRootWeight_pos, curveIntegralFun_add, mem_ball_iff_norm', Real.sqrt_mul_self_eq_abs, NumberField.house_nonneg, CompactlySupportedContinuousMap.toNNRealLinear_apply, norm_div, Real.arctan_lt_zero, ContinuousLinearMap.opNorm_zero_iff, Affine.Simplex.touchpoint_reindex, Real.one_half_lt_eulerMascheroniConstant, MeasureTheory.Measure.map_addHaar_smul, unitInterval.symm_lt_comm, Real.hasDerivAt_fourierChar, NNReal.geom_mean_le_arith_mean_weighted, intervalIntegral.integral_comp_add_right, numDerangements_tendsto_inv_e, Real.tan_add', bilinFormOfRealInner_orthogonal, ContinuousLinearMap.intervalIntegral_apply, MeasureTheory.norm_one_sub_charFun_le_two, Set.OrdConnected.image_real_toNNReal, StieltjesFunction.length_eq, span_fourierLp_closure_eq_top, PMF.integral_eq_sum, analyticWithinAt_sigmoid, MeasureTheory.average_add_measure, nndist_midpoint_midpoint_le, Orientation.kahler_rotation_left, ENNReal.tendsto_rpow_atTop_of_base_lt_one, LindemannWeierstrass.integral_exp_mul_eval, GromovHausdorff.HD_below_aux2, circleIntegrable_zero_radius, MeasureTheory.measureReal_union_add_inter₀', NNReal.image_coe_Iic, intervalIntegral.inv_smul_integral_comp_div, transcendental_liouvilleNumber, UpperHalfPlane.atImInfty_basis, analyticOn_sigmoid, EuclideanGeometry.Sphere.center_mem_orthRadius_iff, unitInterval.coe_lt_one, WithCStarModule.norm_equiv_le_norm_prod, LiouvilleWith.exists_pos, Complex.isUniformEmbedding_ofReal, Asymptotics.IsBigOWith.prod_left, InformationTheory.isMinOn_klFun, GaussianInt.intCast_real_norm, Complex.conjCLE_enorm, EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp, Rat.AbsoluteValue.padic_le_one, expNegInvGlue.monotone, InnerProductSpace.Core.inner_mul_symm_re_eq_norm, ArithmeticFunction.vonMangoldt.residueClass_le, MeasureTheory.integral_fin_nat_prod_eq_prod, Probability.lintegral_cauchyPDF_eq_one, Real.differentiableWithinAt_arccos_Iic, NormedField.completeSpace_iff_isComplete_closedBall, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, MeasureTheory.charFunDual_eq_pi_iff, Complex.exists_norm_mul_eq_self, OrthonormalBasis.orthonormal_adjustToOrientation, norm_div_le_norm_div_add_norm_div, unitInterval.sigmoid_lt_iff, MeasureTheory.aestronglyMeasurable_condExpL1CLM, Hamming.norm_eq_hammingNorm, Affine.Simplex.ExcenterExists.excenter_mem_affineSpan_range, PiLp.norm_eq_of_nat, ProbabilityTheory.variance_id_gaussianReal, Quaternion.imK_coeComplex, MellinConvergent.comp_rpow, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_withOrder, SchwartzMap.iteratedPDeriv_eq_iteratedFDeriv, Complex.re_qsmul, ArithmeticFunction.moebius_mul_log_eq_vonMangoldt, Real.holderConjugate_iff, ValueDistribution.logCounting_sum_top_eventuallyLE, ContDiffBump.integral_le_measure_closedBall, Subgroup.strictWidthInfty_mem_strictPeriods, ProbabilityTheory.mgf_const', SchwartzMap.inner_fourierTransformCLM_toL2_eq, Real.instIsDomain, CFC.nnrpow_le_nnrpow, Real.sin_arctan_eq_zero, range_euclideanQuadrant, MeasureTheory.SimpleFunc.setToSimpleFunc_zero, Complex.ofReal_injective, Real.tendsto_integral_cexp_sq_smul, curveIntegralFun_sub, RCLike.ofReal_one, mdifferentiableWithinAt_comp_projIcc_iff, ContDiffMapSupportedIn.seminorm_apply, Int.not_irrational, Set.infsep_empty, Real.pi_lt_sqrtTwoAddSeries, FormalMultilinearSeries.isLittleO_of_lt_radius, convexHull_ediam, NormedAddCommGroup.tendsto_nhds_zero, MeromorphicOn.log_norm_meromorphicTrailingCoeffAt_extract_zeros_poles, Real.cauchy_neg, CStarAlgebra.norm_le_norm_of_nonneg_of_le, WithSeminorms.tendsto_nhds_atTop, aemeasurable_withDensity_iff, Real.zero_at_infty_fourier, Complex.IsExpCmpFilter.isLittleO_im_pow_exp_re, unitInterval.subtype_Iio_eq_Ico, MeasureTheory.integral_eq_setToFun, Complex.re_tsum, Orientation.inner_sq_add_areaForm_sq, UpperHalfPlane.ModularGroup_T_zpow_mem_verticalStrip, expNegInvGlue.contDiff, Real.enorm_exp_I_mul_ofReal_sub_one_le, Real.log_surjective, TendstoUniformlyOn.re, Real.coe_fib_eq', enorm_norm, Matrix.IsHermitian.exists_eigenvector_of_ne_zero, dist_triangle4_left, IntervalIntegrable.finsum, PiLp.norm_toLp_const, nnnorm_norm, MeasureTheory.lpNorm_const_smul, Real.injOn_sin, HomotopyGroup.one_def, Metric.cthickening_eq_iInter_cthickening, bernoulliFun_mul, ContinuousLinearMap.rotation_apply, Diffeology.isOpen_iff_preimages_plots, AddGroupNorm.sup_apply, Seminorm.smul_closedBall_subset, Complex.div_intCast_re, Complex.toIocMod_arg, ContractingWith.dist_le_of_fixedPoint, MeasureTheory.SignedMeasure.singularPart_sub, lp.tsum_mul_le_mul_norm', RCLike.re_le_re, RCLike.reLm_coe, BoxIntegral.TaggedPrepartition.IsHenstock.card_filter_tag_eq_le, norm_add_sq_real, Real.hasFPowerSeriesOnBall_linear_zero, ProbabilityTheory.gaussianPDFReal_zero_var, NNReal.abs_eq, Real.Angle.coe_nsmul, EisensteinSeries.q_expansion_bernoulli, NNReal.orderIsoIccZeroCoe_symm_apply_coe, SchwartzMap.convolution_continuous_left, MeasureTheory.Lp.coe_posPart, integrableOn_exp_neg_Ioi, HurwitzZeta.completedHurwitzZetaEven_zero, Path.target', Polynomial.mahlerMeasure_one, Topology.RelCWComplex.openCell_zero_eq_singleton, UpperHalfPlane.coe_specialLinearGroup_apply, spectrum.norm_eq_one_of_unitary, Complex.isTheta_cpow_const_rpow, Real.contDiffOn_arccos, Real.Angle.coe_toIocMod, inner_smul_real_left, CovByVAdd.rfl, NumberField.mixedEmbedding.fundamentalCone.expMap_single_symm_apply, eigenvalue_mem_ball, NormedAddCommGroup.uniformity_basis_dist, Real.sin_sub_sin, exists_subset_iUnion_ball_radius_lt, Set.instTietzeExtensionUnitClosedBall, RCLike.natCast_im, HurwitzZeta.cosKernel_def, ContinuousLinearMap.norm_compContinuousAlternatingMap_le, Real.coe_comp_expOrderIso, EuclideanGeometry.cos_eq_zero_iff_angle_eq_pi_div_two, Real.isTheta_exp_comp_exp_comp, HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow, Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero, Set.infsep_le_dist_of_mem, ProbabilityTheory.IsMeasurableRatCDF.continuousWithinAt_stieltjesFunctionAux_Ici, Affine.Triangle.orthocenter_mem_altitude, ODE.FunSpace.dist_iterate_next_le, ENNReal.coe_rpow_def, Polynomial.Chebyshev.integral_eval_T_real_measureT_of_ne_zero, fst_integral, Real.hasDerivAt_Gamma_one_half, CStarAlgebra.star_mul_le_algebraMap_norm_sq, ProbabilityTheory.isPosSemidef_covarianceBilinDual, SeminormClass.map_smul_eq_mul, Complex.ofReal_mem_slitPlane, quarter_mem_preCantorSet, HasFPowerSeriesWithinAt.isBigO_image_sub_norm_mul_norm_sub, GroupSeminorm.coe_sSup_apply', EuclideanGeometry.angle_left_midpoint_eq_pi_div_two_of_dist_eq, MeasureTheory.measureReal_union₀, Complex.I_mul, fderiv_norm_smul, Diffeology.IsContDiffCompatible.isPlot_iff, MeasureTheory.Measure.integrable_integral_norm_of_integrable_comp, MulRingSeminorm.mulRingSeminormClass, InnerProductSpace.laplacian_eq_iteratedFDeriv_complexPlane, MeasureTheory.measureReal_univ_pos, expNegInvGlue.continuous_polynomial_eval_inv_mul, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, isMIntegralCurveAt_comp_mul_ne_zero, ContinuousAlternatingMap.bounds_nonempty, MulRingNorm.isPowMul, MeasureTheory.SimpleFunc.integral_eq_sum_of_subset, MeasureTheory.MemLp.re, Real.instCompleteSpace, EuclideanGeometry.dist_orthogonalProjection_eq_zero_iff, CStarAlgebra.isStrictlyPositive_iff_isUnit_sqrt_and_eq_sqrt_mul_sqrt, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_pos, SchwartzMap.integral_fourier_mul_eq, RCLike.ratCast_re, MeasureTheory.AEStronglyMeasurable.im, cfc_comp_norm, AkraBazziRecurrence.isEquivalent_smoothingFn_sub_self, NumberField.Units.regulator_pos, RCLike.ofReal_eq_re_of_isSelfAdjoint, EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd, StarModule.complexToReal, CFC.abs_intCast, MeasureTheory.SimpleFunc.map_coe_nnreal_restrict, Complex.I_mul_re, Real.sigmoid_zero, Complex.normSq_nonneg, Matrix.IsHermitian.coe_re_apply_self, AkraBazziRecurrence.eventually_atTop_sumTransform_ge, variationOnFromTo.nonneg_of_le, BoxIntegral.integrable_iff_cauchy_basis, MeasureTheory.Measure.iInf_rat_gt_prod_Iic, setOf_riemannianEDist_lt_subset_nhds, MeasureTheory.Integrable.re, range_mfderiv_coe_sphere, Diffeology.IsPlot.continuous, Real.Angle.toReal_add_of_sign_pos_sign_neg, goldConj_neg, eventually_riemannianEDist_le_edist_extChartAt, Complex.volume_preserving_equiv_pi, Complex.arg_eq_zero_iff, Complex.wedgeIntegral_add_wedgeIntegral_eq, AkraBazziRecurrence.exists_eventually_r_le_const_mul, RCLike.ofReal_div, IsMIntegralCurve.comp_mul, WithCStarModule.pi_norm_le_sum_norm, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le, Hyperreal.coe_one, EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_dist, Real.mk_const, PiLp.norm_apply_le, Complex.norm_sub_one_sq_eqOn_sphere, Affine.Triangle.eulerPoint_eq_midpoint, Quaternion.inner_def, NNReal.coe_mono, MeasureTheory.weightedSMul_union', MeasureTheory.integrable_prod_iff', Real.sum_mul_le_sqrt_mul_sqrt, integral_coe_re_add_coe_im, Complex.sqrt_neg_I, ZMod.toAddCircle_intCast, Complex.abs_arg_lt_pi_div_two_iff, RCLike.wInner_one_const_right, GaussianInt.toComplex_im, TopologicalSpace.exists_isInducing_l_infty, RCLike.lt_iff_re_im, IsometricContinuousFunctionalCalculus.norm_spectrum_le, Metric.cthickening_eq_iInter_thickening'', Real.convs_eq_convergent, ENNReal.toReal_sub_of_le, convex_parallelepiped, hahnEmbedding_isOrderedModule_rat, GaussianInt.im_toComplex, MeasureTheory.setIntegral_nonneg_ae, ProbabilityTheory.Kernel.IsMarkovKernel.integrable, Affine.Simplex.sign_signedInfDist_touchpoint_empty, Real.iteratedDeriv_even_sinh, ContinuousLinearMap.norm_id_le, AddGroupSeminorm.coe_smul, HasFDerivAt.le_of_lipschitz, ProbabilityTheory.covariance_zero_measure, EReal.preimage_coe_Iio, Asymptotics.isBigO_principal, Real.posLog_prod, Irrational.eventually_forall_le_dist_cast_div, Real.cos_sq_le_one, MeasureTheory.SignedMeasure.singularPart_add_withDensity_rnDeriv_eq, intervalIntegrable_log_cos, ENNReal.log_rpow, SchwartzMap.pairing_continuous_left, ContinuousMap.toNNReal_apply, Real.one_add_rpow_hasFPowerSeriesAt_zero, integral_sin_pow_odd_mul_cos_pow, Real.Angle.abs_toReal_coe_eq_self_iff, Real.sInf_empty, range_cfc_nnreal_eq_image_cfc_real, signedDist_vadd_right_swap, ProbabilityTheory.integral_condCDF, Complex.im_sum, ValueDistribution.proximity_zero_of_complexValued, ProbabilityTheory.IsRatStieltjesPoint.tendsto_atTop_one, BoxIntegral.Prepartition.injOn_setOf_mem_Icc_setOf_lower_eq, NumberField.exists_ideal_in_class_of_norm_le, Complex.sqrt_eq_real_add_ite, NumberField.mixedEmbedding.normAtPlace_apply, SchwartzMap.integralCLM_apply, linearEquiv_det_rotation, MeasureTheory.lpNorm_one, Complex.coe_selfAdjointEquiv, GroupNorm.lt_def, PolynormableSpace.withSeminorms', RCLike.norm_two, Real.differentiable_mulExpNegMulSq, ConvexBody.isClosed, ContinuousMap.neg_norm_le_apply, ProbabilityTheory.condCDF_le_one, Affine.Simplex.midpoint_faceOppositeCentroid_eulerPoint, NonarchAddGroupSeminorm.toZeroHom_eq_coe, AddCircle.coe_real_preimage_closedBall_period_zero, circleIntegrable_sub_zpow_iff, MeasureTheory.withDensityᵥ_toReal, NumberField.mixedEmbedding.volume_preserving_homeoRealMixedSpacePolarSpace, Real.HolderTriple.right_pos, ProbabilityTheory.Kernel.condExp_densityProcess, CircleDeg1Lift.lt_iterate_pos_iff, EuclideanSpace.volume_ball_fin_two, mem_nullSubmodule_iff, Polynomial.fourierCoeff_toAddCircle_natCast, ContDiffBump.tsupport_eq, UniformSpace.Completion.uniformity_dist, Real.cos_sq_add_sin_sq, Real.eulerMascheroniConstant_lt_eulerMascheroniSeq', Real.differentiableAt_arccos, ContractingWith.one_sub_K_pos, Real.summable_pow_div_factorial, ArithmeticFunction.vonMangoldt.LSeries_residueClass_lower_bound, SimpleGraph.tendsto_turanDensity, norm_add_sq, Polynomial.mahlerMeasure_zero, spectralNorm.spectralNorm_eq_norm_coeff_zero_rpow, Affine.Simplex.sum_reflectionCircumcenterWeightsWithCircumcenter, Complex.not_le_zero_iff, Real.dist_0_eq_abs, RCLike.norm_sq_re_conj_add, SeminormedRing.norm_mul_le, Complex.conjCLE_apply, Real.eulerMascheroniSeq'_six_lt_two_thirds, Real.cos_sub_cos, EuclideanSpace.inner_basisFun_real, Real.not_DifferentiableAt_log_mul_zero, EReal.continuous_coe_iff, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, Real.tendsto_sum_range_one_div_nat_succ_atTop, InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two, iccLeftChart_extend_zero, Real.exp_lt_one_iff, Real.cos_nat_mul_two_pi_sub, BoundedVariationOn.dist_le, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, EuclideanGeometry.Sphere.IsTangentAt.eq_orthogonalProjection, ProbabilityTheory.Kernel.tendsto_densityProcess_limitProcess, CircleDeg1Lift.tendsto_translation_number₀, RCLike.sqrt_neg_I, NumberField.mixedEmbedding.volume_eq_zero, ZMod.toAddCircle_apply, Complex.nndist_conj_self, MeasureTheory.SignedMeasure.singularPart_smul_nnreal, ProbabilityTheory.covarianceBilin_real, Real.measurable_exp, Real.contDiff_sinh, EReal.preimage_coe_Ioo_bot_top, NontriviallyNormedField.non_trivial, imaginaryPart_ofReal, ProbabilityTheory.strong_law_Lp, Real.tendsto_tan_neg_pi_div_two, Real.Angle.tan_eq_sin_div_cos, dist_mul_mul_le, bernoulliFun_eq_integral, RCLike.normSq_pos, EuclideanGeometry.Sphere.IsDiameter.midpoint_eq_center, MeasureTheory.SimpleFunc.eLpNorm'_eq, Real.cosh_le_cosh, ProbabilityTheory.moment_def, Real.Angle.natCast_mul_eq_nsmul, ModularGroup.im_smul_eq_div_normSq, MeasureTheory.integral_const, Complex.pos_iff, tsum_geometric_inv_two, SchwartzMap.fourier_coe, ENNReal.toReal_mul, GroupSeminorm.toFun_eq_coe, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, ProbabilityTheory.iIndepFun.integral_prod_eq_prod_integral, ENNReal.zero_rpow_mul_self, Euclidean.ball_eq_preimage, Real.sInf_univ, MeasureTheory.Measure.exists_regular_eq_of_compactSpace, Real.cos_pi_over_two_pow, Asymptotics.isBigO_const_left_iff_pos_le_norm, Real.not_summable_one_div_natCast, CStarAlgebra.star_left_conjugate_le_norm_smul, Real.binEntropy_two_inv_add, preCantorSet_zero, AddGroupSeminorm.add_apply, norm_iteratedFDeriv_prod_le, abs_dist, SmoothBumpFunction.coe_def, Affine.Simplex.exradius_eq_abs_inv_sum, MeasureTheory.L1.SimpleFunc.setToL1S_zero_left, Real.sin_arccos, ODE.FunSpace.dist_iterate_next_iterate_next_le, NumberField.Ideal.tendsto_norm_le_div_atTop, HurwitzZeta.hurwitzZetaOdd_eq, NumberField.mixedEmbedding.fundamentalCone.expMap_apply, Real.Angle.toIocMod_toReal, UpperHalfPlane.cosh_half_dist, exists_iUnion_ball_eq_radius_lt, Seminorm.zero_or_exists_apply_eq_finset_sup, norm_add_mul_self, SchwartzMap.iteratedLineDerivOp_eq_iteratedFDeriv, SchwartzMap.lineDerivOp_fourierInv_eq, Irrational.add_ratCast, finrank_real_of_complex, CliffordAlgebraComplex.equiv_apply, Asymptotics.IsBigO.exists_eq_mul, Hyperreal.infinitesimal_real_iff, MeasureTheory.exists_measurableEmbedding_real, InformationTheory.rightDeriv_klFun_one, hasDerivAt_abs, NumberField.mixedEmbedding.stdBasis_apply_isReal, Real.cauchy_intCast, RCLike.conj_im, Real.cos_eq_zero_iff_sin_eq, ProbabilityTheory.tilted_mul_apply_mgf, Path.truncate_zero_one, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, Function.RCLike.hasTemperateGrowth_ofReal, Affine.Simplex.sign_excenterWeights_empty, Real.tan_int_mul_pi_sub, ContinuousLinearMap.opNorm_lsmul_le, EuclideanGeometry.Sphere.secondInter_vsub_mem_affineSpan, EuclideanSpace.volume_ball, Real.sign_mul_pos_of_ne_zero, MeasureTheory.Lp.norm_exponent_zero, dist_vsub_vsub_le, BumpCovering.sum_toPartitionOfUnity_eq, MeasureTheory.hasFiniteIntegral_toReal_iff, Real.fourierChar_apply, AntilipschitzWith.le_mul_norm_sub, NumberField.canonicalEmbedding.norm_le_iff, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, ProbabilityTheory.covarianceBilin_of_not_memLp, InformationTheory.rightDeriv_klFun, MeasureTheory.Measure.haar.addPrehaar_nonneg, Unitary.two_mul_one_sub_le_norm_sub_one_sq, dense_addSubgroupClosure_pair_iff, Path.extend_one, interior_range_modelWithCornersEuclideanHalfSpace, BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le, ExistsContDiffBumpBase.y_smooth, LipschitzWith.iff_le_add_mul, Metric.hasBasis_nhdsSet_thickening, Affine.Simplex.ExcenterExists.sum_excenterWeights_eq_one, WeakDual.CharacterSpace.norm_le_norm_one, ValueDistribution.abs_characteristic_sub_characteristic_shift_eqO, Real.Angle.sign_coe_pi_div_two, Real.sinc_le_one, AkraBazziRecurrence.differentiableOn_one_sub_smoothingFn, RingNorm.ringNormClass, contDiff_inner, HasConstantSpeedOnWith.hasLocallyBoundedVariationOn, ProbabilityTheory.condVar_bot', NormedField.exists_one_lt_norm, unitInterval.volume_Ioc, IsMprojection.Mnorm, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, Padic.nonarchimedean, unitInterval.coe_pos, Irrational.sub_natCast, Real.tendsto_logb_comp_add_sub_logb, Real.sq_sqrt', ValueDistribution.characteristic_zero_mul_eventually_le, LipschitzOnWith.dist_le_mul, SmoothBumpCovering.locallyFinite, Affine.Simplex.point_eq_affineCombination_of_pointsWithCircumcenter, gaugeRescale_def, Real.Angle.zsmul_eq_iff, ProbabilityTheory.differentiableOn_complexMGF, Polynomial.Chebyshev.T_real_cosh, PartitionOfUnity.sum_le_one, isNonarchimedean_spectralNorm_of_finiteDimensional_normal, Real.abs_cos_eq_sqrt_one_sub_sin_sq, Real.nnabs_coe, ConvexBody.isCompact, Real.mk_zero, HurwitzZeta.hurwitzZeta_zero, ProbabilityTheory.lintegral_gaussianPDFReal_eq_one, Real.hasDerivAt_Gamma_one, GroupSeminorm.map_one', Asymptotics.isLittleO_abs_right, EReal.tendsto_coe_nhds_top_iff, AffineSubspace.perpBisector_self, Real.fourier_bilin_convolution_eq_integral, NNReal.image_coe_Ioi, Real.hasStrictDerivAt_cos, GroupSeminorm.comp_apply, Real.mapsTo_sin, Complex.coe_smul, MeasureTheory.ComplexMeasure.equivSignedMeasureₗ_symm_apply, ProbabilityTheory.IsRatCondKernelCDFAux.measurable_right, AddCircle.isFiniteMeasure, SchwartzMap.fourierInv_coe, IsUltrametricDist.exists_norm_finset_sum_le_of_nonempty, BoxIntegral.Box.lower_le_upper, InnerProductSpace.Core.inner_self_ofReal_re, NumberField.mixedEmbedding.normAtPlace_apply_of_isComplex, ContinuousLinearMap.isPositive_def', SmoothBumpFunction.isOpen_support, Real.continuousAt_log_iff, Valued.norm_nonneg, ODE.FunSpace.continuous_compProj, CongruenceSubgroup.mem_conjGL, CircleDeg1Lift.tendsto_atTop, Complex.div_ratCast_im, Matrix.frobenius_norm_mul, ProbabilityTheory.Fernique.logRatio_nonneg, Circle.exp_int_mul_two_pi, AkraBazziRecurrence.deriv_smoothingFn, ProperCone.innerDual_empty, inner_vsub_vsub_left_eq_dist_sq_right_iff, stdSimplexHomeomorphUnitInterval_one, Complex.lift_symm_apply_coe, variationOnFromTo.nonpos_of_ge, OpenPartialHomeomorph.univUnitBall_apply, ContinuousLinearMap.norm_compL_le, NonarchAddGroupNorm.coe_le_coe, Seminorm.continuousAt_zero_of_forall, RCLike.hasSum_iff, SeminormFamily.withSeminorms_iff_nhds_eq_iInf, NumberField.mixedEmbedding_injective, Real.cauchy_add, Orientation.oangle_map, NonUnitalNormedRing.norm_mul_le, RCLike.measurable_im, MeasureTheory.Measure.addHaar_preimage_linearMap, EulerSine.antideriv_cos_comp_const_mul, Matrix.IsHermitian.spectrum_real_eq_range_eigenvalues, ProbabilityTheory.condVar_of_sigmaFinite, torusIntegral_radius_zero, CFC.rpow_intCast, NormedAddGroupHom.IsQuotient.norm, InformationTheory.klFun_one, curveIntegral_eq_intervalIntegral_deriv, RCLike.inv_def, Complex.sinh_ofReal_im, MeasureTheory.measureReal_iUnion_fintype_le, InnerProductSpace.gramSchmidtNormed_unit_length', Real.volume_Ici, tendsto_norm, RCLike.sqrt_I, ContinuousMap.Homotopy.continuous, Path.trans_apply, norm_sub_le_norm_add, ContinuousMap.Homotopy.affine_apply, Complex.re_eq_neg_norm, NormedAddGroupHom.opNorm_nonneg, MeasureTheory.JordanDecomposition.toSignedMeasure_smul, PadicInt.not_isUnit_iff, RightDerivMeasurableAux.differentiable_set_eq_D, BoxIntegral.integralSum_smul, Real.ofCauchy_add, ZetaAsymptotics.continuousOn_term_tsum, StarAlgHom.realContinuousMapOfNNReal_injective, Real.convergent_of_int, NumberField.mixedEmbedding.forall_normAtPlace_eq_zero_iff, IsClosed.hausdorffDist_zero_iff_eq, Real.natCastle_toNNReal', Real.arsinh_strictMono, norm_le_zero_iff, NumberField.mixedEmbedding.convexBodyLT_convex, Real.tendsto_integral_exp_smul_cocompact, ArithmeticFunction.vonMangoldt_nonneg, NumberField.FinitePlace.pos_iff, Real.contDiff_arctan, tendsto_closedBall_smallSets, MeasureTheory.setIntegral_tilted', EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_wbtw, UpperHalfPlane.exp_half_dist, ArithmeticFunction.LSeriesSummable_moebius_iff, Real.cos_neg, Complex.normSq_add_mul_I, EuclideanGeometry.oangle_midpoint_rev_right, Orientation.kahler_mul, Polynomial.gaussNorm_C, mem_ball_iff_norm''', LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, IsUltrametricDist.norm_div_eq_max_of_norm_div_ne_norm_div, innerSL_real_flip, ProbabilityTheory.iIndepFun_iff_charFunDual_pi', sameRay_iff_norm_sub, HasDerivAt.real_of_complex, ProbabilityTheory.covarianceBilinDual_comm, Metric.Sum.dist_eq_glueDist, TensorProduct.dist_tmul_le, Real.uniformContinuous_abs, ENNReal.toReal_sSup, ProbabilityTheory.isGaussian_iff_charFunDual_eq, Real.tendsto_arctan_atTop, SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left, ArithmeticFunction.sum_moebius_mul_log_eq, NNReal.summable_one_div_rpow, UpperHalfPlane.vadd_right_cancel_iff, Real.isAlgebraic_sin_rat_mul_pi, RCLike.re_eq_ofReal_of_isSelfAdjoint, AkraBazziRecurrence.isLittleO_smoothingFn_one, Real.ediam_Ioo, IsPicardLindelof.mul_max_le, CPolynomialAt.exists_ball_cpolynomialOn, NumberField.InfinitePlace.one_le_mult, NNReal.forall, tendsto_rpow_div, measurableSet_of_differentiableWithinAt_Ioi, Real.iInter_Iic_rat, integral_sin_mul_cos_sq, ContinuousLinearMap.norm_fst, Archimedean.exists_orderAddMonoidHom_real_injective, norm_inf_sub_inf_le_norm, EisensteinSeries.linear_isTheta_right_add, Real.iteratedDeriv_add_one_sin, Complex.neg_re, EReal.coe_pos, Real.differentiable_iteratedDeriv_sin, ENNReal.rpow_zero, ProbabilityTheory.covariance_smul_right, Nonneg.instNonUnitalContinuousFunctionalCalculus, Real.surjOn_cos, SmoothPartitionOfUnity.exists_pos_of_mem, CovBySMul.rfl, Real.volume_uIoo, Path.trans_range, NNReal.rpow_neg, MeasureTheory.charFun_eq_charFunDual_toDualMap, SchwartzMap.instLocallyConvexSpace, NormedAlgebra.Real.nonempty_algEquiv_or, MeasureTheory.measureReal_compl₀, fourier_neg, Affine.Simplex.incenter_mem_affineSpan_range, BoxIntegral.Box.mem_def, IsUltrametricDist.isUltrametricDist_iff_isNonarchimedean_nnnorm, spectralAlgNorm_of_finiteDimensional_normal_def, Set.OrdConnected.preimage_ennreal_ofReal, HolderOnWith.ediam_image_le_of_le, real_inner_sub_sub_self, Archimedean.embedRealFun_zero, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn, MeasureTheory.Measure.haar.addPrehaar_pos, Path.symm_subpath, tendsto_norm_atTop_iff_cobounded', Real.deriv_sigmoid, LSeries.tendsto_cpow_mul_atTop, ProbabilityTheory.isRatCondKernelCDFAux_preCDF, ENNReal.toReal_zero, LinearMap.IsSymmetric.eigenvalues_def, NNReal.rpow_sub_one', Height.fun_mulHeight_one, ENNReal.measurable_ofReal, ZLattice.volume_image_eq_volume_div_covolume', ProperCone.dual_dual_flip, MeasureTheory.Measure.addHaar_preimage_continuousLinearEquiv, Algebra.trace_complex_apply, PiTensorProduct.mapL_opNorm, Topology.RelCWComplex.mapsTo, IsBoundedSMul.dist_smul_pair', Real.negMulLog_eq_neg, flip_innerₗ, Real.quadratic_root_cos_pi_div_five, Asymptotics.IsBigOWith.exists_nonneg, EisensteinSeries.tendsto_double_sum_S_act, Real.exp_one_lt_d9, RCLike.norm_nnratCast, Real.cos_antiperiodic, NumberField.RingOfIntegers.HeightOneSpectrum.isNonarchimedean_adicAbv, Real.cos_periodic, Affine.Simplex.eulerPoint_reindex, NNReal.coe_pow, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, MeasureTheory.LocallyIntegrableOn.norm, one_add_rpow_hasFPowerSeriesAt_zero, tendsto_norm_atTop_atTop, HomotopyGroup.inv_spec, PathConnectedSpace.exists_path_through_family', ArchimedeanClass.ofArchimedean_stdPart, Real.arsinh_bijective, Real.cosh_strictMonoOn, Complex.arg_inv, Complex.im_mul_ofReal, ProbabilityTheory.iCondIndepFun_iff, Matrix.PosSemidef.re_dotProduct_nonneg, circleAverage_log_norm_sub_const_eq_posLog, Orientation.rightAngleRotation_trans_neg_orientation, Orientation.volumeForm_robust', ArithmeticFunction.vonMangoldt_apply, MeasureTheory.probReal_univ, MeasureTheory.lpNorm_div_natCast, tendsto_norm_cocompact_atTop', AEMeasurable.ereal_toReal, Real.iteratedDeriv_even_sin, exists_smooth_zero_one_of_isClosed, norm_sub_norm_le, Asymptotics.IsLittleO.add_add, Padic.padicNormE.mul, Matrix.linfty_opNorm_mul, AkraBazziRecurrence.dist_r_b, Real.sqrtTwoAddSeries_lt_two, Real.cosh_arsinh, Real.nnnorm_ofNat, instSMulCommClass_sphere_ball_ball, CFC.exists_measure_nnrpow_eq_integral_cfcₙ_rpowIntegrand₀₁, Real.cosh_three_mul, ProbabilityTheory.IsRatStieltjesPoint.tendsto_atBot_zero, ModelWithCorners.convex_range', ArchimedeanClass.stdPart_div, CFC.spectrum_abs, Metric.unitSphere.coe_pow, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIdealLattice, Quaternion.inner_self, Path.range_coe, dist_left_lineMap, CStarAlgebra.rpow_neg_one_le_one, separatesPoints_continuous_of_t35Space_Icc, NormedSpace.toLocallyConvexSpace, Real.sign_apply_eq, real_inner_self_eq_norm_mul_norm, Affine.Simplex.excenterWeights_map, GroupSeminorm.coe_smul, EulerSine.antideriv_sin_comp_const_mul, ProbabilityTheory.Kernel.isRatCondKernelCDFAux_density_Iic, Real.strictConcaveOn_sqrt, Real.exp_injective, InnerProductGeometry.norm_sub_eq_abs_sub_norm_iff_angle_eq_zero, Real.analyticOnNhd_cos, Metric.infDist_le_infDist_add_dist, Real.arcsin_nonneg, Complex.zero_le_real, CongruenceSubgroup.strictPeriods_Gamma, AddCircle.instAddQuotientMeasureEqMeasurePreimageSubtypeAddOppositeRealMemAddSubgroupOpZmultiplesVolume, Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero, coe_normSeminorm, EuclideanGeometry.angle_eq_abs_oangle_toReal, EuclideanGeometry.angle_eq_zero_of_angle_eq_pi_right, MeasureTheory.ae_mem_limsup_atTop_iff, Complex.lim_im, signedDist_vadd_left, Real.le_norm_self, Diffeology.IsPlot.contDiff, ModularGroup.tendsto_lcRow0, Complex.div_natCast_im, ProbabilityTheory.integrable_kernel_prodMk_left, ProbabilityTheory.HasCondSubgaussianMGF.fun_zero, AffineSpace.asymptoticNhds_le_cobounded, RCLike.ofReal_nnratCast, NumberField.Units.dirichletUnitTheorem.logEmbedding_component, Real.comap_exp_nhdsGT_zero, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_algebraMap, parallelepiped_eq_sum_segment, ENNReal.rpow_ofNat, cosetToCuspOrbit_apply_mk, NormedAlgebra.norm_smul_le, HasLineDerivAt.le_of_lipschitzOn, Complex.ofReal_natCast, MeasureTheory.meas_ge_le_mul_pow_eLpNorm_enorm, CircleDeg1Lift.lt_map_map_zero, Real.strictMonoOn_one_add_div_one_sub, Real.ofCauchy_inv, MeasureTheory.charFun_zero_measure, ProbabilityTheory.HasSubgaussianMGF.add_of_hasCondSubgaussianMGF, ContDiffBump.convolution_eq_right, ZetaAsymptotics.term_nonneg, TemperedDistribution.instFourierInvSMul, ExistsContDiffBumpBase.w_def, HurwitzZeta.hurwitzZeta_one_sub, measurable_derivWithin_Ioi, MeasureTheory.Measure.setIntegral_comp_smul, Complex.imCLM_coe, EReal.toReal_mul, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, Real.cauchy_zero, ContinuousMap.norm_restrict_mono_set, isBoundedBilinearMap_inner, RCLike.ofReal_pos, contDiff_stereoInvFunAux, Complex.isQuotientMap_im, Real.inv_sign, tendsto_mul_add_inv_atTop_nhds_zero, expNegInvGlue.contDiff_polynomial_eval_inv_mul, Measurable.dist, ContinuousLinearMap.opNorm_mul_apply_le, Affine.Simplex.incenter_notMem_affineSpan_pair, NNReal.rpow_sub_natCast', Asymptotics.isTheta_norm_left, Seminorm.mem_ball, RCLike.re_le_norm, circleAverage_log_norm_factorizedRational, OrthonormalBasis.norm_le_card_mul_iSup_norm_inner, Complex.ofReal_qsmul, Polynomial.aeval_ofReal, HolderOnWith.comp_holderWith, Int.closedBall_eq_Icc, SmoothBumpCovering.embeddingPiTangent_injective, Asymptotics.isBigO_iff_isBoundedUnder_le_div, Real.pi_gt_three, Hyperreal.ofSeq_le_ofSeq, MeasureTheory.charFunDual_prod', BoxIntegral.Prepartition.eventually_not_disjoint_imp_le_of_mem_splitMany, Chebyshev.theta_nonneg, Real.toNNReal_abs, PadicInt.valuation_coe, SmoothBumpCovering.eventuallyEq_one', ContinuousLinearMap.isPositive_iff_complex, Real.cosPartialEquiv_symm_apply, LinearIsometryEquiv.toMeasurableEquiv_symm, BoundedContinuousFunction.norm_coe_le_norm, MeasureTheory.exists_nat_measurableEquiv_range_coe_fin_of_finite, Real.instContinuousMapUniqueHom, AbsolutelyContinuousOnInterval.sub, ArithmeticFunction.LSeriesSummable_zeta_iff, Real.one_sub_sq_div_two_lt_cos, instIsContMDiffRiemannianBundleTrivial, Real.smoothTransition.nonneg, InformationTheory.strictConvexOn_klFun, SchwartzMap.toLp_fourierTransform_eq, NormedSpace.norm_smul_le, ProbabilityTheory.covarianceBilin_apply, Real.volume_pi_le_diam_pow, exists_contMDiff_support_eq_eq_one_iff, Real.tanh_lt_one, fourierIntegral_half_period_translate, BoxIntegral.integralSum_sub_partitions, EReal.toReal_le_toReal, measurable_coe_nnreal_real, NNReal.coe_nonneg, Path.Homotopy.transReflReparamAux_mem_I, MeasureTheory.stronglyMeasurable_charFun, AffineSubspace.mem_perpBisector_iff_inner_pointReflection_vsub_eq_zero, ProbabilityTheory.gammaPDF_eq, spectrum.pow_norm_pow_one_div_tendsto_nhds_spectralRadius, Orientation.eq_zero_or_oangle_eq_iff_inner_eq_zero, ContinuousLinearMap.opNorm_smul_le, Quaternion.norm_exp, ProbabilityTheory.IsRatCondKernelCDFAux.integrable_iInf_rat_gt, Real.isBigO_exp_comp_exp_comp, AkraBazziRecurrence.isEquivalent_one_add_smoothingFn_one, MeasureTheory.withDensitySMulLI_apply, Path.add_apply, hasDerivAt_gronwallBound, MeasureTheory.Measure.addHaar_nnreal_smul, Quaternion.continuous_coe, Real.uniformContinuous_add, norm_prod_le, Complex.continuous_ofReal, Affine.Simplex.touchpoint_eq_point_rev, Complex.ofReal_zsmul, ENNReal.toReal_iInf, NumberField.mixedEmbedding.logMap_apply, ContinuousMap.comp_attachBound_mem_closure, Real.exp_lt_exp, EuclideanGeometry.hasFDerivAt_inversion, InformationTheory.continuous_klFun, Orientation.kahler_map, Real.ofCauchy_neg, isBigO_deriv_ofReal_cpow_const_atTop, measurable_coe_real_ereal, EReal.preimage_coe_Iio_top, Real.pi_lt_d20, Metric.unitBall.coe_mul, TemperedDistribution.instFourierInvAdd, Absorbs.exists_pos, InformationTheory.stronglyMeasurable_klFun, CFC.isUnit_rpow_iff, dist_div_norm_sq_smul, RCLike.ofNat_im, NormedField.tendsto_norm_zpow_nhdsNE_zero_atTop, Metric.eventually_nhds_prod_iff, MeasureTheory.Lp.fourierInv_toTemperedDistribution_eq, NNReal.isUniformEmbedding_coe, MeasureTheory.JordanDecomposition.toSignedMeasure_neg, stronglyMeasurable_derivWithin_Ici, NumberField.mixedEmbedding.fundamentalCone.injective_expMapBasis, Real.strictMonoOn_log, Finset.infsep_zero_iff_subsingleton, ProbabilityTheory.measurable_exponentialPDFReal, GroupSeminorm.groupSeminormClass, IsSelfAdjoint.map_spectrum_real, posTangentConeAt_mono, AkraBazziRecurrence.a_pos, hasDerivAt_ofReal_cpow_const, NumberField.Units.logEmbeddingQuot_injective, Real.cos_sub_nat_mul_pi, CFC.norm_abs, pi_norm_le_iff_of_nonempty, ArithmeticFunction.vonMangoldt_apply_one, lipschitzOnWith_iff_dist_le_mul, Affine.Simplex.signedInfDist_reindex, isApproximateSubgroup_one, EReal.coe_eq_zero, ZSpan.instDiscreteTopologySubtypeMemAddSubgroupToAddSubgroupIntSpanRangeCoeBasisRealOfFinite, Polynomial.leading_coeff_le_mahlerMeasure, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_fst_ofIsComplex, PadicInt.norm_p, UnitAddTorus.hasSum_prod_mFourierCoeff, inv_gold, Metric.cthickening_max_zero, Irrational.intCast_sub, Real.not_bddBelow_coe, Asymptotics.IsBigOWith.exists_pos, Real.not_continuousAt_deriv_qaryEntropy_zero, Real.tan_pi_div_three, AffineSubspace.isPreconnected_setOf_sOppSide, NumberField.mixedEmbedding.latticeBasis_apply, Path.map_coe, NumberField.mixedEmbedding.unit_smul_eq_zero, MeasureTheory.integrable_comp_mul_right_iff, Hyperreal.coe_add, ProbabilityTheory.isCondKernelCDF_condCDF, ContinuousMap.Homotopy.coe_toContinuousMap, EReal.nhds_bot', Real.pi_div_two_le_arcsin, LiouvilleWith.sub_nat_iff, Real.sin_three_mul, Real.sinc_zero, Real.arccos_lt_pi_div_two, MeasureTheory.Measure.addHaar_submodule, ProbabilityTheory.measurable_gaussianPDFReal, SmoothPartitionOfUnity.sum_finsupport_smul_eq_finsum, tendsto_rpow_neg_div, ContinuousMap.Homotopy.apply_zero, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, signedDist_apply_linear_apply, Seminorm.smul_closedBall_preimage, SchwartzMap.integral_mul_deriv_eq_neg_deriv_mul, ProbabilityTheory.variance_dirac, Complex.selfAdjointEquiv_symm_apply, Real.contDiff_cosh, Real.neg_mulExpNegMulSq_neg, TemperedDistribution.fourierInv_apply, Asymptotics.isBigOWith_snd_prod, Matrix.IsHermitian.cfcAux_id, AnalyticAt.harmonicAt_log_norm, GaussianInt.re_toComplex, inseparable_zero_iff_norm, NNReal.finset_prod_rpow, EuclideanGeometry.inversion_mem_perpBisector_inversion_iff, Path.extend_symm, Complex.UnitDisc.re_zero, Affine.Simplex.neg_one_lt_inner_vsub_altitudeFoot_div, Complex.ofRealHom_eq_coe, image_parallelepiped, Affine.Simplex.ExcenterExists.touchpointWeights_map, ContinuousLinearMap.norm_inl, MeasureTheory.Measure.addHaar_singleton_add_smul_div_singleton_add_smul, norm_le_norm_add_norm_div, NumberField.mixedEmbedding.lintegral_comp_polarCoordReal_symm, Real.sin_add_nat_mul_two_pi, EuclideanGeometry.collinear_of_angle_eq_pi, ProbabilityTheory.covarianceBilin_map, RCLike.real_smul_ofReal, Affine.Simplex.mongePoint_map, BoundedContinuousFunction.integral_add_const, ENNReal.rpow_left_bijective, Complex.mem_slitPlane_iff, HurwitzZeta.hurwitzOddFEPair_f, Affine.Simplex.eulerPoint_map, ENNReal.continuous_truncateToReal, MeasureTheory.L1.norm_of_fun_eq_integral_norm, Real.log_intCast_nonneg, Real.analyticAt_arsinh, Real.tan_eq_zero_iff, Real.arccos_neg_one, AkraBazziRecurrence.GrowsPolynomially.neg_iff, SchwartzMap.instFourierSMul, ENNReal.toReal_add_le, Orientation.two_zsmul_oangle_smul_right_self, MeasureTheory.hausdorffMeasure_real, Affine.Triangle.sOppSide_affineSpan_pair_point_excenter_singleton, Path.subpath_continuous_family, EReal.toReal_one, SchwartzMap.fourierTransformCLM_apply, IsUnifLocDoublingMeasure.scalingScaleOf_pos, ODE.FunSpace.intervalIntegrable_comp_compProj, HasFDerivAt.curveIntegral_segment_source', Metric.mem_closure_range_iff_nat, AffineSubspace.signedInfDist_singleton, RCLike.norm_sq_eq_def, fib_golden_conj_exp, zero_mem_lowerBounds_smoothingSeminormSeq_range, NumberField.mixedEmbedding.measurable_polarCoord_symm, Complex.circleTransformDeriv_periodic, SeminormedGroup.disjoint_nhds_one, Circle.surjOn_exp_neg_pi_pi, UniformConvexOn.neg, ENNReal.toReal_lt_toReal, CircleDeg1Lift.sup_apply, ContinuousMap.apply_le_norm, BoxIntegral.Box.Icc_eq_pi, EuclideanGeometry.angle_midpoint_eq_pi, Asymptotics.isBigO_iff_exists_eq_mul, BoundedContinuousFunction.dist_extend_extend, IsCompact.exists_cthickening_subset_open, NNReal.coe_iInf, LSeries.tendsto_atTop, continuous_real_toNNReal, IsOfFinOrder.norm_eq_one, Matrix.IsHermitian.coe_re_diag, ProbabilityTheory.Kernel.tendsto_densityProcess_fst_atTop_ae_of_monotone, ENNReal.tendsto_rpow_atBot_of_one_lt_base, NumberField.mixedEmbedding.fundamentalCone.intNorm_coe, Orientation.coe_basisRightAngleRotation, NumberField.mixedEmbedding.norm_eq_zero_iff, PointwiseConvergenceCLM.tendsto_nhds_atTop, NumberField.InfinitePlace.Completion.extensionEmbedding_of_isReal_coe, TemperedDistribution.fourierTransform_toTemperedDistributionCLM_eq, intervalIntegral.mul_integral_comp_mul_add, Polynomial.Chebyshev.roots_T_real, MeasureTheory.setIntegral_one_eq_measureReal, Asymptotics.IsBigOWith.sum, ArchimedeanClass.stdPart_nonneg, NumberField.mixedEmbedding.fundamentalCone.expMap_source, Real.tendsto_arctan_atBot, ProbabilityTheory.Kernel.borelMarkovFromReal_apply, SchwartzMap.fderivCLM_fourier_eq, ProbabilityTheory.gaussianReal_map_add_const, GroupNormClass.toNormedGroup_norm_eq, ProbabilityTheory.iIndepFun_iff_charFun_pi, CStarModule.inner_mul_inner_swap_le, HurwitzZeta.completedHurwitzZetaEven₀_neg, JoinedIn.somePath_mem, AkraBazziRecurrence.isBigO_asympBound, Finset.Nonempty.norm_prod_le_sup'_norm, Bundle.ContinuousRiemannianMetric.pos, NNReal.coe_mulIndicator, Metric.unitBall.instIsRightCancelMulZero, Real.nat_sqrt_le_real_sqrt, ENNReal.toReal_sup, NumberField.norm_embedding_le_house, variationOnFromTo.monotoneOn, TemperedDistribution.instLineDerivAdd, ProbabilityTheory.variance_neg, SchwartzMap.derivCLM_apply, Real.Angle.two_nsmul_coe_div_two, ModularGroup.abs_two_mul_re_lt_one_of_mem_fdo, Real.neg_one_le_sin, Complex.norm_sub_eq_iff, Seminorm.gauge_ball, SelbergSieve.one_le_level, MeasureTheory.Measure.toBoxAdditive_apply, NumberField.FinitePlace.norm_eq_one_iff_notMem, Polynomial.supNorm_le_choose_natDegree_div_two_mul_mahlerMeasure, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atTop, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply'', Complex.finrank_real_complex, RCLike.ratCast_im, Polynomial.mahlerMeasure_of_degree_eq_one, ProbabilityTheory.instIsMarkovKernel_toKernel, ProbabilityTheory.condVar_neg, HurwitzZeta.completedHurwitzZetaEven₀_zero, Summable.norm_lt_one, SchwartzMap.isBigO_cocompact_zpow_neg_nat, Real.deriv_cos, Circle.exp_intCast_mul, iteratedDeriv_exp_const_mul, integrableOn_Ioi_exp_neg_mul_sq_iff, norm_le_mul_norm_add, Affine.Simplex.affineCombination_touchpointWeights, MeasureTheory.integral_fun_fst, Orientation.volumeForm_zero_neg, MeasureTheory.pdf.integrable_pdf_smul_iff, BoundedContinuousFunction.nnnorm_coeFn_eq, NNReal.image_coe_Ioo, EReal.exp_mul, Real.continuousAt_const_rpow, Polynomial.Chebyshev.complex_ofReal_eval_U, Seminorm.coe_comp, Real.differentiableAt_binEntropy, Real.smoothTransition.continuous, NumberField.mixedEmbedding.normAtPlace_nonneg, Real.abs_sin_eq_one_iff, Orientation.angle_eq_abs_oangle_toReal, Real.Angle.cos_pos_iff_abs_toReal_lt_pi_div_two, Real.mapsTo_sin_Ioo, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_of_ne_zero, MeasureTheory.measureReal_union, RCLike.I_mul_re, tendsto_mulIndicator_thickening_mulIndicator_closure, SmoothPartitionOfUnity.sum_finsupport, Real.hasDerivAt_arctan', Orientation.areaForm_map, BoxIntegral.Prepartition.upper_sub_lower_of_mem_splitCenter, abs_dist_sub_le_dist_add_add, HasCompactMulSupport.exists_pos_le_norm, Affine.Triangle.orthocenter_mem_affineSpan, EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_not_collinear, instIsAddHaarMeasureProdRealVolume, Topology.RelCWComplex.closedCell_zero_eq_singleton, circleMap_eq_center_iff, RCLike.conj_eq_iff_im, BoundedContinuousFunction.dist_set_exists, ProbabilityTheory.stronglyMeasurable_gaussianPDFReal, deriv_bernoulliFun, PiTensorProduct.norm_eval_le_projectiveSeminorm, NNReal.nnnorm_eq, OrthonormalBasis.adjustToOrientation_apply_eq_or_eq_neg, det_fderivPiPolarCoordSymm, isConformalMap_iff, WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded, Rat.AbsoluteValue.not_real_equiv_padic, BoundedContinuousFunction.toReal_lintegral_coe_eq_integral, injOn_pi_polarCoord_symm, Path.Homotopy.continuous_transReflReparamAux, Hyperreal.tendsto_atBot_iff, cantorToHilbert_continuous, LSeriesSummable.isBigO_rpow, Real.Wallis.W_eq_factorial_ratio, ProbabilityTheory.condVar_bot_ae_eq, Affine.Simplex.faceOppositeCentroid_mem_ninePointCircle, NormedCommGroup.nhds_basis_norm_lt, Real.deriv2_qaryEntropy, Real.differentiableAt_exp, Real.negMulLog_def, Topology.RelCWComplex.disjointBase', Real.locallyFinite_volume, Function.locallyFinsuppWithin.logCounting_mono, Affine.Simplex.mongePoint_mem_affineSpan, MeasureTheory.lpNorm_of_isEmpty, Real.hasStrictDerivAt_arcsin, Complex.finrank_real_complex_fact, Height.logHeight₁_zero, Real.floor_pi_eq_three, real_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, Metric.continuous_infDist_pt, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, IsUltrametricDist.norm_mul_le_max, CircleDeg1Lift.ceil_map_map_zero_le, Metric.unitClosedBall.coe_one, CFC.monotone_sqrt, ENNReal.tsum_coe_eq_top_iff_not_summable_coe, EReal.coe_nsmul, MeasureTheory.tilted_zero', ENNReal.summable_toReal, NumberField.mixedEmbedding.logMap_real, NumberField.mixedEmbedding.commMap_apply_of_isReal, Fourier.norm_fourierIntegral_le_integral_norm, liouvilleWith_one, RCLike.ofReal_real_eq_id, EuclideanGeometry.Sphere.IsTangent.isTangentAt, Rat.infinitePlace_apply, AlgHom.map_coe_real_complex, ZSpan.fundamentalDomain_pi_basisFun, AddGroupSeminorm.addGroupSeminormClass, Real.logb_mul_base, Affine.Simplex.touchpointWeights_singleton_neg, ProperCone.mem_innerDual, WithCStarModule.norm_equiv_le_norm_pi, ProbabilityTheory.Kernel.measurable_density_left, ZLattice.isAddFundamentalDomain, EuclideanGeometry.Sphere.orthRadius_le_orthRadius_iff, BumpCovering.eventuallyEq_one', NormedSpace.of_real_exp_ℝ_ℝ, Real.abs_iteratedDeriv_sin_le_one, smoothingSeminormSeq_bddBelow, Seminorm.finset_sup_smul, MeasureTheory.measureReal_le_one, MeasureTheory.Measure.integrable_comp_iff, Real.Angle.continuous_sin, Real.sin_arctan_strictMono, Complex.cpow_ofReal_im, quasispectrum.isCompact_nnreal, Metric.exists_ball_subset_ball, Metric.eventually_notMem_cthickening_of_infEdist_pos, Bundle.RiemannianMetric.pos, IsOpen.exists_contDiff_support_eq, NumberField.mixedEmbedding.polarCoord_apply, Real.Angle.coe_toIcoMod, Real.log_two_lt_d9, TemperedDistribution.instLineDerivSMulComplex, tendsto_sub_mul_tsum_nat_rpow, Real.not_bddAbove_coe, CStarAlgebra.instNonnegSpectrumClass', CStarAlgebra.conjugate_le_norm_smul, CircleDeg1Lift.map_int_add, RCLike.conj_re_ax, isMIntegralCurveAt_comp_sub, MeasureTheory.lpNorm_sum_le, IsometryEquiv.coeFn_toRealAffineIsometryEquiv, hasSum_zeta_two, MeasureTheory.abs_integral_le_integral_abs, Real.Angle.sin_zero, not_irrational_one, Set.Countable.preimage_circleMap, summable_geometric_iff_norm_lt_one, convexOn_exp, Seminorm.isBounded_sup, NumberField.mixedEmbedding.hasFDerivAt_polarCoordReal_symm, spectralNorm.spectralMulAlgNorm_eq_of_mem_roots, norm_midpoint_lt_iff, CFC.sqrt_eq_cfc, Function.Complex.hasTemperateGrowth_ofReal, ArithmeticFunction.vonMangoldt.continuousOn_LFunctionResidueClassAux, exists_continuousMap_one_of_isCompact_subset_isOpen, NormedAlgebra.Real.exists_isMonicOfDegree_two_and_aeval_eq_zero, MeasureTheory.condExpInd_smul', Real.contDiffOn_arcosh, Real.sin_eq_neg_one_iff, Polynomial.logMahlerMeasure_zero, UpperHalfPlane.det_J, EuclideanGeometry.angle_add_angle_eq_pi_of_angle_eq_pi, Real.mk_inf, Complex.ofReal_comp_nsmul, IsGδ.setOf_liouville, CircleDeg1Lift.monotone, Real.log_multiset_prod, ContinuousMap.Homotopy.prod_apply, ProbabilityTheory.analyticOnNhd_mgf, ModularGroup.coe_one, Real.sin_pi_div_sixteen, AddCircle.lintegral_preimage, Real.differentiable_iteratedDeriv_cosh, Real.hasStrictDerivAt_sin, IsApproximateSubgroup.card_pow_le, RCLike.mul_self_norm, ZMod.toAddCircle_injective, Real.tendsto_sqrt_atTop, ContDiffMapSupportedIn.structureMapLM_zero_injective, Metric.diam_union', MeasureTheory.measureReal_le_measureReal_union_right, integral_one_div_one_add_sq, PiNat.dist_nonneg, EuclideanGeometry.collinear_iff_eq_or_eq_or_angle_eq_zero_or_angle_eq_pi, ContDiffPointwiseHolderAt.contDiffAt, mem_nullSubgroup_iff, Complex.log_eq_integral, BoundedContinuousFunction.add_norm_nonneg, ContinuousAlternatingMap.norm_ofSubsingleton_id, tendsto_indicator_cthickening_indicator_closure, Complex.equivRealProdCLM_symm_apply_re, RingSeminorm.ext_iff, Affine.Simplex.incenter_reindex, NNReal.summable_rpow_inv, Path.refl_range, integral_one, NNReal.coe_lt_coe, MeasureTheory.ProbabilityMeasure.continuous_iff_forall_continuous_integral, NNReal.rpow_eq_zero_iff, UpperHalfPlane.sinh_half_dist_add_dist, Manifold.pathELength_eq_lintegral_mfderiv_Icc, Complex.norm_I, ProbabilityTheory.tendsto_cdf_atTop, Metric.denseRange_iff, ArchimedeanClass.stdPart_sub, ContinuousMap.HomotopyWith.prop, NumberField.mixedEmbedding.continuous_normAtAllPlaces, Matrix.IsHermitian.roots_charpoly_eq_eigenvalues₀, ProbabilityTheory.lintegral_betaPDF, AffineSubspace.mem_perpBisector_iff_dist_eq, Real.toNNReal_zero, MeasureTheory.integrable_withDensity_iff_integrable_coe_smul₀, PadicInt.norm_lt_pow_iff_norm_le_pow_sub_one, Complex.ofReal_div, Padic.norm_rat_le_one, QuasispectrumRestricts.nnreal_of_nonneg, MeasureTheory.charFunDual_eq_pi_iff', MeasureTheory.hasFiniteIntegral_prod_iff, IsUltrametricDist.norm_natCast_le_one, Real.two_mul_arctan_inv_3_add_arctan_inv_7, uniqueDiffOn_Ioi, Chebyshev.psi_eq_sum_Icc, realPart_imaginaryPart, AddGroupSeminorm.coe_comp, MeasureTheory.exists_null_frontiers_thickening, ModularForm.coe_norm, ProbabilityTheory.mgf_zero', BoundedContinuousFunction.toLp_norm_le, intervalIntegral.intervalIntegrable_pow, AbsolutelyContinuousOnInterval.uniformlyContinuousOn, MeasureTheory.charFun_map_mul, EReal.toReal_image_Ioo_zero_top, IsPrimitiveRoot.norm'_eq_one, Complex.sq_nonpos_iff, Similar.exists_pairwise_dist_eq, NonarchAddGroupNorm.lt_def, MeasureTheory.measurable_llr, ContDiffMapSupportedIn.seminorm_postcompLM_le, Subgroup.strictPeriods_SL2Z, inner_mul_symm_re_eq_norm, Real.circleAverage_eq_intervalAverage, MeasureTheory.Lp.continuous_negPart, EReal.coe_mul, MeasureTheory.Measure.tendsto_IicSnd_atTop, ContinuousMultilinearMap.bound, Path.id_apply, MeasureTheory.integral_countable, Nat.preimage_ball, CongruenceSubgroup.mem_conjGL', Complex.ofReal_comp_zsmul, MeasureTheory.Lp.coeFn_negPart, GroupSeminorm.coe_le_coe, Metric.biUnion_lt_closedBall, MeasureTheory.measureReal_compl, Hyperreal.coe_max, dist_eq_zero, NumberField.abs_discr_ge_of_isTotallyComplex, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff, HurwitzZeta.sinZeta_neg, Real.Angle.cos_neg_iff_pi_div_two_lt_abs_toReal, Real.cos_add_pi_div_two, ContinuousMultilinearMap.norm_mkPiAlgebraFin_succ_le, IsSelfAdjoint.instContinuousFunctionalCalculus, ContDiffPointwiseHolderAt.fderiv, CompactlySupportedContinuousMap.toReal_smul, Orientation.inner_rightAngleRotationAux₁_right, hasFDerivAt_pi_polarCoord_symm, Int.instDiscreteTopologySubtypeRealMemAddSubgroupZmultiples, MeasureTheory.lintegral_tilted, Real.tendsto_sum_pi_div_four, Submodule.re_inner_starProjection_nonneg, Nat.norm_cast_le, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt, norm_cfcₙ_one_sub_one_add_inv_lt_one, BoundedContinuousFunction.norm_sub_nonneg, tendsto_norm_cobounded_atTop', Real.analyticAt_cosh, NumberField.mixedEmbedding.latticeBasis_repr_apply, UniformContinuous.dist, ContinuousMap.HomotopyWith.refl_apply, CFC.abs_eq_cfcₙ_norm, NumberField.FinitePlace.instMonoidWithZeroHomClassReal, Complex.dist_mk, norm_tangentSpace_vectorSpace, Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter, Real.sInf_smul_of_nonpos, MeasureTheory.MemLp.im, unitInterval.coe_toNNReal, ModularFormClass.qExpansion_isBigO, InformationTheory.not_differentiableWithinAt_klFun_Ioi_zero, Real.fourierChar_apply', NNReal.hasMeasurablePow, continuousOn_cfcₙ_nnreal, EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi, EuclideanGeometry.Sphere.isIntTangentAt_center_iff, MeasureTheory.StronglyMeasurable.norm, NonarchAddGroupNorm.ext_iff, MeasureTheory.measureReal_diff', surjOn_extremePoints_image, EReal.abs_def, Real.Angle.tan_coe_pi, SchwartzMap.integral_fourierInv_mul_eq, Metric.Sigma.one_le_dist_of_ne, Affine.Simplex.touchpointWeights_eq_zero, Real.cos_sub_two_pi, spectralValueTerms_of_natDegree_le, Real.Angle.cos_pi_div_two_sub, HurwitzZeta.completedCosZeta_eq, NormedAddGroupHom.norm_lift_le, Complex.isCauSeq_im, ArchimedeanClass.stdPart_eq_zero, MeasureTheory.eLpNorm_eq_lintegral_rpow_enorm_toReal, Real.contDiffAt_rpow_const_of_ne, ZLattice.covolume_pos, BoxIntegral.Integrable.smul, LinearMap.IsSymmetric.trace_eq_sum_eigenvalues, TemperedDistribution.laplacian_toTemperedDistributionCLM_eq, ProbabilityTheory.complexMGF_id_gaussianReal, isMIntegralCurveOn_comp_mul_ne_zero, integral_sin_pow_succ_le, Complex.mul_conj, ZLattice.le_norm_of_le_abs_repr, CFC.abs_sq, Real.logb_abs, Complex.summable_one_div_nat_cpow, Complex.im_ofReal_mul, ODE.FunSpace.continuous, IntervalIntegrable.def', ContinuousAffineMap.norm_comp_le, MeasureTheory.L1.SimpleFunc.norm_eq_integral, Real.cos_two_mul, Real.smoothTransition.zero_iff_nonpos, Real.tan_mul_cos, PartitionOfUnity.le_one, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_neg, signedDist_right_lineMap, LiouvilleNumber.partialSum_succ, tendsto_dist_right_cocompact_atTop, StieltjesFunction.measure_Ioc, Complex.norm_eq_one_of_mem_rootsOfUnity, ProbabilityTheory.uncenteredCovarianceBilin_zero, MeasureTheory.eLpNorm_indicator_const', Real.rpow_ofNat, Nat.isClosedEmbedding_coe_real, Delone.DeloneSet.subset_ball_singleton, Real.tendsto_div_pow_mul_exp_add_atTop, Real.cos_int_mul_two_pi_sub_pi, ArchimedeanClass.mk_sub_pos_iff, AddCircle.measurePreserving_mk, MeasureTheory.SimpleFunc.setToSimpleFunc_eq_sum_filter, RCLike.realRingEquiv_apply, MeasureTheory.ofReal_setIntegral_one_of_measure_ne_top, Affine.Simplex.sum_touchpointWeights, Valued.integer.mem_iff, MeasureTheory.Measure.haar.chaar_empty, rank_real_of_complex, circleIntegrable_def, Real.sinh_neg_iff, InformationTheory.convexOn_Ioi_klFun, Real.differentiable_fourierChar, Path.extend_zero, MeasureTheory.SimpleFunc.norm_approxOn_zero_le, Path.source, Affine.Simplex.sum_pointWeightsWithCircumcenter, Real.HolderTriple.lt, Real.sinh_lt_cosh, Asymptotics.IsLittleO.norm_left, ValueDistribution.proximity_pow_top, NumberField.AdeleRing.algebraMap_fst_apply, PiTensorProduct.projectiveSeminormAux_nonneg, lintegral_comp_polarCoord_symm, Metric.eventually_notMem_thickening_of_infEdist_pos, IsScalarTower.complexToReal, ContinuousMap.Homotopy.extend_zero, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf, SmoothBumpCovering.apply_ind, Asymptotics.isBigOWith_principal, BoundedContinuousFunction.bounded, smul_ball, integral_comp_neg_Ioi, EuclideanGeometry.Sphere.mem_tangentSet_iff, RCLike.mul_im, Seminorm.smul_ball_preimage, AddGroupSeminorm.le_def, Real.logDeriv_sin, VectorFourier.fourierPowSMulRight_apply, ProbabilityTheory.mgf_dirac', skewAdjointPart_eq_I_smul_imaginaryPart, TendstoUniformly.re, uniqueDiffOn_Ico, BumpCovering.nonneg, Nat.Primes.summable_rpow, inner_eq_norm_mul_iff_real, Complex.inv_im, dist_norm_norm_le', MeasureTheory.FiniteMeasure.continuous_integral_boundedContinuousFunction, LSeriesSummable_lt_re_of_abscissaOfAbsConv_lt_re, Affine.Simplex.altitude_map, Metric.eventually_nhds_iff_ball, NormedAddGroupHom.lipschitz, NumberField.InfinitePlace.Completion.surjective_extensionEmbedding_of_isReal, dist_anti_right_pi, ValueDistribution.logCounting_pow_zero, ProbabilityTheory.Kernel.eLpNorm_densityProcess_le, HurwitzZeta.hurwitzEvenFEPair_neg, MeasureTheory.L1.SimpleFunc.norm_integral_le_norm, SeparationQuotient.mk_eq_one_iff, RCLike.ofReal_tsum, Real.deriv_cos', Path.coe_toContinuousMap, SmoothBumpCovering.support_toSmoothPartitionOfUnity_subset, isBigO_deriv_rpow_const_atTop, Complex.range_norm, bernsteinApproximation_uniform, polarCoord_apply, SchwartzMap.decay, Real.not_summable_natCast_inv, NormedRing.inverse_add_norm_diff_first_order, tendsto_norm_cobounded_atTop, MeasureTheory.Measure.hausdorffMeasure_apply, AddCircle.measurable_mk', ContinuousMap.Homotopy.map_one_left, Complex.zero_re, RCLike.normSq_div, norm_fderiv_le_of_lipschitzOn, RCLike.im_sq_le_normSq, SzemerediRegularity.pow_mul_m_le_card_part, PadicInt.norm_sub_zmodRepr_lt_one, Real.exp_nonneg, Asymptotics.isLittleO_norm_pow_id, dist_dist_dist_le, Real.deriv_rpow_const', Real.continuous_fourierChar, Dilation.diam_range, ContinuousLinearMap.opNorm_le_iff_lipschitz, ModularGroup.exists_one_half_le_im_smul_and_norm_denom_le, dist_smul₀, spectrum.isCompact_nnreal, ProbabilityTheory.abs_truncation_le_abs_self, MeasureTheory.isAddHaarMeasure_volume_pi, RCLike.lipschitzWith_ofReal, Real.cobounded_eq, SeminormClass.toAddGroupSeminormClass, EuclideanSpace.dist_eq, NumberField.mixedEmbedding.normAtPlace_negAt, Chebyshev.integral_theta_div_log_sq_isBigO, Stirling.stirlingSeq'_pos, SchwartzMap.convolution_flip, Real.sin_sub_nat_mul_pi, norm_pow_le', Dilation.diam_image, MeasureTheory.Measure.haar.prehaar_self, CircleDeg1Lift.coe_toOrderHom, continuousSMul_closedBall_closedBall, Module.Basis.parallelepiped_map, AlternatingMap.measure_def, MeasureTheory.measureReal_union_add_inter', ContinuousMap.Homotopy.apply_one, EisensteinSeries.abs_le_left_of_norm, ContinuousAt.norm, strictConcaveOn_sin_Icc, ProbabilityTheory.IsRatCondKernelCDFAux.nonneg', MeasureTheory.charFunDual_dirac, LipschitzWith.norm_le_mul', CircleDeg1Lift.units_semiconj_of_translationNumber_eq, tendsto_one_iff_norm_tendsto_zero, Urysohns.CU.approx_le_approx_of_U_sub_C, CFC.one_rpow, Metric.uniformity_eq_comap_nhds_zero, Real.pi_gt_d20, ENNReal.trichotomy, WeakFEPair.hg_int, LinearIsometryEquiv.reflections_generate_dim, Hyperreal.coe_div, GroupSeminorm.le_def, Complex.isometryOfOrthonormal_apply, CircleDeg1Lift.le_iterate_pos_iff, intervalIntegral.smul_integral_comp_mul_right, ENNReal.exists_frequently_lt_of_liminf_ne_top, Complex.frontier_setOf_le_re_and_le_im, Real.sin_sq_lt_sq, CStarAlgebra.directedOn_nonneg_ball, SchwartzMap.laplacian_eq_sum, MeasureTheory.Measure.haar.addCHaar_sup_eq, Real.tendsto_Icc_vitaliFamily_left, tendsto_measure_Icc_nhdsWithin_right', Complex.sameRay_iff, SchwartzMap.lineDerivOp_apply_eq_fderiv, AddCircle.norm_le_half_period, Circle.normSq_coe, intervalIntegral.integral_comp_div_add, SingularManifold.instIsManifoldRealM, Real.hasStrictDerivAt_sqrt, EuclideanGeometry.Sphere.isTangentAt_center_iff, Real.tendsto_eulerMascheroniSeq, PadicInt.norm_add_eq_max_of_ne, Real.cosh_sq', Finsupp.log_prod, NumberField.mixedEmbedding.normAtAllPlaces_nonneg, Asymptotics.IsLittleO.norm_norm, integral_gaussian, Rat.AbsoluteValue.eq_on_nat_iff_eq, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply, Metric.eventually_notMem_cthickening_of_infEDist_pos, Real.continuousOn_tan, RCLike.conj_to_real, BoxIntegral.integral_const, Metric.lipschitz_infDist_pt, NumberField.mixedEmbedding.normAtPlace_smul, intervalIntegral.integral_smul_const, ConvexBody.convex', BumpCovering.exists_finset_toPOUFun_eventuallyEq, TestFunction.contDiff', Real.sSup_def, GenLoop.Homotopic.equiv, HurwitzZeta.completedHurwitzZetaEven_neg, Complex.abs_re_lt_norm, NumberField.mixedEmbedding.fundamentalCone.isBounded_normLeOne, Diffeology.isPlot_id, intervalIntegral.mul_integral_comp_sub_mul, IsBoundedBilinearMap.isBigO, BoundedContinuousFunction.abs_diff_coe_le_dist, Real.toNNReal_coe_nat, Real.ofCauchy_one, BoxIntegral.Box.coe_eq_pi, Hyperreal.st_le_of_le, eventually_closedBall_subset, Real.arcsin_lt_pi_div_two, OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le, contMDiffOn_comp_projIcc_iff, intervalIntegral.abs_integral_eq_abs_integral_uIoc, NNReal.coe_multiset_sum, EReal.preimage_coe_Iic, NumberField.mixedEmbedding.finrank, variationOnFromTo.eq_zero_iff, Real.tan_surjective, Orientation.two_zsmul_oangle_smul_right_of_ne_zero, ProbabilityTheory.integral_id_gaussianReal, SchwartzMap.integral_fourier_smul_eq, Real.tan_sub_nat_mul_pi, Real.dimH_segment, Function.Periodic.norm_qParam, Real.inner_le_Lp_mul_Lq, Real.iter_deriv_rpow_const, ZLattice.summable_norm_sub_zpow, NormedSpace.sphere_nonempty, Complex.imCLM_nnnorm, Complex.not_lt_zero_iff, SmoothBumpFunction.contMDiff, Metric.diam_pos, HurwitzZeta.hurwitzOddFEPair_k, GroupSeminormClass.toSeminormedGroup_norm_eq, NNReal.coe_image, Path.truncate_const_continuous_family, Real.map_volume_mul_right, LiouvilleWith.neg, Real.comap_exp_atTop, AkraBazziRecurrence.b_pos, AlgHom.toContinuousLinearMap_norm, Real.arctan_lt_pi_div_two, norm_intCast_eq_abs_mul_norm_one, norm_zpow, NumberField.mixedEmbedding.polarCoordReal_symm_target_ae_eq_univ, AnalyticAt.re_ofReal, exists_continuous_one_zero_of_isCompact_of_isGδ, MeasureTheory.measureReal_union', Circle.argPartialEquiv_target, Orientation.inner_rightAngleRotation_right, CStarAlgebra.isStrictlyPositive_TFAE, unitInterval.measurableEmbedding_coe, Real.hasDerivAt_exp, fourierSubalgebra_closure_eq_top, Stirling.stirlingSeq_zero, Polynomial.Chebyshev.eval_T_real_eq_one_iff, ModularForm.prod_fintype_slash, Real.HolderConjugate.sub_one_mul_conj, volume_euclideanSpace_eq_dirac, selfAdjoint.val_re_map_spectrum, Real.logb_div_base, CStarAlgebra.isStrictlyPositive_iff_isSelfAdjoint_and_spectrum_pos, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, MeasureTheory.lpNorm_of_not_aestronglyMeasurable, Metric.infDist_pos_iff_notMem_closure, Complex.IsExpCmpFilter.isLittleO_log_re_re, RCLike.wInner_one_const_left, circleIntegrable_sub_inv_iff, eventually_norm_mfderivWithin_symm_extChartAt_comp_lt, Summable.norm, summable_norm_iff, HurwitzZeta.cosKernel_neg, QuotientAddGroup.norm_eq_addGroupSeminorm, AbsolutelyContinuousOnInterval.uIoc_subset_of_mem_disjWithin, asymptoticCone_subset_singleton_of_bounded, ValueDistribution.proximity_even, MeasureTheory.Measure.exists_integral_isAddLeftInvariant_eq_smul_of_hasCompactSupport, schnirelmannDensity_le_of_subset, MeasureTheory.pow_mul_meas_ge_le_eLpNorm, NonarchAddGroupNorm.coe_sup, ProbabilityTheory.HasSubgaussianMGF.memLp, NumberField.mixedEmbedding.convexBodySum_isBounded, RCLike.ofReal_mul_neg_iff, CuspFormClass.exp_decay_atImInfty', SzemerediRegularity.one_le_m_coe, integral_sin_sq_mul_cos, BoundedContinuousFunction.norm_eq_of_nonempty, Real.arctan_sqrt_three, RCLike.re_ofReal_pow, ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral_iInf_rat_gt, NumberField.house_nat_mul, Complex.sameRay_iff_arg_div_eq_zero, Affine.Simplex.ExcenterExists.signedInfDist_excenter, Real.hasSum_sin, EisensteinSeries.abs_norm_eq_max_natAbs, ZeroAtInftyContinuousMap.bounded, Complex.norm_cpow_inv_nat, Orientation.volumeForm_apply_le, Real.lipschitzWith_cos, MeasureTheory.eLpNorm_const, ContDiffBump.eventuallyEq_one_of_mem_ball, re_inner_self_nonpos, ContinuousLinearMap.norm_single_le_one, NumberField.mixedEmbedding.polarSpaceCoord_apply, Real.nonempty_algEquiv_or, QuotientGroup.le_norm_iff, AddGroupSeminorm.smul_apply, RCLike.norm_sq_re_add_conj, Real.cos_eq_one_iff, Polynomial.Chebyshev.U_real_cosh, LinearMap.IsSymmetric.im_inner_apply_self, Metric.uniformContinuousOn_iff_le, gold_lt_two, Complex.starConvex_slitPlane, LiouvilleWith.sub_rat_iff, absolutelyContinuousOnInterval_iff, BoundedContinuousFunction.norm_integral_le_mul_norm, ContinuousLinearMap.norm_compSL_le, Matrix.IsHermitian.eigenvalues_mem_spectrum_real, BoxIntegral.Box.volume_apply, MeasureTheory.norm_condExpInd_le, Real.arcsin_pos, curveIntegralFun_trans_aeeq_left, MeasureTheory.BorelCantelli.stronglyAdapted_process, SmoothPartitionOfUnity.finite_tsupport, Metric.lipschitz_infDist, ProbabilityTheory.analyticOn_complexMGF, Rat.AbsoluteValue.real_eq_abs, Complex.ofReal_sub, exists_norm_le_of_cauchySeq, Real.sinh_strictMono, Real.mk_sup, WeakFEPair.hf_int, ENNReal.toReal_inf, Metric.biUnion_lt_ball, NNReal.rpow_one_add', Measurable.ennreal_toReal, ProbabilityTheory.Kernel.eLpNorm_density_le, dual_solid, unitInterval.sigmoid_monotone, CStarAlgebra.norm_negPart_le, polarCoord_source_ae_eq_univ, Set.OrdConnected.preimage_real_toNNReal, Real.measurable_sin, Complex.im_surjective, NumberField.mixedEmbedding.negAt_apply_norm_isReal, Real.rpow_sub_natCast, Hyperreal.isSt_iff_tendsto, MeasureTheory.integrable_comp_smul_iff, Real.tendsto_abs_logb_atTop, dist_le_norm_add_norm', Complex.hasSum_im, MeasureTheory.Measure.addHaar_preimage_linearEquiv, hasFDerivAtFilter_iff_tendsto, Chebyshev.integral_theta_div_log_sq_isLittleO, cfcₙ_nnreal_eq_real, gauge_gaugeRescale_le, InnerProductSpace.laplacian_eq_iteratedFDeriv_orthonormalBasis, RCLike.im_to_complex, CFC.sqrt_algebraMap, Real.expMonoidHom_apply, NNReal.coe_pos, Real.binEntropy_lt_log_two, SchwartzMap.instFourierInvAdd, analyticWithinAt_rexp, Complex.angle_one_left, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunctionAux_def, CFC.posPart_algebraMap, Valued.integer.isUnit_iff_norm_eq_one, abs_real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, InnerProductSpace.Core.cauchy_schwarz_aux', EulerSine.integral_cos_pow_pos, SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left, Asymptotics.isBigOWith_const_const, fourier_zero', Metric.unitSphere.coe_div, SlashInvariantForm.vAdd_width_periodic, CFC.sqrt_one, Real.arctan_le_zero, UpperHalfPlane.coe_vadd, Seminorm.smul_apply, ENNReal.ofReal_zero, UpperHalfPlane.denom_one, abs_norm_sub_norm_le', IsMIntegralCurveAt.comp_mul_ne_zero, tendsto_norm_atTop_iff_cobounded, CovByVAdd.nonneg, MeasureTheory.SignedMeasure.zero_mem_measureOfNegatives, schnirelmannDensity_lt_iff, InnerProductSpace.isIdempotentElem_rankOne_self_iff, Real.Angle.sign_toReal, Real.sub_le_dist, Valued.toNormedField.norm_lt_iff, ContinuousLinearMap.opNorm_nonneg, MeasureTheory.hausdorffMeasure_affineSegment, intervalIntegral.FTCFilter.nhds, ProbabilityTheory.stronglyMeasurable_condCDF, ModularGroup.exists_smul_mem_fd, Complex.UnitDisc.norm_lt_one, ContDiffBump.hasCompactSupport_normed, Real.sin_sq_pi_over_two_pow, Metric.ball_eq_empty, OpenPartialHomeomorph.contDiffOn_univBall_symm, Metric.exists_subseq_summable_dist_of_cauchySeq, Complex.re_surjective, IsCompact.measure_eq_biInf_integral_hasCompactSupport, Real.sq_sin_pi_div_three, UnitAddCircle.mem_addWellApproximable_iff, UpperHalfPlane.I_re, circleMap_zero_radius, ProbabilityTheory.gaussianReal_map_const_sub, CompactlySupportedContinuousMap.nnrealPart_apply, Affine.Triangle.sbtw_touchpoint_empty, Complex.toMatrix_conjAe, ModularGroup.three_le_four_mul_im_sq_of_mem_fd, AddGroupNorm.addGroupNormClass, Cardinal.cantorFunctionAux_zero, ArithmeticFunction.vonMangoldt_eq_zero_iff, OrthogonalFamily.norm_sum, Orientation.rotation_apply, ContinuousOn.norm, Real.neg_one_le_mulExpNegMulSq_one, MeasureTheory.Measure.toSignedMeasure_apply_measurable, MeasureTheory.levyProkhorovDist_self, StieltjesFunction.iInf_Ioi_eq, Tactic.ComputeAsymptotics.WellFormedBasis.tail_isLittleO_head, MeasureTheory.Measure.HasTemperateGrowth.exists_eLpNorm_lt_top, NormedAddCommGroup.tendsto_atTop, Real.strictAntiOn_log, Real.tendsto_pow_logb_div_mul_add_atTop, NumberField.mixedEmbedding.fundamentalCone.expMap_add, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, ContinuousLinearMap.IsPositive.spectrumRestricts, Real.deriv_fourierChar, Seminorm.closedBall_eq_biInter_ball, EuclideanGeometry.Sphere.isIntTangent_iff_dist_center, CFC.nnrpow_eq_cfcₙ_real, ODE.FunSpace.compProj_val, MeasureTheory.norm_Lp_toLp_restrict_le, RCLike.re_eq_complex_re, neg_one_lt_goldConj, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, Rat.AbsoluteValue.not_real_isEquiv_padic, Set.OrdConnected.preimage_coe_nnreal_real, dist_lt_dist_add_dist_iff, NumberField.InfinitePlace.Completion.surjective_extensionEmbeddingOfIsReal, TestFunction.instLocallyConvexSpaceReal, Real.HolderTriple.pos', UpperHalfPlane.im_inv_neg_coe_pos, StieltjesFunction.ae_hasDerivAt, UpperHalfPlane.IsZeroAtImInfty.exp_decay_atImInfty', contDiffWithinAt_abs, MulRingSeminorm.toFun_eq_coe, instSMulCommClass_closedBall_closedBall_ball, Subgroup.strictWidthInfty_pos_iff, Real.abs_sin_le_abs, Stirling.log_stirlingSeq_diff_le_geo_sum, hasSum_sq_fourierCoeff, Real.nnnorm_natCast, Complex.neg_pi_div_two_le_arg_iff, NonarchAddGroupSeminorm.le_def, PartitionOfUnity.sum_nonneg, Hyperreal.coe_abs, ENNReal.ofReal_lt_ofNat, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atBot, MeasureTheory.withDensityᵥ_rnDeriv_smul, Complex.canLift, PositiveLinearMap.norm_apply_le_of_nonneg, EReal.tendsto_toReal, IsometryEquiv.coe_toRealLinearIsometryEquivOfMapZero_symm, EReal.coe_add, Affine.Simplex.touchpoint_empty_notMem_affineSpan_of_ne, ContinuousLinearMap.bddAbove_rayleighQuotient, Behrend.le_sqrt_log, MeasureTheory.condExpInd_disjoint_union_apply, NNReal.continuousOn_rpow_const_compl_zero, Complex.UnitDisc.instSMulCommClass_circle_closedBall, Irrational.add_intCast, ProbabilityTheory.measure_condCDF_Iic, Complex.isOpen_setOf_mem_nhds_and_isMaxOn_norm, Mathlib.Meta.Positivity.nnabs_pos_of_pos, RCLike.norm_to_complex, Complex.isBigO_ofReal_right, Real.contDiffAt_arccos, polynomialFunctions.topologicalClosure, EuclideanGeometry.Sphere.IsTangentAt_iff_angle_eq_pi_div_two, LinearMap.toSeminorm_ball_zero, Real.differentiableAt_negMulLog, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, ProbabilityTheory.HasSubgaussianMGF.aestronglyMeasurable, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding_of_isReal, HolderOnWith.of_le, Metric.eventually_notMem_thickening_of_infEDist_pos, Behrend.two_div_one_sub_two_div_e_le_eight, dist_prod_prod_le, UpperHalfPlane.val_J, Metric.diam_subsingleton, NumberField.toNNReal_valued_eq_adicAbv, Besicovitch.tendsto_filterAt, MeasureTheory.eLpNorm_le_eLpNorm_mul_rpow_measure_univ, Orientation.kahler_apply_apply, PiLp.dist_eq_of_L2, Module.Basis.norm_zero, SmoothBumpFunction.tsupport_subset_extChartAt_source, RCLike.imCLM_coe, RCLike.re_sq_le_normSq, BoxIntegral.Box.lower_lt_upper, Polynomial.isGreatest_supNorm, isMIntegralCurveAt_comp_add, ContinuousLinearMap.reApplyInnerSelf_smul, imaginaryPart_imaginaryPart, Orientation.inner_rightAngleRotationAux₁_left, MeasureTheory.integral_indicator_const, Path.Homotopy.trans_refl_reparam, NNReal.coe_injective, Real.add_one_lt_exp, StieltjesFunction.id_apply, Real.monotoneOn_sin, CompactlySupportedContinuousMap.toReal_nonneg, separatesPoints_continuous_of_t35Space, setOf_riemmanianEDist_lt_subset_nhds', Real.logb_zero, ContinuousMap.Homotopy.congr_fun, ProbabilityTheory.gaussianReal_absolutelyContinuous', ProbabilityTheory.Kernel.densityProcess_fst_univ, Real.HolderTriple.inv_inv_add_inv, ENNReal.toReal_rpow, SzemerediRegularity.coe_m_add_one_pos, Path.extend_extends', ENNReal.rpow_neg_one, EReal.coe_pow, exists_embedding_euclidean_of_compact, Complex.div_ofReal_im, strictConvexOn_zpow, Besicovitch.BallPackage.rpos, Real.measurable_log, EReal.coe_one, Real.HolderTriple.inv_eq, Seminorm.coe_zero, ProbabilityTheory.gaussianReal_map_const_add, Asymptotics.IsBigO.isBoundedUnder_le, Complex.angle_one_right, Real.cos_nat_mul_two_pi_add_pi, ProbabilityTheory.Kernel.instIsMarkovKernelCondKernelReal, LinearMap.toSeminorm_apply, nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts, Complex.IsExpCmpFilter.abs_im_pow_eventuallyLE_exp_re, hasDerivAt_ofReal_cpow_const', Complex.normSq_eq_conj_mul_self, SimpleGraph.lapMatrix_mulVec_eq_zero_iff_forall_reachable, LineDeriv.tensorLineDerivTwo_canonicalCovariantTensor_eq_sum, Orientation.areaForm_apply_self, ModularForm.slash_def, MeasureTheory.Lp.norm_measure_zero, Affine.Simplex.excenterWeights_empty_pos, ProbabilityTheory.measurable_measure_condCDF, CFC.sqrt_le_sqrt, Real.HolderTriple.inv_lt_inv, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, Complex.lim_norm, Real.smul_iSup_of_nonneg, Submodule.starProjection_minimal, Real.analyticOn_arsinh, Real.abs_sin_le_one, InnerProductGeometry.cos_eq_one_iff_angle_eq_zero, HasFPowerSeriesAt.isBigO_sub_partialSum_pow, MeasureTheory.lpNorm_natCast_mul, Orientation.oangle_smul_add_right_eq_zero_or_eq_pi_iff, MeasureTheory.integrable_rnDeriv_smul_iff, Real.cosh_sub_sinh, Irrational.div_natCast, Real.volume_real_Ico, Real.toNNReal_le_iff_le_coe, ProbabilityTheory.hasFiniteIntegral_compProd_iff, Real.analyticWithinAt_sin, StieltjesFunction.outer_Ioc, Complex.re_zsmul, Real.differentiable_fourierChar_neg_bilinear_right, Real.Angle.coe_two_pi, ProbabilityTheory.strong_law_ae_simpleFunc_comp, Complex.conjCLE_norm, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, BoundingSieve.nu_pos_of_dvd_prodPrimes, Real.log_pow, Affine.Simplex.sSameSide_point_excenter_singleton, SchwartzMap.seminorm_apply, norm_apply_le_norm_cfc, unitInterval.instNoAtomsElemRealVolume, ProbabilityTheory.variance_linearMap_gaussianReal, MeasureTheory.Lp.toTemperedDistribution_toLp_eq, MeasureTheory.SignedMeasure.rnDeriv_neg, variationOnFromTo.eq_left_iff, Complex.conj_eq_iff_im, ProbabilityTheory.stronglyMeasurable_gammaPDFReal, HurwitzZeta.completedCosZeta_zero, fourierBasis_repr, MeasureTheory.SignedMeasure.integrable_rnDeriv, ENNReal.toReal_sum, schnirelmannDensity_setOf_modeq_one, UpperHalfPlane.instContinuousGLSMul, AffineSubspace.signedInfDist_def, NNReal.coeNNRealReal_zero, isScalarTower_sphere_ball_ball, Real.tanh_eq, WithLp.norm_snd_le, ProbabilityTheory.mgf_id_gaussianReal, ENNReal.lt_iff_exists_rat_btwn, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply, Path.truncate_continuous_family, ValueDistribution.logCounting_zero_sub_logCounting_top_eq_circleAverage_sub_const, norm_sup_sub_sup_le_add_norm, HolderOnWith.edist_le, Real.arctan_mono, AddGroupSeminorm.zero_apply, Affine.Simplex.acuteAngled_reindex_iff, MeasureTheory.BoundedContinuousFunction.inner_toLp, EReal.toReal_eq_zero_iff, Complex.isQuotientMap_re, AddGroupSeminorm.coe_zero, Submodule.angle_coe, Real.tendsto_integral_gaussian_smul, NNReal.mk_natCast, NumberField.Units.unitLattice_rank, spectrum.instCompactSpaceNNReal, CFC.negPart_def, unitInterval.nonneg, QuotientAddGroup.norm_mk_le_norm, GroupNorm.coe_lt_coe, Cardinal.mk_Ici_real, Metric.controlled_of_isUniformEmbedding, instSecondCountableTopologyReal, ContinuousLinearMap.norm_id, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunctionAux_def', instIsTopologicalAddGroupReal, MeasureTheory.integral_fintype_prod_volume_eq_prod, ProbabilityTheory.Kernel.density_nonneg, BoundingSieve.nu_mult, BoxIntegral.Box.measurableSet_Ioo, tendsto_fib_succ_div_fib_atTop, Complex.subfield_eq_of_closed, Metric.thickening_nonempty_iff, tendsto_measure_cthickening_of_isCompact, RCLike.mul_re, Bornology.IsBounded.exists_norm_le, HurwitzZeta.completedCosZeta_neg, TensorProduct.norm_tmul, dist_pi_const_le, Real.posLog_one, BoundingSieve.nu_pos_of_prime, MeasureTheory.L1.norm_Integral_le_one, StrongFEPair.hf_top', cauchySeq_bdd, MeasureTheory.eLpNorm_eq_lintegral_rpow_enorm, NormedSpace.closedBall_inv_subset_polar_closedBall, Behrend.bound_aux, ProbabilityTheory.Kernel.mem_mutuallySingularSetSlice, ProbabilityTheory.condVar_of_not_sigmaFinite, Real.sin_nat_mul_pi_sub, Real.nnreal_trichotomy, Affine.Simplex.mem_altitude, Affine.Simplex.isDiameter_ninePointCircle, ProbabilityTheory.IsGaussian.integral_dual_conv_map_neg_eq_zero, ENNReal.rpow_mul_intCast, UnitAddTorus.span_mFourier_closure_eq_top, signedDist_lineMap_right, Real.arcsin_image_Icc, ContinuousLinearMap.norm_smulRightL_le, Real.smul_iSup_of_nonpos, TemperedDistribution.laplacian_apply_apply, IsSelfAdjoint.toReal_spectralRadius_eq_norm, schnirelmannDensity_le_of_notMem, ContinuousMap.HomotopyWith.symm_apply, HolderOnWith.ediam_image_inter_le_of_le, spectralValue_le_one_iff, Metric.isUniformEmbedding_iff, Affine.Triangle.sSameSide_affineSpan_pair_point_excenter_singleton, ModularForm.is_invariant_one', Real.expPartialHomeomorph_symm_apply, AkraBazziRecurrence.isLittleO_deriv_one_sub_smoothingFn, MeasureTheory.eLpNorm_indicator_const₀, Affine.Triangle.dist_div_sin_angle_div_two_eq_circumradius, HasFPowerSeriesOnBall.image_sub_sub_deriv_le, Complex.imCLM_enorm, norm_add₄_le, Real.Angle.coe_zsmul, MeasureTheory.Measure.haar.addCHaar_self, EisensteinSeries.eisensteinSeriesSIF_apply, Metric.nhds_basis_ball_inv_nat_succ, SchwartzMap.tsupport_derivCLM_subset, CFC.sqrt_rpow_nnreal, Affine.Simplex.orthogonalProjectionSpan_eulerPoint_mem_ninePointCircle, Real.tendsto_log_atTop, Real.sinh_add_cosh, Filter.Tendsto.cesaro_smul, setOf_liouville_eq_iInter_iUnion, RCLike.normSq_zero, NNReal.toReal_limsup, isLocalHomeomorph_circleExp, MeasureTheory.measureReal_prod_prod, MeasureTheory.Measure.toSignedMeasure_sub_apply, Chebyshev.psi_nonneg, ProbabilityTheory.lintegral_preCDF_fst, NNReal.coe_mul, tendsto_integral_exp_inner_smul_cocompact, coe_normAddGroupSeminorm, Affine.Simplex.mongePlane_reindex, det_rotation, ModularGroup.im_T_inv_smul, Hamming.dist_eq_hammingDist, PadicInt.norm_mahler_eq, MeasureTheory.Lp.norm_eq_zero_iff, MeasureTheory.integrable_continuousLinearMap_prod, ENNReal.toReal_le_toReal, BoundingSieve.siftedSum_le_mainSum_errSum_of_upperMoebius, Real.sin_eq_zero_iff, EReal.lt_iff_exists_rat_btwn, Real.strictConcave_binEntropy, Continuous.fourierPowSMulRight, ZLattice.normBound_spec, EReal.preimage_coe_Ioc_bot, instContinuousStarReal, Hyperreal.st_inv, Asymptotics.isBigO_iff_eventually_isBigOWith, Metric.tendstoUniformlyOnFilter_iff, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_snd, Metric.infDist_le_infDist_add_hausdorffDist, Real.sinh_injective, ContinuousLinearMap.reApplyInnerSelf_continuous, Real.tendsto_abs_tan_atTop, Int.norm_coe_units, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, Real.log_comp_exp, ContDiffBump.normed_le_div_measure_closedBall_rIn, Fact.Manifold.instLeReal, ProbabilityTheory.IsRatCondKernelCDF.measurable, NumberField.house_add_le, SchwartzMap.integral_smul_laplacian_right_eq_left, Real.enorm_abs, Metric.mem_closedBall, SchwartzMap.le_seminorm', UpperHalfPlane.mul_smul', Cardinal.instUncountableReal, EReal.coe_inv, TopologicalSpace.exists_embedding_l_infty, UniformConvexOn.sub, integral_complex_ofReal, tendsto_norm_nhdsNE_zero, Real.cos_sub_int_mul_two_pi, imaginaryPart_smul, mul_mem_closedBall_iff_norm, Seminorm.coeFnAddMonoidHom_apply, RCLike.re_le_neg_norm_iff_eq_neg_norm, Irrational.div_ratCast, CliffordAlgebraComplex.toComplex_involute, NumberField.mixedEmbedding.norm_real, Real.sinc_of_ne_zero, VectorFourier.fourierIntegral_probChar, RCLike.conjAe_coe, Real.sin_arctan_le_zero, Real.rpow_add_natCast, Complex.sin_ofReal_im, Int.preimage_ball, coe_comp_nnnorm, SchwartzMap.instFourierInvPair, HurwitzZeta.cosZeta_neg, Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, ContinuousMap.polynomial_comp_attachBound, Orientation.rightAngleRotation_map, MeasureTheory.upperCrossingTime_succ, integral_inv_one_add_sq, VectorFourier.norm_fourierSMulRight_le, BoundedContinuousFunction.norm_normComp, AlternatingMap.measure_parallelepiped, EuclideanGeometry.Sphere.isTangentAt_iff_dist_sq_eq_power, EisensteinSeries.abs_norm_eq_max_natAbs_neg, RCLike.neg_iff_exists_ofReal, NumberField.mixedEmbedding.normAtAllPlaces_norm_at_real_places, RCLike.wInner_one_eq_sum, Seminorm.preimage_metric_ball, Affine.Simplex.touchpointWeights_singleton_pos, EReal.coe_eq_one, Irrational.mul_ratCast, Real.volume_univ, ENNReal.dichotomy, CompareReals.compare_uc_symm, Real.iteratedDeriv_odd_sin, IsMIntegralCurveOn.continuousOn, KuratowskiEmbedding.embeddingOfSubset_dist_le, EisensteinSeries.eisSummand_extension_differentiableOn, RCLike.to_complex_nonneg_iff, EuclideanSpace.dist_sq_eq, integral_ofReal, MeasureTheory.charFunDual_map, AkraBazziRecurrence.h_rec, summable_geometric_two', Orientation.two_zsmul_oangle_smul_left_self, intervalIntegral.norm_integral_eq_norm_integral_uIoc, MeasureTheory.Measure.haar.addCHaar_mono, Orientation.kahler_rotation_right, Complex.ofRealCLM_enorm, AddMonoidHom.coe_toRealLinearMap, CircleDeg1Lift.map_lt_add_translationNumber_add_one, MeasureTheory.charFun_dirac, norm_commutator_units_sub_one_le, ProbabilityTheory.Kernel.setIntegral_density, CliffordAlgebraComplex.toComplex_ofComplex, MeasureTheory.tendsto_measure_compl_closedBall_of_isTightMeasureSet, MeasureTheory.exp_llr_of_ac, Real.toNNReal_lt_natCast, uniqueDiffWithinAt_Ici, tendsto_exp_div_rpow_atTop, HurwitzZeta.sinKernel_def, DirichletCharacter.LFunctionTrivChar_isBigO_near_one_horizontal, ZSpan.discreteTopology_pi_basisFun, EuclideanGeometry.law_cos, CircleDeg1Lift.coe_pow, isMIntegralCurveAt_iff', Real.exp_zero, NNReal.geom_mean_le_arith_mean3_weighted, BoundingSieve.multSum_eq_main_err, Real.HolderTriple.one_div_pos, NNReal.tendsto_coe, norm_div_eq_zero_iff, ProbabilityTheory.IsMeasurableRatCDF.measurable, Metric.nhds_basis_ball, Real.nnreal_dichotomy, NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis, irrational_cos_rat_mul_pi, TemperedDistribution.lineDerivOp_apply_apply, Real.Gamma_integrand_isLittleO, CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun, MeasureTheory.ComplexMeasure.re_apply, SeminormedSpace.Core.norm_smul, Set.infsep_pos, intervalIntegral.mul_integral_comp_mul_right, Subgroup.strictWidthInfty_pos, Real.eulerMascheroniSeq_lt_eulerMascheroniConstant, Real.one_div_sub_pow_hasFPowerSeriesOnBall_zero, signedDist_apply, Unitization.norm_splitMul_snd_sq, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, Real.goldenRatio_sub_goldenConj, Complex.norm_natCast_cpow_le_norm_natCast_cpow_iff, Matrix.IsHermitian.star_mul_self_mul_eq_diagonal, MeasureTheory.measureReal_univ_eq_one, UpperHalfPlane.modular_T_zpow_smul, Real.neg_pi_div_two_le_arcsin, ProbabilityTheory.iIndepFun.integral_fun_prod_eq_prod_integral, ContinuousMap.HomotopyWith.continuous, CFC.nnrpow_eq_nnrpow_prod, Real.coe_tanPartialHomeomorph_symm, intervalIntegral.norm_integral_le_abs_integral_norm, Valued.toNormedField.setOf_mem_integer_eq_closedBall, AddCircle.norm_eq, Quaternion.coeComplex_imJ, Fin.dist_insertNth_insertNth, fourier_coe_apply', le_egauge_ball_one, Complex.norm_exp_le_exp_norm, NumberField.Units.logEmbeddingEquiv_apply, NumberField.abs_discr_rpow_ge_of_isTotallyComplex, Behrend.lower_bound_le_one', MeasureTheory.Lp.meas_ge_le_mul_pow_enorm, intervalIntegral.integral_comp_add_left, NumberField.mixedEmbedding.polarSpaceCoord_source, Metric.lipschitz_infDist_set, cfc_real_eq_complex, IsUltrametricDist.dist_eq_max_of_dist_ne_dist, UnitAddTorus.hasSum_sq_mFourierCoeff, TemperedDistribution.lineDerivOp_fourierInv_eq, RCLike.im_ofReal_mul, not_integrableOn_Ici_inv, CircleDeg1Lift.map_add_one', Real.qaryEntropy_zero, Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT_of_ne, Complex.re_expect, HurwitzZeta.hurwitzOddFEPair_g, ProbabilityTheory.IsGaussian.charFunDual_eq_of_integral_eq_zero, Orientation.abs_oangle_sub_left_toReal_lt_pi_div_two, sphere_ext_iff, ContinuousMap.toNNReal_neg_one, ContDiffMapSupportedIn.bounded_iteratedFDeriv, MeasureTheory.SimpleFunc.integral_const, Real.HolderTriple.one_div_add_one_div, inner_self_re_eq_norm, UpperHalfPlane.dist_coe_le, Circle.expHom_apply, Real.analyticOn_sinh, ENNReal.ofReal_lt_ofReal_iff', strictConcaveOn_log_Ioi, homeomorphUnitSphereProd_apply_snd_coe, ProbabilityTheory.variance_dual_prod, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_atTop_one, ProbabilityTheory.isGaussian_map_equiv, Tactic.ComputeAsymptotics.Seq.FriendlyOperation.dist_le, Real.sinc_apply, integral_sin_pow_odd, similar_iff_exists_pos_pairwise_dist_eq, Real.differentiableAt_sinh, NNReal.rpow_zero, ProbabilityTheory.Fernique.sq_normThreshold_add_one_le, MeasureTheory.addHaarMeasure_eq_volume, Orientation.oangle_sign_smul_add_smul_right, LiouvilleWith.rat_add, RCLike.normSq_eq_zero, Real.strictAntiOn_cos, Asymptotics.isLittleO_iff, ContDiffBump.one_of_mem_closedBall, Real.Angle.nsmul_toReal_eq_mul, signedDist_eq_dist_iff_vsub_mem_span, Real.continuous_ofDigits, EuclideanGeometry.Sphere.mem_commonIntTangents_iff, uniqueDiffOn_Ioo, Real.continuousAt_logb, Real.differentiable_iteratedDeriv_sinh, Real.HolderTriple.one_div_nonneg', AffineSubspace.direction_perpBisector, Complex.lintegral_comp_pi_polarCoord_symm, HolderOnWith.dist_le, MeasureTheory.DominatedFinMeasAdditive.add, Besicovitch.multiplicity_le, curveIntegralFun_symm, Complex.HadamardThreeLines.sSupNormIm_nonneg, EReal.preimage_coe_Ico, realPart_apply_coe, NumberField.mixedEmbedding.fundamentalCone.expMap_single_apply, AffineSubspace.angle_coe, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn, Real.BohrMollerup.logGammaSeq_add_one, ProbabilityTheory.setLIntegral_condCDF, Real.exp_neg_one_gt_d9, Real.mulExpNegMulSq_one_le_one, Submodule.orthogonalProjectionFn_norm_sq, EReal.coe_real_ereal_eq_coe_toNNReal_sub_coe_toNNReal, Metric.diam_empty, Quaternion.imJ_coeComplex, intervalIntegral.integral_comp_mul_right, CliffordAlgebraComplex.Q_apply, irrational_sub_natCast_iff, PiLp.nnnorm_eq_sum, Complex.ofReal_im, Metric.infDist_zero_of_mem_closure, rotation_symm, OrthonormalBasis.same_orientation_iff_det_eq_det, unitInterval.one_minus_nonneg, MeasureTheory.measureReal_biUnion_finset_le, ProbabilityTheory.IsGaussian.charFun_eq, ContinuousLinearMap.extendTo𝕜'_apply, NumberField.mem_multisetInfinitePlace, Real.exp_one_near_10, Affine.Simplex.ninePointCircle_map, RCLike.I_re, ContinuousAt.inner_bundle, AddCircle.instProperlyDiscontinuousVAddSubtypeAddOppositeRealMemAddSubgroupOpZmultiples, spectralValue_nonneg, VectorFourier.norm_fourierPowSMulRight_le, NormedSpace.norm_expSeries_div_summable, EuclideanGeometry.dist_smul_vadd_eq_dist, unitInterval.symm_lt_symm, derivWithin_Ioi_eq_Ici, dist_birkhoffAverage_birkhoffAverage_le, Complex.equivRealProdCLM_symm_apply_im, Real.exp_le_one_iff, MeasureTheory.integral_singleton, Real.Angle.abs_cos_eq_of_two_nsmul_eq, intervalIntegral.integral_comp_div_sub, Real.Angle.abs_toReal_add_abs_toReal_eq_pi_of_two_nsmul_add_eq_zero_of_sign_eq, circleMap_zero_pow, integrable_exp_neg_mul_sq_iff, Complex.polarCoord_symm_apply, ProbabilityTheory.Kernel.singularPart_def, NNReal.one_rpow, SmoothPartitionOfUnity.mem_fintsupport_iff, EuclideanGeometry.Sphere.center_mem_iff, AddGroupSeminormClass.toSeminormedAddCommGroup_norm_eq, ZetaAsymptotics.term_sum_one, Real.noAtoms_volume, MeasureTheory.Measure.integrableOn_toReal_rnDeriv, not_integrableOn_Ioi_inv, Emetric.exists_smooth_forall_closedBall_subset, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, ConvexBody.hausdorffDist_coe, UnitAddTorus.mFourier_single, Real.hasFDerivAt_fourierChar_neg_bilinear_right, ContinuousMap.Homotopy.ext_iff, ENNReal.abs_toReal, Complex.re_nnqsmul, Real.nnabs_pos, ContinuousWithinAt.inner_bundle, Real.cos_sq, MeasureTheory.memLp_enorm_rpow_iff, Path.delayReflRight_one, ProbabilityTheory.IsMeasurableRatCDF.measurable_measure_stieltjesFunction, RCLike.im_eq_complex_im, PadicInt.coe_neg, HolderWith.edist_le, intervalIntegral.inv_mul_integral_comp_div, MeasureTheory.measureReal_zero_apply, Padic.norm_rat_le_one_iff_padicValuation_le_one, Cardinal.Real.Ico_countable_iff, PadicInt.norm_def, ae_not_liouville, PadicInt.norm_natCast_eq_one_iff, Affine.Simplex.sum_excenterWeightsUnnorm_empty_pos, ProbabilityTheory.measure_condCDF_univ, AffineSubspace.mem_perpBisector_iff_inner_eq, not_summable_one_div_on_primes, WeakFEPair.f_modif_aux1, CStarAlgebra.norm_le_one_iff_of_nonneg, Orientation.rotation_pi_div_two, ContDiffMapSupportedIn.continuous_iff_comp, Complex.ofReal_ratCast, ContinuousMultilinearMap.norm_map_insertNth_le, MeasureTheory.Measure.setIntegral_toReal_rnDeriv_le, Matrix.IsHermitian.posDef_iff_eigenvalues_pos, Complex.IsExpCmpFilter.tendsto_abs_re, Real.cauchy_one, Complex.equiv_limAux, SchwartzMap.integral_inner_fourier_fourier, ProbabilityTheory.lintegral_stieltjesOfMeasurableRat, ValueDistribution.logCounting_eventually_nonneg, Complex.real_le_real, norm_iteratedFDerivWithin_mul_le, Seminorm.uniformContinuous', VectorFourier.norm_fourierSMulRight, RCLike.ofReal_im_ax, LiouvilleWith.mul_nat_iff, Metric.unitClosedBall.coe_pow, MeasureTheory.setLIntegral_tilted', Asymptotics.isBigO_iff'', ENNReal.ofReal_eq_one, Asymptotics.isLittleO_norm_norm, PadicInt.isOpenEmbedding_coe, InnerProductSpace.volume_closedBall, Real.cos_int_mul_two_pi_sub, ContinuousLinearEquiv.coord_norm', Tactic.ComputeAsymptotics.Seq.dist_eq_half_of_head, NumberField.InfinitePlace.eq_iff_eq, unitary.norm_sub_one_lt_two_iff, cantorSequence_eq_self_sub_sum_cantorToTernary, stereographic'_symm_apply, trapezoidal_integral_symm, Seminorm.sup_apply, differentiableOn_abs, Matrix.frobenius_nnnorm_def, WithCStarModule.pi_norm_sq, EisensteinSeries.linear_isTheta_right, NormedAddCommGroup.nhds_zero_basis_norm_lt, ContinuousMap.HomotopyRel.cast_apply, Probability.stronglyMeasurable_cauchyPDFReal, Metric.unitClosedBall.instIsCancelMulZero, NormedSpace.norm_smul_normalize, LiouvilleWith.nat_sub, MeasureTheory.Measure.IicSnd_univ, BoundedContinuousFunction.norm_const_le, EuclideanGeometry.dist_sq_mul_dist_add_dist_sq_mul_dist, NumberField.mixedEmbedding.polarCoord_target_eq_polarCoordReal_target, Padic.norm_le_pow_iff_norm_lt_pow_add_one, Real.smoothTransition.projIcc, Real.Angle.coe_zero, LinearMap.mem_span_iff_bound, MeasureTheory.Measure.volumeIoiPow_apply_Iio, MeasureTheory.ProbabilityMeasure.continuous_integral_continuousMap, ProbabilityTheory.integrable_toReal_condDistrib, InnerProductSpace.laplacian_eq_iteratedDeriv_real, Complex.norm_exp_sub_sum_le_exp_norm_sub_sum, Polynomial.logMahlerMeasure_C_mul_X_add_C, Quaternion.coeComplex_imI, Metric.continuousAt_iff, UpperHalfPlane.pos_real_im, Real.abs_ofDigits_sub_ofDigits_le, Real.binEntropy_le_log_two, Metric.nhds_basis_closedBall, MeasureTheory.Lp.toTemperedDistribution_apply, summable_geometric_two, NumberField.FinitePlace.isFinitePlace, TemperedDistribution.smulLeftCLM_const, ProbabilityTheory.Kernel.measurable_densityProcess_right, Path.subpathAux_zero, Probability.integrable_cauchyPDFReal, IsUltrametricDist.norm_sub_eq_max_of_norm_sub_ne_norm_sub, HurwitzZeta.evenKernel_functional_equation, strongConvexOn_iff_convex, Real.circleAverage_abs_radius, Real.arcsin_zero, BoxIntegral.Box.splitLower_eq_self, MeasureTheory.integrable_toReal_iff, AkraBazziRecurrence.isTheta_asympBound, Asymptotics.IsTheta.norm_right, WithCStarModule.max_le_prod_norm, Real.not_continuousAt_inv_log_one, Polynomial.Chebyshev.node_mem_Icc, norm_add_sub_norm_sub_le_two_mul_min, InnerProductSpace.Core.inner_self_im, Matrix.IsHermitian.eigenvalues_eq_zero_iff, ProbabilityTheory.mgf_const_mul, EuclideanGeometry.angle_right_midpoint_eq_pi_div_two_of_dist_eq, Orientation.oangle_eq_pi_iff_sameRay_neg, CFC.posPart_def, MeasureTheory.charFunDual_pi, strongConvexOn_zero, dist_midpoint_midpoint_le', ContinuousMap.HomotopyWith.coe_toHomotopy, CliffordAlgebraComplex.reverse_eq_id, EReal.coe_div, irrational_neg_iff, CFC.nnrpow_eq_rpow, SchwartzMap.fourier_fderivCLM_eq, ProbabilityTheory.evariance_mul, MeasureTheory.eLpNorm'_measure_zero_of_exponent_zero, Padic.add_eq_max_of_ne, ConvexBody.hausdorffEDist_coe, PartitionOfUnity.finite_tsupport, integrable_mulExpNegMulSq_comp_restrict_of_isCompact, goldConj_mul_gold, NumberField.InfinitePlace.map_intCast, EReal.coe_abs, Real.exp_one_pow, FormalMultilinearSeries.radius_eq_top_iff_summable_norm, Units.norm_pos, MeasureTheory.SimpleFunc.integral_eq, CircleDeg1Lift.tendsto_translationNumber, MeasureTheory.lintegral_rpow_enorm_lt_top_of_eLpNorm_lt_top, dist_algebraMap, integral_withDensity_eq_integral_toReal_smul₀, ENNReal.toReal_ofReal_eq_iff, AbsoluteValue.isEquiv_iff_exists_rpow_eq, SchwartzMap.fourier_convolution_apply, Real.HolderTriple.one_div_pos', UpperHalfPlane.sinh_half_dist, Seminorm.smul_ball_zero, ProbabilityTheory.IsMeasurableRatCDF.monotone_stieltjesFunctionAux, Complex.hasStrictFDerivAt_log_real, CircleDeg1Lift.translationNumber_translate, MeasureTheory.SimpleFunc.setToSimpleFunc_const', HolderOnWith.ediam_image_inter_le, Complex.adjoin_I, Real.summable_one_div_nat_pow, SchwartzMap.instContinuousFourier, HurwitzZeta.hurwitzZetaOdd_neg, LinearIsometry.norm_toContinuousLinearMap_le, Real.hasStrictDerivAt_tan, MeasureTheory.eLpNorm'_eq_lintegral_enorm, MeasureTheory.le_measureReal_diff, EuclideanSpace.coe_measurableEquiv, Real.borelSpace, EReal.measurableEmbedding_coe, Path.Homotopy.eval_one, IsUltrametricDist.isNonarchimedean_algNormOfAlgEquiv, real_inner_smul_left, NNReal.dist_eq, Real.circleAverage_zero_one_congr_inv, norm_add_mul_self_real, NumberField.mixedEmbedding.fundamentalCone.nonneg_of_mem_compactSet, liouville_liouvilleNumber, ProbabilityTheory.Kernel.density_mono_set, UpperHalfPlane.dist_le_iff_le_sinh, ENNReal.continuousOn_toReal, NNReal.tendsto_coe_atTop, MeasureTheory.measureReal_biUnion_finset₀, NNReal.coe_one, SimpleGraph.isEquivalent_extremalNumber, NumberField.mixedEmbedding.fundamentalCone.compactSet_ae, StieltjesFunction.measure_Ico, ArithmeticFunction.vonMangoldt_le_log, Metric.unitClosedBall.instContinuousMul, NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv, Real.tendsto_euler_sin_prod, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, Real.Angle.abs_sin_eq_of_two_zsmul_eq, eventually_residual_liouville, MeasureTheory.FiniteMeasure.continuous_iff_forall_continuousMap_continuous_integral, MeasureTheory.JordanDecomposition.toSignedMeasure_zero, Real.cosPartialEquiv_source, List.norm_prod, NumberField.mixedEmbedding.instIsAddHaarMeasureRealMixedSpaceVolume, Irreducible.maximalIdeal_pow_eq_closedBall_pow, ContinuousMap.HomotopyRel.eq_fst, Dilation.dist_eq, Real.sin_pi_div_eight, IsCompact.exists_thickening_subset_open, zero_lt_one_add_norm_sq, AkraBazziRecurrence.growsPolynomially_rpow, dist_mono_right_pi, MeasureTheory.Lp.coeFn_posPart, Orientation.oangle_rotation_self_right, Real.binEntropy_strictAntiOn, Int.isUniformEmbedding_coe_real, gauge_smul, NumberField.mixedEmbedding.euclidean.finrank, Path.target, Real.Angle.toReal_add_eq_toReal_add_toReal, pi_polarCoord_symm_target_ae_eq_univ, Metric.unitClosedBall.coe_eq_one, ENNReal.continuous_rpow_const, Real.differentiable_fourierChar_neg_bilinear_left, MeasureTheory.lpNorm_expect_le, Real.arctan_eq_pi_div_four, UniformSpace.Completion.dist_triangle, NNReal.tendsto_coe', DilationEquiv.smulTorsor_preimage_ball, ConvexBody.hausdorffEdist_coe, Real.cosh_injOn, abs_norm, IsUltrametricDist.isPowMul_algNormOfAlgEquiv, AffineBasis.centroid_mem_interior_convexHull, unitInterval.instNontrivialElemReal, EReal.isEmbedding_coe, Complex.norm_prod, Urysohns.CU.continuous_lim, Subgroup.IsArithmetic.finiteIndex_comap, MeasureTheory.isTightMeasureSet_iff_tendsto_measure_norm_gt, MeasureTheory.lpNorm_eq_integral_norm_rpow_toReal, ProbabilityTheory.IsGaussian.ext_iff, pow_mem_ball, EuclideanGeometry.concyclic_or_collinear_of_two_zsmul_oangle_eq, AddCircle.integral_liftIoc_eq_intervalIntegral, AEMeasurable.re, integral_Ioi_inv_one_add_sq, Quaternion.coe_ofComplex, Real.hasDerivAt_arctan, NNReal.zero_le_coe, dist_dist_dist_le_left, BoxIntegral.unitPartition.volume_box, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, GroupNorm.sup_apply, Path.Homotopy.source, NonarchAddGroupNorm.apply_one, fourierCoeff_liftIoc_eq, SeminormedSpace.Core.norm_nonneg, dist_right_lineMap, intervalIntegral.FTCFilter.nhdsLeft, MeasureTheory.Measure.tendsto_IicSnd_atBot, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, circleIntegrable_log_norm_sub_const, ZMod.toAddCircle_eq_zero, NNReal.instIsStrictOrderedModule, EuclideanGeometry.angle_nonneg, Asymptotics.IsLittleO.eventuallyLE, EuclideanGeometry.dist_inversion_mul_dist_center_eq, Nat.ratSqrt_mem_Ioc, Metric.pos_of_mem_ball, polynomialFunctions_closure_eq_top', ProbabilityTheory.HasSubgaussianMGF.of_map, schnirelmannDensity_eq_one_iff_of_zero_mem, TemperedDistribution.instContinuousFourierInv, Polynomial.Chebyshev.integral_eval_T_real_mul_self_measureT_zero, ENNReal.one_lt_ofReal, BoundedContinuousFunction.coe_le_coe_add_dist, EReal.denseRange_ratCast, Real.sinh_pos_iff, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero', MeasureTheory.norm_indicatorConstLp', ENNReal.rpow_neg, ArchimedeanClass.stdPart_mul, NonarchAddGroupSeminorm.sup_apply, CStarAlgebra.star_right_conjugate_le_norm_smul, norm_apply_le_norm_cfcₙ, MeasureTheory.SignedMeasure.toComplexMeasure_apply_im, NNReal.instContinuousMapZero.UniqueHom, Complex.nonneg_iff, Real.sqrt_one, ProbabilityTheory.measurable_condCDF, CircleDeg1Lift.map_fract_sub_fract_eq, AddSubgroup.norm_normedMk, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_symm_apply, lp.norm_const_smul_le, Real.exp_sub, bernstein.z_last, bernstein.probability, TestFunction.instContinuousSMulReal, AkraBazziRecurrence.one_mem_range_sumCoeffsExp, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_sub_smoothingFn, Complex.reCLM_norm, Complex.im_eq_zero_iff_isSelfAdjoint, ValueDistribution.proximity_top_mul_le, ContinuousLinearMap.norm_snd_le, ModularForm.SL_slash_apply, Real.cauchy_ratCast, completelyRegularSpace_iff, Subgroup.widthInfty_pos_iff, ContinuousMap.norm_smul_const, NNReal.coe_mulSingle, schnirelmannDensity_setOf_Odd, unitInterval.univ_eq_Icc, IsUnifLocDoublingMeasure.eventually_measure_le_scaling_constant_mul, CircleDeg1Lift.translationNumber_units_inv, Zsqrtd.toReal_apply, Seminorm.closedBall_zero_eq, range_modelWithCornersEuclideanHalfSpace, EReal.toReal_sub, Real.analyticWithinAt_arsinh, Metric.continuousOn_iff', Real.rpow_sub_intCast, ContinuousMapZero.toNNReal_neg_smul, UpperHalfPlane.dist_coe_center_sq, Polynomial.Chebyshev.node_lt, Real.Angle.abs_toReal_add_eq_two_pi_sub_abs_toReal_add_abs_toReal, HolderOnWith.nndist_le, MeasureTheory.SimpleFunc.map_integral, continuousOn_cfc_nnreal_setProd, Real.floor_exp_one_eq_two, FormalMultilinearSeries.summable_norm_mul_pow, Real.instIsOrderedAddMonoid, ProbabilityTheory.instIsGaussianMapHAdd, Metric.dist_le_diam_of_mem', Rat.isUniformEmbedding_coe_real, Asymptotics.isBigOWith_abs_right, norm_mul_le, Tactic.ComputeAsymptotics.Seq.dist_le_one, ProbabilityTheory.covariance_const_mul_left, InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq_sub_two_mul_norm_mul_norm_mul_cos_angle, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, IsApproximateSubgroup.pow_inter_pow_covBySMul_sq_inter_sq, ProbabilityTheory.Fernique.logRatio_mono, Real.toNNReal_eq_one, NumberField.mixedEmbedding.convexBodySum_convex, Padic.norm_p, Complex.arg_nonneg_iff, ProbabilityTheory.iIndepFun.integral_fun_prod_comp, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, ContinuousMap.polynomial_comp_attachBound_mem, integral_exp_neg_Ioi_zero, Complex.normSq_apply, ContinuousLinearMap.opNorm_mulLeftRight_le, Matrix.SpecialLinearGroup.discreteSpecialLinearGroupIntRange, Complex.norm_exp_ofReal_mul_I, Real.abs_rpow_le_exp_log_mul, Real.binEntropy_two_inv, irrational_add_ratCast_iff, NNReal.rpow_mul_natCast, ContinuousMultilinearMap.bounds_nonempty, Circle.coe_exp, convex_halfSpace_im_le, RCLike.re_ofReal_mul, gauge_smul_left, Polynomial.Chebyshev.isLocalExtr_T_real, norm_add_pow_two, setOf_liouville_eq_irrational_inter_iInter_iUnion, MeasureTheory.measure_smul_setAverage, Padic.norm_natCast_p_sub_one, NumberField.mixedEmbedding.fundamentalCone.mem_idealSet, ContDiffPointwiseHolderAt.iteratedFDeriv, Affine.Simplex.sum_excenterWeights, Complex.real_lt_real, Real.sqrt_nonneg, ContinuousLinearMap.norm_compLpL_le, HasCompactSupport.norm, EisensteinSeries.eisSummand_SL2_apply, MeasureTheory.Integrable.comp_smul, ProbabilityTheory.gaussianPDFReal_add, UpperHalfPlane.mem_verticalStrip_iff, ENNReal.toReal_top, NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop, LinearMap.toSeminormFamily_apply, Real.half_mul_log_add_log_abs, ruzsaSzemerediNumberNat_lower_bound, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, MeasureTheory.Measure.LinearMap.quasiMeasurePreserving, nnnorm_tangentSpace_vectorSpace, ProbabilityTheory.stronglyMeasurable_betaPDFReal, NumberField.mixedEmbedding.fundamentalCone.volume_normLeOne, ProbabilityTheory.variance_smul', IntervalIntegrable.aestronglyMeasurable_restrict_uIoc, CFC.abs_one, hasGradientWithinAt_iff_tendsto, OrthonormalBasis.toMatrix_orthonormalBasis_mem_orthogonal, ContDiffMapSupportedIn.structureMapCLM_zero_injective, MeasureTheory.llr_smul_right, real_inner_add_add_self, UpperHalfPlane.I_im, UpperHalfPlane.tendsto_coe_atImInfty, norm_eq_sqrt_re_inner, ProbabilityTheory.IsMeasurableRatCDF.tendsto_stieltjesFunction_atTop, AddGroupSeminorm.map_zero', TemperedDistribution.fourier_apply, NumberField.IsCMField.infinitePlace_complexConj, NNReal.one_lt_coe, Hyperreal.coe_neg, NumberField.prod_archAbsVal_eq, Matrix.IsHermitian.rank_eq_card_non_zero_eigs, Hyperreal.stdPart_omega, inner_self_nonneg, CStarAlgebra.nonneg_TFAE, Complex.isTheta_ofReal_left, RCLike.normSq_to_complex, Matrix.PosSemidef.sqrt_mul_self, Orientation.areaForm_rightAngleRotation_right, MeasureTheory.setIntegral_condExpL1CLM, Complex.arg_exp, SchwartzMap.lineDerivOp_apply, OrthonormalBasis.orientation_adjustToOrientation, NonarchAddGroupNorm.sup_apply, ProbabilityTheory.HasSubgaussianMGF.zero, NumberField.house_prod_le, Real.deriv_arcsin_aux, unitInterval.subtype_Iic_eq_Icc, seminormFromConst_bddBelow, fourier_add', RCLike.continuous_im, Nat.not_irrational, lp.norm_eq_ciSup, Module.Basis.map_addHaar, Circle.exp_zsmul, MeasureTheory.Measure.setIntegral_toReal_rnDeriv_eq_withDensity, Real.log_inv, MeasureTheory.tilted_eq_withDensity_nnreal, ProbabilityTheory.IsCondKernelCDF.lintegral, Real.tan_add_nat_mul_pi, spectralNorm_zero_lt, Complex.div_intCast_im, Real.sinh_le_sinh, exists_contDiff_tsupport_subset, EReal.toReal_pos, LiouvilleWith.nat_add_iff, unitInterval.eq_closedBall, Similar.exists_pos_pairwise_dist_eq, BoxIntegral.unitPartition.tag_apply, IsPrimitiveRoot.arg, ContinuousMap.HomotopyWith.apply_zero, ContDiffBump.nonneg', AddGroupNorm.lt_def, Complex.frontier_setOf_le_re_and_im_le, Real.differentiableAt_qaryEntropy, StieltjesFunction.length_Ioc, NNReal.hasSum_coe, ProbabilityTheory.indepFun_iff_integral_comp_mul, coe_normGroupSeminorm, Complex.isBigO_comp_ofReal_nhds, ENNReal.toReal_strict_mono, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_aestronglyMeasurable, Real.tendsto_sin_pi_div_two, variationOnFromTo.eq_neg_swap, LinearMap.IsSymmetric.re_trace_eq_sum_eigenvalues, intervalIntegral.integral_comp_mul_add, PadicInt.norm_le_one, StrongDual.mem_polar_iff, Submodule.Quotient.norm_mk_le, Real.Angle.cos_sub_pi_div_two, EisensteinSeries.eisensteinSeries_SIF_MDifferentiable, tsum_sq_fourierCoeff, RCLike.normSq_add, Real.arccos_zero, Polynomial.Chebyshev.isExtrOn_T_real, Affine.Simplex.touchpoint_mem_affineSpan_simplex, GroupSeminorm.coe_add, RCLike.div_re, aemeasurable_derivWithin_Ici, Submodule.isPathConnected, Orientation.inner_smul_rotation_pi_div_two_smul_left, integral_sin_pow, NumberField.mixedEmbedding.fundamentalCone.zero_mem_compactSet, mem_closedBall_zero_iff, IsSelfAdjoint.coe_realPart, hasDerivAt_iff_tendsto, ProbabilityTheory.iIndepFun.integral_prod_comp, Real.exp_eq_exp_ℝ, ProbabilityTheory.measurable_betaPDFReal, Polynomial.instTwoPiPos, Polynomial.cyclotomic_mahlerMeasure_eq_one, SchwartzMap.coe_apply, ArchimedeanClass.stdPart_of_mk_nonneg, integral_mul_cpow_one_add_sq, EuclideanGeometry.angle_eq_zero_iff_ne_and_wbtw, Complex.im_sq_le_normSq, Real.isBigO_logb_const_mul_log_atTop, AkraBazziRecurrence.isLittleO_deriv_smoothingFn, Real.differentiable_arsinh, CliffordAlgebraComplex.ofComplex_comp_toComplex, AkraBazziRecurrence.b_lt_one, integral_gaussian_Ioi, NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply, MeasureTheory.condExp_bot', setIntegral_re_add_im, Circle.exp_eq_one, norm_iteratedFDeriv_smul_le, Complex.ofReal_tsum, HolderWith.dist_le, Real.cosh_eq, realPart_smul, MeasureTheory.ComplexMeasure.equivSignedMeasureₗ_apply, MeasureTheory.lpNorm_smul_measure_of_ne_top, MeasureTheory.measureReal_add_diff, PiCountable.dist_eq_tsum, AkraBazziRecurrence.growsPolynomially_one_sub_smoothingFn, abs_real_inner_div_norm_mul_norm_eq_one_iff, spectralValue_eq_zero_iff, Polynomial.supNorm_eq_iSup, NNReal.div_rpow, ContinuousLinearMap.sSup_unitClosedBall_eq_norm, mem_tangentConeAt_iff_exists_seq_norm_tendsto_atTop, Real.strictMonoOn_sin, ContinuousLinearEquiv.coord_norm, Real.cauchy_mul, Height.mulHeight₁_zero, ENNReal.rpow_eq_pow, projIcc_eq_zero, MeasureTheory.lpNorm_one', ProbabilityTheory.instIsGaussianProdProdOfSecondCountableTopologyEither, gold_pos, Real.tendsto_toNNReal_atTop, unitInterval.half_le_symm_iff, BoundedContinuousFunction.map_bounded', Complex.norm_eq_sqrt_sq_add_sq, instLocallyConvexSpaceRealOfPolynormableSpace, UpperHalfPlane.cosh_dist', PartitionOfUnity.mem_fintsupport_iff, Real.Angle.abs_sin_eq_of_two_nsmul_eq, Polynomial.toAddCircle_X_eq_fourier_one, MeasureTheory.GridLines.T_univ, isTheta_deriv_ofReal_cpow_const_atTop, EuclideanGeometry.dist_center_inversion, ExistsContDiffBumpBase.w_nonneg, MeasureTheory.FiniteMeasure.continuous_integral_continuousMap, MeasureTheory.integral_finset, Affine.Simplex.circumsphere_reindex, CStarAlgebra.norm_mem_spectrum_of_nonneg, Complex.neg_ofReal_mem_slitPlane, Metric.unitBall.instIsCancelMulZero, ContinuousMap.Homotopy.refl_apply, ContinuousLinearMap.norm_adjoint_comp_self, ContinuousMap.HomotopyWith.cast_apply, Real.tanh_sq_lt_one, unitary.norm_argSelfAdjoint_le_pi, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWith, QuotientGroup.norm_eq_groupSeminorm, ContDiffBump.tsupport_normed_eq, Orientation.inner_smul_rotation_pi_div_two_smul_right, spectralNorm_zero, Real.cos_arctan_pos, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_restrict_densityProcess_limitProcess, CircleIntegrable.out, NNReal.rpow_inv_natCast_pow, RCLike.intervalIntegral_ofReal, AddCircle.closedBall_ae_eq_ball, PadicInt.mem_nonunits, PadicInt.complete, Irrational.eventually_forall_le_dist_cast_rat_of_den_le, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_image_preimage_expMapBasis, SchwartzMap.integrable_pow_mul, Quaternion.instNormOneClassReal, Complex.le_def, ZLattice.tsumNormRPowBound_pos, LipschitzWith.mapsTo_closedBall, ContinuousMultilinearMap.norm_map_cons_le, KuratowskiEmbedding.exists_isometric_embedding, Complex.div_natCast, ContinuousMultilinearMap.norm_smulRight, IsometricContinuousFunctionalCalculus.isGreatest_norm_spectrum, BumpCovering.toPOUFun_eq_mul_prod, Real.analyticOnNhd_sinh, Complex.ofReal_comp_neg, instSMulCommClass_sphere_closedBall_ball, curveIntegral_def', Real.expPartialHomeomorph_source, ModularGroup.det_coe, NumberField.FinitePlace.instNonarchimedeanHomClassReal, MeasureTheory.SignedMeasure.null_of_totalVariation_zero, AkraBazziRecurrence.continuous_sumCoeffsExp, Real.Angle.toReal_le_pi, LiouvilleWith.rat_mul, re_inner_eq_norm_add_mul_self_sub_norm_sub_mul_self_div_four, EuclideanGeometry.Sphere.direction_orthRadius, ContinuousMap.toNNReal_add_add_neg_add_neg_eq, IntervalIntegrable.smul, CStarAlgebra.isBasis_nonneg_sections, EuclideanSpace.measurableEquiv_toEquiv, mulIndicator_cthickening_eventually_eq_mulIndicator_closure, MeasureTheory.Measure.toSphere_eq_zero_iff_finrank, NNRealRMK.integral_rieszMeasure, Real.cos_add_nat_mul_two_pi, EisensteinSeries.isLittleO_const_left_of_properSpace_of_discreteTopology, Besicovitch.SatelliteConfig.inter, Complex.natCast_arg, Complex.edist_of_re_eq, Complex.rightAngleRotation, NumberField.mixedEmbedding.mixedEmbedding_apply_isComplex, ProbabilityTheory.iInf_rat_gt_defaultRatCDF, EuclideanGeometry.dist_sq_add_dist_sq_eq_two_mul_dist_midpoint_sq_add_half_dist_sq, NonarchAddGroupSeminorm.coe_le_coe, Hyperreal.tendsto_ofSeq, ContinuousAlternatingMap.bound, Affine.Simplex.circumradius_reindex, Real.Angle.two_nsmul_neg_pi_div_two, Metric.Sigma.dist_triangle, Probability.instIsProbabilityMeasure_cauchyMeasure, isCompact_cantorSet, Real.cosh_sq_sub_sinh_sq, CFC.negPart_smul, ArithmeticFunction.vonMangoldt_mul_zeta, NumberField.mixedEmbedding.fundamentalCone.smul_mem_iff_mem, MeasureTheory.Measure.IicSnd_ac_fst, Submodule.norm_orthogonalProjection, Seminorm.coe_iSup_eq, unitInterval.sigmoid_pos, IsBoundedBilinearMap.bound, Asymptotics.isBigO_iff_eventually, Real.volume_uIoc, RingSeminorm.apply_one, EReal.nhds_coe_coe, Asymptotics.IsBigOWith.bound, ContinuousMapZero.toNNReal_smul, Hyperreal.coe_mul, Real.continuousAt_log, SmoothBumpFunction.support_subset_source, MeasureTheory.Measure.toSignedMeasure_restrict_eq_restrict_toSignedMeasure, CircleDeg1Lift.translationNumber_pow, AffineSubspace.signedInfDist_apply_self, Metric.isBounded_iff_exists_ge, Complex.image_exp_Ioc_eq_sphere, Bornology.IsBounded.exists_pos_norm_le, CFC.log_algebraMap, ContinuousLinearMap.opNorm_lsmul, Real.ringEquivCauchy_apply, expNegInvGlue.zero, EuclideanGeometry.Sphere.IsIntTangent.dist_center, norm_le_insert, Real.posLog_nonneg, Complex.measurable_ofReal, approxOrderOf.image_pow_subset, KuratowskiEmbedding.embeddingOfSubset_coe, integral_sin_sq_mul_cos_sq, ProbabilityTheory.covarianceBilinDual_of_not_memLp, HurwitzZeta.completedHurwitzZetaEven_residue_zero, NumberField.mixedEmbedding.fundamentalCone.mem_integerSet, TFAE_exists_lt_isLittleO_pow, norm_inf_le_add, ContinuousLinearMap.norm_id_of_nontrivial_seminorm, integral_mul_rpow_one_add_sq, irrational_intCast_add_iff, MeasureTheory.MemLp.integrable_enorm_rpow, isScalarTower_closedBall_closedBall_ball, Metric.infDist_eq_iInf, MeasureTheory.measureReal_biUnion_eq_sum_powerset, unitInterval.symm_involutive, Real.isSquare_iff, Cardinal.Real.Ioo_countable_iff, Metric.diam_zero, UpperHalfPlane.denom_cocycle', MeasureTheory.FiniteMeasure.continuous_iff_forall_continuous_integral, ProbabilityTheory.strong_law_ae_of_measurable, InnerProductGeometry.angle_eq_pi_iff, ModularGroup.lcRow0_apply, Unitary.norm_argSelfAdjoint_le_pi, Metric.isGLB_infDist, Complex.ofRealAm_coe, deriv_circleMap_eq_zero_iff, SchwartzMap.smooth', CircleDeg1Lift.floor_map_map_zero_le, Complex.imCLM_apply, MeasureTheory.charFun_map_eq_charFunDual_smul, Complex.exists_cthickening_tendstoUniformlyOn, SchwartzMap.isBigO_cocompact_zpow, inner_vsub_vsub_left_eq_dist_sq_left_iff, BoxIntegral.hasIntegral_iff, Int.tendsto_coe_cofinite, Metric.infDist_le_hausdorffDist_of_mem, Real.contDiff_exp, QuotientGroup.norm_lt_iff, Nat.ratSqrt_le_realSqrt, Real.tendsto_log_nat_add_one_sub_log, MeasureTheory.eLpNorm_smul_measure_of_ne_zero, Path.subpath_zero_one, norm_inf_sub_inf_le_add_norm, ProbabilityTheory.gaussianPDFReal_mul, MeasureTheory.integrable_withDensity_iff, ConvexBody.coe_add, exists_tsupport_one_of_isOpen_isClosed, EuclideanGeometry.inversion_eq_center', ContinuousMultilinearMap.norm_def, NNReal.coe_tsum, NormedSpace.double_dual_bound, Real.mk_neg, NumberField.mixedEmbedding.det_fderivPolarCoordRealSymm, Asymptotics.IsBigO.norm_right, spectralAlgNorm_isPowMul, Affine.Simplex.inradius_pos, NNReal.coe_list_sum, PeriodPair.indep, norm_sub_pow_two, UpperHalfPlane.tanh_half_dist, AddCircle.pathConnectedSpace, MulRingNorm.apply_one, MeasureTheory.MemLp.enorm_rpow_div, Real.fourierInv_eq, CFC.isUnit_nnrpow_iff, Archimedean.embedReal_one, isConformalMap_complex_linear, unitInterval.volume_uIoc, Real.Angle.toReal_coe_eq_self_add_two_pi_iff, Real.zero_at_infty_vector_fourierIntegral, ModularForm.coe_translate, Real.map_toNNReal_atTop, Real.rpow_add_intCast, ENNReal.fun_eq_funMulInvSnorm_mul_eLpNorm, ProperCone.innerDual_iUnion, ContDiffBump.le_one, lipschitzWith_max, RCLike.conj_eq_re_sub_im, MeasureTheory.Integrable.norm, NumberField.mixedEmbedding.fundamentalCone.expMap_sum, norm_injOn_ray_left, SzemerediRegularity.card_biUnion_star_le_m_add_one_card_star_mul, SchwartzMap.tsum_eq_tsum_fourierIntegral, Complex.monotone_ofReal, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, Orientation.kahler_rightAngleRotation_right, Real.expPartialHomeomorph_target, Real.smoothTransition.monotone, NNReal.rpow_self_rpow_inv, InnerProductSpace.Core.re_inner_smul_ofReal_smul_self, Real.Angle.sin_antiperiodic, Polynomial.Chebyshev.node_eq_one, ContinuousLinearMap.norm_snd, NumberField.Units.finrank_mul_regulator_eq_det, IsApproximateAddSubgroup.card_add_self_le, MeasureTheory.condExpIndSMul_ae_eq_smul, ExistsContDiffBumpBase.u_compact_support, Complex.norm_two, ENNReal.rpow_inv_natCast_pow, Besicovitch.TauPackage.lastStep_nonempty, Topology.isEmbedding_sigmoid, UpperHalfPlane.neg_smul, Quaternion.linearIsometryEquivTuple_apply, map_sub_le_max, EuclideanGeometry.Sphere.orthRadius_parallel_orthRadius_iff, Complex.norm_cpow_le, Stirling.stirlingSeq_pow_four_div_stirlingSeq_pow_two_eq, Real.analyticWithinAt_cosh, MeasureTheory.lpNorm_const, Real.artanh_injOn, NumberField.InfinitePlace.prod_eq_abs_norm, MeasureTheory.intervalIntegrable_charFun, Real.strictMonoOn_tan, MeasureTheory.Lp.dense_hasCompactSupport_contDiff, Real.volume_Ioi, Polynomial.tendsto_div_exp_atTop, integral_Iic_inv_one_add_sq, IsRiemannianManifold.out, SmoothPartitionOfUnity.toPartitionOfUnity_toFun, isIntegral_two_mul_cos_rat_mul_pi, PiTensorProduct.injectiveSeminorm_tprod_le, Real.lt_toNNReal_iff_coe_lt, CFC.rpow_zero, NNReal.rpow_one, Complex.isAbsoluteValueNorm, ExistsContDiffBumpBase.u_nonneg, IsOpen.affineSpan_eq_top, ENNReal.tendsto_toReal_iff, HurwitzZeta.isBigO_atTop_cosKernel_sub, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_integral_of_monotone, EuclideanGeometry.inner_vsub_vsub_of_mem_sphere_of_mem_sphere, Real.arccos_nonneg, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, Real.div_logb, parallelepiped_eq_convexHull, Path.segment_apply, IsUnifLocDoublingMeasure.exists_eventually_forall_measure_closedBall_le_mul, MeasureTheory.eLpNorm_nnreal_pow_eq_lintegral, Real.tendsto_pow_log_div_mul_add_atTop, approxAddOrderOf.image_nsmul_subset_of_coprime, Metric.uniformity_edist_aux, Seminorm.mem_closedBall, rothNumberNat_le_ruzsaSzemerediNumberNat', ContinuousLinearMap.norm_holderL_le, fourier_add, Real.borel_eq_generateFrom_Iic_rat, ProbabilityTheory.condIndepFun_iff, cantorSet_eq_union_halves, Path.Homotopy.symm₂_apply, PolynormableSpace.withSeminorms, Affine.Triangle.sSameSide_affineSpan_pair_excenter_singleton_point, MeasureTheory.charFun_eq_integral_innerProbChar, Complex.re_nsmul, Topology.CWComplex.mapsTo, LinearMap.polar_mem_iff, interval_average_eq, Asymptotics.IsBigOWith.sub, Complex.isLittleO_ofReal_right, NonarchAddGroupSeminorm.add_le_max', Real.cos_eq_neg_one_iff, Real.abs_cos_eq_one_iff, IsApproximateAddSubgroup.nsmul_inter_nsmul_covByVAdd_sq_inter_sq, gaugeSeminormFamily_ball, Complex.edist_of_im_eq, ValueDistribution.characteristic_top_mul_eventually_le, Real.volume_Ioo, HolderOnWith.ediam_image_le, GroupSeminorm.coe_sSup_apply, RCLike.sqrt_normSq_eq_norm, Real.add_one_le_exp, Real.HolderConjugate.inv_sub_one, BoxIntegral.unitPartition.box.upper_sub_lower, Real.sign_apply_eq_of_ne_zero, Complex.log_im_le_pi, instNonemptySeedRatReal, Asymptotics.IsBigOWith.const_mul_left, HolderOnWith.edist_le_of_le, SchwartzMap.instFourierInvSMul, Hyperreal.coe_le_coe, NumberField.mulHeight₁_eq, Seminorm.comp_smul_apply, Real.sin_sub_two_pi, TemperedDistribution.derivCLM_apply_apply, Real.cos_sub, NormedAddGroupHom.norm_def, NNReal.rpow_left_surjective, Real.Wallis.W_succ, Complex.Gamma_def, integral_cos_sq, TorusIntegrable.function_integrable, EReal.coe_ennreal_ofReal, ENNReal.toReal_div, has_unit_speed_naturalParameterization, ProbabilityTheory.mgf_smul_measure, ContinuousAlternatingMap.norm_compContinuousLinearMap_le, NNReal.exists, integral_re, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne_eq_image, Real.negMulLog_zero, Stirling.tendsto_stirlingSeq_sqrt_pi, RCLike.tendsto_ofReal_atBot_cobounded, ENNReal.ofReal_min, norm_zpow_le_mul_norm, NormedSpace.norm_normalize, abs_signedDist_le_dist, DirichletCharacter.LFunction_isBigO_horizontal, Complex.frontier_setOf_lt_re, Orientation.norm_kahler, dist_midpoint_left, NumberField.mixedEmbedding.disjoint_span_commMap_ker, mfderiv_subtype_coe_Icc_one, BumpCovering.locallyFinite', Real.log_of_nat_eq_posLog, NumberField.FinitePlace.norm_le_one, ENNReal.toReal_le_add', ruzsaSzemerediNumberNat_asymptotic_lower_bound, Metric.continuousOn_iff, NumberField.InfinitePlace.map_natCast, ModularGroup.three_lt_four_mul_im_sq_of_mem_fdo, NumberField.Units.sum_mult_mul_log, Rat.isEmbedding_coe_real, intervalIntegral.FTCFilter.pure_le, Real.tendsto_log_nhdsNE_zero, norm_div_pos_iff, Complex.isometryOfOrthonormal_symm_apply, ContinuousMap.Homotopy.extend_one, ContDiffPointwiseHolderAt.zero_exponent_iff, ENNReal.ofReal_lt_one, MeasureTheory.weightedSMul_smul_measure, unitInterval.tendsto_sigmoid_atBot, MeasureTheory.integrable_count_iff, norm_le_zero_iff', RCLike.normSq_apply, ProperCone.innerDual_toSubmodule, NNReal.coe_zpow, irrational_intCast_div_iff, Real.tanh_arsinh, MeasureTheory.memLp_norm_iff, Real.rpow_neg_natCast, PartitionOfUnity.exists_finset_nhds', Seminorm.coe_lt_coe, Real.cosh_eq_tsum, NormedCommGroup.tendsto_nhds_one, Real.Angle.tan_eq_inv_of_two_zsmul_add_two_zsmul_eq_pi, tendsto_norm_zero, Real.posLog_pow, Real.continuousOn_arcosh, PiLp.norm_eq_of_L2, Real.sinh_three_mul, InnerProductSpace.HarmonicAt.comp_CLM, Metric.diam_one, Orientation.inner_rightAngleRotation_self, Complex.intCast_im, Metric.cauchySeq_iff', Real.exp_one_gt_two, ValueDistribution.proximity_coe, IsApproximateAddSubgroup.addSubgroup, ModularForm.coe_trace, Real.cos_pi_div_three, RCLike.ofRealCLM_coe, NumberField.InfiniteAdeleRing.ringEquiv_mixedSpace_apply, ProbabilityTheory.instIsGaussianMapHSub_1, Real.tanh_zero, Valued.integer.norm_coe_unit, ProbabilityTheory.HasCondSubgaussianMGF.integrable_exp_mul, Complex.frontier_setOf_le_im, zero_lt_one_add_norm_sq', WithSeminorms.isVonNBounded_iff_seminorm_bounded, HurwitzZeta.sinZeta_eq, Real.Icc_eq_closedBall, InnerProductSpace.Core.normSq_eq_zero, Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius, InnerProductSpace.laplacian_CLE_comp_left, MeasureTheory.tendsto_iff_forall_lipschitz_integral_tendsto, HasStrictDerivAt.complexToReal_fderiv, EuclideanGeometry.Sphere.isIntTangent_self_iff, GroupSeminorm.add_apply, Real.cos_zero, Polynomial.norm_coeff_le_choose_mul_mahlerMeasure, ProbabilityTheory.gaussianReal_apply_eq_integral, EuclideanGeometry.affineIndependent_iff_of_two_zsmul_oangle_eq, eventually_norm_trivializationAt_lt, integral_withDensity_eq_integral_smul₀, NNReal.toReal_liminf, hasCompactSupport_norm_iff, NormedAddGroupHom.opNorm_zero, PadicInt.norm_natCast_zmodRepr_eq_iff, ENNReal.young_inequality, Complex.ofReal_nnqsmul, ProbabilityTheory.IsGaussian.charFunDual_eq', norm_lt_iff_of_nonempty_compactlySupported, BoxIntegral.Prepartition.eventually_splitMany_inf_eq_filter, mulIndicator_thickening_eventually_eq_mulIndicator_closure, convex_halfSpace_re_gt, OrthonormalBasis.addHaar_eq_volume, BumpCovering.le_one', Besicovitch.one_lt_goodτ, OrthonormalBasis.det_to_matrix_orthonormalBasis_real, ProbabilityTheory.IsRatCondKernelCDF.mono, SmoothBumpFunction.nonneg, PartitionOfUnity.exists_pos, Hyperreal.coe_lt_coe, NormedSpace.toLocallyConvexSpace', Real.HolderTriple.inv_pos', isConnected_setOf_sameRay, MeasureTheory.integral_prod_smul, ENNReal.tendsto_ofReal_nhds_top, ProbabilityTheory.condExp_eq_zero_or_one_of_condIndepSet_self, IsCompact.exists_isCompact_cthickening, ContinuousMap.Homotopy.curry_one, ProbabilityTheory.covariance_zero_left, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, NonarchAddGroupSeminorm.coe_sSup_apply', MulRingSeminorm.ext_iff, MeasureTheory.integrableOn_Ioi_comp_rpow_iff, Metric.unitClosedBall.coe_zero, CompareReals.compare_uc, SmoothBumpFunction.nhdsWithin_range_basis, Complex.one_re, Real.isLittleO_pow_log_id_atTop, ContinuousLinearMap.bound, ProbabilityTheory.analyticOnNhd_complexMGF, NumberField.mixedEmbedding.convexBodySum_volume, PadicInt.coe_mul, ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral, Complex.im_zsmul, unitInterval.subtype_Ioi_eq_Ioc, AddGroupNorm.coe_lt_coe, Padic.complete, Real.Gamma_nat_eq_factorial, NumberField.mixedEmbedding.convexBodyLT'_neg_mem, EuclideanGeometry.dist_inversion_center, Real.probChar_apply, StrongDual.polar_singleton, AEMeasurable.coe_nnreal_real, spectralValueTerms_of_lt_natDegree, Real.Angle.toReal_eq_pi_div_two_iff, NNReal.list_prod_map_rpow, Real.hasDerivAt_Gamma_nat, ordinaryHypergeometricSeries_norm_div_succ_norm, EuclideanGeometry.cos_eq_one_iff_angle_eq_zero, Complex.abs_cpow_inv_two_im, Path.truncate_one_one, Disjoint.exists_thickenings, Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitary, Real.logb_neg_eq_logb, NumberField.Units.regulator_eq_det', Complex.ofReal_pow, Height.AdmissibleAbsValues.product_formula, UpperHalfPlane.im_pnat_div_pos, Polynomial.finite_mahlerMeasure_le, ContinuousMap.HomotopyRel.pi_apply, Cardinal.not_countable_real, Diffeology.DSmooth.contDiff, Real.map_exp_atTop, MeasureTheory.ContinuousMap.inner_toLp, PiLp.nnnorm_toLp_const, Metric.nhdsWithin_basis_ball, re_inner_le_norm, differentiableAt_abs, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat_rat, InnerProductGeometry.continuousAt_angle, ENNReal.toReal_le_add, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, tendsto_const_div_pow, Asymptotics.isLittleO_pow_sub_sub, Nat.Prime.irrational_sqrt, Complex.norm_le_sqrt_two_mul_max, MeasureTheory.integrable_fun_norm_addHaar, Polynomial.Chebyshev.abs_eval_T_real_le_one_iff, skewAdjoint.I_smul_neg_I, NumberField.mixedEmbedding.polarCoordReal_target, Real.continuousAt_arctan, unitInterval.two_mul_sub_one_mem_iff, Real.posLog_sum, hasSum_zeta_nat, dist_dist_dist_le_right, ProbabilityTheory.isPositive_covarianceOperator, MeasureTheory.Measure.haar.addCHaar_empty, MeasureTheory.dominatedFinMeasAdditive_weightedSMul, Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter, Real.logDeriv_cos, Real.sin_add_pi, ProbabilityTheory.IsRatCondKernelCDF.integrable, Real.arcosh_surjOn, Real.cos_add_int_mul_pi, MeasureTheory.sum_measureReal_le_measureReal_univ, Ideal.Quotient.norm_mk_le, Complex.coe_basisOneI, NNReal.mul_rpow, Affine.Simplex.height_reindex, ProbabilityTheory.charFun_gaussianReal, Real.doublingGamma_one, exists_smooth_zero_one_nhds_of_isClosed, measurable_infDist, CFC.abs_smul, ValueDistribution.characteristic_sum_top_eventuallyLE, BoundedContinuousFunction.norm_eq_iSup_norm, Complex.polarCoord_target, CongruenceSubgroup.IsCongruenceSubgroup.conjGL, RCLike.conj_smul, Circle.isCoveringMap_exp, CStarAlgebra.hasBasis_approximateUnit, MeasureTheory.eLpNorm_smul_measure_of_ne_zero', Real.subfield_eq_of_closed, Real.isLittleO_const_logb_atTop, Real.Angle.toReal_coe_eq_self_sub_two_pi_iff, Real.not_continuousAt_deriv_qaryEntropy_one, NonarchAddGroupNorm.coe_lt_coe, Diffeology.IsPlot.dSmooth_comp, Affine.Simplex.inradius_map, Complex.map_isometryOfOrthonormal, IsApproximateSubgroup.one_le, integral_exp_Iic_zero, Real.fib_succ_sub_goldenConj_mul_fib, IsUltrametricDist.isNonarchimedean_nnnorm, MeasureTheory.tilted_apply_eq_ofReal_integral', ValueDistribution.logCounting_coe, SmoothBumpFunction.eventuallyEq_one, Real.tan_arcsin, AddChar.zmod_intCast, quasispectrum.instCompactSpaceNNReal, TemperedDistribution.fourierTransformInv_apply, ENNReal.toReal_mono, BoxIntegral.unitPartition.diam_boxIcc, norm_mul_sub_norm_div_le_two_mul_min, Orientation.oangle_neg_orientation_eq_neg, UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_right, FormalMultilinearSeries.summable_norm_apply, norm_le_norm_div_add, NNReal.multiset_prod_map_rpow, Orientation.oangle_sign_smul_add_smul_left, Real.surjOn_tan, Real.log_zero, Real.tanh_injective, NormedDivisionRing.norm_le_one_of_discrete, Real.arcsin_eq_neg_pi_div_two, Real.cosh_add, MeasureTheory.eval_integral_piLp, ENNReal.inner_le_Lp_mul_Lq, Metric.nhds_basis_ball_inv_nat_pos, Liouville.transcendental, AddCircle.toCircle_nsmul, Real.logDeriv_cosh, LipschitzWith.diam_image_le, EuclideanGeometry.Sphere.secondInter_eq_lineMap, RCLike.mul_re_ax, measurable_derivWithin_Ici, Real.sin_sub_int_mul_two_pi, intervalIntegral.continuous_primitive, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, hasFDerivWithinAt_iff_tendsto, instSMulCommClass_sphere_sphere_closedBall, Complex.measurableEquivRealProd_symm_apply, dist_le_pi_dist, Complex.isHomeomorphicTrivialFiberBundle_im, irrational_natCast_add_iff, Real.contDiffAt_arcsin, Quaternion.coeComplex_one, ArithmeticFunction.vonMangoldt_apply_prime, NormMulClass.norm_mul, LinearMap.im_inner_adjoint_mul_self_eq_zero, ProbabilityTheory.IndepFun.charFun_map_add_eq_mul, Matrix.IsHermitian.mulVec_eigenvectorBasis, ValueDistribution.log_counting_zero_sub_logCounting_top, MeasureTheory.average_union_mem_openSegment, MeasureTheory.isTightMeasureSet_iff_tendsto_measure_compl_closedBall, MeasureTheory.MemLp.integrable_norm_pow', Hyperreal.st_eq_sSup, Finset.norm_prod_le, MeasureTheory.eLpNorm_lt_top_iff_lintegral_rpow_enorm_lt_top, EuclideanGeometry.inversion_zero_radius, dist_inf_sup_pi, ContDiffBump.rIn_pos, Quaternion.hasSum_coe, CircleDeg1Lift.map_map_zero_le, Real.fourierInv_eq', UniformFun.dist_def, UpperHalfPlane.tendsto_comap_im_ofComplex, signedDist_apply_linear, EuclideanGeometry.Sphere.secondInter_map, Metric.biInter_gt_closedBall, Affine.Simplex.excenterWeightsUnnorm_compl, ConvexBody.coe_nsmul, Real.differentiableAt_sin, CircleDeg1Lift.mul_floor_map_zero_le_floor_iterate_zero, EReal.nhdsWithin_top, MeasureTheory.Measure.toSignedMeasure_zero, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, Complex.cos_ofReal_im, Bundle.RiemannianMetric.continuousAt, ContDiff.real_of_complex, AkraBazziRecurrence.injective_sumCoeffsExp, MeasureTheory.charFun_zero, integral_re_add_im, parallelepiped_orthonormalBasis_one_dim, MeasureTheory.measureReal_eq_zero_iff, EuclideanGeometry.Sphere.isDiameter_iff_left_mem_and_midpoint_eq_center, Real.pi_rpow_zero, closure_halfSpace, PadicInt.coe_add, Real.exp_neg, norm_sub_mul_self_real, NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completion, StrongDual.mem_polar_singleton, Chebyshev.psi_mono, NumberField.dedekindZeta_residue_pos, MeasureTheory.tendsto_integral_norm_approxOn_sub, tendsto_norm_comp_cofinite_atTop_of_isClosedEmbedding, NumberField.Units.dirichletUnitTheorem.logEmbedding_ker, integral_log_from_zero, Padic.norm_lt_pow_iff_norm_le_pow_sub_one, CauchySeq.isCauSeq, ENNReal.tendsto_rpow_atBot_of_base_lt_one, Complex.reCLM_enorm, sqrt_one_add_norm_sq_le, MeasureTheory.integral_fun_snd, ContinuousMultilinearMap.opNorm_prod, MeasureTheory.condExpInd_empty, MeasureTheory.integrable_mconv_iff, intervalIntegral.integral_comp_neg, IsPicardLindelof.exists_forall_mem_closedBall_eq_forall_mem_Icc_hasDerivWithinAt, Complex.norm_exp_I_mul_ofReal, Real.hasDerivAt_sinh, VectorFourier.norm_fourierIntegral_le_integral_norm, Besicovitch.goodδ_lt_one, Complex.nnnorm_real, Polynomial.toAddCircle_C_eq_smul_fourier_zero, EuclideanGeometry.Sphere.angle_eq_pi_div_two_iff_mem_sphere_ofDiameter, MeasureTheory.condExpL1CLM_smul, real_inner_smul_self_right, Manifold.exists_lt_of_riemannianEDist_lt, MeasureTheory.integral_abs_condExp_le, Valued.norm_pos_iff_valuation_pos, Matrix.l2_opNorm_mul, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_source, Subalgebra.SeparatesPoints.rclike_to_real, Subgroup.widthInfty_mem_periods, InnerProductGeometry.sin_angle_add, norm_innerSL_le, SeminormFamily.basisSets_iff, Complex.isCauSeq_exp, MeasureTheory.norm_charFun_le, polynomialFunctions_closure_eq_top, Real.Angle.cos_antiperiodic, VectorFourier.hasFDerivAt_fourierChar_smul, Hyperreal.IsSt.neg, LipschitzWith.norm_compLp_le, OrthonormalBasis.measurePreserving_measurableEquiv, BoxIntegral.Box.coe_splitUpper, Orientation.rotation_pi, SeminormedAddGroup.disjoint_nhds, Real.cosh_neg, Real.cos_sub_pi_div_two, strictConcaveOn_cos_Icc, EReal.image_coe_Ioi, Real.fourierIntegral_real_eq, Complex.norm_intCast, NumberField.mixedEmbedding.logMap_zero, MeasureTheory.lpNorm_eq_zero, ContinuousLinearMap.isLeast_opNorm, InformationTheory.not_differentiableAt_klFun_zero, Real.deriv_cosh, PeriodPair.lattice_eq_span_range_basis, tendsto_mulIndicator_cthickening_mulIndicator_closure, ENNReal.limsup_toReal_eq, Real.ofNat_le_toNNReal, ArithmeticFunction.vonMangoldt.residueClass_apply_zero, MeasureTheory.measurable_charFun, Quaternion.continuous_imK, Urysohns.CU.lim_of_notMem_U, IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus, CStarAlgebra.exists_sum_four_unitary, norm_sum_le, integral_cos_sq_sub_sin_sq, range_norm, Metric.uniformContinuous_iff, NNReal.image_coe_Icc, ValueDistribution.logCounting_monotoneOn, Real.exists_extension_norm_eq, Subadditive.apply_mul_add_le, Seminorm.convex_closedBall, RCLike.norm_le_im_iff_eq_I_mul_norm, RCLike.real_smul_eq_coe_mul, Real.exp_neg_one_lt_half, ProbabilityTheory.HasSubgaussianMGF_add_of_HasCondSubgaussianMGF, NumberField.Units.dirichletUnitTheorem.exists_unit, NonarchAddGroupSeminormClass.map_zero, NumberField.mixedEmbedding.fundamentalCone.measurableSet_paramSet, PadicInt.unitCoeff_coe, ENNReal.ofReal_natCast, RCLike.ofReal_inv, AEMeasurable.ennreal_toReal, Polynomial.Chebyshev.intervalIntegrable_sqrt_one_sub_sq_inv, Metric.exists_closedBall_inter_eq_singleton_of_discrete, ContDiffMapSupportedIn.structureMapLM_zero_apply, SchwartzMap.differentiableAt, nnnorm_cfcₙ_nnreal_le, Complex.frontier_reProdIm, RCLike.ofRealAm_coe, CFC.sqrt_eq_real_sqrt, exists_rat_of_not_irrational, MeasureTheory.mul_meas_ge_le_pow_eLpNorm, RCLike.normSq_one, hasConstantSpeedOnWith_iff_ordered, NumberField.mixedEmbedding.integral_comp_polarCoord_symm, Asymptotics.IsBigO.exists_pos, RCLike.re_to_complex, ContinuousOn.inner_bundle, ProbabilityTheory.cgf_zero_measure, MeasureTheory.average_union, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_add_smoothingFn, OpenPartialHomeomorph.univUnitBall_symm_apply, orthonormal_vecCons_iff, unitInterval.symm_eq_one, Real.deriv_sin, norm_mul_sub_norm_div_le_two_mul, AffineSubspace.mem_perpBisector_pointReflection_iff_inner_eq_zero, Metric.iUnion_closedBall_nat, SmoothBumpCovering.embeddingPiTangent_coe, nsmul_mem_ball, dist_sum_sum_le, Real.Gamma_neg_nat_eq_zero, MeasureTheory.Measure.haar.addPrehaar_sup_le, AddCircle.homeomorphCircle'_apply, Real.injOn_cos, schnirelmannDensity_setOf_mod_eq_one, Real.continuous_arccos, Real.nndist_eq', Seminorm.continuous_of_forall, IsSelfAdjoint.le_algebraMap_norm_self, EuclideanGeometry.angle_self_left, real_inner_comm, dist_norm_norm_le, EisensteinSeries.eisensteinSeriesSIF_mdifferentiable, SchwartzMap.integral_smul_deriv_right_eq_neg_left, Urysohns.CU.disjoint_C_support_lim, SmoothPartitionOfUnity.nonneg', Complex.norm_mul, UpperHalfPlane.isometry_pos_mul, Set.Subsingleton.infsep_zero, tendsto_nhds_unique_dist, ProbabilityTheory.covarianceBilinDual_of_not_memLp', Complex.re_sum, MeasureTheory.SimpleFunc.integral_eq_lintegral', Real.HolderConjugate.sub_one_pos, Affine.Triangle.orthocenter_vsub_circumcenter_eq_sum_vsub, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_le_one, Function.hasTemperateGrowth_one_add_norm_sq_rpow, Orientation.two_zsmul_oangle_smul_smul_self, IsMIntegralCurveAt.comp_add, instIsAddHaarMeasureUnitAddCircleVolume, intervalIntegral.norm_integral_min_max, Real.sin_eq_one_iff, SchwartzMap.fourier_convolution, Complex.log_inv_eq_integral, NumberField.mixedEmbedding.fundamentalCone.expMap_pos, ValueDistribution.abs_characteristic_sub_characteristic_shift_le, Real.tan_pi, RCLike.hasSum_im, Orientation.rotation_symm_apply, ZMod.LFunction_dft, tendsto_iff_dist_tendsto_zero, Real.mem_closure_iff, MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp, Module.Basis.norm_repr_le_norm, ContinuousWithinAt.norm', ContinuousMapZero.continuous_toNNReal, PadicInt.coe_dpow_eq, ProbabilityTheory.analyticOn_iteratedDeriv_mgf, MeasureTheory.Integrable.integral_norm_condKernel, Affine.Simplex.altitudeFoot_mem_affineSpan_faceOpposite, Probability.measurable_cauchyPDF, InnerProductGeometry.inner_eq_zero_iff_angle_eq_pi_div_two, instSMulCommClass_closedBall_closedBall_closedBall, continuous_norm, Valued.toNormedField.norm_lt_one_iff, ProbabilityTheory.poissonPMFRealSum, MeasureTheory.Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_addGroup, AddCircle.homeomorphCircle_apply, intervalIntegral.inv_mul_integral_comp_div_add, ProbabilityTheory.integrable_gaussianPDFReal, Topology.CWComplex.continuousOn_symm, ae_not_liouvilleWith, Real.fib_succ_sub_goldenRatio_mul_fib, expNegInvGlue.differentiable_polynomial_eval_inv_mul, NNReal.coe_le_coe, AmpleSet.image, continuousOn_cfcₙ_nnreal_setProd, AkraBazziRecurrence.sumCoeffsExp_p_eq_one, Asymptotics.IsBigOWith.mul, Real.rpow_intCast, tendsto_factorial_div_pow_self_atTop, ProbabilityTheory.Fernique.normThreshold_add_one, gauge_zero, Real.Angle.sin_sub_pi_div_two, spectralValue_X_pow, spectrum.spectralRadius_le_pow_nnnorm_pow_one_div, CircleDeg1Lift.iterate_pos_eq_iff, Real.cos_nat_mul_two_pi, BoundedContinuousFunction.dist_le_two_norm, posTangentConeAt_univ, Bornology.IsBounded.exists_pos_norm_le', Real.one_lt_sqrt_two, MeasureTheory.StronglyMeasurable.dist, ProbabilityTheory.stronglyMeasurable_paretoPDFReal, Complex.upperHalfPlane_inter_integerComplement, CFC.rpow_neg_mul_rpow, PiNat.dist_self, OrthonormalBasis.abs_det_adjustToOrientation, ENNReal.toReal_smul, norm_le_of_mem_closedBall', Real.sSup_neg, ModularGroup.coeHom_apply, ContinuousLinearMap.dist_le_opNorm, ProbabilityTheory.poissonPMFReal_nonneg, Circle.exp_sub_two_pi, EuclideanSpace.edist_eq, IsCompact.uniform_oscillationWithin, MeasureTheory.isProbabilityMeasure_iff_real, RCLike.isCauSeq_re, Complex.ofReal_inv, Real.ofDigits_const_last_eq_one', ProbabilityTheory.Kernel.HasSubgaussianMGF.aestronglyMeasurable, EuclideanGeometry.inversion_eq_lineMap, HasLineDerivAt.le_of_lipschitz, Path.Homotopy.refl_apply, Seminorm.ball_zero_eq, PadicInt.coe_intCast, Real.exp_sum, Complex.frontier_setOf_im_le, AkraBazziRecurrence.GrowsPolynomially.inv, Subgroup.strictPeriods_eq_zmultiples_strictWidthInfty, Metric.dist_lt_add_of_nonempty_ball_inter_closedBall, PadicInt.norm_natCast_p_sub_one, Complex.range_exp_mul_I, LinearMap.polar_mem, RCLike.I_im', MeasureTheory.Lp.pow_mul_meas_ge_le_enorm, inner_eq_norm_sq_right_iff, MeasureTheory.lpNorm_exponent_top_eq_essSup, Real.log_of_ne_zero, CFC.real_exp_eq_normedSpace_exp, CFC.norm_sqrt, LipschitzOnWith.ae_differentiableWithinAt, Real.sin_mem_Icc, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_integrable_exp_mul, Real.sqrt_eq_one, dist_pi_le_iff', Complex.range_im, swap_dist, NumberField.Units.basisOfIsMaxRank_fundSystem, Subgroup.strictWidthInfty_SL2Z, Metric.hausdorffDist_nonneg, Complex.mem_reProdIm, norm_nonneg, CFC.continuousOn_rpow, Complex.dist_of_re_eq, ContinuousLinearMap.norm_holder_apply_apply_le, Real.continuous_arsinh, Real.qaryEntropy_one, NumberField.mixedEmbedding.fundamentalCone.linearIndependent_completeFamily, IsSelfAdjoint.imaginaryPart, MeasureTheory.lpNorm_of_not_memLp, intervalIntegral.norm_integral_le_integral_norm_uIoc, Circle.argPartialEquiv_symm_apply, Complex.isUniformEmbedding_equivRealProd, ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat, MeasureTheory.charFun_map_const_add, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, ProbabilityTheory.covariance_mul_const_right, Affine.Simplex.affineSpan_pair_eq_altitude_iff, NumberField.mixedEmbedding.fundamentalCone.measurableSet_normLeOne, Complex.normSq_neg, MeasureTheory.charFun_eq_pi_iff, SmoothBumpFunction.eq_one, AffineIsometry.angle_map, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, Orientation.rotation_oangle_eq_iff_norm_eq, SeminormedRing.toRingSeminorm_apply, MeasureTheory.lpNorm_exponent_zero, Affine.Simplex.signedInfDist_apply_of_ne, Chebyshev.theta_le_psi, Submodule.norm_subtypeL_le, CircleDeg1Lift.translate_pow, ProbabilityTheory.continuousOn_mgf, Metric.eventually_isCompact_closedBall, Padic.padicNormE.image, integral_cos_mul_complex, WithLp.prod_norm_eq_of_L2, Real.cos_sq_arctan, BumpCovering.exists_isSubordinate_hasCompactSupport_of_locallyFinite_t2space, IsUltrametricDist.isPowMul_invariantExtension, exists_contMDiffMap_one_nhds_of_subset_interior, ModularForm.summable_eta_q, mul_mem_ball_iff_norm, Seminorm.coeFnAddMonoidHom_injective, Complex.norm_eq_one_of_pow_eq_one, unitInterval.symm_bijective, Polynomial.fourierCoeff_toAddCircle, signedDist_left_lineMap, ContinuousLinearMap.bound_of_antilipschitz, Path.uniformContinuous_extend, ENNReal.trichotomy₂, Affine.Simplex.direction_altitude, Complex.hasSum_iff, Real.deriv_mul_log_zero, AddGroupSeminorm.lt_def, ProbabilityTheory.Kernel.integral_withDensity, Rat.AbsoluteValue.apply_le_sum_digits, Asymptotics.isBigO_const_of_ne, NumberField.mixedEmbedding.norm_negAt, NormedSpace.exists_lt_norm, Orientation.oangle_sign_smul_sub_right, NormedSpace.norm_normalize_eq_one_iff, CovBySMul.of_subset, AbsolutelyContinuousOnInterval.continuousOn, SmoothPartitionOfUnity.sum_le_one, Path.symm_range, unitInterval.sigmoid_lt_one, EReal.exists_rat_btwn_of_lt, CStarRing.norm_one, Metric.diam_union, ArithmeticFunction.vonMangoldt.eqOn_LFunctionResidueClassAux, CurveIntegrable.intervalIntegrable_curveIntegralFun_trans_right, NumberField.mixedEmbedding.norm_unit, MeasureTheory.exp_llr, MeasureTheory.Measure.setIntegral_toReal_rnDeriv, Real.volume_preserving_transvectionStruct, seminormFromConst_seq_def, Real.Wallis.W_pos, Real.log_mul, Real.sin_add_int_mul_two_pi, ProbabilityTheory.HasCondSubgaussianMGF.ae_trim_condExp_le, Real.tendsto_prod_pi_div_two, MeasureTheory.L1.integral_eq, ContDiffPointwiseHolderAt.zero_order_iff, ENNReal.zero_eq_ofReal, one_half_le_sum_primes_ge_one_div, Quaternion.coe_real_complex_mul, Real.exp_sub_sum_range_isBigO_pow, Real.hasDerivAt_sqrt, analyticOn_rexp, Archimedean.embedRealFun_strictMono, GenLoop.boundary, Real.hasLipschitzAdd, IccRightChart_extend_top, schnirelmannDensity_empty, GenLoop.homotopyFrom_apply, GenLoop.const_apply, ContinuousLinearMap.NonlinearRightInverse.bound', SchwartzMap.one_add_le_sup_seminorm_apply, Submodule.exists_norm_eq_iInf_of_complete_subspace, Seminorm.continuous_iff_continuous_comp, norm_indicator_le_norm_self, Metric.uniformCauchySeqOn_iff, Hyperreal.stdPart_epsilon, Real.cot_inv_eq_tan, NNReal.image_coe_uIoo, PartitionOfUnity.continuous_smul, stdSimplex.instCompactSpace_coe, UnitAddCircle.integral_preimage, ModularGroup.SL_neg_smul, NumberField.mixedEmbedding.fundamentalCone.expMap_single_source, Real.tanh_surjOn, padicNorm_two_harmonic, Real.sinh_nonpos_iff, Polynomial.Chebyshev.roots_U_real_nodup, Affine.Simplex.circumcenter_eq_centroid, Real.fourierIntegralInv_eq, Hyperreal.Infinitesimal.eq_zero, dist_le_Ico_sum_dist, Real.exp_log_eq_abs, Real.Angle.continuous_cos, Complex.isOpenMap_re, MeasureTheory.weightedSMul_zero_measure, ProbabilityTheory.Kernel.measurable_density_right, taylor_within_apply, Real.exp_nat_mul, AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_nonneg_or_nonpos, Real.sinc_neg, Real.hasDerivWithinAt_arccos_Iic, NonUnitalStarAlgHom.norm_apply_le, NumberField.Units.regOfFamily_eq_det', Affine.Simplex.excenter_reindex, GroupSeminorm.mul_bddBelow_range_add, measurableSet_of_differentiableWithinAt_Ici, MeasureTheory.measureReal_diff_le_iff_le_add, NumberField.mixedEmbedding.fundamentalCone.normLeOne_eq_preimage, Real.cosh_two_mul, NormedAddCommGroup.tendsto_atTop', Polynomial.isPrimitive_iff_forall_gaussNorm_eq_one, Orientation.eq_zero_or_angle_eq_zero_or_pi_of_sign_oangle_eq_zero, ContinuousMultilinearMap.norm_compContinuousLinearMap_le, MeasureTheory.Lp.fourier_toTemperedDistribution_eq, Hyperreal.ofSeq_lt_ofSeq, CompactlySupportedContinuousMap.nnrealPart_sub_nnrealPart_neg, Real.convexOn_mul_log, Real.Angle.tan_periodic, RingNorm.ext_iff, fderivInnerCLM_apply, AbsoluteValue.isEquiv_iff_isHomeomorph, Orthonormal.sum_inner_products_le, eventually_norm_mfderiv_extChartAt_lt, Padic.norm_int_le_pow_iff_dvd, lipschitzWith_min, Real.exp_add, Complex.ofReal_def, Real.cos_pi, Complex.smul_im, Complex.IsExpCmpFilter.isTheta_cpow_exp_re_mul_log, ProbabilityTheory.variance_smul, Real.contDiffOn_arcsin, PartitionOfUnity.sum_finsupport', Affine.Simplex.ninePointCircle_center, MeasureTheory.JordanDecomposition.real_smul_def, TestFunction.injective_toBoundedContinuousFunctionCLM, EuclideanGeometry.dist_orthogonalProjection_line_eq_of_two_zsmul_oangle_eq, boundary_Icc, Real.Gamma_three_div_two_lt_one, properSpace_iff_isProperMap_dist, SchwartzMap.smooth, Hyperreal.st_neg, tendsto_norm_sub_self_nhdsGE, ProbabilityTheory.covariance_const_right, ProbabilityTheory.Kernel.measurable_rnDerivAux_right, Real.tan_sub_int_mul_pi, Real.contDiffAt_arccos_iff, HasProd.norm, MeasureTheory.charFun_prod, Polynomial.card_roots_toFinset_le_derivative, MeasureTheory.integral_smul_measure, deriv_sqrt_mul_log', spectrum.subset_circle_of_unitary, Real.instNontrivial, Real.strictConcaveOn_negMulLog, Padic.norm_p_zpow, UpperHalfPlane.c_mul_im_sq_le_normSq_denom, EuclideanGeometry.inner_vsub_vsub_of_dist_eq_of_dist_eq, SchwartzMap.denseRange_toLpCLM, isMIntegralCurve_comp_mul_ne_zero, ConformalAt.const_smul, ContDiffPointwiseHolderAt.fst, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_eq_one_iff, ProbabilityTheory.Kernel.rnDeriv_def, ContinuousMap.dist_le_iff_of_nonempty, SchwartzMap.toLp_fourier_eq, Real.range_sigmoid, Real.differentiableAt_binEntropy_iff_ne_zero_one, MeasureTheory.tendsto_integral_meas_thickening_le, EisensteinSeries.vec_add_const_isTheta, LinearMap.IsSymmetric.coe_re_inner_apply_self, MeasureTheory.measureReal_add_measureReal_compl, UpperHalfPlane.coe_im_pos, MeasureTheory.lpNorm_const', Real.sigmoid_strictMono, CFC.nnnorm_nnrpow, SchwartzMap.integrable_pow_mul_iteratedFDeriv, FormalMultilinearSeries.radius_eq_liminf, ContinuousLinearMap.norm_precompL_le, Real.fderiv_fourierChar_neg_bilinear_left_apply, ENNReal.toReal_eq_zero_iff, Function.locallyFinsuppWithin.logCounting_even, Real.deriv_tan, Module.Basis.addHaar_self, ArithmeticFunction.vonMangoldt_apply_pow, Real.sigmoid_lt_one, isConformalMap_iff_is_complex_or_conj_linear, CircleDeg1Lift.dist_map_zero_lt_of_semiconjBy, ContinuousLinearEquiv.contDiffPointwiseHolderAt_left_comp, Real.tendsto_one_add_div_rpow_exp, NNReal.coe_eq_one, Metric.unitBall.coe_zero, CFC.rpow_eq_rpow_prod, tendsto_log_mul_self_nhdsLT_zero, AbsolutelyContinuousOnInterval.smul, RCLike.span_one_I, GenLoop.fromLoop_coe, Real.cos_int_mul_pi, Real.gold_pow_sub_gold_pow, OrthogonalFamily.summable_iff_norm_sq_summable, ContinuousLinearMap.norm_map_removeNth_le, Real.tanh_neg, CFC.rpow_mul_rpow_neg, Real.mk_le, Polynomial.Chebyshev.roots_T_real_nodup, Filter.Tendsto.ennrpow_const, Behrend.exists_large_sphere_aux, hasContDiffBump_of_innerProductSpace, Real.sInf_def, IsometricContinuousFunctionalCalculus.isGreatest_spectrum, Real.cos_pi_div_two_sub, Real.one_sub_goldenRatio, AddCircle.toCircle_neg, tendsto_indicator_thickening_indicator_closure, summable_jacobiTheta₂'_term_iff, HolderOnWith.ediam_image_le_of_subset, ArchimedeanClass.stdPart_ratCast, ENNReal.ofReal_le_natCast, Real.sinc_le_inv_abs, instSMulCommClass_sphere_sphere_ball, Metric.uniformSpace_eq_bot, norm_sup_sub_sup_le_norm, MulRingSeminorm.map_one', PiTensorProduct.mapLMultilinear_opNorm, TestFunctionClass.map_contDiff, Tactic.ComputeAsymptotics.WellFormedBasis.push_log_last, AddCircle.norm_eq_of_zero, Complex.range_normSq, Measurable.carg, MeasureTheory.norm_condExpIndL1Fin_le, BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg, Seminorm.uniformContinuous_of_forall', Real.isLittleO_pow_logb_id_atTop, ContinuousMultilinearMap.norm_image_sub_le', InnerProductGeometry.sin_angle_mul_norm_mul_norm, ValueDistribution.proximity_top, Int.pairwise_one_le_dist, Affine.Triangle.sSameSide_affineSpan_pair_incenter_point, MeasureTheory.measureReal_union_add_inter, Real.volume_preimage_mul_right, SmoothBumpFunction.nhds_basis_tsupport, NumberField.InfinitePlace.apply, ArchimedeanClass.stdPart_real, Metric.infDist_nonneg, NNReal.dist_gm_am_le, CircleDeg1Lift.map_add_one, StieltjesFunction.right_continuous, Polynomial.mahlerMeasure_le_sum_norm_coeff, Real.fourier_eq', Real.smoothTransition.pos_denom, NNReal.coe_list_prod, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt₀, MeasureTheory.charFunDual_eq_prod_iff', MeasureTheory.Measure.toSphere.instIsOpenPosMeasure, ProbabilityTheory.integrable_comp_iff, dist_smul_pair, MeasureTheory.lpMeasToLpTrimLie_symm_toLp, ProbabilityTheory.IsAEKolmogorovProcess.q_pos, norm_norm', UpperHalfPlane.mdifferentiable_iff, EReal.nhdsWithin_bot, Subgroup.IsArithmetic.discreteTopology, Real.ringEquivCauchy_symm_apply_cauchy, ModularFormClass.exp_decay_sub_atImInfty', Complex.neg_re_eq_norm, Real.HolderTriple.inv_sub_inv_eq_inv, UpperHalfPlane.smulAux'_im, Submodule.orthogonalProjection_norm_le, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_add_le_max, NormedRing.toRingNorm_apply, integral_sin_pow_antitone, Complex.arg_neg_eq_arg_sub_pi_iff, Matrix.PosDef.posDef_sqrt, Function.HasTemperateGrowth.isBigO_uniform, MeasureTheory.Measure.haar.addPrehaar_self, dist_vadd_vadd_le, intervalIntegrable_log_sin, integral_pow_abs_sub_uIoc, Valued.toNormedField.one_le_norm_iff, Seminorm.zero_apply, WithSeminorms.hasBasis_ball, norm_cfcₙ_le_iff, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunctionAux_nonneg, DiffeologicalSpace.CorePlotsOn.isPlotOn_univ, ProbabilityTheory.variance_const_mul, ArchimedeanClass.stdPart_inv, EuclideanSpace.volume_closedBall, Orientation.rightAngleRotation_neg_orientation, NumberField.mixedEmbedding.integral_comp_polarCoordReal_symm, unitInterval.qRight_one_right, Orientation.rotationAux_apply, NonarchAddGroupNorm.toNonarchAddGroupSeminorm_eq_coe, intervalIntegrable_inv_iff, Real.cos_mem_Icc, FormalMultilinearSeries.norm_mul_pow_le_of_lt_radius, CStarRing.norm_coe_unitary, BumpCovering.sum_toPOUFun_eq, NumberField.mixedEmbedding.fundamentalCone.compactSet_eq_union, GenLoop.homotopicTo, RCLike.intCast_im, RCLike.ofReal_sum, Real.sqrt_eq_rpow, Real.tendsto_exp_atBot_nhdsGT, MeasureTheory.measureReal_diff_add_inter, Real.Angle.toReal_eq_neg_pi_div_two_iff, PiNat.dist_le_one, Real.inv_logb, Real.sign_intCast, Real.contDiffAt_rpow_of_ne, AddGroupSeminorm.inf_apply, Real.tan_zero, Real.hasStrictDerivAt_exp, CFC.norm_nnrpow, Quaternion.continuous_normSq, Complex.isCauSeq_re, NormedAlgebra.Complex.exists_norm_sub_smul_one_eq_zero, AddCircle.integral_preimage, NonarchAddGroupSeminorm.coe_sSup_apply, Affine.Simplex.centroid_eq_affineCombination_of_pointsWithCircumcenter, Subgroup.periods_eq_zmultiples_widthInfty, ProbabilityTheory.stronglyMeasurable_exponentialPDFReal, Real.two_mul_sin_mul_sin, Height.logHeight_pow, le_egauge_closedBall_one, Real.sqrt_eq_zero', Real.toNNReal_eq_ofNat, AkraBazziRecurrence.bi_min_div_two_lt_one, Quaternion.continuous_re, congruent_iff_pairwise_dist_eq, InformationTheory.deriv_klFun, HolderWith.interpolate, one_add_rpow_hasFPowerSeriesOnBall_zero, CFC.conjugate_rpow_neg_one_half, MeasureTheory.measureReal_inter_add_diff, boundary_product, ArithmeticFunction.zeta_mul_vonMangoldt, MeasureTheory.norm_condExpL2_le_one, HasCompactSupport.convolution_integrand_bound_right, differentiable_sigmoid, Complex.re_nonneg_iff_nonneg, NNReal.bddAbove_coe, Real.rpow_def, CircleDeg1Lift.commute_sub_nat, ProbabilityTheory.tendsto_cdf_atBot, Real.isCauSeq_iff_lift, integral_comp_pi_polarCoord_symm, Real.tendsto_harmonic_sub_log_add_one, Complex.arg_I, ZetaAsymptotics.tendsto_riemannZeta_sub_one_div_nhds_right, Orientation.cos_oangle_eq_inner_div_norm_mul_norm, BumpCovering.coe_single, Real.mk_pos, Affine.Simplex.incenter_notMem_affineSpan_faceOpposite, Affine.Simplex.touchpoint_empty_mem_interior_faceOpposite, Complex.imLm_coe, MeasureTheory.summable_measure_toReal, GromovHausdorff.eq_toGHSpace_iff, Real.posLog_nat_mul, Real.summable_nat_rpow, ODE.FunSpace.dist_iterate_next_apply_le, GenLoop.continuous_toLoop, polarCoord_source, NumberField.mixedEmbedding.measurable_polarSpaceCoord_symm, ENNReal.ofReal_mono, MeasureTheory.condExpL2_comp_continuousLinearMap, Real.HolderTriple.nonneg, inner_im_symm, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, SchwartzMap.laplacian_apply, Polynomial.supNorm_eq_zero_iff, Measurable.norm, Complex.arg_eq_pi_iff, RCLike.re_extendTo𝕜'ₗ, Real.toNNReal_lt_toNNReal_iff', Real.posLog_mul, NumberField.Units.regOfFamily_eq_zero, FormalMultilinearSeries.ofScalars_norm_eq_mul, AddGroupNorm.toAddGroupSeminorm_eq_coe, dist_triangle8, MeasureTheory.Measure.toSignedMeasure_restrict_sub, ProbabilityTheory.tendsto_condCDF_atTop, CFC.log_smul, MeasureTheory.charFun_map_smul, MeasureTheory.L2.eLpNorm_rpow_two_norm_lt_top, ZSpan.setFinite_inter, ENNReal.toReal_ofReal', ProbabilityTheory.IsGaussian.eq_gaussianReal, balanced_iff_closedBall_smul, convex_closedBall, Commute.cfcₙ_real, Real.range_cos_infinite, Real.one_div_sub_sq_hasFPowerSeriesOnBall_zero, Complex.arg_cos_add_sin_mul_I_eq_toIocMod, Real.sinhOrderIso_symm_apply, Complex.div_natCast_re, Real.summable_exp_nat_mul_iff, EuclideanSpace.coe_measurableEquiv_symm, NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlace, ContinuousMap.Homotopy.congr_arg, Real.norm_nnratCast, AEMeasurable.dist, real_inner_self_pos, circleMap_mem_sphere', Complex.neg_im, MeasureTheory.integral_coe_le_of_lintegral_coe_le, unitInterval.le_symm_comm, GenLoop.fromLoop_trans_toLoop, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, Circle.argEquiv_apply_coe, MeasureTheory.memLp_re_im_iff, ContinuousMapZero.toNNReal_apply, EisensteinSeries.tsum_symmetricIco_tsum_eq_S_act, Set.Nontrivial.le_infsep_iff, norm_mul_le', sameRay_iff_norm_smul_eq, Cardinal.mk_Ioi_real, HolderWith.nndist_le, LiouvilleWith.add_nat_iff, irrational_natCast_div_iff, Complex.UnitDisc.instIsScalarTower_closedBall_closedBall, Metric.uniformContinuous_infDist_pt, Metric.isOpen_singleton_iff, continuous_circleMap_inv, Complex.re_nnratCast, ProbabilityTheory.truncation_zero, Real.round_pi_eq_three, ArchimedeanClass.stdPart_nonpos, Real.cos_two_mul', irrational_sqrt_two, ContDiffMapSupportedIn.structureMapLM_apply, Complex.normSq_eq_zero, CircleDeg1Lift.translationNumber_mono, UniformSpace.Completion.uniformity_dist', AffineSubspace.right_mem_perpBisector, ContinuousLinearMap.circleAverage_comp_comm, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangentAt, ProbabilityTheory.stronglyMeasurable_condVar, Complex.isLittleO_ofReal_left, RCLike.normSq_sub, Real.rpow_natCast, Real.zero_rpow_nonneg, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two, Real.norm_eq_abs, Real.fromBinary_continuous, Metric.tendsto_dist_right_atTop_iff, Subgroup.IsArithmetic.conj, Real.exists_int_int_abs_mul_sub_le, NNReal.young_inequality_real, Real.four_mul_arctan_inv_5_sub_arctan_inv_239, HasCompactSupport.convolution_integrand_bound_right_of_subset, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_nonneg, intervalIntegral.integral_mul_const, schnirelmannDensity_mul_le_card_filter, Complex.horizontalSegment_eq, LiouvilleWith.nat_add, SlashInvariantForm.coe_norm, Real.sin_eq_two_mul_tan_half_div_one_add_tan_half_sq, MeasureTheory.integral_comap_eq_mulEquivHaarChar_smul, Real.Angle.tan_zero, Complex.ofReal_mul, le_iff_norm_sqrt_mul_rpow, ContDiffBump.contDiffWithinAt, Real.sqrt_ne_zero', Complex.sin_arg, RCLike.re_tsum, mem_ball_zero_iff, Real.exists_seq_rat_strictMono_tendsto, ContinuousLinearMap.IsPositive.re_inner_nonneg_right, balancedCore_eq_iInter, RCLike.wInner_cWeight_eq_smul_wInner_one, NumberField.mixedEmbedding.fundamentalCone.injective_expMap, norm_sub_le_norm_sub_add_norm_sub, Path.refl_extend, LipschitzWith.norm_compLp_sub_le, EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_left, Complex.det_conjLIE, not_differentiableAt_abs_zero, MeasureTheory.llr_smul_left, Hyperreal.st_add, interior_euclideanQuadrant, hasDerivWithinAt_iff_tendsto, norm_sub_pos_iff, antilipschitzWith_iff_exists_mul_le_norm, Complex.exp_im, Height.mulHeight₁_one, Polynomial.Chebyshev.C_two_mul_real_cos, intervalIntegral.intervalIntegrable_log', NumberField.house.basis_repr_norm_le_const_mul_house, Complex.dist_conj_self, CStarAlgebra.nnnorm_mem_spectrum_of_nonneg, SpectrumRestricts.nnreal_iff_nnnorm, Real.HolderTriple.one_div_nonneg, CircleDeg1Lift.tendsto_translation_number₀', ModularGroup.exists_eq_T_zpow_of_c_eq_zero, Valued.integer.exists_norm_coe_lt_one, ProbabilityTheory.convex_integrableExpSet, MeasureTheory.integral_countable', NonarchAddGroupNormClass.toAddGroupNormClass, BoxIntegral.Box.mem_univ_Ioc, RCLike.realLinearIsometryEquiv_apply, Metric.thickening_thickening_subset, cantorSequence_get_succ, TemperedDistribution.laplacianCLM_apply, Real.strictConcaveOn_qaryEntropy, Metric.Sigma.isOpen_iff, EuclideanGeometry.Sphere.secondInter_eq_self_iff, Hyperreal.coe_sub, SchwartzMap.instFourierAdd, ConvexBody.coe_smul', Real.mul_exp_neg_le_exp_neg_one, EuclideanGeometry.angle_add_angle_add_angle_eq_pi, ZMod.toCircle_eq_circleExp, Unitary.spectrum_subset_circle, CauchySeq.mul_norm_bddAbove, Polynomial.Chebyshev.roots_U_real, MeasureTheory.count_real_singleton, Polynomial.derivRootWeight_nonneg, ValueDistribution.proximity_sub_proximity_inv_eq_circleAverage, MeasureTheory.SignedMeasure.toJordanDecomposition_smul, ProperCone.innerDual_innerDual, UniformSpace.Completion.dist_self, Real.arsinh_le_arsinh, UpperHalfPlane.vadd_im, ProbabilityTheory.mgf_pos_iff, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, curveIntegralFun_def, HurwitzZeta.hurwitzZetaEven_neg, Circle.exp_nsmul, Complex.div_ratCast, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_lt_one_iff, Seminorm.continuousAt_zero, ContinuousLinearMap.norm_smulRightL_apply, Complex.im_tsum, Metric.exists_real_pos_lt_infEDist_of_notMem_closure, MeasureTheory.Measure.haar.addPrehaar_empty, Orientation.areaForm_rightAngleRotation_left, Real.tanh_bijOn, torusIntegral_succAbove, ZLattice.covolume_div_covolume_eq_relIndex', coeFn_fourierLp, CStarAlgebra.exists_sum_four_nonneg, contDiff_sigmoid, Path.truncate_range, cfcₙ_complex_eq_real, Real.pi_gt_d6, RCLike.tendsto_ofReal_atTop_cobounded, ConvexBody.coe_zero, Int.preimage_closedBall, HasDerivAt.le_of_lipschitzOn, ENNReal.tsum_toReal_eq, setOf_riemannianEDist_lt_subset_nhds', similar_iff_exists_pos_dist_eq, Real.geom_goldenConj_isSol_fibRec, norm_lt_of_mem_ball, LinearIsometry.angle_map, fourierCoeff_liftIco_eq, Urysohns.CU.lim_nonneg, NNReal.map_coe_nhdsGE, EuclideanGeometry.dist_set_eq_iff_dist_orthogonalProjection_eq, Quaternion.exp_coe, Metric.uniformity_basis_dist_inv_nat_pos, Real.exp_neg_one_lt_d9, NumberField.mixedEmbedding.disjoint_negAt_plusPart, Real.cos_le_one, ContinuousMap.Homotopy.map_zero_left, Seminorm.closedBall_add_closedBall_subset, unitInterval.continuous_symm, Matrix.IsHermitian.instContinuousFunctionalCalculus, Metric.isBounded_range_iff, HolderWith.comp, lipschitzOnWith_iff_norm_sub_le, MeasureTheory.measurable_embeddingReal, GaussianInt.normSq_div_sub_div_lt_one, IccLeftChart_extend_bot_mem_frontier, fderiv_norm_sq_apply, RCLike.imCLM_apply, ODE.FunSpace.lipschitzWith, SmoothBumpFunction.nonempty_support, CFC.nnrpow_map_prod, Real.norm_ofNat, NNReal.inner_le_Lp_mul_Lq, GroupSeminorm.sup_apply, Real.tan_eq_zero_iff', NNReal.coe_single, GroupSeminorm.coe_lt_coe, Complex.cos_arg, ProbabilityTheory.defaultRatCDF_nonneg, Complex.arg_eq_neg_pi_div_two_iff, ProbabilityTheory.Kernel.tendsto_density_fst_atTop_ae_of_monotone, Real.posLog_norm_sum_le, NormedAddCommGroup.nhds_basis_norm_lt, EuclideanGeometry.Sphere.finrank_orthRadius, CircleDeg1Lift.translationNumber_zpow, norm_mul₃_le', MeasureTheory.probReal_compl_eq_one_sub, NumberField.mixedEmbedding.logMap_mul, AkraBazziRecurrence.growsPolynomially_zpow, NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasis, NNRat.instContinuousSMulRatReal, EulerSine.integral_cos_mul_cos_pow_even, measurable_coe_nnreal_real_iff, Asymptotics.IsLittleO.norm_right, InnerProductGeometry.inner_eq_mul_norm_iff_angle_eq_zero, Quaternion.norm_toLp_equivTuple, Icc_isBoundaryPoint_top, aestronglyMeasurable_withDensity_iff, integral_sin_pow_even, ContinuousAlternatingMap.ratio_le_opNorm, Real.arcsin_projIcc, ContinuousMultilinearMap.norm_mkPiAlgebraFin, Affine.Simplex.points_vsub_eulerPoint, bernoulliFun_eval_half, QuotientGroup.norm_mk_le_norm, Real.summable_one_div_int_add_rpow, Polynomial.card_mahlerMeasure_le_prod, Real.natCast_le_toNNReal, ProbabilityTheory.ofReal_cdf, UpperHalfPlane.modular_T_smul, Real.rpow_zero_pos, MeasureTheory.integral_toReal, MulAlgebraNorm.smul', uniqueDiffOn_Ici, Quaternion.exp_eq, Real.Angle.two_nsmul_toReal_eq_two_mul, Metric.ball_eq_ball', isClosedMap_dist, MulAlgebraNorm.extends_norm, Metric.diam_univ_of_noncompact, RCLike.inner_eq_wInner_one, Real.isLittleO_one_exp_comp, Complex.norm_natCast_cpow_of_re_ne_zero, Orientation.measure_orthonormalBasis, CompactlySupportedContinuousMap.exists_add_nnrealPart_add_eq, Affine.Simplex.ExcenterExists.sSameSide_excenter_point_iff, EMetric.exists_real_pos_lt_infEdist_of_notMem_closure, trapezoidal_integral_eq, LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div, Real.Angle.sign_coe_neg_pi_div_two, MeasureTheory.integral_mul_const, Real.cos_abs, GaussianInt.intCast_complex_norm, RCLike.lipschitzWith_im, Real.continuous_mulExpNegMulSq, MeasureTheory.Measure.integral_comp_div, intervalIntegral.integral_const, fderiv_norm_sq, ContinuousLinearMap.opNorm_le_of_lipschitz, EReal.coe_lt_coe_iff, Seminorm.smul_le_smul, Complex.nonempty_linearEquiv_real, variationOnFromTo.self, MeasureTheory.addEquivAddHaarChar_smul_integral_map, MeasureTheory.Measure.toSphere_apply_univ', Real.pi_lt_d4, Complex.continuous_im, LightProfinite.isClosedEmbedding_natUnionInftyEmbedding, GaussianInt.intCast_re, hasConstantSpeedOnWith_iff_variationOnFromTo_eq, Complex.coe_reAddGroupHom, Complex.ofReal_choose, inner_vsub_vsub_right_eq_dist_sq_right_iff, Int.Matrix.exists_ne_zero_int_vec_norm_le, IsCusp.smul, MeasureTheory.condExp_bot_ae_eq, seminormFromConst_seq_nonneg, Complex.equivRealProdCLM_apply, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_sub_smoothingFn, Function.HasTemperateGrowth.isBigO, HurwitzZeta.isBigO_atTop_sinKernel, NNReal.rpow_sub_intCast', Asymptotics.isBigO_iff', Circle.argPartialEquiv_apply, NumberField.FinitePlace.norm_def, mulLeft_bound, WeakFEPair.hf_top, ValueDistribution.characteristic_mul_top_eventuallyLE, MeasureTheory.charFun_eq_integral_probChar, Behrend.exp_four_lt, SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent, AddGroupSeminorm.coe_sup, NumberField.mixedEmbedding.convexBodySum_mem, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', unitInterval.toNNReal_one, EuclideanGeometry.angle_eq_pi_iff_sbtw, Seminorm.sSup_apply, Real.smul_iInf_of_nonneg, MeasureTheory.condExpL1_eq, hasSum_L_function_mod_four_eval_three, MeasureTheory.L1.SimpleFunc.coe_posPart, ProbabilityTheory.IsMeasurableRatCDF.tendsto_stieltjesFunction_atBot, Urysohns.CU.approx_of_notMem_U, NNReal.norm_eq, Orientation.abs_oangle_sub_right_toReal_lt_pi_div_two, ModularGroup.smul_eq_lcRow0_add, Polynomial.Chebyshev.abs_eval_T_real_eq_one_iff, Real.lt_of_toNNReal_lt, Asymptotics.isBigOWith_fst_prod, LinearMap.IsSymmetric.eigenvalues_antitone, NNReal.lintegral_mul_le_Lp_mul_Lq, Real.cast_natAbs_eq_nnabs_cast, conformalAt_iff', NNReal.coe_max, Real.sinh_bijective, MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_rclike_tendsto, Complex.tendsto_tsum_powerSeries_nhdsWithin_lt, MeasureTheory.tilted_apply', Real.hasDerivWithinAt_arcsin_Iic, ContinuousLinearMap.toSesqForm_apply_norm_le, Real.sin_int_mul_pi, unitInterval.symm_symmMeasurableEquiv, PiLp.edist_eq_of_L2, NumberField.mixedEmbedding.fundamentalCone.expMap_single_target, quarter_mem_cantorSet, ContDiffMapSupportedIn.structureMapLM_eq, Path.Homotopic.concat_subpath, SchwartzMap.isBigO_cocompact_rpow, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left, NonarchAddGroupSeminorm.neg', Real.infinite_rat_abs_sub_lt_one_div_den_sq_iff_irrational, Complex.rank_real_complex, UpperHalfPlane.vadd_left_injective, NumberField.IsCMField.regOfFamily_realFunSystem, ContinuousAlternatingMap.norm_image_sub_le, ProbabilityTheory.IsRatStieltjesPoint.iInf_rat_gt_eq, eventually_riemannianEDist_lt, ProbabilityTheory.instIsGaussianMapNeg, Real.tendsto_mulExpNegMulSq, EuclideanGeometry.Sphere.IsDiameter.dist_left_right_div_two, continuous_sigmoid, NNReal.coe_sub, MeasureTheory.eLpNorm_indicator_const, IsMIntegralCurveAt.eventually_hasDerivAt, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, Real.arctan_lt_arctan_iff, hasFDerivAt_stereoInvFunAux_comp_coe, SimpleGraph.lapMatrix_mulVec_eq_zero_iff_forall_adj, MeasureTheory.integrableOn_Ioi_comp_rpow_iff', dist_lineMap_lineMap, lipschitz_with_lipschitz_const_add, Affine.Simplex.ExcenterExists.exradius_pos, ENNReal.toReal_iSup, ExistsContDiffBumpBase.w_mul_φ_nonneg, MeasureTheory.Measure.ContinuousLinearMap.quasiMeasurePreserving, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_nonneg, Archimedean.ratLt'_add, Affine.Triangle.dist_point_centroid, HurwitzZeta.hurwitzZetaEven_eq, ENNReal.coe_lt_ofReal, integral_im, MeasureTheory.snd_integral_withLp, ODE.picard_apply, summable_geometric_two_encode, Real.log_doublingGamma_eq, MeasureTheory.condExpL2_indicator_nonneg, tendsto_norm_cocompact_atTop, Affine.Triangle.orthocenter_reindex, Path.eqOn_extend_segment, HasCompactSupport.hasFDerivAt_convolution_left, PadicInt.coe_pow, NumberField.mixedEmbedding.convexBodyLT'_convex, Real.tan_eq_sin_div_cos, Affine.Simplex.circumradius_map, AkraBazziRecurrence.max_bi_le, MeasureTheory.charFun_map_add_const, intervalIntegral.integral_const_mul, Complex.abs_re_div_norm_le_one, NNReal.rpow_pos, CFC.abs_eq_zero_iff, instIsManifoldIcc, SeminormedCommGroup.mem_closure_iff, Bundle.ContinuousRiemannianMetric.isVonNBounded, hahnEmbedding_isOrderedAddMonoid, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, HurwitzKernelBounds.isBigO_atTop_F_int_zero_sub, MeasureTheory.integrable_rnDeriv_mul_log_iff, PartitionOfUnity.sum_finsupport, Topology.RelCWComplex.map_zero_mem_closedCell, Real.two_mul_sin_mul_cos, TemperedDistribution.smulLeftCLM_apply_apply, MeasureTheory.hasFiniteIntegral_count_iff, integrableAtFilter_rpow_atTop_iff, CircleDeg1Lift.semiconjBy_iff_semiconj, schnirelmannDensity_finset, CFC.rpow_eq_cfc_real, Complex.not_lt_iff, MeasureTheory.eLpNorm'_exponent_zero, summable_jacobiTheta₂_term_iff, Delone.DeloneSet.exists_dist_le_coveringRadius, Complex.UnitDisc.sq_norm_lt_one, AddCircle.ergodic_zsmul_add, Complex.conjCLE_coe, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, GroupSeminormClass.toSeminormedCommGroup_norm_eq, RCLike.im_le_norm, Complex.continuousOn_one_add_mul_inv, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_tendsto, Real.tendsto_one_add_div_pow_exp, WithSeminorms.hasBasis_zero_ball, ProbabilityTheory.IsMeasurableRatCDF.tendsto_atTop_one, Asymptotics.isLittleO_iff_nat_mul_le', Real.tendsto_pow_mul_exp_neg_atTop_nhds_zero, Orientation.inner_mul_areaForm_sub, EReal.toReal_nonneg, Real.exp_pos, InnerProductGeometry.angle_neg_left, Real.ediam_Icc, Metric.closure_eq_iInter_thickening, ProbabilityTheory.integral_preCDF_fst, contDiffAt_abs, dist_anti_left_pi, norm_inner_le_norm, Real.arcsin_one, Real.binEntropy_eq_negMulLog_add_negMulLog_one_sub, Real.HolderConjugate.div_conj_eq_sub_one, ProbabilityTheory.covarianceOperator_of_not_memLp, PowerSeries.gaussNorm_nonneg, Urysohns.CU.lim_mem_Icc, AffineIsometryEquiv.pointReflection_midpoint_right, Height.mulHeight_one, Matrix.IsHermitian.im_star_dotProduct_mulVec_self, Asymptotics.IsBigOWith.sup', GenLoop.instContinuousEvalConst, uniformConvexOn_zero, MeasureTheory.measureReal_nnreal_smul_apply, NumberField.mixedEmbedding.norm_apply, deriv2_sqrt_mul_log, Real.ofCauchy_inf, SmoothPartitionOfUnity.contMDiff_sum, CompletelyRegularSpace.completely_regular_isOpen, IsUltrametricDist.norm_zpow_le, EuclideanGeometry.Sphere.infDist_eq_radius_iff_isTangent, MeasureTheory.Measure.zero_le_toSignedMeasure, ENNReal.ofReal_ne_zero_iff, ContinuousMultilinearMap.norm_ofSubsingleton_id, Affine.Simplex.altitude_def, DeltaGeneratedSpace.continuous_iff, Real.rpow_neg_ofNat, Hyperreal.isSt_ofSeq_iff_tendsto, unitInterval.volume_Iio, sum_trapezoidal_integral_adjacent_intervals, Diffeology.dSmooth_iff, Complex.cpow_ofReal, RCLike.normSq_conj, Real.volume_interval, ZSpan.fundamentalDomain_ae_parallelepiped, Real.sinhHomeomorph_apply, GaussianInt.toComplex_div_im, ContinuousMap.dist_eq_iSup, contMDiffOn_projIcc, Real.Angle.eq_iff_abs_toReal_eq_of_sign_eq, Complex.equivRealProd_apply_le, MeasureTheory.SignedMeasure.im_toComplexMeasure, Complex.im_ofNat, NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces, DiffeologicalSpace.isOpen_iff_preimages_plots, ContDiffBump.integral_pos, AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T, ContDiffBump.continuous_normed, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, ProbabilityTheory.setLIntegral_toKernel_Iic, Real.log_injOn_pos, InnerProductGeometry.angle_eq_angle_add_add_angle_add, NNReal.summable_rpow, Complex.lim_re, EisensteinSeries.div_max_sq_ge_one, Complex.rotation, Real.coe_sinOrderIso_apply, ProbabilityTheory.IsCondKernelCDF.toKernel_apply, Metric.exists_contMDiffMap_forall_closedEBall_subset, BoxIntegral.unitPartition.tag_mem_smul_span, signedDist_vadd_vadd, UniformSpace.Completion.continuous_dist, MeasureTheory.Lp.mul_meas_ge_le_pow_enorm, Polynomial.Chebyshev.eval_T_real_cos_int_mul_pi_div, parallelepiped_single, ContDiffMapSupportedIn.norm_toBoundedContinuousFunction, SchwartzMap.norm_pow_mul_le_seminorm, contMDiff_circleExp, gronwallBound_ε0, NormedAddGroupHom.norm_id, ProbabilityTheory.instIsProbabilityMeasurecdf, Complex.one_im, Quaternion.nnnorm_coe, Stirling.tendsto_self_div_two_mul_self_add_one, GroupNormClass.toNormedCommGroup_norm_eq, PiLp.norm_eq_card, BoundedContinuousFunction.probCharDual_apply, Real.deriv2_negMulLog, intervalIntegral.inv_smul_integral_comp_add_div, Memℓp.bddAbove, ArchimedeanClass.stdPart_eq_sSup, Real.Wallis.le_W, InnerProductSpace.norm_rankOne, SchwartzMap.tsum_eq_tsum_fourier, NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces, ZLattice.exists_finsetSum_norm_rpow_le_tsum, Stirling.stirlingSeq_has_pos_limit_a, Urysohns.CU.lim_eq_midpoint, Real.Angle.nsmul_eq_iff, ProbabilityTheory.IndepFun.integral_mul_eq_mul_integral, AkraBazziRecurrence.eventually_one_add_smoothingFn_nonneg, Nonneg.instIsometricContinuousFunctionalCalculus, MeasureTheory.Measure.integrable_pow_neg_integrablePower, Asymptotics.isBigO_abs_right, Rat.uniformContinuous_coe_real, Real.sin_pi_div_four, Real.le_coe_toNNReal, RCLike.inv_re, RCLike.ofReal_ratCast, GromovHausdorff.HD_below_aux1, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le, EuclideanGeometry.Sphere.self_mem_orthRadius, Real.Angle.toReal_zero, Set.Icc.convexCombo_zero, ZLattice.abs_repr_le, AkraBazziRecurrence.eventually_one_add_smoothingFn_pos, norm_jacobiTheta₂_term_fderiv_le, SlashInvariantForm.T_zpow_width_invariant, CFC.isUnit_sqrt_iff, Affine.Simplex.insphere_reindex, norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zero, EisensteinSeries.isBoundedAtImInfty_eisensteinSeriesSIF, ContinuousLinearEquiv.norm_pos, real_inner_I_smul_self, kuratowskiEmbedding.isometry, Matrix.PosDef.re_dotProduct_pos, Seminorm.closedBall_smul_closedBall, Complex.normSq_one, Real.binEntropy_eq_zero, ProbabilityTheory.IsAEKolmogorovProcess.p_pos, Real.natCast_lt_toNNReal, PeriodPair.instIsZLatticeRealComplexLattice, pi_norm_const_le, MeasureTheory.Measure.toSphere_eq_zero_iff, Real.ediam_Ico, Real.zero_rpow_le_one, Asymptotics.isLittleO_abs_left, NumberField.Units.regOfFamily_pos, ZLattice.covolume_eq_det, Int.norm_cast_real, Real.isPiSystem_Ioo_rat, Real.posLog_add, irrational_intCast_mul_iff, ENNReal.toReal_eq_one_iff, lp.tsum_mul_le_mul_norm, Real.sin_arctan_lt_zero, NumberField.mixedEmbedding.normAtPlace_real, ContinuousMap.HomotopyRel.eq_snd, bernsteinApproximation.apply, EisensteinSeries.linear_inv_isBigO_right, ampleSet_univ, Behrend.exists_large_sphere, IsMIntegralCurveOn.comp_add, MeasureTheory.SignedMeasure.rnDeriv_add, Real.tendsto_Icc_vitaliFamily_right, Real.tan_add_pi, tendsto_iff_norm_sub_tendsto_zero, MeasureTheory.Lp.continuous_posPart, RCLike.map_to_real, SmoothBumpFunction.closedBall_subset, MeasureTheory.Measure.integrable_toReal_rnDeriv, Affine.Simplex.sum_centroidWeightsWithCircumcenter, Real.isEquivalent_sinh, BoundingSieve.prod_primeFactors_nu, Complex.norm_mul_sin_arg, Real.sin_sq_pi_over_two_pow_succ, LipschitzWith.dist, Metric.dist_le_add_of_nonempty_closedBall_inter_closedBall, Valued.integer.norm_irreducible_pos, WithLp.prod_antilipschitzWith_ofLp, Real.Angle.sin_sub_pi, ContinuousMap.Homotopy.curry_zero, Metric.sphere.instIsTopologicalGroup, AbsolutelyContinuousOnInterval.hasBasis_totalLengthFilter, Orthonormal.tsum_inner_products_le, MeasureTheory.toReal_setLAverage, BoxIntegral.Box.antitone_lower, Int.Matrix.exists_ne_zero_int_vec_norm_le', MeasureTheory.neg_llr, ProbabilityTheory.gaussianPDFReal_nonneg, NumberField.InfinitePlace.instNonnegHomClassReal, Urysohns.CU.approx_le_lim, Hyperreal.tendsto_atTop_iff, RCLike.norm_nnqsmul, Complex.tendsto_exp_comap_re_atBot_nhdsNE, differentiable_circleMap, HolderWith.nndist_le_of_le, Complex.dist_eq_re_im, Archimedean.ratLt'_bddAbove, ENNReal.truncateToReal_nonneg, Metric.mem_ball', BumpCovering.support_toPartitionOfUnity_subset, Real.cos_arctan, Metric.Sigma.dist_ne, Real.goldenRatio_sq, PowerSeries.IsRestricted.isRestricted_iff_abs, pi_norm_le_iff_of_nonempty', ModularForm.slash_apply, Metric.PiNatEmbed.exists_embedding_to_hilbert_cube, NormedRing.norm_mul_le, norm_eq_sqrt_real_inner, Complex.lt_def, ValueDistribution.logCounting_even, SmoothBumpFunction.isCompact_symm_image_closedBall, NormedSpace.Core.norm_eq_zero_iff, Asymptotics.isBigOWith_pure, Real.smoothTransition.contDiff, Real.binEntropy_strictMonoOn, Real.Angle.coe_neg, LiouvilleWith.nat_mul_iff, Complex.angle_exp_exp, MeasureTheory.average_eq, Metric.isUniformEmbedding_iff', ProbabilityTheory.gaussianReal_absolutelyContinuous, AkraBazziRecurrence.isLittleO_self_div_log_id, curveIntegralFun_zero, MeasureTheory.Integrable.im, WithLp.dist_fst_le, Affine.Simplex.sSameSide_point_incenter, NumberField.mixedEmbedding.fundamentalCone.intNorm_idealSetEquiv_apply, Real.instTietzeExtension, ProbabilityTheory.indepFun_iff_charFunDual_prod, le_iff_norm_sqrt_mul_sqrt_inv, Polynomial.Chebyshev.C_two_mul_real_cosh, LinearMap.IsPositive.re_inner_nonneg_left, ProbabilityTheory.Kernel.HasSubgaussianMGF.fun_zero, ProbabilityTheory.IsGaussian.exists_integrable_exp_sq, CauchySeq.norm_bddAbove, Real.Angle.cos_coe_pi, Real.volume_emetric_ball, continuous_iff_continuous_dist, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux, intervalIntegral.smul_integral_comp_add_mul, AnalyticAt.im_ofReal, Real.continuousOn_tan_Ioo, Real.abs_exp, ProbabilityTheory.integrable_stieltjesOfMeasurableRat, Homeomorph.unitBall_symm_apply, Complex.restrictScalars_toSpanSingleton', norm_add_sub_norm_sub_le_two_mul, circleMap_zero_zpow, Complex.re_ofReal_mul, CliffordAlgebraComplex.reverse_apply, Real.differentiableAt_negMulLog_iff, Complex.lim_eq_lim_im_add_lim_re, IsClosed.notMem_iff_infDist_pos, RCLike.zero_im, Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zero, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_mk', EuclideanGeometry.center_eq_inversion', norm_fst_le, MeasureTheory.Measure.integral_comp_inv_mul_right, MeasureTheory.BorelCantelli.process_difference_le, RCLike.ofReal_lt_ofReal, BoundedContinuousFunction.integrable_of_nnreal, unitary.continuousOn_argSelfAdjoint, AffineSubspace.isPreconnected_setOf_sSameSide, GromovHausdorff.HD_candidatesBDist_le, Complex.rectangle_eq_convexHull, Probability.cauchyPDFReal_def, NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply, Real.exists_cos_eq_zero, Matrix.permMatrix_l2_opNorm_eq, NNReal.rpow_left_bijective, NumberField.mixedEmbedding.convexBodySumFun_eq_zero_iff, NumberField.mixedEmbedding.fundamentalCone.closure_paramSet_ae_interior, RCLike.im_eq_zero, ENNReal.log_ofReal, norm_inner_div_norm_mul_norm_eq_one_iff, GroupSeminorm.mul_le', Real.deriv2_mul_log, LinearIsometryEquiv.coe_symm_toMeasurableEquiv, lipschitzWith_one_norm, unitary.spectrum_subset_slitPlane_iff_norm_lt_two, ProbabilityTheory.analyticOnNhd_iteratedDeriv_mgf, CFC.rpow_sqrt, inv_goldConj, SmoothBumpFunction.ball_inter_range_eq_ball_inter_target, MeasureTheory.SignedMeasure.rnDeriv_sub, MeasureTheory.Measure.addHaar_smul, Real.ofDigits_le_one, Quaternion.norm_star, Complex.reCLM_apply, AlgHom.norm_apply_le_self_mul_norm_one, PartitionOfUnity.mem_finsupport, Real.hasDerivAt_negMulLog, NNReal.coe_sInf, Real.arccos_injOn, Diffeology.dSmooth_iff_contDiff, Real.eulerMascheroniSeq'_one, ENNReal.lintegral_mul_le_Lp_mul_Lq_of_ne_zero_of_ne_top, Complex.closure_setOf_im_lt, NumberField.mixedEmbedding.lintegral_comp_polarSpaceCoord_symm, Orientation.abs_volumeForm_apply_le, Affine.Simplex.ExcenterExists.sSameSide_point_excenter_iff, MeasureTheory.exists_continuous_eLpNorm_sub_le_of_closed, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero, Real.instIsStrictOrderedRing, LinearMap.IsSymmetric.eigenvectorBasis_def, Complex.conjLIE_symm, Real.sinh_le_self_iff, BoundedContinuousFunction.exists_extension_norm_eq_of_isClosedEmbedding', intervalIntegral.mul_integral_comp_mul_left, Real.sin_sub_nat_mul_two_pi, UpperHalfPlane.petersson_slash, Real.map_volume_mul_left, PiTensorProduct.projectiveSeminormAux_add_le, one_add_norm_le_sqrt_two_mul_sqrt, unitInterval.instConnectedSpaceElemReal, ENNReal.toReal_sInf, Real.instIsOrderedCancelAddMonoid, expNegInvGlue.zero_iff_nonpos, Real.tendsto_logb_nat_add_one_sub_logb, Hyperreal.coeRingHom_toFun, fourierCoeff_fourier, Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_norm, BoxIntegral.Prepartition.lower_le_lower, Affine.Simplex.signedInfDist_incenter, ProbabilityTheory.Kernel.stronglyAdapted_densityProcess, Urysohns.CU.tendsto_approx_atTop, ODE.FunSpace.compProj_apply, PadicInt.norm_natCast_lt_one_iff, aemeasurable_derivWithin_Ioi, MeasureTheory.L1.norm_eq_integral_norm, schnirelmannDensity_nonneg, AkraBazziRecurrence.strictAntiOn_smoothingFn, MeasureTheory.Measure.addHaar_image_homothety, RCLike.ofReal_lt_zero, measurable_dist, MeasureTheory.setIntegral_const, IsCoveringMap.liftPath_trans, ContDiffBump.rOut_pos, IsUltrametricDist.norm_nsmul_le, norm_iteratedFDeriv_clm_apply_const, ProbabilityTheory.Kernel.tendsto_densityProcess_atTop_of_antitone, StieltjesFunction.right_continuous', isSimplyConnected_iff_exists_homotopy_refl_forall_mem, unitInterval.volume_Ioi, ModularGroup.coe_truncatedFundamentalDomain, Affine.Simplex.inner_vsub_vsub_altitudeFoot_eq_height_sq, AkraBazziRecurrence.asympBound_pos, UpperHalfPlane.continuous_re, Zsqrtd.toReal_injective bridge: MeasureTheory.SimpleFunc.hasBoxIntegral, MeasureTheory.SimpleFunc.box_integral_eq_integral

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