Real

📁 Source: MathlibTest/Real.lean

Statistics

Metric	Count
Definitions Real	1
Theorems	0
Total	1

(root)

Definitions

Name	Category	Theorems
Real 📖	CompData	17731 math, 4 bridge math: AddGroupNorm.add_apply, ContinuousMap.dense_setOf_contDiff, CircleDeg1Lift.mono, List.norm_prod_le, Real.cos_add_nat_mul_pi, cfc_realPart, ArithmeticFunction.vonMangoldt.residueClass_eq, Padic.eq_ratNorm, MeasureTheory.Measure.exists_innerRegular_eq_of_isCompact, Measurable.ereal_toReal, NumberField.FinitePlace.hasFiniteMulSupport_int, Unitary.openPartialHomeomorph_source, withSeminorms_iff_mem_nhds_isVonNBounded, SchwartzMap.norm_toLp_le_seminorm, range_cfcₙ_nnreal, IsUnit.cfcRpow, IsLocalMaxOn.fderivWithin_nonpos, MeasureTheory.IntegrableOn.continuousWithinAt_Ici_primitive_Ioi, MeasureTheory.tendstoInMeasure_iff_measureReal_norm, CircleDeg1Lift.units_inv_apply_apply, ENNReal.ofReal_rpow_of_pos, Orientation.rightAngleRotationAux₁_rightAngleRotationAux₁, Behrend.roth_lower_bound, MeasureTheory.MemLp.eLpNorm_indicator_le_of_meas, MeasureTheory.L1.setToL1_eq_setToL1', ValueDistribution.logCounting_zero, MeasureTheory.exists_pos_preimage_ball, CFC.rpow_inv_rpow, Complex.HadamardThreeLines.norm_le_interpStrip_of_mem_verticalClosedStrip_eps, TestFunction.lineDerivCLM_apply_of_le, EuclideanGeometry.Sphere.mul_dist_eq_abs_power, Polynomial.logMahlerMeasure_one, comap_dist_left_atTop_eq_cocompact, norm_eq_zero, Real.arctan_eq_arccos, CuspFormClass.qExpansion_isBigO, AddCircle.measure_univ, EuclideanGeometry.Sphere.vadd_mem_inter_orthRadius_iff_norm_sq, MeasureTheory.Measure.integral_comp_inv_smul, ProbabilityTheory.paretoPDFReal_pos, EReal.nhds_top_basis, Height.logHeight_eval_ge, ProbabilityTheory.lintegral_exponentialPDF_eq_one, SpectrumRestricts.le_nnreal_iff, MeasureTheory.exists_lt_lowerSemicontinuous_integral_gt_nnreal, HurwitzZeta.hasSum_int_hurwitzZetaOdd, InnerProductGeometry.cos_angle_add_of_inner_eq_zero, geometric_hahn_banach_open, Convex.norm_image_sub_le_of_norm_derivWithin_le, NNReal.summable_and_Lr_rpow_le_Lp_mul_Lq_tsum, Real.Angle.abs_toReal_neg_coe_eq_self_iff, Real.pi_div_four_le_arcsin, Metric.hausdorffDist_empty', ProbabilityTheory.Kernel.measurable_rnDerivAux, Continuous.logb, 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, Polynomial.Chebyshev.isExtrOn_T_real_iff, NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symm, Real.hasDerivAt_arccos, Real.hasDerivAt_fourier, PiLp.lipschitzWith_toLp, HurwitzZeta.isBigO_atTop_evenKernel_sub, AbsoluteValue.IsEquiv.isEmbedding_equivWithAbs, CStarAlgebra.preimage_inr_Icc_zero_one, Metric.hasBasis_cobounded_compl_closedBall, RCLike.map_from_real, RCLike.conj_re, Differentiable.arsinh, norm_sub_sq_real, ConvexOn.leftDeriv_le_rightDeriv_of_mem_interior, HasStrictFDerivAt.log, ArithmeticFunction.vonMangoldt.summable_residueClass_non_primes_div, LipschitzWith.max_const, HurwitzZeta.expZeta_zero, Real.range_sin, ProbabilityTheory.variance_eq_integral, MeasureTheory.tendsto_integral_thickenedIndicator_of_isClosed, TemperedDistribution.lineDerivOpCLM_eq, MeasureTheory.integral_eq_iff_of_ae_le, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', continuousSMul_sphere_ball, IsIntegralCurve.comp_mul, Function.Periodic.intervalIntegrable, CircleDeg1Lift.instOrderHomClassReal, BoundedContinuousFunction.tietze_extension_step, NumberField.mixedEmbedding.fundamentalDomain_integerLattice, Complex.log_conj_eq_ite, aux_hasSum_of_le_geometric, EuclideanGeometry.angle_le_pi_div_two_of_angle_eq_pi_div_two, Complex.verticalSegment_eq, Orientation.oangle_sign_smul_add_right, MeasureTheory.Lp.toTemperedDistributionCLM_apply, InformationTheory.integrable_klFun_rnDeriv_iff, Orientation.kahler_map_complex, RCLike.sqrt_eq_ite, UnitAddTorus.integral_preimage, Filter.Tendsto.logb, 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, hasSum_mellin_pi_mul_sq', MeasureTheory.Integrable.integral_norm_prod_right, MeasureTheory.setToFun_add_left, norm_smul_le, Real.smoothTransition.eq_one_iff_one_le, TendstoUniformly.im, Seminorm.isBounded_const, Real.le_log_one_add_of_nonneg, Real.abs_exp_sub_one_le, Affine.Simplex.altitudeFoot_restrict, MeasureTheory.L1.SimpleFunc.norm_Integral_le_one, isConformalMap_conj, PiLp.norm_toLp_const', LinearMap.mkContinuous₂_norm_le', MeasureTheory.eLpNorm'_norm, NNReal.orderIsoIccZeroCoe_apply_coe_coe, lp.norm_apply_le_norm, Real.continuousOn_rpowIntegrand₀₁_uncurry, NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingOfIsReal, norm_prod_le_of_le, HasDerivWithinAt.clog_real, inner_lt_one_iff_real_of_norm_eq_one, LinearEquiv.norm_extend_le, taylor_integral_remainder, Real.tan_pi_div_four, RCLike.im_le_neg_norm_iff_eq_neg_I_mul_norm, Real.ofDigits_const_last_eq_one, CFC.posPart_smul_of_nonpos, MeasureTheory.mulEquivHaarChar_smul_integral_map, RCLike.measurable_ofReal, EuclideanGeometry.dist_smul_vadd_sq, NumberField.HeightOneSpectrum.NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_natCast_le_one, SemiNormedGrp.explicitCokernelDesc_norm_le, Bundle.ContMDiffRiemannianMetric.isVonNBounded, ProbabilityTheory.tendsto_defaultRatCDF_atBot, SchwartzMap.lineDerivOpCLM_eq, NumberField.InfinitePlace.isNontrivial, Convex.isLittleO_pow_succ, Subgroup.isRegularAtInfty_iff, ProbabilityTheory.stieltjesOfMeasurableRat_ae_eq, Complex.norm_log_one_sub_inv_add_logTaylor_neg_le, 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, SchauderBasis.norm_proj_le_nnnormProjBound, NumberField.InfinitePlace.eq_iff_isEquiv, EuclideanGeometry.euclideanHausdorffMeasure_eq, uniqueDiffOn_Icc, dist_triangle, Real.isBigO_log_mul_const_log_atTop, Metric.cauchySeq_iff, ConformalAt.differentiableAt, IsCoveringMap.eq_liftHomotopy_iff', EuclideanGeometry.sin_oangle_right_mul_dist_of_oangle_eq_pi_div_two, AddGroupNorm.coe_le_coe, Orientation.oangle_ne_zero_and_ne_pi_iff_linearIndependent, Real.rpow_add_of_nonneg, ProbabilityTheory.integral_cauchyPDFReal_eq_one, Real.iteratedDerivWithin_cos_Ioo, MeasureTheory.SignedMeasure.toMeasureOfZeroLE_apply, 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, ContinuousOn.rpow, Height.logHeight₁_pow, Height.mulHeight_sym2_le, ProbabilityTheory.cdf_measure_stieltjesFunction, MeasureTheory.condExpInd_of_measurable, deriv_exp, WithLp.norm_fst_le, SpectrumRestricts.nnreal_of_nonneg, cfcₙL_integral, seminormFromConst_seq_antitone, Real.integrableOn_rpowIntegrand₀₁_Ioi, Complex.mul_im, unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, ContinuousWithinAt.rpow_const, Function.locallyFinsuppWithin.logCounting_single_eq_log_sub_const, MeasureTheory.Lp.mul_meas_ge_le_pow_enorm', PiLp.nndist_eq_sum, isNonneg_inner, AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound, ContinuousLinearMap.le_of_opNorm_le_of_le, ModularGroup.SLOnGLPos_smul_apply, map_mul_zero_of_map_zero, RCLike.pos_iff_exists_ofReal, MeasureTheory.llr_self, norm_lt_of_mem_ball', MeasureTheory.supermartingale_of_setIntegral_succ_le, PadicInt.coe_sub, RCLike.one_re, HasDerivAt.le_of_lipschitz, Complex.tendsto_log_nhdsWithin_im_neg_of_re_neg_of_im_zero, Real.sin_add_sin, Real.logb_zero_left, Bundle.ContMDiffRiemannianMetric.contMDiff, Complex.norm_circleTransformBoundingFunction_le, NNReal.summable_and_inner_le_Lp_mul_Lq_tsum, continuousOn_stereoToFun, Real.exists_floor, SmoothBumpCovering.toSmoothPartitionOfUnity_eq_mul_prod, ModularForm.smul_slash, MeasureTheory.llr_smul_inv_left_eq_smul_right, geom_le, lt_norm_sub_of_not_sameRay, completelyRegularSpace_iff_isOpen, MeasureTheory.lintegral_enorm_le_of_forall_fin_meas_integral_eq, Complex.re_mul_ofReal, ValueDistribution.characteristic_even, LiouvilleWith.nat_sub_iff, Height.mulHeight_mul_mulHeight, ContDiffBump.ae_convolution_tendsto_right_of_locallyIntegrable, Finset.Nonempty.norm_sum_le_sup'_norm, ContinuousAlternatingMap.opNorm_prod, MonotoneOn.intervalIntegral_slope_le, HasDerivAt.const_rpow, Complex.div_ofReal_re, Distribution.delta_apply, Real.expNear_succ, Real.Angle.sign_two_zsmul_eq_sign_iff, Real.goldenConj_mul_fib_succ_add_fib, summable_sigma_of_nonneg, ProbabilityTheory.condIndepFun_iff_condExp_inter_preimage_eq_mul, ProbabilityTheory.condCDF_ae_eq, gauge_lt_one_eq_self_of_isOpen, ProbabilityTheory.isGaussian_iff_gaussian_charFun, GroupSeminorm.apply_one, Function.locallyFinsuppWithin.logCounting_strictMono, CircleDeg1Lift.translationNumber_mul_of_commute, Function.Periodic.intervalIntegrable_iff, Real.Angle.neg_coe_abs_toReal_of_sign_nonpos, NNReal.rpow_sub_intCast, Real.iInf_Ioi_eq_iInf_rat_gt, StandardSubspace.toClosedSubmodule_injective, Real.differentiable_arctan, MeasureTheory.SimpleFunc.posPart_sub_negPart, ProbabilityTheory.gaussianReal_map_const_mul, ProperCone.innerDual_le_innerDual, EReal.coe_le_coe_iff, NNReal.toReal_lt, Real.map_exp_nhds, NormedCommGroup.tendsto_nhds_nhds, imaginaryPart_eq_zero_iff, Real.iInf_nonpos', Seminorm.mem_ball_zero, RCLike.map_apply, exists_contMDiffMap_zero_one_of_isClosed, Continuous.rexp, Real.arcosh_bijOn, QuotientAddGroup.exists_norm_mk_lt, InformationTheory.integral_llr_add_mul_log_nonneg, IsUltrametricDist.isNonarchimedean_invariantExtension, norm_torusIntegral_le_of_norm_le_const, CStarMatrix.norm_entry_le_norm, LinearMap.bound_of_shell, Real.Lr_le_Lp_mul_Lq_tsum_of_nonneg, Real.differentiableAt_mulExpNegMulSq, EuclideanGeometry.Cospherical.subtype_val_iff, NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace, EuclideanGeometry.Sphere.thales_theorem, Path.subpath_self, Collinear.wbtw_of_dist_eq_of_dist_le, EReal.image_coe_Icc, Real.sqrt_eq_iff_eq_sq, Real.sinh_eq, Asymptotics.IsBigO.of_norm_eventuallyLE, Set.extremePoints_Icc, Commute.realPart_imaginaryPart, Complex.restrictScalars_one_smulRight', MeasureTheory.eval_integral, MeasureTheory.aestronglyMeasurable_condExpInd, MeasureTheory.eLpNorm_condExp_le, BoundedContinuousMapClass.map_bounded, MeasureTheory.setIntegral_nonpos_ae, Seminorm.bound_of_shell, Real.one_le_cosh, Real.not_continuousAt_inv_log_neg_one, HasCompactSupport.convolution_integrand_bound_left, Besicovitch.SatelliteConfig.hlast', MeasureTheory.Measure.euclideanHausdorffMeasure_zero, Real.Angle.toReal_add_of_sign_eq_neg_sign, HasStrictFDerivAt.abs_of_pos, MeasureTheory.lintegral_rpow_enorm_lt_top_of_eLpNorm'_lt_top, Irreducible.natDegree_le_two, IsPathConnected.exists_path_through_family', Real.iInf_of_isEmpty, ProbabilityTheory.lintegral_condCDF, MeasureTheory.Martingale.smul, Real.isLittleO_logb_id_atTop, Mathlib.Meta.Positivity.log_pos_of_isNat, RCLike.geometric_hahn_banach_point_open, ENNReal.max_rpow, Complex.coe_realPart, Distribution.dsupport_delta, Real.toNNReal_lt_natCast', quasispectrum_imaginaryPart, Real.log_le_self, ContDiffBump.nonneg_normed, IsSelfAdjoint.quasispectrumRestricts, comap_gauge_nhds_zero_le, lp.norm_le_of_tsum_le, Real.sinh_log, ContDiffOn.cos, LinearMap.coe_toSeminorm, eventually_residual_irrational, NumberField.mixedEmbedding.logMap_one, EisensteinSeries.linear_inv_isBigO_left, MeasureTheory.integral_convexOn_of_integrand_ae, mellin_eq_fourier, Real.sSup_smul_of_nonpos, IsLocalMaxOn.norm_add_self, Real.HolderTriple.inv_add_inv_eq_inv, ENNReal.toReal_min, Affine.Triangle.oangle_excenter_singleton_eq_add_pi, SchwartzMap.instLineDerivLeftSMulReal, Real.hasMeasurablePow, MonotoneOn.ae_differentiableWithinAt_of_mem, lp.isLUB_norm, BumpCovering.eventuallyEq_one, HasDerivWithinAt.liminf_right_slope_norm_le, bernsteinApproximation.apply_zero, 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, Real.sin_le_sin_of_le_of_le_pi_div_two, Real.isGLB_of_tendsto_antitone_bddBelow, taylorWithin_succ, Asymptotics.IsBigO.rpow_rpow_nhdsGE_zero_of_le, Complex.isTheta_exp_arg_mul_im, 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, GaussianFourier.integrable_cexp_neg_mul_sq_add_real_mul_I, ProbabilityTheory.gammaPDF_of_nonneg, ProbabilityTheory.condDistrib_ae_eq_condExp, deriv_arctan, 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', MeasureTheory.Integrable.comp_mul_left', DiffContOnCl.circleAverage_poissonKernel_smul', Real.hasFDerivAt_fourierChar_neg_bilinear_left, ModularGroup.exists_bound_of_invariant, Real.tan_pi_sub, isApproximateAddSubgroup_zero, instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, Real.differentiableAt_arcsin, geometric_hahn_banach_point_point, tendsto_smoothingFun_of_ne_zero, ProbabilityTheory.gaussian_charFun_congr, NumberField.mixedEmbedding.fundamentalCone.interior_paramSet, segment_subset_closedBall_right, isConnected_compl_of_one_lt_codim, real_inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mul, Complex.linearEquiv_det_conjLIE, NumberField.mixedEmbedding.measurable_polarCoordReal_symm, NormedRing.inverse_one_sub_norm, NumberField.mixedEmbedding.fundamentalCone.preimageOfMemIntegerSet_mixedEmbedding, Real.arcsin_eq_pi_div_two_sub_arccos, MeasureTheory.condExpInd_ae_eq_condExpIndSMul, Real.range_log, Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, DifferentiableWithinAt.log, ConvexOn.map_condExp_le_univ, Real.instIsOrderedRing, Complex.normSq_pos, MeasureTheory.levyProkhorovDist_triangle, Function.hasTemperateGrowth_inner_right, ConvexOn.le_slope_of_hasDerivAt, Real.logb_le_iff_le_rpow, intervalIntegral.continuousOn_primitive_interval, Isometry.preimage_perpBisector, norm_zsmul, AntitoneOn.concaveOn_of_deriv, ProbabilityTheory.condCDF_nonneg, RCLike.reCLM_apply, ContinuousLinearMap.opNorm_le_of_unit_norm, HasStrictDerivAt.rpow, 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, StrictConvexOn.slope_lt_leftDeriv, 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, InnerProductSpace.volume_closedBall_of_dim_even, Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_face, MeasureTheory.L1.setToL1_indicatorConstLp, RCLike.div_re_ofReal, SimpleGraph.turanDensity_eq_csInf, MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left, cfc_im_id, Continuous.log, ProbabilityTheory.mgf_anti_of_nonpos, Affine.Simplex.smul_mongePoint_vsub_circumcenter_eq_sum_vsub, CStarAlgebra.mem_Icc_algebraMap_iff_norm_le, ContDiffOn.rpow_const_of_le, IsPicardLindelof.of_contDiffAt_one, ENNReal.rpow_lt_top_iff_of_pos, dist_midpoint_right, Real.sqrt_eq_cases, AddDissociated.randomisation, Complex.reProdIm_nonempty, Real.fourierCoeff_tsum_comp_add, ProbabilityTheory.measure_ge_le_exp_cgf, TsirelsonInequality.sqrt_two_inv_mul_self, CFC.abs_eq_cfc_norm, ZLattice.summable_norm_sub_inv_pow, ConvexOn.continuousOn_tfae, Orientation.inner_rotation_pi_div_two_right_smul, intervalIntegral.intervalIntegrable_one_div_one_add_sq, Complex.lim_conj, Real.contDiffOn_log, tendsto_tsum_div_pow_atTop_integral, RCLike.separate_convex_open_set, Orientation.oangle_add_left_smul_rotation_pi_div_two, ContinuousLinearMap.exists_preimage_norm_le, GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I, Convex.norm_image_sub_le_of_norm_fderivWithin_le', CFC.monotoneOn_one_sub_one_add_inv, ConcaveOn.locallyLipschitz, ProbabilityTheory.tendsto_defaultRatCDF_atTop, Real.fourierIntegral_comp_linearIsometry, ProbabilityTheory.IsCondKernelCDF.toKernel_Iic, Real.fderiv_fourierIntegral, Path.continuousMapClass, ODE.FunSpace.next_apply, ProbabilityTheory.measure_sum_ge_le_of_HasCondSubgaussianMGF, Metric.isBounded_iff_subset_ball, ProbabilityTheory.stronglyMeasurable_cauchyPDFReal, Affine.Simplex.sSameSide_excenter_singleton_point, ProbabilityTheory.IsMeasurableRatCDF.iInf_rat_gt_eq, MeasureTheory.integral_smul_nnreal_measure, MeasureTheory.contDiff_charFun', MeasureTheory.taylor_charFun_two, MeasureTheory.condExp_bilin_of_stronglyMeasurable_left, ExistsContDiffBumpBase.u_support, CFC.sqrt_eq_one_iff', CFC.posPart_one, Real.smul_map_volume_mul_right, ConvexOn.rightDeriv_le_slope_of_mem_interior, NumberField.mixedEmbedding.norm_eq_sup'_normAtPlace, Real.logb_neg_of_base_lt_one, gauge_le_one_of_mem, ContinuousMap.abs_mem_subalgebra_closure, Seminorm.le_finset_sup_apply, SzemerediRegularity.energy_increment, squeeze_zero, unitInterval.volume_Ioo, AddGroupNorm.ext_iff, Affine.Simplex.neg_mul_lt_inner_vsub_altitudeFoot, unitInterval.volume_Iic, EuclideanGeometry.Sphere.isExtTangent_iff_dist_center, norm_eq_iInf_iff_real_inner_le_zero, GroupSeminorm.coe_sup, Real.Gamma_pos_of_pos, ContinuousMap.HomotopyWith.coe_toContinuousMap, hasDerivAt_sqrt_mul_log, NumberField.Units.logEmbedding_fundSystem, EuclideanGeometry.sin_oangle_right_of_oangle_eq_pi_div_two, 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, StrongDual.norm_extendRCLike, Polynomial.isNonarchimedean_gaussNorm, Affine.Triangle.oangle_incenter_eq, ConvexOn.differentiableWithinAt_Iio_of_mem_interior, HurwitzZeta.hasSum_int_cosKernel₀, Complex.isOpenMap_im, IsometryEquiv.toRealLinearIsometryEquiv_symm_apply, Real.cos_add_pi, nnnorm_cfcₙ_nnreal_le_iff, 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, Real.mk_le_of_forall_le, realPart_idem, NumberField.mixedEmbedding.convexBodyLT'_mem, ProbabilityTheory.aemeasurable_exp_mul, Real.arctan_eq_arcsin, HurwitzZeta.hasSum_int_hurwitzZetaEven, BoxIntegral.Box.splitLower_def, Complex.norm_sub_one_sq_eq_of_norm_eq_one, ContinuousLinearMap.opNorm_bound_of_ball_bound, Complex.ofRealCLM_coe, ContractingWith.dist_fixedPoint_le, Complex.kahler, Complex.norm_polarCoord_symm, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left, spectrum.norm_le_norm_of_mem, MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv, 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, Real.rpow_lt_one_iff_of_pos, ContinuousLinearMap.sSup_unit_ball_eq_norm, SchwartzMap.inner_fourier_toL2_eq, Real.arsinh_surjective, Convex.convex_isRCLikeNormedField, 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, rank_le_card_isVisible, unitInterval.volume_def, CliffordAlgebraComplex.ofComplex_conj, unitInterval.sigmoid_lt, finrank_real_complex_fact', ProbabilityTheory.covariance_neg_left, ProbabilityTheory.betaPDF_eq, Real.tsum_eq_tsum_fourier, intervalIntegral.derivWithin_integral_of_tendsto_ae_left, ContinuousMap.dist_lt_iff, Metric.exists_continuous_real_forall_closedEBall_subset, Real.tan_nonpos_of_nonpos_of_neg_pi_div_two_le, Complex.instIsComplete, Metric.hausdorffDist_le_of_mem_dist, ClosedSubmodule.mem_iff, 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, taylorWithinEval_hasDerivAt_Ioo, HurwitzZeta.LSeriesHasSum_cos, UnitAddCircle.lintegral_preimage, seminormFromBounded_ker, Real.analyticOn_cos, ContDiffMapSupportedIn.seminorm_monoLM_eq, MeasureTheory.integral_image_eq_integral_abs_det_fderiv_smul, ProbabilityTheory.lintegral_toKernel_univ, NonarchAddGroupSeminorm.coe_iSup_apply, EuclideanGeometry.Sphere.isDiameter_iff_right_mem_and_midpoint_eq_center, Complex.HadamardThreeLines.norm_le_sSupNormIm, ProbabilityTheory.analyticOn_mgf, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, Complex.ofReal_eq_one, eqOn_of_isMIntegralCurveOn_Ioo, Metric.unitSphere.coe_one, Real.rpow_add_natCast', IsCoveringMap.liftPath_apply_one_eq_of_homotopicRel, summable_riemannZetaSummand, Asymptotics.IsBigOWith.abs_right, complexOfReal_hasDerivWithinAt, 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, MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul_of_measurable_of_sigmaFinite, Real.sqrt_one_add_le, Mathlib.Tactic.Rify.ratCast_le, ContinuousMap.Homotopy.extend_apply_of_one_le, Matrix.IsHermitian.det_abs, volume_iUnion_setOf_liouvilleWith, Real.tan_inv_eq_cot, Real.ringHom_apply, ContinuousMultilinearMap.le_mul_prod_of_opNorm_le_of_le, MeasureTheory.exists_notMem_null_le_integral, Real.contDiffAt_arcosh, IsLocalMin.hasDerivAt_eq_zero, RCLike.ofRealLI_apply, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, Polynomial.norm_leadingCoeff_eq_one_of_mahlerMeasure_eq_one, SlashInvariantForm.slash_action_eq', Complex.comap_exp_cobounded, Metric.continuousWithinAt_iff', RightDerivMeasurableAux.measurableSet_B, Metric.diam_mono, GroupNorm.toGroupSeminorm_eq_coe, HasCompactSupport.integral_Ioi_deriv_eq, Asymptotics.IsLittleO.of_abs_left, PadicInt.coe_zero, exists_hasDerivAt_eq_zero, ModularForm.mul_slash, Real.sin_add_two_pi, Height.mulHeight₁_eq, ProbabilityTheory.gaussianReal_const_mul, OpenPartialHomeomorph.contDiff_unitBallBall_symm, Padic.norm_intCast_eq_one_iff, Real.strictMonoOn_sqrt, intervalIntegrable_iff', ProbabilityTheory.condIndep_iff, deriv_abs, EuclideanSpace.closedBall_zero_eq, integral_sin_mul_cos₂, Asymptotics.isLittleO_const_left, EuclideanGeometry.dist_inversion_inversion, curveIntegrable_segment, ZMod.LFunction_stdAddChar_eq_expZeta, Padic.eq_padicNorm, strictMono_of_hasDerivAt_pos, 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, intervalIntegral.tsum_intervalIntegral_eq_of_summable_norm, NumberField.FinitePlace.mk_apply, Complex.norm_le_abs_re_add_abs_im, MeasureTheory.Submartingale.sum_mul_sub', Sbtw.angle₁₃₂_eq_zero, 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, Real.nnnorm_deriv_mulExpNegMulSq_le_one, 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, norm_jacobiTheta₂_term_le, Real.deriv_binEntropy, MeasureTheory.upcrossingStrat_nonneg, CFC.monotone_nnrpow, AffineSubspace.mem_perpBisector_iff_inner_eq_zero', lebesgue_number_lemma_of_metric_sUnion, ProbabilityTheory.variance_fun_sum', RightDerivMeasurableAux.norm_sub_le_of_mem_A, intervalIntegral.integral_derivWithin_uIcc_of_contDiffOn_uIcc, ProbabilityTheory.mgf_const_add, RingSeminorm.seminorm_one_eq_one_iff_ne_zero, LiouvilleWith.rat_sub_iff, HasDerivWithinAt.liminf_right_slope_le, Metric.closedBall_eq_bInter_ball, Complex.integral_boundary_rect_eq_zero_of_differentiableOn, has_pointwise_sum_fourier_series_of_summable, RCLike.re_add_im, CFC.posPart_natCast, MeasureTheory.toReal_rnDeriv_trim, 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, Complex.norm_sub_mem_Icc_angle, UpperHalfPlane.instContinuousSMulGL2R, tendsto_div_of_monotone_of_tendsto_div_floor_pow, 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, conformalAt_iff, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, DifferentiableOn.sqrt, Complex.GammaIntegral_eq_mellin, ProbabilityTheory.variance_fun_id_gaussianReal, Real.rpow_eq_nhds_of_neg, Complex.isTheta_cpow_rpow, NNReal.coe_indicator, Polynomial.mahlerMeasure_eq_leadingCoeff_mul_prod_roots, Metric.hasAntitoneBasis_cobounded_compl_ball, intervalIntegral.integral_hasDerivWithinAt_right, IsSelfAdjoint.norm_mul_self, isLittleO_exp_neg_mul_sq_cocompact, BoundedContinuousFunction.integral_eq_integral_nnrealPart_sub, ProbabilityTheory.hasGaussianLaw_iff_charFunDual_map_eq, Real.iInf_nonneg, Real.young_inequality, norm_jacobiTheta₂_term_fderiv_ge, unitInterval.zero_mem, AntilipschitzWith.hausdorffMeasure_preimage_le, 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, Real.le_log_of_zpow_le, ContinuousLinearMap.norm_inl_le_one, CFC.tendsto_cfc_rpow_sub_one_log, MeasureTheory.lpNorm_fun_div_natCast, Real.one_le_rpow_of_pos_of_le_one_of_nonpos, MeasureTheory.norm_condExpL2_le, IsLocalMaxOn.hasFDerivWithinAt_nonpos, contDiffAt_norm_smul_iff, IsIntegralCurve.comp_add, AkraBazziRecurrence.T_gt_zero', integrableOn_exp_mul_Iic, dist_convexComboPair_convexComboPair_le, ProbabilityTheory.IsGaussian.integrable_dual, Real.dist_mulExpNegMulSq_le_two_mul_sqrt, HurwitzZeta.cosZeta_two_mul_nat', ExistsContDiffBumpBase.y_eq_one_of_mem_closedBall, Real.rpowIntegrand₀₁_monotoneOn, 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', PadicInt.val_mkUnits, Real.log_div_le_sum_range_add, norm_iteratedFDerivWithin_smul_le, ContinuousLinearMap.opNorm_le_bound', ProbabilityTheory.Kernel.density_fst_univ, AnalyticOn.im_ofReal, Asymptotics.IsLittleO.sum_congr', BumpCovering.toPartitionOfUnity_apply, ENNReal.rpow_mul, Complex.norm_nonneg, ContDiffMapSupportedIn.iteratedFDerivLM_apply, Real.tan_int_mul_pi, Real.real_sqrt_le_nat_sqrt_succ, Affine.Triangle.altitude_replace_orthocenter_eq_affineSpan, IsLprojection.Lnorm, Real.sSup_empty, AbsolutelyContinuousOnInterval.ae_differentiableAt, Complex.real_smul, MeasureTheory.weightedSMul_apply, ContinuousMultilinearMap.norm_map_snoc_le, AbsolutelyContinuousOnInterval.integral_deriv_eq_sub, NumberField.InfinitePlace.le_iff_le, ProbabilityTheory.HasSubgaussianMGF.integrable_exp_mul, ENNReal.rpow_lt_rpow_iff, ContinuousLinearMap.comp_condExp_comm, not_differentiableWithinAt_of_deriv_tendsto_atTop_Ioi, MeasureTheory.probReal_compl_eq_one_sub₀, Complex.real_algHom_eq_id_or_conj, Padic.withValUniformEquiv_norm_le_one_iff, ContDiff.sigmoid, SmoothBumpFunction.rOut_pos, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, Real.analyticOnNhd_sin, Commute.cfcₙ_nnreal, NumberField.norm_norm_le_norm_mul_house_pow, inseparable_one_iff_norm, Valued.toNormedField.norm_le_one_iff, Real.rpow_le_self_of_one_le, ProbabilityTheory.setLIntegral_preCDF_fst, Orthonormal.norm_eq_one, countingFunction_finsum_eq_finsum_add, Polynomial.card_rootSet_le_derivative, HasDerivWithinAt.cosh, 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, Wbtw.dist_add_dist, Real.neg_pi_div_two_eq_arcsin, Metric.mem_cocompact_iff_closedBall_compl_subset, Real.log2_le_logb, intervalIntegrable_iff, NormedCommGroup.cauchySeq_iff, ProbabilityTheory.covariance_add_left, Polynomial.Chebyshev.integral_measureT_eq_integral_cos, Real.sign_one, geometric_hahn_banach_open_point, dist_smul_le, norm_natCast_eq_mul_norm_one, Orientation.linearEquiv_det_rotation, MeasureTheory.measureReal_symmDiff_le, ModularGroup.coe_fd, Real.mapsTo_cos, ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, EuclideanGeometry.Sphere.wbtw_secondInter, 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, hasDerivWithinAt_taylorWithinEval, ContinuousWithinAt.arcsin, Real.sinh_nonneg_iff, Complex.reProdIm_subset_iff', MeasureTheory.llr_smul_nnreal_same, Function.HasTemperateGrowth.fun_pow, Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_faceOpposite, SeminormedGroup.disjoint_nhds, Real.mapsTo_cos_Ioo, Real.toNNReal_mul, Complex.equivRealProdAddHom_symm_apply, Matrix.l2_opNorm_mulVec, MeasureTheory.fst_integral_withLp, Cardinal.mk_Iio_real, frontier_halfSpace, MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAt, range_circleMap, Real.sin_periodic, NumberField.mixedEmbedding.convexBodySumFun_add_le, Metric.infDist_le_dist_of_mem, Real.binEntropy_continuous, Real.log_sqrt, EuclideanGeometry.Cospherical.affineIndependent_of_mem_of_ne, Real.strictAntiOn_logb, Metric.PiNatEmbed.continuous_distDenseSeq_inv, ValueDistribution.characteristic_mul_top_le, Complex.continuousWithinAt_arg_of_re_neg_of_im_zero, 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, Asymptotics.IsBigO.mul_atTop_rpow_natCast_of_isBigO_rpow, PeriodPair.basis_one, Real.monotone_rpow_of_base_ge_one, ENNReal.rpow_intCast_mul, ProbabilityTheory.gaussianReal_map_neg, MeasureTheory.L1.norm_setToL1_le, Path.extend_extends, StrictConvexOn.deriv_lt_slope, MeasureTheory.Measure.eventually_nonempty_inter_smul_of_density_one, norm_pos_iff, NonarchAddGroupSeminormClass.toNonarchimedeanHomClass, Real.lt_sin, hasFDerivAt_integral_of_dominated_loc_of_lip_interval, AddSubgroup.norm_normedMk_le, isBounded_iff_forall_norm_le', Real.Angle.cos_zero, intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_right, Submodule.re_inner_starProjection_eq_normSq, RCLike.conjCLE_norm, ContinuousLinearMap.iSup_rayleigh_eq_iSup_rayleigh_sphere, 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, Asymptotics.IsBigO.abs_left, OnePoint.isBoundedAt_iff_exists_SL2Z, Complex.locally_lipschitz_exp, HasDerivWithinAt.complexToReal_fderiv', CStarAlgebra.inr_mem_Icc_iff_norm_le, Affine.Simplex.affineSpan_pair_altitudeFoot_eq_altitude, Asymptotics.IsLittleO.rpow, Orientation.kahler_comp_rightAngleRotation', dist_sq_lineMap_lineMap_of_inner_eq_zero, integral_const_on_unit_interval, InformationTheory.mul_log_le_klDiv, circleIntegral_def_Icc, Differentiable.cosh, integral_exp_mul_Iic, MeasureTheory.submartingale_iff_expected_stoppedValue_mono, 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, QuadraticForm.posDef_toMatrix', exists_monotone_Icc_subset_open_cover_Icc, setIntegral_withDensity_eq_setIntegral_smul₀, WithSeminorms.toLocallyConvexSpace, Nat.isUniformEmbedding_coe_real, Affine.Simplex.excenter_singleton_mem_affineSpan_range, NumberField.isInfinitePlace_iff, ODE.FunSpace.dist_comp_iterate_next_le, ProbabilityTheory.hasSum_integral_poissonMeasure, ContDiffBump.integrable, CircleDeg1Lift.commute_nat_add, SchwartzMap.seminorm_le_bound, EuclideanGeometry.law_sin, Orientation.sin_oangle_sub_right_mul_norm_of_oangle_eq_pi_div_two, Real.arctan_nonneg, ENNReal.zero_rpow_of_pos, MeasureTheory.StronglyMeasurable.tendsto_approxBounded_ae, isIntegralCurveOn_comp_add, intervalIntegral.intervalIntegral_eq_integral_uIoc, not_bounded_iff_exists_ne_zero_mem_asymptoticCone, parallelogram_law_with_norm_mul, ENNReal.rpow_left_injective, Polynomial.exists_partition_polynomial, 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, ProbabilityTheory.tendsto_choose_mul_pow_of_tendsto_mul_atTop, QuotientGroup.norm_mk_eq_zero, ENNReal.lintegral_mul_prod_norm_pow_le, ProbabilityTheory.gammaPDFReal_nonneg, Real.pow_le_of_le_log, ContDiffBump.support_normed_eq, circleIntegrable_iff, LinearMap.polar_eq_iInter, ProbabilityTheory.covarianceBilinDual_apply, Real.posLog_norm_add_le, ProbabilityTheory.isProbabilityMeasure_paretoMeasure, Complex.one_le_normSq_iff, 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, InnerProductGeometry.angle_sub_eq_arccos_of_inner_eq_zero, Real.strictConcaveOn_rpow, Real.iInf_of_not_bddBelow, 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, hensels_lemma, MeasureTheory.AEStronglyMeasurable.memLp_truncation, NormedCommGroup.nhds_one_basis_norm_lt, Real.instStarOrderedRing, Real.le_mk_of_forall_le, Metric.cthickening_cthickening_subset, MeasureTheory.integral_fintype_prod_volume_eq_pow, LiouvilleWith.sub_nat, Real.fderiv_fourierChar_neg_bilinear_right_apply, UpperHalfPlane.analyticAt_smul, LiouvilleWith.int_sub, ProbabilityTheory.isGaussian_multivariateGaussian, 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, Real.fourier_continuousLinearMap_apply, MeasureTheory.iteratedDeriv_charFun_zero, ConvexOn.map_set_average_le, intervalIntegral.integral_deriv_of_contDiffOn_uIcc, Nat.dist_cast_real, LiouvilleWith.rat_add_iff, NNReal.rpow_lt_one, Unitization.real_cfcₙ_eq_cfc_inr, PMF.bernoulli_expectation, LocallyIntegrable.ae_hasDerivAt_integral, norm_iteratedFDeriv_comp_le', real_inner_smul_self_left, ProbabilityTheory.IndepFun.charFunDual_map_fun_add_eq_mul, norm_iteratedFDeriv_mul_le, Real.toNNReal_le_toNNReal_iff', intervalIntegral.fderiv_integral_of_tendsto_ae, Units.val_cfcRpow, flip_innerSL_real, ContDiffBumpBase.smooth, Real.rpow_pos_of_pos, norm_cfc_lt_iff, LipschitzWith.memLp_lineDeriv, Orientation.volumeForm_robust_neg, Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq, Real.iSup_nonneg', EReal.image_coe_Ioc, NormedSpace.isBounded_iff_subset_smul_ball, Irrational.ratCast_mul, dist_triangle4_right, AnalyticOnNhd.re_ofReal, NumberField.mixedEmbedding.normAtAllPlaces_apply, HolderWith.of_le, Real.analyticOn_cosh, WeakFEPair.hf_modif_int, Quaternion.continuous_imI, Metric.hausdorffDist_triangle, intervalIntegrable_bernoulliFun, SmoothPartitionOfUnity.contMDiffAt_finsum, RCLike.norm_I_of_ne_zero, smoothingFun_of_powMul, CircleDeg1Lift.iterate_eq_of_map_eq_add_int, LinearMap.IsSymmetric.im_inner_self_apply, Chebyshev.abs_psi_sub_theta_le_sqrt_mul_log, UpperHalfPlane.instSMulInvariantMeasureGeneralLinearGroupFinOfNatNatRealVolume, EuclideanGeometry.dist_div_tan_oangle_right_of_oangle_eq_pi_div_two, imaginaryPart_I_smul, Real.exp_mul, Real.inv_rpow, Disjoint.exists_cthickenings, UpperHalfPlane.deriv_smul, ContinuousLinearMap.norm_compLp_le, ConvexOn.uniformConvexOn_zero, Asymptotics.IsBigOWith.pow, PseudoMetricSpace.dist_self, Real.one_add_mul_le_cos, measurable_norm, Affine.Simplex.dist_point_faceOppositeCentroid, Quaternion.coeComplex_mul, Real.geom_goldenRatio_isSol_fibRec, differentiableWithinAt_abs_pos, Polynomial.Chebyshev.zero_lt_prod_node_sub_node, ContDiffBump.eventuallyEq_one, Stirling.log_stirlingSeq_sub_log_stirlingSeq_succ, ContDiffMapSupportedIn.structureMapCLM_apply, RCLike.sub_conj, MeasureTheory.Integrable.continuous_primitive, StrictConcaveOn.lt_slope_of_hasDerivAt, Complex.uniformlyContinuous_im, lp.norm_eq_zero_iff, RCLike.re_sqrt_ofReal, Real.logb_le_logb_of_base_lt_one, 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, Module.Dual.extendRCLikeₗ_symm_apply, ProbabilityTheory.tendsto_condCDF_atBot, MeasureTheory.condExpL2_ae_eq_zero_of_ae_eq_zero, ProbabilityTheory.integrable_preCDF, EuclideanGeometry.Sphere.inter_orthRadius_eq_of_dist_le_radius, nnnorm_norm', LipschitzWith.ae_lineDeriv_sum_eq, NumberField.mixedEmbedding.norm_eq_zero_iff', SchwartzMap.lineDerivOp_fourier_eq, Polynomial.logMahlerMeasure_C_mul, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, ProbabilityTheory.mgf_neg, SeparationQuotient.norm_liftNormedAddGroupHom_apply_le, intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right, ValueDistribution.logCounting_zero_mul_le, Orientation.areaForm_le, ProbabilityTheory.Fernique.lt_normThreshold_zero, Complex.norm_eq_zero_iff, Asymptotics.IsBigO.of_norm_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, IsCusp.smul_of_mem, IntervalIntegrable.comp_sub_right_iff, ENNReal.toReal_mono', schnirelmannDensity_le_one, PadicInt.norm_intCast_lt_one_iff, DifferentiableWithinAt.norm, 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, LipschitzWith.norm_inv_mul_le_of_le, Metric.Snowflaking.preimage_ofSnowflaking_closedBall, MeasureTheory.smul_le_stoppedValue_hittingBtwn, CircleDeg1Lift.iterate_pos_lt_iff, Rat.AbsoluteValue.exists_minimal_nat_zero_lt_and_lt_one, Metric.equicontinuousAt_iff_pair, MeasureTheory.Integrable.neg_part, RCLike.norm_expect_le, ContinuousAt.log, MeasureTheory.integral_mul_norm_le_Lp_mul_Lq, ProbabilityTheory.rnDeriv_gaussianReal, ProbabilityTheory.condVar_const, tendsto_rpow_mul_exp_neg_mul_atTop_nhds_zero, EisensteinSeries.summand_bound_of_mem_verticalStrip, EuclideanGeometry.Sphere.IsExtTangent.dist_center, Real.Ioo_eq_ball, Complex.measurable_arg, MeasureTheory.norm_setToFun_le_mul_norm', SmoothPartitionOfUnity.locallyFinite, InnerProductGeometry.sin_angle, seminormFromConst_seq_one, MeasureTheory.lpNorm_nonneg, Real.le_pow_iff_log_le, ContinuousLinearEquiv.subsingleton_or_norm_symm_pos, MeasureTheory.ae_eq_zero_restrict_of_forall_setIntegral_eq_zero_real, ProbabilityTheory.covarianceBilin_multivariateGaussian, ProbabilityTheory.aemeasurable_of_mem_interior_integrableExpSet, DifferentiableWithinAt.sqrt, Topology.RelCWComplex.continuousOn_symm, Real.Angle.sin_eq_zero_iff, deriv.lhopital_zero_atBot_on_Iio, ProbabilityTheory.Kernel.densityProcess_le_one, Metric.nhds_basis_closedBall_pow, 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, Real.lt_rpow_inv_iff_of_pos, MeasureTheory.mem_L1_toReal_of_lintegral_ne_top, Asymptotics.isLittleO_abs_abs, LinearMap.singularValues_zero, indicator_indepFun_pi_of_prod_bcf, 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, UpperHalfPlane.tendsto_smul_atImInfty, Metric.eventually_prod_nhds_iff, AkraBazziRecurrence.isLittleO_deriv_one_add_smoothingFn, ENNReal.toReal_add, NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm_apply_fst, Real.mul_log_nonneg, GaussianFourier.integral_cexp_neg_mul_sq_norm, tendsto_integral_peak_smul_of_integrable_of_tendsto, ENNReal.rpow_add_le_add_rpow, RCLike.geometric_hahn_banach_of_nonempty_interior_point, ContinuousMap.Homotopy.curveIntegral_add_curveIntegral_eq_of_hasFDerivWithinAt, unitInterval.toNNReal_continuous, EReal.coe_coe_eq_natCast, Metric.tendsto_atTop, RCLike.map_same_eq_id, MeasureTheory.Integrable.measure_norm_ge_lt_top, 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, ExistsContDiffBumpBase.y_eq_zero_of_notMem_ball, ContinuousWithinAt.arccos, closure_one_eq, unitInterval.measurePreserving_coe, intervalIntegrable_iff_integrableOn_Icc_of_le, Real.continuous_rpow_const, DiffeologicalSpace.CorePlotsOn.isOpen_iff_preimages_plots, expNegInvGlue.not_analyticAt_zero, MeasureTheory.Integrable.hasSum_intervalIntegral, dist_left_midpoint, Seminorm.bddAbove_range_iff, AffineSubspace.left_mem_perpBisector, Complex.continuousOn_arg, Valuation.norm_add_le, Real.tendsto_toNNReal_atTop_iff, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, Real.summable_log_one_add_of_summable, Complex.lipschitz_equivRealProd, Function.Periodic.norm_qParam_le_of_one_half_le_im, Real.sqrt_div_self, NormedSpace.image_isVonNBounded_iff, EuclideanGeometry.preimage_inversion_perpBisector_inversion, BoundedContinuousFunction.dist_le, Asymptotics.isBigOWith_norm_right, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, AkraBazziRecurrence.differentiableAt_one_add_smoothingFn, Real.tsum_eq_tsum_fourierIntegral_of_rpow_decay_of_summable, EuclideanSpace.norm_sq_eq, Affine.Triangle.sSameSide_affineSpan_pair_point_incenter, UpperHalfPlane.dist_le_iff_dist_coe_center_le, Real.le_tan, 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, StrictConcaveOn.slope_lt_rightDeriv, TemperedDistribution.fourierMultiplierCLM_smul, FormalMultilinearSeries.norm_le_div_pow_of_pos_of_lt_radius, UpperHalfPlane.subset_verticalStrip_of_isCompact, AkraBazziRecurrence.tendsto_atTop_sumCoeffsExp, Height.logHeight_sym2_le, 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, ProbabilityTheory.integral_id_stdGaussian, Orientation.volumeForm_neg_orientation, BoxIntegral.Box.isBounded, ValueDistribution.proximity_zero_mul_le, QuasispectrumRestricts.nnreal_iff, HomotopyGroup.symmAt_indep, UpperHalfPlane.im_pos, ProbabilityTheory.sum_prob_mem_Ioc_le, hasSum_one_div_nat_pow_mul_fourier, Real.continuous_mul_log, NumberField.mixedEmbedding.norm_unit_smul, ProbabilityTheory.iIndepFun.mgf_sum₀, Real.log_prod, Complex.arg_of_re_nonneg, norm_iteratedFDerivWithin_comp_le_aux, Complex.nndist_self_conj, Real.sin_arctan_nonneg, Real.log_abs, AddCircle.toCircle_add, intervalIntegral.integral_deriv_smul_comp', IsUltrametricDist.norm_intCast_le_one, CFC.nnnorm_sqrt, Complex.betaIntegral_scaled, BoxIntegral.unitPartition.box_upper, NumberField.HeightOneSpectrum.NumberField.RingOfIntegers.HeightOneSpectrum.isNonarchimedean_adicAbv, norm_abs_sub_abs, ContinuousMap.dist_le_two_norm, NumberField.mixedEmbedding.norm_eq_norm, covByVAdd_zero, Set.instTietzeExtensionUnitBall, UpperHalfPlane.isOpenMap_norm, IsometryEquiv.toRealLinearIsometryEquiv_apply, MeasureTheory.pdf.integral_mul_eq_integral, MeasureTheory.condExpIndL1Fin_smul, Asymptotics.IsBigO.of_abs_abs, ContDiffOn.cosh, MeasureTheory.measureReal_le_measureReal_union_left, NormedAddGroupHom.NormNoninc.normNoninc_iff_norm_le_one, AbsolutelyContinuousOnInterval.add, Tactic.ComputeAsymptotics.Seq.dist_cons_nil, GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace, ContDiffBump.integrable_normed, ContinuousMap.norm_le, MeasureTheory.integrableOn_Ioi_deriv_of_nonneg, NormedAddGroupHom.norm_id_le, NNReal.canLift, Metric.exists_forall_closedEBall_subset_aux₂, Real.Gamma_nonneg_of_nonneg, intervalIntegral.sub_le_integral_of_hasDeriv_right_of_le, NumberField.mixedEmbedding.norm_le_convexBodySumFun, Filter.Tendsto.arccos_nhdsGE, SlashInvariantForm.quotientFunc_mk, Real.instArchimedean, ProbabilityTheory.uncenteredCovarianceBilin_apply, Real.add_sqrt_self_sq_sub_one_inv, MeasureTheory.exp_llr_of_ac', InnerProductGeometry.angle_smul_right_of_pos, Real.cosh_abs, Complex.UnitDisc.instSMulCommClass_closedBall_circle, HolderOnWith.comp, StrongDual.norm_extendRCLike_bound, TemperedDistribution.lineDerivOp_fourier_eq, ApproximatesLinearOn.surjOn_closedBall_of_nonlinearRightInverse, Complex.frontier_setOf_re_le, MeasureTheory.charFun_neg, intervalIntegral.intervalIntegrable_inv, ContDiffPointwiseHolderAt.isBigO, Real.deriv_log, ModularForm.SL_slash, selfAdjoint.norm_sq_expUnitary_sub_one, CStarAlgebra.norm_or_neg_norm_mem_spectrum, CongruenceSubgroup.conjGL_coe, StrictConvexOn.rightDeriv_lt_slope, Real.arctan_pos, SchwartzMap.decay', ContinuousLinearMap.image_rayleigh_eq_image_rayleigh_sphere, Real.rpow_neg_one, Complex.mul_re, Metric.sphere_zero, derivWithin_arctan, intervalIntegral.integral_comp_sub_div, MeasureTheory.measurableEmbedding_embeddingReal, Isometry.coe_affineIsometryOfStrictConvexSpace, Complex.ofRealCLM_norm, Behrend.roth_lower_bound_explicit, Real.limsup_of_not_isBoundedUnder, intervalIntegral.integral_deriv_mul_eq_sub_of_hasDerivAt, ContinuousAlternatingMap.le_mul_prod_of_opNorm_le_of_le, 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, Path.range_subpath_of_ge, Complex.reLm_coe, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp, Real.goldenRatio_mul_goldenConj, ContinuousLinearMap.opNorm_lsmul_apply_le, ContDiffMapSupportedIn.fderivLM_eq_of_scalars, intervalIntegral.integral_comp_mul_left, uniqueDiffOn_Iic, Real.continuous_arcsin, LipschitzWith.ae_exists_fderiv_of_countable, IsUltrametricDist.norm_add_one_le_max_norm_one, Antitone.tendsto_alternating_series_of_tendsto_zero, closedBall_sub_ball, BumpCovering.point_finite, Besicovitch.SatelliteConfig.centerAndRescale_radius, HurwitzZeta.cosZeta_two_mul_nat, rotation_injective, Continuous.integral_hasStrictDerivAt, Metric.comap_dist_left_atTop, ContinuousMap.norm_coe_le_norm, NNReal.coe_sSup, intervalIntegral.integrableOn_deriv_of_nonneg, Continuous.exists_contDiff_dist_le_of_forall_mem_ball_dist_le, Besicovitch.ae_tendsto_measure_inter_div_of_measurableSet, NumberField.mixedEmbedding.mem_idealLattice, Real.exp_lt_exp_of_lt, Polynomial.one_le_prod_max_one_norm_roots, circleAverage_log_norm_sub_const₁, ProbabilityTheory.HasSubgaussianMGF.sum_of_iIndepFun, 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, exists_eq_const_mul_intervalIntegral_of_nonneg, ContinuousMap.HomotopyWith.prop', cauchySeq_iff_tendsto_dist_atTop_0, antitoneOn_of_hasDerivWithinAt_nonpos, ProbabilityTheory.measurePreserving_restrict₂_multivariateGaussian, ENNReal.monotone_rpow_of_nonneg, SchwartzMap.bilinLeftCLM_apply, TopologicalSpace.Opens.CompleteCopy.dist_eq, Set.Countable.exists_pos_hasSum_le, ContDiffBump.integral_normed, ODE.FunSpace.range_toContinuousMap, Real.HolderTriple.holderConjugate_div_div, Real.tendsto_cos_pi_div_two, Complex.norm_eq_one_iff', Real.rpow_zpow_comm, IsConformalMap.is_complex_or_conj_linear, MeasureTheory.integral_fintype_prod_eq_prod, Affine.Simplex.mongePointVSubFaceCentroidWeightsWithCircumcenter_eq_sub, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, AkraBazziRecurrence.isBigO_apply_r_sub_b, NumberField.Units.regOfFamily_eq_det, CocompactMapClass.norm_le, SimplexCategory.toTopHomeo_symm_naturality, HasGradientAt.hasDerivAt', MeasureTheory.L1.SimpleFunc.setToL1SCLM_const, SmoothBumpCovering.exists_immersion_euclidean, AnalyticOnNhd.circleAverage_log_norm, BumpCovering.toPartitionOfUnity_zero_of_zero, AEMeasurable.sinc, Affine.Simplex.circumradius_nonneg, DifferentiableAt.sigmoid, IsOpen.exists_msmooth_support_eq, Affine.Triangle.sbtw_touchpoint_singleton, Affine.Triangle.dist_point_faceOppositeCentroid, OrderedFinpartition.norm_applyOrderedFinpartition_le, SzemerediRegularity.le_sum_distinctPairs_edgeDensity_sq, OrthonormalBasis.det_to_matrix_orthonormalBasis_of_same_orientation, Complex.equivRealProd_apply, IsCompact.exists_bound_of_continuousOn', UpperHalfPlane.specialLinearGroup_apply, ArchimedeanClass.stdPart_zero, BoxIntegral.Box.le_TFAE, Submodule.starProjection_singleton, EuclideanHalfSpace.ext_iff, ContinuousMap.dist_le, IsOpen.exists_smooth_support_eq, Real.artanh_pos, Complex.cpow_mul_ofReal_nonneg, HasSolidNorm.solid, ContinuousLinearMap.comp_condExp_add_const_comm, ContDiffMapSupportedIn.seminorm_fderivLM_le, SmoothPartitionOfUnity.locallyFinite', isUltrametricDist_iff_forall_norm_natCast_le_one, Real.rpow_eq_const_mul_integral, MeasureTheory.Lp.nnnorm_le_of_ae_bound, MeasureTheory.pdf.IsUniform.mul_pdf_integrable, ProbabilityTheory.integrable_toReal_condExpKernel, HasDerivWithinAt.liminf_right_norm_slope_le, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_le_one, CFC.rpow_eq_pow, ProbabilityTheory.mgf_dirac, Real.isIntegral_two_mul_sin_rat_mul_pi, instSMulCommClass_sphere_sphere_sphere, interval_average_eq_div, Bundle.RiemannianMetric.isVonNBounded, Real.ediam_eq, MeasureTheory.toReal_rnDeriv_tilted_left, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, MeasureTheory.hasFiniteIntegral_iff_ofNNReal, RingSeminorm.ringSeminormClass, MeasureTheory.tilted_neg_same', PowerSeries.gaussNorm_monomial, ContDiffMapSupportedIn.seminorm_fderivLM_top, Orientation.tan_oangle_add_right_smul_rotation_pi_div_two, BoundedContinuousFunction.indicator_apply, Affine.Simplex.mem_circumsphere, ProbabilityTheory.setIntegral_condCDF, ProbabilityTheory.integrable_rpow_mul_cexp_of_re_mem_interior_integrableExpSet, PadicInt.nonarchimedean, MeasureTheory.le_eLpNorm_of_bddBelow, NumberField.FinitePlace.mulSupport_finite, Complex.convexHull_reProdIm, EuclideanGeometry.exists_circumradius_eq_of_cospherical_subset, tendsto_norm_nhdsNE_one, Complex.conjLIE_apply, Polynomial.sub_one_pow_totient_le_cyclotomic_eval, ENNReal.rpow_inv_rpow, one_mem_posTangentConeAt_iff_frequently, Real.hasDerivAt_sin, IsVisible.mem_convexHull_isVisible, LipschitzWith.norm_sub_le_of_le, Seminorm.continuous_of_forall', Circle.starRingEnd_addChar, CircleDeg1Lift.isUnit_iff_bijective, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, Real.ContinuousOn.circleAverage, unitInterval.pos_iff_ne_zero, InnerProductGeometry.norm_div_cos_angle_sub_of_inner_eq_zero, QuotientAddGroup.le_norm_iff, Path.Homotopy.map_apply, MeasureTheory.Integrable.simpleFunc_mul', curveIntegralFun_smul, LiouvilleWith.mul_int_iff, NumberField.mixedEmbedding.measurableSet_plusPart, Real.tendsto_one_add_pow_exp_of_tendsto, ProbabilityTheory.IsGaussianProcess.iIndepFun_of_covariance_eq_zero, intervalIntegral.integral_deriv_eq_sub, intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDerivWithinAt, ProbabilityTheory.mgf_zero_fun, EisensteinSeries.abs_le_right_of_norm, Real.smoothTransition.zero_of_nonpos, MeasureTheory.Integrable.summable_of_dirac, Module.Basis.exists_opNorm_le, ProbabilityTheory.IsCondKernelCDF.tendsto_atTop_one, Complex.closure_preimage_im, CFC.sqrt_rpow, Path.pi_coe, RCLike.ofReal_re, Real.neg_sqrt_lt_of_sq_lt, integral_pow, UpperHalfPlane.isOpenMap_im, ProbabilityTheory.variance_sum_pi, Quaternion.imI_coeComplex, ENNReal.ofReal_le_ofReal_iff, MeasureTheory.SeparableSpace.exists_measurable_partition_diam_le, Real.summable_one_div_nat_add_rpow, NumberField.HeightOneSpectrum.NumberField.toNNReal_valued_eq_adicAbv, fourierIntegral_gaussian_innerProductSpace', ProbabilityTheory.integral_gaussianReal_eq_integral_smul, Matrix.linfty_opNorm_replicateRow, convexOn_of_hasDerivWithinAt2_nonneg, Hyperreal.IsSt.map, 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.dist_orthogonalProjection_eq_iff_oangle_eq, Orientation.sin_oangle_add_left_mul_norm_of_oangle_eq_pi_div_two, EuclideanGeometry.Sphere.mem_commonExtTangents_iff, not_IntegrableOn_Ioi_inv, unitInterval.coe_symmMeasurableEquiv, variationOnFromTo.eq_of_ge, Height.logHeight₁_add_le, EisensteinSeries.r_lower_bound_on_verticalStrip, NNReal.tendsto_dist_agmSequences_atTop_zero, Complex.sqrt_I, Real.norm_exp_sub_one_sub_id_le, Diffeology.isPlot_id', Real.logb_le_iff_le_rpow_of_base_lt_one, intervalIntegral.integral_comp_sub_left, NumberField.FinitePlace.prod_eq_inv_abs_norm, Real.tendsto_tsum_powerSeries_nhdsWithin_lt, Real.continuousAt_tan, CircleDeg1Lift.commute_iff_commute, PadicInt.norm_p_pow, Real.round_exp_one_eq_three, Urysohns.CU.approx_le_succ, Real.add_neg_lt_sSup, InnerProductSpace.canonicalCovariantTensor_eq_sum, RCLike.re_add_im_ax, fourier_gaussian_pi', MeasureTheory.charFun_eq_fourierIntegral, ContinuousMap.continuousMap_mem_subalgebra_closure_of_separatesPoints, mem_ball_iff_norm'', Real.hasSum_log_one_add_inv, Real.strictAntiOn_arccos, Real.differentiableOn_log, ProbabilityTheory.integral_continuousLinearMap_gaussianReal, Real.abs_tanh_lt_one, ENNReal.rpow_le_rpow_of_exponent_ge, isLittleO_log_rpow_rpow_atTop, Differentiable.fderiv_norm_rpow, combo_mem_ball_of_ne, Behrend.sphere_subset_preimage_metric_sphere, integral_log_sin_zero_pi_div_two, FDerivMeasurableAux.le_of_mem_A, 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, Set.OrdConnected.image_deriv, UnitAddTorus.mFourierSubalgebra_coe, LSeries_sub_eventuallyEq_zero_of_LSeries_eventually_eq, TemperedDistribution.smulLeftCLM_compL_smulLeftCLM, mulRight_bound, monotone_of_deriv_nonneg, Subgroup.widthInfty_pos, AlternatingMap.bound_of_shell_of_continuous, exists_eq_interval_average_of_noAtoms, Complex.range_re, TestFunction.monoCLM_eq_zero, Real.volume_closedEBall, Bornology.IsCobounded.closedBall_compl_subset, TopologicalGroup.IsSES.integral_inducedMeasure, ProbabilityTheory.lintegral_gammaPDF_of_nonpos, Path.ofLine_extend, NumberField.Units.dirichletUnitTheorem.seq_decreasing, CStarAlgebra.mem_Icc_iff_norm_le_one, Orientation.oangle_add_left_eq_arctan_of_oangle_eq_pi_div_two, Real.exp_nsmul, Path.range_subpathAux, Real.lt_zpow_of_log_lt, fourierCoeff.sum, ENNReal.rpow_le_self_of_le_one, unitInterval.volume_Ico, ProbabilityTheory.mgf_mono_of_nonneg, LiouvilleNumber.partialSum_eq_rat, MeasureTheory.Measure.addHaarScalarFactor_eq_integral_div, Complex.continuousWithinAt_log_of_re_neg_of_im_zero, ConvexOn.set_average_mem_epigraph, UpperHalfPlane.σ_sq, MeasureTheory.Submartingale.mul_integral_upcrossingsBefore_le_integral_pos_part, MeasureTheory.integral_const_mul, MeasureTheory.AECover.integral_eq_of_tendsto_of_nonneg_ae, 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, HasConstantSpeedOnWith.ratio, signedDist_right_congr, StrictConcaveOn.ae_eq_const_or_lt_map_average, IntervalIntegrable.neg, ProbabilityTheory.sub_half_inf_sub_mem_Ioo, norm_add_pow_two_real, intervalIntegral.integral_ofReal, Real.HolderConjugate.inv_inv, EuclideanGeometry.dist_eq_add_dist_iff_angle_eq_pi, Complex.reProdIm_subset_iff, InformationTheory.rnDeriv_compProd_mul_log_eq_mul_add, Besicovitch.SatelliteConfig.hlast, PadicInt.coe_eq_zero, sum_geometric_two_le, EuclideanGeometry.pi_div_three_le_angle_of_le_of_le, ProbabilityTheory.hasGaussianLaw_iff_charFun_map_eq, InnerProductSpace.gramSchmidtNormed_unit_length_coe, AddCircle.isAddFundamentalDomain_of_ae_ball, MeasureTheory.Measure.toSignedMeasure_le_toSignedMeasure_iff, IsUnifLocDoublingMeasure.eventually_measure_mul_le_scalingConstantOf_mul, instStarModuleNNRealOfReal, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear_of_le_one, RCLike.is_real_TFAE, PadicInt.padic_norm_e_of_padicInt, enorm_norm', Seminorm.continuous', NNReal.rpow_add_rpow_le_add, seminormFromConst_isMul_of_isMul, MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul, BoundedContinuousFunction.coe_normComp, mem_ball_one_iff, Real.BohrMollerup.le_logGammaSeq, 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, ProbabilityTheory.variance_const_sub, GaussianFourier.integral_cexp_neg_mul_sq_norm_add, Real.differentiableOn_arcsin, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunctionAux_eq, Real.artanh_nonneg, ContinuousMap.HomotopyLike.map_zero_left, norm_cexp_neg_mul_sq, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux1, ContinuousMap.Homotopy.evalAt_eq, UpperHalfPlane.num_neg, ContDiffOn.inner, Polynomial.Chebyshev.eval_T_real_node, norm_smul, ENNReal.ofReal_iInf, Polynomial.Chebyshev.complex_ofReal_eval_T, norm_nonneg', ProbabilityTheory.cgf_gaussianReal, MeasureTheory.Submartingale.sum_sub_upcrossingStrat_mul, ContinuousMap.dist_lt_of_nonempty, conformal_const_smul, ENNReal.ofReal_eq_zero, MeasureTheory.SignedMeasure.exists_compl_positive_negative, MeasureTheory.MemLp.integrable_norm_rpow', le_schnirelmannDensity_iff, LiouvilleWith.neg_iff, ProbabilityTheory.HasGaussianLaw.toLp_pi, UniformSpace.Completion.mem_uniformity_dist, Real.rpow_def_of_pos, Complex.hasStrictFDerivAt_exp_real, integral_exp, integral_inv_of_pos, Set.infsep_zero_iff_subsingleton_of_finite, Polynomial.Chebyshev.sumNodes_le_sumNodes_T, measurable_ereal_toReal, UpperHalfPlane.moebius_im, summable_norm_mul_geometric_of_norm_lt_one, ContinuousMultilinearMap.opNorm_zero_iff, RCLike.abs_im_div_norm_le_one, ModularForm.prod_slash, Real.one_le_exp_iff, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_sub_smoothingFn, intervalIntegrable_iff_integrableOn_Ico_of_le, comap_norm_atTop', EReal.nhds_coe, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, MeasureTheory.AEStronglyMeasurable.sinc, Continuous.sigmoid, ProbabilityTheory.HasSubgaussianMGF.mgf_le, norm_sub_mul_self, Topology.RelCWComplex.pairwiseDisjoint', CircleDeg1Lift.translationNumber_le_of_le_add, PhragmenLindelof.quadrant_IV, Seminorm.coe_le_coe, NumberField.abs_discr_ge', WithCStarModule.prod_norm_sq, MeasureTheory.lintegral_prod_lintegral_pow_le, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, uniqueDiffOn_Ioc, ContDiffWithinAt.cosh, Module.Basis.parallelepiped_basisFun, EuclideanGeometry.angle_eq_arctan_of_angle_eq_pi_div_two, NumberField.mixedEmbedding.instIsAddHaarMeasureMixedSpaceVolume, ProbabilityTheory.covariance_mul_right, Height.fun_mulHeight_zero, log_add_one_le_harmonic, SchwartzMap.laplacianCLM_eq, Metric.diam_le_of_subset_closedBall, NNReal.pow_rpow_inv_natCast, intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDerivAt, LiouvilleWith.sub_int, ProbabilityTheory.Kernel.HasSubgaussianMGF.add_compProd, monomial_has_deriv_aux, NormedGroup.nhds_one_basis_norm_lt, Real.Angle.toReal_coe_eq_self_iff_mem_Ioc, ENNReal.one_lt_rpow, norm_le_norm_add_const_of_dist_le, MeasureTheory.L1.norm_setToL1_le_norm_setToL1SCLM, DirichletCharacter.LSeries_twist_vonMangoldt_eq, Real.norm_exp_I_mul_ofReal_sub_one_le, exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensional, Cardinal.Real.Ioc_countable_iff, StieltjesFunction.measure_Ioo, Real.HolderTriple.inv_nonneg', MeasureTheory.hasFiniteIntegral_prod_iff', Affine.Simplex.ExcenterExists.affineCombination_eq_excenter_iff, Real.vector_fourierIntegral_eq_integral_exp_smul, StrictConvexOn.strictMonoOn_deriv, Archimedean.embedRealFun_add, MeasureTheory.Integrable.comp_mul_right', HasFDerivAt.le_of_lipschitzOn, NumberField.mixedEmbedding.fundamentalCone.compactSet_eq_union_aux₁, PiTensorProduct.projectiveSeminormAux_smul, MeasureTheory.integral_div, ContinuousMap.coeNNRealReal_apply, CompactlySupportedContinuousMap.nnrealPart_smul_neg, 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, Function.locallyFinsuppWithin.zero_iff_logCounting_bounded, Real.hasDerivAt_mul_log, ModularGroup.one_lt_normSq_T_zpow_smul, Real.iInf_mul_of_nonneg, ProbabilityTheory.IsGaussian.integrable_exp_sq_of_conv_neg, lp.sum_rpow_le_norm_rpow, IsLowerSet.exists_subset_ball, Real.fourier_real_eq_integral_exp_smul, Dilation.mapsTo_sphere, MeasureTheory.intervalIntegral_integral_swap, EuclideanGeometry.Sphere.mem_tangentsFrom_iff, Real.pi_nonneg, NumberField.abs_discr_ge, derivWithin_cosh, Real.rpowIntegrand₀₁_zero_right, NNReal.enorm_eq, ENNReal.rpow_left_surjective, Filter.tendsto_ofReal_iff', ENNReal.lintegral_rpow_funMulInvSnorm_eq_one, norm_cfc_le_iff, ProbabilityTheory.covarianceOperator_apply, WithLp.prod_nnnorm_eq_add, NumberField.mixedEmbedding.polarCoordReal_apply, fderivWithin_sinh, InnerProductGeometry.angle_smul_left_of_neg, lp.norm_le_of_forall_le', ProbabilityTheory.cdf_paretoMeasure_eq_integral, 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, ContDiffAt.laplacian_CLM_comp_left, Asymptotics.isLittleO_const_id_atTop, UpperHalfPlane.isometry_real_vadd, Complex.instFiniteDimensionalReal, Mathlib.Tactic.Rify.ratCast_lt, NNReal.orderIsoRpow_apply, EuclideanGeometry.Sphere.IsDiameter.dist_left_right, isMIntegralCurveOn_Ioo_eqOn_of_contMDiff, Real.tendsto_sigmoid_atTop, CStarAlgebra.span_nonneg_inter_unitBall, image_norm_le_of_norm_deriv_right_le_deriv_boundary', Complex.nnnorm_ratCast, SimpleGraph.card_connectedComponent_eq_finrank_ker_toLin'_lapMatrix, Real.continuous_sinc, Real.deriv_arccos, Complex.arg_le_pi, IntervalIntegrable.zero, hasDerivAt_of_hasDerivAt_of_ne, lp.norm_sum_single, smul_unitClosedBall, intervalIntegral.integrable_comp_mul_deriv_iff_of_deriv_nonneg, 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, Polynomial.exists_partition_polynomial_aux, CongruenceSubgroup.strictPeriods_Gamma0, Polynomial.Chebyshev.eval_T_real_eq_neg_one_iff, ProbabilityTheory.ae_eq_integral_of_variance_eq_zero, ProbabilityTheory.integrable_pow_abs_of_integrable_exp_mul, Real.tendsto_exp_atTop, UpperHalfPlane.center_zero, Distribution.IsVanishingOn.smulLeftCLM, Complex.normSq_ratCast, LocallyBoundedVariationOn.ae_differentiableWithinAt, entry_norm_bound_of_unitary, Complex.norm_one_add_mul_inv_le, integral_sin_pow_three, MeasureTheory.Measure.toSphere_real_apply_univ, Real.Gamma_strictAntiOn_Ioc, dist_le_norm_add_norm, Real.sin_lt, ConvexOn.univ_sSup_of_countable_affine_eq, Real.cos_le_one_div_sqrt_sq_add_one, Real.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_quasispectrum, Matrix.PosDef.eigenvalues_pos, integrableOn_exp_Iic, Real.log_mul_self_monotoneOn, Real.binEntropy_nonneg, unitInterval.volume_apply, RCLike.hasSum_ofReal, CStarAlgebra.norm_le_natCast_iff_of_nonneg, CFC.negPart_algebraMap, torusIntegral_succ, ContDiffOn.sqrt, Real.analyticWithinAt_sinh, cfcₙHom_nnreal_eq_restrict, unitInterval.mul_mem, integral_mul_fderiv_eq_neg_fderiv_mul_of_integrable, NonUnitalIsometricContinuousFunctionalCalculus.norm_quasispectrum_le, ContDiffMapSupportedIn.contDiff, Height.logHeight₁_sub_le, CircleDeg1Lift.dist_map_zero_translationNumber_le, instIsManifoldRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc, norm_iteratedFDeriv_clm_apply, TestFunction.toBoundedContinuousFunctionCLM_apply, circleAverage_log_norm_sub_const_of_mem_closedBall, Metric.unitBall.instContinuousMul, IsCompact.exists_thickening_image_subset, Real.sin_le_one, RCLike.continuous_normSq, Conformal.const_smul, Complex.conjCAE_apply, ProbabilityTheory.IsCondKernelCDF.nonneg, CircleDeg1Lift.le_translationNumber_of_add_int_le, ContinuousAlternatingMap.norm_def, ContinuousLinearEquiv.hasTemperateGrowth, AntilipschitzWith.mul_le_dist, ValueDistribution.logCounting_eval_zero, SmoothBumpFunction.le_one, NNReal.rpow_natCast, Real.sInf_of_not_bddBelow, summable_norm_mul_geometric_of_norm_lt_one', stronglyMeasurable_derivWithin_Ioi, variationOnFromTo.antitoneOn, ENNReal.orderIsoRpow_symm_apply, PadicInt.norm_units, Real.contDiffAt_rpow_const_of_le, SchwartzMap.fderivCLM_apply, hasStrictDerivAt_abs_pos, CStarRing.norm_of_mem_unitary, Module.Dual.re_extendRCLike_apply, deriv_sqrt_mul_log, Filter.Tendsto.arcsin, IsClopen.upperClosure_pi, Complex.norm_cos_add_sin_mul_I, ProbabilityTheory.cdf_expMeasure_eq, ProbabilityTheory.gaussianReal_zero_var, Real.volume_closedBall, Function.Periodic.norm_qParam_lt_iff, ProbabilityTheory.tilted_mul_apply_cgf, ProbabilityTheory.isProbabilityMeasure_expMeasure, Besicovitch.exists_closedBall_covering_tsum_measure_le, Real.abs_sin_eq_sin_abs_of_abs_le_pi, AkraBazziRecurrence.T_pos, hasDerivWithinAt_abs_pos, Real.le_toNNReal_iff_coe_le, Real.Wallis.W_le, Submodule.norm_starProjection_apply_le, ContDiffBump.pos_of_mem_ball, ContinuousLinearMap.norm_extendTo𝕜, IsLocalMax.fderiv_eq_zero, Rat.AbsoluteValue.eq_one_of_not_dvd, InnerProductGeometry.tan_angle_sub_mul_norm_of_inner_eq_zero, StrictConcaveOn.slope_lt_derivWithin, InformationTheory.klFun_eq_zero_iff, Real.tendsto_mul_log_one_add_of_tendsto, 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, HasFDerivAt.norm_sq, 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, Height.mulHeight_fun_prod_eq, ProbabilityTheory.IsRatCondKernelCDF.setIntegral, ProbabilityTheory.covariance_mul_left, Real.one_sub_sq_div_two_le_cos, MeasureTheory.Submartingale.sum_upcrossingStrat_mul, norm_le_norm_add_norm_neg_add, intervalIntegral.deriv_integral_right, RCLike.ofNat_re, AlgebraNorm.extends_norm, Complex.norm_pow, Metric.uniformity_basis_dist_le_inv_nat_pos, 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, Convex.image_sub_le_mul_sub_of_deriv_le, NumberField.mixedEmbedding.commMap_apply_of_isComplex, AddCircle.integral_haarAddCircle, Real.hasStrictFDerivAt_rpow_of_pos, Real.sin_pi, Complex.arg_one, HurwitzKernelBounds.f_int_negSucc, Asymptotics.IsLittleO.abs_left, Real.arcsin_nonpos, centerMass_mem_ball_of_strictConvexSpace, InnerProductSpace.HarmonicAt.const_smul, exists_partition_approximatesLinearOn_of_hasFDerivWithinAt, MeasureTheory.IntegrableOn.continuousOn_Iic_primitive_Iio, eventually_nhds_norm_smul_sub_lt, differentiableAt_sigmoid, exists_dist_slope_lt_pairwiseDisjoint_hasSum, NumberField.Units.pos_at_place, AEMeasurable.norm, TemperedDistribution.fourierMultiplierCLM_compL_fourierMultiplierCLM, Affine.Simplex.excenterWeightsUnnorm_reindex, Real.rpow_sum_le_const_mul_sum_rpow_of_nonneg, MeasureTheory.integrableOn_image_iff_integrableOn_abs_det_fderiv_smul, mem_closedBall_iff_norm'', BumpCovering.support_toPOUFun_subset, NumberField.InfinitePlace.Completion.norm_coe, PointwiseConvergenceCLM.tendsto_nhds, Real.arcosh_nonneg, RCLike.ofReal_balance, MeasureTheory.eLpNorm_le_of_ae_nnnorm_bound, ProbabilityTheory.Kernel.densityProcess_empty, NNReal.coe_add, norm_pow, SpectrumRestricts.nnreal_iff, MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_image, GroupSeminorm.lt_def, scalarSMulCLE_symm_apply, Real.fourier_deriv, Asymptotics.IsBigOWith_def, Real.toNNReal_pow, geometric_hahn_banach_compact_closed, IsometryEquiv.midpoint_fixed, ProbabilityTheory.Kernel.density_le_one, Height.mulHeight_mul_le, ProbabilityTheory.IsCondKernelCDF.integral, ENNReal.tendsto_rpow_atTop_of_one_lt_base, Real.integrable_prod_sub, intervalIntegral.integral_mono_on, Polynomial.exists_min_eq_gaussNorm, Seminorm.mem_closedBall_zero, Real.analyticAt_cos, Orientation.oangle_smul_left_of_neg, MeasureTheory.eLpNorm_mono_real, OrthogonalFamily.norm_sq_diff_sum, MeasureTheory.mul_meas_ge_le_pow_eLpNorm', circleMap_zero_inv, Real.smul_map_diagonal_volume_pi, DirichletCharacter.norm_LSeries_product_ge_one, NNReal.coe_iSup, Irrational.ratCast_div, PadicAlgCl.isNonarchimedean, Real.goldenRatio_lt_two, norm_smul_inv_norm, norm_sub_mul_le', CircleDeg1Lift.translationNumber_eq_rat_iff, Real.HolderTriple.one_div_eq, unitInterval.sigmoid_strictMono, abs_setIntegral_mulExpNegMulSq_comp_sub_le_mul_measure, Orientation.norm_div_cos_oangle_add_left_of_oangle_eq_pi_div_two, 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, Real.lt_pow_of_log_lt, RCLike.nonpos_iff, Complex.normSq_mk, MeasureTheory.Measure.addHaar_ball_of_pos, convexHull_union_neg_eq_absConvexHull, WeakFEPair.hf_zero', RCLike.smul_re, Icc_isBoundaryPoint_bot, RCLike.nonpos_iff_exists_ofReal, MeasureTheory.not_frequently_of_upcrossings_lt_top, Real.one_sub_le_exp_neg, mellin_convergent_zero_of_isBigO, Real.sigmoid_neg, dist_birkhoffSum_birkhoffSum_le, ContinuousWithinAt.sqrt, GaussianInt.toComplex_def₂, OrthonormalBasis.sum_sq_inner_right, Real.volume_val, Polynomial.Chebyshev.integral_T_real_mul_self_measureT_of_ne_zero, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_fun_sum, ProbabilityTheory.iIndepFun.charFunDual_map_finset_sum_eq_prod, Real.borel_eq_generateFrom_Iio_rat, mem_posTangentConeAt_of_frequently_mem, deriv_abs_neg, ProbabilityTheory.evariance_lt_top_iff_memLp, MeasureTheory.continuous_charFun, ProbabilityTheory.moment_one, Tactic.ComputeAsymptotics.Majorized.tendsto_zero_of_neg, integral_exp_neg_mul_rpow, Mathlib.Meta.NormNum.rpow_isRat_eq_inv_rpow, HurwitzKernelBounds.isBigO_atTop_F_int_one, Asymptotics.isBigOWith_refl, Seminorm.lt_def, BoxIntegral.unitPartition.prepartition_isSubordinate, 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, tendsto_setIntegral_peak_smul_of_integrableOn_of_tendsto, CliffordAlgebraComplex.toComplex_comp_ofComplex, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt₀, Real.sinc_eq_dslope, summable_condensed_iff_of_eventually_nonneg, Real.Angle.abs_toReal_eq_pi_div_two_iff, IntervalIntegrable.comp_sub_left_iff, LinearMap.polar_singleton, NNReal.rpow_lt_rpow_iff_of_neg, Orientation.oangle_add_right_eq_arcsin_of_oangle_eq_pi_div_two, Real.arcosh_zero, HurwitzZeta.hurwitzZetaEven_zero, OrthonormalBasis.toBasis_adjustToOrientation, ModularForm.prod_slash_sum_weights, Real.qaryEntropy_nonneg, MeasureTheory.convolution_tendsto_right, 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, AnalyticOn.rexp, DifferentiableWithinAt.abs_of_pos, ENNReal.tendsto_const_mul_rpow_nhds_zero_of_pos, Tactic.ComputeAsymptotics.WellFormedBasis.head_eventually_pos, EuclideanGeometry.dist_eq_abs_sub_dist_of_angle_eq_zero, ENNReal.hasMeasurablePow, irrational_sqrt_ratCast_iff, measurableSet_graph, ProbabilityTheory.Kernel.notMem_mutuallySingularSetSlice, smul_unitClosedBall_of_nonneg, AddGroupNorm.coe_add, Polynomial.Chebyshev.eval_T_real_mem_Icc, Real.iUnion_Iic_rat, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_dvd_norm_le, Complex.neg_pi_div_two_lt_arg_iff, Chebyshev.theta_eq_zero_of_lt_two, deriv.log, Real.exp_bound, Real.cos_add_int_mul_two_pi, Polynomial.Chebyshev.integral_measureT, ENNReal.ofReal_sum_of_nonneg, Real.log_neg_eq_log, SchwartzMap.compCLMOfContinuousLinearEquiv_apply, intervalIntegral.integral_div, AffineIsometryEquiv.pointReflection_midpoint_left, HarmonicAt.analyticAt_complex_partial, MeasureTheory.tilted_zero, MeasureTheory.SimpleFunc.setToSimpleFunc_const, EuclideanGeometry.angle_pos_of_angle_eq_pi_div_two, ProbabilityTheory.stronglyMeasurable_geometricPMFReal, GaussianInt.normSq_le_normSq_of_re_le_of_im_le, integrableOn_Ioi_rpow_of_lt, Real.iSup_nonpos, Real.volume_pi_ball, Multipliable.norm, HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principal, stereographic'_source, interior_convexHull_nonempty_iff_affineSpan_eq_top, image_le_of_deriv_right_le_deriv_boundary, MeasureTheory.Measure.iInf_IicSnd_gt, Real.monotone_arcsin, IsCompact.uniform_oscillation, EReal.image_coe_Iio, Metric.cthickening_thickening_subset, ProbabilityTheory.mgf_le_of_mem_Icc_of_integral_eq_zero, InnerProductSpace.HarmonicOnNhd.circleAverage_poissonKernel_smul, intervalIntegral.continuousOn_primitive, Real.tendsto_exp_div_pow_atTop, Real.log_div_log, AnalyticAt.rexp, isIntegralCurveAt_comp_mul_ne_zero, Behrend.bound_aux', Real.aestronglyMeasurable_rpowIntegrand₀₁, BoxIntegral.Box.upper_sub_lower_splitCenterBox, integral_sin_pow_pos, SimplexCategory.toTopHomeo_naturality_apply, Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter, AmpleSet.preimage_iff, Real.list_prod_map_rpow', MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero, 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', seminormFromConst_one_le, NonarchAddGroupSeminorm.coe_sup, ProbabilityTheory.centralMoment_one, Affine.Simplex.sum_mongePointWeightsWithCircumcenter, ProbabilityTheory.HasSubgaussianMGF.const_mul, MeasureTheory.weightedSMul_nonneg, ConcaveOn.slope_le_of_hasDerivAt, NumberField.mixedEmbedding.convexBodyLT_volume, signedDist_left_congr, UnitAddTorus.coe_symm_measurableEquivPiIoc, MeasureTheory.measure_integral_le_pos, ModularGroup.coe_apply_complex, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, Real.artanh_zero, instStarModuleNNRealReal, ContinuousMap.toLp_norm_le, exists_deriv_eq_zero, Real.cos_neg_of_pi_div_two_lt_of_lt, 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, Finset.small_alternating_pow_of_small_tripling, Function.locallyFinsuppWithin.logCounting_nonneg, Affine.Simplex.ExcenterExists.touchpoint_map, comap_norm_nhdsGT_zero, StieltjesFunction.mono', WeakFEPair.h_feq, NNReal.coe_div, LipschitzWith.hasFDerivAt_of_hasLineDerivAt_of_closure, ENNReal.lintegral_mul_rpow_le_lintegral_rpow_mul_lintegral_rpow, norm_le_norm_add_norm_sub', cfcₙ_integral, List.norm_prod_le', Seminorm.closedBall_smul_ball, Orientation.inner_rightAngleRotation_swap', BoundedVariationOn.continuousWithinAt_variationOnFromTo_rightLim_Ici, spectralAlgNorm_def, EuclideanGeometry.angle_eq_iff_oangle_eq_or_wbtw, InformationTheory.klFun_apply, integrableOn_Ioi_norm_cpow_of_lt, ProbabilityTheory.variance_fun_neg, ContDiffMapSupportedIn.contDiff', MeasureTheory.Measure.haar.prehaar_le_index, Complex.integral_rpow_mul_exp_neg_rpow, NNReal.sqrt_eq_rpow, MeasureTheory.Measure.addHaar_preimage_smul, IsClosed.lowerClosure_pi, setIntegral_withDensity_eq_setIntegral_toReal_smul', Real.sign_inv, QuadraticForm.equivalent_signType_weighted_sum_squared, mem_tangentConeAt_of_segment_subset, Asymptotics.isBigO_norm_right, OrthonormalBasis.measurePreserving_repr, Complex.exp_def, InformationTheory.leftDeriv_klFun_one, EuclideanGeometry.Cospherical.inclusion_iff, IsBoundedBilinearMap.isBigO_comp, Module.Basis.parallelepiped_reindex, RCLike.ofReal_comp_balance, Real.sin_pi_div_three, Real.abs_sinh, integral_Ioi_rpow_of_lt, Complex.arg_mul_eq_add_arg_iff, RCLike.abs_re_le_norm, IsClosed.mem_iff_infDist_zero, curveIntegralFun_segment, 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, SlashInvariantForm.quotientFunc_smul, Real.logb_mul, exists_smooth_tsupport_subset, strictConvexOn_pow, ProbabilityTheory.stieltjesOfMeasurableRat_nonneg, AnalyticOnNhd.rexp, Circle.exp_eq_exp, RCLike.reCLM_norm, Seminorm.bound_of_continuous_normedSpace, ENNReal.rpow_add_of_add_pos, IsCoercive.unique_continuousLinearEquivOfBilin, exists_hasDerivWithinAt_eq_of_gt_of_lt, Complex.volume_sum_rpow_le, HolderOnWith.ediam_image_le_of_subset_of_le, RCLike.geometric_hahn_banach_closed_point, GenLoop.homotopyTo_apply, Besicovitch.SatelliteConfig.exists_normalized_aux2, MeasureTheory.withDensityᵥ_eq_withDensity_pos_part_sub_withDensity_neg_part, signedDist_triangle, HasDerivWithinAt.sin, Height.logHeight_eval_ge', IsUltrametricDist.invariantExtension_apply, Real.hasDerivAt_arcosh, MeasureTheory.intervalIntegral_tendsto_integral_Iic, Complex.tendsto_mul_log_one_add_of_tendsto, Similar.exists_pos_dist_eq, AEMeasurable.im, Real.inv_logb_div_base, Besicovitch.SatelliteConfig.h, ConcaveOn.locallyLipschitzOn_interior, Real.arctan_eq_zero_iff, cfcₙ_setIntegral, SchwartzMap.inner_toL2_toL2_eq, ProbabilityTheory.Kernel.isCondKernelCDF_condKernelCDF, Real.zpow_le_iff_le_log, Complex.UnitDisc.im_neg, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_integrableOn, Real.sigmoid_le, IsMaxOn.norm_add_self, Irrational.natCast_add, Real.sinh_zero, ContDiffAt.arsinh, Real.inv_goldenConj, PartitionOfUnity.locallyFinite, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, AnalyticOn.sigmoid, integral_bernoulliFun, MeasureTheory.SignedMeasure.toComplexMeasure_apply, instIsAddHaarMeasureEuclideanSpaceRealFinHausdorffMeasureCast, Asymptotics.isBigO_abs_left, ModularForm.levelOne_neg_weight_rank_zero, LipschitzWith.dist_le_mul_of_le, Path.Homotopy.continuous_transAssocReparamAux, Complex.norm_log_one_add_le, Complex.UnitDisc.im_star, dist_inv_inv₀, Complex.mul_angle_le_norm_sub, ConvexOn.monotoneOn_rightDeriv, tendsto_self_mul_const_pow_of_lt_one, Height.logHeight₁_mul_le, Metric.iUnion_ball_nat_succ, ContDiffOn.rpow, intervalIntegral.integral_hasDerivAt_of_tendsto_ae_right, UniformSpace.Completion.uniformContinuous_dist, Real.rpow_inv_log, SmoothBumpCovering.mem_extChartAt_source_of_eq_one, AkraBazziRecurrence.GrowsPolynomially.const_mul, Subgroup.IsArithmetic.is_commensurable, Complex.coe_orthonormalBasisOneI, Subgroup.IsArithmetic.inter, Polynomial.Chebyshev.isLocalMin_T_real, Filter.Tendsto.arccos, Real.expPartialHomeomorph_apply, EuclideanGeometry.Cospherical.inclusion, Projectivization.mulHeight_pos, enorm_fderiv_norm_rpow_le, Real.iteratedDerivWithin_cos_Icc, Height.logHeight₁_one, MeasureTheory.condExp_bilin_of_aestronglyMeasurable_right, Metric.equicontinuousAt_iff, Complex.integral_circleTransform, tendsto_norm_inv_nhdsNE_zero_atTop, HarmonicOnNhd.circleAverage_eq, MeasureTheory.tendsto_zero_of_hasDerivAt_of_integrableOn_Ioi, Real.sigmoid_nonneg, AddGroupSeminorm.ext_iff, schnirelmannDensity_setOf_prime, Continuous.exists_contDiff_approx_and_eqOn, Real.sum_ofDigitsTerm_digits_le, closedBall_add_closedBall, formalMultilinearSeries_geometric_apply_norm_le, NormedField.norm_mul, convexOn_univ_dist, ModularGroup.sl_moeb, RCLike.ofReal_sub, lp.sum_rpow_le_of_tendsto, norm_le_add_norm_add, Padic.norm_int_le_one, Path.extend_symm_apply, ENNReal.inv_rpow, norm_pow_le_mul_norm, HasDerivAt.arctan, Real.le_logb_iff_rpow_le, Archimedean.embedReal_apply, LocallyBoundedVariationOn.ae_differentiableAt, Polynomial.toAddCircle_X_pow_eq_fourier, ProbabilityTheory.iIndepFun.charFunDual_map_fun_sum_eq_prod, 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, Unitization.sqrt_inr, NumberField.InfinitePlace.smul_apply, MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_det_fderiv_mul, MeasureTheory.Integrable.simpleFunc_mul, MeasureTheory.Submartingale.stoppedValue_leastGE, MonotoneOn.intervalIntegrable_deriv, Real.toNNReal_add, MeasureTheory.AEStronglyMeasurable.ae_integrable_condKernel_iff, Orientation.oangle_sub_right_eq_arccos_of_oangle_eq_pi_div_two, Irrational.intCast_add, Complex.arg_le_pi_div_two_iff, Real.Icc_mem_vitaliFamily_at_left, NNReal.rpow_mul_intCast, Real.instZeroLEOneClass, NormedSpace.isBounded_iff_subset_smul_closedBall, IsClopen.lowerClosure_pi, HasDerivAt.sqrt, Complex.HadamardThreeLines.F_BddAbove, Continuous.cfc_nnreal', Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform_aux, MeasureTheory.Measure.hausdorffMeasure_le_liminf_sum, Path.Homotopy.target, Real.Angle.toReal_coe, Real.cos_arcsin, Polynomial.le_gaussNorm, NumberField.HeightOneSpectrum.adicAbv_natCast_le_one, RCLike.norm_sq_eq_def_ax, MeasureTheory.L1.SimpleFunc.norm_setToL1S_le, InnerProductGeometry.sin_angle_div_norm_eq_sin_angle_div_norm, Orientation.abs_volumeForm_apply_of_orthonormal, Real.rpow_mul_intCast, ContDiffBump.normed_def, BoxIntegral.Integrable.dist_integralSum_le_of_memBaseSet, signedDist_linear_apply_apply, HurwitzZeta.oddKernel_def', MeromorphicOn.extract_zeros_poles_log, aemeasurable_coe_nnreal_real_iff, Real.sInf_le_sSup, CFC.abs_coe_unitary, MeasureTheory.exists_average_le, gauge_le_of_mem, Affine.Simplex.sSameSide_incenter_point, ProbabilityTheory.covariance_sub_const_right, MeasureTheory.MemLp.exist_eLpNorm_sub_le, IsApproximateAddSubgroup.one_le, GenLoop.genLoopGenLoopEquiv_apply_coe, intervalIntegral.intervalIntegrable_zpow, spectrum.spectralRadius_le_liminf_pow_nnnorm_pow_one_div, Circle.exp_two_pi_mul_int, SemilinearMapClass.bound_of_continuous, isSymm_inner, Real.arctan_mem_Ioo, EuclideanGeometry.collinear_iff_of_two_zsmul_oangle_eq, ContinuousMap.norm_add_eq_max, nullMeasurableSet_region_between_co, BoxIntegral.hasIntegral_GP_pderiv, setIntegral_withDensity_eq_setIntegral_toReal_smul₀, setIntegral_Ioi_zero_rpow, SchwartzMap.integral_bilin_fourierIntegral_eq, MeasureTheory.SignedMeasure.bddBelow_measureOfNegatives, TopologicalGroup.IsSES.pushforward_def, fourier_gaussian_innerProductSpace, SchwartzMap.fourierMultiplierCLM_compL_fourierMultiplierCLM, Matrix.norm_entry_le_entrywise_sup_norm, AddCircle.ae_empty_or_univ_of_forall_vadd_ae_eq_self, ProbabilityTheory.Kernel.measurable_singularPart_fun_right, Real.fourierIntegral_continuousMultilinearMap_apply, AddGroupNorm.coe_sup, EuclideanGeometry.oangle_midpoint_right, ENNReal.mul_rpow_of_nonneg, ProbabilityTheory.HasGaussianLaw.smul, MeasureTheory.integral_Ioi_of_hasDerivAt_of_nonneg, ValueDistribution.logCounting_add_top_le, Real.Angle.two_zsmul_coe_div_two, SchwartzMap.norm_toLp_one, Affine.Simplex.ExcenterExists.excenter_map, IsLocalExtr.lineDeriv_eq_zero, Metric.tendsto_nhds, EReal.coe_nonpos, MeasureTheory.integral_eq_integral_pos_part_sub_integral_neg_part, Real.ofCauchy_zero, integral_rpow_mul_exp_neg_rpow, analyticAt_rexp, NumberField.mixedEmbedding.polarSpaceCoord_target, AddCircle.scaled_exp_map_periodic, OnePoint.isZeroAt_iff_exists_SL2Z, PiNat.dist_triangle_nonarch, Real.logb_lt_iff_lt_rpow, 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, LinearMap.singularValues_antitone, NumberField.mixedEmbedding.negAt_apply_snd, MeasureTheory.SignedMeasure.subset_negative_null_set, CircleDeg1Lift.translationNumber_one, ae_eq_const_or_norm_setIntegral_lt_of_norm_le_const, StrictConvexOn.lt_slope_of_hasDerivAt, Real.GammaIntegral_convergent, MeasureTheory.measure_lt_one_eq_integral_div_gamma, Real.logb_eq_zero, CStarRing.norm_mul_self_le, MeasureTheory.lintegral_image_eq_lintegral_deriv_mul_of_monotoneOn, Affine.Simplex.dist_circumcenter_sq_eq_sq_sub_circumradius, Real.tan_arccos, nnnorm_algebraMap_nnreal, ProbabilityTheory.HasGaussianLaw.neg, Real.tendsto_atTop_csSup_of_monotoneOn_bddAbove_nat_Ici, MeasureTheory.setIntegral_prod_mul, Orientation.neg_rotation_neg_pi_div_two, MeasureTheory.integral_Ioi_of_hasDerivAt_of_nonpos', EReal.isOpenEmbedding_coe, Real.borel_eq_generateFrom_Ioo_rat, NNReal.young_inequality, MeasureTheory.measureReal_mono, Real.hasSum_sinh, Real.sinh_arcosh, ContinuousMultilinearMap.uniformity_eq_seminorm, Complex.im_nnqsmul, CFC.rpow_def, mem_closedBall_iff_norm_inv_mul_le, Real.tendsto_eulerMascheroniSeq', MeasureTheory.SignedMeasure.toJordanDecomposition_eq_of_eq_add_withDensity, NNReal.map_coe_atTop, IsExtrOn.lineDerivWithin_eq_zero, ENNReal.rpow_ofNNReal, Real.one_add_rpow_hasFPowerSeriesOnBall_zero, ProbabilityTheory.monotone_cdf, intervalIntegral.continuousOn_primitive_interval_left, Real.arccos_pos, ContinuousLinearMap.sSup_sphere_eq_nnnorm, Polynomial.Chebyshev.integral_measureT_eq_integral_cos_of_continuous, Mathlib.Meta.NormNum.isRat_rpow_pos, VectorFourier.fourierPowSMulRight_eq_comp, AnalyticAt.sigmoid', 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, NNReal.rpow_inv_lt_iff_of_pos, WithSeminorms.tendsto_nhds', norm_multiset_sum_le, Finset.ruzsa_covering_add, 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, Sbtw.angle₃₁₂_eq_zero, LiouvilleNumber.aux_calc, VitaliFamily.eventually_filterAt_iff, AlgebraNormClass.map_smul_eq_mul, Complex.uniformContinuous_im, le_gauge_of_notMem, 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, mfderivWithin_projIcc_one, StieltjesFunction.measure_singleton, ContDiffMapSupportedIn.fderivCLM_apply_of_gt, TestFunction.fderivCLM_apply_of_le, InnerProductSpace.harmonicOnNhd_comp_CLE_iff, NumberField.Units.dirichletUnitTheorem.seq_next, sameRay_iff_inv_norm_smul_eq_of_ne, Complex.frontier_preimage_re, exists_of_schnirelmannDensity_eq_zero, CuspForm.coe_trace, intervalIntegral.integral_pos_iff_support_of_nonneg_ae', antilipschitzWith_iff_le_mul_dist, Real.Polynomial.isRoot_cos_pi_div_five, AlternatingMap.bound_of_shell, MeasureTheory.ae_nonneg_of_forall_setIntegral_nonneg_of_sigmaFinite, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_add_compProd, indicator_thickening_eventually_eq_indicator_closure, Real.surjOn_log', comap_norm_nhds_zero, abs_lt_norm_sub_of_not_sameRay, norm_sum_lt_of_strictConvexSpace, 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, UniformConvexOn.strictConvexOn, Real.exp_one_lt_three, ENNReal.lintegral_prod_norm_pow_le, Real.sInf_smul_of_nonneg, TemperedDistribution.smulLeftCLM_neg, Module.Dual.im_extendRCLike_apply, integral_cos_pow, Complex.cosh_ofReal_im, Real.neg_pi_div_two_lt_arctan, Metric.inseparable_iff, Orientation.oangle_sign_sub_smul_left, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge', UpperHalfPlane.glPos_smul_def, MeasureTheory.SimpleFunc.integral_eq_sum_filter, Real.cos_nat_mul_two_pi_sub_pi, HasFDerivAt.arctan, Real.comap_exp_nhds_zero, AkraBazziRecurrence.eventually_one_sub_smoothingFn_gt_const, MeasureTheory.SignedMeasure.eq_rnDeriv, Real.cosPartialEquiv_target, isLocalMin_of_deriv_deriv_pos, ContinuousAt.arccos, Height.mulHeight₁_zpow, Real.analyticAt_sinh, Real.toNNReal_lt_toNNReal_iff_of_nonneg, instHasSolidNormReal, HomotopyGroup.isUnital_auxGroup, ContDiff.arctan, BoxIntegral.hasIntegral_GP_divergence_of_forall_hasDerivWithinAt, Real.hasStrictDerivAt_arccos, Complex.sub_im, IsCusp.of_isFiniteRelIndex_conj, RCLike.conjCLE_apply, Real.cauSeq_converges, NumberField.mixedEmbedding.convexBodySumFun_apply', ContinuousLinearMap.norm_fst_le, Chebyshev.psi_eq_sum_theta, CStarModule.norm_nonneg, MeasureTheory.integrable_norm_rpow_iff, Stirling.log_stirlingSeq_diff_hasSum, TestFunction.lineDerivOpCLM_eq_lineDerivCLM, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_norm_eq_mul_torsion, AntilipschitzWith.le_mul_norm, gauge_le_eq, Affine.Simplex.circumradius_restrict, IsUltrametricDist.norm_tsum_le, AnalyticAt.harmonicAt_im, ProbabilityTheory.integral_stieltjesOfMeasurableRat, ProbabilityTheory.variance_of_integral_eq_zero, ENNReal.liminf_toReal_eq, Real.inv_goldenRatio, not_differentiableWithinAt_of_deriv_tendsto_atBot_Ioi, MeasureTheory.Measure.quasiMeasurePreserving_smul, MeasureTheory.MemLp.exists_boundedContinuous_integral_rpow_sub_le, MeasureTheory.measureReal_symmDiff_eq, Affine.Simplex.ExcenterExists.touchpoint_notMem_affineSpan_of_ne, unitInterval.mem_unitIntervalSubmonoid, Real.sin_antiperiodic, Path.delayReflRight_zero, MeasureTheory.dominatedFinMeasAdditive_condExpInd, Real.sphere_eq_pair, CovBySMul.nonneg, Complex.reCLM_nnnorm, Real.log_list_prod, Real.arsinh_neg, Polynomial.logMahlerMeasure_of_degree_eq_one, abs_fst_of_mem_pi_polarCoord_target, norm_sub_pow_two_real, EuclideanGeometry.Sphere.isTangentAt_of_dist_sq_eq_power, Affine.Simplex.abs_inner_vsub_altitudeFoot_div_lt_one, Asymptotics.IsEquivalent.add_add_of_nonneg, Polynomial.cyclotomic_eval_lt_add_one_pow_totient, Real.zpow_lt_iff_lt_log, HasStrictFDerivAt.abs, MeasureTheory.Measure.integral_isAddLeftInvariant_eq_smul_of_hasCompactSupport, 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, BoxIntegral.Box.face_mk, IsUnit.cfcSqrt, Real.HolderConjugate.two_two, MeasureTheory.integral_norm_eq_lintegral_enorm, CFC.continuousOn_log, isLocalMax_of_deriv', 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, TestFunction.fderivCLM_ofSupportedIn, MeasureTheory.SignedMeasure.toJordanDecomposition_zero, RCLike.mul_im_ax, Real.Gamma_two, Function.locallyFinsuppWithin.logCounting_eval_zero, intervalIntegral.intervalIntegrable_inv_one_add_sq, Real.self_le_rpow_of_le_one, Real.artanh_eq_half_log, RCLike.ofReal_injective, ModularGroup.coe_T_zpow_smul_eq, Real.toNNReal_prod_of_nonneg, nullMeasurableSet_regionBetween, SingularManifold.isManifold, ProbabilityTheory.IndepFun.integral_comp_mul_comp, continuous_convexComboPair_of_isBounded, 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, LipschitzWith.le_add_mul, Affine.Simplex.touchpoint_singleton_mem_interior_faceOpposite, NumberField.mixedEmbedding.fundamentalCone.expMap_target, Complex.sin_bound, Real.continuousOn_log, MeasureTheory.Measure.integral_isMulLeftInvariant_isMulRightInvariant_combo, CircleDeg1Lift.strictMono_iff_injective, NumberField.mixedEmbedding.convexBodySum_neg_mem, Finset.ruzsa_covering_mul, intervalIntegral.FTCFilter.finiteAt_inner, IsIntegralCurveOn.comp_mul, 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.range_logb, Real.sigmoid_lt_iff, isScalarTower_sphere_closedBall_closedBall, ProbabilityTheory.Kernel.HasSubgaussianMGF.memLp_exp_mul, ContDiffPointwiseHolderAt.differentiableAt, Complex.hasDerivAt_GammaIntegral, PadicInt.norm_lt_one_iff_dvd, QuadraticForm.equivalent_one_neg_one_weighted_sum_squared, Real.logb_eq_iff_rpow_eq, Absorbent.gauge_set_nonempty, Complex.deriv_ofReal_cpow_const, exists_continuous_zero_one_of_isClosed, AbsoluteValue.exists_partition_int, Real.arsinh_injective, Real.tan_int_mul_pi_div_two, HurwitzKernelBounds.f_le_g_nat, MonotoneOn.convexOn_of_deriv, Affine.Simplex.excenterExists_reindex, Complex.starConvex_ofReal_slitPlane, Real.Wallis.tendsto_W_nhds_pi_div_two, Real.zpow_lt_of_lt_log, Convex.cthickening, Chebyshev.psi_sub_theta_eq_sum_not_prime, Real.isOpenEmbedding_exp, Real.Angle.sign_two_nsmul_eq_neg_sign_iff, mem_closedBall_iff_norm_neg_add_le, SchwartzMap.integral_sesq_fourier_eq, Real.cos_add_two_pi, norm_le_norm_add_norm_sub, Real.ofCauchy_mul, AbsolutelyContinuousOnInterval.boundedVariationOn, ProbabilityTheory.charFun_multivariateGaussian, 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.fderiv_fourier, Real.isIntegral_two_mul_cos_rat_mul_pi, ApproximatesLinearOn.norm_fderiv_sub_le, MeasureTheory.norm_setIntegral_le_of_norm_le_const_ae', MeasureTheory.charFunDual_pi', intervalIntegral.integral_mono_ae_restrict, MeasureTheory.integral_eq_zero_of_hasDerivAt_of_integrable, MeasureTheory.L1.setToL1_smul_left, RCLike.toIsStrictOrderedModule, stdSimplex_subset_closedBall, ValueDistribution.logCounting_const_zero, NumberField.house_intCast, ContinuousOn.cfc_nnreal', IsGreatest.nnnorm_cfc_nnreal, NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, Rat.isDenseEmbedding_coe_real, RCLike.abs_re_div_norm_le_one, MeasureTheory.eLpNorm_norm, NNReal.rpow_zero_pos, HurwitzZeta.hasSum_nat_sinZeta, BoxIntegral.unitPartition.integralSum_eq_tsum_div, Mathlib.Meta.NormNum.IsNat.nnreal_rpow_isNNRat, MeasureTheory.hasFiniteIntegral_toReal_of_lintegral_ne_top, MeasureTheory.integrable_toReal_rnDeriv_mul_iff, norm_sub_le_mul_volume_of_norm_lineDeriv_le, MeasureTheory.Measure.addHaar_ball_mul, InformationTheory.toReal_klDiv_eq_integral_klFun, EisensteinSeries.r1_aux_bound, NumberField.Units.dirichletUnitTheorem.logEmbedding_component_le, ProbabilityTheory.Kernel.HasSubgaussianMGF.add_comp, ValueDistribution.logCounting_mul_zero_eventuallyLE, Real.instPathConnectedSpace, Real.norm_deriv_mulExpNegMulSq_le_one, norm_sub_sq, ValueDistribution.logCounting_top, Height.abs_logHeight_sym2_sub_le, ProbabilityTheory.covarianceBilin_stdGaussian, MeasureTheory.L1.setToL1_zero_left, Quaternion.linearIsometryEquivTuple_symm_apply, image_norm_le_of_norm_deriv_right_lt_deriv_boundary', trapezoidal_error_eq, EuclideanGeometry.Sphere.dist_div_sin_oangle_div_two_eq_radius, EuclideanGeometry.angle_orthogonalProjection_self, abs_norm_sub_norm_le_norm_inv_mul, PiLp.dist_eq_card, Affine.Simplex.ninePointCircle_eq_circumsphere_medial, EuclideanGeometry.Sphere.inner_vsub_center_midpoint_vsub, EuclideanGeometry.angle_eq_pi_div_two_of_oangle_eq_neg_pi_div_two, EuclideanGeometry.angle_le_iff_dist_le, ContinuousMap.norm_le_of_nonempty, SpectrumRestricts.smul_of_nonneg, NNReal.rpow_lt_rpow_of_neg, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, MeasureTheory.SignedMeasure.singularPart_smul, uniformContinuous_norm, MeasureTheory.integrable_sum_measure_iff, ComputeAsymptotics.MultiseriesExpansion.Multiseries.destruct_cons, WithLp.prod_dist_eq_of_L2, dist_convexComboPair_left, PowerSeries.gaussNorm_zero, WithLp.prod_norm_eq_of_nat, Metric.Snowflaking.image_toSnowflaking_emetricClosedBall, ProbabilityTheory.covarianceBilin_apply_basisFun_self, LipschitzOnWith.ae_differentiableWithinAt_of_mem_real, MeasureTheory.tendsto_of_integral_tendsto_of_antitone, WithAbs.isometry_of_comp, NumberField.mixedEmbedding.normAtPlace_apply_of_isReal, RCLike.I_re_ax, MeasureTheory.condExpInd_nonneg, MeasureTheory.charFun_apply_real, balancedHull_subset_convexHull_union_neg, Convex.norm_image_sub_le_of_norm_hasFDerivWithin_le, image_norm_le_of_liminf_right_slope_norm_lt_deriv_boundary, StrictConvex.extremePoints_eq_diff_interior, EuclideanGeometry.tan_oangle_right_of_oangle_eq_pi_div_two, Complex.norm_eventually_eq_of_isLocalMax, Real.arctan_le_arctan, Topology.RelCWComplex.union', tendsto_setIntegral_peak_smul_of_integrableOn_of_tendsto_aux, EuclideanGeometry.dist_orthogonalProjection_eq_of_oangle_eq, StrictConcaveOn.deriv_lt_slope, MeasureTheory.measureReal_empty, SmoothBumpFunction.exists_r_pos_lt_subset_ball, Orientation.areaForm_to_volumeForm, Real.rpowIntegrand₀₁_le_rpow_sub_two_mul_self, Path.Homotopy.eval_zero, stereoInvFunAux_apply, lp.norm_rpow_eq_tsum, norm_curveIntegral_segment_le, Icc_isInteriorPoint_interior, 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, Metric.uniformity_basis_dist_lt, UpperHalfPlane.denom_cocycle_σ, EuclideanGeometry.angle_pos_of_not_collinear, VectorFourier.fourierIntegral_continuousLinearMap_apply, ContinuousAffineMap.norm_def, circleAverage_log_norm_sub_const_eq_log_radius_add_posLog, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, Convex.closure_subset_interior_image_homothety_of_one_lt, signedDist_le_dist, seminormFromBounded_of_mul_is_mul, Real.not_continuousAt_deriv_mul_log_zero, integrable_one_add_norm, ProbabilityTheory.integrable_condCDF, MeasureTheory.integral_Ioi_deriv_mul_eq_sub, NNReal.algebraMap_eq_coe, MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto', ContinuousLinearMap.norm_iteratedFDerivWithin_comp_left, Real.Gamma_mul_Gamma_add_half, HasStrictFDerivAt.arsinh, 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, Real.sin_gt_sub_cube, integrableOn_add_rpow_Ioi_of_lt, AddGroupNorm.le_def, ZMod.LFunction_def_odd, LinearMap.IsSymmetric.coe_re_inner_self_apply, Complex.norm_eventually_eq_of_mdifferentiableAt_of_isLocalMax, ENNReal.lintegral_mul_norm_pow_le, LiouvilleWith.rat_sub, AffineSubspace.isConnected_setOf_wOppSide, Complex.norm_le_norm_of_mapsTo_ball, CStarMatrix.norm_le_of_forall_inner_le, Real.two_mul_arctan_inv_2_sub_arctan_inv_7, Finsupp.logb_prod, HolderOnWith.nndist_le_of_le, HasFDerivWithinAt.exp, InformationTheory.klDiv_eq_top_iff, UpperHalfPlane.isOpenMap_re, ContinuousOn.log, EuclideanGeometry.dist_lt_of_sbtw_of_inner_eq_zero, torusMap_zero_radius, EulerSine.integral_cos_mul_cos_pow_aux, Affine.Simplex.ninePointCircle_radius, Polynomial.zero_le_negOnePow_mul_eval_of_le_roots_of_leadingCoeff_nonneg, IsPowMul.map_one_le_one, summable_mul_of_bigO_atTop, AntilipschitzWith.le_mul_dist, ExistsContDiffBumpBase.w_compact_support, 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, ProbabilityTheory.Kernel.compProd_fst_borelMarkovFromReal_eq_comapRight_compProd, LindemannWeierstrass.exp_polynomial_approx, Real.norm_natCast, DirichletCharacter.norm_le_one, NNReal.image_coe_uIoc, Cardinal.cantorFunctionAux_false, norm_iteratedFDerivWithin_clm_apply_const, RCLike.iInter_countable_halfSpaces_eq, Polynomial.Chebyshev.complex_ofReal_eval_C, Real.pi_lt_d6, ENNReal.ofReal_lt_ofReal_iff_of_nonneg, 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, tendsto_card_div_pow_atTop_volume, blimsup_thickening_mul_ae_eq_aux, EuclideanGeometry.Sphere.mul_dist_eq_neg_power_of_dist_center_le_radius, NumberField.FinitePlace.norm_embedding_eq, Real.logb_surjective, HasUnitSpeedOn.union, Complex.tan_arg, Asymptotics.IsBigOWith.sum_congr', Real.cos_two_neg, Complex.normSq_mul, MeasureTheory.iteratedFDeriv_charFun, RCLike.ofReal_nonneg, Real.closedBall_eq_Icc, schnirelmannDensity_finite, Real.sin_add_nat_mul_pi, Real.sin_lt_sin_of_lt_of_le_pi_div_two, Real.hasSum_cosh, AffineBasis.interior_convexHull, ProbabilityTheory.iIndepFun.hasGaussianLaw_fun_sum, Real.cos_nat_mul_pi, NNReal.coe_rpow, Real.infinite_rat_abs_sub_lt_one_div_den_sq_of_irrational, Set.ruzsa_covering_add, EuclideanGeometry.inversion_vsub_center, ProbabilityTheory.tendsto_stieltjesOfMeasurableRat_atTop, Real.harm_mean_le_geom_mean_weighted, NNReal.rpow_add_intCast', Complex.interior_setOf_le_re, Real.singleton_eq_inter_Icc, MeasureTheory.Measure.haar.prehaar_sup_le, EuclideanGeometry.dist_orthogonalProjection_eq_iff_angle_eq, fderivWithin_sin, InnerProductGeometry.angle_le_pi, Height.logHeight_eval_le', set_smul_sphere_zero, EuclideanGeometry.oangle_eq_zero_iff_angle_eq_zero, isMIntegralCurveAt_eventuallyEq_of_contMDiffAt_boundaryless, Orientation.rightAngleRotation_trans_rightAngleRotation, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, IsBoundedBilinearMap.isBigO', ENNReal.tendsto_toReal, StrictConcaveOn.slope_lt_deriv, Irrational.mul_intCast, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, MeasureTheory.pdf.integral_pdf_smul, Real.one_lt_goldenRatio, Filter.tendsto_ofReal_iff, Function.Periodic.sInf_add_zsmul_le_integral_of_pos, ValueDistribution.proximity_nonneg, IsUltrametricDist.norm_tprod_le, NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd, CFC.continuousOn_sqrt, Real.binEntropy_neg_of_neg, ProbabilityTheory.mgf_const, AddSubgroup.norm_trivial_quotient_mk, AEMeasurable.exp, Monotone.ae_differentiableAt, Metric.mem_closure_iff_infDist_zero, ConvexOn.slope_le_deriv, 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, ProbabilityTheory.centralMoment_one', MeasureTheory.integral_fin_nat_prod_volume_eq_prod, intervalIntegral.continuous_parametric_primitive_of_continuous, ExistsContDiffBumpBase.u_continuous, TemperedDistribution.fourierInv_lineDerivOp_eq, ConvexOn.map_condExp_le_of_finiteDimensional, Polynomial.mahlerMeasure_nonneg, CircleDeg1Lift.le_iterate_of_add_int_le_map, norm_algebraMap_nnreal, MeasureTheory.condExpL2_indicator_ae_eq_smul, Affine.Simplex.excenter_eq_affineCombination, ContinuousLinearMap.exists_lt_apply_of_lt_opNorm, LipschitzWith.norm_div_le, Differentiable.abs, 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, EuclideanGeometry.oangle_right_eq_arcsin_of_oangle_eq_pi_div_two, IsMIntegralCurveOn.hasDerivWithinAt, PartitionOfUnity.sum_eq_one', InnerProductGeometry.tan_angle_add_mul_norm_of_inner_eq_zero, DifferentiableOn.rpow, Metric.Sum.one_le_dist_inr_inl, RCLike.complexRingEquiv_apply, Metric.hausdorffDist_self_closure, WithAbs.uniformSpace_comap_eq_of_comp, 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, HarmonicContOnCl.circleAverage_eq, NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, NNReal.dist_agmSequences_fst_snd, EuclideanGeometry.Sphere.nonempty_iff, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_complexPlane, ContinuousMap.HomotopyRel.refl_apply, NumberField.mixedEmbedding.fundamentalCone.volume_interior_eq_volume_closure, Real.fourier_iteratedFDeriv, re_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, LiouvilleWith.mul_nat, ProbabilityTheory.covariance_fst_snd_prod, NNReal.one_le_rpow, CFC.negPart_smul_of_nonpos, SmoothPartitionOfUnity.sum_finsupport', SchwartzMap.smulLeftCLM_real_smul, AddCircle.norm_div_natCast, EReal.toReal_nonpos, Stirling.le_log_factorial_stirling, ProbabilityTheory.variance_le_sub_mul_sub, MeasureTheory.integral_eq_of_hasDerivAt_off_countable_of_le, abs_real_inner_le_norm, Real.dimH_univ_eq_finrank, EuclideanGeometry.Sphere.commonIntTangents_union_commonExtTangents, analyticOnNhd_rexp, Finset.infsep_pos_iff_nontrivial, IntervalIntegrable.comp_sub_right, ODE_solution_unique_of_mem_Icc, MeasureTheory.Measure.integral_comp_inv_mul_left, HasSum.norm_le_of_bounded, ValueDistribution.logCounting_mul_top_eventuallyLE, Metric.comap_dist_right_atTop, ContDiffBump.measure_closedBall_div_le_integral, Orientation.kahler_eq_zero_iff, Real.tanh_eq_sinh_div_cosh, ComputeAsymptotics.MultiseriesExpansion.Multiseries.mem_cons_iff, Real.sqrt_monotone, MeasureTheory.probReal_add_probReal_compl, Real.tan_neg, NormedAddGroup.uniformity_basis_dist, curveIntegralFun_trans_aeeq_right, IsMIntegralCurve.periodic_xor_injective, ContinuousOn.logb, norm_indicator_eq_indicator_norm, TestFunction.contDiff, Real.not_summable_indicator_one_div_natCast, EuclideanGeometry.Sphere.IsTangentAt.angle_eq_pi_div_two, PhragmenLindelof.quadrant_III, unitInterval.qRight_one_left, Metric.uniformEquicontinuous_iff, ModularGroup.tendsto_abs_re_smul, tsum_geometric_le_of_norm_lt_one, BoundedContinuousFunction.integral_const_sub, MeasureTheory.measure_smul_average, Metric.tendsto_atTop', ProbabilityTheory.support_gaussianPDF, cantorStep_mem_cantorSet, MeasureTheory.condExpL1CLM_of_aestronglyMeasurable', Polynomial.gaussNorm_eq_zero_iff, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable, ContinuousMap.Homotopy.ulift_apply, UpperHalfPlane.dist_eq_iff_eq_sinh, Complex.arg_of_re_neg_of_im_nonneg, Module.Basis.norm_mul_le_const_mul_norm, spectralValueTerms_bddAbove, InnerProductSpace.HarmonicOnNhd.comp_CLM, Orientation.oangle_sign_sub_smul_right, Real.continuous_tan, IsUltrametricDist.isUltrametricDist_iff_isNonarchimedean_norm, ZLattice.tsum_norm_rpow_le, PadicInt.exists_mem_range_of_norm_rat_le_one, ProperCone.innerDual_sUnion, AffineSubspace.perpBisector_nonempty, Complex.integral_comp_polarCoord_symm, Seminorm.map_eq_zero_of_norm_zero, DifferentiableAt.rpow_const, smul_closedBall', Complex.uniformContinuous_re, signedDist_apply_apply, HasStrictFDerivAt.hasStrictDerivAt_norm_smul_neg, InformationTheory.measurable_klFun, seminormFromBounded_zero, 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, Real.arcsin_eq_pi_div_two, MeasureTheory.integral_divergence_prod_Icc_of_hasFDerivAt_off_countable_of_le, Orientation.oangle_smul_left_self_of_nonneg, PiTensorProduct.norm_def, strictConcaveOn_log_Iio, Affine.Simplex.altitudeFoot_mem_affineSpan_image_compl, NNReal.rpow_le_one_of_one_le_of_nonpos, UnitAddTorus.mFourierCoeff_toLp, ProbabilityTheory.gaussianReal_map_continuousLinearMap, Real.logb_prod, Manifold.pathELength_def, StieltjesFunction.measure_univ, EuclideanGeometry.oangle_right_eq_arctan_of_oangle_eq_pi_div_two, ODE.FunSpace.continuousOn_comp_compProj, HolderWith.holderWith_zero_of_bounded, Real.exp_sub_sum_range_succ_isLittleO_pow, ContDiff.cos, EuclideanSpace.volume_closedBall_fin_three, strictConcaveOn_univ_of_deriv2_neg, BoxIntegral.Box.isCompact_Icc, NumberField.exists_conjugate_one_le_norm, Metric.unitSphere.coe_mul, seminormFromBounded_one_le, ProbabilityTheory.covariance_fun_div_right, IccLeftChart_extend_interior_pos, Real.isTheta_exp_comp_one, NNReal.rpow_lt_rpow, Congruent.pairwise_dist_eq, Real.hasDerivAt_arsinh, MeasureTheory.SignedMeasure.mutuallySingular_ennreal_iff, Complex.ratCast_im, NumberField.InfinitePlace.norm_embedding_eq, taylor_integral_remainder_of_absolutelyContinuous, norm_lineDeriv_le_of_lipschitz, re_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, SchwartzMap.differentiable, MeasureTheory.integral_Ioi_mul_deriv_eq_deriv_mul, Real.HolderTriple.all_pos, NormedField.exists_norm_lt_one, LinearMap.extendTo𝕜'_apply, Real.cauchy_sub, Real.le_sqrt', pow_mem_closedBall, Orientation.areaForm_swap, ZeroAtInftyContinuousMapClass.norm_le, AkraBazziRecurrence.eventually_one_sub_smoothingFn_gt_const_real, ProperCone.hyperplane_separation', ContinuousLinearMap.iInf_rayleigh_eq_iInf_rayleigh_sphere, hasSum_zeta_four, NumberField.mixedEmbedding.fundamentalCone.smul_mem_of_mem, taylor_tendsto, 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, rescale_to_shell_semi_normed_zpow, ContinuousMultilinearMap.unit_le_opNorm, Real.cos_pi_div_four, Real.Angle.cos_sq_add_sin_sq, HasDerivWithinAt.cos, Real.arith_mean_weighted_of_constant, MeasureTheory.SignedMeasure.exists_isCompl_positive_negative, ProbabilityTheory.Kernel.instIsMarkovKernelCondKernelUnitReal, Real.uniformContinuous_const_mul, Finset.small_alternating_nsmul_of_small_tripling, NumberField.mixedEmbedding.convexBodySum_volume_eq_zero_of_le_zero, ArithmeticFunction.vonMangoldt.support_residueClass_prime_div, Differentiable.sinh, ProbabilityTheory.covarianceOperator_zero, HasFDerivAt.curveIntegral_segment_source, integrableOn_Ioi_cpow_iff, ProbabilityTheory.tendsto_choose_mul_pow_atTop, SameRay.norm_sub, Polynomial.supNorm_X, EReal.nhds_bot_basis, LinearMap.isLowerSet_support_singularValues, isLocalMax_of_sign_deriv, Bundle.ContinuousRiemannianMetric.symm, Real.volume_preimage_mul_left, hasDerivWithinAt_Iic_of_tendsto_deriv, InnerProductGeometry.sin_angle_mul_norm_eq_sin_angle_mul_norm, Path.delayReflLeft_one, norm_indicator_le_of_subset, mellin_hasDerivAt_of_isBigO_rpow, integral_exp_mul_complex_Ioi, exists_hasDerivWithinAt_eq_of_le_of_ge, Chebyshev.psi_eq_zero_of_lt_two, LinearIsometryEquiv.measurePreserving, ProbabilityTheory.cgf_zero_fun, Real.summable_abs_int_rpow, MeasureTheory.SignedMeasure.withDensityᵥ_rnDeriv_eq, setIntegral_Ioi_zero_cpow, Real.multiset_prod_map_rpow, ProbabilityTheory.integrable_rpow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, Function.locallyFinsuppWithin.logCounting_eventually_le, MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left', Subgroup.instIsArithmeticMapSpecialLinearGroupFinOfNatNatIntGeneralLinearGroupRealMapGLOfFiniteIndex, Complex.ofNat_arg, fderiv.log, descPochhammer_eval_div_factorial_le_sum_choose, HasStrictDerivAt.arctan, CircleDeg1Lift.map_le_of_map_zero, dist_pair_smul, ENNReal.ofReal_div_of_pos, FDerivMeasurableAux.norm_sub_le_of_mem_A, ProbabilityTheory.Kernel.tendsto_density_atTop_ae_of_antitone, MulRingSeminorm.map_mul', PeriodPair.weierstrassP_bound, ENNReal.ofReal_mul, Affine.Simplex.finrank_direction_altitude, Real.tan_neg_of_neg_of_pi_div_two_lt, Real.volume_pi_Ico, InformationTheory.tendsto_rightDeriv_klFun_atTop, deriv_norm_ofReal_cpow, norm_sub_le, Real.mk_one, Complex.natCast_im, TemperedDistribution.instFourierAdd, Metric.le_glueDist_inr_inl, intervalIntegral.integral_mono, IntervalIntegrable.comp_add_left_iff, 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, TemperedDistribution.laplacian_eq_fourierMultiplierCLM, Complex.ofReal_zpow, Real.exp_list_sum, Metric.biInter_gt_ball, isBigO_norm_Icc_restrict_atTop, MeasureTheory.Lp.norm_zero, NonUnitalSeminormedRing.norm_mul_le, Module.Dual.norm_extendRCLike_apply_sq, Complex.measurableEquivRealProd_apply, MeasureTheory.ComplexMeasure.singularPart_add_withDensity_rnDeriv_eq, Path.truncate_self, Height.mulHeight_comp_le, nullMeasurableSet_region_between_cc, ProbabilityTheory.stieltjesOfMeasurableRat_le_one, PointedCone.minTensorProduct_eq_max_of_simplicial_generating_right, Real.sin_sq_arctan, Tactic.NormNum.isNat_realSqrt, Polynomial.exists_aroots_norm_sub_lt_of_norm_coeff_sub_lt, EuclideanGeometry.Sphere.IsDiameter.wbtw, Metric.measure_closedBall_pos_iff, hasDerivAt_abs_neg, Affine.Simplex.mongePoint_mem_mongePlane, Orientation.kahler_swap, BoxIntegral.Prepartition.mem_split_iff', intervalIntegral.integral_Iio_sub_Iio', MeasureTheory.integral_mul_upcrossingsBefore_le_integral, 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, ProbabilityTheory.integrable_exp_mul_of_nonneg_of_le, NumberField.tendsto_sub_one_mul_dedekindZeta_nhdsGT, intervalIntegral.integral_comp_add_div, volume_setOf_liouville, StieltjesFunction.id_leftLim, Real.volume_real_Ioo_of_le, Asymptotics.IsBigO.sum_congr, re_herglotzRieszKernel_le, Real.deriv_sqrt_aux, PiLp.nnnorm_toLp_one, intervalIntegral.integral_mono_interval, norm_one', gauge_zero', norm_sub_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zero, exists_contMDiffSection_forall_mem_convex_of_local, Real.iSup_prod_eq_prod_iSup_of_nonneg, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero_aux1, CircleDeg1Lift.ext_iff, UpperHalfPlane.dist_log_im_le, Affine.Simplex.isTangentAt_insphere_touchpoint, InnerProductGeometry.norm_add_eq_add_norm_iff_angle_eq_zero, Complex.ofReal_cpow, 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, ProbabilityTheory.integrable_exp_mul_abs, MeasureTheory.integral_eq_zero_iff_of_nonneg, curveIntegralFun_symm_apply, MeasureTheory.condExp_smul_of_aestronglyMeasurable_right, MeasureTheory.SignedMeasure.mutuallySingular_singularPart, LipschitzWith.locallyBoundedVariationOn, Real.tan_nat_mul_pi_sub, ModularGroup.exists_max_im, Hyperreal.not_infinite_iff_exist_lt_gt, Polynomial.logMahlerMeasure_mul_eq_add_logMahlerMeasure, WithAbs.instUniformContinuousConstSMulReal, Complex.norm_map_zero', 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, tendsto_rpow_atTop, convexOn_of_deriv2_nonneg', norm_le_of_mem_closedBall, LinearEquiv.toSpanNonzeroSingleton_homothety, NumberField.house_mul_le, SeparationQuotient.norm_normedMk_le, ProbabilityTheory.stieltjesOfMeasurableRat_unit_prod, BoxIntegral.Box.splitUpper_def, AddCircle.instIsAddHaarMeasureRealVolume, Matrix.PosSemidef.det_sqrt, StrictConvexSpace.of_norm_combo_ne_one, multipliable_norm_one_add_of_summable_norm, Real.arccos_eq_pi_div_two_sub_arcsin, norm_circleMap_zero, MeasureTheory.Measure.exists_measurable_map_eq, ProbabilityTheory.cdf_eq_real, ProbabilityTheory.cgf_zero, Orientation.rotation_map_complex, Real.cos_add_cos, BoxIntegral.HasIntegral.smul, Real.deriv_rpow_const, Real.sqrt_sq_eq_abs, ProbabilityTheory.integrable_exp_mul_of_abs_le, 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, Complex.tendsto_one_add_cpow_exp_of_tendsto, 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, EuclideanSpace.real_norm_sq_eq, Continuous.integral_pos_of_hasCompactSupport_nonneg_nonzero, SameRay.inv_norm_smul_eq, StrictConcaveOn.lt_slope_of_hasDerivWithinAt_Iio, DifferentiableWithinAt.dist, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff', MeasureTheory.integrable_thickenedIndicator, TestFunction.limitCLM_apply, Real.tendsto_exp_neg_atTop_nhds_zero, NormedField.denselyOrdered_range_norm, convexOn_rpow_left, exists_dist_eq, Real.liminf_of_not_isBoundedUnder, hasDerivWithinAt_abs, ProbabilityTheory.integrable_pow_mul_exp_of_integrable_exp_mul, Path.continuous_extend, contDiff_circleMap, ContDiffBump.nonneg, ProbabilityTheory.covariance_mul_const_left, ProbabilityTheory.covariance_fun_neg_right, Real.sin_pos_of_pos_of_le_two, IsUltrametricDist.dist_triangle_max, riemannZeta_im_eq_zero_of_one_lt, MeasureTheory.MemLp.pos_part, HurwitzZeta.hasSum_hurwitzZeta_of_one_lt_re, Subgroup.IsArithmetic.isCusp_iff_isCusp_SL2Z, MeasureTheory.integrable_of_tendsto, Affine.Simplex.ExcenterExists.affineSpan_faceOpposite_eq_orthRadius, Real.Angle.sin_add_pi, Real.pow_lt_iff_lt_log, ContinuousLinearEquiv.one_le_norm_mul_norm_symm, tendsto_smoothingFun_comp, ProbabilityTheory.IndepFun.variance_fun_add, Real.Angle.toReal_coe_eq_self_iff, HurwitzZeta.evenKernel_eq_cosKernel_of_zero, ContDiffMapSupportedIn.seminorm_le_iff, intervalIntegral.integral_mono_on_of_le_Ioo, SzemerediRegularity.eps_pos, PartitionOfUnity.exists_finset_nhds, eventually_norm_mfderivWithin_symm_extChartAt_lt, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_integral_of_antitone, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, ModularGroup.exists_bound_of_subgroup_invariant_of_isBigO, Affine.Simplex.inner_mongePoint_vsub_face_centroid_vsub, Hyperreal.tendsto_iff_forall, AkraBazziRecurrence.sumTransform_def, ContinuousMultilinearMap.norm_compContinuous_linearIsometry_le, norm_pow_le, Complex.arg_of_im_pos, Path.extend_trans_of_le_half, Affine.Simplex.ninePointCircle_restrict, instPathConnectedSpaceElemForallRealStdSimplexOfNonempty, EuclideanGeometry.tan_oangle_left_mul_dist_of_oangle_eq_pi_div_two, UpperHalfPlane.im_le_im_mul_exp_dist, BoundedVariationOn.intervalIntegrable_deriv, 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, Asymptotics.IsLittleO.abs_abs, MeasureTheory.tendstoInMeasure_iff_norm, Real.rpow_lt_rpow_of_neg, AbsolutelyContinuousOnInterval.tendsto_volume_totalLengthFilter_nhds_zero, Complex.tendsto_exp_comap_re_atTop, MeasureTheory.Measure.integral_comp_smul_of_nonneg, measurable_circleMap, convex_halfSpace_re_le, Complex.reCLM_coe, VectorFourier.hasFDerivAt_fourierIntegral, SzemerediRegularity.hundred_lt_pow_initialBound_mul, MeasureTheory.Measure.haar.prehaar_pos, Real.toNNReal_sum_of_nonneg, BoundedContinuousFunction.exists_extension_norm_eq_of_isClosedEmbedding, norm_pos_iff', Tactic.ComputeAsymptotics.Majorized.mul, Real.Angle.sin_neg, ContDiffAt.sinh, Continuous.pathExtend, FiniteDimensional.complexToReal, intervalIntegral.hasSum_intervalIntegral_of_summable_norm, AntilipschitzWith.le_mul_norm', HurwitzZeta.hurwitzZetaEven_apply_zero, Mathlib.Meta.NormNum.isNNRat_rpow_pos, MeasureTheory.Measure.addHaar_unitClosedBall_eq_addHaar_unitBall, HomotopyGroup.genLoopEquivOfUnique_transAt, NNReal.coe_eq_zero, Complex.arg_neg_eq_arg_sub_pi_of_im_pos, exists_iUnion_ball_eq_radius_pos_lt, Real.neg_one_lt_goldenConj, IsUltrametricDist.norm_tprod_le_of_forall_le_of_nonneg, MeasureTheory.eLpNorm_ofReal, Seminorm.ball_norm_mul_subset, Real.sSup_nonpos, DirichletCharacter.unit_norm_eq_one, EReal.nhds_top', IsMinOn.of_isLocalMinOn_of_convexOn_Icc, Padic.norm_eq_zpow_log_mulValuation, lipschitzOnWith_iff_norm_inv_mul_le, MeasureTheory.ofReal_setAverage, deriv.lhopital_zero_left_on_Ioo, Real.arcsin_le_pi_div_two, Complex.continuous_re, Valued.integer.exists_norm_lt_one, Real.sin_sub, Real.deriv_sinh, intervalIntegral.integral_mul_deriv_eq_deriv_mul, exists_ratio_deriv_eq_ratio_slope, MeasureTheory.Integrable.tendsto_eLpNorm_condExp, UpperHalfPlane.isBoundedAtImInfty_iff, ClosedSubmodule.inner_real_eq_re_inner, NNReal.arith_mean_le_rpow_mean, not_summable_of_antitone_of_neg, CircleDeg1Lift.forall_map_sub_of_Icc, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding, ContinuousMap.norm_eq_iSup_norm, norm_cfcₙ_lt, ContinuousMultilinearMap.opNorm_smul_le, Real.continuousAt_rpow_const, Asymptotics.div_isBoundedUnder_of_isBigO, Real.cos_three_mul, ENNReal.prod_rpow_of_ne_top, Real.cos_two_pi, EuclideanGeometry.oangle_pointReflection_left, MeasureTheory.upcrossingStrat_le_one, LipschitzOnWith.norm_sub_le_of_le, PartitionOfUnity.IsSubordinate.continuous_finsum_smul, MeasureTheory.convolution_precompR_apply, Irrational.neg, AlgebraNorm.ext_iff, ProbabilityTheory.IsMeasurableRatCDF.instIsProbabilityMeasure_stieltjesFunction, EReal.canLift, MultilinearMap.norm_image_sub_le_of_bound', Metric.isBounded_iff_eventually, SimpleGraph.triangleRemovalBound_mul_cube_lt, orthonormal_fourier, SchwartzMap.compSubConstCLM_apply, ProbabilityTheory.condIndepSets_singleton_iff, Real.log_rpow, ContMDiff.piecewise_Iic, irrational_intCast_sub_iff, isCusp_SL2Z_iff', BoundedVariationOn.ae_differentiableAt_of_mem_uIcc, Real.mul_le_sin, VectorFourier.fourierIntegral_iteratedFDeriv, InnerProductGeometry.angle_neg_right, ModularGroup.lcRow0Extend_symm_apply, TopologicalAddGroup.IsSES.pushforward_apply_apply, Polynomial.Chebyshev.coeff_eq_iff_of_forall_abs_le_one, ZLattice.covolume.tendsto_card_div_pow, Real.volume_Icc_pi, ProbabilityTheory.Kernel.rnDeriv_def', MonotoneOn.sum_le_integral, ContinuousMap.Homotopy.cast_apply, norm_injOn_ray_right, Metric.diam_eq_zero_of_unbounded, InformationTheory.hasDerivAt_klFun, Real.binEntropy_nonpos_of_nonpos, MeasureTheory.IntegrableOn.continuousOn_Ici_primitive_Ici, Real.abs_exp_sub_one_sub_id_le, MeasureTheory.setIntegral_condExpL2_indicator, ContinuousMap.toNNReal_algebraMap, norm_image_sub_le_of_norm_deriv_le_segment, Path.toHomotopyConst_apply, MeasureTheory.eLpNorm_indicator_sub_le_of_dist_bdd, NumberField.IsCMField.regulator_div_regulator_eq_two_pow_mul_indexRealUnits_inv, integrableOn_Ioi_norm_cpow_iff, contMDiff_coe_sphere, niven_sin, Real.tsum_exp_neg_mul_int_sq, integral_cos_pow_aux, HurwitzZeta.expZeta_one_sub, MeasureTheory.JordanDecomposition.real_smul_nonneg, IsConvexMetricSpace.dist_convexCombination_map_le', CircleDeg1Lift.inf_apply, unitInterval.measurePreserving_symm, ContinuousMultilinearMap.norm_restr, Real.tan_two_mul, antilipschitzWith_iff_exists_mul_le_norm', StrictConvexOn.slope_lt_deriv, ContinuousMultilinearMap.norm_image_sub_le, Seminorm.closedBall_zero_eq_preimage_closedBall, EisensteinSeries.r_pos, gauge_eq_zero, Metric.mem_thickening_iff, ProbabilityTheory.isPosSemidef_covarianceBilin, tendsto_norm_neg_add_self_nhdsGE, diam_stdSimplex, BoundedContinuousFunction.mem_charPoly, NNReal.image_coe_uIcc, Real.negMulLog_mul, EisensteinSeries.r1_pos, MeasureTheory.L1.SimpleFunc.integral_eq_norm_posPart_sub, MeasureTheory.JordanDecomposition.real_smul_neg, intervalIntegral.intervalIntegrable_sin, stereographic_apply_neg, LinearIsometry.norm_toContinuousLinearMap, intervalIntegral.abs_intervalIntegral_eq, StarAlgHom.continuous_realContinuousMapOfNNReal, Convex.image_sub_lt_mul_sub_of_deriv_lt, ModularGroup.denom_apply, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_left, Orientation.kahler_comp_rightAngleRotation, Polynomial.card_eq_of_natDegree_le_of_coeff_le, Real.inner_le_Lp_mul_Lq_hasSum_of_nonneg, Seminorm.ball_smul, Even.strictConvexOn_pow, LiouvilleNumber.summable, InformationTheory.toReal_klDiv, TemperedDistribution.instFourierPairInv, Real.Gamma_one, BoundedContinuousFunction.charAlgHom_apply, InnerProductGeometry.sin_angle_nonneg, MeasureTheory.SimpleFunc.setToSimpleFunc_add_left, Complex.norm_natCast, EuclideanGeometry.oangle_eq_pi_iff_sbtw, TemperedDistribution.instFourierPair, Complex.arg_ofReal_of_nonneg, 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.sqrt_mul_self, Real.sinhHomeomorph_symm_apply, Complex.lift_apply, ENNReal.rpow_one, HasDerivAt.lhopital_zero_atBot_on_Iio, ContinuousLinearMap.rayleighQuotient_apply_zero, intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_left, IsApproximateSubgroup.subgroup, Real.arccos_image_Icc, ProbabilityTheory.covariance_add_const_right, Commute.cfc_real, Real.smoothTransition.one_of_one_le, Icc_chartedSpaceChartAt_of_le_top, dist_triangle4, TemperedDistribution.delta_apply, torusMap_eq_center_iff, Urysohns.CU.approx_nonneg, isTheta_choose, MeasureTheory.memLp_haarAddCircle_iff, EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical, affinity_unitClosedBall, ProbabilityTheory.gaussianReal_of_var_ne_zero, ContinuousLinearMap.contDiffPointwiseHolderAt, NumberField.Units.instZLattice_unitLattice, Manifold.pathELength_eq_lintegral_mfderivWithin_Icc, Real.continuous_log, ENNReal.rpow_natCast, Asymptotics.IsBigOWith.trans, NNReal.rpow_inv_rpow, ContDiffBump.normed_le_div_measure_closedBall_rOut, curveIntegralFun_refl, Asymptotics.IsBigOWith.rpow, Path.extend_apply, IsUltrametricDist.norm_sum_le_of_forall_le_of_nonempty, Affine.Simplex.circumcenter_eq_affineCombination_of_pointsWithCircumcenter, geometric_hahn_banach_of_nonempty_interior_point, Submodule.norm_eq_iInf_iff_inner_eq_zero, mem_closure_one_iff_norm, NumberField.FinitePlace.norm_embedding, InnerProductGeometry.angle_zero_right, UpperHalfPlane.dist_eq_iff_eq_sq_sinh, Real.rpow_mul_natCast, MeasureTheory.BorelCantelli.predictablePart_process_ae_eq, AddCircle.ergodic_nsmul_add, Finset.coe_infsep_of_offDiag_nonempty, Module.Dual.extendRCLike_apply, Real.ediam_Ioc, Real.log_neg_of_lt_zero, ProbabilityTheory.iIndepSet.condExp_indicator_filtrationOfSet_ae_eq, eigenvalue_nonneg_of_nonneg, MeasureTheory.integral_singleton', ContinuousWithinAt.rexp, NumberField.InfiniteAdeleRing.mixedEmbedding_eq_algebraMap_comp, MeasureTheory.measureReal_union_null_iff, MeasureTheory.lpNorm_mul_natCast, lp.summable_mul, NumberField.mulHeight_eq, ProbabilityTheory.tendsto_integral_truncation, ProbabilityTheory.noAtoms_gaussianReal, MeasureTheory.integral_exp_tilted, NNReal.isCoboundedUnder_le_toReal, NumberField.mixedEmbedding.convexBodySum_compact, Unitary.norm_sub_one_lt_two_iff, exists_norm_le_le_norm_sub_of_finset, ContinuousMap.continuous_toNNReal, Orientation.volumeForm_zero_pos, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_mgf', Real.continuous_sqrt, NNReal.coe_prod, spectralNorm_eq_iSup_of_finiteDimensional_normal, Metric.exists_forall_closedEBall_subset_aux₁, ContinuousMap.Homotopy.pathExtend_evalAt, Polynomial.coeff_le_of_roots_le, ProbabilityTheory.isProbabilityMeasure_gammaMeasure, Set.Nontrivial.infsep_of_fintype, Real.HolderConjugate.one_sub_inv, Real.cos_pi_div_sixteen, fourierIntegral_gaussian_pi, MeasureTheory.L1.setToL1_mono_left', CircleDeg1Lift.lt_map_of_nat_lt_translationNumber, Real.Angle.cos_add_pi, selfAdjoint.imaginaryPart_coe, Rat.AbsoluteValue.equiv_real_of_unbounded, Real.zpow_le_of_le_log, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, MeasureTheory.AEFinStronglyMeasurable.ae_nonneg_of_forall_setIntegral_nonneg, PhragmenLindelof.eqOn_quadrant_II, AddCircle.dense_addSubgroup_iff_ne_zmultiples, Bundle.ContinuousRiemannianMetric.continuous, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_adicAbv, AddSubgroup.tendsto_zmultiples_subtype_cofinite, Real.ofCauchy_nnratCast, ProbabilityTheory.complexMGF_mul_I, Affine.Simplex.affineSpan_faceOpposite_eq_orthRadius_insphere, ModularGroup.im_T_smul, Metric.diam_closedBall_eq, indiscreteTopology_iff_forall_norm_eq_zero, Matrix.IsHermitian.charpoly_cfc_eq, Nat.preimage_closedBall, Real.BohrMollerup.f_nat_eq, NormedSpace.norm_expSeries_summable, UniformConvexSpace.uniform_convex, Real.coe_toNNReal', Real.pow_arith_mean_le_arith_mean_pow_of_even, MeasureTheory.llr_tilted_right, CFC.rpow_one, IsGreatest.norm_cfcₙ, Real.one_add_tan_sq_mul_cos_sq_eq_one, CFC.rpow_neg, ModularGroup.exists_bound_of_subgroup_invariant, 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, MeasureTheory.condExp_mul_of_aestronglyMeasurable_right, Multipliable.eventually_bounded_finset_prod, Real.rpow_sub', RCLike.re_monotone, Real.logb_neg_base_eq_logb, LSeries.summable_real_of_abscissaOfAbsConv_lt, Complex.norm_exp_I_mul_ofReal_sub_one, injOn_circleMap_of_abs_sub_le', integral_exp_mul_complex, Polynomial.exists_eq_gaussNorm, Real.limsSup_of_not_isCobounded, ContDiff.log, dist_le_of_approx_trajectories_ODE, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, Real.measurable_sinc, CuspFormClass.petersson_bounded_left, Asymptotics.IsLittleO.of_abs_right, Set.infsep_le_of_mem_of_edist_le, memℓp_norm_iff, MeasureTheory.AEStronglyMeasurable.dist, CircleDeg1Lift.translate_iterate, Quaternion.nnnorm_star, UpperHalfPlane.coe_toSL2R, Continuous.rpow, 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, DifferentiableAt.fderiv_norm_self, Real.GammaSeq_tendsto_Gamma, ProbabilityTheory.Kernel.integrable_densityProcess, edist_le_ofReal, norm_zero, finite_integral_rpow_sub_one_pow_aux, RCLike.im_ofReal_pow, IsCoveringMap.liftPath_zero, Real.holderTriple_iff, Real.cos_two_pi_sub, EuclideanGeometry.Sphere.orthRadius_center, NumberField.Units.span_basisOfIsMaxRank, convexOn_dist, MultilinearMap.bound_of_shell_of_norm_map_coord_zero, EReal.preimage_coe_Ioo_top, ConcaveOn.condExp_map_le, Real.arctan_add_arctan_lt_pi_div_two, ConvexOn.locallyLipschitz, ENNReal.measurable_toReal, UpperHalfPlane.isPretransitiveGL2R, Complex.ofReal_comp_sub, AkraBazziRecurrence.g_nonneg, MeasureTheory.Submartingale.sum_mul_sub, nnnorm_cfcₙ_nnreal_lt, NumberField.mixedEmbedding.fundamentalCone.norm_pos_of_mem, CFC.sqrt_eq_rpow, ProbabilityTheory.covariance_zero_right, Real.arsinh_nonpos_iff, mem_posTangentConeAt_of_segment_subset, real_linearMap_map_smul_complex, instIsManifoldRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, SmoothBumpCovering.toSmoothPartitionOfUnity_apply, Complex.arg_mul_cos_add_sin_mul_I_eq_toIocMod, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, 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, MeasureTheory.setToFun_smul_left', Complex.sub_re, EuclideanGeometry.dist_orthogonalProjection_eq_of_two_zsmul_oangle_eq, Real.Angle.coe_add, cfcₙ_re_id, Function.hasTemperateGrowth_iff_isBigO, range_stereographic_symm, FiniteDimensional.rclike_to_real, Complex.sq_norm_sub_sq_re, Complex.comap_exp_nhds_zero, Complex.equivRealProdCLM_symm_apply, ContinuousLinearMap.norm_eq_iSup_rayleighQuotient, AnalyticAt.log, Asymptotics.IsBigOWith.right_le_sub_of_lt_one, Real.hasSum_log_one_add, IsLocalMaxOn.norm_add_sameRay, ProbabilityTheory.covariance_sum_right', ProbabilityTheory.monotone_defaultRatCDF, Seminorm.convexOn, Real.BohrMollerup.f_add_nat_ge, 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, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left', mellinInv_eq_fourierIntegralInv, ProbabilityTheory.strong_law_ae, ODE_solution_unique, NumberField.HeightOneSpectrum.adicAbv_def, PhragmenLindelof.eq_zero_on_right_half_plane_of_superexponential_decay, AkraBazziRecurrence.GrowsPolynomially.add, PhragmenLindelof.eq_zero_on_vertical_strip, Filter.Tendsto.arccos_nhdsLE, Real.tanh_arcosh, zero_eq_dist, Real.HolderTriple.inv_nonneg, HasDerivWithinAt.norm_sq, Complex.norm_add_eq, HasGradientAtFilter.hasDerivAtFilter', Real.Gamma_one_half_eq, CFC.norm_star_mul_mul_self_of_nonneg, 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, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_of_norm_le, Orientation.volumeForm_robust, NNReal.continuous_coe, MonotoneOn.integral_le_sum_Ico, PiLp.volume_preserving_toLp, Real.smoothTransition.zero, Real.pi_div_two_eq_arcsin, CompactlySupportedContinuousMap.coe_toRealLinearMap, Complex.norm_cpow_of_ne_zero, Polynomial.mahlerMeasure_le_sqrt_natDegree_add_one_mul_supNorm, LowerSemicontinuousOn.isClosed_re_epigraph, Complex.interior_preimage_re, dist_nonneg, InnerProductGeometry.norm_toLp_symm_crossProduct, QuotientAddGroup.norm_lt_iff, ContractingWith.aposteriori_dist_iterate_fixedPoint_le, lt_geom, Real.tendsto_of_bddAbove_monotone, IsLocalExtr.fderiv_eq_zero, NNReal.bddBelow_coe, ZSpan.measureReal_fundamentalDomain, PhragmenLindelof.eq_zero_on_quadrant_IV, Real.two_le_pi, Orientation.tan_oangle_sub_right_mul_norm_of_oangle_eq_pi_div_two, SmoothPartitionOfUnity.contDiffAt_finsum, memℓp_gen_iff, intervalIntegral.intervalIntegral_pos_of_pos, MeasureTheory.Submartingale.bddAbove_iff_exists_tendsto, fourier_one, Affine.Simplex.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, IsIntegralCurveAt.comp_sub, isOpenEmbedding_stereographic_symm, 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, ProbabilityTheory.covariance_add_const_left, Module.Basis.norm_smul, intervalIntegral.integral_hasDerivWithinAt_left, Similar.exists_dist_eq, ContinuousLinearMap.bounds_nonempty, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, continuous_convexComboPair', 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, ContinuousLinearMap.opNorm_le_of_shell', coe_normGroupNorm, ENNReal.ofReal_lt_iff_lt_toReal, MeasureTheory.measureReal_nonneg, not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_within_diff_singleton, Real.toNNReal_div, Real.exp_arcosh, Complex.im_le_norm, Real.totallyBounded_ball, TopCat.toSSetObj₀Equiv_symm_apply, exists_extension_of_le_sublinear, 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, Polynomial.gaussNorm_mul, MeasureTheory.MemLp.integrable_norm_pow, norm_sub_norm_le_norm_neg_add, continuousMap_mem_polynomialFunctions_closure, AkraBazziRecurrence.isBigO_symm_asympBound, Orientation.measure_eq_volume, ProbabilityTheory.abs_truncation_le_bound, BoxIntegral.Box.nndist_le_distortion_mul, Complex.integral_exp_neg_rpow, ContinuousLinearMapWOT.instLocallyConvexSpace, inner_self_im, measurableEmbedding_sigmoid, Asymptotics.isLittleO_norm_right, LipschitzOnWith.norm_neg_add_le, MeasureTheory.Measure.measure_preimage_isAddLeftInvariant_eq_smul_of_hasCompactSupport, lintegral_comp_pi_polarCoord_symm, MeasureTheory.lpNorm_smul_measure_of_ne_zero, BoundingSieve.one_le_y, Real.harm_mean_le_geom_mean, SimplexCategory.toTop_obj, irrational_sqrt_natCast_iff, Real.HolderTriple.left_pos, NumberField.mixedEmbedding.fundamentalCone.subset_interior_normLeOne, isBigO_rpow_top_log_smul, LipschitzWith.of_le_add, GenLoop.mk_apply, spectrum_star_mul_self_nonneg, 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, NNReal.rpow_inv_rpow_eq_iff, Complex.sq_norm, Complex.norm_log_sub_logTaylor_le, Metric.Snowflaking.image_ofSnowflaking_eball, MeasureTheory.SimpleFunc.exists_forall_norm_le, Polynomial.gaussNorm_zero, NNReal.rpow_sub_natCast, Real.arsinh_nonneg_iff, EReal.coe_natCast, Real.volume_singleton, ContinuousMap.Homotopy.curveIntegral_add_curveIntegral_eq_of_hasFDerivWithinAt_off_countable, HomotopyGroup.transAt_indep, SchwartzMap.smulLeftCLM_sum, PiTensorProduct.projectiveSeminorm_tprod_le, EReal.tendsto_toReal_atTop, MeasureTheory.Measure.haar.prehaar_empty, Real.smoothTransition.contDiffAt, Complex.measurable_re, NNReal.isEmbedding_coe, le_ofDigits_cantorToTernary_sum, mem_closedBall_iff_norm, taylor_mean_remainder_lagrange_iteratedDeriv, 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, IsIntegralCurveOn.comp_add, TopCat.I.homeomorph_one, 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, Real.le_zpow_iff_log_le, ProbabilityTheory.analyticAt_mgf, BoxIntegral.Box.measure_coe_lt_top, Real.two_mul_arctan, cfc_real_eq_nnreal, 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, NumberField.Units.regulator_eq_det, ProbabilityTheory.HasLaw.covariance_comp, orthonormalBasis_one_dim, Height.AdmissibleAbsValues.isNonarchimedean, ConvexOn.isBoundedUnder_abs, ContDiffBump.contDiff, Complex.closure_setOf_lt_im, Real.hasDerivWithinAt_arccos_Ici, IsLocalHomeomorph.continuous_lift, RightDerivMeasurableAux.differentiable_set_subset_D, EuclideanGeometry.Sphere.power_pos_iff_radius_lt_dist_center, Real.continuousAt_rpow_of_pos, cfcₙHom_integral, MeasureTheory.posConvolution_eq_convolution_indicator, unitInterval.symm_projIcc, MeasureTheory.setIntegral_condExpInd, ContinuousLinearMap.isPositive_def, indicator_norm_le_norm_self, ball_add_ball, MeasureTheory.Measure.haar.addCHaar_nonneg, continuous_dist, ContinuousMap.Homotopy.compContinuousMap_apply, AddCircle.add_projection_respects_measure, Seminorm.gaugeSeminorm_ball, integral_le_sum_mul_Ico_of_antitone_monotone, ContinuousMap.dist_lt_of_dist_lt_modulus, LipschitzWith.ae_lineDifferentiableAt, Metric.Snowflaking.preimage_toSnowflaking_emetricClosedBall, Metric.eventually_nhds_iff, EuclideanGeometry.oangle_midpoint_rev_left, ProbabilityTheory.lintegral_exponentialPDF_eq_antiDeriv, EReal.tendsto_toReal_atBot, ENNReal.mul_rpow_of_ne_zero, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_add, InnerProductGeometry.norm_add_eq_add_norm_of_angle_eq_zero, stereo_left_inv, Real.toNNReal_le_one, InformationTheory.leftDeriv_klFun, Real.exp_monotone, Real.lt_cauchy, integral_bernoulliFun_eq_zero, Path.cast_coe, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux1, tendsto_integral_exp_smul_cocompact, ENNReal.ofNat_le_ofReal, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, ContinuousMap.Homotopy.comp_apply, Real.logb_zero_left_eq_zero, MeasureTheory.integral_comp_rpow_Ioi_of_pos, Real.pi_div_two_pos, Orientation.sin_oangle_add_right_mul_norm_of_oangle_eq_pi_div_two, Complex.dist_self_conj, Affine.Triangle.touchpoint_singleton_sbtw, ProbabilityTheory.eqOn_complexMGF_of_mgf, Complex.HadamardThreeLines.mem_verticalClosedStrip_of_scale_id_mem_verticalClosedStrip, Real.le_exp_log, intervalIntegral.FTCFilter.pure, StarAlgHom.realContinuousMapOfNNReal_apply, curveIntegral_segment, MultilinearMap.restr_norm_le, TestFunction.postcompCLM_apply, irrational_sqrt_ratCast_iff_of_nonneg, InnerProductSpace.Core.normSq_eq_zero_of_eq_zero, Path.ofLine_mem, tendsto_norm_div_self_nhdsNE, Complex.ofReal_neg, ProbabilityTheory.Kernel.measurable_density, controlled_closure_of_complete, LiouvilleWith.add_rat, Real.rpow_eq_zero_iff_of_nonneg, MeasureTheory.integrable_posConvolution, NormedAddGroupHom.mkNormedAddGroupHom_norm_le, Real.tan_div_sqrt_one_add_tan_sq, AddCircle.exists_norm_nsmul_le, ProbabilityTheory.covariance_sum_right, Real.arctan_eq_neg_pi_div_four, isEquivalent_choose, Real.log_lt_iff_lt_exp, Real.fourierIntegral_continuousLinearMap_apply, MeasureTheory.SignedMeasure.totalVariation_zero, Real.sqrt_le_iff, NNReal.lt_iff_exists_rat_btwn, PadicInt.mk_coe, NNReal.rpow_sub, ExistsContDiffBumpBase.u_le_one, ProbabilityTheory.integrable_rpow_abs_mul_exp_of_mem_interior_integrableExpSet, MeasureTheory.Integrable.tendsto_ae_condExp, HasFDerivWithinAt.abs_of_neg, 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, NNReal.rpow_sub', IsGreatest.norm_cfc, eqOn_abs_add_one_of_isMIntegralCurveOn_Ioo, inner_re_zero_left, summable_schlomilch_iff_of_nonneg, IsSelfAdjoint.neg_algebraMap_norm_le_self, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, Real.sqrt_lt_sqrt_iff_of_pos, Metric.cthickening_eq_iInter_thickening, Real.exists_isMinOn_Gamma_Ioi, Affine.Simplex.exradius_map, Hyperreal.isSt_sSup, AbsoluteValue.Completion.locallyCompactSpace, IsCoercive.range_eq_top, 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, Real.prod_one_add_le_exp_sum, Complex.div_ofNat, intervalIntegral.FTCFilter.nhdsWithinSingleton, MeasureTheory.MemLp.memLp_liftIoc, ProbabilityTheory.differentiableAt_mgf, InnerProductSpace.Core.cauchy_schwarz_aux, InnerProductGeometry.angle_add_le_pi_div_two_of_inner_eq_zero, ODE.FunSpace.dist_iterate_iterate_next_le_of_lipschitzWith, Set.OrdConnected.image_ennreal_ofReal, Real.tendsto_exp_comp_nhds_zero, EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero, Real.surjOn_logb', 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, Metric.Snowflaking.image_toSnowflaking_eball, PhragmenLindelof.right_half_plane_of_bounded_on_real, Asymptotics.IsLittleO.bound, ODE_solution_unique_of_mem_Ioo, Orientation.oangle_eq_zero_iff_sameRay, RCLike.conjLIE_apply, ValueDistribution.logCounting_nonneg, Real.measurable_cos, unitSphereToUnits_apply_coe, closedBall_add_ball, Complex.uniformlyContinuous_re, ENNReal.rpow_arith_mean_le_arith_mean_rpow, WithAbs.tendsto_one_div_one_add_pow_nhds_one, Complex.map_exp_comap_re_atTop, Real.continuousAt_const_rpow', Real.isPiSystem_Iic_rat, ProbabilityTheory.moment_zero, convexOn_univ_norm, ZLattice.tsumNormRPowBound_spec, BoxIntegral.Box.measure_Icc_lt_top, RCLike.summable_ofReal, edist_lt_ofReal, LinearIsometryEquiv.reflections_generate_dim_aux, Projectivization.logHeight_nonneg, 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, ContDiffOn.rpow_const_of_ne, 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, MeasureTheory.L1.setToL1_eq_setToL1SCLM, intervalIntegral.integral_deriv_comp_smul_deriv', Quaternion.coeComplex_add, MeasureTheory.integral2_divergence_prod_of_hasFDerivAt_off_countable, ZLattice.covolume_div_covolume_eq_relIndex, Real.volume_emetric_closedBall, analyticOn_log, ConvexOn.exists_affine_le_real, MeasureTheory.Measure.haar.mem_prehaar_empty, gauge_lt_of_mem_smul, Affine.Triangle.dist_circumcenter_reflection_orthocenter, MeasureTheory.norm_condExpL2_coe_le, LipschitzWith.mapsTo_ball, Seminorm.ball_zero_eq_preimage_ball, Real.sq_le, IsometryEquiv.coe_toRealAffineIsometryEquiv, lp.norm_const_smul, MeasureTheory.lpNorm_measure_zero, AkraBazziRecurrence.GrowsPolynomially.norm, HurwitzZeta.hasSum_nat_completedCosZeta, NormedAlgebra.exists_isMinOn_norm_sub_smul, tendsto_sub_mul_tsum_nat_cpow, Polynomial.toAddCircle.integrable, IsApproximateAddSubgroup.nsmul_inter_nsmul, intervalIntegral.FTCFilter.le_nhds, Complex.norm_cderiv_le, MeasureTheory.IntegrableOn.continuousOn_Iic_primitive_Iic, Cardinal.cantorFunctionAux_nonneg, AddCircle.instHasAddFundamentalDomainSubtypeAddOppositeRealMemAddSubgroupOpZmultiples, ENNReal.ofReal_limsup_toReal, Besicovitch.ae_tendsto_rnDeriv, BumpCovering.contMDiff_toPartitionOfUnity, fourier_zero, ContDiffBump.hasCompactSupport, PhragmenLindelof.right_half_plane_of_tendsto_zero_on_real, Real.log_pos_iff, WithCStarModule.prod_norm_le_norm_add, Real.arcosh_injOn, Complex.normSq_I, MeasureTheory.Submartingale.smul_nonneg, EReal.mem_nhds_bot_iff, RCLike.imLm_coe, EuclideanGeometry.Sphere.inter_orthRadius_eq_empty_of_finrank_eq_one, Metric.ball_eq_ball, PiLp.edist_eq_sum, Complex.partialGamma_add_one, ContinuousLinearMap.exists_approx_preimage_norm_le, Real.sqrt_two_lt_three_halves, MeasureTheory.L1.setToL1_nonneg, BoundedContinuousFunction.bddAbove_range_norm_comp, fourier_neg', openSegment_subset_ball_of_ne, ValueDistribution.logCounting_const, NormedSpace.normalize_smul, Tactic.NormNum.isNNRat_realSqrt_of_isNNRat, Real.cos_le_one_sub_mul_cos_sq, analyticOnNhd_log, ProbabilityTheory.condVar_smul, NNReal.coe_multiset_prod, SchwartzMap.fourierMultiplierCLM_sum, 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.nnabs_of_nonneg, Real.coe_expOrderIso_apply, Complex.norm_cpow_of_imp, Real.abs_le_sqrt, ContinuousMultilinearMap.le_opNorm, approxOrderOf.image_pow_subset_of_coprime, ConvexBody.coe_smul, MeasureTheory.MemLp.neg_part, 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, ProbabilityTheory.iteratedDeriv_mgf, Asymptotics.isBigOWith_norm_norm, isAddFundamentalDomain_Ioc, Path.subpathAux_one, Real.sqrt_le_sqrt_iff, SchwartzMap.delta_apply, InnerProductGeometry.angle_eq_zero_iff, Path.continuous_delayReflRight, Affine.Simplex.abs_inner_vsub_altitudeFoot_lt_mul, MeasureTheory.AEContinuous.hasBoxIntegral, 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, sum_mul_eq_sub_integral_mul', IsMinOn.hasLineDerivAt_eq_zero, RCLike.div_im, norm_le_add_norm_add', Real.rpow_lt_rpow_left_iff, HasDerivWithinAt.const_rpow, 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, hasFDerivAt_norm_rpow, measurableEmbedding_sigmoid_comp_embeddingReal, Real.ofDigitsTerm_le, intervalIntegral.integral_eq_sub_of_hasDerivAt_of_tendsto, lebesgue_number_lemma_of_metric, Complex.re_comp_balance, MulAlgebraNormClass.toMulRingNormClass, trapezoidal_error_le_of_c2, LocallyLipschitz.const_max, dist_birkhoffAverage_apply_birkhoffAverage, StrictConvexSpace.of_pairwise_sphere_norm_ne_two, ProbabilityTheory.cdf_nonneg, isMIntegralCurveOn_comp_add, ProbabilityTheory.exponentialPDFReal_nonneg, MeasureTheory.lowerCrossingTime_zero, MeasureTheory.exists_subset_real_measurableEquiv, unitInterval.lt_symm_comm, curveIntegral_def, ENNReal.ofReal_limsup, ENNReal.rpow_inv_le_iff, Real.volume_ball, ENNReal.eventually_pow_one_div_le, mellinInv_eq_fourierInv, MeasureTheory.lintegral_rpow_eq_lintegral_meas_le_mul, intervalIntegral.integrableOn_Ioo_rpow_iff, Real.Angle.coe_abs_toReal_of_sign_nonneg, GenLoop.instContinuousEval, AkraBazziRecurrence.one_add_smoothingFn_le_two, CFC.rpow_rpow_inv, MeasureTheory.Measure.addHaar_preimage_continuousLinearMap, NormSMulClass.norm_smul, Euclidean.nhds_basis_closedBall, Path.Homotopy.hcomp_half, HasFPowerSeriesOnBall.uniform_geometric_approx, ENNReal.rpow_inv_rpow_eq_iff, MeasureTheory.integrableOn_image_iff_integrableOn_deriv_smul_of_monotoneOn, Stirling.stirlingSeq_one, ProperCone.innerDual_zero, Real.logb_div, Real.volume_Icc_pi_toReal, BoundedContinuousFunction.dist_eq, Set.Nonempty.intrinsicInterior, NNReal.rpow_le_rpow, 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, ODE.contDiffOn_nat_picard_Icc, norm_sub_le_mul_volume_of_norm_deriv_le_of_le, EuclideanGeometry.collinear_of_angle_eq_zero, ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior, StieltjesFunction.iInf_rat_gt_eq, intervalIntegral.integral_eq_sub_of_hasDeriv_right_of_le, 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, LinearMap.singularValues_nonneg, SmoothBumpFunction.support_eq_inter_preimage, Real.isBigO_one_exp_comp, Real.dist_right_le_of_mem_uIcc, 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, Metric.Snowflaking.ediam_image_ofSnowflaking, 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, fourier_gaussian_innerProductSpace', NormedAddGroupHom.norm_comp_le_of_le, norm_smul_of_nonneg, dist_affineCombination_lt_of_strictConvexSpace, norm_image_of_norm_zero, NNReal.comap_coe_atTop, HurwitzZeta.hasSum_nat_hurwitzZetaEven, UpperHalfPlane.dist_of_re_eq, NumberField.Units.finrank_mul_regOfFamily_eq_det, dist_le_zero, InnerProductGeometry.cos_angle, Affine.Simplex.sum_mongePointVSubFaceCentroidWeightsWithCircumcenter, ContDiffBump.convolution_tendsto_right, Polynomial.gaussNorm_isAbsoluteValue, Filter.IsIncreasingApproximateUnit.eventually_norm, NNReal.rpow_sum_le_const_mul_sum_rpow, Real.expNear_sub, Real.sinh_sub_id_strictMono, Complex.re_le_re, Real.concaveOn_rpow, Real.dimH_univ_pi_fin, Set.Nontrivial.infsep_eq_iInf, dist_lineMap_left, PartitionOfUnity.exists_finset_nhds_support_subset, Convex.span_tangentConeAt, HurwitzZeta.hasSum_int_cosKernel, 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, ContDiffAt.contDiffAt_norm_smul, norm_sub_le_of_geometric_bound_of_hasSum, Real.fourier_real_eq, ContinuousAlternatingMap.le_opNorm, ProbabilityTheory.ofReal_condCDF_ae_eq, exists_homeomorph_image_interior_closure_frontier_eq_unitBall, norm_natCast, Asymptotics.isBigO_top, Path.continuous_delayReflLeft, Seminorm.rescale_to_shell_zpow, AnalyticAt.rexp', ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_univ, intervalIntegral.intervalIntegrable_log, Real.cot_eq_cos_div_sin, circleIntegrable_posLog_norm_meromorphicOn, eq_zero_or_norm_pos, Function.Periodic.intervalIntegrable₀, UpperHalfPlane.norm_σ, Affine.Simplex.ExcenterExists.isTangentAt_touchpoint, Subgroup.instIsArithmeticAdjoinNegOne, Real.mul_rpow, quarters_mem_preCantorSet, OnePoint.isZeroAt_infty_iff, Path.Homotopy.symm_apply, ProbabilityTheory.defaultRatCDF_le_one, intervalIntegral.integral_lt_integral_of_continuousOn_of_le_of_exists_lt, IsPicardLindelof.continuousOn, Orientation.cos_oangle_sub_right_of_oangle_eq_pi_div_two, MeasureTheory.L1.integral_def, Real.rpow_le_rpow_of_nonpos, MeasureTheory.volume_sum_rpow_lt, 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, hasDerivAt_abs_rpow, LipschitzWith.projIcc, BoundedContinuousFunction.Lp_nnnorm_le, MeasureTheory.Measure.integral_comp_inv_smul_of_nonneg, Real.Angle.coe_eq_zero_iff, Real.hasSum_ofDigitsTerm_digits, Tactic.ComputeAsymptotics.Seq.dist_cons_cons_eq_one, Seminorm.smul_closedBall_zero, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_fun_add, signedDist_eq_zero_of_orthogonal, EuclideanGeometry.preimage_inversion_perpBisector, hasSum_fourier_series_L2, Real.iSup_mul_of_nonpos, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, MeasureTheory.integrable_comp_div_iff, isMIntegralCurveOn_comp_sub, Complex.div_ratCast_re, unitInterval.volume_uIcc, integral_cpow, IsSelfAdjoint.val_re_map_spectrum, norm_commutator_sub_one_le, realPart.norm_le, ProbabilityTheory.memLp_of_mem_interior_integrableExpSet, Real.cos_nonpos_of_pi_div_two_le_of_le, InnerProductGeometry.angle_add_eq_arctan_of_inner_eq_zero, ZSpan.volume_fundamentalDomain, StrictMonoOn.exists_slope_lt_deriv_aux, MeasureTheory.L1.SimpleFunc.setToL1S_smul_real, ProbabilityTheory.iteratedDeriv_complexMGF, Path.instContinuousEvalElemRealUnitInterval, NNReal.eq_rpow_inv_iff, Complex.tendsto_normSq_cocompact_atTop, Real.isBigO_exp_comp_one, ProbabilityTheory.covarianceBilin_zero, dist_le_coe, Path.symm_continuous_family, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIdealLattice, CFC.posPart_algebraMap_nnreal, NumberField.mixedEmbedding.convexBodySumFun_apply, RCLike.conjCLE_coe, Path.Homotopy.transAssocReparamAux_mem_I, Irrational.add_natCast, Real.logb_rpow_eq_mul_logb_of_pos, Ioo_smul_sphere_zero, Height.mulHeight_pow, Real.dimH_ball_pi, Real.tendsto_integral_gaussian_smul', EuclideanGeometry.angle_le_pi_div_three_of_le_of_le, ContDiffAt.inversion, EReal.toReal_neg, ContinuousAlternatingMap.bounds_bddBelow, contDiffOn_stereoToFun, Real.lt_log_iff_exp_lt, Real.hasFDerivAt_fourier, VectorFourier.differentiable_fourierIntegral, isIntegralCurve_comp_sub, ZetaAsymptotics.term_tsum_of_lt, MeasureTheory.Measure.haar.add_prehaar_le_addIndex, Affine.Simplex.incenter_mem_interior, NNReal.hasSum_real_toNNReal_of_nonneg, ENNReal.ofReal_add_le, Real.finrank_eq_int_finrank_of_discrete, SeminormedAddGroup.mem_closure_iff, MDifferentiableOn.norm_eqOn_of_isPreconnected_of_isMaxOn, Affine.Simplex.mongePoint_eq_affineCombination_of_pointsWithCircumcenter, HasDerivAt.log, Hyperreal.coe_eq_one, exists_seq_norm_le_one_le_norm_sub, MeasureTheory.condExp_mul_of_stronglyMeasurable_right, HasDerivAt.lhopital_zero_nhdsNE, unitInterval.volume_Ici, Rat.AbsoluteValue.exists_nat_rpow_iff_isEquiv, Real.analyticAt_sin, AddCircle.ergodic_add_left, Real.rpow_arith_mean_le_arith_mean_rpow, RCLike.ext_iff, abs_dist_sub_le_dist_mul_mul, Affine.Simplex.altitudeFoot_map, smul_sphere', AddCircle.norm_half_period_eq, Real.eq_one_of_pos_of_logb_eq_zero_of_base_lt_one, Diffeology.IsPlot.dSmooth, HurwitzZeta.hurwitzZeta_neg_nat, Polynomial.Chebyshev.isLocalMax_T_real, Real.sSup_nonneg, SchwartzMap.smulLeftCLM_fun_neg, ClosedSubmodule.mulI_sup, analyticOnNhd_sigmoid, Complex.norm_log_one_add_sub_self_le, LiouvilleWith.add_rat_iff, ContinuousOn.norm', Convex.norm_image_sub_le_of_norm_fderivWithin_le, map_pow_le_pow, Metric.hausdorffDist_triangle', Real.Angle.coe_coeHom, ZSpan.measure_fundamentalDomain, MeasureTheory.setIntegral_countable, convex_halfSpace_im_gt, Real.tendsto_cos_neg_pi_div_two, Real.measurable_arctan, Complex.continuous_circleTransform, norm_jacobiTheta₂_term, Real.logb_abs_base, Path.Homotopy.eval_apply, dist_midpoint_midpoint_le, CircleDeg1Lift.units_apply_inv_apply, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image, RCLike.normSq_inv, Padic.norm_natCast_lt_one_iff, Differentiable.sin, Real.Angle.toReal_neg_eq_neg_toReal_iff, MeasureTheory.integral_tendsto_of_tendsto_of_antitone, MeasureTheory.crossing_pos_eq, ProbabilityTheory.HasGaussianLaw.add, ProbabilityTheory.integral_truncation_eq_intervalIntegral, ProbabilityTheory.condExpKernel_ae_eq_condExp', Height.mulHeight₁_prod_le, Real.deriv_Gamma_nat, strictMono_of_deriv_pos, trapezoidal_integral_ext, coe_mem_spectrum_real_of_nonneg, real_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, Path.Homotopy.transAssocReparamAux_zero, GaussianFourier.integrable_cexp_neg_mul_sum_add, eq_one_or_norm_pos, ENNReal.rpow_zero_pos, EuclideanGeometry.dist_div_tan_angle_of_angle_eq_pi_div_two, MeasureTheory.integrable_add_iff_of_nonneg, CFC.exists_sqrt_of_isSelfAdjoint_of_quasispectrumRestricts, AnalyticOnNhd.eq_const_add_im_mul_I_of_re_eq_const, Convex.interior_nonempty_iff_affineSpan_eq_top, Real.iInf_const_zero, EuclideanGeometry.angle_le_angle_add_angle, Real.log_nonpos, BoxIntegral.unitPartition.mem_box_iff, Real.LogDeriv_exp, AkraBazziRecurrence.isTheta_smoothingFn_sub_self, stereoInvFun_apply, MeasureTheory.Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_group, ContDiff.norm_rpow, PhragmenLindelof.eqOn_quadrant_I, 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, ConvexBody.coe_mk, EReal.range_coe_eq_Ioo, ProbabilityTheory.memLp_two_of_variance_ne_zero, MeasureTheory.integral_tendsto_of_tendsto_of_monotone, Real.tan_pi_div_two, ProbabilityTheory.isGaussian_map_equiv_iff, Asymptotics.IsBigO.comp_summable_norm, MeasureTheory.eLpNorm_one_le_of_le', Circle.exp_two_pi, Distribution.delta_eq_zero_of_notMem, Complex.polarCoord_apply, NNReal.rpow_le_rpow_of_exponent_ge, HurwitzZeta.continuousOn_cosKernel, Measurable.sinc, Affine.Simplex.circumcenter_eq_point, Real.fourierIntegral_convergent_iff', ENNReal.toReal_mul_top, BoxIntegral.Integrable.dist_integralSum_integral_le_of_memBaseSet, EuclideanGeometry.dist_eq_add_dist_of_angle_eq_pi, NNReal.rpow_mul, MeasureTheory.measureReal_zero, Real.cos_nonneg_of_mem_Icc, Real.exp_le_exp_of_le, AkraBazziRecurrence.GrowsPolynomially.pow, Seminorm.continuous, dist_le_of_le_geometric_of_tendsto₀, 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, ENNReal.ofReal_rpow_of_nonneg, ContinuousMap.Homotopy.apply_one_path, MeasureTheory.tendstoInMeasure_iff_dist, UpperHalfPlane.center_im, Irrational.inv, MeasureTheory.lintegral_mul_prod_lintegral_pow_le, 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, integrable_rpow_neg_one_add_norm_sq, MeasureTheory.Measure.toSphere_apply_univ, HasStrictDerivAt.sin, NormedAddGroupHom.le_of_opNorm_le, CFC.nnrpow_map_pi, Real.hasDerivAt_binEntropy, Submodule.norm_sq_eq_add_norm_sq_starProjection, UpperHalfPlane.volume_def, hasDerivAt_gronwallBound_shift, SeminormedAddGroup.disjoint_nhds_zero, RCLike.re_eq_norm_of_mul_conj, ProbabilityTheory.multivariateGaussian_of_not_posSemidef, PartitionOfUnity.sum_le_one', HasStrictDerivAt.clog_real, HasUnitSpeedOn.Icc_Icc, MeasureTheory.norm_integral_le_integral_norm, Height.mulHeight_pos, Bundle.ContMDiffRiemannianMetric.symm, Real.rpow_zero, hasDerivAt_of_hasDerivAt_of_ne', MeasureTheory.hausdorffMeasure_pi_real, Real.arccos_le_pi_div_two, MeasureTheory.charFunDual_eq_prod_iff, ValueDistribution.characteristic_sub_characteristic_inv_of_ne_zero, isMIntegralCurveOn_piecewise, SchwartzMap.pairing_apply, Complex.abs_im_le_norm, Real.nnnorm_nnratCast, Real.exp_one_mul_le_exp, Real.continuous_cosh, DiffeologicalSpace.CorePlotsOn.isPlotOn_reparam, Real.fourier_comp_linearIsometry, HasDerivWithinAt.sqrt, MeasureTheory.Measure.integral_comp_smul, IsSelfAdjoint.hasEigenvector_of_isMaxOn, variationOnFromTo.eq_zero_iff_of_le, ComputeAsymptotics.MultiseriesExpansion.Multiseries.head_nil, 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, GenLoop.currySum_apply_coe, 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, ENNReal.coe_rpow_of_nonneg, NNReal.one_le_coe, StandardSubspace.IsSeparating, AkraBazziRecurrence.GrowsPolynomially.add_isLittleO, intervalIntegral.FTCFilter.nhdsUIcc, spectralNorm_eq_invariantExtension, UpperHalfPlane.cosh_dist, LSeries_eq_mul_integral_of_nonneg, WithCStarModule.norm_apply_le_norm, MeasureTheory.Measure.hausdorffMeasure_smul₀, ContDiffBumpBase.mem_Icc, ProbabilityTheory.analyticOnNhd_cgf, Padic.norm_p_pow, MultilinearMap.exists_bound_of_continuous, Wbtw.dist_le_max_dist, real_inner_div_norm_mul_norm_eq_one_iff, Real.le_rpow_add, SmoothBumpFunction.tsupport_subset_symm_image_closedBall, Filter.Tendsto.cesaro, UpperHalfPlane.image_coe_closedBall, Affine.Simplex.altitude_restrict_eq_comap_subtype, Real.goldenRatio_pow_sub_goldenRatio_pow, MeasureTheory.lintegral_nnnorm_condExpL2_le, EisensteinSeries.G2_S_transform, Asymptotics.isBigO_nat_atTop_iff, UpperHalfPlane.isProperMap_smul_I, SmoothPartitionOfUnity.le_one, LinearGrowth.Real.eventually_atTop_exists_int_between, Chebyshev.sum_PrimePow_eq_sum_sum, 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, dist_convexComboPair_convexComboPair, Real.HolderTriple.pos, MeasureTheory.measureReal_union_le, Complex.re_sq_le_normSq, Monotone.ae_hasDerivAt, MeasureTheory.condExp_bilin_of_aestronglyMeasurable_left, Filter.Tendsto.arcsin_nhdsGE, CircleDeg1Lift.le_floor_map_map_zero, HurwitzZeta.oddKernel_def, Hyperreal.st_mul, irrational_ratCast_mul_iff, StrongFEPair.hf_zero', SimplexCategory.toTop₀_map, Real.toNNReal_le_toNNReal_iff, NonarchAddGroupSeminorm.coe_smul, Polynomial.contentIdeal_eq_top_iff_forall_gaussNorm_eq_one, Quaternion.expSeries_odd_of_imaginary, MeasureTheory.integrableOn_Icc_deriv_smul_iff_of_deriv_nonpos, ProbabilityTheory.IsCondKernelCDF.setIntegral, CircleDeg1Lift.coe_mk, MeasureTheory.integrable_withDensity_iff_integrable_smul₀', AffineSubspace.signedInfDist_eq_signedDist_of_mem, exists_pos_bound_of_bound, MeasureTheory.L1.setToFun_eq_setToL1, pi_norm_le_iff_of_nonneg, 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, ENNReal.rpow_le_rpow_of_exponent_le, unitSphereToUnits_injective, SchwartzMap.norm_fourierTransformCLM_toL2_eq, Real.integrable_sinc, Continuous.dist, gaugeSeminorm_ball_one, seminormFromConst_isNonarchimedean, RealRMK.rieszMeasure_le_of_eq_one, 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, SpectrumRestricts.nnreal_lt_iff, ContDiffMapSupportedIn.uniformSpace_eq_iInf, Real.sq_cos_pi_div_six, NormedSpace.norm_expSeries_summable_of_mem_ball', MeasureTheory.Measure.haar.chaar_mono, PhragmenLindelof.eqOn_quadrant_III, DifferentiableAt.log, deriv.lhopital_zero_atBot, Real.strictMonoOn_logb_of_base_lt_one, 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.sqrt_div', Real.sign_zero, NNReal.coe_zero, Cardinal.cantorFunctionAux_succ, ProbabilityTheory.stronglyMeasurable_poissonPMFReal, MonotoneOn.locallyBoundedVariationOn, ProbabilityTheory.tsum_prob_mem_Ioi_lt_top, intervalIntegrable_iff_integrableOn_Ioc_of_le, ModularFormClass.one_mem_strictPeriods_SL2Z, IsStarProjection.norm_le, Continuous.norm', Int.ball_eq_Ioo, Complex.norm_nnratCast, MeasureTheory.stoppedValue_lowerCrossingTime, HasFDerivAt.abs_of_pos, NumberField.mixedEmbedding.polarCoordReal_source, MeasureTheory.tendsto_of_uncrossing_lt_top, NormedSpace.inclusionInDoubleDual_norm_le, Real.logb_self_eq_one, Real.Angle.two_zsmul_toReal_eq_two_mul_sub_two_pi, MeasureTheory.norm_integral_sub_setIntegral_le, not_IntegrableOn_Ici_inv, Real.volume_pi_Ioc_toReal, AkraBazziRecurrence.tendsto_atTop_r_real, Set.OrdConnected.image_derivWithin, LinearIsometryEquiv.coe_toMeasurableEquiv, LinearIsometry.re_apply_eq_re_of_add_conj_eq, stereographic'_target, RCLike.rank_le_two, Real.abs_cos_int_mul_pi, curveIntegral_segment_const, IntervalIntegrable.comp_mul_left, ProbabilityTheory.measurable_gaussianPDF, NumberField.FinitePlace.hasFiniteMulSupport, Real.real_sqrt_lt_nat_sqrt_succ, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv_aux1, Continuous.exists_contMDiff_approx, Irrational.instOrderTopologySubtypeReal, Real.le_log_iff_exp_le, Real.sin_nonneg_of_nonneg_of_le_pi, Real.ofCauchy_sub, Complex.tan_ofReal_im, PiNat.dist_triangle, NumberField.mixedEmbedding.fundamentalCone.mem_normLeOne, EuclideanGeometry.Sphere.dist_sq_eq_mul_dist_of_tangent_and_secant, Complex.norm_add_eq_iff, HasFDerivAt.abs, not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter, MeasureTheory.memLp_two_iff_integrable_sq, ConcaveOn.slope_le_of_hasDerivWithinAt_Ioi, tendsto_measure_cthickening, Metric.hausdorffDist_empty, MeasureTheory.L1.integral_eq_setToL1, Seminorm.finset_sup_apply_lt, Real.self_lt_sinh_iff, Convex.second_derivative_within_at_symmetric, 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, Rat.AbsoluteValue.equiv_real_or_padic, ProbabilityTheory.HasGaussianLaw.fun_smul, Real.volume_real_Ioc_of_le, MeasureTheory.SignedMeasure.toMeasureOfLEZero_toSignedMeasure, norm_le_insert', Real.HolderTriple.nonneg', ConvexOn.sSup_of_countable_affine_eq, VectorFourier.iteratedFDeriv_fourierIntegral, EuclideanGeometry.Sphere.IsTangentAt.power_eq_dist_sq, NumberField.HeightOneSpectrum.NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_intCast_le_one, Real.differentiableAt_rpow_of_ne, exists_contMDiffMap_zero_one_nhds_of_isClosed, Circle.exp_sub, ProbabilityTheory.integrable_pow_abs_mul_exp_of_mem_interior_integrableExpSet, Convex.uniformContinuous_gauge, CFC.sqrt_eq_one_iff, ProbabilityTheory.HasCondSubgaussianMGF.ae_condExp_le, intervalIntegral.integral_deriv_comp_mul_deriv', HasStrictFDerivAt.abs_of_neg, SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux, Behrend.norm_of_mem_sphere, Real.one_div_one_sub_hasFPowerSeriesOnBall_zero, Metric.uniformity_basis_dist_rat, BoundedVariationOn.sub_le, MeasureTheory.measureReal_union₀', convexHull_exists_dist_ge, Metric.Snowflaking.image_ofSnowflaking_ball, RCLike.reCLM_coe, MulAlgebraNorm.toFun_eq_coe, Stirling.log_stirlingSeq_diff_le, HasFDerivWithinAt.abs, Irrational.intCast_div, ContDiffBump.normed_convolution_eq_right, ContinuousAt.logb, EuclideanGeometry.Sphere.IsTangentAt.inner_right_eq_zero_of_mem, continuousSMul_closedBall_ball, UpperHalfPlane.dist_coe_center, ProbabilityTheory.gaussianReal_map_linearMap, ProbabilityTheory.iIndepFun.hasGaussianLaw_add, LinearMap.norm_mkContinuous₂_aux, Int.dist_eq', PiTensorProduct.bddBelow_projectiveSemiNormAux, InnerProductGeometry.sin_angle_sub_of_inner_eq_zero, 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, Real.rpow_lt_rpow_of_exponent_neg, Complex.tendsto_arg_nhdsWithin_im_nonneg_of_re_neg_of_im_zero, norm_sub_eq_sqrt_iff_real_inner_eq_zero, HasDerivWithinAt.inner, ball_one_eq, EuclideanGeometry.Sphere.dist_div_sin_oangle_eq_two_mul_radius, PiLp.dist_eq_of_L1, Real.exists_seq_rat_strictAnti_tendsto, AbsolutelyContinuousOnInterval.integral_deriv_mul_eq_sub, Real.tendsto_sin_neg_pi_div_two, bernoulliFun_endpoints_eq_of_ne_one, MeasureTheory.toReal_condLExp, ConvexBody.convex, BoxIntegral.integral_nonneg, DifferentiableAt.inner, Path.mul_apply, intervalIntegral.intervalIntegrable_cos, MeasureTheory.norm_integral_le_of_norm_le, NNReal.range_coe, Polynomial.gaussNorm_intAdicAbv_le_one, tendsto_measure_Icc, exists_mem_interior_convexHull_affineBasis, Real.sqrtTwoAddSeries_two, Real.Angle.cos_sub_pi, HarmonicAt.differentiableAt_complex_partial, Real.differentiable_fourierIntegral, Stirling.le_factorial_stirling, Polynomial.Chebyshev.strictAntiOn_node, EuclideanGeometry.angle_self_right, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, ProbabilityTheory.exists_cgf_eq_iteratedDeriv_two_cgf_mul, MeasureTheory.Measure.integral_toReal_rnDeriv, dist_right_midpoint, IntervalIntegrable.absolutelyContinuousOnInterval_intervalIntegral, Real.le_arcsin_iff_sin_le', NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, Complex.equivRealProd_apply_le', tendsto_norm_neg_add_self_nhdsNE, integral_smul_fderiv_eq_neg_fderiv_smul_of_integrable, AkraBazziRecurrence.eventually_asympBound_pos, Real.coe_fib_eq, EisensteinSeries.div_linear_zpow_differentiableOn, Real.iSup_pow, Seminorm.comp_smul, IsGreatest.nnnorm_cfcₙ_nnreal, Real.uniformContinuous_inv, 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, Real.fourierIntegral_iteratedDeriv, intervalIntegral.smul_integral_comp_mul_sub, AkraBazziRecurrence.GrowsPolynomially.eventually_zero_of_frequently_zero, ContDiff.sin, 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, MeasureTheory.integral_deriv_mul_eq_sub, ProbabilityTheory.integrable_rpow_abs_mul_exp_of_integrable_exp_mul, NumberField.InfinitePlace.ext_iff, CStarAlgebra.span_nonneg_inter_unitClosedBall, ProbabilityTheory.IsGaussian.charFun_eq', deriv_neg_left_of_sign_deriv, Real.deriv_inv_log, Real.Gamma_strictMonoOn_Ici, ProbabilityTheory.covarianceBilinDual_eq_covariance, ContDiffBumpBase.support, Liouville.exists_one_le_pow_mul_dist, ProbabilityTheory.gaussianReal_add_const, Real.iteratedDeriv_add_one_cosh, NNReal.isClosedEmbedding_coe, Real.isLUB_of_tendsto_monotone_bddAbove, NormedGroup.tendsto_nhds_nhds, taylor_isLittleO_univ, InnerProductSpace.Core.inner_im_symm, Real.le_rpow_inv_iff_of_neg, OrthonormalBasis.sum_sq_norm_inner_right, Real.sin_zero, signedDist_zero, StieltjesFunction.measurable_measure, EReal.coe_sub, MeasureTheory.exists_notMem_null_le_average, mellin_convergent_of_isBigO_scalar, MeasureTheory.condExpL1CLM_indicatorConstLp, SchwartzMap.postcompCLM_apply, Real.mul_self_sqrt, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_mul, Real.log_le_rpow_div, EMetric.exists_forall_closedBall_subset_aux₂, Real.sinh_lt_self_iff, Orientation.oangle_eq_zero_iff_angle_eq_zero, ConcaveOn.continuousOn, 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, Orientation.cos_oangle_add_left_of_oangle_eq_pi_div_two, spectralMulAlgNorm_def, integral_exp_Iic, Chebyshev.primeCounting_eq_theta_div_log_add_integral, UnitAddCircle.measure_univ, RCLike.isUniformEmbedding_ofReal, dist_center_homothety, Real.sqrt_eq_zero_of_nonpos, CompactlySupportedContinuousMap.toRealLinearMap_apply, integral_mul_cexp_neg_mul_sq, intervalIntegral.continuousOn_primitive_Icc, Seminorm.smul', summable_norm_sum_mul_range_of_summable_norm, IsLocalExtr.deriv_eq_zero, AddGroupSeminorm.toFun_eq_coe, IsLocalMax.deriv_eq_zero, Real.zero_eq_arcsin_iff, Convex.norm_image_sub_le_of_norm_hasDerivWithin_le, jacobiTheta_S_smul, aestronglyMeasurable_derivWithin_Ioi, MeasureTheory.integrable_comp, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, InformationTheory.integral_llr_add_sub_measure_univ_nonneg, norm_sub_norm_le', not_irrational_zero, PartitionOfUnity.sum_eq_one, Complex.normSq_eq_norm_sq, ArchimedeanClass.stdPart_add, AkraBazziRecurrence.differentiableAt_one_sub_smoothingFn, exists_bounded_zero_one_of_closed, MeasureTheory.Integrable.integral_norm_prod_left, Real.exp_eq_one_iff, AlternatingMap.mkContinuousAlternating_norm_le, 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, intervalIntegral.intervalIntegrable_rpow, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn, HurwitzZeta.hasSum_nat_sinKernel, 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, MeasureTheory.aemeasurable_ofReal_abs_det_fderivWithin, Real.iteratedDeriv_add_one_sinh, Real.circleAverage_zero, HasConstantSpeedOnWith.union, Quaternion.coeComplex_zero, AddCircle.instIsUnifLocDoublingMeasureRealVolume, eventually_norm_sub_lt, Metric.closedBall_compl_subset_of_mem_cocompact, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_mul, SchwartzMap.norm_iteratedFDeriv_le_seminorm, ProbabilityTheory.covarianceBilinDual_zero, Complex.inv_cpow_eq_ite', ContDiffBump.rIn_lt_rOut, TemperedDistribution.fourierMultiplierCLM_fourierMultiplierCLM_apply, EuclideanGeometry.wbtw_of_collinear_of_dist_center_le_radius, AlgHom.norm_apply_le_self, Irrational.eventually_forall_le_dist_cast_div_of_denom_le, MeasureTheory.L1.setToL1_add_left', Submodule.norm_orthogonalProjection_apply_le, ContinuousLinearMap.bounds_bddBelow, ProbabilityTheory.IsRatCondKernelCDFAux.mono, Affine.Simplex.ExcenterExists.sOppSide_excenter_point_iff, HasStrictDerivAt.exp, MeasureTheory.integrable_of_intervalIntegral_norm_tendsto, contDiff_bernoulliFun, Affine.Simplex.incenter_notMem_affineSpan_face, RealRMK.integral_rieszMeasure, Complex.antilipschitz_equivRealProd, ContDiffAt.rpow, Hyperreal.coe_nonneg, SchwartzMap.seminorm_le_bound', MeasureTheory.submartingale_of_setIntegral_le_succ, dense_irrational, CFC.continuous_abs, ModularForm.levelOne_weight_zero_rank_one, ofDigits_bool_to_fin_three_mem_cantorSet, bernstein.variance, tsum_geometric_of_lt_one, Real.continuous_probChar, ModularGroup.re_T_smul, ENNReal.prod_coe_rpow, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, HasFDerivWithinAt.inner, NormedSpace.polar_ball_subset_closedBall_div, BoxIntegral.Integrable.dist_integralSum_sum_integral_le_of_memBaseSet, EuclideanSpace.instIsManifoldSphere, Complex.abs_im_eq_norm, Affine.Triangle.affineSpan_pair_eq_orthRadius, Real.diam_Ioo, HasDerivAt.lhopital_zero_nhdsGT, Metric.isUniformInducing_iff, CongruenceSubgroup.strictWidthInfty_Gamma0, MeasureTheory.SimpleFunc.integral_eq_sum, Complex.ratCast_re, MeasureTheory.tendsto_sum_indicator_atTop_iff, Orientation.abs_volumeForm_apply_of_pairwise_orthogonal, BoxIntegral.Box.Ioo_ae_eq_Icc, RCLike.I_eq_zero_or_im_I_eq_one, lp.norm_nonneg', Asymptotics.IsBigOWith.norm_left, SmoothBumpCovering.locallyFinite', ContDiffWithinAt.arctan, Real.arcsin_neg_one, NNReal.rpow_lt_rpow_of_exponent_gt, LiouvilleWith.add_int, ProbabilityTheory.variance_add_const, bernstein_apply, Complex.isometry_ofReal, Real.logb_nat_eq_sum_factorization, norm_fderiv_le_of_lipschitz, Complex.norm_cpow_real, EuclideanGeometry.angle_eq_pi_div_two_of_oangle_eq_pi_div_two, Real.isEquivalent_sin, IsNonarchimedean.eval_mvPolynomial_le, Real.tendsto_sigmoid_atBot, geometric_hahn_banach_point_closed, Metric.dist_le_infDist_add_diam, Quaternion.instCompleteSpaceReal, UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_left, Prod.dist_eq, MeasureTheory.integral_Icc_deriv_smul_of_deriv_nonneg, LiouvilleNumber.remainder_summable, ProbabilityTheory.covariance_sub_right, DifferentiableWithinAt.abs, NNReal.image_coe_Iio, sum_div_nat_floor_pow_sq_le_div_sq, CFC.posPart_smul, UpperHalfPlane.hasStrictDerivAt_smul, Complex.isTheta_ofReal, enorm'_le_iff_norm_le, ENNReal.toReal_inv, IsIntegralCurveOn.comp_sub, Asymptotics.IsTheta.of_norm_eventuallyEq, MeasureTheory.L1.SimpleFunc.coe_negPart, RCLike.normSq_nonneg, ENNReal.lt_rpow_inv_iff, contraction_of_isPowMul, NumberField.mixedEmbedding.convexBodySumFun_smul, HolderWith.ediam_image_le, MeasureTheory.integral_norm_le_of_forall_fin_meas_integral_eq, Real.pow_arith_mean_le_arith_mean_pow, Complex.interior_preimage_im, HasDerivAt.cosh, 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, BumpCovering.exists_isSubordinate_of_prop, IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul', Height.logHeight_zero, Height.mulHeight₁_add_le, Real.sin_nat_mul_two_pi_sub, Filter.Eventually.volume_pos_of_nhds_real, ENNReal.mul_rpow_eq_ite, MeasureTheory.L1.setToL1_mono_left, Real.Gamma_mul_add_mul_le_rpow_Gamma_mul_rpow_Gamma, Real.differentiable_exp, intervalIntegral.integral_cases, NormedSpace.normalize_smul_of_pos, uniqueDiffWithinAt_convex, NumberField.mixedEmbedding.logMap_real_smul, tendsto_iff_norm_inv_mul_tendsto_zero, Polynomial.ncard_boxPoly, Complex.isBigO_re_sub_re, measurable_real_toNNReal, MeasureTheory.lintegral_enorm_of_nonneg, MeasureTheory.condExpInd_disjoint_union, fderivWithin_cos, norm_exp_mul_sq_le, isLittleO_exp_mul_rpow_of_lt, mul_sub_le_image_sub_of_le_deriv, Metric.diam_thickening_le, ValueDistribution.proximity_sum_top_le, circleAverage_log_norm_sub_const₀, Orientation.oangle_rotation_oangle_right, Metric.infDist_zero_of_mem, Real.le_sqrt_of_sq_le, lipschitzWith_one_norm', irrational_mul_intCast_iff, ProbabilityTheory.condIndepSet_iff, MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul_of_measurable, Metric.boundedSpace_iff, ENNReal.rpow_two, ComplexStarModule.ext_iff, ProbabilityTheory.differentiableOn_mgf, Real.abs_mulExpNegMulSq_comp_le_norm, AlternatingMap.mkContinuous_norm_le, NormedAddGroupHom.le_opNorm_of_le, Real.rpow_eq_zero, ContDiffMapSupportedIn.seminorm_monoLM_le, intervalIntegral.integral_comp_smul_deriv'', 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, Real.hasStrictDerivAt_arcosh, LinearMap.extendTo𝕜_apply, Real.coe_nnabs, Height.logHeight₁_eq, cfcHom_integral, Complex.isBigO_cpow_rpow, Real.logb_pos_of_base_lt_one, Complex.log_exp_eq_sub_toIocDiv, UnitAddTorus.coeFn_mFourierLp, Real.rpowIntegrand₀₁_apply_mul_eqOn_Ici, Dilation.mapsTo_closedBall, MeasureTheory.Integrable.integral_norm_condExpKernel, UpperHalfPlane.exists, norm_sum_neg_one_pow_le, intervalIntegral.integral_comp_smul_deriv, HurwitzKernelBounds.F_nat_one_le, Matrix.l2_opNorm_conjTranspose_mul_self, EReal.coe_zsmul, InnerProductGeometry.angle_self, ProbabilityTheory.lintegral_exponentialPDF_of_nonpos, Asymptotics.IsBigOWith.pow', IsLocalMax.norm_add_sameRay, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, CircleDeg1Lift.transnumAuxSeq_zero, ProbabilityTheory.variance_sub, Real.isAlgebraic_tan_rat_mul_pi, AddCircle.volume_of_add_preimage_eq, Orientation.cos_oangle_add_right_mul_norm_of_oangle_eq_pi_div_two, UpperHalfPlane.denom_cocycle, LocallyLipschitz.max, Real.differentiableAt_cos, IsLocalExtr.hasLineDerivAt_eq_zero, MeasureTheory.Measure.instIsFiniteMeasureElemSphereOfNatRealToSphere, IsCoveringMap.eq_liftPath_iff', Real.isBigO_log_const_mul_log_atTop, Complex.norm_exp_sub_sum_le_norm_mul_exp, isClosed_preCantorSet, CompactlySupportedContinuousMap.nnrealPart_neg_toReal_eq, CircleDeg1Lift.lt_map_of_int_lt_translationNumber, ContinuousWithinAt.norm, Filter.Tendsto.rexp, EuclideanGeometry.image_inversion_perpBisector, cthickening_thickening, ProbabilityTheory.Kernel.HasSubgaussianMGF.neg, CircleDeg1Lift.iterate_mono, MeasureTheory.SimpleFunc.norm_approxOn_y₀_le, Polynomial.le_supNorm, innerₗ_apply, GenLoop.ext_iff, dist_integral_mulExpNegMulSq_comp_le, SmoothBumpFunction.contMDiffAt, CircleDeg1Lift.tendsto_translation_number', MeasureTheory.setIntegral_condExpIndSMul, StieltjesFunction.length_subadditive_Icc_Ioo, MeasureTheory.integral_divergence_prod_Icc_of_hasFDerivAt_of_le, 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, Complex.dist_le_mul_div_pow_of_mapsTo_ball_of_isLittleO, 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, Real.arcsin_le_arcsin, IsMaxOn.hasLineDerivAt_eq_zero, Affine.Triangle.acuteAngled_iff_angle_lt, ContinuousMap.dist_lt_iff_of_nonempty, SmoothBumpFunction.hasCompactSupport, ProbabilityTheory.complexMGF_id_mul_I, isLocalMin_of_deriv', MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le, AddGroupSeminorm.coe_lt_coe, Polynomial.intervalIntegrable_mahlerMeasure, ProbabilityTheory.Kernel.measurable_densityProcess, WithLp.prod_norm_eq_idemFst_sup_idemSnd, ENNReal.tendsto_rpow_at_top, exists_continuous_one_zero_of_isCompact, ProbabilityTheory.betaPDF_of_pos_lt_one, ModularGroup.lcRow0Extend_apply, irrational_natCast_mul_iff, Cardinal.increasing_cantorFunction, concaveOn_of_deriv2_nonpos', lipschitzOnWith_iff_norm_div_le, Real.volume_real_closedBall, Real.ball_eq_openSegment, IsUltrametricDist.norm_tsum_le_of_forall_le, MeasureTheory.ProbabilityMeasure.continuous_iff_forall_continuousMap_continuous_integral, Complex.HadamardThreeLines.norm_invInterpStrip, Real.deriv_log', Circle.exp_neg, MeasureTheory.lintegral_rpow_eq_lintegral_meas_lt_mul, ProbabilityTheory.IsCondKernelCDF.setLIntegral, Submodule.norm_eq_iInf_iff_real_inner_eq_zero, ProbabilityTheory.map_pi_eq_stdGaussian, 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, MeasureTheory.integrableOn_Iic_of_intervalIntegral_norm_bounded, BoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homothetic, ae_restrict_of_ae_restrict_inter_Ioo, 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, ProbabilityTheory.integral_id_multivariateGaussian, AlternatingMap.exists_bound_of_continuous, Convex.mul_sub_le_image_sub_of_le_deriv, Complex.liftAux_neg_I, TemperedDistribution.fourierMultiplierCLM_apply, Metric.PiNatEmbed.separation, SchwartzMap.lineDeriv_eq_fourierMultiplierCLM, Real.log_zpow, Polynomial.Chebyshev.leadingCoeff_le_of_forall_abs_le_one, ProbabilityTheory.integrable_exp_abs_mul_abs_add, UpperHalfPlane.lt_dist_iff_lt_dist_coe_center, dist_div_div_le_of_le, UpperHalfPlane.coe_smul_of_det_pos, Real.isLittleO_pow_exp_atTop, unitInterval.continuous_sigmoid, Seminorm.bound_of_continuous, ODE_solution_unique_of_mem_Icc_right, Metric.infDist_empty, ContDiff.euclidean_dist, Besicovitch.exists_disjoint_closedBall_covering_ae_of_finiteMeasure_aux, MeasureTheory.SignedMeasure.of_diff_eq_zero_of_symmDiff_eq_zero_negative, MeasureTheory.integrable_of_le_of_le, norm_sub_eq_zero_iff, HasCompactSupport.exists_bound_of_continuous, measurableSet_pi_polarCoord_target, DifferentiableOn.log, cfcₙ_real_eq_complex, Real.logb_lt_logb_of_base_lt_one, WithLp.dist_snd_le, expNegInvGlue.pos_of_pos, MeasureTheory.lpMeasToLpTrimLie_symm_indicator, intervalIntegral.integral_comp_add_mul, IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn_real, NumberField.InfinitePlace.isInfinitePlace, ContinuousMap.HomotopyWith.coeFn_injective, Real.two_mul_le_exp, ProbabilityTheory.integrableExpSet_fun_id_gaussianReal, Complex.ofReal_intCast, Complex.ofReal_add, GenLoop.continuous_currySum, WithLp.prod_norm_eq_add, Real.exp_one_near_20, ConvexBody.ext_iff, MeasureTheory.condExp_mul_of_aestronglyMeasurable_left, MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable_of_equiv, MeasureTheory.norm_setToFun_le', MeasureTheory.integrableOn_Ioc_of_intervalIntegral_norm_bounded_right, HasBesicovitchCovering.no_satelliteConfig, NumberField.Units.dirichletUnitTheorem.map_logEmbedding_sup_torsion, MeasureTheory.setIntegral_rnDeriv_smul, instIsTopologicalRingReal, StrictMonoOn.exists_deriv_lt_slope_aux, PseudoMetricSpace.dist_ofPreNNDist_le, isMIntegralCurveAt_iff, norm_le_pi_norm, ContinuousLinearMap.rayleighQuotient_zero_apply, irrational_div_natCast_iff, Real.log_of_pos, seminormFromBounded_le, MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_det_fderiv_mul, Metric.cthickening_zero, Complex.UnitDisc.coe_closedBall_smul, Height.zero_le_logHeight₁, Path.truncate_zero_zero, selfAdjoint.unitarySelfAddISMul_coe, Bundle.ContMDiffRiemannianMetric.pos, Real.arccos_eq_pi_div_two, HasStrictFDerivAt.sqrt, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_cgf', Monotone.cauchySeq_series_mul_of_tendsto_zero_of_bounded, quasispectrum_imaginaryPart', NNReal.rpow_lt_rpow_of_exponent_lt, Metric.unitClosedBall.coe_mul, HasDerivWithinAt.complexToReal_fderiv, signedDist_triangle_left, Real.Gamma_eq_zero_iff, Real.sum_le_exp_of_nonneg, Real.tsum_eq_tsum_fourier_of_rpow_decay_of_summable, HurwitzKernelBounds.isBigO_atTop_F_nat_one, Affine.Simplex.altitudeFoot_eq_point_rev, Real.tendsto_comp_exp_atTop, Matrix.norm_le_iff, Real.strictAntiOn_rpow_Ioi_of_exponent_neg, Affine.Simplex.dist_lt_of_mem_interior_of_strictConvexSpace, circleIntegral.norm_integral_le_of_norm_le_const, ProbabilityTheory.measurable_paretoPDFReal, UnitAddTorus.lintegral_preimage, ProbabilityTheory.centralMoment_zero, MeasureTheory.ae_nonneg_restrict_of_forall_setIntegral_nonneg, 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, ENNReal.div_rpow_of_nonneg, sum_Ico_le_integral_of_le, Affine.Simplex.excenterExists_map, IsUltrametricDist.exists_norm_multiset_sum_le, Complex.add_re, integral_sin_pow_mul_cos_pow_odd, NNReal.summable_mul_rpow_of_Lp_Lq, controlled_sum_of_mem_closure_range, LipschitzOnWith.norm_inv_mul_le, MeasureTheory.Lp.norm_const_le, Mathlib.Meta.Positivity.log_pos_of_isNNRat, Seminorm.coe_add, MeasureTheory.volume_sum_rpow_le, AnalyticAt.exists_ball_analyticOnNhd, ProbabilityTheory.covariance_sum_left, Polynomial.zero_lt_eval_of_roots_lt_of_leadingCoeff_nonneg, Real.geom_mean_eq_arith_mean_weighted_iff', ProbabilityTheory.covariance_fun_sum_right', MeasureTheory.SignedMeasure.singularPart_add, Real.toNNReal_le_natCast, Real.arccos_neg, Complex.nhdsWithin_lt_le_nhdsWithin_stolzSet, integral_conj, ProbabilityTheory.IsGaussianProcess.restrict, Complex.hasSum_ofReal, Real.ofDigits_eq_sum_add_ofDigits, IsClosed.exists_wbtw_isVisible, dist_triangle_right, Affine.Simplex.exradius_nonneg, MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_deriv_mul', HasDerivWithinAt.arsinh, Height.fun_logHeight_zero, Real.natCeil_logb_natCast, isBounded_iff_asymptoticCone_subset_singleton, Path.Homotopy.transAssocReparamAux_one, BoundedContinuousFunction.norm_le, ProbabilityTheory.instIsGaussianMapHSub, NumberField.FinitePlace.norm_lt_one_iff_mem, MeasureTheory.measureReal_add_apply, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_intAdicAbv, Real.isAlgebraic_cos_rat_mul_pi, Real.exists_natCast_add_one_lt_pow_of_one_lt, MeasureTheory.tendsto_indicator_ge, Complex.ofRealCLM_nnnorm, Complex.imCLM_norm, Real.artanh_le_artanh_iff, Real.deriv2_binEntropy, Real.cos_pi_div_two, ArithmeticFunction.LSeries_vonMangoldt_eq_deriv_riemannZeta_div, SeminormedSpace.Core.norm_triangle, RCLike.geometric_hahn_banach_of_nonempty_interior', MeasureTheory.SimpleFunc.ennrealRatEmbed_encode, ProbabilityTheory.mgf_sum_of_identDistrib₀, MeasureTheory.integrableOn_Ioi_comp_mul_left_iff, ball_add_closedBall, 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, ProbabilityTheory.exponentialPDF_of_nonneg, Quaternion.norm_coe, exists_pos_lt_subset_ball, integral_rpow_mul_exp_neg_mul_rpow, CFC.nnrpow_def, SmoothBumpCovering.sum_toSmoothPartitionOfUnity_eq, ContinuousAt.sqrt, NormMulClass.isAbsoluteValue_norm, HasDerivAt.exp, UnitAddTorus.mFourier_neg, SmoothBumpFunction.updateRIn_rOut, IsExtrOn.lineDeriv_eq_zero, StrictMonoOn.strictConvexOn_of_deriv, interior_halfSpace, LiouvilleWith.mul_rat, ProbabilityTheory.paretoPDF_of_le, gronwallBound_K0, gauge_closure_zero, NumberField.mixedEmbedding.unit_smul_eq_iff_mul_eq, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq_inner, ProbabilityTheory.cauchyMeasure_of_scale_ne_zero, SimplexCategory.toTop₀_obj, Convex.taylor_approx_two_segment, MeasureTheory.measure_le_setAverage_pos, ContDiffOn.inversion, MeasureTheory.integral_image_eq_integral_abs_deriv_smul, DifferentiableAt.sqrt, PiLp.dist_eq_iSup, Metric.tendsto_dist_left_cobounded_atTop, ProbabilityTheory.integral_gaussianPDFReal_eq_one, Height.one_le_mulHeight₁, HasStrictFDerivAt.rpow, ProbabilityTheory.HasSubgaussianMGF.fun_zero, PhragmenLindelof.vertical_strip, CircleDeg1Lift.map_nat_add, Matrix.PosSemidef.eigenvalues_nonneg, RCLike.exists_norm_eq_mul_self, EReal.preimage_coe_Icc, Complex.continuousOn_norm_circleTransformBoundingFunction, Real.rpow_def_of_neg, Affine.Simplex.vectorSpan_isOrtho_altitude_direction, exists_continuous_nonneg_pos, Hyperreal.coe_pos, Real.posLog_neg, le_rpow_one_add_norm_iff_norm_le, 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, cfcₙ_comp_re, MeasureTheory.Lp.coeFn_negPart_eq_max, Orientation.inner_rotation_pi_div_two_right, integral_comp_polarCoord_symm, Affine.Simplex.exsphere_reindex, RingSeminorm.exists_index_pow_le, EuclideanGeometry.sin_eq_zero_iff_angle_eq_zero_or_angle_eq_pi, NNReal.coe_mk, ContinuousAffineMap.norm_contLinear_le, Complex.arg_one_add_mem_Ioo, Real.exp_bound_div_one_sub_of_interval, gauge_ball, Polynomial.Chebyshev.node_eq_neg_one, Complex.normSq_sub, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, Function.Periodic.im_invQParam, ProbabilityTheory.covariance_const_add_left, HurwitzZeta.cosZeta_eq, RCLike.measurable_re, Metric.nonempty_ball, ENNReal.ofReal_le_ofNat, Real.volume_Ico, UnitAddTorus.measurePreserving_equivPiIoc, ProbabilityTheory.mgf_add_measure, Matrix.SpecialLinearGroup.isClosedEmbedding_mapGLInt, ProbabilityTheory.IsGaussianProcess.comp_left, MeasureTheory.integral_llr_tilted_left, GaussianInt.toComplex_im_div, ProperCone.innerDual_singleton, star_mul_self_eq_realPart_sq_add_imaginaryPart_sq, ExistsContDiffBumpBase.w_support, 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, InformationTheory.integral_klFun_rnDeriv, cfc_comp_im, differentiable_inner, InnerProductSpace.Core.inner_self_eq_norm_mul_norm, exists_locallyFinite_iUnion_eq_ball_radius_lt, MeasureTheory.Measure.haar.prehaar_nonneg, MeasureTheory.eLpNorm'_smul_measure, TemperedDistribution.fourierMultiplierCLM_const, Real.analyticOn_arcosh, ProbabilityTheory.Kernel.rnDeriv_toReal_pos, CFC.abs_natCast, VitaliFamily.ae_tendsto_average_norm_sub, interior_subset_gauge_lt_one, Urysohns.CU.bddAbove_range_approx, Real.lt_log_of_rpow_lt, 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, intervalIntegral.abs_integral_mono_interval, Asymptotics.IsBigOWith.of_abs_right, spectralNorm_mul, Polynomial.Chebyshev.integral_eq_sumZeroes, CStarAlgebra.isStrictlyPositive_iff_isStrictlyPositive_sqrt_and_eq_sqrt_mul_sqrt, RCLike.im_eq_conj_sub, Polynomial.Chebyshev.abs_eval_T_real_le_one, MeasureTheory.eLpNorm'_le_eLpNorm'_mul_rpow_measure_univ, OrthonormalBasis.volume_parallelepiped, Real.hasDerivAt_tan, ProbabilityTheory.cauchyPDFReal_def, Real.logb_pow, HurwitzZeta.hasSum_int_cosZeta, hasFDerivAt_integral_of_dominated_loc_of_lip', Real.Angle.toReal_mem_Ioo_iff_sign_pos, CircleDeg1Lift.translationNumber_of_map_pow_eq_add_int, 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, Real.tan_add, Affine.Simplex.ExcenterExists.touchpointWeights_restrict, EuclideanGeometry.Sphere.IsTangentAt.radius_lt_dist_center, Behrend.bound, Complex.arg_exp_mul_I, ENNReal.rpow_le_one_of_one_le_of_neg, Behrend.four_zero_nine_six_lt_exp_sixteen, Icc_chartedSpaceChartAt, LiouvilleWith.add_int_iff, IsLocalMinOn.hasFDerivWithinAt_nonneg, Complex.arg_of_re_neg_of_im_neg, Real.arctan_neg, NonarchAddGroupSeminorm.lt_def, Orientation.oangle_rotation, PiLp.norm_eq_sum, Real.deriv_tan_sub_id, ExistsContDiffBumpBase.u_int_pos, Mathlib.Meta.Positivity.log_pos_of_isRat_neg, LinearMap.singularValues_eq_zero_iff, Real.instIsOrderBornology, DifferentiableOn.inversion, RCLike.conj_im_ax, PadicInt.continuousAddCharEquiv_of_norm_mul_apply, AddCircle.volume_closedBall, Real.pi_upper_bound_start, Real.contDiffAt_log, mul_gauge_le_norm, norm_add_le, EuclideanGeometry.Sphere.ncard_inter_orthRadius_eq_two_of_dist_lt_radius, ArchimedeanClass.stdPart_ofNat, Real.leftDeriv_mul_log, Complex.preimage_equivRealProd_prod, Real.inner_le_weight_mul_Lp_of_nonneg, SchwartzMap.integral_mul_laplacian_right_eq_left, realPart_one, Finset.norm_prod_one_add_sub_one_le, circleIntegrable_log_norm_factorizedRational, Measurable.sinh, WeakFEPair.h_feq', Real.tan_sub_pi, ENNReal.rpow_natCast_mul, UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_ne_zero, Real.spectralRadius_mem_spectrum, 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, Real.arcsin_eq_arccos, ContDiffOn.abs, Real.rpow_sum_le_const_mul_sum_rpow, MeasureTheory.lpNorm_fun_mul_natCast, unitInterval.one_minus_le_one, Real.differentiableAt_Gamma, deriv.lhopital_zero_nhdsLT, HasDerivAt.cos, Real.exists_nat_abs_mul_sub_round_le, Real.pow_mul_norm_iteratedFDeriv_fourier_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, PadicInt.norm_lt_one_mul, Orientation.norm_div_tan_oangle_add_left_of_oangle_eq_pi_div_two, Real.hasStrictDerivAt_cosh, LiouvilleWith.int_add_iff, AlgebraNorm.toFun_eq_coe, ConvexOn.real_univ_sSup_of_countable_affine_eq, 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, CircleDeg1Lift.continuous_pow, NumberField.mixedEmbedding.mem_span_latticeBasis, irrational_sqrt_intCast_iff_of_nonneg, EuclideanGeometry.angle_lt_iff_dist_lt, Polynomial.mahlerMeasure_C_mul_X_add_C, ProbabilityTheory.evariance_eq_top_iff, PadicInt.coe_one, Complex.tendsto_norm_tan_atTop, AddGroupSeminorm.add_bddBelow_range_add, AkraBazziRecurrence.asympBound_def, MeasureTheory.MemLp.integrable_sq, Orientation.tan_oangle_add_left_mul_norm_of_oangle_eq_pi_div_two, ProbabilityTheory.evariance_eq_lintegral_ofReal, ProbabilityTheory.lintegral_betaPDF_eq_one, ProbabilityTheory.IsGaussian.charFunDual_eq_of_forall_strongDual_eq_zero, TemperedDistribution.fourierTransformInv_toTemperedDistributionCLM_eq, ProbabilityTheory.integral_condVar_add_variance_condExp, Polynomial.prod_max_one_norm_roots_le_mahlerMeasure_of_one_le_leadingCoeff, CFC.rpow_rpow, TopologicalSpace.Opens.CompleteCopy.dist_val_le_dist, Real.sinhEquiv_symm_apply, dist_convexComboPair_right, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', CircleDeg1Lift.translationNumber_of_eq_add_int, ContinuousMap.Homotopy.evalAt_apply, ContDiffWithinAt.norm_sq, Real.arctan_inv_of_neg, Real.log_one, Complex.HadamardThreeLines.F_edge_le_one, CircleDeg1Lift.continuous_iff_surjective, Function.hasTemperateGrowth_norm_sq, BoundedContinuousFunction.innerProbChar_apply, Mathlib.Meta.NormNum.isNat_rpow_neg, ProbabilityTheory.analyticOn_cgf, MeasureTheory.integral_pos_iff_support_of_nonneg_ae, IsometryEquiv.map_midpoint, Complex.ofReal_prod, norm_multiset_prod_le, MeasureTheory.integrableOn_Ioc_of_intervalIntegral_norm_bounded, QuasispectrumRestricts.le_nnreal_iff, BoundedContinuousFunction.exists_norm_eq_restrict_eq_of_closed, MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_sum_mul_norm, SimpleGraph.binomialRandom_zero, Complex.IsExpCmpFilter.tendsto_re, ProbabilityTheory.Kernel.HasSubgaussianMGF.add, Real.strictConvexOn_mul_log, UniformSpace.Completion.norm_toComplL, Seminorm.uniformContinuous_of_continuousAt_zero, Real.zero_at_infty_fourierIntegral, closure_upperClosure_comm_pi, interval_average_symm, diam_stdSimplex_of_subsingleton, IsUltrametricDist.norm_mul_eq_max_of_norm_ne_norm, ProbabilityTheory.covarianceBilin_comm, descPochhammer_eval_le_sum_descFactorial, intervalIntegral.integral_congr_codiscreteWithin, ProbabilityTheory.Kernel.tendsto_integral_density_of_monotone, EReal.sign_coe, instSMulCommClass_sphere_closedBall_closedBall, Orientation.inner_rotation_pi_div_two_left, HasStrictDerivAt.cosh, ProbabilityTheory.centralMoment_zero_measure, ProbabilityTheory.Kernel.measurable_densityProcess_left, AmpleSet.preimage, ContDiffAt.cosh, ProbabilityTheory.Kernel.memL1_limitProcess_densityProcess, UniformConcaveOn.sub, isIntegralCurveAt_iff_exists_pos, gauge_empty, Affine.Simplex.sign_excenterWeights_singleton_neg, Polynomial.Chebyshev.sumNodes_eq_sumNodes_T_iff, ProbabilityTheory.cdf_le_one, MeasureTheory.lintegral_ofReal_ne_top_iff_integrable, Real.ofDigits_SurjOn, Subgroup.strictPeriods_eq_zmultiples_one_of_T_mem, Hyperreal.IsSt.add, Complex.HadamardThreeLines.scale_bound_left, 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, Real.logb_neg_iff_of_base_lt_one, Metric.ball_zero, InformationTheory.klDiv_of_ac_of_integrable, gradient_eq_deriv', Orientation.oangle_rotation_self_left, Complex.sub_conj, ProbabilityTheory.HasSubgaussianMGF.measure_sum_ge_le_of_iIndepFun, Real.strictAnti_eulerMascheroniSeq', gauge_eq_one_iff_mem_frontier, RCLike.ofReal_add, ZetaAsymptotics.continuousOn_term, ProbabilityTheory.covariance_neg_right, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_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, DifferentiableWithinAt.arctan, MeasureTheory.lpNorm_sub_le, EuclideanGeometry.Sphere.orthogonalProjection_orthRadius_center, summable_iff_vanishing_norm, Real.logb_self_eq_one_iff, Orientation.kahler_neg_orientation, EuclideanGeometry.exists_of_range_subset_orthocentricSystem, FormalMultilinearSeries.radius_inv_eq_limsup, Real.BohrMollerup.f_add_nat_le, Real.hasStrictDerivAt_log, IsMinOn.lineDerivWithin_eq_zero, EuclideanGeometry.inner_pos_or_eq_of_dist_le_radius, ComputeAsymptotics.MultiseriesExpansion.Multiseries.Pairwise_nil, IsSelfAdjoint.cfc_arg, InnerProductSpace.HarmonicContOnCl.const_smul, MeasureTheory.L2.integral_inner_eq_sq_eLpNorm, ENNReal.ofReal_tsum_of_nonneg, Real.iteratedDeriv_add_one_cos, affinity_unitBall, MonotoneOn.intervalIntegrable_slope, 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, EuclideanGeometry.image_inversion_affineSubspace_of_mem, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, EuclideanGeometry.Sphere.dist_center_lt_radius_of_sbtw, 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, Real.rpow_sum_of_pos, indiscreteTopology_iff_forall_norm_eq_zero', NumberField.rootDiscr_def, Filter.HasBasis.cobounded_of_norm', AffineIsometryEquiv.dist_pointReflection_self, NonarchAddGroupSeminormClass.toAddGroupSeminormClass, BoxIntegral.Box.dist_le_distortion_mul, tendsto_rpow_atTop_of_base_lt_one, 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, SchwartzMap.compCLMOfAntilipschitz_apply, spectrum.pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius, ProbabilityTheory.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero, intervalIntegral.integrableOn_Ioo_cpow_iff, AffineIsometryEquiv.dist_pointReflection_self_real, Padic.norm_eq_zpow_neg_valuation, NumberField.house.exists_ne_zero_int_vec_house_le, SmoothBumpFunction.ball_subset, Real.abs_log_sub_add_sum_range_le, Cardinal.mk_real, ProbabilityTheory.variance_zero_measure, SchwartzMap.fourierInv_apply_eq, UniformSpace.ofDist_aux, ENNReal.rpow_eq_zero_iff_of_pos, SchwartzMap.smulRightCLM_apply_apply, IsUnifLocDoublingMeasure.measure_mul_le_scalingConstantOf_mul, Real.log_pos, MeasureTheory.Lp.norm_le_norm_of_ae_le, 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, MeasureTheory.mul_integral_upcrossingsBefore_le_integral_pos_part_aux, volume_regionBetween_eq_lintegral', ProbabilityTheory.analyticAt_cgf, MeasureTheory.Submartingale.bddAbove_iff_exists_tendsto_aux, Complex.conjCLE_toLinearEquiv, Real.arsinh_pos_iff, SlashInvariantForm.exists_one_half_le_im_and_norm_le, unitInterval.range_sigmoid, Complex.arg_lt_pi_div_two_iff, MeasureTheory.setToFun_smul_left, InformationTheory.klDiv_def, HasDerivAt.complexToReal_fderiv', PartitionOfUnity.exists_isSubordinate_of_locallyFinite_t2space, Filter.hasBasis_cobounded_norm, MeasureTheory.L2.inner_indicatorConstLp_one, Nat.dist_eq, taylor_mean_remainder, StrictMono.strictConvexOn_univ_of_deriv, MeasureTheory.Integrable.norm_integral_condKernel, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin, RCLike.abs_wInner_le, RCLike.ofReal_neg, WithLp.prod_norm_eq_add_idemFst, 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', MeasureTheory.L1.setToL1_smul_left', ConvexOn.slope_le_leftDeriv, SlashInvariantForm.slash_action_generators, MeasureTheory.exists_null_frontier_thickening, NNReal.rpow_right_inj, Unitary.norm_sub_one_sq_eq, PiNat.lipschitz_with_one_iff_forall_dist_image_le_of_mem_cylinder, EuclideanGeometry.image_inversion_sphere_dist_center, Real.sin_add, InnerProductSpace.volume_ball, Orientation.norm_div_sin_oangle_sub_right_of_oangle_eq_pi_div_two, RCLike.ofReal_zpow, Real.Angle.sin_two_nsmul, NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, MeasureTheory.JordanDecomposition.exists_compl_positive_negative, Real.sqrt_mul, ProbabilityTheory.IsRatCondKernelCDF.tendsto_atTop_one, MeasureTheory.aemeasurable_fderivWithin, ProbabilityTheory.memLp_id_gaussianReal', RCLike.im_mul_ofReal, circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const, EuclideanGeometry.two_zsmul_oangle_self_orthogonalProjection, Real.cosh_sq, lipschitzWith_circleMap, Complex.tendsto_arg_nhdsWithin_im_neg_of_re_neg_of_im_zero, fderiv_norm_smul_neg, SchwartzMap.toTemperedDistributionCLM_apply_apply, EisensteinSeries.q_expansion_riemannZeta, Seminorm.continuousAt_zero', HasDerivAt.complexToReal_fderiv, Measurable.cos, Real.continuousOn_cos, EuclideanGeometry.dist_div_sin_oangle_left_of_oangle_eq_pi_div_two, LiouvilleWith.sub_int_iff, integrableOn_Ioi_deriv_ofReal_cpow, ExistsContDiffBumpBase.u_exists, ConvexCone.hyperplane_separation_of_nonempty_of_isClosed_of_notMem, Real.sigmoid_injective, EuclideanGeometry.Sphere.sbtw_secondInter, BoundedContinuousFunction.dist_lt_iff_of_nonempty_compact, Affine.Simplex.sum_excenterWeightsUnnorm_singleton_pos, Metric.Snowflaking.image_ofSnowflaking_closedEBall, CompactlySupportedContinuousMap.toReal_apply, HurwitzZeta.hurwitzZetaOdd_neg_two_mul_nat, StandardSubspace.IsCyclic, NumberField.house_sum_le_sum_house, PositiveLinearMap.exists_norm_apply_le, MeasureTheory.measureReal_inter_add_diff₀, seminormFromBounded_is_norm_iff, PhragmenLindelof.eq_zero_on_horizontal_strip, Real.norm_inv_mul_rpow_sub_one_sub_log_le, Real.fourierIntegral_real_eq_integral_exp_smul, Complex.map_exp_comap_re_atBot, Complex.intCast_re, ProbabilityTheory.covariance_add_right, Real.deriv_mulExpNegMulSq, EuclideanHalfSpace.convex, Real.sin_neg, exists_dist_lt_le, norm_le_norm_of_abs_le_abs, fourier_coe_apply, Set.le_edist_of_le_infsep, NormedStarGroup.norm_star_le, Real.cos_pi_div_eight, LipschitzWith.min, Real.deriv_fourierIntegral, ProbabilityTheory.iIndepFun.integrable_exp_mul_sum, Complex.liftAux_I, Complex.interior_setOf_le_im, unitInterval.coe_unitIntervalSubmonoid, dist_right_pointReflection, Polynomial.supNorm_nonneg, integral_exp_mul_I_eq_sin, NNReal.continuousAt_rpow, InnerProductGeometry.norm_div_tan_angle_sub_of_inner_eq_zero, MeasureTheory.Integrable.exists_boundedContinuous_integral_sub_le, InnerProductGeometry.inner_eq_neg_mul_norm_of_angle_eq_pi, EisensteinSeries.norm_eq_max_natAbs, norm_jacobiTheta_sub_one_le, 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, MeasureTheory.integral_eq_of_hasDerivAt_off_countable, CircleDeg1Lift.iterate_monotone, schnirelmannDensity_le_of_le, Metric.Snowflaking.preimage_toSnowflaking_closedBall, Complex.integral_boundary_rect_of_hasFDerivAt_real_off_countable, WithLp.prod_dist_eq_sup, Orientation.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero, Metric.uniformContinuousOn_iff, GromovHausdorff.ghDist_le_hausdorffDist, Orientation.oangle_sub_left_eq_arcsin_of_oangle_eq_pi_div_two, RieszExtension.exists_top, unitInterval.mul_le_left, periodizedBernoulli.continuous, NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_top, Real.goldenConj_mul_goldenRatio, GenLoop.continuous_fromLoop, NormedAddGroupHom.mkNormedAddGroupHom_norm_le', PiNat.mem_cylinder_iff_dist_le, quotient_norm_add_le, SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux, intervalIntegral.integral_mul_deriv_eq_deriv_mul_of_hasDeriv_right, inner_smul_real_right, Affine.Triangle.sOppSide_affineSpan_pair_excenter_singleton_point, intervalIntegral.integral_eq_zero_iff_of_le_of_nonneg_ae, fourierSubalgebra_separatesPoints, AffineSubspace.isConnected_setOf_wSameSide, exists_polynomial_near_of_continuousOn, LinearMap.injective_iff_forall_lt_finrank_singularValues_pos, IndiscreteTopology.norm_eq_zero, enorm_le_iff_norm_le, NonarchAddGroupSeminorm.coe_lt_coe, Real.strictMono_rpow_of_base_gt_one, ProbabilityTheory.cgf_const, cfcₙ_comp_im, isLittleO_rpow_exp_pos_mul_atTop, 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, Quaternion.exp_of_re_eq_zero, NumberField.HeightOneSpectrum.isNonarchimedean_adicAbv, Real.arcsin_lt_iff_lt_sin, ProbabilityTheory.cauchyPDF_pos, NumberField.HeightOneSpectrum.adicAbv_add_le_max, EuclideanGeometry.Sphere.dist_sq_eq_iff_mem_orthRadius, Metric.unitBall.coe_eq_zero, MeasureTheory.SignedMeasure.re_toComplexMeasure, snd_integral, AntitoneOn.sum_le_integral_Ico, NNReal.val_eq_coe, TemperedDistribution.smulLeftCLM_sub, CStarAlgebra.instNonnegSpectrumClass, FormalMultilinearSeries.ofScalars_norm_le, IsCoercive.bounded_below, ContDiffBump.support_eq, IsPreconnected.convex, MeasureTheory.submartingale_of_setIntegral_le, HurwitzZeta.hasSum_nat_cosZeta, preCantorSet_subset_unitInterval, SmoothBumpFunction.eqOn_source, ModularGroup.denom_S, Complex.HadamardThreeLines.norm_le_interpStrip_of_mem_verticalClosedStrip, Hyperreal.Infinite.st_eq, Set.Nontrivial.infsep_lt_iff, SchwartzMap.postcompCLM_postcompCLM, NumberField.mixedEmbedding.covolume_idealLattice, HurwitzZeta.continuousOn_evenKernel, Real.lipschitzWith_sin, Real.sigmoid_lt, Affine.Simplex.ExcenterExists.excenter_restrict, tendsto_norm_inv_mul_self_nhdsNE, Complex.zero_im, ProbabilityTheory.lintegral_paretoPDF_of_le, Real.one_rpow, Real.injOn_tan, ValueDistribution.proximity_add_top_le, NumberField.place_apply, Submodule.norm_subtypeL, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_eq, intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, ContDiff.norm_sq, Complex.continuous_circleTransformDeriv, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos, EuclideanGeometry.Sphere.IsTangentAt.inner_left_eq_zero_of_mem, fourierCoeff.const_smul, MonotoneOn.intervalIntegral_deriv_mem_uIcc, MeasureTheory.SignedMeasure.mutuallySingular_iff, ContractingWith.dist_le_mul, NumberField.mixedEmbedding.volume_preserving_negAt, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, EuclideanSpace.sphere_zero_eq, StarAlgHom.realContinuousMapOfNNReal_apply_comp_toReal, cantorSet_eq_zero_two_ofDigits, NumberField.mixedEmbedding.normAtPlace_add_le, setIntegral_withDensity_eq_setIntegral_toReal_smul₀', Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, 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, strictMonoOn_of_hasDerivWithinAt_pos, IsUltrametricDist.norm_fwdDiff_iter_apply_le, MeasureTheory.IntegrableOn.continuousOn_Ici_primitive_Ioi, contDiffPointwiseHolderAt_iff, InformationTheory.integrable_llr_compProd_iff, mem_closure_zero_iff_norm, CircleDeg1Lift.commute_sub_int, SpectrumRestricts.nnreal_le_iff, Real.deriv_arctan, Urysohns.CU.lim_of_mem_C, LinearMap.coe_complexOfReal, AffineSubspace.isPreconnected_setOf_wOppSide, continuousSMul_sphere_closedBall, HurwitzZeta.completedHurwitzZetaEven_eq, MeasureTheory.lintegral_deriv_eq_volume_image_of_antitoneOn, Tactic.ComputeAsymptotics.isBigOWith_of_tendsto_bot, monotoneOn_deriv_descPochhammer_eval, NNReal.rpow_ofNat, RingNorm.apply_one, dist_mul_mul_le_of_le, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt, Real.toNNReal_inv, AddCircle.instIsProbabilityMeasureRealHaarAddCircle, MulAlgebraNorm.coe_AlgebraNorm, SchwartzMap.smulLeftCLM_const, eventually_nhdsWithin_sign_eq_of_deriv_neg, ProbabilityTheory.IsAEKolmogorovProcess.kolmogorovCondition, NumberField.house_pow_le, Metric.closure_eq_iInter_cthickening, ProbabilityTheory.HasSubgaussianMGF.memLp_exp_mul, MeasureTheory.tilted_tilted, one_le_gauge_of_notMem, intervalIntegrable_of_odd₀, MeasureTheory.integral_fintype, mellin_convergent_top_of_isBigO, ProbabilityTheory.condVar_of_stronglyMeasurable, Metric.tendsto_dist_right_cobounded_atTop, Asymptotics.isLittleO_pow_sub_pow_sub, GroupSeminorm.inf_apply, MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left, Mathlib.Meta.NormNum.IsNat.rpow_isNNRat, HasDerivWithinAt.rpow, IsLocalMinOn.hasFDerivWithinAt_eq_zero, SmoothPartitionOfUnity.sum_eq_one', OrthonormalBasis.sum_sq_inner_left, Circle.exp_inj, Tactic.ComputeAsymptotics.Seq.dist_cons_cons, Real.sinh_eq_tsum, MeasureTheory.integrableOn_Ioi_deriv_of_nonpos, Real.sign_eq_zero_iff, NumberField.InfinitePlace.coe_mk_comp, Real.mk_mul, Differentiable.arctan, Irrational.sub_ratCast, MeasureTheory.setToFun_indicator_const, 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, MeasureTheory.uniformIntegrable_average_real, integral_sin_mul_cos₁, intervalIntegral.smul_integral_comp_sub_mul, MeasureTheory.Integrable.exists_hasCompactSupport_integral_sub_le, Matrix.permMatrix_l2_opNorm_le, Real.cos_eq_tsum, Metric.exists_ball_inter_eq_singleton_of_mem_discrete, deriv.lhopital_zero_nhds, MeasureTheory.Lp.norm_const', Function.locallyFinsuppWithin.toClosedBall_divisor, NumberField.mixedEmbedding.neg_of_mem_negA_plusPart, 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', ConvexOn.le_slope_of_hasDerivWithinAt_Ioi, ProperCone.hyperplane_separation_point, ComputeAsymptotics.MultiseriesExpansion.Multiseries.map_comp, ContinuousLinearMap.opNorm_le_of_ball, NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_pow, EuclideanGeometry.oangle_midpoint_left, RCLike.wInner_one_eq_inner, ae_eq_const_or_norm_average_lt_of_norm_le_const, StieltjesFunction.countable_leftLim_ne, ProbabilityTheory.iCondIndepSets_singleton_iff, NumberField.mixedEmbedding.negAt_apply_isComplex, MeasureTheory.tilted_neg_same, Real.integral_rpowIntegrand₀₁_one_pos, 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, smul_sphere, GroupSeminorm.coe_comp, ProbabilityTheory.mgf_zero, HasCompactSupport.integral_Iic_deriv_eq, LinearMap.extendTo𝕜'_apply_re, ContDiffAt.rpow_const_of_ne, Complex.ofReal_one, ProbabilityTheory.mgf_zero_measure, Int.norm_eq_abs, ENNReal.toReal_nonneg, lp.norm_le_of_tendsto, Filter.Tendsto.norm', NumberField.mixedEmbedding.fundamentalCone.expMapBasis_closure_subset_compactSet, Real.monotoneOn_rpow_Ici_of_exponent_nonneg, Real.iteratedDerivWithin_sinh_Icc, Real.sqrtTwoAddSeries_zero_nonneg, Orientation.sin_oangle_add_left_of_oangle_eq_pi_div_two, Asymptotics.IsBigO.norm_norm, UpperHalfPlane.σ_num, MeasureTheory.Measure.toSignedMeasure_smul, irrational_div_intCast_iff, MeasureTheory.integrableOn_Ioi_deriv_of_nonpos', InnerProductGeometry.inner_eq_neg_mul_norm_iff_angle_eq_pi, ProbabilityTheory.lintegral_exp_mul_sq_norm_le_of_map_rotation_eq_self, Real.arccos_eq_arcsin, OnePoint.isBoundedAt_iff, Hyperreal.IsSt.map₂, MeasureTheory.setToFun_zero_left, Complex.arg_zero, Real.goldenRatio_mul_fib_succ_add_fib, ProbabilityTheory.integral_truncation_eq_intervalIntegral_of_nonneg, MeasureTheory.lintegral_rpow_enorm_eq_rpow_eLpNorm', MeasureTheory.lintegral_image_eq_lintegral_abs_det_fderiv_mul, 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, Real.arcsin_le_iff_le_sin', AbsolutelyContinuousOnInterval.exists_bound, Affine.Simplex.circumsphere_unique_dist_eq, Complex.algHom_ext_iff, Real.artanh_eq_zero_iff, swap_integral, HasDerivAt.lhopital_zero_left_on_Ioo, InnerProductGeometry.angle_sub_le_pi_div_two_of_inner_eq_zero, MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero_aux2, Topology.CWComplex.union', Path.uniformContinuous, Real.ofNat_lt_toNNReal, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv_aux2, Matrix.inner_toEuclideanCLM, IsLocalMax.hasFDerivAt_eq_zero, RingSeminorm.isBoundedUnder, Quaternion.re_exp, Path.extend_of_one_le, measurableSet_region_between_co, ContinuousLinearMap.norm_precompR_le, Real.measurable_of_measurable_exp, PadicInt.coe_natCast, dist_lineMap_right, dist_le_range_sum_of_dist_le, NumberField.mixedEmbedding.fundamentalCone.continuous_expMap, ContinuousMap.exists_mem_subalgebra_near_continuousMap_of_separatesPoints, continuous_circleMap, CircleDeg1Lift.dist_map_zero_lt_of_semiconj, 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, Real.continuousAt_logb_iff, AbsolutelyContinuousOnInterval.uniformContinuousOn, RCLike.neg_iff, isScalarTower_closedBall_ball_ball, PowerSeries.IsRestricted.isRestricted_iff, MeasureTheory.Measure.haar.chaar_nonneg, integral_sin_pow_aux, hasDerivWithinAt_taylorWithinEval_at_Icc, RingSeminorm.mul_le', tendsto_measure_thickening, ProbabilityTheory.instIsGaussianDirac, NNReal.rpow_arith_mean_le_arith_mean_rpow, ProbabilityTheory.measurable_cauchyPDFReal, Convex.norm_image_sub_le_of_norm_fderiv_le, Continuous.cfc_nnreal_of_mem_nhdsSet, Real.rpowIntegrand₀₁_zero_left, ProbabilityTheory.Kernel.measurable_countableFiltration_densityProcess, norm_sum_le_of_le, NormedSpace.ofReal_exp_ℝ_ℝ, integral_comp_abs, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat, MeasureTheory.hausdorffMeasure_prod_real, Complex.sq_nonneg_iff, dist_triangle_left, Cube.boundary_sum_iff, ProbabilityTheory.iIndepFun.charFun_map_fun_sum_eq_prod, 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, Path.image_extend_of_subset, DiffeologicalSpace.plot_reparam, tendsto_rpow_sub_one_log, MeasureTheory.lpNorm_le_lpNorm_add_lpNorm_sub', NNReal.one_lt_rpow_of_pos_of_lt_one_of_neg, Padic.padicNormE.is_rat, Complex.norm_le_of_forall_mem_frontier_norm_le, ENNReal.rpow_eq_top_iff, Manifold.pathELength_comp_of_antitoneOn, 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, intervalIntegrable_of_odd, SmoothPartitionOfUnity.mem_finsupport, Real.binEntropy_zero, ProbabilityTheory.IsKolmogorovProcess.kolmogorovCondition, Continuous.inner_bundle, RCLike.inv_im, IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus, ContinuousLinearMap.opNorm_le_bound, DifferentiableWithinAt.inversion, Real.Wallis.W_eq_integral_sin_pow_div_integral_sin_pow, Real.convergent_of_zero, EuclideanGeometry.angle_eq_angle_add_pi_div_two_of_oangle_eq_add_pi_of_sSameSide, Metric.isBounded_iff, TestFunction.lineDerivCLM_add, Set.Icc.eq_convexCombo, enorm_sub_le_lintegral_derivWithin_Icc_of_contDiffOn_Icc, intervalIntegral.integral_deriv_comp_smul_deriv, Real.logb_injOn_pos, MeasureTheory.measureReal_add_measureReal_compl₀, Real.sq_sqrt, 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, Polynomial.Chebyshev.one_lt_abs_eval_T_real, IsMIntegralCurve.comp_add, ZLattice.summable_norm_rpow, BoxIntegral.Box.continuousOn_face_Icc, OpenPartialHomeomorph.univUnitBall_target, ModularForm.discriminant_eq_q_prod, Real.differentiableAt_log_iff, MeasureTheory.integral_target_eq_integral_abs_det_fderiv_smul, Complex.ofReal_nnratCast, norm_iteratedFDerivWithin_prod_le, TopCat.I.homeomorph_zero, SmoothBumpFunction.tsupport_mem_nhds, EReal.coe_zero, IsOpen.exists_contMDiff_support_eq, Metric.diam_ball, Real.uniformContinuous_neg, Real.convexOn_log_Gamma, ProbabilityTheory.cdf_gammaMeasure_eq_lintegral, UnitAddTorus.mFourier_norm, Convex.isLittleO_alternate_sum_square, CStarModule.norm_inner_le, BoundedVariationOn.continuousWithinAt_variationOnFromTo_Ici, measurableSet_region_between_oc, NNReal.zero_rpow_def, Orientation.rotation_neg_orientation_eq_neg, rescale_to_shell, 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, IntervalIntegrable.log, MultilinearMap.mkContinuousLinear_norm_le, WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup, hasFDerivAt_iff_tendsto, Complex.equivRealProdAddHom_symm_apply_im, Orientation.eq_rotation_self_iff, monotoneOn_of_hasDerivWithinAt_nonneg, GenLoop.toLoop_apply, Bornology.IsBounded.subset_ball_lt, LiouvilleWith.rat_mul_iff, Height.mulHeight_zero, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, Real.exp_mul_le_cosh_add_mul_sinh, Real.negMulLog_nonneg, AddGroupSeminorm.coe_add, Complex.selfAdjointEquiv_apply, MeasureTheory.MemLp.integral_indicator_norm_ge_nonneg_le_of_meas, DifferentiableAt.norm_sq, DifferentiableWithinAt.sin, norm_sub_le_norm_mul, Real.isPiSystem_Iio_rat, BoundedContinuousFunction.nnrealPart_coeFn_eq, UpperHalfPlane.im_smul, RCLike.ofReal_prod, Polynomial.Chebyshev.abs_iterate_derivative_T_real_le, tsum_geometric_two, Real.arith_mean_le_rpow_mean, closure_convexHull_extremePoints, 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, ProbabilityTheory.sum_variance_truncation_le, HasFDerivWithinAt.log, Complex.range_liftAux, Orientation.areaForm'_apply, Affine.Triangle.two_zsmul_oangle_excenter_eq, Padic.padicNormE.is_norm, NumberField.mixedEmbedding.fundamentalCone.expMap_smul, Real.continuous_const_rpow, ProbabilityTheory.HasGaussianLaw.indepFun_of_covariance_eq_zero, Asymptotics.isBigO_const_iff, IsApproximateAddSubgroup.card_nsmul_le, ENNReal.rpow_rpow_inv, ExistsContDiffBumpBase.y_pos_of_mem_ball, IsGδ.setOf_irrational, inner_eq_norm_sq_left_iff, Complex.HadamardThreeLines.interpStrip_eq_of_pos, SzemerediRegularity.biUnion_star_subset_nonuniformWitness, ENNReal.top_rpow_of_pos, MeasureTheory.hausdorffMeasure_lineMap_image, Real.log_eq_zero, Set.infsep_of_fintype, UpperHalfPlane.normSq_denom_pos, Metric.mem_closure_iff, ENNReal.continuous_ofReal, HurwitzZeta.hasSum_expZeta_of_one_lt_re, Real.antitone_arccos, Real.cauchy_inv, Real.le_sInf, Continuous.cfcₙ_nnreal, MeasureTheory.condExp_stronglyMeasurable_mul_of_bound, 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, monotoneOn_of_deriv_nonneg, RCLike.ofReal_mul_pos_iff, HurwitzZeta.hasSum_int_evenKernel, Real.summable_exp_neg_nat, Real.sin_nat_mul_pi, Real.abs_sin_sub_sin_le, unitInterval.one_mem, Real.rpow_logb_eq_abs, 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, NormedAddGroupHom.IsQuotient.norm_lift, Complex.inv_cpow_eq_ite, ArithmeticFunction.log_apply, Complex.liftAux_apply_I, BoxIntegral.Box.volume_face_mul, ProbabilityTheory.variance_eval_multivariateGaussian, RCLike.ofReal_finsupp_sum, Asymptotics.IsTheta.norm_left, intervalIntegral.integral_smul_measure, ContDiffPointwiseHolderAt.prodMk, hasSum_one_div_nat_pow_mul_cos, Asymptotics.IsTheta.isBoundedUnder_le_iff, ProbabilityTheory.iIndepFun.cgf_sum, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_lt_one_iff, ENNReal.le_rpow_inv_iff, StrictConcaveOn.slope_lt_of_hasDerivAt, Metric.hasBasis_cobounded_compl_ball, signedDist_smul_of_pos, MeasureTheory.BorelCantelli.integrable_process, Distribution.mapCLM_apply, Real.neg_inv_le_log, Filter.Tendsto.rpow_const, Wbtw.angle₃₁₂_eq_zero_of_ne, Asymptotics.IsEquivalent.log, OnePoint.IsZeroAt.smul_iff, unitInterval.fract_mem, CFC.rpow_map_prod, FormalMultilinearSeries.norm_compContinuousLinearMap_le, intervalIntegral.FTCFilter.meas_gen, continuous_gauge, MeasureTheory.intervalIntegral_tendsto_integral, Quaternion.normSq_eq_norm_mul_self, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, ProbabilityTheory.covariance_fun_sum_left, MeasureTheory.SignedMeasure.singularPart_zero, IsCoveringMap.exists_path_lifts, Orientation.sin_oangle_sub_left_mul_norm_of_oangle_eq_pi_div_two, Summable.summable_log_norm_one_add, tendsto_real_toNNReal_atTop, Real.one_lt_rpow_iff_of_pos, Real.hasStrictDerivAt_const_rpow_of_neg, AkraBazziRecurrence.GrowsPolynomially.div, Real.logb_nonneg_of_base_lt_one, EuclideanGeometry.oangle_orthogonalProjection_self, AkraBazziRecurrence.GrowsPolynomially.neg, tendsto_pow_const_mul_const_pow_of_abs_lt_one, NNReal.nnrpow_def, Real.eq_one_of_pos_of_log_eq_zero, Affine.Simplex.map_altitude_restrict, spectralValueTerms_nonneg, Besicovitch.TauPackage.one_lt_tau, UpperHalfPlane.σ_neg, Orientation.oangle_add_left_eq_arcsin_of_oangle_eq_pi_div_two, UpperHalfPlane.smulFDeriv_J_mul, mem_nullAddSubgroup_iff, Metric.diam_nonneg, IsContinuousRiemannianBundle.exists_continuous, Orientation.cos_oangle_sub_right_mul_norm_of_oangle_eq_pi_div_two, EuclideanGeometry.cospherical_def, HasDerivWithinAt.lhopital_zero_nhdsWithin_convex, norm_zsmul_le, Set.OrdConnected.null_frontier, ModularGroup.normSq_S_smul_lt_one, InnerProductSpaceable.inner_.norm_sq, NNReal.add_rpow_le_rpow_add, ProbabilityTheory.gaussianReal_apply, EuclideanGeometry.exterior_angle_eq_angle_add_angle, Real.logb_nonpos_iff_of_base_lt_one, ArithmeticFunction.vonMangoldt_pos_iff, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn, ModularFormClass.exp_decay_sub_atImInfty, Besicovitch.SatelliteConfig.inter', ConvexOn.sSup_of_nat_affine_eq, Real.contDiff_arsinh, Real.log_lt_sub_one_of_pos, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le', ProbabilityTheory.covariance_sum_sum, ProbabilityTheory.Kernel.densityProcess_fst_univ_ae, EuclideanGeometry.cos_oangle_left_mul_dist_of_oangle_eq_pi_div_two, Height.logHeight_mul_le, NumberField.FinitePlace.IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, Seminorm.ball_add_ball_subset, MeasureTheory.Submartingale.ae_tendsto_limitProcess_of_uniformIntegrable, Complex.frontier_preimage_im, MeasureTheory.MemLp.integrable_norm_rpow, LipschitzWith.min_const, HasDerivAt.sinh, ENNReal.lt_iff_exists_real_btwn, HasDerivWithinAt.limsup_norm_slope_le, Real.contDiff_fourierIntegral, EuclideanGeometry.angle_eq_zero_of_angle_eq_pi_left, NNReal.rpow_two, ComputeAsymptotics.MultiseriesExpansion.Multiseries.destruct_nil, Real.tan_lt_tan_of_nonneg_of_lt_pi_div_two, CircleDeg1Lift.commute_add_nat, Irrational.natCast_sub, ProbabilityTheory.gaussianReal_neg, Real.comap_toNNReal_atTop, gauge_of_subset_zero, SimplexCategory.toTopHomeo_symm_naturality_apply, Finset.doubling_lt_two, ContinuousAt.pathExtend, Polynomial.mahlerMeasure_pos_of_ne_zero, MeasureTheory.tilted_apply_eq_ofReal_integral, Real.sum_range_le_log_div, Real.exp_strictMono, Real.log_lt_log, ContinuousAlternatingMap.le_opNorm_mul_pow_of_le, ModularFormClass.exists_petersson_le, Affine.Simplex.exradius_reindex, MonotoneOn.sum_le_integral_Ico, Submodule.smul_starProjection_singleton, NumberField.Units.mem_torsion, Metric.tendsto_nhdsWithin_nhdsWithin, Affine.Simplex.ninePointCircle_reindex, MeasureTheory.SignedMeasure.toMeasureOfZeroLE_real_apply, norm_of_subsingleton, InformationTheory.integrable_llr_of_integrable_llr_compProd, NumberField.FinitePlace.IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply, SMulCommClass.complexToReal, StieltjesFunction.measure_Ici, Real.arctan_injective, Circle.invOn_arg_exp, ContinuousLinearMap.opNorm_comp_le, ProbabilityTheory.condExp_set_generateFrom_singleton, Chebyshev.primeCounting_sub_theta_div_log_isBigO, isLittleO_log_rpow_nhdsGT_zero, IsPicardLindelof.exists_shrink_radius, NNReal.sub_def, intervalIntegral.integral_deriv_smul_comp_of_deriv_nonpos, MeasureTheory.dist_convolution_le, Real.two_pi_pos, norm_mul, Path.Homotopy.trans_assoc_reparam, RCLike.one_im, ArchimedeanClass.lt_of_lt_stdPart, UpperHalfPlane.coe_smul, Metric.cthickening_eq_iInter_cthickening', ProbabilityTheory.gaussianPDFReal_def, mul_bounded_of_bounded_of_bounded, MeasureTheory.lintegral_eq_lintegral_meas_le, Complex.inv_def, LipschitzWith.dist_lt_mul_of_lt, MeasureTheory.Measure.addHaar_real_closedBall', Complex.equivRealProdLm_apply, Orientation.inner_comp_rightAngleRotation, Complex.div_intCast, intervalIntegral.integral_hasStrictFDerivAt, Real.contDiffAt_arcsin_iff, Real.le_sqrt, Real.isPiSystem_Ioi_rat, CStarAlgebra.linear_combination_nonneg, RCLike.natCast_re, ProbabilityTheory.HasCondSubgaussianMGF.zero, Real.tendsto_comp_exp_atBot, Cardinal.mk_Icc_real, Real.smoothTransition.lt_one_of_lt_one, Complex.IsExpCmpFilter.tendsto_norm, HasFPowerSeriesWithinOnBall.image_sub_sub_deriv_le, NNReal.coe_lt_one, Real.abs_rpow_of_nonneg, instSeparatingDualRealOfIsTopologicalAddGroupOfContinuousSMulOfLocallyConvexSpaceOfT1Space, Real.logb_lt_logb_iff_of_base_lt_one, Real.sqrt_le_sqrt, intervalIntegral.integral_deriv_smul_eq_sub_of_hasDeriv_right, Asymptotics.isBigOWith_self_const_mul, BoxIntegral.Box.mem_mk, ContDiffAt.arctan, EReal.range_coe, MeasureTheory.Lp.norm_smul_le, dist_pi_le_iff, Real.iSup_fun_mul_eq_iSup_mul_iSup_of_nonneg, Valued.integer.norm_le_one, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, Urysohns.CU.approx_mem_Icc_right_left, ENNReal.rpow_add_le_mul_rpow_add_rpow, ProbabilityTheory.lintegral_paretoPDF_eq_one, Real.cos_eq_cos_iff, TestFunction.lineDerivOp_eq_lineDerivCLM, UpperHalfPlane.IsZeroAtImInfty.exp_decay_atImInfty, 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, ProbabilityTheory.HasGaussianLaw.iIndepFun_of_covariance_eq_zero, AkraBazziRecurrence.differentiableOn_one_add_smoothingFn, ENNReal.ofReal_eq_natCast, Real.arsinh_lt_arsinh, Asymptotics.IsLittleO.isBigOWith, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform, sum_trapezoidal_error_adjacent_intervals, InnerProductSpace.Core.inner_self_nonneg, RCLike.ofReal_finsuppProd, MeasureTheory.SignedMeasure.of_inter_eq_of_symmDiff_eq_zero_negative, MeasureTheory.setIntegral_eq_zero_iff_of_nonneg_ae, BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_isClosedEmbedding, PartitionOfUnity.finsum_smul_mem_convex, differentiableAt_complex_iff_differentiableAt_real, mfderiv_coe_sphere_injective, Mathlib.Meta.NormNum.isRat_rpow_neg, ProbabilityTheory.variance_eq_sub, 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, hasDerivWithinAt_taylor_coeff_within, inner_re_symm, Mathlib.Meta.NormNum.IsNNRat.nnreal_rpow_isNNRat, WithLp.volume_preserving_toLp, UniformConvexOn.convexOn, 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, SchwartzMap.fourierMultiplierCLM_apply, concaveOn_of_hasDerivWithinAt2_nonpos, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, NumberField.Units.regOfFamily_of_isMaxRank, MeasureTheory.Measure.setIntegral_toReal_rnDeriv', circleIntegral.integral_radius_zero, ArithmeticFunction.vonMangoldt_sum, CFC.rpow_eq_rpow_pi, Orientation.norm_div_cos_oangle_add_right_of_oangle_eq_pi_div_two, IsUnifLocDoublingMeasure.eventually_measure_le_doublingConstant_mul, dist_triangle_max, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, SmoothBumpFunction.nhds_basis_support, Complex.arg_neg_eq_arg_add_pi_of_im_neg, ClosedSubmodule.mem_symplComp_iff, Behrend.exp_neg_two_mul_le, InnerProductGeometry.angle_zero_left, ContinuousAt.cfcₙ_nnreal, ProbabilityTheory.gaussianReal_conv_gaussianReal, LipschitzOnWith.extend_real, 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, Complex.arg_conj, inner_map_complex, Real.mul_iInf_of_nonneg, analyticAt_sigmoid, Real.sinh_sub, Real.toNNReal_pos, NNReal.ContinuousMap.canLift, Filter.Tendsto.dist, Real.dist_le_of_mem_Icc, Metric.hasAntitoneBasis_cobounded_compl_closedBall, HomotopyGroup.mul_spec, Metric.hausdorffDist_self_zero, ConvexOn.differentiableWithinAt_Ioi_of_mem_interior, Rat.AbsoluteValue.padic_eq_padicNorm, Function.Periodic.intervalIntegral_add_eq_add, HurwitzZeta.completedCosZeta₀_neg, isLittleO_log_rpow_atTop, intervalIntegrable_of_even₀, 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, Hyperreal.exists_st_iff_not_infinite, contDiffAt_norm, BoxIntegral.Prepartition.exists_splitMany_inf_eq_filter_of_finite, tendsto_integral_mul_one_add_inv_smul_sq_pow, derivWithin_cos, Submodule.starProjection_norm_le, UniformConvexOn.add, MeasureTheory.pdf.IsUniform.pdf_toReal_ae_eq, NNReal.strictMono_rpow_of_pos, MeasureTheory.charFun_conv, Complex.arg_eq_nhds_of_im_neg, RCLike.norm_le_re_iff_eq_norm, NumberField.Units.regOfFamily_div_regulator, PadicComplex.isNonarchimedean, expNegInvGlue.tendsto_polynomial_inv_mul_zero, ContDiffOn.log, AnalyticOnNhd.circleAverage_log_norm_of_ne_zero, Real.le_rpow_iff_log_le, WithSeminorms.isOpen_iff_mem_balls, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, NNReal.lt_rpow_inv_iff, EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radius, PiLp.volume_preserving_ofLp, Affine.Simplex.exradius_restrict, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbeddingOfIsReal, Real.div_rpow, Real.fourier_fderiv, BoundedContinuousFunction.norm_integral_le_norm, exists_lt_subset_ball, MeasureTheory.lpNorm_sub_le_lpNorm_sub_add_lpNorm_sub, rescale_to_shell_semi_normed, EuclideanGeometry.sin_eq_one_iff_angle_eq_pi_div_two, integral_sin_pow_even_mul_cos_pow_even, Real.tendsto_nat_mul_log_one_add_of_tendsto, isLittleO_exp_neg_mul_rpow_atTop, Real.arctan_zero, ProbabilityTheory.variance_zero, Metric.diam_closedBall, 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, tendsto_rpow_abs_mul_exp_neg_mul_sq_cocompact, Complex.tendsto_exp_comap_re_atBot, continuous_bernoulliFun, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_one, EuclideanGeometry.sin_angle_div_dist_eq_sin_angle_div_dist, measurableSet_of_differentiableWithinAt_Ici_of_isComplete, Complex.normSq_ofNat, signedDist_vadd_left_swap, EuclideanGeometry.Sphere.power_neg_iff_dist_center_lt_radius, IsSelfAdjoint.spectrumRestricts, Real.sInf_neg, Complex.UnitDisc.re_neg, Real.qaryEntropy_strictAntiOn, diam_stdSimplex_le, gronwallBound_x0, SeparationQuotient.mk_eq_zero_iff, UpperHalfPlane.instProperSMul, 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, Asymptotics.isBigOWith_of_le, imaginaryPart.norm_le, Seminorm.const_isBounded, OpenPartialHomeomorph.contDiffOn_univUnitBall_symm, Seminorm.preimage_metric_closedBall, Real.sinOrderIso_apply, ContinuousOn.cfc_nnreal_of_mem_nhdsSet, Mathlib.Meta.NormNum.IsNNRat.rpow_isNNRat, MeasureTheory.integrable_prod_iff, SchwartzMap.compSubConstCLM_zero, ContDiffMapSupportedIn.seminorm_top_le_iff, Polynomial.eq_centerMass_of_eval_derivative_eq_zero, Real.rpow_lt_one, sum_mul_Ico_le_integral_of_monotone_antitone, ProbabilityTheory.IsGaussianProcess.shift, Tactic.ComputeAsymptotics.WellFormedBasis.tendsto_atTop, ProbabilityTheory.IsMeasurableRatCDF.le_one, ValueDistribution.characteristic_eventually_nonneg, ENNReal.funMulInvSnorm_rpow, Real.tan_lt_tan_of_lt_of_lt_pi_div_two, abs_norm', ConvexOn.monotoneOn_deriv, image_norm_le_of_norm_deriv_right_lt_deriv_boundary, instCStarRingReal, AddGroupSeminorm.coe_iSup_apply, Real.exp_sub_cosh, HasFDerivWithinAt.norm_sq, CFC.abs_algebraMap, preCantorSet_antitone, MeasureTheory.norm_weightedSMul_le, NumberField.mixedEmbedding.convexBodySumFun_neg, ProbabilityTheory.integrable_exp_mul_of_nonpos_of_ge, Complex.restrictScalars_one_smulRight, Tactic.ComputeAsymptotics.Seq.dist_eq_two_inv_pow, LipschitzWith.coordinate, PartitionOfUnity.nonneg, ProbabilityTheory.meas_ge_le_variance_div_sq, GroupSeminorm.smul_apply, differentiableAt_abs_neg, Real.isPiSystem_Ici_rat, geometric_hahn_banach_of_nonempty_interior', real_inner_self_abs, Complex.summable_ofReal, SmoothBumpFunction.updateRIn_rIn, 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, AEMeasurable.sin, ArchimedeanClass.stdPart_intCast, MeasureTheory.withDensityᵥ_smul_eq_withDensityᵥ_withDensity', Tactic.ComputeAsymptotics.Seq.Stream'.dist_le_one, Real.floor_real_sqrt_eq_nat_sqrt, ProbabilityTheory.variance_of_ae_eq_zero_or_one, ContDiffWithinAt.sinh, derivWithin_const_rpow, ProbabilityTheory.HasGaussianLaw.map, IsPrimitiveRoot.arg_eq_zero_iff, norm_fderiv_norm_rpow_le, ProbabilityTheory.exponentialPDFReal_pos, ProbabilityTheory.variance_fun_sum, Real.mul_log_nonpos, MellinConvergent.comp_mul_left, integral_inner, NumberField.FinitePlace.add_le, Real.Lp_add_le_tsum_of_nonneg, schnirelmannDensity_eq_zero_of_one_notMem, Complex.nonpos_iff, Metric.continuous_iff', Real.leTotal_R, deriv_abs_zero, VectorFourier.fderiv_fourierIntegral, AnalyticAt.harmonicAt_conj, tendsto_norm_inv_mul_self, Summable.of_nonneg_of_le, RCLike.ofReal_im, NumberField.FinitePlace.instNonnegHomClassReal, SemilinearMapClass.bound_of_shell_semi_normed, 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, exists_taylor_mean_remainder_bound, Algebra.norm_complex_eq, StrongDual.extendRCLikeₗ_apply, LinearMap.bound_of_ball_bound', exists_hasDerivWithinAt_eq_of_lt_of_gt, Real.sin_two_mul, realPart_comp_subtype_selfAdjoint, Real.convergent_zero, ProbabilityTheory.gaussianPDFReal_sub, ContinuousLinearMap.rayleighQuotient_le_of_norm_mem_resolventSet, HasCompactSupport.enorm_le_lintegral_Ici_deriv, Metric.exists_continuous_real_forall_closedBall_subset, Real.circleMap.continuous, Real.doublingGamma_log_convex_Ioi, InnerProductGeometry.norm_ofLp_crossProduct, MeasureTheory.intervalIntegral_tendsto_integral_Ioi, MeasureTheory.integral_posConvolution, hasStrictDerivAt_abs, BoundingSieve.siftedSum_eq_sum_support_mul_ite, fourier_eval_zero, Real.iteratedDerivWithin_sin_Icc, norm_mul_le_of_le', Real.rpowIntegrand₀₁_nonneg, Real.toNNReal_lt_iff_lt_coe, Orientation.sin_oangle_sub_left_of_oangle_eq_pi_div_two, InnerProductSpace.volume_ball_of_dim_odd, Asymptotics.isBigOWith_iff, Matrix.IsHermitian.roots_charpoly_eq_eigenvalues, ContinuousAlternatingMap.isLeast_opNorm, EuclideanGeometry.OrthocentricSystem.affineIndependent, le_limsup_mul, Irrational.natCast_div, Complex.arg_lt_pi_iff, Matrix.IsHermitian.cfcAux_apply, Polynomial.Chebyshev.integrable_measureT, SchwartzMap.fourierInv_lineDerivOp_eq, Affine.Simplex.touchpointWeights_reindex, Real.le_log_of_pow_le, LipschitzOnWith.extend_lp_infty, RCLike.abs_im_le_norm, curveIntegralFun_trans_of_half_lt, ContinuousMap.norm_sub_eq_max, RCLike.finrank_le_two, MeasureTheory.StronglyMeasurable.exists_spanning_measurableSet_norm_le, IsOpen.smul_sphere, Real.cos_int_mul_two_pi_add_pi, EuclideanGeometry.Sphere.secondInter_smul, ProbabilityTheory.monotone_preCDF, InnerProductSpace.harmonicAt_comp_CLE_iff, Complex.arg_of_im_nonneg_of_ne_zero, smoothingFun_le, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric, Bundle.RiemannianMetric.symm, PadicInt.norm_lt_one_add, MeasureTheory.integral_charFun_Icc, EReal.preimage_coe_Ici, dist_homothety_self, BoundedContinuousFunction.dist_coe_le_dist, Finset.doubling_lt_golden_ratio, LinearMap.hasEigenvalue_adjoint_comp_self_sq_singularValues, MeasureTheory.stoppedValue_upperCrossingTime, OneHomClass.bound_of_antilipschitz, real_inner_add_sub_eq_zero_iff, Complex.normSq_ofReal_add_I_mul_sqrt_one_sub, strongConcaveOn_iff_convex, Real.iteratedDeriv_odd_sinh, Affine.Simplex.height_map, Complex.dist_le_div_mul_dist_of_mapsTo_ball, Real.lt_zpow_iff_log_lt, Real.toNNReal_lt_toNNReal_iff, Asymptotics.isLittleO_const_id_atBot, Real.smul_iInf_of_nonpos, MeasureTheory.tendsto_zero_of_hasDerivAt_of_integrableOn_Iic, NNReal.rpow_natCast_mul, ContinuousMap.toNNReal_one, ProbabilityTheory.Kernel.tendsto_integral_density_of_antitone, EReal.image_coe_Ioo, cantorSequence_mem_cantorSet, MeasureTheory.Lp.lipschitzWith_pos_part, linear_isometry_complex, ContDiffWithinAt.dist, closure_open_halfSpace, sum_mul_eq_sub_integral_mul₀', MeasureTheory.condExpIndL1_smul, ModularGroup.re_T_zpow_smul, ProbabilityTheory.tendstoInDistribution_inv_sqrt_mul_sum, Path.extend_range, Real.Angle.toCircle_coe, eventually_norm_pow_le, ProbabilityTheory.Fernique.normThreshold_eq, Complex.dist_of_im_eq, deriv_rpow_const, MeasureTheory.measureReal_diff, Unitization.norm_eq_sup, ProbabilityTheory.moment_truncation_eq_intervalIntegral_of_nonneg, RCLike.nonneg_iff, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_lt', Real.le_sum_ofDigitsTerm_digits, Real.sin_pos_of_pos_of_lt_pi, unitInterval.symm_one, AbsoluteValue.IsEquiv.equivWithAbs_image_mem_nhds_zero, ProbabilityTheory.isGaussian_map, instIsZLatticeRealSpan, Affine.Simplex.orthogonalProjection_circumcenter, Real.norm_of_nonpos, Real.Angle.tan_eq_inv_of_two_nsmul_add_two_nsmul_eq_pi, instFiniteDimensionalRealComplex, Real.hasDerivAt_cos, GenLoop.fromLoop_symm_toLoop, ENNReal.truncateToReal_le, Differentiable.sigmoid, Topology.CWComplex.source_eq, RCLike.ofReal_zero, Quaternion.expSeries_even_of_imaginary, NumberField.mixedEmbedding.convexBodySumFun_continuous, Topology.CWComplex.pairwiseDisjoint', Real.toNNReal_one, AffineSubspace.signedInfDist_eq_const_of_mem, coe_comp_nnnorm', summable_pow_div_add, ProbabilityTheory.IsMeasurableRatCDF.nonneg, deriv.lhopital_zero_nhdsWithin_convex, Real.sin_eq_sin_iff, HurwitzZeta.continuousOn_sinKernel, intervalIntegral.norm_intervalIntegral_eq, ProbabilityTheory.HasSubgaussianMGF.integrable, IsStrictlyPositive.nnrpow, GroupSeminorm.zero_apply, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_increments, Affine.Triangle.prod_dist_eq_prod_dist_of_mem_line_of_mem_line, Real.toNNReal_div', Orientation.oangle_sub_left_eq_arccos_of_oangle_eq_pi_div_two, ContinuousLinearMap.le_of_opNorm_le, NNReal.geom_mean_le_arith_mean4_weighted, BoundedContinuousFunction.norm_eq_zero_of_empty, BoxIntegral.Box.volume_apply', Real.log_le_iff_le_exp, CStarModule.norm_pos, Complex.arg_eq_pi_div_two_iff, MeasureTheory.measureReal_iUnion_fintype, PiNat.isOpen_iff_dist, MeasureTheory.mul_le_integral_rnDeriv_of_ac, intervalIntegral.inv_mul_integral_comp_sub_div, ProbabilityTheory.gaussianReal_mul_const, 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, NNReal.tendsto_rpow_atTop, Submodule.norm_starProjection, Real.disjoint_residual_ae, Circle.star_addChar, memℓp_gen_iff'', IsSelfAdjoint.norm_pow_two_pow, MeasureTheory.Submartingale.sum_mul_upcrossingStrat_le, Path.delayReflLeft_zero, indicator_indepFun_pi_of_bcf, StrictConvexOn.strictMonoOn_derivWithin, fderiv_cos, Real.sqrt_div_self', Real.comap_sqrt_atTop, Asymptotics.IsBigOWith.triangle, FormalMultilinearSeries.isLittleO_one_of_lt_radius, circleIntegral.norm_integral_lt_of_norm_le_const_of_lt, concaveOn_univ_of_deriv2_nonpos, Function.Periodic.tendsto_atBot_intervalIntegral_of_pos', ContinuousMap.sup_mem_subalgebra_closure, RCLike.continuous_re, isBigO_at_im_infty_jacobiTheta_sub_one, AddCircle.exists_norm_eq_of_isOfFinAddOrder, Asymptotics.IsBigO.exists_mem_basis, AEStronglyMeasurable.norm_condExp_le, Bornology.IsBounded.exists_pos_norm_lt, Real.log_div_self, MeasureTheory.weightedSMul_add_measure, ENNReal.rpow_lt_rpow_of_exponent_lt, Real.limsup_of_not_isCoboundedUnder, NormedAddGroupHom.ratio_le_opNorm, nhds_comap_dist, MeasureTheory.Measure.NullMeasurableSet.const_smul, Real.geom_mean_le_arith_mean4_weighted, Tactic.ComputeAsymptotics.Seq.dist_nil_cons, MDifferentiable.slash, ContDiff.rpow, InnerProductSpace.HarmonicOnNhd.contDiffOn, Real.zero_rpow_eq_iff, MeasureTheory.Measure.map_conv_continuousLinearMap, Polynomial.mahlerMeasure_X_add_C, HurwitzKernelBounds.isBigO_atTop_F_nat_zero_sub, AkraBazziRecurrence.bi_min_div_two_pos, exists_dual_vector, CStarModule.norm_zero, Asymptotics.IsBigOWith.exists_eq_mul, norm_nsmul_le, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, HasFDerivAt.abs_of_neg, ProbabilityTheory.Fernique.lintegral_closedBall_diff_exp_logRatio_mul_sq_le, Real.sign_mul_nonneg, DifferentiableOn.norm_sq, NumberField.mixedEmbedding.logMap_eq_logEmbedding, Affine.Triangle.orthocenter_replace_orthocenter_eq_point, ContDiffMapSupportedIn.locallyConvexSpace, Complex.conjAe_coe, tsum_geometric_of_abs_lt_one, ContinuousMultilinearMap.bounds_bddBelow, banach_steinhaus, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, OnePoint.isBoundedAt_infty_iff, fourierCoeff_toLp, Orientation.oangle_rotation_oangle_left, nsmul_mem_closedBall, HasDerivWithinAt.limsup_slope_norm_le, Real.logb_lt_logb_iff, ContinuousLinearMap.rayleighQuotient_le_norm, OrthonormalBasis.det_to_matrix_orthonormalBasis, SzemerediRegularity.edgeDensity_chunk_uniform, CircleDeg1Lift.transnumAuxSeq_def, mem_balancedHull_iff, smul_unitBall_of_pos, MeasureTheory.L1.SimpleFunc.setToL1S_indicatorConst, ProbabilityTheory.hasDerivAt_complexMGF, Real.continuous_logb, EReal.continuousOn_toReal, Differentiable.norm_rpow, gauge_smul_left_of_nonneg, RingSeminorm.eq_zero_iff, Polynomial.tendsto_norm_atTop, intervalIntegral.integral_mono_ae, 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, Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, coe_fourierBasis, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, tendsto_measure_Icc_nhdsWithin_right, Asymptotics.IsBigOWith.smul, CFC.monotone_rpow, Real.Angle.sin_coe_pi, ENNReal.monotone_truncateToReal, lipschitzWith_iff_norm_sub_le, Real.differentiableWithinAt_arcsin_Ici, InnerProductGeometry.norm_div_sin_angle_add_of_inner_eq_zero, mem_closedBall_iff_norm''', Height.mulHeight₁_sum_le, Complex.ofReal_comp_add, NNReal.rpow_inv_eq_iff, ContinuousLinearMap.le_opNorm_of_le, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, Affine.Simplex.exists_forall_dist_eq_iff_exists_excenterExists_and_eq_excenter, norm_inner_eq_norm_tfae, Real.circleAverage_def, spectrum_imaginaryPart, mem_ball_iff_norm, TopCat.I.ext_iff, BoxIntegral.Box.coe_mk', Real.exp_log_of_neg, abs_norm_sub_norm_le, ProbabilityTheory.Kernel.density_ae_eq_limitProcess, convexOn_of_deriv2_nonneg, irrational_add_intCast_iff, ContDiff.exp, BumpCovering.continuous_toPOUFun, BoxIntegral.Prepartition.upper_le_upper, intervalIntegral.FTCFilter.toTendstoIxxClass, Set.infsep_nonneg, Polynomial.mahlerMeasure_mul, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_eval, intervalIntegral.integral_eq_sub_of_hasDerivAt, NormedAddGroup.tendsto_nhds_nhds, MeasureTheory.isTightMeasureSet_range_iff_tendsto_limsup_inner, Seminorm.map_eq_zero_of_norm_eq_zero, CuspForm.coe_translate, InformationTheory.klDiv_ne_top_iff, Complex.norm_real, Polynomial.zero_le_eval_of_roots_le_of_leadingCoeff_nonneg, RCLike.sqrt_map, Real.toNNReal_eq_natCast, ProbabilityTheory.covariance_eq_sub, derivWithin_exp, Chebyshev.theta_eq_log_primorial, CuspFormClass.petersson_bounded_right, MeasureTheory.integrable_conv_iff, Polynomial.exists_forall_norm_le, ConvexOn.integrable_apply_rnDeriv_of_integrable_compProd, Stirling.sqrt_pi_le_stirlingSeq, ProbabilityTheory.Kernel.IsFiniteKernel.integrable, ProbabilityTheory.charFun_map_add_prod_eq_mul, Real.hasDerivWithinAt_arcsin_Ici, Seminorm.add_apply, UpperHalfPlane.norm_qParam_lt_one, signedDist_vadd_right, ProbabilityTheory.Kernel.compProd_fst_condKernelReal, NNReal.rpow_le_one, InnerProductGeometry.cos_angle_sub_of_inner_eq_zero, Real.HolderTriple.of_pos, HasStrictFDerivAt.arctan, 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, NumberField.sum_nonarchAbsVal_eq, ProbabilityTheory.IsRatCondKernelCDFAux.mono', Real.neg_one_lt_tanh, hasSum_sq_fourierCoeffOn, Matrix.instFiniteElemRealSpectrum, unitInterval.symmMeasurableEquiv_symm_apply, Archimedean.embedReal_injective, ConcaveOn.uniformConcaveOn_zero, InnerProductSpace.Core.inner_re_symm, Vitali.exists_disjoint_subfamily_covering_enlargement_closedBall, Real.logb_lt_iff_lt_rpow_of_base_lt_one, Real.circleAverage_mono_on_of_le_circle, EuclideanGeometry.Sphere.isExtTangentAt_center_iff, unitInterval.qRight_zero_right, ProbabilityTheory.gaussianReal_const_add, Real.liminf_of_not_isCoboundedUnder, rotationOf_rotation, not_sameRay_iff_of_norm_eq, Irrational.natCast_mul, MeasureTheory.DominatedFinMeasAdditive.smul, NumberField.mixedEmbedding.logMap_apply_of_norm_eq_one, CFC.rpow_neg_one_eq_cfc_inv, CStarModule.norm_zero_iff, NormedSpace.equicontinuous_TFAE, hasDerivAt_taylorWithinEval_succ, ProbabilityTheory.strong_law_aux6, CFC.monotoneOn_one_sub_one_add_inv_real, AlternatingMap.norm_image_sub_le_of_bound, 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, exists_contMDiffOn_forall_mem_convex_of_local, NNReal.rpow_add_natCast, BoundedContinuousFunction.exists_forall_mem_restrict_eq_of_closed, unitary.norm_argSelfAdjoint, skewAdjoint.negISMul_apply_coe, Real.lt_log_of_zpow_lt, isNonarchimedean_spectralNorm, deriv_neg_right_of_sign_deriv, Besicovitch.exists_goodδ, PMF.integral_eq_tsum, SpectrumRestricts.real_iff, MeasureTheory.tendsto_of_integral_tendsto_of_monotone, Complex.log_mul_eq_add_log_iff, dist_self_homothety, hasSum_geometric_two, MeasureTheory.lpNorm_abs, ContinuousAt.norm', gauge_pos, NNReal.coe_natCast, Real.tsum_le_of_sum_range_le, LipschitzWith.const_min, 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, Real.dist_le_of_mem_uIcc, RCLike.tendsto_ofReal_cobounded_cobounded, Set.Icc.convexCombo_zero_one, ProbabilityTheory.norm_complexMGF_le_mgf, Complex.UnitDisc.im_conj, intervalIntegral.deriv_integral_left, EReal.toReal_neg_eq, ProbabilityTheory.aemeasurable_of_integrable_exp_mul, Real.injOn_arcsin, Pi.sum_norm_apply_le_norm, IsLocalMin.hasLineDerivAt_eq_zero, Real.cosh_zero, ModularFormClass.exists_bound, ProbabilityTheory.variance_le_sq_of_bounded, Metric.le_infDist, NumberField.mixedEmbedding.volume_preserving_mixedSpaceToRealMixedSpace_symm, Real.antitone_rpow_of_base_le_one, EisensteinSeries.auxbound1, unitary.spectrum_subset_circle, ModularGroup.eq_smul_self_of_mem_fdo_mem_fdo, ProbabilityTheory.Kernel.measurable_singularPart_fun, MeasureTheory.integral_prod_mul, intervalIntegral.integral_comp_div, Affine.Simplex.orthogonalProjection_eq_circumcenter_of_exists_dist_eq, norm_div_sub_norm_div_le_norm_div, Complex.rank_real_complex', contDiff_norm_sq, Real.concaveOn_negMulLog, ContinuousLinearMap.opNorm_add_le, InnerProductGeometry.norm_div_tan_angle_add_of_inner_eq_zero, Valued.toNormedField.norm_le_iff, Metric.Snowflaking.ediam_preimage_ofSnowflaking, 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, intervalAverage_congr_codiscreteWithin, Polynomial.logMahlerMeasure_def, Real.pi_gt_d2, aestronglyMeasurable_derivWithin_Ici, Real.sin_nonneg_of_mem_Icc, MeasureTheory.lpNorm_nnreal_eq_integral_norm_rpow, NNReal.coe_tsum_of_nonneg, BoxIntegral.norm_integral_le_of_le_const, NNReal.image_coe_Ioc, Complex.frontier_setOf_lt_im, Polynomial.logMahlerMeasure_X, MulRingNorm.mulRingNormClass, Real.continuous_logb', Orientation.oangle_sign_smul_left, seminormFromBounded_eq_zero_iff, ModularGroup.im_lt_im_S_smul, HurwitzZeta.sinKernel_zero, MeasureTheory.integrableOn_Iic_of_intervalIntegral_norm_tendsto, deriv_abs_pos, CFC.IsSelfAdjoint.norm_mul_mul_self_of_nonneg, StieltjesFunction.add_apply, Complex.exp_ofReal_im, ContDiffPointwiseHolderAt.continuousLinearMap_comp, derivWithin_rpow_const, EuclideanGeometry.dist_div_sin_angle_of_angle_eq_pi_div_two, Height.mulHeight₁_pos, indicator_indepFun_process_of_bcf, ContinuousWithinAt.cfcₙ_nnreal, SmoothBumpCovering.point_finite, unitInterval.mul_le_right, padic_polynomial_dist, Height.mulHeight₁_sub_le, PartitionOfUnity.locallyFinite', EuclideanGeometry.oangle_pointReflection_right, Polynomial.aeval_conj, ProbabilityTheory.hasFPowerSeriesAt_mgf, InnerProductGeometry.angle_le_angle_add_angle, Complex.integral_exp_neg_mul_rpow, ContinuousLinearMap.NonlinearRightInverse.bound, SchauderBasis.exists_norm_proj_le, ContinuousLinearMap.norm_inr, Asymptotics.IsBigO.sqrt, EReal.ENNReal.rpow_eq_exp_mul_log, Metric.closedBall_zero, lp.norm_eq_card_dsupport, DifferentiableOn.sinh, EuclideanGeometry.Sphere.sOppSide_faceOpposite_secondInter_of_mem_interior_faceOpposite, MeasureTheory.setAverage_eq, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, isIntegralCurve_comp_add, MeasureTheory.smul_le_stoppedValue_hitting, MeasureTheory.convolution_mono_right_of_nonneg, ConvexBody.isBounded, Real.Angle.intCast_mul_eq_zsmul, exists_polynomial_near_continuousMap, PiLp.norm_sq_eq_of_L2, iInter_halfSpaces_eq, RCLike.re_eq_add_conj, Subadditive.tendsto_lim, Complex.slitPlane_eq_union, Real.le_rpow_inv_iff_of_pos, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMap, ZSpan.isAddFundamentalDomain', MeasureTheory.Measure.integrable_compProd_iff, Polynomial.prod_mahlerMeasure_eq_mahlerMeasure_prod, ContDiff.inner, Set.Icc.continuous_convexCombo, ProbabilityTheory.covariance_sub_left, Real.abs_sin_half, Complex.interior_reProdIm, geometric_hahn_banach_closed_compact, InnerProductGeometry.tan_angle_sub_of_inner_eq_zero, 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, Real.qaryEntropy_nonpos_of_nonpos, Conformal.differentiable, Real.tendsto_mul_log_one_add_div_atTop, AkraBazziRecurrence.GrowsPolynomially.mul, Tactic.ComputeAsymptotics.WellFormedBasis.compare_right_aux, NormedAddGroupHom.opNorm_le_bound, Real.sqrtTwoAddSeries_succ, Real.differentiableAt_cosh, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae, Set.Icc.le_convexCombo, Complex.mul_I_re, Path.range_subpath, EuclideanGeometry.oangle_eq_zero_or_eq_pi_iff_collinear, MeasureTheory.Measure.toSignedMeasure_apply, homeomorphUnitSphereProd_symm_apply_coe, GenLoop.coe_coe, WithLp.prod_nndist_eq_add, ProbabilityTheory.iIndepFun.charFunDual_map_sum_eq_prod, TemperedDistribution.fourierMultiplierCLM_toTemperedDistributionCLM_eq, ProbabilityTheory.covarianceBilin_self_nonneg, exists_monotone_Icc_subset_open_cover_unitInterval_prod_self, Orientation.rightAngleRotation_rightAngleRotation, NNReal.rpow_inv_le_iff_of_pos, add_mem_closedBall_iff_norm, PiLp.norm_eq_of_L1, dist_pi_lt_iff, DifferentiableOn.abs, MeasureTheory.Egorov.notConvergentSeqLTIndex_spec, taylorWithinEval_succ, Real.posLog_le_posLog, NNReal.coe_sum, QuotientAddGroup.nhds_zero_hasBasis, HasDerivAt.norm_sq, controlled_prod_of_mem_closure_range, Real.mul_logb, WeakBilin.locallyConvexSpace, GromovHausdorff.ghDist_eq_hausdorffDist, Complex.I_re, ContinuousLinearMap.opNorm_extend_le, ENNReal.rpow_lt_one_of_one_lt_of_neg, 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, NumberField.HeightOneSpectrum.embedding_mul_absNorm, ZLattice.covolume.tendsto_card_le_div', Real.abs_sin_eq_sqrt_one_sub_cos_sq, AddCircle.coe_real_preimage_closedBall_inter_eq, conformalAt_iff_isConformalMap_fderiv, complexOfReal_deriv, exists_msmooth_support_eq_eq_one_iff, EuclideanGeometry.Sphere.abs_oangle_center_right_toReal_lt_pi_div_two, MeasureTheory.norm_setIntegral_le_of_norm_le_const, nonunits.subset_compl_ball, Real.fourier_eq, ProbabilityTheory.HasSubgaussianMGF.aemeasurable, Real.iInf_mul_of_nonpos, Real.pow_rpow_inv_natCast, EuclideanQuadrant.convex, AntilipschitzWith.le_hausdorffMeasure_image, instOrderTopologyReal, Real.volume_Iic, AkraBazziRecurrence.GrowsPolynomially.abs, Real.nnnorm_mul_toNNReal, 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, EuclideanGeometry.oangle_eq_of_dist_orthogonalProjection_eq, seminormFromConst_le_seminorm, AEMeasurable.log, Real.log_le_log, seminormFromConst_const_mul, pi_norm_lt_iff, Polynomial.Chebyshev.integral_eval_T_real_measureT_zero, ZetaAsymptotics.term_one, MeasureTheory.MemLp.eLpNorm_eq_integral_rpow_norm, Real.rpow_one_add', norm_norm, unitInterval.nonneg', Real.closedBall_zero_eq_Icc, NormedAddGroupHom.SurjectiveOnWith.exists_pos, ValueDistribution.logCounting_mul_top_le, MeasureTheory.integral_le_liminf_integral_of_forall_isOpen_measure_le_liminf_measure, deriv.lhopital_zero_nhdsGT, 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, Polynomial.exists_roots_norm_sub_lt_of_norm_coeff_sub_lt, isLittleO_pow_pow_of_abs_lt_left, ProbabilityTheory.condVar_of_not_le, AkraBazziRecurrence.growsPolynomially_pow, Real.summable_and_inner_le_Lp_mul_Lq_tsum_of_nonneg, EuclideanGeometry.Sphere.ncard_inter_orthRadius_le_two, Real.rpow_le_rpow_of_exponent_ge', ContinuousLinearMap.reApplyInnerSelf_apply, MeasureTheory.Submartingale.stoppedProcess, imaginaryPart_realPart, MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable', BoundedContinuousFunction.tendsto_integral_of_forall_integral_le_liminf_integral, MeasureTheory.rnDeriv_trim, 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, Real.tendsto_logb_atTop, norm_sup_le_add, fderiv_exp, Affine.Simplex.direction_mongePlane, ContDiffAt.log, AntilipschitzWith.le_mul_norm_div, AddCircle.continuous_toCircle, Differentiable.log, intervalIntegral.derivWithin_integral_right, NumberField.logHeight₁_eq, MeasureTheory.integrable_of_integral_eq_one, MeasureTheory.integrable_norm_iff, thickening_closedBall, UnconditionalSchauderBasis.norm_proj_le_nnnormProjBound, integral_inv_of_neg, Real.analyticOnNhd_arsinh, ProbabilityTheory.Fernique.measure_gt_normThreshold_le_exp, BoxIntegral.unitPartition.box_lower, Complex.normSq_zero, smoothingFun_nonneg, 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', eventually_nhdsWithin_sign_eq_of_deriv_pos, MeasureTheory.eLpNormLESNormFDerivOneConst_def, RCLike.wInner_const_left, circleIntegrable_log_norm_meromorphicOn, fderiv_arctan, Hyperreal.IsSt.mul, uniqueDiffWithinAt_Ioo, ProbabilityTheory.covarianceBilinDual_self_eq_variance, ENNReal.natCast_le_ofReal, HurwitzZeta.hasSum_int_sinKernel, Real.ofReal_le_enorm, QuasispectrumRestricts.lt_nnreal_iff, ENNReal.lintegral_Lp_add_le, MeasureTheory.log_rnDeriv_tilted_left_self, NormedAddGroupHom.bounds_nonempty, ProperCone.innerDual_union, CompactlySupportedContinuousMap.integralLinearMap_apply, dist_sub_sub_le_of_le, ProbabilityTheory.iCondIndepSet_iff, Affine.Simplex.dist_point_centroid, ProbabilityTheory.gaussianReal_map_div_const, Circle.exp_add, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, Path.Homotopy.trans_apply, Real.analyticAt_arcosh, geometric_hahn_banach_open_open, ContDiffAt.real_of_complex, CircleDeg1Lift.coe_mul, ProbabilityTheory.measurable_measure_stieltjesOfMeasurableRat, IntervalIntegrable.comp_add_right, Orientation.areaForm_comp_linearIsometryEquiv, MeasureTheory.eLpNorm_indicator_const_le, Asymptotics.isBigOWith_abs_abs, inner_self_eq_norm_mul_norm, HurwitzZeta.oddKernel_functional_equation, hasStrictFDerivAt_norm_sq, NNReal.rpow_eq_left_iff, MeasureTheory.MemLp.exists_hasCompactSupport_integral_rpow_sub_le, ProbabilityTheory.Kernel.withDensity_one_sub_rnDerivAux, Affine.Simplex.altitudeFoot_reindex, intervalIntegral.integral_Iio_add_Ici, Height.fun_logHeight_one, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self', SmoothPartitionOfUnity.coe_finsupport, AbsoluteValue.eval_mvPolynomial_le, SchwartzMap.fourier_evalCLM_eq, ContinuousMap.sublattice_closure_eq_top, ENNReal.lintegral_rpow_add_lt_top_of_lintegral_rpow_lt_top, RingNorm.toFun_eq_coe, finite_integral_one_add_norm, mem_ball_iff_norm_neg_add_lt, NumberField.one_le_house_of_isIntegral, unitInterval.symm_le_comm, Real.diam_eq, Mathlib.Tactic.Rify.ratCast_eq, Asymptotics.IsBigOWith.of_abs_left, NNReal.rpow_le_self_of_le_one, Matrix.IsHermitian.sort_roots_charpoly_eq_eigenvalues₀, Real.toNNReal_add_le, WeakFEPair.hg_top, ENNReal.ofReal_le_one, Real.tan_pi_div_two_sub, ContinuousWithinAt.integral_sub_linear_isLittleO_ae, ProbabilityTheory.charFun_map_sum_pi_eq_prod, ConcaveOn.le_map_integral, ProbabilityTheory.stronglyMeasurable_stieltjesOfMeasurableRat, Complex.interior_setOf_im_le, Real.sqrt_lt', Finset.coe_infsep, Real.tendsto_log_nhdsGT_zero, Affine.Simplex.affineCombination_eq_touchpoint_iff, Real.cos_add, RCLike.norm_nsmul, Emetric.exists_contMDiffMap_forall_closedBall_subset, SchwartzMap.contDiffAt, CovBySMul.trans, GroupSeminorm.coe_zero, Real.spectralRadius_mem_spectrum_or, 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, ContDiffOn.sin, EuclideanGeometry.Sphere.power_eq_zero_iff_mem_sphere, Real.cos_arcsin_nonneg, isLittleO_abs_log_rpow_rpow_nhdsGT_zero, EisensteinSeries.norm_le_tsum_norm, Real.isFiniteMeasure_restrict_Ioo, PadicInt.mk_zero, Real.arcsin_of_le_neg_one, NumberField.mixedEmbedding.convexBodySumFun_nonneg, StieltjesFunction.mono, hasMellin_one_Ioc, BumpCovering.nonneg', Real.deriv_exp, IsMIntegralCurveAt.continuousAt, norm_add_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zero, Real.sin_nonpos_of_nonpos_of_neg_pi_le, NumberField.FinitePlace.mulSupport_finite_int, ENNReal.continuousAt_toReal, ValueDistribution.proximity_mul_top_le, Orientation.oangle_sign_smul_sub_left, Liouville.frequently_exists_num, intervalIntegral.integral_Ioi_sub_Ioi', Hyperreal.IsSt.inv, Real.contDiff_sin, NormedAddGroupHom.opNorm_zero_iff, AlgebraNormClass.toRingNormClass, NNReal.rpow_lt_rpow_iff, DirichletCharacter.LSeriesSummable_twist_vonMangoldt, CircleDeg1Lift.translate_apply, SchwartzMap.hasFDerivAt, Affine.Simplex.excenterWeightsUnnorm_empty_apply, Measurable.cosh, ContinuousMultilinearMap.opNorm_add_le, Complex.norm_ratCast, Real.cos_one_pos, QuasispectrumRestricts.real_iff, MeasureTheory.memL1_smul_of_L1_withDensity, ProbabilityTheory.HasGaussianLaw.fun_add, unitInterval.instTietzeExtension, Real.cos_pi_sub, imaginaryPart_eq_neg_I_smul_skewAdjointPart, Submodule.reflection_sub, Real.sin_int_mul_two_pi_sub, MeasureTheory.Measure.toSphere_apply', ContinuousMap.exists_mem_subalgebra_near_continuous_of_isCompact_of_separatesPoints, TemperedDistribution.instLineDerivSMulReal, deriv_sinh, Function.HasTemperateGrowth.pow, EuclideanGeometry.Sphere.mem_inter_orthRadius_iff_radius_nonneg_and_vsub_mem_and_norm_sq, MeasureTheory.MemLp.condExp, eventually_cobounded_le_norm', Real.ball_zero_eq_Ioo, ProbabilityTheory.differentiableAt_iteratedDeriv_mgf, NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero, MeasureTheory.integral_image_eq_integral_deriv_smul_of_antitoneOn, PadicInt.one_le_norm_iff, MeasureTheory.llr_smul_nnreal_left, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_le, ProbabilityTheory.gaussianPDF_zero_var, range_cfcₙ_nnreal_eq_image_cfcₙ_real, SchwartzMap.evalCLM_apply_apply, Real.volume_Icc, StrictConcaveOn.derivWithin_lt_slope, Affine.Simplex.altitudeFoot_mem_altitude, Real.tan_eq_one_sub_tan_half_sq_div_one_add_tan_half_sq, ContinuousAt.rpow, HurwitzZeta.isBigO_atTop_oddKernel, unitary.two_mul_one_sub_le_norm_sub_one_sq, HasStrictDerivAt.log, EisensteinSeries.summable_one_div_norm_rpow, Real.ofCauchy_natCast, Topology.CWComplex.mapsTo', NNReal.list_prod_map_rpow', Real.rpow_le_rpow_left_iff, Complex.conj_cpow_eq_ite, Orientation.rotation_eq_self_iff_angle_eq_zero, Complex.abs_im_lt_norm, isClosed_cantorSet, InnerProductGeometry.angle_smul_right_of_neg, Int.toNat_add_toNat_neg_eq_norm, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, AbsoluteValue.IsEquiv.log_div_log_pos, Real.Lr_rpow_le_Lp_mul_Lq_tsum_of_nonneg, SmoothBumpCovering.eventuallyEq_one, Real.cos_pi_div_six, NormedRing.inverse_add_norm, UpperHalfPlane.ofComplex_apply_eq_ite, IsSelfAdjoint.sq_spectrumRestricts, HasDerivAt.lhopital_zero_left_on_Ioc, Multipliable.norm_tprod, Height.mulHeight_eq, ProbabilityTheory.condVar_ae_le_condExp_sq, MDifferentiableOn.inner_bundle, InformationTheory.mul_log_le_toReal_klDiv, NNReal.rpow_inv_le_iff, ENNReal.one_le_ofReal, SingularManifold.boundaryless, EuclideanGeometry.Sphere.sOppSide_faceOpposite_secondInter_of_mem_interior, Nat.pairwise_one_le_dist, PadicInt.norm_natCast_zmodRepr_eq_one_iff, NumberField.FinitePlace.coe_apply, intervalIntegral.integral_comp_mul_deriv, MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_deriv_mul, dist_mono_left_pi, Real.sin_half_eq_neg_sqrt, Metric.unitBall.instIsLeftCancelMulZero, DifferentiableAt.cosh, Real.sqrt_le_one, Affine.Simplex.inradius_eq_abs_inv_sum, ENNReal.ofReal_lt_natCast, isBounded_convexHull, MeasureTheory.Measure.toTemperedDistribution_apply, Filter.Tendsto.cfcₙ_nnreal, TopologicalGroup.IsSES.integrate_apply, UpperHalfPlane.volume_eq_lintegral, Real.range_arcsin, EReal.preimage_coe_Ioc, tendsto_integral_exp_smul_cocompact_of_inner_product, Continuous.mulExpNegMulSq, dist_le_tsum_of_dist_le_of_tendsto₀, NumberField.InfiniteAdeleRing.norm_eq_zero_of_not_isUnit, ProbabilityTheory.Kernel.exists_measurable_map_eq_unitInterval, ProbabilityTheory.withDensity_preCDF, Real.nnnorm_two, CircleDeg1Lift.translationNumber_le_ceil_sub, ProbabilityTheory.Kernel.setIntegral_densityProcess, BoxIntegral.Box.Icc_def, Affine.Simplex.circumcenter_restrict, PUnit.norm_eq_zero, SchwartzMap.instContinuousFourierInv, InnerProductGeometry.sin_angle_sub_mul_norm_of_inner_eq_zero, EuclideanGeometry.angle_rev_eq_pi_div_two_of_oangle_eq_pi_div_two, LinearMap.re_inner_adjoint_mul_self_nonneg, range_euclideanHalfSpace, NNReal.isBoundedUnder_le_toReal, mem_parallelepiped_iff, HurwitzZeta.LSeriesHasSum_exp, dist_le_of_le_geometric_two_of_tendsto, StrictConvexOn.slope_lt_derivWithin, Asymptotics.isBigOWith_norm_left, MeasureTheory.integral_biUnion_eq_sum_powerset, seminormFromBounded_one, Real.hasDerivAt_rpow_const, UpperHalfPlane.isPretransitiveSL2R, IsUltrametricDist.norm_sum_eq_sup'_of_pairwise_ne, EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_affineIndependent, IsMinOn.lineDeriv_eq_zero, DirichletCharacter.convolution_twist_vonMangoldt, ModularGroup.im_T_zpow_smul, InnerProductGeometry.angle_add_lt_pi_div_two_of_inner_eq_zero, MeasureTheory.ae_nonneg_restrict_of_forall_setIntegral_nonneg_inter, Orientation.oangle_rotation_right, Complex.neg_pi_lt_log_im, Affine.Simplex.height_restrict, LocallyLipschitz.min_const, Complex.ofReal_comp_balance, rothNumberNat_isLittleO_id, ValueDistribution.characteristic_mul_zero_eventuallyLE, Real.toNNReal_mul_nnnorm, exists_bounded_mem_Icc_of_closed_of_le, real_inner_le_norm, Real.tendsto_log_nhdsLT_zero, Real.rpow_logb, Affine.Triangle.affineSpan_orthocenter_point_le_altitude, MeasureTheory.Integrable.re_im_iff, Path.Homotopy.continuous_reflTransSymmAux, Real.arccos_eq_pi, RCLike.normSq_mul, InnerProductGeometry.norm_sub_eq_add_norm_iff_angle_eq_pi, Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded, ConvexOn.slope_le_of_hasDerivWithinAt, EisensteinSeries.isBoundedAtImInfty_eisensteinSeries_SIF, Real.rpow_lt_rpow_iff_of_neg, ValueDistribution.characteristic_pow_zero, Mathlib.Meta.NormNum.IsNat.nnreal_rpow_eq_nnreal_pow, Path.inv_apply, Real.artanh_lt_artanh_iff, differentiableAt_norm_smul, EuclideanGeometry.Sphere.dist_sq_eq_of_mem_orthRadius, 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, fderivWithin.log, Real.coe_intFib_eq, MeasureTheory.SignedMeasure.singularPart_neg, intervalIntegral.integral_eq_sub_of_hasDeriv_right_of_le_real, ContinuousLinearMap.norm_map_tail_le, ProbabilityTheory.HasGaussianLaw.fun_sub, Complex.I_im, AntitoneOn.integral_le_sum_Ico, 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, ProbabilityTheory.IsGaussianProcess.indepFun_of_covariance_eq_zero, MeasureTheory.AEStronglyMeasurable.norm, EReal.image_coe_Ici, Real.iter_deriv_exp, HasFDerivWithinAt.sinh, LipschitzOnWith.norm_div_le_of_le, intervalIntegral.inv_smul_integral_comp_div_sub, seminormFromConst_apply_of_isMul, EReal.toReal_top, Real.rpowIntegrand₀₁_apply_mul, Module.Basis.prod_parallelepiped, ProbabilityTheory.measurable_poissonPMFReal, Metric.exists_contMDiffMap_forall_closedBall_subset, ProbabilityTheory.IndepFun.integral_fun_comp_mul_comp, Real.convexOn_Gamma, summable_dirichletSummand, ValueDistribution.characteristic_top_mul_le, Real.summable_Lp_add_of_nonneg, intervalIntegral.integral_of_ge, NumberField.mixedEmbedding.norm_nonneg, TopCat.toSSetObj₀Equiv_apply, 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, szemeredi_regularity, Real.Gamma_nat_add_one_add_half, intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDeriv_right, EReal.coe_neg', Seminorm.convex_ball, Real.cos_eq_one_iff_of_lt_of_lt, ContinuousMap.Homotopy.trans_apply, ENNReal.lintegral_mul_le_Lp_mul_Lq_of_ne_zero_of_eq_top, Real.rpow_one, unitInterval.div_mem, Differentiable.norm_sq, Hyperreal.coe_inv, InnerProductGeometry.angle_add_pos_of_inner_eq_zero, ContinuousMap.HomotopyRel.symm_apply, IsUnit.cfcNNRpow, ProbabilityTheory.iIndepFun.charFun_map_sum_eq_prod, exists_dual_vector'', exists_msmooth_zero_iff_one_iff_of_isClosed, ConcaveOn.set_average_mem_hypograph, map_pow_le_pow', PiTensorProduct.injectiveSeminorm_apply, Metric.infDist_le_infDist_of_subset, InnerProductGeometry.tan_angle_add_of_inner_eq_zero, Homeomorph.unitBall_apply_coe, RCLike.norm_wInner_le, NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_le, PartitionOfUnity.sum_finsupport_smul_eq_finsum, MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_part, StieltjesFunction.measure_Ioi, Real.continuous_sinh, BoundedContinuousFunction.Lp_norm_le, harmonic_floor_le_one_add_log, ProbabilityTheory.IsGaussian.memLp_dual, LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re, MeasureTheory.exists_integral_le, EuclideanGeometry.dist_mul_of_eq_angle_of_dist_mul, Asymptotics.isBigO_atTop_iff_eventually_exists_pos, Units.val_inv_cfcRpow, Asymptotics.isBigOWith_iff_exists_eq_mul, Complex.normSq_conj, Set.OrdConnected.image_coe_nnreal_real, Height.mulHeight_eq_one_of_subsingleton, schnirelmannDensity_univ, Path.refl_apply, IsCompact.extremePoints_nonempty, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul_real, Module.Dual.extendRCLikeₗ_apply, isConnected_setOf_sameRay_and_ne_zero, curveIntegralFun_neg, Behrend.ceil_lt_mul, Real.continuousOn_exp, ZetaAsymptotics.term_tsum_one, mem_closedBall_iff_norm_neg_add_le', ENNReal.rpow_intCast, WithLp.prod_lipschitzWith_toLp, UpperHalfPlane.dist_eq_iff_dist_coe_center_eq, Complex.norm_sub_le_angle, ENNReal.toNNReal_natCast_eq_toNNReal, TestFunction.lineDerivCLM_eq_fderivCLM, Complex.continuous_normSq, Chebyshev.theta_mono, TopologicalAddGroup.IsSES.integrate_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, conformalFactorAt_inner_eq_mul_inner', NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst, BoxIntegral.Box.isBounded_Icc, StrictConvexOn.slope_lt_of_hasDerivWithinAt_Iio, ball_eq', Path.range_segment, MeasureTheory.VectorMeasure.of_nonneg_disjoint_union_eq_zero, HasFDerivAt.log, Height.mulHeight_eval_ge, Metric.mem_closedBall', ContDiffBump.measure_closedBall_le_integral, Tactic.ComputeAsymptotics.isBigO_of_div_tendsto_atBot, ProbabilityTheory.isGaussian_map_of_measurable, Real.iSup_of_isEmpty, Metric.Sum.one_le_dist_inl_inr, ContinuousOn.sqrt, HasDerivWithinAt.arctan, TemperedDistribution.fourier_lineDerivOp_eq, convexHull_sphere_eq_closedBall, isCusp_SL2Z_iff, NumberField.mixedEmbedding.fundamentalCone.continuous_expMapBasis, Complex.equivRealProdLm_symm_apply, ContDiffPointwiseHolderAt.clm_apply, PadicInt.isUnit_iff, Irrational.sub_intCast, ProbabilityTheory.setIntegral_tilted_mul_eq_cgf', ValueDistribution.logCounting_top_mul_eventually_le, Complex.norm_zpow, norm_lt_iff_of_compactlySupported, Real.log_div_self_antitoneOn, ENNReal.ofReal_one, isOpen_deltaGenerated_iff, ProbabilityTheory.mgf_pos', NonarchAddGroupSeminorm.smul_apply, UniformFun.dist_le, ProbabilityTheory.Kernel.integral_densityProcess, MeasureTheory.charFunDual_map_const_add, MeasureTheory.Integrable.integral_eq_integral_meas_le, NNReal.one_le_rpow_of_pos_of_le_one_of_nonpos, Real.binEntropy_neg_of_one_lt, Real.rpow_left_inj, Metric.mem_closure_range_iff, MeasurableEmbedding.gaussianReal_comap_apply, EuclideanGeometry.Sphere.IsTangentAt_of_angle_eq_pi_div_two, PiCountable.dist_le_dist_pi_of_dist_lt, MeasureTheory.L1.SimpleFunc.setToL1S_const, tendsto_smoothingFun_of_map_one_le_one, SmoothPartitionOfUnity.finsum_smul_mem_convex, Real.Angle.sign_two_nsmul_eq_sign_iff, HurwitzKernelBounds.F_int_eq_of_mem_Icc, 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, Orientation.inner_eq_zero_of_oangle_eq_neg_pi_div_two, IntervalIntegrable.aestronglyMeasurable, Complex.coe_basisOneI_repr, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, Complex.volume_sum_rpow_lt, realPart_I_smul, Complex.conjCLE_coe_toLinearMap, ProbabilityTheory.evariance_zero, Orientation.rotation_trans, NormedAddCommGroup.tendsto_nhds_nhds, ProbabilityTheory.IsRatCondKernelCDFAux.le_one', NNReal.isCoboundedUnder_ge_toReal, ProbabilityTheory.aestronglyMeasurable_exp_mul_sum, uniqueDiffWithinAt_Ioi, RCLike.norm_im_le_norm, Seminorm.exists_apply_eq_finset_sup, ENNReal.toNNReal_rpow, lp.norm_compl_sum_single, Path.continuous_uncurry_iff, PiLp.norm_eq_ciSup, inner_lt_one_iff_real_of_norm_one, ProbabilityTheory.Kernel.densityProcess_nonneg, mem_ball_iff_norm_neg_add_lt', Metric.hausdorffDist_le_diam, MeasureTheory.Measure.toSignedMeasure_add, KuratowskiEmbedding.embeddingOfSubset_isometry, DifferentiableOn.cos, NNReal.coe_min, Polynomial.quadratic_dvd_of_aeval_eq_zero_im_ne_zero, CFC.rpow_neg_one_eq_inv, signedDist_lineMap_left, selfAdjoint.realPart_unitarySelfAddISMul, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_orthonormalBasis, MeasureTheory.ae_le_lpNorm_exponent_top, gauge_def, TestFunction.lineDerivCLM_apply, ProbabilityTheory.variance_mul_const, dist_add_add_le, ModularGroup.tendsto_normSq_coprime_pair, WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded, HurwitzZeta.hurwitzZetaEven_one_sub_two_mul_nat, ProbabilityTheory.covarianceBilin_real_self, Real.enorm_eq_ofReal_abs, Real.toNNReal_lt_one, MeasureTheory.BoundedContinuousFunction.integral_eq_integral_meas_le, contraction_of_isPowMul_of_boundedWrt, ContinuousOn.cfc_nnreal, MeasureTheory.Measure.IicSnd_apply, MeasureTheory.setIntegral_condExpL1CLM_of_measure_ne_top, BoundingSieve.siftedSum_le_sum_of_upperMoebius, ProbabilityTheory.IndepFun.cgf_add, nnnorm_cfcₙ_nnreal_lt_iff, Real.tendsto_rightDeriv_mul_log_atTop, Real.lt_tan, 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, Real.fourier_iteratedDeriv, Complex.abs_arg_inv, MeasureTheory.lpNorm_norm, Complex.normSq_intCast, unitInterval.qRight_zero_left, EuclideanGeometry.cos_oangle_left_of_oangle_eq_pi_div_two, MeasureTheory.integral_comp_rpow_Ioi, cfc_integral, NormedAlgebra.toMulAlgebraNorm_apply, EuclideanGeometry.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, bernsteinApproximation.apply_one, convex_closedEBall, HarmonicAt.analyticAt, LiouvilleWith.add_nat, MeasureTheory.condExp_ae_eq_condExpL1CLM, NumberField.FinitePlace.equivHeightOneSpectrum_symm_apply, EuclideanGeometry.Sphere.dist_center_midpoint_lt_radius, Real.strictMonoOn_logb, Module.Basis.norm_isNonarchimedean, integral_univ_inv_one_add_sq, Real.sin_int_mul_pi_sub, ProbabilityTheory.covariance_const_mul_right, Real.posLog_abs, ProbabilityTheory.add_half_inf_sub_mem_Ioo, Real.multipliable_one_add_of_summable, ConvexOn.convex_re_epigraph, Real.posLog_def, ProbabilityTheory.cgf_neg, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric, tendsto_self_mul_const_pow_of_abs_lt_one, 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, InnerProductGeometry.mul_norm_eq_abs_sub_sq_norm, real_inner_le_one_of_norm_eq_one, Real.logb_one_left_eq_zero, ValueDistribution.characteristic_sub_characteristic_inv, MeasureTheory.Lp.eLpNorm'_lim_eq_lintegral_liminf, integrable_rpow_mul_exp_neg_mul_sq, 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, integral_exp_neg_rpow, ProbabilityTheory.covariance_fun_sum_fun_sum', WeakFEPair.hf_zero, RCLike.realLinearIsometryEquiv_symm_apply, Convex.exists_subset_interior_convexHull_finset_of_isCompact, convex_ball, ProbabilityTheory.Kernel.rnDerivAux_nonneg, Polynomial.Chebyshev.U_real_cos, AlternatingMap.norm_image_sub_le_of_bound', real_inner_smul_right, HolderOnWith.holderOnWith_zero_of_bounded, Metric.continuousAt_iff', WithLp.prod_norm_eq_of_L1, EuclideanGeometry.Sphere.mem_of_mem_tangentsFrom, scalarSMulCLE_apply, Real.inv_sqrt_two_sub_one, HurwitzKernelBounds.summable_f_nat, ProbabilityTheory.IsCondKernelCDF.measurable, Continuous.arccos, Asymptotics.isBigOWith_top, Circle.leftInverse_exp_arg, AnalyticWithinAt.re_ofReal, norm_sub_le_of_mem_segment, ContinuousLinearMap.hasTemperateGrowth, Complex.measurable_im, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, Seminorm.uniformContinuous, Complex.continuousAt_ofReal_cpow, ProbabilityTheory.HasSubgaussianMGF.neg, HolderWith.comp_holderOnWith, UpperHalfPlane.pos_real_smul_injective, mul_sub_lt_image_sub_of_lt_deriv, Orientation.tan_oangle_sub_left_of_oangle_eq_pi_div_two, MeasureTheory.eLpNorm_le_of_ae_enorm_bound, infDist_smul₀, not_differentiableWithinAt_of_deriv_tendsto_atTop_Iio, InformationTheory.klDiv_eq_integral_klFun, NormedAddGroupHom.Equalizer.norm_map_le, Orientation.oangle_sub_right_smul_rotation_pi_div_two, ProbabilityTheory.lintegral_toKernel_mem, 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', ConcaveOn.le_slope_of_hasDerivWithinAt, EuclideanGeometry.continuousAt_angle, EisensteinSeries.linear_inv_isBigO_right_add, ValueDistribution.characteristic_nonneg, Path.prod_coe, Urysohns.CU.approx_le_one, MeasureTheory.hasFiniteIntegral_iff_ofReal, abs_real_inner_div_norm_mul_norm_le_one, integrable_mul_exp_neg_mul_sq, LinearMap.isPositive_iff_complex, GaussianInt.toComplex_re_div, PhragmenLindelof.isBigO_sub_exp_exp, Real.Angle.sin_pi_div_two_sub, Real.sin_add_pi_div_two, NNReal.one_lt_rpow, ENNReal.toReal_ofReal_mul, bernstein_nonneg, VectorFourier.fourierSMulRight_apply, Real.contDiff_cos, inner_self_eq_norm_sq, tendsto_fib_div_fib_succ_atTop, Real.cosh_pos, HasCompactSupport.rpow_const, Real.volume_pi_Ioo, LocallyBoundedVariationOn.ae_differentiableWithinAt_of_mem, 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, LipschitzWith.norm_neg_add_le_of_le, MeasureTheory.Integrable.integral_eq_integral_meas_lt, stereographic_neg_apply, StrongConcaveOn.strictConcaveOn, integral_cexp_quadratic, Metric.hasBasis_nhdsSet_cthickening, Real.sq_lt, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, NormedRing.inverse_add_norm_diff_second_order, MeasureTheory.Measure.addHaar_image_linearMap, Metric.Snowflaking.preimage_toSnowflaking_eball, continuousAt_gauge_zero, ProbabilityTheory.tendsto_stieltjesOfMeasurableRat_atBot, seminormFromBounded_isNonarchimedean, ProbabilityTheory.integrable_exp_mul_of_le_of_le, ODE_solution_unique_of_eventually, 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, exists_closed_cover_approximatesLinearOn_of_hasFDerivWithinAt, Real.closedBall_eq_segment, ProbabilityTheory.evariance_def', MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, Real.Angle.sin_add, RCLike.lipschitzWith_re, NumberField.mixedEmbedding.fundamentalCone.expMap_symm_apply, Seminorm.coe_sSup_eq', PadicInt.limNthHom_spec, GromovHausdorff.eq_toGHSpace, ContinuousOn.isBigOWith_principal, Real.HolderConjugate.conjugate_eq, Real.binEntropy_one, CongruenceSubgroup.strictWidthInfty_Gamma1, NonarchAddGroupSeminorm.ext_iff, Seminorm.closedBall_smul, Real.lt_rpow_inv_iff_of_neg, instIsRiemannianManifoldModelWithCornersSelfReal, PartitionOfUnity.locallyFinite_tsupport, exists_hasDerivAt_eq_zero', uniqueDiffOn_convex, Measurable.re, MeasureTheory.L1.tendsto_setToL1, eventually_norm_symmL_trivializationAt_self_comp_lt, MeasureTheory.eLpNorm_const', MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le', RCLike.ofReal_pow, Real.stronglyMeasurable_sinc, OrthonormalBasis.det_adjustToOrientation, dist_add_add_le_of_le, Cardinal.mk_Iic_real, NumberField.Units.dirichletUnitTheorem.unitLattice_inter_ball_finite, NumberField.mixedEmbedding.polarCoord_source, MeasureTheory.condExpL1CLM_indicatorConst, nnnorm_cfc_nnreal_lt, integral_inv, HurwitzZeta.sinKernel_undef, SchwartzMap.fourierMultiplierCLM_ofReal, unique_unit_speed, NormedAddGroupHom.bound, Real.isScalarTower, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, MeasureTheory.AEStronglyMeasurable.truncation, SmoothBumpFunction.isClosed_image_of_isClosed, Real.sInf_nonpos, UpperHalfPlane.J_smul, MeasureTheory.norm_integral_le_of_norm_le_const, Real.circleAverage_eq_circleAverage_zero_one, Asymptotics.isLittleO_norm_pow_norm_pow, Real.continuous_log', Real.logb_nonpos_iff', variationOnFromTo.eq_zero_iff_of_ge, ContinuousMap.modulus_pos, NormedSpace.normalize_smul_of_neg, ContMDiffOn.inner_bundle, Complex.orthonormalBasisOneI_repr_symm_apply, SlashInvariantForm.slash_action_eqn'', Real.sqrt_lt_sqrt_iff, Real.aemeasurable_of_aemeasurable_exp_mul, SmoothPartitionOfUnity.sum_nonneg, ProbabilityTheory.Kernel.tendsto_densityProcess_fst_atTop_univ_of_monotone, MeasureTheory.L1.nnnorm_Integral_le_one, intervalIntegral.abs_integral_le_integral_abs, HasFDerivAt.exp, irrational_sqrt_of_multiplicity_odd, seminormFromBounded_mul, HurwitzZeta.sinZeta_two_mul_nat_add_one', LinearGrowth.Real.eventually_atTop_exists_nat_between, ContDiffWithinAt.laplacianWithin_CLM_comp_left, 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, cfcₙ_imaginaryPart, Subgroup.instHasDetPlusMinusOneFinOfNatNatRealOfIsArithmetic, WithLp.prod_dist_eq_add, spectralNorm_one, curveIntegralFun_fun_zero, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_zero_of_antitone, hasFDerivWithinAt_closure_of_tendsto_fderiv, Real.one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, EuclideanGeometry.oangle_homothety, Real.Angle.toReal_injective, MeasureTheory.ProbabilityMeasure.continuous_integral_boundedContinuousFunction, ClosedSubmodule.mulI_inf, RCLike.ofReal_alg, Polynomial.Chebyshev.eval_iterate_derivative_le_of_forall_abs_le_one, MeasureTheory.integral_fun_norm_addHaar, Complex.norm_iteratedDeriv_le_of_forall_mem_sphere_norm_le, Affine.Simplex.ExcenterExists.sOppSide_point_excenter_iff, tendsto_sum_mul_atTop_nhds_one_sub_integral₀, AnalyticAt.sigmoid, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae', MeasureTheory.setIntegral_ge_of_const_le, isScalarTower_sphere_sphere_closedBall, MeasureTheory.L1.integral_eq_norm_posPart_sub, signedDist_anticomm, Metric.exists_subseq_bounded_of_cauchySeq, Irrational.instDenselyOrderedSubtypeReal, ENNReal.ofReal_max, ArchimedeanClass.lt_of_stdPart_lt, imaginaryPart_apply_coe, BumpCovering.locallyFinite_tsupport, Affine.Simplex.height_pos, Complex.UnitDisc.instSMulCommClass_closedBall_right, IsOpen.measure_eq_biSup_integral_continuous, Real.binEntropy_pos, real_inner_self_eq_norm_sq, PartitionOfUnity.continuous_finsum_smul, AkraBazziRecurrence.eventually_one_sub_smoothingFn_pos_real, EuclideanGeometry.dist_le_of_wbtw_of_mem_perpBisector, EuclideanGeometry.oangle_left_eq_arccos_of_oangle_eq_pi_div_two, Nat.realSqrt_lt_ratSqrt_add_inv_prec, PseudoMetricSpace.cobounded_sets, continuousAt_gauge, Real.add_rpow_le_rpow_add, MeasureTheory.Martingale.ae_not_tendsto_atTop_atTop, Asymptotics.IsBigO.mul_atTop_rpow_of_isBigO_rpow, StrictAntiOn.strictConcaveOn_of_deriv, SchwartzMap.smulLeftCLM_add, Real.ratCast_lt, Real.iteratedDeriv_even_cos, Complex.cos_bound, MeasureTheory.JordanDecomposition.real_smul_posPart_nonneg, MeasureTheory.weightedSMul_smul, ContinuousLinearEquiv.norm_symm_pos, MeasureTheory.integral_continuousLinearMap_prod, EisensteinSeries.eisensteinSeries_SIF_apply, Metric.closedBall_zero', norm_deriv_le_of_lipschitz, intervalIntegral.integral_sub_linear_isLittleO_of_tendsto_ae, Real.goldenConj_neg, EuclideanGeometry.dist_lt_of_sbtw_of_mem_perpBisector, segment_subset_closedBall_left, CFC.rpow_le_rpow, Real.sInf_nonneg, Real.continuousAt_rpow_of_ne, MultilinearMap.mkContinuousLinear_norm_le', Real.taylor_tendsto, MeasureTheory.Lp.norm_const, ProbabilityTheory.Kernel.HasSubgaussianMGF.of_map, Complex.HadamardThreeLines.sSupNormIm_eps_pos, ProbabilityTheory.mgf_add_const, Complex.cpow_inv_two_im_eq_sqrt, Real.zero_lt_one, TemperedDistribution.laplacian_eq_sum, MeasureTheory.eLpNorm_indicator_le_of_bound, tendsto_uniformity_iff_dist_tendsto_zero, Affine.Simplex.dist_circumcenter_eq_circumradius, curveIntegralFun_def', NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, MeasureTheory.VectorMeasure.of_nonpos_disjoint_union_eq_zero, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, exists_subset_iUnion_ball_radius_pos_lt, 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, intervalIntegral.continuousWithinAt_primitive, 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, Real.lt_logb_iff_rpow_lt, NumberField.Units.dirichletUnitTheorem.logEmbedding_eq_zero_iff, ContinuousWithinAt.arsinh, ENNReal.lt_ofReal_iff_toReal_lt, UnitAddCircle.mem_approxAddOrderOf_iff, instProperSpaceReal, dist_self, EuclideanGeometry.cos_angle_of_angle_eq_pi_div_two, IsUltrametricDist.norm_zsmul_le, tendsto_log_div_rpow_nhdsGT_zero, Real.tendsto_logb_nhdsNE_zero_of_base_lt_one, ContinuousMultilinearMap.ratio_le_opNorm, Real.geom_mean_le_arith_mean3_weighted, ZSpan.fundamentalDomain_subset_parallelepiped, Real.iSup_pow_of_ne_zero, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux2, not_summable_indicator_mod_of_antitone_of_neg, ZetaAsymptotics.zeta_limit_aux1, ContinuousLinearMap.norm_extendTo𝕜'_bound, NNReal.le_rpow_inv_iff, Real.pi_gt_sqrtTwoAddSeries, sum_mem_ball_of_strictConvexSpace, ball_eq_norm_neg_add_lt, CStarRing.norm_star_mul_self, Tactic.ComputeAsymptotics.Majorized.add, SmoothBumpFunction.isClosed_symm_image_closedBall, MeasureTheory.hausdorffMeasure_homothety_image, ProbabilityTheory.measurable_stieltjesOfMeasurableRat, 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, ENNReal.toReal_pos, pi_norm_const_le', uniqueDiffWithinAt_Iio, NNReal.rpow_inv_rpow_self, eq_lineMap_of_dist_eq_mul_of_dist_eq_mul, Real.rpow_intCast_mul, Manifold.pathELength_comp_of_monotoneOn, spectralNorm_smul, ContDiffWithinAt.rpow, ProbabilityTheory.IsGaussianProcess.comp_right, ProbabilityTheory.HasGaussianLaw.fun_neg, Height.logHeight_eq_zero_of_subsingleton, Real.cosh_le_exp_half_sq, Real.list_prod_map_rpow, CFC.inverse_rpow, DenseRange.exists_dist_lt, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, Real.measurable_arccos, Complex.im_balance, ArchimedeanClass.stdPart_neg, LinearIsometryEquiv.contDiffPointwiseHolderAt_left_comp, smoothingSeminorm_apply_of_map_mul_eq_mul, Real.rpow_inv_le_iff_of_neg, Complex.ofReal_expect, IsSelfAdjoint.im_eq_zero_of_mem_spectrum, EuclideanGeometry.cos_eq_neg_one_iff_angle_eq_pi, differentiableWithinAt_abs_neg, sum_mul_eq_sub_integral_mul₁, ContDiffAt.norm_sq, MeasureTheory.integral_comp, Affine.Simplex.sum_circumcenterWeightsWithCircumcenter, ProbabilityTheory.stieltjesOfMeasurableRat_eq, TemperedDistribution.instContinuousLineDeriv, Chebyshev.psi_eq_theta_add_sum_theta, RCLike.I_im, MeasureTheory.integral_pos_iff_support_of_nonneg, GroupNorm.groupNormClass, ProbabilityTheory.iteratedDeriv_mgf_zero, EisensteinSeries.r1_eq, NormedField.exists_lt_norm, ENNReal.toReal_limsup, MeasureTheory.GridLines.T_empty, MeasureTheory.L1.setToL1_unique, AddGroupSeminorm.sup_apply, tsirelson_inequality, UpperHalfPlane.instIsIsometricSMulSpecialLinearGroupFinOfNatNatReal, ProbabilityTheory.moment_truncation_eq_intervalIntegral, RCLike.complexLinearIsometryEquiv_symm_apply, Real.differentiableOn_negMulLog, MeasureTheory.average_union_mem_segment, Real.Gamma_ofNat_eq_factorial, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt_1d, UpperHalfPlane.denom_neg, BoxIntegral.Box.mapsTo_insertNth_face, Submonoid.coe_unitSphere, Complex.div_re, Real.convex_iff_isPreconnected, NNReal.rpow_add_rpow_le, Complex.abs_arg_le_pi_div_two_iff, Height.logHeight₁_prod_le, ProbabilityTheory.integrable_exp_mul_gaussianReal, hasGradientAt_iff_tendsto, unitInterval.symm_eq_zero, MulRingNorm.mulRingNormEquivAbsoluteValue_symm_apply, MeasureTheory.integrable_add_iff_of_nonpos, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, InformationTheory.convexOn_klFun, image_sub_le_mul_sub_of_deriv_le, NormedSpace.norm_le_dual_bound, cfcₙ_real_eq_nnreal, HasDerivAt.arsinh, dist_right_convexComboPair, hasDerivAt_fourier, Real.logb_inv_base, cfc_comp_re, ProbabilityTheory.cdf_expMeasure_eq_integral, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup, UniformConcaveOn.add, Real.rpow_lt_one_of_one_lt_of_neg, BoxIntegral.Box.monotone_upper, Real.arcsin_eq_zero_iff, complexOfReal_fderivWithin, Real.inv_logb_mul_base, NumberField.Units.regOfFamily_div_regOfFamily, MeasureTheory.rnDeriv_ae_eq_condExp, 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, DiffContOnCl.circleAverage_poissonKernel_smul, spectrum.limsup_pow_nnnorm_pow_one_div_le_spectralRadius, stdSimplexHomeomorphUnitInterval_apply_coe, AddGroupSeminorm.coe_sSup_apply, EuclideanGeometry.sin_angle_of_angle_eq_pi_div_two, SeparationQuotient.norm_liftNormedAddGroupHom_le, Complex.measurableEquivRealProd_symm_polarCoord_symm_apply, HurwitzZeta.completedHurwitzZetaOdd_neg, PMF.binomial_apply_of_le, Besicovitch.ae_tendsto_measure_inter_div, SmoothBumpFunction.c_mem_support, Complex.UnitDisc.instIsScalarTower_closedBall, ArchimedeanClass.stdPart_sub_eq_right, Real.isFiniteMeasure_restrict_Icc, rpow_mul_exp_neg_mul_sq_isLittleO_exp_neg, Hyperreal.IsSt.sub, Complex.volume_preserving_equiv_real_prod, Real.summable_one_div_nat_rpow, Real.ceil_exp_one_eq_three, ProbabilityTheory.variance_add_prod, Real.rpow_sub_one, EuclideanGeometry.Sphere.direction_orthRadius_le_iff, NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, MeasureTheory.integrable_comp_mul_left_iff, intervalIntegral.integral_deriv_mul_eq_sub, ProbabilityTheory.gaussianReal_map_mul_const, Metric.continuousWithinAt_iff, MeasureTheory.llr_smul_same, ContinuousLinearMap.IsPositive.re_inner_nonneg_left, Metric.thickening_ball, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_rclike_tendsto, Real.ofDigitsTerm_nonneg, StrongDual.extendRCLikeₗᵢ_symm_apply, Metric.sphere.instContinuousMul, Polynomial.IsMonicOfDegree.eq_isMonicOfDegree_one_or_two_mul, ProbabilityTheory.HasGaussianLaw.map_of_measurable, Real.rightDeriv_mul_log, dist_add_dist_eq_iff, LiouvilleWith.frequently_lt_rpow_neg, ProbabilityTheory.Kernel.integrable_density, Measurable.log, intervalIntegral.integral_of_le, nnnorm_cfc_nnreal_le, ZLattice.summable_norm_pow_inv, ComputeAsymptotics.MultiseriesExpansion.Multiseries.Pairwise_cons_nil, AkraBazziRecurrence.asympBound_def', Metric.mem_thickening_iff_infDist_lt, ZMod.LFunction_def_even, Metric.uniformity_basis_dist_le, Real.volume_real_Ico_of_le, ValueDistribution.characteristic_sum_top_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.HasGaussianLaw.indepFun_of_covariance_eval, ProbabilityTheory.hasFiniteIntegral_prodMk_left, Asymptotics.IsBigOWith.sum_congr, UpperHalfPlane.le_dist_coe, IsSelfAdjoint.norm_eq_max_norm_posPart_negPart, MeasureTheory.Measure.haarScalarFactor_eq_integral_div, IsLocalExtrOn.exists_linear_map_of_hasStrictFDerivAt, Real.ofCauchy_ratCast, Prod.norm_def, ContinuousOn.cfcₙ_nnreal_of_mem_nhdsSet, Real.continuousOn_sin, Real.volume_pi_Ioo_toReal, EuclideanGeometry.Sphere.IsTangentAt.mem_and_mem_iff_eq, AddCircle.le_add_order_smul_norm_of_isOfFinAddOrder, Asymptotics.IsBigOWith.abs_abs, homeomorphSphereProd_symm_apply_coe, ContinuousMap.HomotopyWith.extendProp, Real.isLittleO_const_log_atTop, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, Height.mulHeight₁_mul_le, Asymptotics.IsBigO.trans_tendsto_norm_atTop, Polynomial.gaussNorm_monomial, fourier_apply, ContinuousLinearMap.le_opNorm₂, ProbabilityTheory.tendsto_zero_of_tendsto_mul_atTop, Real.one_sub_mul_le_cos, 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, Seminorm.continuous_iff, ProbabilityTheory.hasFiniteIntegral_comp_iff', circleMap_neg_radius, MeasureTheory.integrable_tilted_iff, irrational_ratCast_div_iff, schnirelmannDensity_le_div, ContinuousLinearMap.norm_iteratedFDeriv_comp_left, Real.Angle.two_nsmul_toReal_eq_two_mul_add_two_pi, TopologicalGroup.IsSES.pushforward_apply_apply, isIntegralCurveOn_comp_mul_ne_zero, RCLike.wInner_const_right, ProbabilityTheory.covarianceOperator_inner, real_inner_self_nonpos, Real.goldenRatio_add_goldenConj, CongruenceSubgroup.finiteIndex_conjGL, NumberField.InfinitePlace.Completion.instIsTopologicalRing, WithLp.unitization_norm_def, ProbabilityTheory.HasGaussianLaw.sub, HasDerivAt.le_of_lip', EuclideanGeometry.eq_or_eq_reflection_of_dist_eq, Complex.HadamardThreeLines.diffContOnCl_interpStrip, ContinuousLinearMap.opNorm_mul_le, MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one, Affine.Simplex.incenter_restrict, HasCompactMulSupport.exists_bound_of_continuous, Polynomial.exists_approx_polynomial, Real.tan_nat_mul_pi, ODE.FunSpace.isFixedPt_next_iff, Metric.mk_uniformity_basis_le, ContinuousMap.Homotopy.curry_apply, EuclideanGeometry.Sphere.IsDiameter.sbtw, Real.log_div_sqrt_antitoneOn, EuclideanSpace.norm_eq, irrational_natCast_sub_iff, ContinuousLinearMap.opNorm_subsingleton, TestFunction.instLineDerivLeftSMulRealTopENat, mellin_eq_fourierIntegral, Asymptotics.IsBigO.exists_nonneg, DeltaGeneratedSpace.isOpen_iff, unitInterval.mul_pos_mem_iff, Continuous.cfc_nnreal, unitInterval.sigmoid_injective, hasStrictDerivAt_abs_neg, MDifferentiableWithinAt.inner_bundle, Orientation.inner_rightAngleRotation_left, MeasureTheory.AEStronglyMeasurable.fourierPowSMulRight, PowerSeries.gaussNorm_C, MeasureTheory.setIntegral_nonpos, Orientation.cos_oangle_add_right_of_oangle_eq_pi_div_two, WithSeminorms.continuous_seminorm, RCLike.isCauSeq_norm, Height.mulHeight₁_nonneg, AffineSubspace.mem_perpBisector_iff_inner_eq_inner, Real.lt_arcsin_iff_sin_lt, Real.HolderTriple.inv_pos, extremePoints_closedBall_subset_sphere, ProbabilityTheory.IdentDistrib.truncation, CliffordAlgebraComplex.equiv_symm_apply, MeasureTheory.Integrable.measure_norm_gt_lt_top, Real.cosh_add_sinh, PadicInt.continuousAddCharEquiv_of_norm_mul_symm_apply, ProbabilityTheory.iIndepFun_iff_charFunDual_pi, InnerProductGeometry.angle_eq_angle_add_angle_iff, intervalIntegral.deriv_integral_of_tendsto_ae_right, HurwitzZeta.hasSum_nat_completedSinZeta, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, NormedField.tendsto_norm_inv_nhdsNE_zero_atTop, Topology.RelCWComplex.map_zero_mem_openCell, DifferentiableWithinAt.abs_of_neg, integral_cos_pow_three, absorbs_iff_norm, MeasureTheory.SignedMeasure.measurable_rnDeriv, VitaliFamily.mem_filterAt_iff, MeasureTheory.stronglyMeasurable_llr, isScalarTower_sphere_sphere_ball, Orientation.oangle_sub_right_eq_arcsin_of_oangle_eq_pi_div_two, Real.isLittleO_exp_comp_exp_comp, IsUltrametricDist.algNormOfAlgEquiv_apply, ProbabilityTheory.variance_mul, nnnorm_cfc_nnreal_le_iff, Real.abs_cos_sub_cos_le, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_le_one, ProbabilityTheory.Kernel.condKernelUnitReal.instIsCondKernel, integrableOn_exp_mul_complex_Iic, Complex.zero_lt_real, Affine.Triangle.oangle_excenter_singleton_eq, DifferentiableWithinAt.cosh, Complex.tanh_ofReal_im, SchwartzMap.fourierMultiplierCLM_const, EuclideanGeometry.Sphere.IsTangent.infDist_eq_radius, SchwartzMap.integral_sesq_fourierIntegral_eq, bernoulliFun_eval_zero, Distribution.IsVanishingOn.iteratedLineDerivOp, LSeries_eq_mul_integral, 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, TestFunction.monoCLM_eq_of_scalars, Real.artanh_nonpos, EReal.toReal_add, ProbabilityTheory.integrable_rpow_abs_mul_exp_add_of_integrable_exp_mul, HurwitzZeta.oddKernel_neg, HasFDerivAt.inner, WithAbs.norm_eq_abv, Complex.frontier_setOf_le_re, Tactic.ComputeAsymptotics.Majorized.self, ModularGroup.exists_one_half_le_im_smul, HasDerivAt.rpow, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left', intervalIntegral.integral_comp_smul_deriv', DirichletCharacter.LSeriesSummable_iff, MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd, Seminorm.le_def, MeasureTheory.integrable_withDensity_iff_integrable_smul, ENNReal.rpow_add_rpow_le, MeasureTheory.Measure.instSigmaFiniteElemRealIoiOfNatVolumeIoiPow, CStarModule.norm_sq_eq, RCLike.conj_eq_iff_real, Real.self_le_sinh_iff, LinearMap.singularValues_pos_iff_lt_finrank_range, SimplexCategory.toTopHomeo_naturality, 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, antitone_of_deriv_nonpos, Real.lt_arcsin_iff_sin_lt', intervalIntegral.integral_comp_mul_deriv_of_deriv_nonneg, RCLike.ofNat_mul_im, Quaternion.im_exp, Complex.norm_natCast_cpow_of_pos, Function.HasTemperateGrowth.fun_mul, HasCompactSupport.exists_pos_le_norm, Metric.diam_ball_eq, LiouvilleWith.int_mul, ProbabilityTheory.integrable_pow_of_mem_interior_integrableExpSet, PiLp.antilipschitzWith_ofLp, MeasureTheory.condExpL1CLM_lpMeas, Module.Basis.coe_parallelepiped, fderivWithin_exp, 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, ProbabilityTheory.HasGaussianLaw.map_fun, Real.arctan_one, CFC.sqrt_sq, SmoothBumpCovering.exists_finset_toSmoothPartitionOfUnity_eventuallyEq, integral_one_div_of_pos, intervalIntegral.integral_Ioi_sub_Ioi, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt, ENNReal.rpow_lt_rpow, convex_halfSpace_re_ge, NormedAddGroup.tendsto_nhds_zero, EuclideanGeometry.inversion_def, deriv_circleMap, CircleDeg1Lift.semiconj_of_group_action_of_forall_translationNumber_eq, cthickening_closedBall, InnerProductSpaceable.parallelogram_identity, Algebra.leftMulMatrix_complex, Real.arccos_eq_arctan, Affine.Simplex.inner_vsub_altitudeFoot_vsub_altitudeFoot_eq_zero, ValueDistribution.characteristic_add_top_le, dist_le_tsum_dist_of_tendsto₀, Real.analyticWithinAt_cos, ProbabilityTheory.covarianceBilin_apply_pi, NormedAddCommGroup.exists_norm_nsmul_le, MeasureTheory.Measure.haar.chaar_sup_eq, EisensteinSeries.auxbound2, norm_le_norm_sub_add, EuclideanGeometry.oangle_left_eq_arcsin_of_oangle_eq_pi_div_two, Affine.Simplex.sum_excenterWeights_eq_one_iff, Real.pi_lower_bound_start, ProbabilityTheory.exp_neg_integrableOn_Ioc, ConvexBody.smul_le_of_le, GromovHausdorff.ghDist_le_nonemptyCompacts_dist, ProbabilityTheory.deriv_mgf, self_subset_gauge_le_one, SchwartzMap.integral_bilinear_laplacian_right_eq_left, ProbabilityTheory.covariance_fun_sum_right, Projectivization.one_le_mulHeight, EuclideanGeometry.Sphere.mul_dist_eq_power_of_radius_le_dist_center, ExistsContDiffBumpBase.u_smooth, IntervalIntegrable.comp_sub_left, Real.lipschitzWith_one_mulExpNegMulSq, AddGroupSeminorm.add_le', AbsoluteValue.IsAdmissible.exists_approx, CauSeq.tendsto_limit, Seminorm.comp_apply, ZLattice.covolume_eq_det_mul_measureReal, MeasureTheory.Martingale.bddAbove_range_iff_bddBelow_range, FormalMultilinearSeries.compAlongComposition_norm, Path.Homotopy.transReflReparamAux_zero, intervalIntegral.intervalIntegral_pos_of_pos_on, NonarchAddGroupSeminorm.apply_one, Complex.norm_div, Matrix.IsHermitian.spectrum_eq_image_range, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral', isLittleO_rpow_exp_atTop, ExistsContDiffBumpBase.y_nonneg, AddCircle.measurePreserving_equivIoc, intervalIntegral.integral_comp_sub_mul, Real.contDiff_fourier, dist_pi_eq_iff, BoxIntegral.Box.mapsTo_insertNth_face_Icc, Quaternion.re_coeComplex, ProbabilityTheory.integral_strongDual_stdGaussian, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le, 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, tendsto_rpow_neg_nhdsGT_zero, ProbabilityTheory.Kernel.isRatCondKernelCDF_density_Iic, RCLike.isCauSeq_im, ProbabilityTheory.tendstoInDistribution_inv_sqrt_mul_sum_sub, Asymptotics.isBigO_norm_left, CFC.posPart_smul_of_nonneg, SchwartzMap.norm_fourier_Lp_top_leq_toLp_one, Real.Angle.two_nsmul_eq_pi_iff, InnerProductSpace.norm_sq_eq_re_inner, Complex.HadamardThreeLines.norm_le_interpStrip_of_mem_verticalStrip_zero, BoxIntegral.Box.splitLower_eq_bot, smoothingFun_apply_of_map_mul_eq_mul, NumberField.mixedEmbedding.covolume_integerLattice, LipschitzWith.ae_differentiableAt, Real.nnnorm_abs, realPart_surjective, Orientation.kahler_apply_self, MeasureTheory.L1.setToL1_apply_coeToLp, MeasureTheory.integrableOn_image_iff_integrableOn_abs_deriv_smul, Complex.frontier_setOf_re_lt, MeasureTheory.MemLp.enorm_rpow, Metric.nonempty_closedBall, Affine.Simplex.dist_circumcenter_eq_circumradius', IsUltrametricDist.norm_prod_le_of_forall_le_of_nonempty, Real.differentiableWithinAt_arcsin_Iic, ModularGroup.exists_bound_fundamental_domain_of_isBigO, SchwartzMap.norm_toBoundedContinuousFunction_le, EuclideanGeometry.Sphere.IsTangent.notMem_of_dist_lt, Metric.mem_of_closed', ProbabilityTheory.Kernel.HasSubgaussianMGF.id_map_iff, NNReal.rpow_sub_one, signedDist_triangle_right, Polynomial.hermite_eq_deriv_gaussian, LiouvilleNumber.remainder_pos, isCompact_closedAbsConvexHull_of_totallyBounded, Real.neg_sqrt_le_of_sq_le, LipschitzWith.norm_neg_add_le, Asymptotics.isBigOWith_zero', Real.one_half_lt_eulerMascheroniSeq_six, Real.logb_le_logb_of_le, Asymptotics.IsBigO.sum_congr', isIntegralCurveOn_univ, Real.exp_half, PadicInt.fwdDiff_iter_le_of_forall_le, 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, Complex.norm_eqOn_of_isPreconnected_of_isMaxOn, EuclideanGeometry.Sphere.IsIntTangentAt.wbtw, Orientation.inner_eq_zero_of_oangle_eq_pi_div_two, EReal.tendsto_coe, UniformConcaveOn.concaveOn, Unitary.spectrum_subset_slitPlane_iff_norm_lt_two, InformationTheory.integral_llr_compProd_eq_add, Complex.conjCLE_nnorm, LipschitzOnWith.le_add_mul, Path.Homotopy.cast_apply, StrongDual.extendRCLikeₗ_symm_apply, MeasureTheory.StronglyAdapted.upcrossingStrat, HasStrictDerivAt.complexToReal_fderiv', isLittleO_zpow_exp_pos_mul_atTop, Convex.curveIntegral_segment_add_eq_of_hasFDerivWithinAt_symmetric, StrictConcaveOn.strictAntiOn_deriv, contMDiffWithinAt_comp_projIcc_iff, Orientation.inner_mul_areaForm_sub', hasFDerivAt_polarCoord_symm, EuclideanGeometry.exists_dist_eq_circumradius_of_subset_insert_orthocenter, smoothingSeminorm_map_one_le_one, fourierIntegral_gaussian_innerProductSpace, Filter.Tendsto.rpow, Real.sSup_le, egauge_ball_one_le_of_one_lt_norm, NormedSpace.norm_expSeries_summable', MeasureTheory.dist_convolution_le', continuous_norm', Metric.isBounded_image_iff, Real.sin_pi_over_two_pow_succ, Real.continuous_exp, trapezoidal_integral_one, ConcaveOn.slope_le_derivWithin, Asymptotics.isLittleO_const_left_of_ne, EuclideanGeometry.Sphere.IsTangentAt.le_orthRadius, Asymptotics.isLittleO_norm_left, EuclideanGeometry.Sphere.isDiameter_of_angle_eq_pi_div_two, Real.sign_of_pos, Dilation.mapsTo_ball, IsBoundedSMul.dist_pair_smul', MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_deriv_mul, MeasureTheory.eLpNorm_nnreal_eq_lintegral, NumberField.mixedEmbedding.mixedSpaceToRealMixedSpace_apply, AnalyticWithinAt.im_ofReal, ProbabilityTheory.HasGaussianLaw.charFun_map_eq, MeasureTheory.measureReal_ennreal_smul_apply, IsometryEquiv.coe_toRealLinearIsometryEquivOfMapZero, HasFDerivWithinAt.rpow_const, ProbabilityTheory.variance_nonneg, Real.bijOn_sin, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, Real.toNNReal_lt_ofNat, Polynomial.supNorm_def', ZSpan.isAddFundamentalDomain, CircleDeg1Lift.coe_toOrderIso, Metric.exists_dist_lt_of_hausdorffDist_lt, Real.one_le_rpow, BoxIntegral.Box.mk'_eq_bot, CircleDeg1Lift.translate_zpow, EReal.coe_nonneg, Real.cosh_bijOn, NormedSpace.norm_expSeries_div_summable_of_mem_ball, ContinuousMap.Homotopy.extend_apply_of_mem_I, RCLike.I_to_real, LinearMap.singularValues_fin, RingSeminorm.toFun_eq_coe, LinearMap.opNorm_extendOfNorm_le, NNReal.rpow_inv_le_iff_of_neg, dist_homothety_center, Tactic.ComputeAsymptotics.isBigO_of_div_tendsto_atTop, EuclideanGeometry.sin_angle_mul_dist_eq_sin_angle_mul_dist, EReal.toReal_image_Ioo_bot_zero, LinearMap.sq_singularValues_of_lt, MeasureTheory.HasFiniteIntegral.of_mem_Icc, intervalIntegral.intervalIntegrable_exp, ODE.contDiffOn_comp, IntervalIntegrable.norm, Real.sign_neg, MeasureTheory.integral_continuousLinearMap_prod', Complex.hasSum_re, Subgroup.two_mul_widthInfty_mem_strictPeriods, ConvexOn.real_univ_sSup_affine_eq, EuclideanGeometry.oangle_left_eq_arctan_of_oangle_eq_pi_div_two, MeasureTheory.SignedMeasure.toComplexMeasure_apply_re, MeasureTheory.weightedSMul_union, pi_norm_le_iff_of_nonneg', 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, EuclideanGeometry.measurePreserving_vaddConst, MeasureTheory.uniformIntegrable_average, cexp_neg_quadratic_isLittleO_abs_rpow_cocompact, ArithmeticFunction.LSeries_vonMangoldt_eq, Quaternion.coeComplex_coe, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_densityProcess_limitProcess, BumpCovering.toFun_eq_coe, ContinuousOn.arcsin, NNReal.rpow_one_sub', MultilinearMap.mkContinuousMultilinear_norm_le', SchwartzMap.le_seminorm, NNReal.rpow_intCast, AddCircle.closedBall_eq_univ_of_half_period_le, ConvexOn.monotoneOn_leftDeriv, CircleDeg1Lift.translationNumber_le_of_le_add_int, ContinuousMap.toNNReal_mul_add_neg_mul_add_mul_neg_eq, LipschitzWith.norm_sub_le, Real.bijOn_cos, Real.summable_exp_nat_mul_of_ge, AbsolutelyContinuousOnInterval.biUnion_uIoc_subset_of_mem_disjWithin, circleMap_zero_mul, gauge_lt_one_subset_self, Real.cos_sq', Valuation.norm_nonneg, Real.tan_add_int_mul_pi, tendsto_pow_atTop_nhds_zero_of_abs_lt_one, GenLoop.toLoop_apply_coe, Real.iteratedDeriv_fourier, tendsto_gauge_nhds_zero_nhdsGE, UniformConvexSpace.toStrictConvexSpace, AmpleSet.image_iff, SchwartzMap.eLpNorm_le_seminorm, EuclideanGeometry.Concyclic.Coplanar, MeasureTheory.L1.setToL1_congr_left', EuclideanGeometry.Sphere.mem_tangentSet_of_mem_tangentsFrom, Affine.Simplex.ExcenterExists.isTangentAt_exsphere_iff_eq_touchpoint, le_gronwallBound_of_liminf_deriv_right_le, Real.qaryEntropy_strictMonoOn, NumberField.Units.instDiscrete_unitLattice, NNReal.continuousOn_rpow_const, UpperHalfPlane.petersson_slash_SL, Real.tan_pi_div_six, Finset.norm_prod_le', EuclideanGeometry.dist_div_tan_oangle_left_of_oangle_eq_pi_div_two, ENNReal.toReal_le_coe_of_le_coe, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le, linear_isometry_complex_aux, IsLocalExtrOn.linear_dependent_of_hasStrictFDerivAt, selfAdjoint.star_coe_unitarySelfAddISMul, summable_one_div_pow_of_le, Orientation.kahler_rotation_left', MeasureTheory.Measure.addHaar_affineSubspace, NumberField.mixedEmbedding.fundamentalCone.closure_paramSet, Irrational.ratCast_add, Real.differentiable_sin, MeasureTheory.setIntegral_rnDeriv_smul', Real.cos_pos_of_mem_Ioo, NNReal.rpow_left_injective, RCLike.hasSum_re, ContinuousMultilinearMap.norm_ofSubsingleton_id_le, ValueDistribution.characteristic_mul_zero_le, norm_prod, ArchimedeanClass.stdPart_natCast, MeasureTheory.integrableOn_Icc_deriv_smul_iff_of_deriv_nonneg, Real.volume_Ioc, NumberField.mixedEmbedding.euclidean.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, ProbabilityTheory.Kernel.integral_density, CliffordAlgebraComplex.toComplex_ι, UpperHalfPlane.σ_ofReal, ContDiff.fourierPowSMulRight, Real.enorm_of_nonneg, MeasureTheory.StronglyAdapted.smul, LipschitzOnWith.norm_div_le, Stirling.stirlingSeq'_bounded_by_pos_constant, Distribution.dsupport_smulLeftCLM_subset, irrational_sub_intCast_iff, IsUltrametricDist.norm_tsum_le_of_forall_le_of_nonneg, Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_pair, ProbabilityTheory.variance_fun_sub, WithLp.prod_dist_eq_of_L1, Affine.Simplex.pointsWithCircumcenter_point, convex_halfSpace_im_ge, Real.integrable_of_summable_norm_Icc, ContinuousLinearMap.sSup_unit_ball_eq_nnnorm, NormedAddGroupHom.le_opNorm, Real.strictMonoOn_arcsin, intervalIntegral.integral_comp_mul_deriv''', WithLp.prod_dist_eq_card, HasFPowerSeriesOnBall.uniform_geometric_approx', Real.mul_abs_le_abs_sin, tendsto_dist_left_cocompact_atTop, Real.one_sub_lt_exp_neg, intervalIntegral.smul_integral_comp_mul_left, EuclideanGeometry.tan_angle_of_angle_eq_pi_div_two, Rat.AbsoluteValue.exists_pos_eq_pow_neg, DiffContOnCl.circleAverage_re_herglotzRieszKernel_smul, Real.arccos_lt_pi, Orientation.oangle_eq_zero_or_eq_pi_iff_not_linearIndependent, EuclideanGeometry.concyclic_of_two_zsmul_oangle_eq_of_not_collinear, IsBoundedLinearMap.bound, Real.continuous_arctan, Hyperreal.coe_eq_zero, InnerProductGeometry.norm_div_sin_angle_sub_of_inner_eq_zero, ContinuousLinearMap.extendTo𝕜_apply, not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter, AkraBazziRecurrence.isEquivalent_one_sub_smoothingFn_one, derivWithin_sin, ProbabilityTheory.integrable_exp_mul_abs_add, EuclideanGeometry.angle_eq_pi_sub_angle_div_two_of_oangle_eq_add_pi_of_sOppSide, HasFDerivAt.sinh, Real.natLog_le_logb, Complex.ofReal_eq_zero, rotation_trans, CStarAlgebra.rpow_neg_one_le_rpow_neg_one, Valued.toNormedField.one_lt_norm_iff, integrableOn_Ioi_rpow_iff, mem_ball_iff_norm_inv_mul_lt', eventually_norm_symmL_trivializationAt_comp_self_lt, Complex.angle_le_mul_norm_sub, Real.Angle.sign_two_zsmul_eq_neg_sign_iff, ZetaAsymptotics.term_sum_of_lt, disjoint_ball_closedBall_iff, Real.eulerMascheroniConstant_eq_neg_deriv, MeasureTheory.SimpleFunc.setToSimpleFunc_indicator, MeasureTheory.MeasuredSets.lipschitzWith_measureReal, Metric.PiNatEmbed.continuous_distDenseSeq, Real.arsinh_neg_iff, not_sameRay_iff_abs_lt_norm_sub, deriv_const_rpow, EuclideanSpace.volume_ball_fin_three, MeasureTheory.SignedMeasure.toMeasureOfLEZero_apply, Convex.gauge_le, Real.not_differentiableAt_inv_log_zero, Affine.Simplex.inradius_restrict, 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, ContDiffAt.rpow_const_of_le, instNoncompactSpaceReal, seminormFromBounded_nonneg, Complex.linearEquiv_det_conjAe, Real.goldenRatio_pos, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_stdOrthonormalBasis, enorm_sub_le_lintegral_deriv_of_contDiffOn_Icc, Orientation.abs_areaForm_le, Metric.Snowflaking.preimage_toSnowflaking_closedEBall, EuclideanGeometry.cospherical_or_collinear_of_two_zsmul_oangle_eq, Complex.ofReal_zero, Affine.Simplex.ExcenterExists.sign_touchpointWeights, Real.mul_add_one_le_add_one_pow, Real.deriv_mul_log, ZLattice.exists_forall_abs_repr_le_norm, intervalIntegrable_const_iff, ContDiffWithinAt.laplacianWithin_CLM_comp_left_nhds, ArithmeticFunction.log_mul_moebius_eq_vonMangoldt, MeasureTheory.Lp.norm_le_of_ae_bound, Real.rpowIntegrand₀₁_eq_pow_div, measurableSet_regionBetween, Metric.le_glueDist_inl_inr, BoxIntegral.Prepartition.splitMany_empty, IsOpen.exists_msmooth_support_eq_aux, SeminormedAddCommGroup.mem_closure_iff, Sbtw.angle₂₃₁_eq_zero, NumberField.mixedEmbedding.polarCoord_target, Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter, PadicInt.norm_le_pow_iff_norm_lt_pow_add_one, Real.contDiffAt_rpow_const, isIntegralCurveAt_iff_exists_mem_nhds, EuclideanGeometry.Sphere.dist_div_cos_oangle_center_eq_two_mul_radius, Complex.continuousAt_arg_coe_angle, EuclideanGeometry.angle_homothety, IsApproximateSubgroup.of_small_tripling, 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, SchwartzMap.norm_toLp', InnerProductGeometry.angle_smul_smul, Metric.Snowflaking.preimage_ofSnowflaking_ball, integral_log_sin_zero_pi, integrableOn_rpow_mul_exp_neg_rpow, MeasureTheory.Measure.hausdorffMeasure_le_liminf_tsum, GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I', Cardinal.mk_univ_real, IsLocalHomeomorph.monodromy_theorem, Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT, Asymptotics.bound_of_isBigO_nat_atTop, MeasureTheory.lintegral_image_eq_lintegral_deriv_mul_of_antitoneOn, InnerProductGeometry.angle_sub_lt_pi_div_two_of_inner_eq_zero, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMapBasis, ContinuousMapZero.toContinuousMapHom_toNNReal, ModularForm.SL_slash_def, AddChar.norm_apply, Path.Homotopy.coeFn_injective, not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_punctured, cauchySeq_iff_le_tendsto_0, IsUltrametricDist.norm_pow_le, Valued.isNonarchimedean_norm, intervalIntegral.integral_pos_iff_support_of_nonneg_ae, Convex.image_derivWithin, Matrix.PosDef.toQuadraticForm', Path.range_reparam, Asymptotics.IsBigO.bound, NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isReal, Real.tendsto_abs_tan_of_cos_eq_zero, Complex.div_ofReal, OpenPartialHomeomorph.contDiff_unitBallBall, 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, InnerProductGeometry.cos_angle_add_mul_norm_of_inner_eq_zero, Complex.norm_le_norm_of_mapsTo_ball_self, ModelWithCorners.convex_range, NNReal.spectralRadius_mem_spectrum, Quaternion.summable_coe, Complex.instStarModuleReal, MeasureTheory.Integrable.integral_norm_condDistrib, summable_iff_not_tendsto_nat_atTop_of_nonneg, ENNReal.tendsto_ofReal_atTop, PadicInt.norm_intCast_eq_one_iff, NumberField.mixedEmbedding.euclidean.instIsZLatticeRealMixedSpaceIntegerLattice, SchwartzMap.compSubConstCLM_comp, TemperedDistribution.smulLeftCLM_add, IsUltrametricDist.exists_norm_finset_sum_le, cfcₙ_im_id, MeasureTheory.measureReal_mono_null, 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, ProbabilityTheory.covarianceBilin_apply_basisFun, ContDiffBump.integral_normed_smul, ProbabilityTheory.IsRatCondKernelCDFAux.integrable, exists_contMDiff_zero_iff_one_iff_of_isClosed, hasSum_geometric_two', Complex.ball_one_subset_slitPlane, Real.arcsin_of_one_le, ProbabilityTheory.instIsGaussianMapHAdd_1, CFC.spectrum_rpow, Real.arsinh_eq_zero_iff, norm_sub_sq_eq_norm_sq_add_norm_sq_real, Complex.restrictScalars_toSpanSingleton, integrableOn_exp_mul_Ioi, ProbabilityTheory.measure_cdf, Orientation.oangle_sign_smul_right, Orientation.normSq_kahler, Complex.norm_prime_cpow_le_one_half, Real.Angle.toReal_neg_iff_sign_neg, ProbabilityTheory.gaussianReal_add_gaussianReal_of_indepFun, AddGroupSeminorm.coe_sSup_apply', ProbabilityTheory.IsCondKernelCDF.integrable, Complex.UnitDisc.mk_neg, Complex.tendsto_one_add_div_cpow_exp, Real.hasPDF_iff_of_aemeasurable, MeasureTheory.SimpleFunc.integral_eq_lintegral, Padic.isAbsoluteValue, poissonKernel_eq_re_herglotzRieszKernel, Real.rpow_sub_one', ContDiff.rpow_const_of_le, 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, Real.nonemptyOrderRingHom, unitInterval.image_coe_preimage_symm, Complex.closure_setOf_re_lt, ProbabilityTheory.integrable_of_mem_integrableExpSet, Real.Angle.abs_cos_eq_of_two_zsmul_eq, Real.arcsin_lt_zero, Function.Periodic.compact_of_continuous, Real.rpow_lt_rpow, ENNReal.mul_rpow_of_ne_top, WithLp.prod_norm_eq_sup, ProbabilityTheory.measurable_toRatCDF, ProbabilityTheory.condExpKernel_ae_eq_trim_condExp, integral_inv_sq_add_sq, Real.rpow_two, IsMaxOn.lineDerivWithin_eq_zero, Real.sigmoid_le_one, intervalIntegral.integral_deriv_mul_eq_sub_of_hasDeriv_right, 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, MeasureTheory.setIntegral_nonneg_of_ae_restrict, Real.qaryEntropy_neg_of_neg, Real.sigmoid_le_iff, NNReal.smul_def, ProbabilityTheory.iIndepFun.charFun_map_fun_finset_sum_eq_prod, Complex.stolzCone_subset_stolzSet_aux, SmoothBumpFunction.contMDiff_smul, Real.sinh_lt_sinh, MeasureTheory.nnnorm_indicatorConstLp_le, locallyFinsuppWithin.logCounting_divisor, ContDiffOn.arctan, MultilinearMap.norm_image_sub_le_of_bound, Height.logHeight_nonneg, ProbabilityTheory.paretoPDF_eq, gauge_unit_ball, Complex.norm_cderiv_sub_lt, eventually_ball_subset, ProbabilityTheory.setIntegral_preCDF_fst, norm_image_of_norm_eq_zero, EReal.coe_injective, isMIntegralCurve_iff_isMIntegralCurveOn, ENNReal.ofNat_lt_ofReal, NNReal.summable_Lp_add, intervalIntegral.derivWithin_integral_of_tendsto_ae_right, IsIntegralCurve.comp_sub, intervalIntegral.integral_Iic_sub_Iic, norm_root_le_spectralValue, Real.pi_lt_d2, Real.differentiableAt_tan, Real.sin_div_le_inv_abs, quasispectrum_realPart, ENNReal.Lp_add_le, CFC.rpow_nonneg, ContinuousAlternatingMap.norm_image_sub_le', ConvexOn.locallyLipschitzOn_iff_continuousOn, Real.differentiable_cosh, PiNat.dist_eq_of_ne, norm_le_pi_norm', GromovHausdorff.hausdorffDist_optimal_le_HD, NumberField.InfinitePlace.Completion.extensionEmbedding_coe, MeasureTheory.Submartingale.mul_lintegral_upcrossings_le_lintegral_pos_part, NumberField.mixedEmbedding.negAt_symm, IsSelfAdjoint.instIsometricContinuousFunctionalCalculus, LinearMap.sq_singularValues_fin, neg_one_le_real_inner_of_norm_eq_one, Stirling.log_stirlingSeq_bounded_by_constant, Real.isFiniteMeasure_restrict_Ico, MeasureTheory.iteratedDeriv_charFun, EuclideanGeometry.sbtw_of_collinear_of_dist_center_lt_radius, Bornology.IsBounded.subset_closedBall, LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div_and_nonneg, DifferentiableAt.rpow, MeasureTheory.setLIntegral_tilted, VectorFourier.contDiff_fourierIntegral, UpperHalfPlane.continuous_toSL2R, Real.isGLB_of_tendsto_antitoneOn_bddBelow_nat_Ici, PadicInt.norm_le_pow_iff_le_valuation, norm_div_le_of_le, ProbabilityTheory.integrable_exp_abs_mul_abs, ConcaveOn.le_map_average, MeasureTheory.L1.setToL1_congr_left, Path.trans_continuous_family, irrational_div_ratCast_iff, Real.fromBinary_surjective, Real.sqrt_pos, BumpCovering.exists_isSubordinate_of_locallyFinite_of_prop_t2space, EuclideanGeometry.mul_dist_add_mul_dist_eq_mul_dist_of_cospherical, MeasureTheory.count_real_singleton', ProbabilityTheory.HasSubgaussianMGF.sub_of_indepFun, concaveOn_of_deriv2_nonpos, ProbabilityTheory.iIndepFun.hasGaussianLaw_fun_add, fourierSubalgebra_coe, NumberField.InfinitePlace.denseRange_algebraMap_pi, Complex.norm_ofNat, Wbtw.angle₁₃₂_eq_zero_of_ne, MeasureTheory.lpNorm_le_lpNorm_add_lpNorm_sub, intervalIntegral.integral_Iio_sub_Iio, NNReal.rpow_add_le_mul_rpow_add_rpow, AddGroupNorm.apply_one, ConcaveOn.leftDeriv_le_slope, DiffContOnCl.circleAverage_re_herglotzRieszKernel_smul', dist_le_tsum_dist_of_tendsto, Irrational.instNoMinOrderSubtypeReal, ODE.FunSpace.exists_forall_closedBall_funSpace_dist_le_mul, Complex.norm_eqOn_closure_of_isPreconnected_of_isMaxOn, Real.eulerMascheroniSeq_lt_eulerMascheroniSeq', ProbabilityTheory.integrable_compProd_iff, Complex.norm_canonicalFactor_eval_circle_eq_one, intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left, CircleDeg1Lift.map_add_int, Polynomial.toAddCircle_monomial_eq_smul_fourier, Metric.dist_le_diam_of_mem, Complex.inner, sameRay_iff_inv_norm_smul_eq, ProbabilityTheory.variance_dual_stdGaussian, RCLike.instStarModuleReal, Real.Convex.dimH_eq_finrank_vectorSpan, 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, ContDiffMapSupportedIn.fderivCLM_eq_of_scalars, CompletelyRegularSpace.completely_regular, ENNReal.ofReal_pos, NumberField.mixedEmbedding.fundamentalCone.mixedEmbedding_preimageOfMemIntegerSet, preCantorSet_succ, HasDerivWithinAt.sinh, Metric.uniformity_basis_dist_le_inv_nat_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, Real.rpow_logb_of_neg, ContractingWith.dist_inequality, MeasureTheory.L1.setToL1_smul, 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, MeasureTheory.withDensity_ofReal_mutuallySingular, IntervalIntegrable.comp_mul_left_iff, Complex.polarCoord_source, Module.Basis.norm_nonneg, Polynomial.sum_sq_norm_coeff_eq_circleAverage, Metric.isOpen_iff, Real.exists_convs_eq_rat, Real.one_sub_goldenConj, MeasureTheory.integral_le_measure, ProbabilityTheory.IdentDistrib.norm, Real.Lp_add_le, ContDiffBump.contDiff_normed, Euclidean.nhds_basis_ball, ENNReal.toReal_pos_iff_ne_top, Real.arcosh_pos, norm_cfcₙ_le, Real.tan_nonneg_of_nonneg_of_le_pi_div_two, ProbabilityTheory.integral_tilted_mul_eq_mgf, Real.ofCauchy_intCast, NNReal.rpow_le_rpow_of_nonpos, MeasureTheory.MemLp.integral_indicator_norm_ge_nonneg_le, integral_rpow, EuclideanGeometry.angle_lt_pi_div_two_of_angle_eq_pi_div_two, ConcaveOn.derivWithin_le_slope, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_paramSet_exp, MeasureTheory.integral_simpleFunc_larger_space, Real.Lp_add_le_of_nonneg, variationOnFromTo.sub_self_monotoneOn, Complex.coe_imAddGroupHom, CircleDeg1Lift.le_ceil_map_map_zero, Real.rpow_add', ValueDistribution.logCounting_zero_mul_eventually_le, PhragmenLindelof.quadrant_II, MeasureTheory.exists_lt_lowerSemicontinuous_integral_lt, Tactic.ComputeAsymptotics.Majorized.smul, AnalyticAt.harmonicAt_re, isLocalMax_of_deriv_deriv_neg, Polynomial.mahlerMeasure_X_sub_C, RCLike.mul_im_I_ax, ContDiffBump.apply, isProperMap_dist, EuclideanGeometry.dist_eq_dist_mul_sin_angle_div_sin_angle, Convex.isLittleO_pow_succ_real, EMetric.exists_continuous_real_forall_closedBall_subset, CircleDeg1Lift.coe_one, BoundedContinuousFunction.lintegral_of_real_lt_top, MeasureTheory.L1.SimpleFunc.posPart_toSimpleFunc, Mathlib.Meta.NormNum.IsInt.rpow_eq_inv_pow, intervalIntegral.intervalIntegrable_const, Orientation.oangle_sign_add_smul_left, MeasureTheory.MemLp.norm_rpow_div, NNReal.rpow_add_intCast, intervalIntegral.integral_eq_sub_of_hasDerivAt_of_le, Height.mulHeightBound_eq, NumberField.mixedEmbedding.polarCoord_symm_eq, NormedAddGroupHom.bounds_bddBelow, ProbabilityTheory.iCondIndepSets_iff, MeasureTheory.Measure.IicSnd_le_fst, HasFDerivAt.lim_real, tsum_geometric_inv_two_ge, strictConvexOn_rpow, Real.tendsto_tan_pi_div_two, upperHemicontinuous_spectrum_nnreal, Diffeology.isPlot_iff_contDiff, Real.one_le_toNNReal, signedDist_vsub_self_rev, ProbabilityTheory.cauchyPDFReal_def', ODE.contDiffOn_enat_picard_Icc, BumpCovering.ind_apply, InformationTheory.toReal_klDiv_of_measure_eq, Real.rpow_le_rpow_left_iff_of_base_lt_one, Real.probChar_apply', Real.rpow_inv_log_le_exp_one, intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae, ContDiff.rpow_const_of_ne, ProbabilityTheory.variance_map, 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, HasFDerivAt.rpow_const, 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, ContinuousAlternatingMap.le_opNorm_mul_pow_card_of_le, NNReal.le_rpow_inv_iff_of_neg, Real.tendsto_log_comp_add_sub_log, contDiffAt_inner, Int.Matrix.one_le_norm_A_of_ne_zero, Complex.normSq_div, ContinuousMap.subalgebra_topologicalClosure_eq_top_of_separatesPoints, InnerProductGeometry.norm_sub_eq_add_norm_of_angle_eq_pi, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, Complex.continuousOn_prod_circle_transform_function, BoxIntegral.Box.exists_seq_mono_tendsto, AddGroupSeminorm.comp_apply, EuclideanGeometry.angle_eq_arccos_of_angle_eq_pi_div_two, OrthonormalBasis.measurePreserving_repr_symm, Real.measurable_arcsin, Diffeology.isPlot_iff_dSmooth, Real.pow_div_factorial_le_exp, Orientation.linearIsometryEquiv_comp_rightAngleRotation, BoxIntegral.IntegrationParams.RCond.min, MeasureTheory.ContinuousOn.hasBoxIntegral, ZLattice.normBound_pos, bernoulliFun_zero, ContinuousMap.HomotopyWith.ext_iff, CFC.IsSelfAdjoint.norm_mul_mul_self_of_nonneg', Real.geom_mean_lt_arith_mean_weighted_iff_of_pos, Hyperreal.coe_zero, Icc_chartedSpaceChartAt_of_top_le, Real.sSup_univ, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIntegerLattice, Real.abs_sin_lt_abs, Measurable.infDist, norm_fderiv_norm, MeasureTheory.JordanDecomposition.coe_smul, MeasureTheory.measureReal_abs_gt_le_integral_charFun, BoundedContinuousFunction.norm_sub_eq_max, ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior, SimpleGraph.triangle_counting', DifferentiableOn.inner, MeasureTheory.ofReal_integral_norm_eq_lintegral_enorm, ENNReal.ofReal_essSup, eventually_enorm_mfderiv_extChartAt_lt, PadicInt.norm_eq_padic_norm, StrongDual.extendRCLikeₗᵢ_apply, MeasureTheory.exp_neg_llr, UniformConcaveOn.strictConcaveOn, RightDerivMeasurableAux.A_mono, enorm_tangentSpace_vectorSpace, Hyperreal.coe_min, IntervalIntegrable.comp_mul_right, integral_exp_neg_Ioi, NNReal.rpow_eq_rpow_iff, ContinuousMap.norm_lt_iff, Real.volume_eball, Real.ceil_pi_eq_four, HasDerivAt.ofReal_comp, FormalMultilinearSeries.norm_mul_pow_le_mul_pow_of_lt_radius, ProbabilityTheory.IsKolmogorovProcess.p_pos, ContinuousOn.cfcₙ_nnreal', Differentiable.inner, Tactic.ComputeAsymptotics.WellFormedBasis.eventually_pos, ContinuousMap.norm_lt_iff_of_nonempty, UpperHalfPlane.dist_center_dist, ENNReal.ofReal_lt_coe_iff, Asymptotics.IsBigOWith.add, LinearMap.mkContinuous₂_norm_le, Real.surjOn_log, NNReal.coe_sub_def, add_bounded_of_bounded_of_bounded, EuclideanGeometry.mul_dist_eq_abs_sub_sq_dist, AbsoluteValue.IsAdmissible.exists_partition, Complex.normSq_ofReal, DifferentiableAt.sin, ENNReal.rpow_pos_of_nonneg, DifferentiableAt.ofReal_cpow_const, norm_sub_le_of_le, signedDist_linear_apply, PreInnerProductSpace.Core.re_inner_nonneg, Complex.isBigO_ofReal_left, UpperHalfPlane.isZeroAtImInfty_iff, ofDigits_cantorToTernary_sum_le, 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, ProbabilityTheory.IsGaussianProcess.of_isGaussianProcess, 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, ProbabilityTheory.HasSubgaussianMGF.measureReal_le_le_exp, RCLike.ofReal_intCast, Real.inv_sqrt_one_add_tan_sq, Vitali.exists_disjoint_subfamily_covering_enlargement, Complex.isHomeomorphicTrivialFiberBundle_re, Affine.Simplex.circumradius_pos, UpperHalfPlane.atImInfty_mem, Real.cosh_lt_cosh, EuclideanGeometry.mul_dist_le_mul_dist_add_mul_dist, QuadraticForm.posDef_of_toMatrix', Real.cosh_sub, HasStrictFDerivAt.const_rpow, bernoulliFun_one, Metric.closedBall_eq_empty, Orientation.inner_rightAngleRotation_swap, Hyperreal.infinite_iff_not_exists_st, dist_sq_of_inner_eq_zero, MulRingNorm.toFun_eq_coe, NumberField.Units.abs_det_eq_abs_det, Metric.uniformity_basis_dist_pow, 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', MeasureTheory.condExp_smul_of_aestronglyMeasurable_left, IsPicardLindelof.norm_le, PhragmenLindelof.eqOn_right_half_plane_of_superexponential_decay, EuclideanQuadrant.ext_iff, Real.abs_circleAverage_le_circleAverage_abs, Matrix.IsHermitian.instContinuousFunctionalCalculusIsClosedEmbedding, RCLike.normSq_eq_def', Path.continuous_uncurry_extend_of_continuous_family, AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_zero_or_pos_or_neg, Stirling.log_stirlingSeq'_antitone, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isReal, BoundedContinuousFunction.norm_lt_iff_of_compact, intervalIntegral.integral_eq_sub_of_hasDeriv_right, AbsolutelyContinuousOnInterval.const_mul, UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_eq_zero, MulRingNorm.mulRingNormEquivAbsoluteValue_apply, intervalIntegrable_iff_integrableOn_Ioo_of_le, RCLike.ofReal_eq_zero, CircleDeg1Lift.commute_int_add, IccRightChart_extend_top_mem_frontier, Metric.unitSphere.coe_zpow, intervalIntegral.integral_smul_deriv_eq_deriv_smul, integral_comp_neg_Iic, ConcaveOn.deriv_le_slope, MeasureTheory.ofReal_setIntegral_one, CongruenceSubgroup.strictPeriods_Gamma1, BoxIntegral.unitPartition.index_apply, NNReal.continuousAt_rpow_const, Asymptotics.IsTheta.tendsto_norm_atTop_iff, rotationOf_coe, Real.nndist_eq, Orientation.norm_div_sin_oangle_sub_left_of_oangle_eq_pi_div_two, AnalyticWithinAt.rexp, CompactlySupportedContinuousMap.toReal_add, GenLoop.genLoopGenLoopEquiv_symm_apply_coe, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_eq, cantorSet_subset_unitInterval, Algebra.norm_complex_apply, NumberField.mixedEmbedding.volume_negAt_plusPart, 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, sub_bounded_of_bounded_of_bounded, ProbabilityTheory.moment_zero_measure, StrongDual.norm_toLpₗ_le, ContDiffMapSupportedIn.iteratedFDeriv_zero_on_compl, Path.source_mem_range, niven_angle_eq, Real.continuousOn_rpowIntegrand₀₁_Ici, Orientation.oangle_sub_left_smul_rotation_pi_div_two, Real.sin_sq_le_one, InnerProductSpace.laplacianWithin_eq_iteratedDerivWithin_real, HasDerivAt.lhopital_zero_right_on_Ioo, tangentConeAt_real_subset_isRCLikeNormedField, HasFDerivWithinAt.abs_of_pos, ProperCone.innerDual_insert, ProbabilityTheory.IsCondKernelCDF.tendsto_atBot_zero, InnerProductGeometry.angle_sub_pos_of_inner_eq_zero, Height.logHeight_fun_mul_eq, ENNReal.toReal_prod, ProbabilityTheory.integral_truncation_le_integral_of_nonneg, Module.Basis.parallelepiped_eq_map, Filter.HasBasis.cobounded_of_norm, Liouville.exists_pos_real_of_irrational_root, Metric.cthickening_eq_iInter_thickening', selfAdjoint.realPart_coe, ContinuousMap.HomotopyLike.map_one_left, EuclideanGeometry.tan_oangle_right_mul_dist_of_oangle_eq_pi_div_two, 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, Real.sqrt_eq_iff_mul_self_eq, Complex.UnitDisc.im_zero, ProbabilityTheory.cgf_const', Tactic.ComputeAsymptotics.WellFormedBasis.compare_left_aux, NumberField.InfinitePlace.isometry_embedding_of_isReal, Complex.isBigO_comp_ofReal_nhds_ne, Real.HolderConjugate.inv_add_inv_eq_one, isCauSeq_iff_cauchySeq, HasDerivAt.lhopital_zero_nhds, pow_mul_le_of_le_of_pow_mul_le, Path.target_mem_range, ODE.contDiffOn_enat_Icc_of_hasDerivWithinAt, DifferentiableAt.differentiableAt_norm_of_smul, 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, ENNReal.ofReal_inv_of_pos, EuclideanGeometry.Sphere.inter_orthRadius_eq_singleton_iff, GroupNorm.coe_add, Seminorm.inf_apply, Asymptotics.isBigO_one_nat_atTop_iff, PiLp.dist_sq_eq_of_L2, ContDiffBump.continuous, MeasureTheory.integrableOn_image_iff_integrableOn_deriv_smul_of_antitoneOn, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_or_eq_zero, Polynomial.Chebyshev.isMaxOn_T_real, ContinuousLinearMap.instNonnegSpectrumClassRealId, HasStrictFDerivAt.cos, MeasureTheory.eLpNorm_one_condExp_le_eLpNorm, NumberField.ComplexEmbedding.IsReal.coe_embedding_apply, Affine.Simplex.incenter_eq_affineCombination, LiouvilleWith.mul_rat_iff, ContDiffWithinAt.cos, Complex.abs_im_div_norm_le_one, MeasureTheory.integral_of_ae_eq_zero_or_one, Real.limsInf_of_not_isBounded, WithAbs.norm_toAbs_eq, NNReal.mk_zero, ENNReal.prod_rpow_of_nonneg, Complex.norm_int_of_nonneg, LinearMap.mem_polar_singleton, integral_log, ODE.FunSpace.compProj_of_mem, Real.exp_le_exp, tendsto_norm_comp_cofinite_atTop_of_isClosedEmbedding', signedDist_self, MeasureTheory.MemLp.norm, MeasureTheory.toReal_rnDeriv_map_ae_eq_trim, comap_norm_nhds_one, exists_smooth_section_forall_mem_convex_of_local, Matrix.PosDef.of_toQuadraticForm', circleMap_zero_div, PiTensorProduct.projectiveSeminorm_zero, QuotientAddGroup.norm_mk_eq_zero, MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left', CuspFormClass.exists_bound, Real.ofCauchy_div, Real.strictAntiOn_logb_of_base_lt_one, CFC.rpow_add, Real.volume_real_Icc, MeasureTheory.L1.norm_integral_le, Unitization.nnreal_cfcₙ_eq_cfc_inr, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_prodMk, hasDerivAtFilter_iff_tendsto, dist_convexCombination_map_le, ProperCone.dual_flip_dual, ProbabilityTheory.measure_stieltjesOfMeasurableRat_univ, RCLike.ofRealCLM_norm, Tactic.ComputeAsymptotics.Majorized.mul_bounded, integral_sqrt_one_sub_sq, NonarchAddGroupSeminorm.add_bddBelow_range_add, unitInterval.tendsto_sigmoid_atTop, QuotientGroup.exists_norm_mk_lt, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_measure_nhdsWithin_pos, spectrum.coe_le_norm_of_mem, integrable_inv_one_add_sq, Complex.IsExpCmpFilter.isLittleO_log_norm_re, Real.strictMonoOn_arcosh, CStarModule.inner_smul_left_real, Real.rank_rat_real, dist_left_convexComboPair, ENNReal.tsum_coe_ne_top_iff_summable_coe, Complex.sqrt_map, Set.infsep_singleton, InnerProductSpace.HarmonicOnNhd.const_smul, circleAverage_log_norm_add_const_eq_posLog, deriv_cos, Complex.UnitDisc.coe_smul_closedBall, LipschitzOnWith.extend_pi, Complex.norm_natCast_cpow_pos_of_pos, ProbabilityTheory.gaussianReal_map_sub_const, MeasureTheory.setIntegral_indicatorConstLp, InnerProductSpace.HarmonicContOnCl.fun_const_smul, Real.Gamma_eq_integral, signedDist_vsub_self, Archimedean.ratLt'_nonempty, Real.Gamma_zero, isBoundedLinearMap_iff, NNReal.lt_rpow_inv_iff_of_neg, DifferentiableAt.arsinh, spectralAlgNorm_one, irrational_ratCast_sub_iff, LocallyBoundedVariationOn.ae_differentiableWithinAt_of_mem_pi, EuclideanGeometry.inversion_mul, Complex.re_le_norm, EReal.tendsto_coe_nhds_bot_iff, Real.cos_nat_mul_pi_sub, lp.norm_zero, MeasureTheory.lintegral_eq_lintegral_meas_lt, UpperHalfPlane.pos_real_re, Subgroup.strictWidthInfty_nonneg, PathConnectedSpace.exists_path_through_family, stereographic_target, MeasureTheory.SignedMeasure.rnDeriv_smul, ContDiffBump.contDiffAt, UpperHalfPlane.IsZeroAtImInfty.zero_at_infty_comp_ofComplex, ContinuousMap.realToNNReal_apply, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, ProbabilityTheory.iIndepFun.hasGaussianLaw, ProbabilityTheory.isGaussian_conv, NNReal.Lp_add_le_hasSum, ProbabilityTheory.integrable_rpow_abs_of_integrable_exp_mul, Affine.Simplex.exists_forall_signedInfDist_eq_iff_eq_incenter, MeasureTheory.sum_measureReal_preimage_singleton, Metric.unitClosedBall.coe_eq_zero, Complex.norm_add_mul_I, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_continuousOn, Real.le_sin, Polynomial.Chebyshev.rootMultiplicity_U_real, MeasureTheory.hausdorffMeasure_smul_right_image, NNReal.convex_iff, instIsUniformAddGroupReal, signedDist_smul, MeasureTheory.tendsto_integral_smul_of_tendsto_average_norm_sub, HasStrictFDerivAt.hasStrictDerivAt_norm_smul_pos, CStarAlgebra.norm_le_iff_le_algebraMap, EReal.tendsto_coe_atBot, ContinuousAlternatingMap.le_of_opNorm_le, ENNReal.tendsto_toReal_zero_iff, MeasureTheory.eLpNorm_mono_ae_real, Metric.diam_singleton, RCLike.im_tsum, ENNReal.ofReal_le_coe, HasFDerivWithinAt.arsinh, MeasureTheory.rnDeriv_tilted_left, TemperedDistribution.fourierTransform_apply, ContinuousLinearMap.opNorm_zero, ConcaveOn.isBoundedUnder_abs, Orientation.oangle_add_right_smul_rotation_pi_div_two, MeromorphicOn.circleAverage_log_norm, ProbabilityTheory.gaussianPDFReal_inv_mul, variationOnFromTo.add, not_sameRay_iff_norm_add_lt, StieltjesFunction.measure_Icc, Real.continuous_cos, geometric_hahn_banach_point_open, TestFunction.mkCLM_apply, Real.abs_log_mul_self_rpow_lt, NNReal.coe_expect, Complex.equivRealProdAddHom_apply, Real.hasStrictDerivAt_arctan, one_le_norm_one, ProbabilityTheory.charFun_inv_sqrt_mul_sum, IntervalIntegrable.comp_add_left, Real.sin_bound, ContinuousMultilinearMap.norm_iteratedFDeriv_le, ENNReal.lintegral_mul_le_Lp_mul_Lq, MeasureTheory.le_sub_of_le_upcrossingsBefore, Complex.interior_setOf_re_le, LipschitzOnWith.coordinate, Quaternion.tsum_coe, sub_isBigO_norm_rpow_add_one_of_fderiv, intervalIntegrable_posLog_norm_meromorphicOn, Complex.abs_re_le_norm, Orientation.inner_smul_rotation_pi_div_two_left, InformationTheory.klFun_zero, taylor_isLittleO, Real.surjOn_sin, CFC.abs_ofNat, unitInterval.symm_zero, Real.dimH_univ_pi, ProbabilityTheory.compProd_toKernel, BoxIntegral.hasIntegral_const, ProbabilityTheory.IndepFun.covariance_eq_zero, Real.tendsto_logb_atTop_of_base_lt_one, ZLattice.volume_image_eq_volume_div_covolume, StrictConcaveOn.strictAntiOn_derivWithin, MeasureTheory.Supermartingale.smul_nonpos, EuclideanGeometry.Sphere.power_nonneg_iff_radius_le_dist_center, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, UpperHalfPlane.im_pos_of_dist_center_le, ContinuousWithinAt.log, ProbabilityTheory.poissonMeasure_singleton, Real.rpow_left_injOn, ConcaveOn.continuousOn_interior, Real.sin_pi_div_thirty_two, ContDiffOn.norm_sq, 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, NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_apply, TestFunction.fderivCLM_eq_of_scalars, Complex.arg_neg_iff, Int.dist_eq, CFC.negPart_one, intervalIntegral.inv_mul_integral_comp_div_sub, RCLike.norm_re_le_norm, IsIntegralCurve.continuous, IntervalIntegrable.comp_add_right_iff, BoxIntegral.Box.diam_Icc_le_of_distortion_le, LinearMap.mkContinuous_norm_le', setIntegral_withDensity_eq_setIntegral_smul, CFC.log_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, EisensteinSeries.E_qExpansion_coeff, TendstoUniformlyOn.im, RightDerivMeasurableAux.A_mem_nhdsGT, Real.neg_pi_div_two_lt_arcsin, ProbabilityTheory.HasSubgaussianMGF.integrableExpSet_eq_univ, trapezoidal_error_le, lipschitzWith_iff_dist_le_mul, Euclidean.closedBall_eq_preimage, integral_pair, mellin_comp_rpow, ProbabilityTheory.integral_poissonMeasure, MeasureTheory.integrableOn_Ioi_of_intervalIntegral_norm_bounded, tendsto_norm', EReal.exists, Real.sqrtTwoAddSeries_step_down, re_inner_self_pos, MeasureTheory.integrable_continuousLinearMap_prod', Quaternion.continuous_im, GroupNorm.add_apply, MeasureTheory.Submartingale.sum_smul_sub', Real.mulExpNegMulSq_eq_sqrt_mul_mulExpNegMulSq_one, EReal.toReal_bot, MeasureTheory.MemLp.integral_indicator_norm_ge_le, Real.rpow_sub_intCast', HasDerivAt.lhopital_zero_right_on_Ico, NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, ArithmeticFunction.vonMangoldt.residueClass_nonneg, MeasureTheory.norm_stoppedValue_leastGE_le, dist_partial_sum_le_of_le_geometric, AffineSubspace.mem_perpBisector_iff_dist_eq', Matrix.PosSemidef.inv_sqrt, ContinuousMultilinearMap.norm_iteratedFDeriv_le', uniqueDiffOn_Iio, MeasureTheory.Measure.haar.chaar_sup_le, Matrix.IsHermitian.cfcHom_eq_cfcAux, MeasureTheory.Measure.toSphereBallBound_mul_measureReal_unitBall_le_toSphere_ball, MulAlgebraNormClass.map_smul_eq_mul, Rat.not_irrational, IsLocalMax.lineDeriv_eq_zero, TestFunction.lineDerivCLM_eq_of_scalars, AffineSubspace.isPreconnected_setOf_wSameSide, ProbabilityTheory.IsMeasurableRatCDF.measurable_stieltjesFunction, InformationTheory.toReal_klDiv_smul_right_eq_smul_left, 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', Complex.tendsto_partialGamma, summable_finset_prod_of_summable_nonneg, Set.infsep_pair_le_toReal_inf, NNReal.rpow_lt_one_of_one_lt_of_neg, intervalIntegral.differentiable_integral_of_continuous, Real.cos_eq_two_mul_tan_half_div_one_sub_tan_half_sq, Orientation.tan_oangle_sub_left_mul_norm_of_oangle_eq_pi_div_two, Asymptotics.isBigO_cofinite_iff, Matrix.linfty_opNorm_mulVec, intervalIntegral.smul_integral_comp_mul_add, ProbabilityTheory.Fernique.logRatio_pos, isIntegralCurveAt_comp_sub, integral_log_from_zero_of_pos, IsIntegralCurveAt.comp_mul_ne_zero, MeasureTheory.setIntegral_nonpos_le, Real.iteratedDeriv_odd_cosh, Matrix.finite_real_spectrum, EuclideanGeometry.cos_angle_mul_dist_of_angle_eq_pi_div_two, Complex.tendsto_norm_tan_of_cos_eq_zero, Polynomial.eval_lt_zero_of_roots_lt_of_leadingCoeff_nonpos, LipschitzWith.locallyIntegrable_lineDeriv, InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_fst_ofIsReal, DirichletCharacter.norm_LFunction_product_ge_one, Tactic.ComputeAsymptotics.Majorized.const, Affine.Simplex.ninePointCircle_center_mem_affineSpan, dist_lt_coe, log_le_harmonic_floor, AddCircle.norm_neg_period, SmoothBumpCovering.embeddingPiTangent_injOn, Real.sqrt_eq_iff_mul_self_eq_of_pos, MeasureTheory.memLp_norm_rpow_iff, Height.mulHeight_eval_le, ConvexOn.isMinOn_of_leftDeriv_nonpos_of_rightDeriv_nonneg, ConvexOn.map_condExp_le, Real.Angle.continuous_coe, Complex.measurableEquivPi_symm_apply, AddCircle.compactSpace, ContinuousAffineMap.norm_image_zero_le, strictAnti_of_deriv_neg, 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.measureReal_abs_dual_gt_le_integral_charFunDual, RieszExtension.step, AbsoluteValue.IsAdmissible.exists_partition', 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, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, Real.analyticOn_sin, AbsoluteValue.Completion.isClosedEmbedding_extensionEmbedding_of_comp, MeasureTheory.measureReal_union_null, strictConvexOn_of_deriv2_pos', ConcaveOn.slope_le_of_hasDerivWithinAt, Real.rpow_sum_of_nonneg, Filter.Eventually.isBigO, Matrix.norm_lt_iff, NumberField.InfinitePlace.Completion.bijective_extensionEmbeddingOfIsReal, ConvexOn.average_mem_epigraph, ENNReal.zero_rpow_of_neg, UnitAddTorus.hasSum_mFourier_series_of_summable, NormedAddGroupHom.ofLipschitz_norm_le, Real.hasDerivAt_mulExpNegMulSq, Mathlib.Meta.NormNum.isNNRat_rpow_neg, LSeriesSummable_one_iff, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, Real.tendstoLocallyUniformlyOn_rpow_sub_one_log, HasFDerivAt.le_of_lip', EuclideanGeometry.angle_add_of_ne_of_ne, norm_le_gronwallBound_of_norm_deriv_right_le, GroupNorm.ext_iff, Real.sqrt_zero, SchwartzMap.tsupport_smulLeftCLM_subset, Orientation.kahler_comp_linearIsometryEquiv, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, Real.fourierIntegral_fderiv, Function.Periodic.invQParam_tendsto, MeasureTheory.integral_condExp_indicator, AkraBazziRecurrence.eventually_deriv_one_sub_smoothingFn, IsIntegralCurveOn.continuousOn, dist_norm_norm_le_norm_neg_add, separate_convex_open_set, Real.image_tan_Ioo, controlled_sum_of_mem_closure, eventually_norm_symmL_trivializationAt_lt, AkraBazziRecurrence.eventually_atTop_sumTransform_le, ContinuousMultilinearMap.le_opNorm_mul_pow_card_of_le, cfcₙHom_real_eq_restrict, Real.posLog_zero, isIntegralCurveOn_comp_sub, CFC.abs_algebraMap_nnreal, Function.FactorizedRational.log_norm_meromorphicTrailingCoeffAt, Asymptotics.IsBigOWith.norm_right, Real.Angle.toReal_eq_zero_iff, Complex.equivRealProdLm_symm_apply_re, MeasureTheory.lpNorm_zero, EuclideanGeometry.Sphere.power_nonpos_iff_dist_center_le_radius, ContDiffWithinAt.abs, MeasureTheory.ComplexMeasure.im_apply, ProbabilityTheory.covariance_map_equiv, InformationTheory.klFun_nonneg, PowerSeries.IsRestricted.convergenceSet_BddAbove, Real.sin_sub_pi, intervalIntegral.integrable_comp_mul_deriv_iff_of_deriv_nonpos, mem_closedBall_one_iff, Metric.infDist_lt_iff, LiouvilleWith.int_mul_iff, Function.locallyFinsuppWithin.logCounting_divisor_eq_circleAverage_sub_const, AffineSubspace.perpBisector_eq_top, ENNReal.inner_le_weight_mul_Lp_of_nonneg, NNReal.inner_le_weight_mul_Lp, Real.smoothTransition.continuousAt, Complex.im_nsmul, Complex.closure_setOf_lt_re, UnitAddTorus.mFourierSubalgebra_separatesPoints, NNReal.rpow_add_one', ENNReal.toReal_nsmul, UnitAddTorus.coe_measurableEquivPiIoc_apply, Monotone.convexOn_univ_of_deriv, Real.log_le_log_iff, Complex.betaIntegral_convergent, dist_pointReflection_right, MeasureTheory.Measure.addHaar_smul_of_nonneg, RCLike.nonneg_iff_exists_ofReal, ContinuousLinearMap.opNorm_le_iff, RCLike.geometric_hahn_banach_open, Seminorm.continuous_iSup, NumberField.mixedEmbedding.normAtPlace_neg, NormedDivisionRing.norm_mul, IsLocalMax.hasLineDerivAt_eq_zero, Asymptotics.IsBigOWith.add_add, RCLike.ofReal_expect, Real.differentiableOn_arccos, Orientation.oangle_smul_right_of_neg, EisensteinSeries.linear_isTheta_left, Metric.mem_nhds_iff, EuclideanGeometry.tan_angle_mul_dist_of_angle_eq_pi_div_two, tendsto_zero_iff_norm_tendsto_zero, Seminorm.ball_smul_ball, CStarRing.norm_self_mul_star, Complex.coe_algebraMap, Bornology.IsBounded.subset_ball, Real.fourierIntegral_convergent_iff, Real.lt_sqrt_of_sq_lt, Summable.mul_of_nonneg, smoothingFun_le_self, Real.lipschitzWith_toNNReal, IsLocalMin.deriv_eq_zero, ZeroHomClass.bound_of_antilipschitz, harmonic_is_realOfHolomorphic, Real.hasDerivAt_cosh, ConcaveOn.le_slope_of_hasDerivWithinAt_Iio, MultilinearMap.bound_of_shell_of_continuous, Real.tendsto_deriv_mul_log_atTop, HasFDerivAt.sin, intervalIntegral.integral_comp_mul_deriv_of_deriv_nonpos, Real.dist_eq, BoundedContinuousFunction.norm_lt_iff_of_nonempty_compact, ProbabilityTheory.HasGaussianLaw.map_equiv, Orientation.abs_areaForm_of_orthogonal, Isometry.affineIsometryOfStrictConvexSpace_apply, ProbabilityTheory.Kernel.tendsto_setIntegral_densityProcess, MeasureTheory.AECover.integrable_of_integral_tendsto_of_nonneg_ae, Orientation.sin_oangle_add_right_of_oangle_eq_pi_div_two, ProbabilityTheory.stdGaussian_map, LipschitzOnWith.ae_differentiableWithinAt_real, Real.one_lt_exp_iff, MeasureTheory.AEStronglyMeasurable.ae_integrable_condDistrib_map_iff, UnitAddCircle.norm_eq, WithLp.prod_norm_sq_eq_of_L2, lp.hasSum_norm, IsCoveringMap.liftHomotopy_zero, Real.self_lt_rpow_of_lt_one, upperHemicontinuous_quasispectrum_nnreal, SmoothBumpCovering.mem_extChartAt_ind_source, integral_sin, FDerivMeasurableAux.mem_A_of_differentiable, Asymptotics.isBigO_atTop_natCast_rpow_of_tendsto_div_rpow, ENNReal.ofReal_nsmul, SlashInvariantForm.slash_action_eqn_SL'', ProbabilityTheory.setLIntegral_toKernel_prod, mem_ball_iff_norm_inv_mul_lt, innerₗ_apply_apply, ProbabilityTheory.HasGaussianLaw.prodMk, Metric.nhds_basis_closedBall_inv_nat_pos, indicator_cthickening_eventually_eq_indicator_closure, Affine.Simplex.sign_touchpointWeights_singleton_neg, IsIntegralCurveAt.hasDerivAt, Complex.ofReal_comp_pow, Real.logb_nonneg_iff_of_base_lt_one, ProbabilityTheory.Kernel.stronglyMeasurable_countableFiltration_densityProcess, Real.sin_sq_add_cos_sq, MeasureTheory.integral_eq_zero_iff_of_nonneg_ae, Set.infsep_triple, InnerProductSpace.HarmonicOnNhd.circleAverage_re_herglotzRieszKernel_smul, LinearMap.polar_eq_biInter_preimage, IsUltrametricDist.norm_add_le_max, ProbabilityTheory.HasSubgaussianMGF.add, NumberField.InfinitePlace.eq_one_of_rpow_eq, NNReal.iInf_real_pos_eq_iInf_nnreal_pos, EuclideanGeometry.sin_angle_mul_dist_of_angle_eq_pi_div_two, Seminorm.coe_sSup_eq, SchwartzMap.norm_toLp_top_le, tendsto_gauge_nhds_zero, Metric.cauchy_iff, MeasureTheory.eLpNorm_norm_rpow, 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, StrictConvexOn.lt_slope_of_hasDerivWithinAt, gauge_nonneg, ProbabilityTheory.mgf_smul_left, Path.subpathAux_continuous, Real.rpow_le_self_of_le_one, NumberField.mixedEmbedding.unitSMul_smul, fourierCoeff_eq_intervalIntegral, ENNReal.le_ofReal_iff_toReal_le, Continuous.bounded_above_of_compact_support, ProbabilityTheory.Fernique.measure_le_mul_measure_gt_normThreshold_le_of_map_rotation_eq_self, CFC.inverse_eq_rpow_neg_one, Seminorm.bddBelow_range_add, MeasureTheory.Measure.setIntegral_toReal_rnDeriv_eq_withDensity', Real.map_exp_atBot, CStarAlgebra.conjugate_le_norm_smul', ENNReal.ofReal_prod_of_nonneg, RCLike.ofReal_nonpos, Asymptotics.IsLittleO.of_abs_abs, 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, Continuous.exists_contMDiff_approx_and_eqOn, exists_eq_const_mul_intervalIntegral_of_ae_nonneg, UpperHalfPlane.continuous_im, Bornology.IsBounded.subset_closedBall_lt, tendsto_mod_div_atTop_nhds_zero_nat, ProbabilityTheory.measure_sum_ge_le_of_hasCondSubgaussianMGF, ProbabilityTheory.gaussianReal_const_sub, NNReal.lt_rpow_inv_iff_of_pos, EuclideanGeometry.abs_oangle_left_toReal_lt_pi_div_two_of_dist_eq, ContDiffAt.contDiffAt_norm_of_smul, NNReal.rpow_le_rpow_iff_of_neg, AffineSubspace.midpoint_mem_perpBisector, EuclideanGeometry.Sphere.radius_nonneg_of_mem, inner_sum_smul_sum_smul_of_sum_eq_zero, lp.norm_le_of_forall_sum_le, Complex.exp_bound, dist_pos, Complex.closure_reProdIm, Polynomial.sum_derivRootWeight_pos, curveIntegralFun_add, StrictConvexSpace.extremePoints_closedBall_eq_sphere, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, mem_ball_iff_norm', ContinuousOn.ofReal_map_toNNReal, MeasureTheory.norm_setIntegral_le_of_norm_le_const_ae, 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, tendsto_rpow_atBot_of_base_lt_one, MeasureTheory.Measure.map_addHaar_smul, unitInterval.symm_lt_comm, Real.hasDerivAt_fourierChar, smoothingSeminorm_of_mul, NNReal.geom_mean_le_arith_mean_weighted, intervalIntegral.integral_comp_add_right, numDerangements_tendsto_inv_e, Real.tan_add', Real.le_integral_rpowIntegrand₀₁_one, bilinFormOfRealInner_orthogonal, ContinuousLinearMap.intervalIntegral_apply, MeasureTheory.norm_one_sub_charFun_le_two, Set.OrdConnected.image_real_toNNReal, ConvexOn.locallyLipschitzOn_interior, StieltjesFunction.length_eq, Diffeology.isPlot_reparam, span_fourierLp_closure_eq_top, Orientation.oangle_add_right_eq_arctan_of_oangle_eq_pi_div_two, Real.tendsto_of_bddBelow_antitone, Mathlib.Meta.Positivity.log_nonneg_of_isNegNat, PMF.integral_eq_sum, analyticWithinAt_sigmoid, MeasureTheory.average_add_measure, EuclideanGeometry.inner_weightedVSub, 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, ProbabilityTheory.variance_le_expectation_sq, MeasureTheory.Integrable.withDensityᵥ_trim_eq_integral, circleIntegrable_zero_radius, MeasureTheory.measureReal_union_add_inter₀', isBigO_norm_rpow_add_one_of_fderiv_of_apply_eq_zero, NNReal.image_coe_Iic, SchwartzMap.smulLeftCLM_neg, LipschitzWith.of_le_add_mul, intervalIntegral.inv_smul_integral_comp_div, transcendental_liouvilleNumber, UpperHalfPlane.atImInfty_basis, analyticOn_sigmoid, EuclideanGeometry.Sphere.center_mem_orthRadius_iff, Real.one_lt_rpow_of_pos_of_lt_one_of_neg, unitInterval.coe_lt_one, WithCStarModule.norm_equiv_le_norm_prod, LiouvilleWith.exists_pos, Complex.isUniformEmbedding_ofReal, Besicovitch.exists_disjoint_closedBall_covering_ae, Asymptotics.IsBigOWith.prod_left, MeasureTheory.eLpNorm'_le_eLpNormEssSup_mul_rpow_measure_univ, lp.norm_le_of_forall_le, ContinuousWithinAt.logb, Set.Icc.continuous_convexCombo_prod, InformationTheory.isMinOn_klFun, GaussianInt.intCast_real_norm, Complex.conjCLE_enorm, intervalIntegral.integrable_deriv_smul_comp_iff_of_deriv_nonpos, 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, Complex.HadamardThreeLines.sSupNormIm_scale_left, Real.differentiableWithinAt_arccos_Iic, NormedField.completeSpace_iff_isComplete_closedBall, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, NNReal.Lr_le_Lp_mul_Lq, CFC.nnnorm_rpow, MeasureTheory.charFunDual_eq_pi_iff, Complex.exists_norm_mul_eq_self, EuclideanGeometry.collinear_of_sin_eq_zero, OrthonormalBasis.orthonormal_adjustToOrientation, Wbtw.angle₂₁₃_eq_zero_of_ne, MeasureTheory.Measure.integral_isMulLeftInvariant_eq_smul_of_hasCompactSupport, norm_div_le_norm_div_add_norm_div, Real.rpow_add_rpow_le_add, unitInterval.sigmoid_lt_iff, Continuous.inner_, MeasureTheory.aestronglyMeasurable_condExpL1CLM, ProbabilityTheory.variance_add, Hamming.norm_eq_hammingNorm, Affine.Simplex.ExcenterExists.excenter_mem_affineSpan_range, PiLp.norm_eq_of_nat, CantorScheme.VanishingDiam.dist_lt, MeasureTheory.submartingale_of_expected_stoppedValue_mono, ProbabilityTheory.variance_id_gaussianReal, Quaternion.imK_coeComplex, smoothingFun_of_map_mul_eq_mul, Continuous.cfcₙ_nnreal_of_mem_nhdsSet, MellinConvergent.comp_rpow, controlled_closure_range_of_complete, intervalIntegral.integral_derivWithin_Icc_of_contDiffOn_Icc, 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, Polynomial.gaussNorm_zero_right, ProbabilityTheory.mgf_const', NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_lt, SchwartzMap.inner_fourierTransformCLM_toL2_eq, Real.instIsDomain, CFC.nnrpow_le_nnrpow, Real.sin_arctan_eq_zero, intervalIntegral.continuousAt_parametric_primitive_of_dominated, range_euclideanQuadrant, Asymptotics.IsBigOWith.of_const_mul_right, MeasureTheory.SimpleFunc.setToSimpleFunc_zero, Complex.ofReal_injective, Real.tendsto_integral_cexp_sq_smul, UpperHalfPlane.meromorphicOrderAt_comp_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, exists_contMDiffMap_forall_mem_convex_of_local, ProbabilityTheory.iIndepFun.hasGaussianLaw_sub, convexHull_ediam, NormedAddCommGroup.tendsto_nhds_zero, MeromorphicOn.log_norm_meromorphicTrailingCoeffAt_extract_zeros_poles, Real.cauchy_neg, Real.iSup_mul_of_nonneg, HasDerivWithinAt.limsup_slope_le', 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, Real.iteratedDerivWithin_sinh_Ioo, MeasureTheory.integral_eq_setToFun, ZLattice.covolume.tendsto_card_le_div, SzemerediRegularity.hundred_div_ε_pow_five_le_m, 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, intervalIntegral.integral_nonneg_of_ae_restrict, TendstoUniformlyOn.re, Real.coe_fib_eq', ODE.hasDerivWithinAt_picard_Icc, signedDist_smul_of_neg, enorm_norm, ProbabilityTheory.gaussianReal_sub_const, Matrix.IsHermitian.exists_eigenvector_of_ne_zero, Polynomial.Chebyshev.sumZeroes_T_of_not_dvd, dist_triangle4_left, IntervalIntegrable.finsum, PiLp.norm_toLp_const, nnnorm_norm, MeasureTheory.lpNorm_const_smul, Real.injOn_sin, disjoint_closedBall_closedBall_iff, HomotopyGroup.one_def, Metric.cthickening_eq_iInter_cthickening, bernoulliFun_mul, ContinuousLinearMap.rotation_apply, Real.iteratedFDeriv_fourier, Diffeology.isOpen_iff_preimages_plots, AddGroupNorm.sup_apply, Seminorm.smul_closedBall_subset, PiTensorProduct.projectiveSeminorm_add_le, dist_prod_prod_le_of_le, MultilinearMap.bound_of_shell, Complex.div_intCast_re, Complex.toIocMod_arg, ContractingWith.dist_le_of_fixedPoint, MeasureTheory.SignedMeasure.singularPart_sub, lp.tsum_mul_le_mul_norm', TopologicalAddGroup.IsSES.pushforward_def, RCLike.re_le_re, intervalIntegral.norm_integral_le_of_norm_le_const_ae, RCLike.reLm_coe, BoxIntegral.TaggedPrepartition.IsHenstock.card_filter_tag_eq_le, ProbabilityTheory.integrable_rpow_mul_exp_of_integrable_exp_mul, nnnorm_fderiv_norm_rpow_le, norm_add_sq_real, Real.hasFPowerSeriesOnBall_linear_zero, Function.Periodic.im_invQParam_pos_of_norm_lt_one, differentiableAt_abs_pos, ProbabilityTheory.gaussianPDFReal_zero_var, NNReal.abs_eq, Differentiable.exp, Real.Angle.coe_nsmul, EisensteinSeries.q_expansion_bernoulli, NNReal.orderIsoIccZeroCoe_symm_apply_coe, Convex.norm_image_sub_le_of_norm_deriv_le, SchwartzMap.convolution_continuous_left, ProbabilityTheory.integrable_rpow_abs_of_mem_interior_integrableExpSet, MeasureTheory.Lp.coe_posPart, integrableOn_exp_neg_Ioi, HurwitzZeta.completedHurwitzZetaEven_zero, Real.logb_injOn_pos_of_base_lt_one, Path.target', ContDiff.inversion, Polynomial.mahlerMeasure_one, Topology.RelCWComplex.openCell_zero_eq_singleton, UpperHalfPlane.coe_specialLinearGroup_apply, spectrum.norm_eq_one_of_unitary, ContDiffMapSupportedIn.structureMapCLM_top_apply, Complex.isTheta_cpow_const_rpow, Real.contDiffOn_arccos, Real.Angle.coe_toIocMod, norm_iteratedFDerivWithin_comp_le, inner_smul_real_left, CovByVAdd.rfl, NumberField.mixedEmbedding.fundamentalCone.expMap_single_symm_apply, Metric.Snowflaking.preimage_toSnowflaking_ball, eigenvalue_mem_ball, AddMonoidHom.mkNormedAddGroupHom_norm_le, 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, BoxIntegral.norm_volume_sub_integral_face_upper_sub_lower_smul_le, EuclideanGeometry.cos_eq_zero_iff_angle_eq_pi_div_two, norm_le_spectralNorm, Real.isTheta_exp_comp_exp_comp, InnerProductGeometry.angle_add_eq_arccos_of_inner_eq_zero, HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow, LipschitzWith.max, Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero, EuclideanGeometry.cospherical_iff_exists_mem_of_complete, 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, Real.sqrt_pos_of_pos, SeminormClass.map_smul_eq_mul, HasStrictDerivAt.arsinh, 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, InformationTheory.toReal_klDiv_smul_right, MeasureTheory.measureReal_union₀, Complex.I_mul, fderiv_norm_smul, Diffeology.IsContDiffCompatible.isPlot_iff, MeasureTheory.Measure.integrable_integral_norm_of_integrable_comp, MulRingSeminorm.mulRingSeminormClass, NumberField.mixedEmbedding.volume_eq_two_pow_mul_two_pi_pow_mul_integral, Real.dist_le_of_mem_Icc_01, InnerProductSpace.laplacian_eq_iteratedFDeriv_complexPlane, MeasureTheory.measureReal_univ_pos, Affine.Simplex.excenterWeights_restrict, stereoInvFunAux_mem, expNegInvGlue.continuous_polynomial_eval_inv_mul, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, isMIntegralCurveAt_comp_mul_ne_zero, ProbabilityTheory.IndepFun.variance_add, ContinuousAlternatingMap.bounds_nonempty, WithLp.volume_preserving_symm_measurableEquiv_toLp_prod, MulRingNorm.isPowMul, norm_tsum_le_tsum_norm, liminf_mul_le, MeasureTheory.SimpleFunc.integral_eq_sum_of_subset, Metric.Snowflaking.edist_toSnowflaking_toSnowflaking, MeasureTheory.MemLp.re, EuclideanSpace.ball_zero_eq, HasFDerivAt.hasFDerivAt_norm_smul, Real.instCompleteSpace, EuclideanGeometry.dist_orthogonalProjection_eq_zero_iff, Real.rpow_inv_natCast_pow, CStarAlgebra.isStrictlyPositive_iff_isUnit_sqrt_and_eq_sqrt_mul_sqrt, HurwitzZeta.hasSum_int_oddKernel, Real.Gamma_mul_Gamma_add_half_of_pos, Real.rpow_def_of_nonneg, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_pos, SchwartzMap.integral_fourier_mul_eq, RCLike.ratCast_re, MeasureTheory.AEStronglyMeasurable.im, cfc_comp_norm, Complex.arg_of_im_neg, AkraBazziRecurrence.isEquivalent_smoothingFn_sub_self, NumberField.Units.regulator_pos, exists_lt_of_gauge_lt, RCLike.ofReal_eq_re_of_isSelfAdjoint, EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd, ENNReal.rpow_le_rpow, StarModule.complexToReal, IsMinOn.hasLineDerivWithinAt_eq_zero, CFC.abs_intCast, MeasureTheory.SimpleFunc.map_coe_nnreal_restrict, Complex.I_mul_re, Cardinal.cantorFunction_succ, Real.sigmoid_zero, Complex.normSq_nonneg, Matrix.IsHermitian.coe_re_apply_self, AkraBazziRecurrence.eventually_atTop_sumTransform_ge, GaussianFourier.tendsto_verticalIntegral, variationOnFromTo.nonneg_of_le, apply_le_nnnorm_cfc_nnreal, 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, eventually_riemannianEDist_le_edist_extChartAt, Complex.volume_preserving_equiv_pi, Complex.arg_eq_zero_iff, ContinuousMap.Homotopy.extend_of_mem_I, Complex.wedgeIntegral_add_wedgeIntegral_eq, ProbabilityTheory.strong_law_aux7, 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, MeasureTheory.eLpNorm'_add_le_of_le_one, PiLp.norm_apply_le, Complex.norm_sub_one_sq_eqOn_sphere, exists_ratio_hasDerivAt_eq_ratio_slope, HasFDerivWithinAt.curveIntegral_segment_source, Affine.Triangle.eulerPoint_eq_midpoint, Quaternion.inner_def, StrictConcaveOn.slope_lt_of_hasDerivWithinAt, NNReal.coe_mono, MeasureTheory.weightedSMul_union', MeasureTheory.integrable_prod_iff', Real.sum_mul_le_sqrt_mul_sqrt, MeasureTheory.Measure.addHaar_closedBall_mul_of_pos, stereographic_source, ProbabilityTheory.Fernique.measure_gt_normThreshold_le_rpow, ProbabilityTheory.charFunDual_map_sum_pi_eq_prod, 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, ZLattice.summable_norm_sub_rpow, HurwitzZeta.sinZeta_two_mul_nat_add_one, NumberField.Embeddings.coeff_bdd_of_norm_le, 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, MeasureTheory.setIntegral_gt_gt, GaussianInt.im_toComplex, summable_geometric_of_abs_lt_one, ConvexOn.derivWithin_le_slope, MeasureTheory.setIntegral_nonneg_ae, ProbabilityTheory.Kernel.IsMarkovKernel.integrable, HasFDerivWithinAt.sqrt, MeasureTheory.setIntegral_nonpos_of_ae, gauge_mono, Affine.Simplex.sign_signedInfDist_touchpoint_empty, Real.iteratedDeriv_even_sinh, ContinuousLinearMap.norm_id_le, AddGroupSeminorm.coe_smul, HasFDerivAt.le_of_lipschitz, ContDiffMapSupportedIn.structureMapLM_top_apply, ProbabilityTheory.covariance_zero_measure, EReal.preimage_coe_Iio, Real.iSup_of_not_bddAbove, 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, ConvexOn.univ_sSup_affine_eq, ContinuousMap.toNNReal_apply, MultilinearMap.mkContinuous_norm_le, Real.lt_sin_mul, 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.integral_boundary_rect_eq_zero_of_differentiable_on_off_countable, 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, LinearMap.singularValues_of_finrank_le, Real.hasFDerivAt_fourierIntegral, intervalIntegral.integral_hasDerivAt_of_tendsto_ae_left, Complex.sqrt_eq_real_add_ite, NumberField.mixedEmbedding.normAtPlace_apply, NNReal.rpow_rpow_inv_eq_iff, SchwartzMap.integralCLM_apply, EulerSine.tendsto_integral_cos_pow_mul_div, linearEquiv_det_rotation, Real.inner_le_Lp_mul_Lq_tsum_of_nonneg, MeasureTheory.lpNorm_one, Complex.coe_selfAdjointEquiv, GroupNorm.lt_def, PolynormableSpace.withSeminorms', RCLike.norm_two, Real.differentiable_mulExpNegMulSq, EuclideanGeometry.exists_dist_eq_iff_exists_dist_orthogonalProjection_eq, ConvexBody.isClosed, Measurable.sqrt, thickening_thickening, ContinuousMap.neg_norm_le_apply, ProbabilityTheory.condCDF_le_one, Affine.Simplex.midpoint_faceOppositeCentroid_eulerPoint, Height.logHeight_eval_le, MeasureTheory.Submartingale.stoppedAbove, NonarchAddGroupSeminorm.toZeroHom_eq_coe, AddCircle.coe_real_preimage_closedBall_period_zero, circleIntegrable_sub_zpow_iff, MeasureTheory.withDensityᵥ_toReal, NumberField.mixedEmbedding.volume_preserving_homeoRealMixedSpacePolarSpace, integrable_of_isBigO_exp_neg, Real.HolderTriple.right_pos, ProbabilityTheory.Kernel.condExp_densityProcess, MeasureTheory.SignedMeasure.jordanDecomposition_add_withDensity_mutuallySingular, CircleDeg1Lift.lt_iterate_pos_iff, EuclideanSpace.volume_ball_fin_two, mem_nullSubmodule_iff, Polynomial.fourierCoeff_toAddCircle_natCast, Real.cos_lt_cos_of_nonneg_of_le_pi_div_two, ContDiffBump.tsupport_eq, UniformSpace.Completion.uniformity_dist, Real.cos_sq_add_sin_sq, Real.eulerMascheroniConstant_lt_eulerMascheroniSeq', Real.differentiableAt_arccos, ConvexOn.real_univ_sSup_of_nat_affine_eq, ContractingWith.one_sub_K_pos, Real.summable_pow_div_factorial, ArithmeticFunction.vonMangoldt.LSeries_residueClass_lower_bound, RCLike.im_eq_zero_of_le, image_sub_lt_mul_sub_of_deriv_lt, SimpleGraph.tendsto_turanDensity, norm_add_sq, CFC.nnrpow_eq_nnrpow_pi, Polynomial.mahlerMeasure_zero, spectralNorm.spectralNorm_eq_norm_coeff_zero_rpow, fderivWithin_sqrt, Affine.Simplex.sum_reflectionCircumcenterWeightsWithCircumcenter, Complex.not_le_zero_iff, AbsolutelyContinuousOnInterval.mul, Real.dist_0_eq_abs, RCLike.norm_sq_re_conj_add, SeminormedRing.norm_mul_le, MeasureTheory.levyProkhorovDist_le_of_forall_le, Complex.conjCLE_apply, NormedSpace.polar_ball, Real.eulerMascheroniSeq'_six_lt_two_thirds, Real.cos_sub_cos, EuclideanSpace.inner_basisFun_real, summable_condensed_iff_of_nonneg, Real.not_DifferentiableAt_log_mul_zero, MeasureTheory.integral_image_eq_integral_deriv_smul_of_antitone, 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, norm_jacobiTheta₂'_term_le, LinearMap.mkContinuous_norm_le, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, ProbabilityTheory.mgf_map, EuclideanGeometry.Sphere.IsTangentAt.eq_orthogonalProjection, MeasureTheory.Submartingale.tendsto_eLpNorm_one_limitProcess, dist_le_dist_of_le_pi, EuclideanGeometry.angle_eq_arcsin_of_angle_eq_pi_div_two, IsOpen.exists_between_affineIndependent_span_eq_top, ProbabilityTheory.Kernel.tendsto_densityProcess_limitProcess, CircleDeg1Lift.tendsto_translation_number₀, RCLike.sqrt_neg_I, fourierCoeffOn_of_hasDerivAt_Ioo, NumberField.mixedEmbedding.volume_eq_zero, ENNReal.one_le_rpow_of_pos_of_le_one_of_neg, norm_iteratedFDeriv_comp_le, IsNonarchimedean.iSup_abv_linearMap_apply_le, thickening_cthickening, ZMod.toAddCircle_apply, Complex.nndist_conj_self, MeasureTheory.ofReal_integral_eq_lintegral_ofReal, Real.ceil_logb_natCast, 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, MeasureTheory.eLpNorm_one_le_of_le, ProbabilityTheory.strong_law_Lp, ProbabilityTheory.condVar_of_ae_eq_zero_or_one, Real.tendsto_tan_neg_pi_div_two, geom_lt, Real.Angle.tan_eq_sin_div_cos, dist_mul_mul_le, ModularGroup.exists_bound_of_subgroup_invariant_of_isArithmetic_of_isBigO, Real.lt_sqrt, bernoulliFun_eq_integral, RCLike.normSq_pos, EuclideanGeometry.Sphere.IsDiameter.midpoint_eq_center, MeasureTheory.SimpleFunc.eLpNorm'_eq, Real.cosh_le_cosh, ModularGroup.exists_bound_of_invariant_of_isBigO, variationOnFromTo.abs_le_eVariationOn, ProbabilityTheory.moment_def, Hyperreal.stdPart_map₂, 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, Orientation.tan_oangle_sub_right_of_oangle_eq_pi_div_two, GroupSeminorm.toFun_eq_coe, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, MeasureTheory.taylorWithinEval_charFun_two_zero, ProbabilityTheory.iIndepFun.integral_prod_eq_prod_integral, ENNReal.zero_rpow_mul_self, Wbtw.angle₂₃₁_eq_zero_of_ne, Euclidean.ball_eq_preimage, IsCoveringMap.liftHomotopy_apply, Real.sInf_univ, MeasureTheory.Measure.exists_regular_eq_of_compactSpace, Real.cos_pi_over_two_pow, fderiv_sinh, 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, ConvexOn.leftDeriv_eq_sSup_slope_of_mem_interior, preCantorSet_zero, Real.one_sub_div_pow_le_exp_neg, AddGroupSeminorm.add_apply, norm_iteratedFDeriv_prod_le, abs_dist, MeasureTheory.LocallyIntegrable.exists_contDiff_dist_le_of_forall_mem_ball_dist_le, 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, Polynomial.Chebyshev.eval_iterate_derivative_eq_iff_of_bounded, 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, EulerProduct.norm_tsum_factoredNumbers_sub_tsum_lt, 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, MeasureTheory.measure_le_eq_lt, hasDerivAt_abs, NumberField.mixedEmbedding.stdBasis_apply_isReal, Real.cauchy_intCast, RCLike.conj_im, Real.toNNReal_le_toNNReal_iff_of_pos, EuclideanGeometry.Sphere.mul_dist_eq_zero_of_mem_sphere, seminormFromConst_one, RealRMK.exists_open_approx, LinearEquiv.norm_extend_symm_le, Real.cos_eq_zero_iff_sin_eq, ProbabilityTheory.tilted_mul_apply_mgf, Path.truncate_zero_one, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, MeasureTheory.SignedMeasure.of_inter_eq_of_symmDiff_eq_zero_positive, Function.RCLike.hasTemperateGrowth_ofReal, Affine.Simplex.sign_excenterWeights_empty, AbsoluteValue.Completion.isometry_extensionEmbedding_of_comp, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt', Real.tan_int_mul_pi_sub, ContinuousLinearMap.opNorm_lsmul_le, EuclideanGeometry.Sphere.secondInter_vsub_mem_affineSpan, EuclideanSpace.volume_ball, Real.sqrt_le_left, Real.sign_mul_pos_of_ne_zero, MeasureTheory.Lp.norm_exponent_zero, dist_vsub_vsub_le, ContDiffAt.norm, BumpCovering.sum_toPartitionOfUnity_eq, MeasureTheory.hasFiniteIntegral_toReal_iff, Real.fourierChar_apply, AntilipschitzWith.le_mul_norm_sub, CircleDeg1Lift.translationNumber_le_of_le_add_nat, EuclideanGeometry.inner_nonneg_of_dist_le_radius, ProbabilityTheory.iIndepFun.charFun_map_finset_sum_eq_prod, NumberField.canonicalEmbedding.norm_le_iff, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, ProbabilityTheory.covarianceBilin_of_not_memLp, InformationTheory.rightDeriv_klFun, MultilinearMap.mkContinuousMultilinear_norm_le, SimpleGraph.triangleRemovalBound_pos, MeasureTheory.Measure.haar.addPrehaar_nonneg, Unitary.two_mul_one_sub_le_norm_sub_one_sq, dense_addSubgroupClosure_pair_iff, IsUnifLocDoublingMeasure.eventually_measure_le_scaling_constant_mul', Path.extend_one, IsMIntegralCurveOn.continuousWithinAt, Complex.HadamardThreeLines.interpStrip_eq_of_mem_verticalStrip, LocallyLipschitz.max_const, interior_range_modelWithCornersEuclideanHalfSpace, BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le, ENNReal.toReal_essSup, ExistsContDiffBumpBase.y_smooth, LipschitzWith.iff_le_add_mul, Metric.hasBasis_nhdsSet_thickening, Affine.Simplex.ExcenterExists.sum_excenterWeights_eq_one, Real.toNNReal_zpow, 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', ConvexOn.real_sSup_of_countable_affine_eq, NormedField.exists_one_lt_norm, eigenvalue_pos_of_pos, unitInterval.volume_Ioc, cfcL_integral, IsMprojection.Mnorm, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, Padic.nonarchimedean, Real.dimH_ball_pi_fin, unitInterval.coe_pos, Irrational.sub_natCast, Real.toNNReal_add_toNNReal, Real.tendsto_logb_comp_add_sub_logb, Real.sq_sqrt', ValueDistribution.characteristic_zero_mul_eventually_le, MeasureTheory.L1.norm_setToL1_le_mul_norm', LipschitzOnWith.dist_le_mul, Seminorm.rescale_to_shell, SmoothBumpCovering.locallyFinite, Affine.Simplex.point_eq_affineCombination_of_pointsWithCircumcenter, gaugeRescale_def, AddCircle.addWellApproximable_ae_empty_or_univ, Real.Angle.zsmul_eq_iff, ProbabilityTheory.differentiableOn_complexMGF, Polynomial.Chebyshev.T_real_cosh, PartitionOfUnity.sum_le_one, ball_eq_norm_inv_mul_lt, closure_ordConnected_inter_rat, ProbabilityTheory.integrable_pow_abs_of_mem_interior_integrableExpSet, Real.dist_le_of_mem_pi_Icc, isNonarchimedean_spectralNorm_of_finiteDimensional_normal, Real.abs_cos_eq_sqrt_one_sub_sin_sq, Real.lt_log_of_pow_lt, Real.nnabs_coe, ConvexBody.isCompact, Real.mk_zero, NormedAddGroupHom.norm_comp_le_of_le', HurwitzZeta.hurwitzZeta_zero, ProbabilityTheory.lintegral_gaussianPDFReal_eq_one, Real.hasDerivAt_Gamma_one, GroupSeminorm.map_one', Complex.arg_mul, StrictConcaveOn.slope_lt_of_hasDerivWithinAt_Ioi, Real.logb_nonpos, Asymptotics.isLittleO_abs_right, ProbabilityTheory.variance_of_not_memLp, intervalIntegral.intervalIntegrable_deriv_of_nonneg, ENNReal.ofReal_eq_coe_nnreal, 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, IntervalIntegrable.intervalIntegrable_slope, range_cfcₙ_nnreal_subset, 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, Function.Periodic.qParam_tendsto, Real.continuousAt_log_iff, ODE.FunSpace.continuous_compProj, ContDiffWithinAt.exp, CongruenceSubgroup.mem_conjGL, CircleDeg1Lift.tendsto_atTop, OpenPartialHomeomorph.unitBallBall_source, Complex.div_ratCast_im, Matrix.frobenius_norm_mul, ProbabilityTheory.Fernique.logRatio_nonneg, Circle.exp_int_mul_two_pi, exists_deriv_eq_zero', ContinuousAt.rpow_const, AkraBazziRecurrence.deriv_smoothingFn, Real.not_differentiableAt_rpow_const_zero, ProperCone.innerDual_empty, Orientation.cos_oangle_sub_left_mul_norm_of_oangle_eq_pi_div_two, inner_vsub_vsub_left_eq_dist_sq_right_iff, HurwitzZeta.cosKernel_undef, stdSimplexHomeomorphUnitInterval_one, Complex.HadamardThreeLines.norm_lt_sSupNormIm_eps, ConvexOn.map_integral_le, Complex.lift_symm_apply_coe, variationOnFromTo.nonpos_of_ge, OpenPartialHomeomorph.univUnitBall_apply, ContinuousLinearMap.norm_compL_le, NonarchAddGroupNorm.coe_le_coe, integrableOn_Ioi_cpow_of_lt, Seminorm.continuousAt_zero_of_forall, RCLike.hasSum_iff, Differentiable.dist, SeminormFamily.withSeminorms_iff_nhds_eq_iInf, Convex.lipschitz_gauge, GaussianFourier.integral_cexp_neg_mul_sq_add_real_mul_I, NumberField.mixedEmbedding_injective, NormedGroup.tendsto_nhds_one, Real.cauchy_add, Orientation.oangle_map, AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_ge, NonUnitalNormedRing.norm_mul_le, RCLike.measurable_im, MeasureTheory.Measure.addHaar_preimage_linearMap, antitone_of_hasDerivAt_nonpos, EulerSine.antideriv_cos_comp_const_mul, Matrix.IsHermitian.spectrum_real_eq_range_eigenvalues, Real.cos_half, ProbabilityTheory.condVar_of_sigmaFinite, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae, torusIntegral_radius_zero, CFC.rpow_intCast, NormedAddGroupHom.IsQuotient.norm, Real.rpow_le_iff_le_log, InformationTheory.klFun_one, curveIntegral_eq_intervalIntegral_deriv, RCLike.inv_def, Complex.sinh_ofReal_im, MeasureTheory.measureReal_iUnion_fintype_le, InnerProductSpace.gramSchmidtNormed_unit_length', MeasureTheory.MemLp.haarAddCircle, MeasureTheory.setIntegral_nonneg, Real.volume_Ici, tendsto_norm, RCLike.sqrt_I, ContinuousMap.Homotopy.continuous, Path.trans_apply, norm_sub_le_norm_add, ContinuousMap.Homotopy.affine_apply, Differentiable.sqrt, Complex.re_eq_neg_norm, NormedAddGroupHom.opNorm_nonneg, NumberField.InfinitePlace.Completion.algebraMap_coe, MeasureTheory.JordanDecomposition.toSignedMeasure_smul, PadicInt.not_isUnit_iff, RightDerivMeasurableAux.differentiable_set_eq_D, ProbabilityTheory.HasGaussianLaw.fun_sum, BoxIntegral.integralSum_smul, taylor_integral_remainder_aux, Real.ofCauchy_add, ZetaAsymptotics.continuousOn_term_tsum, StarAlgHom.realContinuousMapOfNNReal_injective, Real.convergent_of_int, NumberField.mixedEmbedding.forall_normAtPlace_eq_zero_iff, MeasureTheory.mul_meas_ge_le_integral_of_nonneg, IsClosed.hausdorffDist_zero_iff_eq, ProbabilityTheory.variance_dual_prod', Orientation.norm_div_sin_oangle_add_left_of_oangle_eq_pi_div_two, MeasureTheory.AECover.integrable_of_integral_bounded_of_nonneg_ae, HasFDerivWithinAt.arctan, Real.natCastle_toNNReal', Real.arsinh_strictMono, norm_le_zero_iff, Polynomial.Chebyshev.sumZeroes_T_zero, isIntegralCurve_comp_mul_ne_zero, NumberField.mixedEmbedding.convexBodyLT_convex, MeasureTheory.Measure.measure_preimage_isMulLeftInvariant_eq_smul_of_hasCompactSupport, Real.tendsto_integral_exp_smul_cocompact, intervalIntegral.integrableOn_deriv_right_of_nonneg, MeasureTheory.HasFiniteIntegral.max_zero, ArithmeticFunction.vonMangoldt_nonneg, exp_neg_mul_rpow_isLittleO_exp_neg, NumberField.FinitePlace.pos_iff, mellin_convergent_iff_norm, Real.contDiff_arctan, tendsto_closedBall_smallSets, MeasureTheory.setIntegral_tilted', EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_wbtw, UpperHalfPlane.exp_half_dist, ContDiffAt.dist, ArithmeticFunction.LSeriesSummable_moebius_iff, QuotientGroup.exists_norm_mul_lt, Real.cos_neg, Complex.normSq_add_mul_I, LocallyBoundedVariationOn.exists_monotoneOn_sub_monotoneOn, BoxIntegral.Prepartition.splitMany_le_split, locallyIntegrableOn_mul_sum_Icc, 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, GaussianFourier.integral_cexp_neg_mul_sum_add, ProbabilityTheory.iIndepFun_iff_charFunDual_pi', tsum_sq_fourierCoeffOn, Complex.continuous_ofReal_cpow_const, ProbabilityTheory.eq_condKernel_of_measure_eq_compProd_real, sameRay_iff_norm_sub, HasDerivAt.real_of_complex, ProbabilityTheory.covarianceBilinDual_comm, Metric.Sum.dist_eq_glueDist, TensorProduct.dist_tmul_le, affineSpan_eq_top_of_nonempty_interior, ProbabilityTheory.truncation_eq_of_nonneg, Real.uniformContinuous_abs, Metric.diam_sphere_eq, ENNReal.toReal_sSup, ProbabilityTheory.isGaussian_iff_charFunDual_eq, ProbabilityTheory.iteratedDeriv_two_cgf, ContinuousOn.integral_sub_linear_isLittleO_ae, Real.tendsto_arctan_atTop, SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left, DifferentiableWithinAt.rpow_const, ArithmeticFunction.sum_moebius_mul_log_eq, NNReal.summable_one_div_rpow, UpperHalfPlane.vadd_right_cancel_iff, exp_neg_mul_sq_isLittleO_exp_neg, Real.isAlgebraic_sin_rat_mul_pi, RCLike.re_eq_ofReal_of_isSelfAdjoint, EuclideanGeometry.Sphere.inter_orthRadius_eq_of_dist_le_radius_of_norm_eq_one, AkraBazziRecurrence.isLittleO_smoothingFn_one, Real.ediam_Ioo, EuclideanGeometry.dist_div_cos_oangle_right_of_oangle_eq_pi_div_two, MeasureTheory.Integrable.pos_part, IsPicardLindelof.mul_max_le, CPolynomialAt.exists_ball_cpolynomialOn, PhragmenLindelof.eq_zero_on_quadrant_II, integral_exp_mul_Ioi, NumberField.InfinitePlace.one_le_mult, NNReal.forall, tendsto_rpow_div, measurableSet_of_differentiableWithinAt_Ioi, deriv.lhopital_zero_right_on_Ioo, isStarProjection_iff_spectrum_subset_and_isSelfAdjoint, Real.iInter_Iic_rat, integral_sin_mul_cos_sq, ContinuousLinearMap.norm_fst, ConcaveOn.condExp_map_le_of_finiteDimensional, Archimedean.exists_orderAddMonoidHom_real_injective, norm_inf_sub_inf_le_norm, EisensteinSeries.linear_isTheta_right_add, HasFDerivWithinAt.rpow, 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, ProbabilityTheory.deriv_mgf_zero, CovBySMul.rfl, Real.volume_uIoo, Path.trans_range, NNReal.rpow_neg, MeasureTheory.charFun_eq_charFunDual_toDualMap, EuclideanGeometry.OrthocentricSystem.eq_insert_orthocenter, SchwartzMap.instLocallyConvexSpace, NormedAlgebra.Real.nonempty_algEquiv_or, MeasureTheory.measureReal_compl₀, BumpCovering.toPOUFun_zero_of_zero, fourier_neg, NNReal.rpow_add_le_add_rpow, ContinuousOn.arsinh, IsPiSystem.tendsto_measureReal_biUnion, Affine.Simplex.incenter_mem_affineSpan_range, dist_le_of_approx_trajectories_ODE_of_mem, BoxIntegral.Box.mem_def, IsUltrametricDist.isUltrametricDist_iff_isNonarchimedean_nnnorm, spectralAlgNorm_of_finiteDimensional_normal_def, intervalIntegral.integral_le_sub_of_hasDeriv_right_of_le, Set.OrdConnected.preimage_ennreal_ofReal, HolderOnWith.ediam_image_le_of_le, real_inner_sub_sub_self, Orientation.oangle_smul_smul_self_of_nonneg, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv, fourierIntegral_gaussian, Complex.norm_exp_sub_one_le, Archimedean.embedRealFun_zero, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn, MeasureTheory.Measure.haar.addPrehaar_pos, HurwitzKernelBounds.F_nat_zero_zero_sub_le, Path.symm_subpath, tendsto_norm_atTop_iff_cobounded', ProbabilityTheory.isGaussian_of_charFunDual_eq, conformalFactorAt_pos, Real.deriv_sigmoid, LSeries.tendsto_cpow_mul_atTop, ProbabilityTheory.isRatCondKernelCDFAux_preCDF, ENNReal.toReal_zero, exists_ratio_deriv_eq_ratio_slope', LinearMap.IsSymmetric.eigenvalues_def, norm_cfc_le, 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, Polynomial.IsMonicOfDegree.eq_isMonicOfDegree_two_mul_isMonicOfDegree, ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior, Real.quadratic_root_cos_pi_div_five, Real.nnnorm_of_nonneg, SchwartzMap.compCLM_apply, Asymptotics.IsBigOWith.exists_nonneg, Real.geom_mean_eq_arith_mean_weighted_iff, EisensteinSeries.tendsto_double_sum_S_act, Real.exp_one_lt_d9, RCLike.norm_nnratCast, AbsolutelyContinuousOnInterval.dist_le_of_pairwiseDisjoint_hasSum, MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le, TemperedDistribution.fourierMultiplierCLM_apply_apply, Real.cos_antiperiodic, intervalIntegral.fderivWithin_integral_of_tendsto_ae, NNReal.orderIsoRpow_symm_eq, Real.cos_periodic, Affine.Simplex.eulerPoint_reindex, Real.iSup_le, NNReal.coe_pow, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, Polynomial.eval_le_zero_of_roots_le_of_leadingCoeff_nonpos, MeasureTheory.LocallyIntegrableOn.norm, one_add_rpow_hasFPowerSeriesAt_zero, tendsto_norm_atTop_atTop, HomotopyGroup.inv_spec, PathConnectedSpace.exists_path_through_family', Real.rpow_sub_natCast', Real.geom_mean_le_arith_mean, LipschitzWith.norm_div_le_of_le, seminormFromBounded_aux, ArchimedeanClass.ofArchimedean_stdPart, Real.arsinh_bijective, Real.cosh_strictMonoOn, Complex.arg_inv, Complex.im_mul_ofReal, ProbabilityTheory.iCondIndepFun_iff, Matrix.PosSemidef.re_dotProduct_nonneg, rescale_to_shell_zpow, MeasureTheory.integral_eq_lintegral_of_nonneg_ae, Path.coe_mk_mk, Complex.integrable_pow_mul_norm_one_add_mul_inv, MeasureTheory.Measure.addHaar_ball_mul_of_pos, 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', intervalIntegral.integral_mul_deriv_eq_deriv_mul_of_hasDerivAt, AEMeasurable.ereal_toReal, Real.iteratedDeriv_even_sin, exists_smooth_zero_one_of_isClosed, ProbabilityTheory.HasGaussianLaw.map_equiv_fun, norm_sub_norm_le, Asymptotics.IsLittleO.add_add, Padic.padicNormE.mul, Matrix.linfty_opNorm_mul, AkraBazziRecurrence.dist_r_b, integrableOn_peak_smul_of_integrableOn_of_tendsto, tendsto_measure_cthickening_of_isClosed, Real.sqrtTwoAddSeries_lt_two, Real.cosh_arsinh, Real.nnnorm_ofNat, HurwitzZeta.hasSum_nat_hurwitzZetaEven_of_mem_Icc, injOn_circleMap_of_abs_sub_le, instSMulCommClass_sphere_ball_ball, lp.norm_sub_norm_compl_sub_single, CFC.exists_measure_nnrpow_eq_integral_cfcₙ_rpowIntegrand₀₁, MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_measure, Real.cosh_three_mul, ProbabilityTheory.IsRatStieltjesPoint.tendsto_atBot_zero, Metric.closure_eq_iInter_thickening', ModelWithCorners.convex_range', ArchimedeanClass.stdPart_div, EuclideanGeometry.dist_le_of_wbtw_of_inner_eq_zero, Real.rpow_le_of_le_log, CFC.spectrum_abs, Metric.unitSphere.coe_pow, Real.rpow_le_one, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIdealLattice, Quaternion.inner_self, Metric.diam_le_of_forall_dist_le_of_nonempty, Path.range_coe, dist_left_lineMap, CStarAlgebra.rpow_neg_one_le_one, Complex.norm_deriv_le_one_of_mapsTo_ball, HasDerivAt.hasGradientAt', separatesPoints_continuous_of_t35Space_Icc, NormedSpace.toLocallyConvexSpace, Real.sign_apply_eq, Real.volume_pi_Ico_toReal, Real.exp_approx_start, ContMDiff.inner_bundle, real_inner_self_eq_norm_mul_norm, Affine.Simplex.excenterWeights_map, GroupSeminorm.coe_smul, seminormFromConst_isLimit, MeasureTheory.setIntegral_ge_of_const_le_real, EulerSine.antideriv_sin_comp_const_mul, ProbabilityTheory.Kernel.isRatCondKernelCDFAux_density_Iic, Real.strictConcaveOn_sqrt, Real.exp_injective, DifferentiableOn.arctan, InnerProductGeometry.norm_sub_eq_abs_sub_norm_iff_angle_eq_zero, IsExtrOn.hasLineDerivWithinAt_eq_zero, ProbabilityTheory.HasLaw.variance_eq, Real.rpow_lt_one_iff, Real.analyticOnNhd_cos, Metric.infDist_le_infDist_add_dist, Real.arcsin_nonneg, Complex.zero_le_real, CongruenceSubgroup.strictPeriods_Gamma, AddCircle.instAddQuotientMeasureEqMeasurePreimageSubtypeAddOppositeRealMemAddSubgroupOpZmultiplesVolume, isLittleO_pow_exp_pos_mul_atTop, Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero, PhragmenLindelof.quadrant_I, Polynomial.Chebyshev.one_le_abs_eval_T_real, coe_normSeminorm, IsUltrametricDist.norm_sum_le_of_forall_le_of_nonneg, ConvexOn.locallyLipschitzOn, analyticAt_log, EuclideanGeometry.angle_eq_abs_oangle_toReal, IntervalIntegrable.intervalIntegrable_norm_iff, ApproximatesLinearOn.closedBall_subset_target, EuclideanGeometry.angle_eq_zero_of_angle_eq_pi_right, MeasureTheory.ae_mem_limsup_atTop_iff, NumberField.mixedEmbedding.fundamentalCone.logMap_expMap, Complex.lim_im, signedDist_vadd_left, seminormFromConst_apply_c, Real.le_norm_self, Diffeology.IsPlot.contDiff, Filter.Tendsto.log, Asymptotics.IsBigO.rpow_rpow_nhdsGE_zero_of_le_of_imp, ModularGroup.tendsto_lcRow0, Complex.div_natCast_im, ProbabilityTheory.integrable_kernel_prodMk_left, ProbabilityTheory.HasCondSubgaussianMGF.fun_zero, AffineSpace.asymptoticNhds_le_cobounded, Dense.exists_dist_lt, 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, monotone_of_hasDerivAt_nonneg, NormedAlgebra.norm_smul_le, HasLineDerivAt.le_of_lipschitzOn, CircleDeg1Lift.exists_eq_add_translationNumber, Real.toNNReal_eq_nnnorm_of_nonneg, Complex.ofReal_natCast, MeasureTheory.meas_ge_le_mul_pow_eLpNorm_enorm, ProbabilityTheory.cauchyPDFReal_scale_zero, CircleDeg1Lift.lt_map_map_zero, Real.strictMonoOn_one_add_div_one_sub, Real.ofCauchy_inv, ContDiffOn.exp, MeasureTheory.charFun_zero_measure, MeasureTheory.ProbabilityMeasure.tendsto_charPoly_of_tendsto_charFun, NormedSpace.sInter_polar_eq_closedBall, ProbabilityTheory.HasSubgaussianMGF.add_of_hasCondSubgaussianMGF, ContDiffBump.convolution_eq_right, ZetaAsymptotics.term_nonneg, TemperedDistribution.instFourierInvSMul, MeasureTheory.JordanDecomposition.real_smul_posPart_neg, ExistsContDiffBumpBase.w_def, Affine.Simplex.orthogonalProjection_eq_circumcenter_of_dist_eq, HurwitzZeta.hurwitzZeta_one_sub, measurable_derivWithin_Ioi, ProbabilityTheory.deriv_cgf, MeasureTheory.Measure.setIntegral_comp_smul, ProbabilityTheory.Fernique.normThreshold_strictMono, 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, DifferentiableOn.cosh, RCLike.ofReal_pos, WeakFEPair.hf_modif_FE, integral_gaussian_sq_complex, contDiff_stereoInvFunAux, MeasureTheory.SignedMeasure.exists_subset_restrict_nonpos, Complex.isQuotientMap_im, Real.inv_sign, tendsto_mul_add_inv_atTop_nhds_zero, fourierCoeff.add, expNegInvGlue.contDiff_polynomial_eval_inv_mul, Measurable.dist, NNReal.Lp_add_le_tsum', ContinuousLinearMap.opNorm_mul_apply_le, Real.lt_sq_of_sqrt_lt, Real.artanh_le_artanh, Affine.Simplex.incenter_notMem_affineSpan_pair, NNReal.rpow_sub_natCast', Asymptotics.isTheta_norm_left, Seminorm.mem_ball, intervalIntegral.integral_hasFDerivWithinAt, Real.HolderConjugate.one_sub_inv_inv, RCLike.re_le_norm, Real.rpow_add_rpow_le, circleAverage_log_norm_factorizedRational, OrthonormalBasis.norm_le_card_mul_iSup_norm_inner, Complex.ofReal_qsmul, Polynomial.aeval_ofReal, TopologicalGroup.IsSES.pushforward_mono, 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, ProbabilityTheory.memLp_tilted_mul, Real.toNNReal_abs, isLittleO_pow_pow_of_lt_left, PadicInt.valuation_coe, SmoothBumpCovering.eventuallyEq_one', ContinuousLinearMap.isPositive_iff_complex, Real.cosPartialEquiv_symm_apply, LinearIsometryEquiv.toMeasurableEquiv_symm, Real.quadratic_le_exp_of_nonneg, BoundedContinuousFunction.norm_coe_le_norm, MeasureTheory.exists_nat_measurableEquiv_range_coe_fin_of_finite, exists_contMDiffOn_section_forall_mem_convex_of_local, 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, ContDiff.dist, NNReal.continuous_rpow_const, Real.summable_pow_mul_exp_neg_nat_mul, tendsto_iff_norm_neg_add_tendsto_zero, NormedSpace.norm_smul_le, gauge_lt_one_eq_interior, HasDerivWithinAt.rpow_const, ProbabilityTheory.covarianceBilin_apply, Real.volume_pi_le_diam_pow, Affine.Simplex.mongePoint_restrict, exists_contMDiff_support_eq_eq_one_iff, ProbabilityTheory.measurePreserving_eval_multivariateGaussian, IsCoveringMap.liftPath_lifts, Real.tanh_lt_one, fourierIntegral_half_period_translate, BoxIntegral.integralSum_sub_partitions, Monotone.tendsto_alternating_series_of_tendsto_zero, EReal.toReal_le_toReal, measurable_coe_nnreal_real, ProbabilityTheory.HasSubgaussianMGF.add_of_indepFun, ProbabilityTheory.measure_stieltjesOfMeasurableRat_Iic, NNReal.coe_nonneg, Path.Homotopy.transReflReparamAux_mem_I, HasFDerivAt.cos, 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, Measurable.arctan, Chebyshev.theta_le_log4_mul_x, DifferentiableWithinAt.arsinh, ContinuousLinearMap.opNorm_smul_le, Quaternion.norm_exp, StrictConvexSpace.sphere_subset_extremePoints_closedBall, ProbabilityTheory.IsRatCondKernelCDFAux.integrable_iInf_rat_gt, Real.artanh_neg, MeasureTheory.L1.norm_setToL1_le', Real.isBigO_exp_comp_exp_comp, AkraBazziRecurrence.isEquivalent_one_add_smoothingFn_one, TestFunction.fderivCLM_apply_of_gt, MeasureTheory.withDensitySMulLI_apply, Path.add_apply, MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto, MeasureTheory.integrableOn_Ioi_deriv_of_nonneg', 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, NormedAddGroupHom.lift_norm_le, Complex.ofReal_zsmul, ENNReal.toReal_iInf, NumberField.mixedEmbedding.logMap_apply, ContinuousMap.comp_attachBound_mem_closure, PhragmenLindelof.isBigO_sub_exp_rpow, Real.exp_lt_exp, Distribution.dsupport_iteratedLineDerivOp_subset, PadicInt.exists_pow_neg_lt, EuclideanGeometry.hasFDerivAt_inversion, InformationTheory.continuous_klFun, Orientation.kahler_map, EuclideanGeometry.abs_oangle_toReal_lt_pi_div_two_of_angle_eq_pi_div_two, Real.ofCauchy_neg, isBigO_deriv_ofReal_cpow_const_atTop, measurable_coe_real_ereal, EReal.preimage_coe_Iio_top, ContinuousMultilinearMap.le_opNorm_mul_prod_of_le, Real.pi_lt_d20, MeasureTheory.restrict_map_withDensity_abs_det_fderiv_eq_addHaar, ContDiffWithinAt.rpow_const_of_ne, Metric.unitBall.coe_mul, TemperedDistribution.instFourierInvAdd, ProbabilityTheory.setIntegral_condVar, Absorbs.exists_pos, InformationTheory.stronglyMeasurable_klFun, CFC.isUnit_rpow_iff, PiTensorProduct.projectiveSeminorm_smul_le, dist_div_norm_sq_smul, RCLike.ofNat_im, NormedField.tendsto_norm_zpow_nhdsNE_zero_atTop, Metric.eventually_nhds_prod_iff, Asymptotics.IsBigOWith.const_mul_right', MeasureTheory.Lp.fourierInv_toTemperedDistribution_eq, volume_regionBetween_eq_integral', NNReal.isUniformEmbedding_coe, MeasureTheory.JordanDecomposition.toSignedMeasure_neg, stronglyMeasurable_derivWithin_Ici, Real.inner_le_Lp_mul_Lq_of_nonneg', exists_deriv_eq_slope', dist_le_tsum_of_dist_le_of_tendsto, NumberField.mixedEmbedding.fundamentalCone.injective_expMapBasis, Real.strictMonoOn_log, Finset.infsep_zero_iff_subsingleton, ProbabilityTheory.measurable_exponentialPDFReal, MeasureTheory.exists_le_setAverage, GroupSeminorm.groupSeminormClass, IsSelfAdjoint.map_spectrum_real, CircleDeg1Lift.le_translationNumber_of_add_le, BoxIntegral.Prepartition.coe_eq_of_mem_split_of_mem_le, posTangentConeAt_mono, AkraBazziRecurrence.a_pos, hasDerivAt_ofReal_cpow_const, NumberField.Units.logEmbeddingQuot_injective, MeasureTheory.ae_bdd_condExp_of_ae_bdd, Real.surjOn_logb, Real.cos_sub_nat_mul_pi, PadicInt.norm_sub_modPart, CFC.norm_abs, pi_norm_le_iff_of_nonempty, ArithmeticFunction.vonMangoldt_apply_one, UnitAddTorus.coe_measurableEquivPiIoc, Affine.Simplex.eulerPoint_restrict, Mathlib.Meta.Positivity.log_nonneg_of_isNat, FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1, ProbabilityTheory.HasSubgaussianMGF.measure_ge_le, hasDerivAt_norm_rpow, lipschitzOnWith_iff_dist_le_mul, Affine.Simplex.signedInfDist_reindex, isApproximateSubgroup_one, EReal.coe_eq_zero, ContinuousOn.arccos, ZSpan.instDiscreteTopologySubtypeMemAddSubgroupToAddSubgroupIntSpanRangeCoeBasisRealOfFinite, Polynomial.leading_coeff_le_mahlerMeasure, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_fst_ofIsComplex, PadicInt.norm_p, UnitAddTorus.hasSum_prod_mFourierCoeff, Real.two_mul_arctan_sub_pi, GromovHausdorff.ghDist_le_of_approx_subsets, Real.arcsin_lt_iff_lt_sin', Metric.cthickening_max_zero, Irrational.intCast_sub, isLittleO_coe_const_pow_of_one_lt, Real.not_bddBelow_coe, Real.differentiableAt_tan_of_mem_Ioo, Asymptotics.IsBigOWith.exists_pos, Real.not_continuousAt_deriv_qaryEntropy_zero, Real.tan_pi_div_three, ContMDiffAt.inner_bundle, AffineSubspace.isPreconnected_setOf_sOppSide, exists_dist_le_lt, NumberField.mixedEmbedding.latticeBasis_apply, Path.map_coe, EuclideanGeometry.Sphere.inter_orthRadius_eq_empty_of_radius_lt_dist, NumberField.mixedEmbedding.unit_smul_eq_zero, MeasureTheory.integrable_comp_mul_right_iff, Hyperreal.coe_add, ConcaveOn.condExp_map_le_univ, ProbabilityTheory.isCondKernelCDF_condCDF, ProbabilityTheory.rpow_abs_le_mul_max_exp, ContinuousMap.Homotopy.coe_toContinuousMap, EReal.nhds_bot', Real.pi_div_two_le_arcsin, MeasureTheory.ae_nonneg_of_forall_setIntegral_nonneg, LiouvilleWith.sub_nat_iff, Real.sin_three_mul, Real.sinc_zero, ProbabilityTheory.complexMGF_id_map, Real.arccos_lt_pi_div_two, MeasureTheory.Measure.addHaar_submodule, ProbabilityTheory.measurable_gaussianPDFReal, SmoothPartitionOfUnity.sum_finsupport_smul_eq_finsum, tendsto_rpow_neg_div, MeasureTheory.L1.SimpleFunc.integral_eq_lintegral, ContinuousMap.Homotopy.apply_zero, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, signedDist_apply_linear_apply, Seminorm.smul_closedBall_preimage, Real.le_arcsin_iff_sin_le, SchwartzMap.integral_mul_deriv_eq_neg_deriv_mul, ProbabilityTheory.variance_dirac, Complex.selfAdjointEquiv_symm_apply, MeasureTheory.charFun_map_mul_comp, Real.contDiff_cosh, Real.neg_mulExpNegMulSq_neg, TemperedDistribution.fourierInv_apply, riesz_lemma_of_norm_lt, InnerProductSpace.HarmonicContOnCl.circleAverage_re_herglotzRieszKernel_smul, Asymptotics.isBigOWith_snd_prod, ProbabilityTheory.poissonMeasure_real_singleton, Matrix.IsHermitian.cfcAux_id, AnalyticAt.harmonicAt_log_norm, EuclideanGeometry.dist_div_cos_oangle_left_of_oangle_eq_pi_div_two, ProbabilityTheory.IsGaussianProcess.smul, GaussianInt.re_toComplex, Ideal.Quotient.norm_mk_lt, inseparable_zero_iff_norm, NNReal.finset_prod_rpow, MeasureTheory.contDiff_charFun, ProbabilityTheory.cauchyPDF_scale_zero, EuclideanGeometry.inversion_mem_perpBisector_inversion_iff, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq_fun, 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, ProbabilityTheory.covariance_sum_left', MeasureTheory.Measure.addHaar_singleton_add_smul_div_singleton_add_smul, IsSelfAdjoint.hasEigenvector_of_isMinOn, norm_le_norm_add_norm_div, MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_le, 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, Real.HolderConjugate.inv_one_sub_inv, HurwitzZeta.hurwitzOddFEPair_f, Affine.Simplex.eulerPoint_map, ENNReal.continuous_truncateToReal, MeasureTheory.L1.norm_of_fun_eq_integral_norm, Real.log_intCast_nonneg, AnalyticWithinAt.sigmoid, Real.analyticAt_arsinh, Real.tan_eq_zero_iff, Real.arccos_neg_one, AkraBazziRecurrence.GrowsPolynomially.neg_iff, SchwartzMap.instFourierSMul, AnalyticOnNhd.sum_divisor_le, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, ENNReal.toReal_add_le, ProbabilityTheory.stronglyMeasurable_cauchyPDF, Affine.Simplex.ExcenterExists.touchpoint_restrict, 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, dist_sum_sum_le_of_le, IsUnifLocDoublingMeasure.scalingScaleOf_pos, ODE.FunSpace.intervalIntegrable_comp_compProj, HasFDerivAt.curveIntegral_segment_source', Complex.exists, Metric.mem_closure_range_iff_nat, AffineSubspace.signedInfDist_singleton, Real.volume_real_ball, RCLike.norm_sq_eq_def, zero_mem_lowerBounds_smoothingSeminormSeq_range, gauge_sum_le, NumberField.mixedEmbedding.measurable_polarCoord_symm, Complex.circleTransformDeriv_periodic, Real.tsum_eq_tsum_fourier_of_rpow_decay, Seminorm.bound_of_shell_sup, intervalIntegral.integral_deriv_eq_sub', SeminormedGroup.disjoint_nhds_one, Circle.surjOn_exp_neg_pi_pi, UniformConvexOn.neg, tendsto_rpow_neg_atTop, ENNReal.toReal_lt_toReal, CircleDeg1Lift.sup_apply, ContinuousMap.apply_le_norm, Height.logHeight_linearMap_apply_le, EuclideanGeometry.dist_div_cos_angle_of_angle_eq_pi_div_two, BoxIntegral.Box.Icc_eq_pi, EuclideanGeometry.angle_midpoint_eq_pi, intervalIntegral.integral_deriv_smul_deriv_comp, Asymptotics.isBigO_iff_exists_eq_mul, BoundedContinuousFunction.dist_extend_extend, rexp_neg_quadratic_isLittleO_rpow_atTop, IsCompact.exists_cthickening_subset_open, NNReal.coe_iInf, LSeries.tendsto_atTop, continuous_real_toNNReal, IsOfFinOrder.norm_eq_one, Differentiable.inversion, MeasureTheory.AEStronglyMeasurable.integrable_truncation, Matrix.IsHermitian.coe_re_diag, hasSum_one_div_nat_pow_mul_sin, 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, MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv_aux, NumberField.mixedEmbedding.norm_eq_zero_iff, PointwiseConvergenceCLM.tendsto_nhds_atTop, AkraBazziRecurrence.differentiableAt_smoothingFn, NumberField.mixedEmbedding.logMap_apply_of_norm_one, TemperedDistribution.fourierTransform_toTemperedDistributionCLM_eq, HasFDerivAt.const_rpow, intervalIntegral.mul_integral_comp_mul_add, Polynomial.Chebyshev.roots_T_real, MeasureTheory.setIntegral_one_eq_measureReal, LipschitzOnWith.of_le_add, mem_tangentConeAt_of_openSegment_subset, Asymptotics.IsBigOWith.sum, Real.mul_lt_sin, ArchimedeanClass.stdPart_nonneg, NumberField.mixedEmbedding.fundamentalCone.expMap_source, IsLowerSet.mem_interior_of_forall_lt, Real.tendsto_arctan_atBot, ProbabilityTheory.Kernel.borelMarkovFromReal_apply, SchwartzMap.fderivCLM_fourier_eq, ProbabilityTheory.gaussianReal_map_add_const, Real.two_mul_arctan_add_pi, GroupNormClass.toNormedGroup_norm_eq, Complex.norm_deriv_le_div_of_mapsTo_ball, ProbabilityTheory.iIndepFun_iff_charFun_pi, intrinsicInterior_nonempty, CStarModule.inner_mul_inner_swap_le, HurwitzZeta.completedHurwitzZetaEven₀_neg, JoinedIn.somePath_mem, AkraBazziRecurrence.isBigO_asympBound, Finset.Nonempty.norm_prod_le_sup'_norm, Real.logb_le_logb, Bundle.ContinuousRiemannianMetric.pos, NNReal.coe_mulIndicator, ProbabilityTheory.strong_law_aux4, Metric.unitBall.instIsRightCancelMulZero, Real.nat_sqrt_le_real_sqrt, ENNReal.toReal_sup, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt, Summable.tsum_lt_tsum_of_nonneg, 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, intervalIntegral.integral_indicator, EuclideanGeometry.Sphere.orthRadius_map, Complex.norm_sub_eq_iff, Seminorm.gauge_ball, SelbergSieve.one_le_level, RCLike.map_nonneg_iff, MeasureTheory.Measure.toBoxAdditive_apply, StrictAnti.strictConcaveOn_univ_of_deriv, hasSum_fourier_series_of_summable, NumberField.FinitePlace.norm_eq_one_iff_notMem, Polynomial.supNorm_le_choose_natDegree_div_two_mul_mahlerMeasure, Real.rpow_inv_lt_iff_of_neg, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atTop, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply'', Complex.finrank_real_complex, Metric.ball_half_subset, Convex.image_deriv, StrictConvexOn.lt_slope_of_hasDerivWithinAt_Ioi, RCLike.ratCast_im, ConvexOn.isMinOn_of_rightDeriv_eq_zero, Polynomial.mahlerMeasure_of_degree_eq_one, Real.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, ProbabilityTheory.instIsMarkovKernel_toKernel, ProbabilityTheory.condVar_neg, Real.volume_real_Icc_of_le, MeasureTheory.setIntegral_toReal_rnDeriv_mul', HurwitzZeta.completedHurwitzZetaEven₀_zero, Summable.norm_lt_one, SchwartzMap.isBigO_cocompact_zpow_neg_nat, Real.deriv_cos, IsCoercive.continuousLinearEquivOfBilin_apply, Circle.exp_intCast_mul, iteratedDeriv_exp_const_mul, Affine.Simplex.excenterWeightsUnnorm_restrict, Real.sqrtTwoAddSeries_nonneg, LinearMap.singularValues_finrank_range_self, integrableOn_Ioi_exp_neg_mul_sq_iff, MeasureTheory.MemLp.eLpNorm_indicator_le, norm_le_mul_norm_add, Affine.Simplex.affineCombination_touchpointWeights, intervalIntegral.integral_nonneg_of_ae, MeasureTheory.integral_fun_fst, Orientation.volumeForm_zero_neg, SmoothPartitionOfUnity.contMDiff_finsum_smul, CFC.abs_of_mem_unitary, MeasureTheory.pdf.integrable_pdf_smul_iff, BoundedContinuousFunction.nnnorm_coeFn_eq, ContDiffWithinAt.rpow_const_of_le, ProbabilityTheory.mgf_sum_of_identDistrib, NNReal.image_coe_Ioo, EReal.exp_mul, PowerSeries.gaussNorm_eq_zero_iff, Polynomial.zero_lt_negOnePow_mul_eval_of_lt_roots_of_leadingCoeff_nonneg, ENNReal.exists_upcrossings_of_not_bounded_under, Real.continuousAt_const_rpow, Polynomial.Chebyshev.complex_ofReal_eval_U, Seminorm.coe_comp, NNReal.rpow_eq_rpow_right_iff, Real.smoothTransition.pos_of_pos, Real.differentiableAt_binEntropy, Real.smoothTransition.continuous, NumberField.mixedEmbedding.normAtPlace_nonneg, ArchimedeanClass.stdPart_le_of_le, Real.abs_sin_eq_one_iff, Orientation.angle_eq_abs_oangle_toReal, ContDiffBump.dist_normed_convolution_le, disjoint_ball_ball_iff, 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, Asymptotics.IsTheta.rpow, WithAbs.isUniformInducing_of_comp, RCLike.I_mul_re, Real.Continuous.mul_log, QuadraticForm.equivalent_sign_ne_zero_weighted_sum_squared, Real.exists_nat_pos_inv_lt, Real.sInf_le_iff, tendsto_mulIndicator_thickening_mulIndicator_closure, ProbabilityTheory.covariance_const_sub_left, SmoothPartitionOfUnity.sum_finsupport, lp.norm_apply_le_of_tendsto, Real.hasDerivAt_arctan', circleIntegral.norm_integral_le_of_norm_le_const', AlgebraNorm.extends_norm', Orientation.areaForm_map, Real.log_nonneg, Real.enorm_rpow_of_nonneg, 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, Complex.GammaSeq_eq_approx_Gamma_integral, SimpleGraph.triangleRemovalBound_le, Real.sin_pos_of_mem_Ioo, gauge_lt_eq', ConcaveOn.locallyLipschitzOn, instIsAddHaarMeasureProdRealVolume, Topology.RelCWComplex.closedCell_zero_eq_singleton, circleMap_eq_center_iff, ProbabilityTheory.integrable_of_mem_interior_integrableExpSet, RCLike.conj_eq_iff_im, BoundedContinuousFunction.dist_set_exists, ProbabilityTheory.stronglyMeasurable_gaussianPDFReal, Real.floor_logb_natCast, deriv_bernoulliFun, PiTensorProduct.norm_eval_le_projectiveSeminorm, NNReal.nnnorm_eq, OrthonormalBasis.adjustToOrientation_apply_eq_or_eq_neg, Real.summable_and_Lr_rpow_le_Lp_mul_Lq_tsum_of_nonneg, intervalIntegral.integral_hasDerivAt_right, indicator_indepFun_of_bcf, det_fderivPiPolarCoordSymm, abs_norm_sub_norm_le_norm_neg_add, isConformalMap_iff, WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded, BoundedContinuousFunction.toReal_lintegral_coe_eq_integral, ProbabilityTheory.poissonMeasure_real_singleton_pos, Real.tsum_le_of_sum_le, BoundedContinuousFunction.exists_extension_forall_mem_Icc_of_isClosedEmbedding, injOn_pi_polarCoord_symm, Path.Homotopy.continuous_transReflReparamAux, Hyperreal.tendsto_atBot_iff, cantorToHilbert_continuous, LSeriesSummable.isBigO_rpow, Real.Wallis.W_eq_factorial_ratio, IsConvexMetricSpace.of_convex, ProbabilityTheory.condVar_bot_ae_eq, Balanced.starConvex, Affine.Simplex.faceOppositeCentroid_mem_ninePointCircle, NormedCommGroup.nhds_basis_norm_lt, WithLp.volume_preserving_ofLp, Real.deriv2_qaryEntropy, PhragmenLindelof.eqOn_quadrant_IV, Height.AdmissibleAbsValues.hasFiniteMulSupport, ContinuousMap.Homotopy.curveIntegral_add_curveIntegral_eq_of_diffContOnCl, 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, riemannZeta_re_pos_of_one_lt, Complex.finrank_real_complex_fact, Chebyshev.psi_le, Height.logHeight₁_zero, Rat.AbsoluteValue.equiv_padic_of_bounded, Real.floor_pi_eq_three, ConvexOn.slope_le_of_hasDerivAt, 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, ProbabilityTheory.charFunDual_map_add_prod_eq_mul, RCLike.ofReal_real_eq_id, intervalIntegral.integral_deriv_comp_mul_deriv, PowerSeries.le_gaussNorm, Complex.norm_add_le', EuclideanGeometry.Sphere.IsTangent.isTangentAt, Rat.infinitePlace_apply, AlgHom.map_coe_real_complex, MeasureTheory.integral_Ioi_of_hasDerivAt_of_nonpos, ZSpan.fundamentalDomain_pi_basisFun, comap_gauge_nhds_zero, ker_imaginaryPart, AddGroupSeminorm.addGroupSeminormClass, Real.logb_mul_base, Affine.Simplex.touchpointWeights_singleton_neg, ConvexBody.iInter_smul_eq_self, LipschitzWith.ae_differentiableAt_of_real, ProperCone.mem_innerDual, WithCStarModule.norm_equiv_le_norm_pi, ProbabilityTheory.Kernel.measurable_density_left, cexp_neg_quadratic_isLittleO_rpow_atTop, Orientation.norm_div_tan_oangle_sub_left_of_oangle_eq_pi_div_two, MeasureTheory.Submartingale.ae_tendsto_limitProcess, ZLattice.isAddFundamentalDomain, EuclideanGeometry.Sphere.orthRadius_le_orthRadius_iff, BumpCovering.eventuallyEq_one', NormedSpace.of_real_exp_ℝ_ℝ, SmoothBumpFunction.one_of_dist_le, NNReal.rpow_inv_lt_iff, Real.le_pow_of_log_le, 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, Complex.integral_boundary_rect_of_continuousOn_of_hasFDerivAt_real, 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, integral_zpow, Real.Angle.coe_toIcoMod, Real.log_two_lt_d9, TemperedDistribution.instLineDerivSMulComplex, ProbabilityTheory.integrable_pow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, dist_convexCombination_left_le, MeasureTheory.MemLp.of_haarAddCircle, Metric.isCobounded_iff_closedBall_compl_subset, tendsto_sub_mul_tsum_nat_rpow, exists_eq_interval_average_of_measure, Real.not_bddAbove_coe, CStarAlgebra.instNonnegSpectrumClass', CStarAlgebra.conjugate_le_norm_smul, CircleDeg1Lift.map_int_add, exists_hasDerivAt_eq_slope, RCLike.conj_re_ax, isMIntegralCurveAt_comp_sub, Complex.exp_bound', MeasureTheory.lpNorm_sum_le, IsometryEquiv.coeFn_toRealAffineIsometryEquiv, Cardinal.cantorFunction_injective, hasSum_zeta_two, ENNReal.ofReal_sub, WithAbs.norm_eq_apply_ofAbs, MeasureTheory.abs_integral_le_integral_abs, Real.Angle.sin_zero, ContDiffMapSupportedIn.fderivLM_apply, AEMeasurable.sinh, not_irrational_one, Set.Countable.preimage_circleMap, Real.contDiff_rpow_const_of_le, exists_smooth_forall_mem_convex_of_local_const, summable_geometric_iff_norm_lt_one, GenLoop.currySum_apply_inl_inr, convexOn_exp, Seminorm.isBounded_sup, NumberField.mixedEmbedding.hasFDerivAt_polarCoordReal_symm, spectralNorm.spectralMulAlgNorm_eq_of_mem_roots, ValueDistribution.characteristic_zero_mul_le, norm_midpoint_lt_iff, CFC.sqrt_eq_cfc, Function.Complex.hasTemperateGrowth_ofReal, InformationTheory.toReal_klDiv_smul_same, ArithmeticFunction.vonMangoldt.continuousOn_LFunctionResidueClassAux, exists_continuousMap_one_of_isCompact_subset_isOpen, InnerProductGeometry.inner_eq_mul_norm_of_angle_eq_zero, NormedAlgebra.Real.exists_isMonicOfDegree_two_and_aeval_eq_zero, MeasureTheory.integral_comp_mul_right_Ioi, MeasureTheory.condExpInd_smul', ProbabilityTheory.betaPDFReal_pos, Real.contDiffOn_arcosh, isMIntegralCurve_abs_add_one_of_isMIntegralCurveOn_Ioo, Real.sin_eq_neg_one_iff, Polynomial.logMahlerMeasure_zero, HasFDerivAt.arsinh, Real.cos_lt_one_div_sqrt_sq_add_one, UpperHalfPlane.det_J, ConvexOn.map_average_le, AffineSubspace.isConnected_setOf_sOppSide, MeasureTheory.integrable_norm_pow_of_le, EuclideanGeometry.angle_add_angle_eq_pi_of_angle_eq_pi, Real.mk_inf, Real.rpow_lt_iff_lt_log, LinearMap.norm_extendOfNorm_apply_le, Complex.ofReal_comp_nsmul, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq, IsGδ.setOf_liouville, CircleDeg1Lift.monotone, isLocalMin_of_sign_deriv, MeasureTheory.L1.setToL1_add_left, Real.log_multiset_prod, ContinuousMap.Homotopy.prod_apply, ProbabilityTheory.analyticOnNhd_mgf, ModularGroup.coe_one, Real.sin_pi_div_sixteen, AddCircle.lintegral_preimage, MeasureTheory.Submartingale.sum_smul_sub, Real.differentiable_iteratedDeriv_cosh, Real.hasStrictDerivAt_sin, IsApproximateSubgroup.card_pow_le, Complex.HadamardThreeLines.scale_bddAbove, RCLike.mul_self_norm, ProbabilityTheory.covariance_fun_sub_right, ZMod.toAddCircle_injective, Real.tendsto_sqrt_atTop, ContDiffMapSupportedIn.structureMapLM_zero_injective, Metric.diam_union', summable_of_absolute_convergence_real, DifferentiableAt.abs, MeasureTheory.measureReal_le_measureReal_union_right, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add, strictConvexOn_univ_of_deriv2_pos, Asymptotics.IsLittleO.sqrt, sub_mem_posTangentConeAt_of_segment_subset, 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, EuclideanGeometry.Sphere.IsTangentAt.dist_sq_eq_of_mem, mem_nullSubgroup_iff, Complex.log_eq_integral, BoundedContinuousFunction.add_norm_nonneg, HasLineDerivAt.le_of_lip', ContinuousAlternatingMap.norm_ofSubsingleton_id, tendsto_indicator_cthickening_indicator_closure, MeasureTheory.BoundedContinuousFunction.integral_le_of_levyProkhorovEDist_lt, IsClosed.convexHull_subset_affineSpan_isVisible, Set.Nontrivial.le_infsep, Complex.equivRealProdCLM_symm_apply_re, intervalIntegral.integral_comp_smul_deriv''', RingSeminorm.ext_iff, Affine.Simplex.incenter_reindex, NNReal.summable_rpow_inv, Path.refl_range, integral_one, NNReal.coe_lt_coe, circleAverage_log_norm_sub_const₂, MeasureTheory.ProbabilityMeasure.continuous_iff_forall_continuous_integral, NNReal.rpow_eq_zero_iff, AkraBazziRecurrence.GrowsPolynomially.zpow, UpperHalfPlane.sinh_half_dist_add_dist, Manifold.pathELength_eq_lintegral_mfderiv_Icc, gauge_le_one_iff_mem_closure, Complex.norm_I, ProbabilityTheory.tendsto_cdf_atTop, Metric.denseRange_iff, Real.toNNReal_of_nonneg, IsSelfAdjoint.linearly_dependent_of_isLocalExtrOn, Polynomial.Chebyshev.one_lt_eval_T_real, MeasureTheory.dist_integral_le_lintegral_edist, exists_locallyFinite_subset_iUnion_ball_radius_lt, ArchimedeanClass.stdPart_sub, ContinuousMap.HomotopyWith.prop, NumberField.mixedEmbedding.continuous_normAtAllPlaces, Matrix.IsHermitian.roots_charpoly_eq_eigenvalues₀, lipschitzOnWith_iff_norm_neg_add_le, ProbabilityTheory.lintegral_betaPDF, AffineSubspace.mem_perpBisector_iff_dist_eq, Real.toNNReal_zero, MeasureTheory.integrable_withDensity_iff_integrable_coe_smul₀, ProbabilityTheory.HasSubgaussianMGF.measure_sum_range_ge_le_of_iIndepFun, PadicInt.norm_lt_pow_iff_norm_le_pow_sub_one, IntervalIntegrable.abs, Complex.ofReal_div, NNReal.toReal_le, IntervalIntegrable.iff_comp_neg, 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, Real.rpow_le_rpow, uniqueDiffOn_Ioi, Besicovitch.card_le_of_separated, Chebyshev.psi_eq_sum_Icc, ProbabilityTheory.HasGaussianLaw.snd, realPart_imaginaryPart, WithAbs.pseudoMetricSpace_induced_of_comp, AddGroupSeminorm.coe_comp, SchwartzMap.norm_fourier_toBoundedContinuousFunction_le_toLp_one, MeasureTheory.exists_null_frontiers_thickening, ModularForm.coe_norm, ProbabilityTheory.mgf_zero', BoundedContinuousFunction.toLp_norm_le, intervalIntegral.intervalIntegrable_pow, AbsolutelyContinuousOnInterval.uniformlyContinuousOn, MeasureTheory.charFun_map_mul, DifferentiableAt.cos, EReal.toReal_image_Ioo_zero_top, Asymptotics.IsLittleO.eventuallyLT_norm_of_eventually_pos, IsPrimitiveRoot.norm'_eq_one, Complex.sq_nonpos_iff, Similar.exists_pairwise_dist_eq, NonarchAddGroupNorm.lt_def, MeasureTheory.measurable_llr, ContDiffMapSupportedIn.seminorm_postcompLM_le, Real.BohrMollerup.tendsto_logGammaSeq, Subgroup.strictPeriods_SL2Z, inner_mul_symm_re_eq_norm, Real.circleAverage_eq_intervalAverage, MeasureTheory.Lp.continuous_negPart, Metric.Snowflaking.image_toSnowflaking_closedBall, EReal.coe_mul, MeasureTheory.Measure.tendsto_IicSnd_atTop, MeasureTheory.integrable_llr_tilted_right, ContinuousMultilinearMap.bound, Path.id_apply, LinearIsometry.im_apply_eq_im, MeasureTheory.integral_countable, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_sum, Filter.Tendsto.cfc_nnreal, Nat.preimage_ball, Real.mul_log_eq_log_iff, Complex.ofReal_comp_zsmul, MeasureTheory.Lp.coeFn_negPart, NNReal.rpow_arith_mean_le_arith_mean2_rpow, GroupSeminorm.coe_le_coe, Real.one_le_exp, Metric.biUnion_lt_closedBall, MeasureTheory.measureReal_compl, Hyperreal.coe_max, lp.norm_tsum_le, ProbabilityTheory.charFun_stdGaussian, dist_eq_zero, EuclideanGeometry.Sphere.mem_inter_orthRadius_iff_vsub_mem_and_norm_sq, NumberField.abs_discr_ge_of_isTotallyComplex, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff, HurwitzZeta.sinZeta_neg, MeasureTheory.exists_setAverage_le, Real.Angle.cos_neg_iff_pi_div_two_lt_abs_toReal, Padic.rat_dense, Real.cos_add_pi_div_two, ContinuousMultilinearMap.norm_mkPiAlgebraFin_succ_le, isBigO_norm_Icc_restrict_atBot, IsSelfAdjoint.instContinuousFunctionalCalculus, ContDiffPointwiseHolderAt.fderiv, ProbabilityTheory.rpow_abs_le_mul_exp_abs, CompactlySupportedContinuousMap.toReal_smul, Real.strictAnti_rpow_of_base_lt_one, Real.tendsto_one_add_rpow_exp_of_tendsto, Orientation.inner_rightAngleRotationAux₁_right, Real.arctan_inv_of_pos, hasFDerivAt_pi_polarCoord_symm, Int.instDiscreteTopologySubtypeRealMemAddSubgroupZmultiples, Real.lt_log_one_add_of_pos, MeasureTheory.lintegral_tilted, Real.tendsto_sum_pi_div_four, Submodule.re_inner_starProjection_nonneg, Nat.norm_cast_le, ContDiffWithinAt.inner, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt, Convex.lipschitzWith_gauge, norm_cfcₙ_one_sub_one_add_inv_lt_one, rpow_neg_one_add_norm_sq_le, BoundedContinuousFunction.norm_sub_nonneg, MeromorphicOn.intervalIntegrable_log, summable_of_sum_le, tendsto_norm_cobounded_atTop', isStarProjection_iff_quasispectrum_subset_and_isSelfAdjoint, Real.analyticAt_cosh, NumberField.mixedEmbedding.latticeBasis_repr_apply, UniformContinuous.dist, ConcaveOn.exists_lipschitzOnWith_of_isBounded, 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, NNReal.monotone_rpow_of_nonneg, derivWithin_sqrt, ModularFormClass.qExpansion_isBigO, InformationTheory.not_differentiableWithinAt_klFun_Ioi_zero, PhragmenLindelof.eqOn_vertical_strip, IsCoveringMap.eq_liftHomotopy_iff, Real.fourierChar_apply', MeasureTheory.SignedMeasure.subset_positive_null_set, ProbabilityTheory.condVar_of_aestronglyMeasurable, NNReal.hasMeasurablePow, continuousOn_cfcₙ_nnreal, DifferentiableWithinAt.norm_sq, EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi, EuclideanGeometry.Sphere.isIntTangentAt_center_iff, MeasureTheory.StronglyMeasurable.norm, Polynomial.negOnePow_mul_eval_le_zero_of_le_roots_of_leadingCoeff_nonpos, NonarchAddGroupNorm.ext_iff, MeasureTheory.SignedMeasure.toMeasureOfLEZero_real_apply, 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, Real.fourierIntegral_continuousLinearMap_apply', 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, Continuous.exists_contDiff_approx, BumpCovering.exists_isSubordinate_of_locallyFinite_of_prop, ConvexOn.deriv_le_slope, ProbabilityTheory.complexMGF_id_gaussianReal, isMIntegralCurveOn_comp_mul_ne_zero, MeasureTheory.norm_setToFun_le_mul_norm, IsUltrametricDist.norm_tprod_le_of_forall_le, Tactic.ComputeAsymptotics.isBigOWith_of_tendsto_top, integral_sin_pow_succ_le, ProbabilityTheory.integrable_pow_abs_mul_exp_of_integrable_exp_mul, Complex.mul_conj, ZLattice.le_norm_of_le_abs_repr, ProbabilityTheory.iteratedDeriv_two_cgf_eq_integral, Real.arcosh_le_arcosh, ContinuousAlternatingMap.opNorm_le_iff, CFC.abs_sq, Real.logb_abs, Real.limsInf_of_not_isCobounded, Complex.summable_one_div_nat_cpow, Complex.im_ofReal_mul, ODE.FunSpace.continuous, MeasureTheory.lintegral_image_eq_lintegral_abs_deriv_mul, Finset.card_mul_finset_lt_two, IntervalIntegrable.def', EuclideanGeometry.oangle_self_orthogonalProjection, ValueDistribution.logCounting_top_mul_le, Real.tendsto_mul_exp_add_div_pow_atTop, 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, InnerProductSpace.HarmonicContOnCl.circleAverage_poissonKernel_smul, LiouvilleNumber.partialSum_succ, tendsto_dist_right_cocompact_atTop, ENNReal.ofReal_add, StrongDual.extendRCLike_apply, StieltjesFunction.measure_Ioc, ENNReal.rpow_lt_one, ConvexOn.rightDeriv_le_slope, Complex.norm_eq_one_of_mem_rootsOfUnity, Polynomial.exists_monic_and_natDegree_eq_and_norm_map_algebraMap_coeff_sub_lt, ProbabilityTheory.uncenteredCovarianceBilin_zero, MeasureTheory.eLpNorm_indicator_const', EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_tsum, Real.rpow_ofNat, tendsto_integral_comp_smul_smul_of_integrable, Nat.isClosedEmbedding_coe_real, Delone.DeloneSet.subset_ball_singleton, Real.tendsto_div_pow_mul_exp_add_atTop, Metric.Snowflaking.image_ofSnowflaking_emetricClosedBall, Real.cos_int_mul_two_pi_sub_pi, integral_mulExpNegMulSq_comp_eq, ArchimedeanClass.mk_sub_pos_iff, AddCircle.measurePreserving_mk, MeasureTheory.SimpleFunc.setToSimpleFunc_eq_sum_filter, IsUpperSet.null_frontier, 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, ContDiffMapSupportedIn.continuous_iff_comp_order_le, 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, Mathlib.Meta.NormNum.isInt_rpow_pos, Asymptotics.IsLittleO.norm_left, MeasureTheory.llr_tilted_left, Tactic.NormNum.isNat_realSqrt_neg, ValueDistribution.proximity_pow_top, NumberField.AdeleRing.algebraMap_fst_apply, hasFDerivAt_integral_of_dominated_of_fderiv_le, PiTensorProduct.projectiveSeminormAux_nonneg, lintegral_comp_polarCoord_symm, Metric.Snowflaking.edist_ofSnowflaking_ofSnowflaking, TopologicalAddGroup.IsSES.integral_inducedMeasure, Metric.eventually_notMem_thickening_of_infEdist_pos, IsScalarTower.complexToReal, ContinuousMap.Homotopy.extend_zero, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf, Real.le_zpow_of_log_le, SmoothBumpCovering.apply_ind, Asymptotics.isBigOWith_principal, Polynomial.coeff_bdd_of_roots_le, EuclideanGeometry.Sphere.inter_orthRadius_eq_empty_iff, BoundedContinuousFunction.bounded, smul_ball, integral_comp_neg_Ioi, tendsto_pow_const_mul_const_pow_of_lt_one, EuclideanGeometry.Sphere.mem_tangentSet_iff, RCLike.mul_im, Seminorm.smul_ball_preimage, AddGroupSeminorm.le_def, Real.logDeriv_sin, Real.logb_pos_iff_of_base_lt_one, ContDiff.abs, VectorFourier.fourierPowSMulRight_apply, ProbabilityTheory.mgf_dirac', skewAdjointPart_eq_I_smul_imaginaryPart, Real.rpow_add, TendstoUniformly.re, OrthonormalBasis.norm_dual, uniqueDiffOn_Ico, BumpCovering.nonneg, Nat.Primes.summable_rpow, DifferentiableOn.sin, MeasureTheory.MemLp.eLpNorm_indicator_norm_ge_pos_le, 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, intervalIntegral.norm_integral_le_of_norm_le_const, NormedAddGroupHom.lipschitz, Metric.Snowflaking.preimage_ofSnowflaking_eball, ContinuousLinearEquiv.homothety_inverse, dist_anti_right_pi, ValueDistribution.logCounting_pow_zero, ProbabilityTheory.Kernel.eLpNorm_densityProcess_le, MeasureTheory.Submartingale.exists_ae_tendsto_of_bdd, HurwitzZeta.hurwitzEvenFEPair_neg, MeasureTheory.L1.SimpleFunc.norm_integral_le_norm, SeparationQuotient.mk_eq_one_iff, MeasureTheory.JordanDecomposition.real_smul_negPart_neg, MeasureTheory.Submartingale.smul_nonpos, RCLike.ofReal_tsum, Real.deriv_cos', MeasureTheory.measure_le_integral_pos, Path.coe_toContinuousMap, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_cgf, SmoothBumpCovering.support_toSmoothPartitionOfUnity_subset, isBigO_deriv_rpow_const_atTop, Complex.range_norm, bernsteinApproximation_uniform, polarCoord_apply, SchwartzMap.decay, MeasureTheory.lpNorm_mono_real, SimpleGraph.FarFromTriangleFree.le_card_cliqueFinset, ContinuousAt.arcsin, 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, Continuous.deriv_integral, Complex.zero_re, RCLike.normSq_div, norm_fderiv_le_of_lipschitzOn, RCLike.im_sq_le_normSq, DifferentiableOn.dist, CFC.rpow_rpow_of_exponent_nonneg, SzemerediRegularity.pow_mul_m_le_card_part, PadicInt.norm_sub_zmodRepr_lt_one, MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable, Real.exp_nonneg, Asymptotics.isLittleO_norm_pow_id, Rat.AbsoluteValue.one_lt_of_not_bounded, dist_dist_dist_le, Real.deriv_rpow_const', Convex.mul_sub_lt_image_sub_of_lt_deriv, Real.continuous_fourierChar, Dilation.diam_range, ContinuousLinearMap.opNorm_le_iff_lipschitz, tendsto_norm_inv_mul_self_nhdsGE, Real.arctan_lt_arctan, ModularGroup.exists_one_half_le_im_smul_and_norm_denom_le, dist_smul₀, hasDerivWithinAt_forall_lt_or_forall_gt_of_forall_ne, StrictConcaveOn.lt_slope_of_hasDerivWithinAt, spectrum.isCompact_nnreal, ProbabilityTheory.abs_truncation_le_abs_self, MeasureTheory.integrableOn_Ioc_of_intervalIntegral_norm_bounded_left, Asymptotics.isLittleO_iff_nat_mul_le_aux, MeasureTheory.isAddHaarMeasure_volume_pi, IsUltrametricDist.norm_prod_eq_sup'_of_pairwise_ne, SameRay.norm_add, RCLike.lipschitzWith_ofReal, Real.cobounded_eq, SeminormClass.toAddGroupSeminormClass, max_norm_root_eq_spectralValue, NNReal.Lr_rpow_le_Lp_mul_Lq_tsum, integrableOn_mul_sum_Icc, EuclideanSpace.dist_eq, MeasureTheory.integral_mul_le_Lp_mul_Lq_of_nonneg, NumberField.mixedEmbedding.normAtPlace_negAt, Chebyshev.integral_theta_div_log_sq_isBigO, Asymptotics.IsLittleO.sum_congr, Stirling.stirlingSeq'_pos, ContinuousLinearMap.norm_pi_le_of_le, SchwartzMap.convolution_flip, MeasureTheory.aemeasurable_toNNReal_abs_det_fderivWithin, Real.sin_sub_nat_mul_pi, Real.differentiableAt_arcosh, Distribution.dsupport_lineDerivOp_subset, MeasureTheory.L1.norm_setToL1_le_mul_norm, norm_pow_le', ContinuousLinearMap.opNorm_le_of_nhds_zero, Dilation.diam_image, StrictConvexOn.derivWithin_lt_slope, HasDerivAt.rpow_const, MeasureTheory.Measure.haar.prehaar_self, Complex.le_of_eq_sum_of_eq_sum_norm, exists_forall_sphere_dist_add_le_two_sub, Orientation.tan_oangle_add_left_of_oangle_eq_pi_div_two, ENNReal.add_rpow_le_rpow_add, Matrix.l2_opNorm_le_one_of_mem_doublyStochastic, CircleDeg1Lift.coe_toOrderHom, continuousSMul_closedBall_closedBall, Module.Basis.parallelepiped_map, IsLocalMaxOn.fderivWithin_eq_zero, AlternatingMap.measure_def, MeasureTheory.measureReal_union_add_inter', MeasureTheory.Integrable.of_mem_Icc, ContinuousMap.Homotopy.apply_one, MeasureTheory.maximal_ineq, EisensteinSeries.abs_le_left_of_norm, ContinuousAt.norm, Seminorm.bound_of_shell_smul, strictConcaveOn_sin_Icc, ProbabilityTheory.IsRatCondKernelCDFAux.nonneg', InnerProductGeometry.sin_angle_add_of_inner_eq_zero, MeasureTheory.charFunDual_dirac, MeasureTheory.SignedMeasure.of_symmDiff_compl_positive_negative, ENNReal.ofReal_lt_ofReal_iff, Filter.Tendsto.integral_sub_linear_isLittleO_ae, LocallyLipschitz.const_min, LipschitzWith.norm_le_mul', SmoothBumpFunction.eventuallyEq_one_of_dist_lt, SimpleGraph.isGLB_turanDensity, HasDerivAtFilter.hasGradientAtFilter', CircleDeg1Lift.units_semiconj_of_translationNumber_eq, tendsto_one_iff_norm_tendsto_zero, Urysohns.CU.approx_le_approx_of_U_sub_C, CFC.one_rpow, seminormFromBounded_add, limit_zero_of_norm_tendsto_zero, isMIntegralCurveOn_Ioo_eqOn_of_contMDiff_boundaryless, Metric.uniformity_eq_comap_nhds_zero, Polynomial.Chebyshev.one_le_eval_T_real, Real.pi_gt_d20, MeasureTheory.lintegral_coe_le_coe_iff_integral_le, Real.exp_artanh, ENNReal.trichotomy, WeakFEPair.hg_int, LinearIsometryEquiv.reflections_generate_dim, convexOn_univ_of_deriv2_nonneg, seminormFromBounded_ge, Hyperreal.coe_div, GroupSeminorm.le_def, IsUpperSet.exists_subset_ball, Complex.isometryOfOrthonormal_apply, CircleDeg1Lift.le_iterate_pos_iff, ConvexOn.exists_lipschitzOnWith_of_isBounded, ProbabilityTheory.IndepFun.hasGaussianLaw, intervalIntegral.smul_integral_comp_mul_right, ProbabilityTheory.cdf_expMeasure_eq_lintegral, Metric.Snowflaking.image_toSnowflaking_closedEBall, MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono_left', 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, MeasureTheory.withDensityᵥ_smul_eq_withDensityᵥ_withDensity, 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, LinearMap.bound_of_sphere_bound, intervalIntegral.integral_comp_div_add, SingularManifold.instIsManifoldRealM, ContinuousLinearMap.abs_rayleighQuotient_le_of_norm_mem_resolventSet, ConvexBody.zero_mem_of_symmetric, integral_le_sum_Ico_of_le, MeasureTheory.integral_bilinear_hasDerivAt_right_eq_sub, Real.hasStrictDerivAt_sqrt, EuclideanGeometry.Sphere.isTangentAt_center_iff, Real.tendsto_eulerMascheroniSeq, PadicInt.norm_add_eq_max_of_ne, Real.cosh_sq', conformalFactorAt_inner_eq_mul_inner, Finsupp.log_prod, InnerProductGeometry.angle_sub_eq_arcsin_of_inner_eq_zero, NumberField.mixedEmbedding.normAtAllPlaces_nonneg, BoundedContinuousFunction.exists_extension_forall_mem_of_isClosedEmbedding, Asymptotics.IsLittleO.norm_norm, integral_gaussian, TemperedDistribution.fourierMultiplierCLM_sum, NumberField.HeightOneSpectrum.adicAbv_intCast_le_one, Rat.AbsoluteValue.eq_on_nat_iff_eq, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply, Orientation.areaForm_map_complex, 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', Complex.HadamardThreeLines.eventuallyle, BumpCovering.exists_finset_toPOUFun_eventuallyEq, DifferentiableOn.rpow_const, TestFunction.contDiff', Set.ruzsa_covering_mul, strictConcaveOn_of_deriv2_neg', Real.sSup_def, GenLoop.Homotopic.equiv, strictAntiOn_of_deriv_neg, HurwitzZeta.completedHurwitzZetaEven_neg, TestFunction.lineDerivCLM_smul, Complex.abs_re_lt_norm, NumberField.mixedEmbedding.fundamentalCone.isBounded_normLeOne, ENNReal.rpow_eq_top_iff_of_pos, ProbabilityTheory.hasDerivAt_iteratedDeriv_complexMGF, Seminorm.continuous_of_lowerSemicontinuous, Diffeology.isPlot_id, intervalIntegral.mul_integral_comp_sub_mul, IsBoundedBilinearMap.isBigO, Complex.one_lt_normSq_iff, BoundedContinuousFunction.abs_diff_coe_le_dist, isPathConnected_compl_of_isPathConnected_compl_zero, Real.toNNReal_coe_nat, Real.ofCauchy_one, BoxIntegral.Box.coe_eq_pi, Hyperreal.st_le_of_le, eventually_closedBall_subset, Real.hasDerivAt_tan_of_mem_Ioo, Real.arcsin_lt_pi_div_two, OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le, HasConstantSpeedOnWith.Icc_Icc, 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, ContinuousMultilinearMap.le_of_opNorm_le, Real.tan_surjective, Orientation.two_zsmul_oangle_smul_right_of_ne_zero, MeasureTheory.integral_pos_of_integrable_nonneg_nonzero, MeasureTheory.StronglyMeasurable.sinc, integral_one_div, 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, ProbabilityTheory.meas_ge_le_evariance_div_sq, 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.cosh_log, Real.comap_exp_atTop, AkraBazziRecurrence.b_pos, ValueDistribution.logCounting_sum_top_le, AlgHom.toContinuousLinearMap_norm, Real.arctan_lt_pi_div_two, ContDiffAt.laplacian_CLM_comp_left_nhds, norm_intCast_eq_abs_mul_norm_one, norm_zpow, Real.rpow_add_le_add_rpow, NumberField.mixedEmbedding.polarCoordReal_symm_target_ae_eq_univ, Sbtw.angle₂₁₃_eq_zero, AnalyticAt.re_ofReal, MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_deriv_mul', exists_continuous_one_zero_of_isCompact_of_isGδ, Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, MeasureTheory.exists_notMem_null_integral_le, Metric.closure_eq_iInter_cthickening', ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_of_le_one, MeasureTheory.measureReal_union', Circle.argPartialEquiv_target, Orientation.inner_rightAngleRotation_right, CStarAlgebra.isStrictlyPositive_TFAE, CircleDeg1Lift.semiconj_of_bijective_of_translationNumber_eq, HasFDerivAt.hasFDerivAt_norm_smul_neg, ContinuousLinearMap.opNorm_le_of_shell, unitInterval.measurableEmbedding_coe, NNReal.summable_mk, Real.hasDerivAt_exp, fourierSubalgebra_closure_eq_top, Stirling.stirlingSeq_zero, ProbabilityTheory.variance_const_add, fderiv_sqrt, Polynomial.Chebyshev.eval_T_real_eq_one_iff, ModularForm.prod_fintype_slash, GaussianFourier.integral_cexp_neg_sum_mul_add, ProbabilityTheory.tendsto_charFun_inv_sqrt_mul_pow, ProbabilityTheory.gammaPDFReal_pos, 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, EuclideanGeometry.sin_oangle_left_of_oangle_eq_pi_div_two, MeasureTheory.setIntegral_pos_iff_support_of_nonneg_ae, Metric.infDist_pos_iff_notMem_closure, Complex.IsExpCmpFilter.isLittleO_log_re_re, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_fun_sub, RCLike.wInner_one_const_left, circleIntegrable_sub_inv_iff, eventually_norm_mfderivWithin_symm_extChartAt_comp_lt, EuclideanGeometry.Sphere.orthRadius_injective, Summable.norm, summable_norm_iff, AlternatingMap.mkContinuousLinear_norm_le, HurwitzZeta.cosKernel_neg, QuotientAddGroup.norm_eq_addGroupSeminorm, ModularFormClass.bounded_at_infty_comp_ofComplex, AbsolutelyContinuousOnInterval.uIoc_subset_of_mem_disjWithin, AbsoluteValue.IsAdmissible.exists_approx_aux, asymptoticCone_subset_singleton_of_bounded, ValueDistribution.proximity_even, MeasureTheory.Measure.exists_integral_isAddLeftInvariant_eq_smul_of_hasCompactSupport, schnirelmannDensity_le_of_subset, ProperCone.hyperplane_separation_of_notMem, MeasureTheory.pow_mul_meas_ge_le_eLpNorm, LiouvilleNumber.partialSum_add_remainder, NonarchAddGroupNorm.coe_sup, ProbabilityTheory.HasSubgaussianMGF.memLp, NumberField.mixedEmbedding.convexBodySum_isBounded, RCLike.ofReal_mul_neg_iff, CuspFormClass.exp_decay_atImInfty', ConcaveOn.average_mem_hypograph, SzemerediRegularity.one_le_m_coe, NNReal.inner_le_Lp_mul_Lq_tsum', integral_sin_sq_mul_cos, BoundedContinuousFunction.norm_eq_of_nonempty, MeasureTheory.charFun_map_smul_comp, Real.arctan_sqrt_three, ExistsContDiffBumpBase.y_support, RCLike.re_ofReal_pow, ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral_iInf_rat_gt, convexHull_exists_dist_ge2, intervalIntegral.norm_integral_le_integral_norm, AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_le, NumberField.house_nat_mul, Complex.sameRay_iff_arg_div_eq_zero, Affine.Simplex.ExcenterExists.signedInfDist_excenter, Real.hasSum_sin, Complex.arg_eq_nhds_of_im_pos, 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, EuclideanGeometry.pi_div_three_lt_angle_of_le_of_le_of_ne, re_inner_self_nonpos, ContinuousLinearMap.norm_single_le_one, NumberField.mixedEmbedding.polarSpaceCoord_apply, Real.nonempty_algEquiv_or, BoxIntegral.Prepartition.coe_eq_of_mem_split_of_lt_mem, ProbabilityTheory.stdGaussian_eq_map_pi_orthonormalBasis, Cardinal.mk_Ioo_real, Real.rpow_one_sub', 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, Complex.starConvex_slitPlane, exists_norm_eq_iInf_of_complete_convex, NNReal.Lp_add_le, LiouvilleWith.sub_rat_iff, MeasureTheory.lintegral_enorm_le_liminf_of_tendsto, 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, TestFunction.monoCLM_apply, Real.arcsin_pos, curveIntegralFun_trans_aeeq_left, Complex.norm_eqOn_closedBall_of_isMaxOn, MeasureTheory.BorelCantelli.stronglyAdapted_process, SmoothPartitionOfUnity.finite_tsupport, Metric.lipschitz_infDist, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral, ProbabilityTheory.iIndepFun.hasGaussianLaw_sum, ProbabilityTheory.analyticOn_complexMGF, Real.sqrt_sq, Rat.AbsoluteValue.real_eq_abs, ProbabilityTheory.rpow_abs_le_mul_max_exp_of_pos, Complex.ofReal_sub, exists_norm_le_of_cauchySeq, Real.sinh_strictMono, circleIntegrable_neg_radius, Real.mk_sup, WeakFEPair.hf_int, ENNReal.toReal_inf, Complex.integral_rpow_mul_exp_neg_mul_rpow, Metric.biUnion_lt_ball, NNReal.rpow_one_add', Function.Periodic.isBounded_of_continuous, Measurable.ennreal_toReal, ProbabilityTheory.Kernel.eLpNorm_density_le, ContDiffAt.exists_eventually_eq_hasDerivAt, Real.iteratedDerivWithin_cosh_Icc, dual_solid, unitInterval.sigmoid_monotone, CStarAlgebra.norm_negPart_le, polarCoord_source_ae_eq_univ, Real.pow_le_iff_le_log, Set.OrdConnected.preimage_real_toNNReal, Real.measurable_sin, Complex.im_surjective, TopologicalAddGroup.IsSES.pushforward_mono, NumberField.mixedEmbedding.negAt_apply_norm_isReal, Continuous.sqrt, Real.rpow_sub_natCast, Hyperreal.isSt_iff_tendsto, not_intervalIntegrable_of_sub_inv_isBigO_punctured, hasSum_geometric_of_abs_lt_one, star_mul_self_sub_self_mul_star, MeasureTheory.integrable_comp_smul_iff, Real.tendsto_abs_logb_atTop, dist_le_norm_add_norm', Complex.hasSum_im, MeasureTheory.Measure.addHaar_preimage_linearEquiv, Convex.subset_interior_image_homothety_of_one_lt, hasFDerivAtFilter_iff_tendsto, Chebyshev.integral_theta_div_log_sq_isLittleO, mem_openSegment_of_gauge_lt_one, cfcₙ_nnreal_eq_real, gauge_gaugeRescale_le, InnerProductSpace.laplacian_eq_iteratedFDeriv_orthonormalBasis, eqOn_piecewise_of_isMIntegralCurveOn_Ioo, deriv_inner_apply, ProbabilityTheory.setIntegral_tilted_mul_eq_cgf, RCLike.im_to_complex, CFC.sqrt_algebraMap, Real.expMonoidHom_apply, NNReal.coe_pos, Real.binEntropy_lt_log_two, SchwartzMap.instFourierInvAdd, analyticWithinAt_rexp, riesz_lemma_of_lt_one, Complex.angle_one_left, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunctionAux_def, InnerProductGeometry.norm_sub_eq_abs_sub_norm_of_angle_eq_zero, 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, MonotoneOn.integral_le_sum, Real.log_lt_log_iff, 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, stereo_right_inv, Asymptotics.IsBigO.of_abs_left, HurwitzZeta.hasSum_int_sinZeta, ConvexOn.continuousOn_interior, Real.arctan_le_zero, UpperHalfPlane.coe_vadd, Real.rpow_inv_eq, Seminorm.smul_apply, ENNReal.ofReal_zero, MeasureTheory.pdf.IsUniform.integral_eq, UpperHalfPlane.denom_one, abs_norm_sub_norm_le', LipschitzOnWith.hausdorffMeasure_image_le, ContDiff.norm, exists_irrational_btwn, Real.cos_nonneg_of_neg_pi_div_two_le_of_le, IsMIntegralCurveAt.comp_mul_ne_zero, tendsto_norm_atTop_iff_cobounded, CovByVAdd.nonneg, intervalIntegral.integral_interval_add_Ioi', 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, CircleDeg1Lift.iterate_le_of_map_le_add_int, ContDiffBump.hasCompactSupport_normed, Real.sin_sq_pi_over_two_pow, Metric.ball_eq_empty, Complex.conj_eq_iff_real, OpenPartialHomeomorph.contDiffOn_univBall_symm, Metric.exists_subseq_summable_dist_of_cauchySeq, Complex.re_surjective, AntitoneOn.sum_le_integral, IsCompact.measure_eq_biInf_integral_hasCompactSupport, Real.sq_sin_pi_div_three, UnitAddCircle.mem_addWellApproximable_iff, sub_mem_posTangentConeAt_of_openSegment_subset, Real.BohrMollerup.f_add_nat_eq, UpperHalfPlane.I_re, circleMap_zero_radius, ProbabilityTheory.gaussianReal_map_const_sub, LipschitzOnWith.norm_neg_add_le_of_le, CompactlySupportedContinuousMap.nnrealPart_apply, stereographic_apply, ProbabilityTheory.variance_sub_const, Affine.Triangle.sbtw_touchpoint_empty, Complex.toMatrix_conjAe, Function.Periodic.tendsto_at_I_inf, ENNReal.one_lt_rpow_of_pos_of_lt_one_of_neg, ProbabilityTheory.geometricPMFReal_nonneg, 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, PadicInt.mkUnits_eq, MeasureTheory.Measure.toSignedMeasure_apply_measurable, MeasureTheory.levyProkhorovDist_self, StieltjesFunction.iInf_Ioi_eq, SameRay.norm_smul_eq, IsLocalMin.hasFDerivAt_eq_zero, Tactic.ComputeAsymptotics.WellFormedBasis.tail_isLittleO_head, MeasureTheory.Measure.HasTemperateGrowth.exists_eLpNorm_lt_top, integral_pow_mul_le_of_le_of_pow_mul_le, Function.locallyFinsuppWithin.logCounting_le, 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, strictMonoOn_of_deriv_pos, 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, homeomorphSphereProd_apply_snd_coe, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, StieltjesFunction.measure_Iio, Real.sInf_nonpos', Rat.AbsoluteValue.not_real_isEquiv_padic, Real.iteratedFDeriv_fourierIntegral, intervalIntegral.integrable_deriv_smul_comp_iff_of_deriv_nonneg, HasStrictDerivAt.sinh, HurwitzKernelBounds.isBigO_exp_neg_mul_of_le, Set.OrdConnected.preimage_coe_nnreal_real, IsCoercive.ker_eq_bot, dist_lt_dist_add_dist_iff, NumberField.InfinitePlace.Completion.surjective_extensionEmbeddingOfIsReal, not_summable_iff_tendsto_nat_atTop_of_nonneg, Real.log_finprod, hasDerivWithinAt_abs_neg, TestFunction.instLocallyConvexSpaceReal, seminormFromConst_def, Real.HolderTriple.pos', UpperHalfPlane.im_inv_neg_coe_pos, StieltjesFunction.ae_hasDerivAt, UpperHalfPlane.IsZeroAtImInfty.exp_decay_atImInfty', contDiffWithinAt_abs, algNormFromConst_def, MulRingSeminorm.toFun_eq_coe, Subadditive.eventually_div_lt_of_div_lt, instSMulCommClass_closedBall_closedBall_ball, Real.rpow_eq_nhds_of_pos, Subgroup.strictWidthInfty_pos_iff, Real.abs_sin_le_abs, Stirling.log_stirlingSeq_diff_le_geo_sum, hasSum_sq_fourierCoeff, ProbabilityTheory.strong_law_aux1, Real.nnnorm_natCast, Complex.neg_pi_div_two_le_arg_iff, NonarchAddGroupSeminorm.le_def, PartitionOfUnity.sum_nonneg, Hyperreal.coe_abs, ENNReal.ofReal_lt_ofNat, EuclideanGeometry.dist_lt_of_angle_lt, 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, Real.diam_Ico, Complex.isOpen_setOf_mem_nhds_and_isMaxOn_norm, Mathlib.Meta.Positivity.nnabs_pos_of_pos, norm_sub_le_mul_volume_of_norm_fderiv_le, RCLike.norm_to_complex, Complex.isBigO_ofReal_right, Real.contDiffAt_arccos, polynomialFunctions.topologicalClosure, EuclideanGeometry.Sphere.IsTangentAt_iff_angle_eq_pi_div_two, NumberField.mixedEmbedding.norm_eq_of_normAtPlace_eq, ZLattice.covolume_comap, LinearMap.toSeminorm_ball_zero, MonotoneOn.eVariationOn_le, Real.differentiableAt_negMulLog, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, ProbabilityTheory.HasSubgaussianMGF.aestronglyMeasurable, intervalIntegrable_of_even, tendsto_div_of_monotone_of_exists_subseq_tendsto_div, NumberField.HeightOneSpectrum.NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, continuous_convexComboPair, HolderOnWith.of_le, CircleDeg1Lift.translationNumber_lt_of_forall_lt_add, Metric.eventually_notMem_thickening_of_infEDist_pos, Behrend.two_div_one_sub_two_div_e_le_eight, dist_prod_prod_le, UpperHalfPlane.val_J, NumberField.InfiniteAdeleRing.coe_norm_eq_abs_norm, Metric.diam_subsingleton, Besicovitch.tendsto_filterAt, isPathConnected_compl_of_one_lt_codim, StrongConvexOn.strictConvexOn, MeasureTheory.eLpNorm_le_eLpNorm_mul_rpow_measure_univ, ProbabilityTheory.mgf_gaussianReal, Orientation.kahler_apply_apply, PiLp.dist_eq_of_L2, Module.Basis.norm_zero, SmoothBumpFunction.tsupport_subset_extChartAt_source, IsUpperSet.mem_interior_of_forall_lt, RCLike.imCLM_coe, RCLike.re_sq_le_normSq, BoxIntegral.Box.lower_lt_upper, Polynomial.isGreatest_supNorm, isMIntegralCurveAt_comp_add, Asymptotics.IsBigO.abs_abs, ContinuousLinearMap.reApplyInnerSelf_smul, imaginaryPart_imaginaryPart, Asymptotics.IsBigO.isBigOWith, Orientation.inner_rightAngleRotationAux₁_left, MeasureTheory.integral_indicator_const, Subgroup.isCusp_of_mem_strictPeriods, Path.Homotopy.trans_refl_reparam, MeasureTheory.L1.setToL1_simpleFunc_indicatorConst, not_differentiableWithinAt_of_deriv_tendsto_atBot_Iio, NNReal.coe_injective, Real.add_one_lt_exp, StieltjesFunction.id_apply, LinearMap.IsSymmetric.roots_charpoly_eq_eigenvalues, Complex.nhdsWithin_stolzCone_le_nhdsWithin_stolzSet, LinearMap.singularValues_pos_iff_ne_zero, Real.monotoneOn_sin, CompactlySupportedContinuousMap.toReal_nonneg, separatesPoints_continuous_of_t35Space, 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, MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left, EReal.coe_pow, Real.tendsto_logb_nhdsGT_zero_of_base_lt_one, exists_embedding_euclidean_of_compact, Complex.div_ofReal_im, strictConvexOn_zpow, Complex.norm_fderiv_le_one_of_mapsTo_ball, Besicovitch.BallPackage.rpos, Real.measurable_log, EReal.coe_one, Real.HolderTriple.inv_eq, SimpleGraph.regularityReduced_edges_card_aux, VectorFourier.fourierIntegral_continuousMultilinearMap_apply, Seminorm.coe_zero, ProbabilityTheory.iIndepFun.charFunDual_map_fun_finset_sum_eq_prod, MeasureTheory.exists_le_integral, ProbabilityTheory.gaussianReal_map_const_add, Asymptotics.IsBigO.rpow, Asymptotics.IsBigO.isBoundedUnder_le, HasDerivAt.inner, Complex.angle_one_right, Real.cos_nat_mul_two_pi_add_pi, ProbabilityTheory.Kernel.instIsMarkovKernelCondKernelReal, LinearMap.toSeminorm_apply, nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts, Real.continuousAt_rpow, Complex.IsExpCmpFilter.abs_im_pow_eventuallyLE_exp_re, hasDerivAt_ofReal_cpow_const', ContDiff.sqrt, MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_image₀, Complex.normSq_eq_conj_mul_self, SimpleGraph.lapMatrix_mulVec_eq_zero_iff_forall_reachable, riesz_extension, LineDeriv.tensorLineDerivTwo_canonicalCovariantTensor_eq_sum, Orientation.areaForm_apply_self, intervalIntegral.integral_deriv_smul_comp_of_deriv_nonneg, 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, ContinuousAlternatingMap.opNorm_le_bound, Real.smul_iSup_of_nonneg, Real.arccos_lt_arccos, Submodule.starProjection_minimal, Real.analyticOn_arsinh, SeminormedGroup.mem_closure_iff, Real.abs_sin_le_one, InnerProductGeometry.cos_eq_one_iff_angle_eq_zero, HasFPowerSeriesAt.isBigO_sub_partialSum_pow, MeasureTheory.lpNorm_natCast_mul, rpow_one_add_lt_one_add_mul_self, StrictConvexOn.slope_lt_of_hasDerivWithinAt, Orientation.oangle_smul_add_right_eq_zero_or_eq_pi_iff, MeasureTheory.integrable_rnDeriv_smul_iff, AlternatingMap.mkContinuousAlternating_norm_le_max, Real.cosh_sub_sinh, Irrational.div_natCast, MeasureTheory.Integrable.real_toNNReal, Real.volume_real_Ico, summable_of_sum_range_le, 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, MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one_aux, Complex.conjCLE_norm, IsNonarchimedean.apply_sum_le, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, BoundingSieve.nu_pos_of_dvd_prodPrimes, Real.log_pow, ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_ge_le, Affine.Simplex.sSameSide_point_excenter_singleton, SchwartzMap.seminorm_apply, Real.logb_nonpos_iff, Real.le_iInf, 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, closedBall_rpow_sub_one_eq_empty_aux, HurwitzZeta.completedCosZeta_zero, fourierBasis_repr, quasispectrum_realPart', MeasureTheory.SignedMeasure.integrable_rnDeriv, ENNReal.toReal_sum, MeasureTheory.condExp_stronglyMeasurable_mul_of_bound₀, ConvexOn.monotoneOn_derivWithin, schnirelmannDensity_setOf_modeq_one, UpperHalfPlane.instContinuousGLSMul, BumpCovering.coe_toSmoothPartitionOfUnity, AffineSubspace.signedInfDist_def, NNReal.coeNNRealReal_zero, Complex.norm_log_one_sub_inv_sub_self_le, isScalarTower_sphere_ball_ball, MeasureTheory.Measure.addHaar_closedBall, ContinuousLinearMap.unit_le_opNorm, Real.tanh_eq, WithLp.norm_snd_le, ProbabilityTheory.mgf_id_gaussianReal, ENNReal.lt_iff_exists_rat_btwn, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply, Convex.norm_image_sub_le_of_norm_hasFDerivWithin_le', ProbabilityTheory.mgf_id_map, Path.truncate_continuous_family, ValueDistribution.logCounting_zero_sub_logCounting_top_eq_circleAverage_sub_const, norm_sup_sub_sup_le_add_norm, ContDiffWithinAt.arsinh, HolderOnWith.edist_le, Real.arctan_mono, AddGroupSeminorm.zero_apply, Affine.Simplex.acuteAngled_reindex_iff, ConcaveOn.slope_le_rightDeriv, MeasureTheory.L1.setToL1_zero_left', Complex.norm_deriv_le_of_forall_mem_sphere_norm_le, ContDiffMapSupportedIn.fderivCLM_apply_of_le, MeasureTheory.BoundedContinuousFunction.inner_toLp, EReal.toReal_eq_zero_iff, isMIntegralCurveAt_eventuallyEq_of_contMDiffAt, Complex.isQuotientMap_re, AddGroupSeminorm.coe_zero, cfc_re_id, exists_ratio_hasDerivAt_eq_ratio_slope', Submodule.angle_coe, MeasureTheory.taylorWithinEval_charFun_two_zero', ProbabilityTheory.measure_le_le_exp_mul_mgf, 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, EuclideanGeometry.Sphere.inter_orthRadius_eq_singleton_of_dist_eq_radius, Padic.padicNormE_lim_le, ProbabilityTheory.integrable_exp_mul_of_le, Cardinal.mk_Ici_real, Metric.controlled_of_isUniformEmbedding, instSecondCountableTopologyReal, ContinuousLinearMap.norm_id, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunctionAux_def', instIsTopologicalAddGroupReal, hasFDerivAt_integral_of_dominated_of_fderiv_le'', Real.exp_bound', ConcaveOn.antitoneOn_derivWithin, Real.mk_near_of_forall_near, MeasureTheory.integral_fintype_prod_volume_eq_prod, ProbabilityTheory.Kernel.density_nonneg, DifferentiableAt.sinh, BoundingSieve.nu_mult, BoxIntegral.Box.measurableSet_Ioo, exists_dist_lt_lt, sum_div_pow_sq_le_div_sq, tendsto_fib_succ_div_fib_atTop, Complex.subfield_eq_of_closed, Metric.thickening_nonempty_iff, tendsto_measure_cthickening_of_isCompact, RCLike.mul_re, Besicovitch.SatelliteConfig.exists_normalized_aux1, 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, ProbabilityTheory.instIsProbabilityMeasure_stieltjesOfMeasurableRat, StrongFEPair.hf_top', Real.rpow_le_rpow_of_exponent_nonpos, MeasureTheory.condExp_bilin_of_stronglyMeasurable_right, cauchySeq_bdd, Orientation.oangle_sub_left_eq_arctan_of_oangle_eq_pi_div_two, MeasureTheory.eLpNorm_eq_lintegral_rpow_enorm, NormedSpace.closedBall_inv_subset_polar_closedBall, Behrend.bound_aux, ProbabilityTheory.Kernel.mem_mutuallySingularSetSlice, ProbabilityTheory.condVar_of_not_sigmaFinite, EuclideanGeometry.oangle_right_eq_arccos_of_oangle_eq_pi_div_two, Real.sin_nat_mul_pi_sub, MeasureTheory.integral2_divergence_prod_of_hasFDerivAt, Real.nnreal_trichotomy, Affine.Simplex.mem_altitude, Affine.Simplex.isDiameter_ninePointCircle, norm_le_norm_add_norm_inv_mul, ProbabilityTheory.IsGaussian.integral_dual_conv_map_neg_eq_zero, ENNReal.rpow_mul_intCast, MeasureTheory.convolution_mono_right, UnitAddTorus.span_mFourier_closure_eq_top, ContDiff.dimH_range_le, 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, ProbabilityTheory.integral_id_multivariateGaussian', MeasureTheory.Integrable.uniformIntegrable_condExp_filtration, Metric.isUniformEmbedding_iff, Affine.Triangle.sSameSide_affineSpan_pair_point_excenter_singleton, NNReal.isometry_coe, ModularForm.is_invariant_one', ContinuousMap.exists_restrict_eq_forall_mem_of_closed, Real.expPartialHomeomorph_symm_apply, AkraBazziRecurrence.isLittleO_deriv_one_sub_smoothingFn, MeasureTheory.eLpNorm_indicator_const₀, Affine.Triangle.dist_div_sin_angle_div_two_eq_circumradius, Height.logHeight_sym2_ge, HasFPowerSeriesOnBall.image_sub_sub_deriv_le, Complex.imCLM_enorm, TemperedDistribution.smulLeftCLM_smulLeftCLM_apply, norm_add₄_le, Polynomial.cyclotomic_eval_le_add_one_pow_totient, Real.Angle.coe_zsmul, MeasureTheory.Measure.haar.addCHaar_self, EisensteinSeries.eisensteinSeriesSIF_apply, Metric.nhds_basis_ball_inv_nat_succ, Real.integral_rpow_mul_exp_neg_mul_Ioi, SchwartzMap.tsupport_derivCLM_subset, Real.rpow_le_one_of_one_le_of_nonpos, CFC.sqrt_rpow_nnreal, Affine.Simplex.orthogonalProjectionSpan_eulerPoint_mem_ninePointCircle, intervalIntegral.integral_deriv_smul_comp''', Real.tendsto_log_atTop, ProbabilityTheory.hasSum_one_poissonMeasure, Real.sinh_add_cosh, Filter.Tendsto.cesaro_smul, Real.artanh_lt_artanh, Polynomial.Chebyshev.sumZeroes_sum, setOf_liouville_eq_iInter_iUnion, RCLike.normSq_zero, NNReal.toReal_limsup, isLocalHomeomorph_circleExp, MeasureTheory.measureReal_prod_prod, Function.HasTemperateGrowth.mul, MeasureTheory.Measure.toSignedMeasure_sub_apply, Chebyshev.psi_nonneg, Real.rpow_le_rpow_iff, 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, TopCat.I.homeomorph_symm, IsMaxOn.lineDeriv_eq_zero, Hamming.dist_eq_hammingDist, PadicInt.norm_mahler_eq, MeasureTheory.Lp.norm_eq_zero_iff, MeasureTheory.integrable_continuousLinearMap_prod, ENNReal.toReal_le_toReal, Real.hasSum_arctan, BoundingSieve.siftedSum_le_mainSum_errSum_of_upperMoebius, Complex.cpow_inv_two_im_eq_neg_sqrt, MeasureTheory.Measure.haarScalarFactor_eq_integral_div_of_continuous_nonneg_pos, Real.sin_eq_zero_iff, EReal.lt_iff_exists_rat_btwn, Real.strictConcave_binEntropy, Complex.HadamardThreeLines.norm_le_interpStrip_of_mem_verticalClosedStrip₀₁, Continuous.fourierPowSMulRight, ZLattice.normBound_spec, EReal.preimage_coe_Ioc_bot, ENNReal.rpow_le_one, instContinuousStarReal, Hyperreal.st_inv, ae_of_mem_of_ae_of_mem_inter_Ioo, Sbtw.dist_lt_max_dist, Asymptotics.isBigO_iff_eventually_isBigOWith, TemperedDistribution.isVanishingOn_delta, ProbabilityTheory.HasGaussianLaw.fst, nnnorm_cfc_nnreal_lt_iff, Metric.tendstoUniformlyOnFilter_iff, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_snd, Metric.infDist_le_infDist_add_hausdorffDist, Orientation.sin_oangle_sub_right_of_oangle_eq_pi_div_two, ProbabilityTheory.Fernique.lintegral_exp_mul_sq_norm_le_mul, Real.sinh_injective, ContinuousLinearMap.reApplyInnerSelf_continuous, Real.tendsto_abs_tan_atTop, Int.norm_coe_units, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, AbsoluteValue.iSup_abv_linearMap_apply_le, Real.log_comp_exp, ENNReal.lintegral_Lp_add_le_of_le_one, 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, MeasureTheory.setToFun_const, Complex.arg_eq_nhds_of_re_pos, EReal.coe_inv, Orientation.norm_div_tan_oangle_add_right_of_oangle_eq_pi_div_two, TopologicalSpace.exists_embedding_l_infty, UniformConvexOn.sub, integral_complex_ofReal, tendsto_norm_nhdsNE_zero, Real.cos_sub_int_mul_two_pi, imaginaryPart_smul, Real.rpow_max, mul_mem_closedBall_iff_norm, ProbabilityTheory.measure_ge_le_exp_mul_mgf, Seminorm.coeFnAddMonoidHom_apply, RCLike.re_le_neg_norm_iff_eq_neg_norm, Irrational.div_ratCast, CliffordAlgebraComplex.toComplex_involute, SzemerediRegularity.edgeDensity_chunk_not_uniform, StrongDual.im_extendRCLike_apply, complexOfReal_fderiv, NumberField.mixedEmbedding.norm_real, differentiable_norm_rpow, 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, SlashInvariantFormClass.norm_petersson_smul, Affine.Simplex.dist_lt_of_mem_closedInterior_of_strictConvexSpace, SchwartzMap.instFourierInvPair, HurwitzZeta.cosZeta_neg, Metric.Snowflaking.edist_def, CompactlySupportedContinuousMap.nnrealPart_smul_pos, Affine.Simplex.height_eq_dist, Real.log_natCast_le_rpow_div, Affine.Simplex.sign_signedInfDist_incenter, ConcaveOn.continuousOn_tfae, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, ContinuousMap.polynomial_comp_attachBound, Orientation.rightAngleRotation_map, MeasureTheory.upperCrossingTime_succ, ProbabilityTheory.evariance_eq_zero_iff, integral_inv_one_add_sq, VectorFourier.norm_fourierSMulRight_le, BoundedContinuousFunction.norm_normComp, AlternatingMap.measure_parallelepiped, EuclideanGeometry.Sphere.isTangentAt_iff_dist_sq_eq_power, ConvexOn.le_slope_of_hasDerivWithinAt, blimsup_thickening_mul_ae_eq, EisensteinSeries.abs_norm_eq_max_natAbs_neg, RCLike.neg_iff_exists_ofReal, Real.abs_mulExpNegMulSq_le, ConvexOn.slope_le_derivWithin, NumberField.mixedEmbedding.normAtAllPlaces_norm_at_real_places, RCLike.wInner_one_eq_sum, Seminorm.preimage_metric_ball, Affine.Simplex.touchpointWeights_singleton_pos, IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary, EuclideanGeometry.angle_lt_pi_div_three_of_le_of_le_of_ne, summable_norm_geometric_of_norm_lt_one, EReal.coe_eq_one, Irrational.mul_ratCast, ContDiffWithinAt.inversion, Real.volume_univ, ContDiffAt.sin, Asymptotics.IsBigOWith.of_abs_abs, ENNReal.dichotomy, CompareReals.compare_uc_symm, tsum_comp_le_tsum_of_inj, Real.iteratedDeriv_odd_sin, IsMIntegralCurveOn.continuousOn, RCLike.toContinuousLinearMap_complexLinearIsometryEquiv, 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, Memℓp.summable, unique_unit_speed_on_Icc_zero, ContinuousLinearMap.le_of_opNorm₂_le_of_le, MeasureTheory.Measure.haar.addCHaar_mono, Orientation.kahler_rotation_right, Complex.ofRealCLM_enorm, AddMonoidHom.coe_toRealLinearMap, isNonarchimedean_smoothingFun, integral_Ioi_cpow_of_lt, Finset.small_pow_of_small_tripling, CircleDeg1Lift.map_lt_add_translationNumber_add_one, deriv.lhopital_zero_right_on_Ico, 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, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le, Real.toNNReal_lt_natCast, uniqueDiffWithinAt_Ici, tendsto_exp_div_rpow_atTop, HurwitzZeta.sinKernel_def, DenselyNormedField.lt_norm_lt, 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, ProbabilityTheory.covariance_fun_div_left, BoundingSieve.multSum_eq_main_err, Real.HolderTriple.one_div_pos, NNReal.tendsto_coe, norm_div_eq_zero_iff, Affine.Simplex.signedInfDist_affineCombination, Complex.HadamardThreeLines.scale_diffContOnCl, ProbabilityTheory.IsMeasurableRatCDF.measurable, Antitone.cauchySeq_alternating_series_of_tendsto_zero, Metric.nhds_basis_ball, tendsto_sum_mul_atTop_nhds_one_sub_integral, Real.nnreal_dichotomy, LipschitzOnWith.of_le_add_mul', NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis, irrational_cos_rat_mul_pi, TemperedDistribution.lineDerivOp_apply_apply, Real.Gamma_integrand_isLittleO, Complex.HadamardThreeLines.diffContOnCl_invInterpStrip, CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun, MeasureTheory.ComplexMeasure.re_apply, SeminormedSpace.Core.norm_smul, ENNReal.rpow_le_rpow_iff, ProbabilityTheory.strong_law_aux2, MeasureTheory.integral_Iic_of_hasDerivAt_of_tendsto, Set.infsep_pos, SimpleGraph.triangle_removal, intervalIntegral.mul_integral_comp_mul_right, intervalIntegral.intervalIntegrable_cpow', Subgroup.strictWidthInfty_pos, EuclideanGeometry.sin_oangle_left_mul_dist_of_oangle_eq_pi_div_two, Filter.Tendsto.sqrt, Real.eulerMascheroniSeq_lt_eulerMascheroniConstant, Real.rpow_nonneg, Real.one_div_sub_pow_hasFPowerSeriesOnBall_zero, Complex.norm_exp_sub_one_sub_id_le, 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, UnitAddTorus.hasSum_mFourier_series_apply_of_summable, MeasureTheory.IntegrableOn.continuousWithinAt_Iic_primitive_Iio, norm_le_norm_add_const_of_dist_le', MeasureTheory.measureReal_univ_eq_one, MeasureTheory.integrable_right_of_integrable_add_of_nonneg, UpperHalfPlane.modular_T_zpow_smul, Real.neg_pi_div_two_le_arcsin, ProbabilityTheory.iIndepFun.integral_fun_prod_eq_prod_integral, exists_isMIntegralCurve_of_isMIntegralCurveOn, ContinuousMap.HomotopyWith.continuous, CFC.nnrpow_eq_nnrpow_prod, Real.coe_tanPartialHomeomorph_symm, EuclideanGeometry.angle_self_orthogonalProjection, Complex.norm_natCast_cpow_le_norm_natCast_cpow_of_pos, GenLoop.coe_copy, intervalIntegral.norm_integral_le_abs_integral_norm, NumberField.HeightOneSpectrum.NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_add_le_max, Valued.toNormedField.setOf_mem_integer_eq_closedBall, AddCircle.norm_eq, Complex.norm_cpow_eq_rpow_re_of_nonneg, Fin.dist_insertNth_insertNth, Metric.Snowflaking.preimage_ofSnowflaking_emetricBall, 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, ZLattice.covolume.tendsto_card_le_div'', TestFunction.instLineDerivSMulTopENat, exists_isMIntegralCurve_iff_exists_isMIntegralCurveOn_Ioo, NumberField.mixedEmbedding.polarSpaceCoord_source, cfcₙ_realPart, Metric.lipschitz_infDist_set, Unitary.norm_argSelfAdjoint, cfc_real_eq_complex, IsUltrametricDist.dist_eq_max_of_dist_ne_dist, UnitAddTorus.hasSum_sq_mFourierCoeff, TemperedDistribution.lineDerivOp_fourierInv_eq, CFC.norm_rpow, RCLike.im_ofReal_mul, not_integrableOn_Ici_inv, CircleDeg1Lift.map_add_one', norm_image_sub_le_of_norm_deriv_le_segment_01', Real.qaryEntropy_zero, Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT_of_ne, fourierCoeffOn_eq_integral, Complex.re_expect, HurwitzZeta.hurwitzOddFEPair_g, HurwitzKernelBounds.F_nat_zero_le, ProbabilityTheory.IsGaussian.charFunDual_eq_of_integral_eq_zero, Real.self_lt_rpow_of_one_lt, exists_monotone_Icc_subset_open_cover_unitInterval, Orientation.abs_oangle_sub_left_toReal_lt_pi_div_two, MeasureTheory.measure_average_le_pos, 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, Behrend.div_lt_floor, UpperHalfPlane.dist_coe_le, Circle.expHom_apply, Real.rpow_pow_comm, 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, strictAntiOn_of_hasDerivWithinAt_neg, tendsto_pow_const_div_const_pow_of_one_lt, integral_sin_pow_odd, EuclideanGeometry.dist_affineCombination, Complex.circleTransformDeriv_bound, intervalIntegral.intervalIntegrable_rpow', HasStrictFDerivAt.sin, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, similar_iff_exists_pos_pairwise_dist_eq, Real.differentiableAt_sinh, NNReal.rpow_zero, ContractingWith.fixedPoint_lipschitz_in_map, ProbabilityTheory.Fernique.sq_normThreshold_add_one_le, MeasureTheory.addHaarMeasure_eq_volume, Asymptotics.IsTheta.sqrt, Orientation.oangle_sign_smul_add_smul_right, LiouvilleWith.rat_add, spectralNorm_unique_field_norm_ext, 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, LipschitzWith.norm_inv_mul_le, Real.continuousAt_logb, Real.differentiable_iteratedDeriv_sinh, LipschitzWith.hausdorffMeasure_image_le, Real.HolderTriple.one_div_nonneg', AffineSubspace.direction_perpBisector, Complex.lintegral_comp_pi_polarCoord_symm, MeasureTheory.integral_deriv_smul_comp_Ioi, HolderOnWith.dist_le, IsLocalExtr.hasDerivAt_eq_zero, MeasureTheory.DominatedFinMeasAdditive.add, Besicovitch.multiplicity_le, curveIntegralFun_symm, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_expMapBasis_image, Complex.HadamardThreeLines.sSupNormIm_nonneg, EReal.preimage_coe_Ico, volume_regionBetween_eq_integral, realPart_apply_coe, NumberField.mixedEmbedding.fundamentalCone.expMap_single_apply, AffineSubspace.angle_coe, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn, Real.logb_lt_logb, HasFDerivWithinAt.const_rpow, Real.BohrMollerup.logGammaSeq_add_one, ProbabilityTheory.setLIntegral_condCDF, Real.exp_neg_one_gt_d9, ZetaAsymptotics.term_welldef, MeasureTheory.measure_setAverage_le_pos, MeasureTheory.Integrable.measure_le_integral, Real.mulExpNegMulSq_one_le_one, ContDiffMapSupportedIn.fderivCLM_apply, Submodule.orthogonalProjectionFn_norm_sq, exp_neg_integrableOn_Ioi, EReal.coe_real_ereal_eq_coe_toNNReal_sub_coe_toNNReal, Complex.norm_exp_mul_exp_add_exp_neg_le_of_abs_im_le, MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_sum_mul_norm_of_integrable, Metric.diam_empty, Quaternion.imJ_coeComplex, RCLike.geometric_hahn_banach_of_nonempty_interior, intervalIntegral.integral_comp_mul_right, CliffordAlgebraComplex.Q_apply, ProbabilityTheory.IndepFun.variance_sum, ProbabilityTheory.paretoPDFReal_nonneg, Real.instStrictConvexSpace, 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, PointedCone.minTensorProduct_eq_max_of_simplicial_generating_left, CStarAlgebra.norm_sub_mul_self_le, unitInterval.one_minus_nonneg, le_liminf_mul, ProbabilityTheory.measure_le_mul_measure_gt_le_of_map_rotation_eq_self, MeasureTheory.measureReal_biUnion_finset_le, ProbabilityTheory.IsGaussian.charFun_eq, Real.geom_mean_eq_arith_mean_weighted_of_constant, MeasureTheory.L1.setToL1_mono, ContinuousLinearMap.extendTo𝕜'_apply, nullMeasurableSet_region_between_oc, Real.cos_lt_cos_of_nonneg_of_le_pi, NumberField.mem_multisetInfinitePlace, Real.tan_eq_zero_of_cos_eq_zero, Real.exp_one_near_10, TestFunction.fderivCLM_apply, fderivWithin_cosh, Affine.Simplex.ninePointCircle_map, RCLike.I_re, ContinuousAt.inner_bundle, MeasureTheory.integral_concaveOn_of_integrand_ae, MeasureTheory.lintegral_enorm_of_ae_nonneg, AddCircle.instProperlyDiscontinuousVAddSubtypeAddOppositeRealMemAddSubgroupOpZmultiples, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, Real.rpow_div_two_eq_sqrt, ProbabilityTheory.isProbabilityMeasureBeta, spectralValue_nonneg, VectorFourier.norm_fourierPowSMulRight_le, NormedSpace.norm_expSeries_div_summable, EuclideanGeometry.dist_smul_vadd_eq_dist, deriv_pos_left_of_sign_deriv, unitInterval.symm_lt_symm, derivWithin_Ioi_eq_Ici, dist_birkhoffAverage_birkhoffAverage_le, Complex.equivRealProdCLM_symm_apply_im, integral_gaussian_complex, Real.exp_le_one_iff, MeasureTheory.integral_singleton, summable_pow_mul_jacobiTheta₂_term_bound, riesz_lemma, 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, SchwartzMap.fourierMultiplierCLM_fourierMultiplierCLM_apply, 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, Measurable.sin, CFC.rpow_map_pi, AddGroupSeminormClass.toSeminormedAddCommGroup_norm_eq, ZetaAsymptotics.term_sum_one, Real.noAtoms_volume, Real.young_inequality_of_nonneg, MeasureTheory.Measure.integrableOn_toReal_rnDeriv, not_integrableOn_Ioi_inv, Emetric.exists_smooth_forall_closedBall_subset, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, complexOfReal_hasDerivAt, Complex.isCauSeq_norm, ConvexBody.hausdorffDist_coe, UnitAddTorus.mFourier_single, Real.hasFDerivAt_fourierChar_neg_bilinear_right, MeasureTheory.integral_comp_smul_deriv_Ioi, Real.antitoneOn_rpow_Ioi_of_exponent_nonpos, ContinuousMap.Homotopy.ext_iff, ENNReal.abs_toReal, NumberField.InfiniteAdeleRing.norm_def, Complex.re_nnqsmul, ProbabilityTheory.geometricPMFReal_pos, Real.nnabs_pos, ContinuousWithinAt.inner_bundle, InnerProductGeometry.angle_sub_eq_arctan_of_inner_eq_zero, RCLike.re_extendTo𝕜ₗ, Real.fourier_continuousMultilinearMap_apply, Real.cos_sq, MeasureTheory.memLp_enorm_rpow_iff, ModularFormClass.differentiableOn_cuspFunction_ball, Path.delayReflRight_one, MeasureTheory.measure_le_average_pos, 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, Metric.Snowflaking.dist_ofSnowflaking_ofSnowflaking, Cardinal.Real.Ico_countable_iff, deriv.lhopital_zero_atTop, ProbabilityTheory.IndepFun.integrable_exp_mul_add, PadicInt.norm_def, ae_not_liouville, BoundedContinuousFunction.dist_lt_of_nonempty_compact, PadicInt.norm_natCast_eq_one_iff, Affine.Simplex.sum_excenterWeightsUnnorm_empty_pos, Real.logb_pos, ProbabilityTheory.measure_condCDF_univ, lp.norm_eq_tsum_rpow, AffineSubspace.mem_perpBisector_iff_inner_eq, not_summable_one_div_on_primes, WeakFEPair.f_modif_aux1, Cube.insertAt_boundary, CStarAlgebra.norm_le_one_iff_of_nonneg, Orientation.rotation_pi_div_two, spectrum_realPart, ContDiffMapSupportedIn.continuous_iff_comp, Complex.ofReal_ratCast, ContinuousMultilinearMap.norm_map_insertNth_le, HasCompactSupport.exists_simpleFunc_approx_of_prod, MeasureTheory.Measure.setIntegral_toReal_rnDeriv_le, Matrix.IsHermitian.posDef_iff_eigenvalues_pos, Complex.IsExpCmpFilter.tendsto_abs_re, Real.cauchy_one, ProbabilityTheory.strong_law_aux3, UniformContinuous.exists_contDiff_dist_le, MeasureTheory.BoundedContinuousFunction.integral_eq_integral_meas_le_of_hasFiniteIntegral, intervalIntegrable_log_norm_meromorphicOn, Complex.equiv_limAux, SchwartzMap.integral_inner_fourier_fourier, ProbabilityTheory.lintegral_stieltjesOfMeasurableRat, ValueDistribution.logCounting_eventually_nonneg, MonotoneOn.nnnorm_cfc, Complex.real_le_real, Asymptotics.isBigO_iff_isBigOWith, ProbabilityTheory.HasGaussianLaw.iIndepFun_of_covariance_eval, Orientation.finOrthonormalBasis_orientation, norm_iteratedFDerivWithin_mul_le, Seminorm.uniformContinuous', VectorFourier.norm_fourierSMulRight, RCLike.ofReal_im_ax, LiouvilleWith.mul_nat_iff, Metric.unitClosedBall.coe_pow, WithAbs.norm_eq_abv', MeasureTheory.setLIntegral_tilted', DifferentiableAt.inversion, Asymptotics.isBigO_iff'', ENNReal.ofReal_eq_one, Asymptotics.isLittleO_norm_norm, PadicInt.isOpenEmbedding_coe, InnerProductSpace.volume_closedBall, Real.geom_mean_weighted_of_constant, BoundedContinuousFunction.norm_add_eq_max, Real.cos_int_mul_two_pi_sub, MeasureTheory.integral_Iic_of_hasDerivAt_of_tendsto', ContinuousLinearEquiv.coord_norm', Tactic.ComputeAsymptotics.Seq.dist_eq_half_of_head, NumberField.InfinitePlace.eq_iff_eq, unitary.norm_sub_one_lt_two_iff, Asymptotics.IsBigO.abs_right, spectrum_imaginaryPart', GaussianFourier.integrable_cexp_neg_sum_mul_add, cantorSequence_eq_self_sub_sum_cantorToTernary, Function.Periodic.integral_le_sSup_add_zsmul_of_pos, NNReal.rpow_le_rpow_of_exponent_le, stereographic'_symm_apply, trapezoidal_integral_symm, cfc_setIntegral', ProbabilityTheory.integrable_pow_mul_exp_of_mem_interior_integrableExpSet, Asymptotics.IsBigO.id_rpow_of_le_one, Seminorm.sup_apply, HolderWith.dist_le_of_le, differentiableOn_abs, norm_sub_le_integral_of_norm_deriv_le_of_le, Real.log_neg, Matrix.frobenius_nnnorm_def, WithCStarModule.pi_norm_sq, EisensteinSeries.linear_isTheta_right, NormedAddCommGroup.nhds_zero_basis_norm_lt, ProbabilityTheory.hasDerivAt_mgf, ContinuousMap.HomotopyRel.cast_apply, Metric.unitClosedBall.instIsCancelMulZero, NormedSpace.norm_smul_normalize, ENNReal.orderIsoRpow_apply, LiouvilleWith.nat_sub, MeasureTheory.Measure.IicSnd_univ, BoundedContinuousFunction.norm_const_le, EuclideanGeometry.dist_sq_mul_dist_add_dist_sq_mul_dist, NormedAddGroupHom.coe_mk, cfcₙ_setIntegral', NumberField.mixedEmbedding.polarCoord_target_eq_polarCoordReal_target, Padic.norm_le_pow_iff_norm_lt_pow_add_one, Real.smoothTransition.projIcc, tendsto_atTop_of_geom_le, Real.Angle.coe_zero, indicator_indepFun_process_of_prod_bcf, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left, LinearMap.support_singularValues, NumberField.mixedEmbedding.fundamentalCone.sum_eq_zero_of_mem_span_completeFamily, ProbabilityTheory.IndepFun.hasGaussianLaw_sub_of_sub, integral_exp_mul_complex_Iic, LinearMap.mem_span_iff_bound, homeomorphSphereProd_apply_fst_coe, dist_le_of_trajectories_ODE, MeasureTheory.Measure.volumeIoiPow_apply_Iio, MeasureTheory.ProbabilityMeasure.continuous_integral_continuousMap, ProbabilityTheory.integrable_toReal_condDistrib, ContinuousOn.cfcₙ_nnreal, ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_sub, InnerProductSpace.laplacian_eq_iteratedDeriv_real, ENNReal.rpow_inv_lt_iff, Circle.arg_exp, Complex.norm_exp_sub_sum_le_exp_norm_sub_sum, taylor_mean_remainder_cauchy, Polynomial.logMahlerMeasure_C_mul_X_add_C, Metric.continuousAt_iff, UpperHalfPlane.pos_real_im, Real.abs_ofDigits_sub_ofDigits_le, norm_add_le_of_le, Real.binEntropy_le_log_two, Metric.nhds_basis_closedBall, MeasureTheory.Lp.toTemperedDistribution_apply, SchwartzMap.smulLeftCLM_sub, summable_geometric_two, NumberField.FinitePlace.isFinitePlace, MeasureTheory.Egorov.exists_notConvergentSeq_lt, Orientation.norm_div_sin_oangle_add_right_of_oangle_eq_pi_div_two, TemperedDistribution.smulLeftCLM_const, Metric.Snowflaking.image_ofSnowflaking_closedBall, MeasureTheory.Martingale.ae_eq_condExp_limitProcess, ProbabilityTheory.Kernel.measurable_densityProcess_right, Path.subpathAux_zero, SchwartzMap.smulLeftCLM_apply_apply, 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, ENNReal.toReal_le_of_le_ofReal, BoxIntegral.Box.splitLower_eq_self, MeasureTheory.integrable_toReal_iff, Complex.norm_log_natCast_le_rpow_div, ContDiff.contDiffBump, 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, Complex.HadamardThreeLines.norm_le_interp_of_mem_verticalClosedStrip', 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, ContDiff.sinh, tendsto_card_div_pow_atTop_volume', intervalIntegral.integral_hasStrictDerivAt_right, 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, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc_of_integral_eq_zero, EReal.coe_div, irrational_neg_iff, CFC.nnrpow_eq_rpow, SchwartzMap.fourier_fderivCLM_eq, SpectrumRestricts.nnreal_iff_spectralRadius_le, ProbabilityTheory.evariance_mul, intervalIntegral.integral_deriv_mul_eq_sub_of_hasDerivWithinAt, MeasureTheory.eLpNorm'_measure_zero_of_exponent_zero, Padic.add_eq_max_of_ne, ConvexBody.hausdorffEDist_coe, Real.sum_range_sub_log_div_le, exists_deriv_eq_slope, PartitionOfUnity.finite_tsupport, integrable_mulExpNegMulSq_comp_restrict_of_isCompact, CircleDeg1Lift.map_lt_of_translationNumber_lt_nat, ContDiffAt.abs, NumberField.InfinitePlace.map_intCast, EReal.coe_abs, Real.exp_one_pow, FormalMultilinearSeries.radius_eq_top_iff_summable_norm, Real.posLog_eq_log_max_one, Units.norm_pos, MeasureTheory.SimpleFunc.integral_eq, Real.exp_approx_end, CircleDeg1Lift.tendsto_translationNumber, MeasureTheory.lintegral_rpow_enorm_lt_top_of_eLpNorm_lt_top, integrableOn_rpow_mul_exp_neg_mul_sq, dist_algebraMap, le_geom, integral_withDensity_eq_integral_toReal_smul₀, ContDiffAt.cos, ENNReal.toReal_ofReal_eq_iff, StrongDual.re_extendRCLike_apply, EuclideanGeometry.angle_pointReflection_right, AbsoluteValue.isEquiv_iff_exists_rpow_eq, SchwartzMap.fourier_convolution_apply, Real.HolderTriple.one_div_pos', UpperHalfPlane.sinh_half_dist, intervalIntegral.integral_eq_zero_iff_of_nonneg_ae, Seminorm.smul_ball_zero, ProbabilityTheory.IsMeasurableRatCDF.monotone_stieltjesFunctionAux, Complex.hasStrictFDerivAt_log_real, Real.analyticWithinAt_arcosh, cthickening_cthickening, ProbabilityTheory.strong_law_ae_real, CircleDeg1Lift.translationNumber_translate, Filter.Tendsto.pathExtend, MeasureTheory.SimpleFunc.setToSimpleFunc_const', Real.iteratedDeriv_fourierIntegral, HolderOnWith.ediam_image_inter_le, Complex.adjoin_I, Real.summable_one_div_nat_pow, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux2, ProbabilityTheory.covariance_sum_sum', SchwartzMap.instContinuousFourier, HurwitzZeta.hurwitzZetaOdd_neg, LinearIsometry.norm_toContinuousLinearMap_le, Real.hasStrictDerivAt_tan, MeasureTheory.eLpNorm'_eq_lintegral_enorm, MeasureTheory.setIntegral_finset, EuclideanGeometry.cos_oangle_right_mul_dist_of_oangle_eq_pi_div_two, MeasureTheory.le_measureReal_diff, EuclideanSpace.coe_measurableEquiv, Real.borelSpace, ContDiffAt.inner, MeasureTheory.Measure.ext_of_complexMGF_eq, EReal.measurableEmbedding_coe, Path.Homotopy.eval_one, IsUltrametricDist.isNonarchimedean_algNormOfAlgEquiv, ProbabilityTheory.aestronglyMeasurable_exp_mul_add, InnerProductSpace.volume_closedBall_of_dim_odd, real_inner_smul_left, NNReal.dist_eq, Real.circleAverage_zero_one_congr_inv, ProbabilityTheory.strong_law_aux5, norm_add_mul_self_real, NumberField.mixedEmbedding.fundamentalCone.nonneg_of_mem_compactSet, ProbabilityTheory.variance_sum', ODE_solution_unique_of_mem_Icc_left, liouville_liouvilleNumber, ExistsContDiffBumpBase.w_integral, ProbabilityTheory.Kernel.density_mono_set, UpperHalfPlane.dist_le_iff_le_sinh, CFC.cfcₙ_rpowIntegrand₀₁_eq_cfcₙ_rpowIntegrand₀₁_one, ENNReal.continuousOn_toReal, Real.sin_neg_of_neg_of_neg_pi_lt, NNReal.tendsto_coe_atTop, Irreducible.degree_le_two, MeasureTheory.measureReal_biUnion_finset₀, NNReal.coe_one, TemperedDistribution.smulLeftCLM_sum, SimpleGraph.isEquivalent_extremalNumber, Polynomial.sub_one_pow_totient_lt_cyclotomic_eval, Polynomial.Chebyshev.one_lt_negOnePow_mul_eval_T_real, NumberField.mixedEmbedding.fundamentalCone.compactSet_ae, StieltjesFunction.measure_Ico, MeasureTheory.integrable_norm_rpow_of_le, ArithmeticFunction.vonMangoldt_le_log, Metric.unitClosedBall.instContinuousMul, Real.nnnorm_rpow_of_nonneg, NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv, Real.tendsto_euler_sin_prod, NormedAddGroup.nhds_zero_basis_norm_lt, intervalIntegral.integral_hasStrictDerivAt_left, 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, ProbabilityTheory.deriv_cgf_zero, DifferentiableOn.exp, sum_mul_eq_sub_sub_integral_mul', intervalIntegral.integral_comp_mul_deriv', Irreducible.maximalIdeal_pow_eq_closedBall_pow, InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq', IsLocalMaxOn.hasFDerivWithinAt_eq_zero, ContinuousMap.HomotopyRel.eq_fst, Dilation.dist_eq, Real.sin_pi_div_eight, IsCompact.exists_thickening_subset_open, ProbabilityTheory.measurable_cauchyPDF, 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, Real.arctan_add, Int.isUniformEmbedding_coe_real, ProbabilityTheory.HasSubgaussianMGF.id_map_iff, gauge_smul, BoxIntegral.Prepartition.IsPartition.exists_splitMany_le, FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos_aux2, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul, NumberField.mixedEmbedding.euclidean.finrank, ProbabilityTheory.multivariateGaussian_zero_one, DifferentiableAt.norm, Path.target, Real.Angle.toReal_add_eq_toReal_add_toReal, Complex.arg_eq_nhds_of_re_neg_of_im_pos, pi_polarCoord_symm_target_ae_eq_univ, MeasureTheory.Measure.toSphereBallBound_mul_measure_unitBall_le_toSphere_ball, Metric.unitClosedBall.coe_eq_one, Bertrand.real_main_inequality, 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, ContDiffMapSupportedIn.fderivLM_apply_of_le, abs_norm, MeasureTheory.integrable_left_of_integrable_add_of_nonneg, Antitone.concaveOn_univ_of_deriv, IsUltrametricDist.isPowMul_algNormOfAlgEquiv, AffineBasis.centroid_mem_interior_convexHull, ProbabilityTheory.HasGaussianLaw.toLp_prodMk, 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, fderiv_norm_smul_pos, PhragmenLindelof.horizontal_strip, pow_mem_ball, CFC.sqrt_map_pi, EuclideanGeometry.concyclic_or_collinear_of_two_zsmul_oangle_eq, AddCircle.integral_liftIoc_eq_intervalIntegral, MeasureTheory.StronglyAdapted.integrable_upcrossingsBefore, AEMeasurable.re, integral_Ioi_inv_one_add_sq, Quaternion.coe_ofComplex, Real.hasDerivAt_arctan, NNReal.zero_le_coe, Real.circleAverage_mono, dist_dist_dist_le_left, BoxIntegral.unitPartition.volume_box, UpperHalfPlane.σ_conj, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, GroupNorm.sup_apply, ProbabilityTheory.covariance_fun_sub_left, Path.Homotopy.source, NonarchAddGroupNorm.apply_one, Real.rpow_lt_self_of_one_lt, fourierCoeff_liftIoc_eq, UnitAddTorus.mFourierCoeff_eq_integral, MeasureTheory.Measure.addHaar_closedBall_mul, SeminormedSpace.Core.norm_nonneg, ProbabilityTheory.variance_id_map, dist_right_lineMap, Complex.volume_sum_rpow_lt_one, NumberField.InfinitePlace.LiesOver.instLiesOverRealValAbsoluteValueExistsRingHomComplexEqPlaceMkOfLiesOver, intervalIntegral.FTCFilter.nhdsLeft, MeasureTheory.Measure.tendsto_IicSnd_atBot, taylor_mean_remainder_bound, Real.rpow_le_rpow_iff_of_neg, Real.rpow_def_of_nonpos, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, circleIntegrable_log_norm_sub_const, ProbabilityTheory.geometricPMFRealSum, MeasureTheory.Measure.integral_isAddLeftInvariant_isAddRightInvariant_combo, tendsto_seminormFromConst_seq_atTop, geometric_hahn_banach_closed_point, ZMod.toAddCircle_eq_zero, Complex.betaIntegral_convergent_left, Real.rpow_le_rpow_of_exponent_ge, NNReal.instIsStrictOrderedModule, ContinuousOn.rpow_const, EuclideanGeometry.angle_nonneg, Asymptotics.IsLittleO.eventuallyLE, EuclideanGeometry.dist_inversion_mul_dist_center_eq, Nat.ratSqrt_mem_Ioc, hasSum_one_div_pow_mul_fourier_mul_bernoulliFun, Height.mulHeight_sym2_ge, 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, NumberField.mixedEmbedding.measurableSet_negAt_plusPart, Mathlib.Meta.NormNum.IsNat.rpow_eq_pow, ENNReal.one_lt_ofReal, Hyperreal.exists_st_of_not_infinite, BoundedContinuousFunction.coe_le_coe_add_dist, EReal.denseRange_ratCast, LipschitzOnWith.locallyBoundedVariationOn, Real.sinh_pos_iff, ProbabilityTheory.lintegral_gammaPDF_eq_one, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero', ENNReal.rpow_add_of_nonneg, MeasureTheory.norm_indicatorConstLp', ENNReal.rpow_neg, ArchimedeanClass.stdPart_mul, NonarchAddGroupSeminorm.sup_apply, CStarAlgebra.star_right_conjugate_le_norm_smul, lp.norm_toNorm, Convex.second_derivative_within_at_symmetric_of_mem_interior, norm_apply_le_norm_cfcₙ, MeasureTheory.SignedMeasure.toComplexMeasure_apply_im, NNReal.instContinuousMapZero.UniqueHom, Complex.nonneg_iff, EuclideanGeometry.dist_div_sin_oangle_right_of_oangle_eq_pi_div_two, ContinuousLinearMap.exists_mul_lt_of_lt_opNorm, Real.sqrt_one, pi_norm_lt_iff', ProbabilityTheory.measurable_condCDF, CircleDeg1Lift.map_fract_sub_fract_eq, AddSubgroup.norm_normedMk, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_symm_apply, MeasureTheory.HasFiniteIntegral.min_zero, lp.norm_const_smul_le, Real.exp_sub, bernstein.z_last, gauge_lt_one_iff_mem_interior, bernstein.probability, TestFunction.instContinuousSMulReal, cthickening_ball, MeasureTheory.integral_comp_mul_left_Ioi, AkraBazziRecurrence.one_mem_range_sumCoeffsExp, IsLocalMinOn.fderivWithin_nonneg, Real.exp_approx_succ, UpperHalfPlane.denom_J_mul, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_sub_smoothingFn, Complex.reCLM_norm, Orientation.tan_oangle_add_right_mul_norm_of_oangle_eq_pi_div_two, strictConcaveOn_of_deriv2_neg, 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, MeasureTheory.integral_mul_deriv_eq_deriv_mul_of_integrable, ContinuousMap.norm_smul_const, NNReal.coe_mulSingle, schnirelmannDensity_setOf_Odd, unitInterval.univ_eq_Icc, Metric.Snowflaking.ediam_preimage_toSnowflaking, 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, Continuous.rpow_const, ContinuousMapZero.toNNReal_neg_smul, ProbabilityTheory.integrable_pow_abs_mul_exp_add_of_integrable_exp_mul, 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, VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, ProbabilityTheory.condVar_of_not_integrable, Real.rpow_le_one_iff_of_pos, MeasureTheory.SimpleFunc.map_integral, Metric.Snowflaking.preimage_ofSnowflaking_emetricClosedBall, continuousOn_cfc_nnreal_setProd, blimsup_cthickening_mul_ae_eq, Real.floor_exp_one_eq_two, LinearMap.singularValues_of_lt, InnerProductSpace.euclideanHausdorffMeasure_eq_volume, FormalMultilinearSeries.summable_norm_mul_pow, Real.instIsOrderedAddMonoid, ProbabilityTheory.instIsGaussianMapHAdd, MeasureTheory.exists_upperSemicontinuous_le_integral_le, Metric.dist_le_diam_of_mem', Rat.isUniformEmbedding_coe_real, Asymptotics.isBigOWith_abs_right, AlternatingMap.bound_of_shell_of_norm_map_coord_zero, norm_mul_le, Real.sqrt_div, ContDiffMapSupportedIn.fderivLM_apply_of_gt, Tactic.ComputeAsymptotics.Seq.dist_le_one, ProbabilityTheory.covariance_const_mul_left, SemiNormedGrp.explicitCokernelDesc_norm_le_of_norm_le, InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq_sub_two_mul_norm_mul_norm_mul_cos_angle, Convex.norm_image_sub_le_of_norm_fderiv_le', Real.iteratedDerivWithin_cosh_Ioo, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, IsApproximateSubgroup.pow_inter_pow_covBySMul_sq_inter_sq, ProbabilityTheory.Fernique.logRatio_mono, measurableSet_region_between_cc, Real.norm_rpow_of_nonneg, strictAnti_of_hasDerivAt_neg, Real.toNNReal_eq_one, DiffContOnCl.ball_subset_image_closedBall, NumberField.mixedEmbedding.convexBodySum_convex, Padic.norm_p, Polynomial.Chebyshev.one_le_negOnePow_mul_eval_T_real, Complex.arg_nonneg_iff, ProbabilityTheory.iIndepFun.integral_fun_prod_comp, MeasureTheory.sub_eq_zero_of_upcrossingsBefore_lt, Real.logb_neg, AddMonoidHom.mkNormedAddGroupHom_norm_le', 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, RCLike.iInter_halfSpaces_eq', 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, EuclideanGeometry.Cospherical.subtype_val, RCLike.re_ofReal_mul, gauge_smul_left, Polynomial.Chebyshev.isLocalExtr_T_real, norm_add_pow_two, setOf_liouville_eq_irrational_inter_iInter_iUnion, HasFDerivAt.sqrt, MeasureTheory.measure_smul_setAverage, Padic.norm_natCast_p_sub_one, NumberField.mixedEmbedding.fundamentalCone.mem_idealSet, ContDiffPointwiseHolderAt.iteratedFDeriv, ProbabilityTheory.IndepFun.mgf_add, ContDiffWithinAt.contDiffBump, 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, HasCompactSupport.exist_eLpNorm_sub_le_of_continuous, ProbabilityTheory.gaussianPDFReal_add, UpperHalfPlane.mem_verticalStrip_iff, ENNReal.toReal_top, MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono_left, 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, QuotientAddGroup.exists_norm_add_lt, OrthonormalBasis.toMatrix_orthonormalBasis_mem_orthogonal, ContDiffMapSupportedIn.structureMapCLM_zero_injective, Real.le_sSup_iff, MeasureTheory.integrable_llr_tilted_left, Real.sqrtTwoAddSeries_step_up, MeasureTheory.llr_smul_right, sum_mul_eq_sub_integral_mul, 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, RCLike.iInter_halfSpaces_eq, NumberField.IsCMField.infinitePlace_complexConj, NNReal.one_lt_coe, Hyperreal.coe_neg, NumberField.prod_archAbsVal_eq, Real.rpow_sub, exists_eq_const_mul_setIntegral_of_nonneg, Matrix.IsHermitian.rank_eq_card_non_zero_eigs, unitary.norm_sub_one_sq_eq, Hyperreal.stdPart_omega, inner_self_nonneg, HasFDerivWithinAt.curveIntegral_segment_source', CStarAlgebra.nonneg_TFAE, deriv_sin, Complex.isTheta_ofReal_left, RCLike.normSq_to_complex, ArithmeticFunction.LSeriesSummable_vonMangoldt, IsIntegralCurveAt.continuousAt, Orientation.areaForm_rightAngleRotation_right, MeasurableEquiv.gaussianReal_map_symm_apply, MeasureTheory.setIntegral_condExpL1CLM, Complex.arg_exp, SchwartzMap.lineDerivOp_apply, OrthonormalBasis.orientation_adjustToOrientation, MDifferentiableAt.inner_bundle, NonarchAddGroupNorm.sup_apply, hofer, ProbabilityTheory.HasSubgaussianMGF.zero, NumberField.house_prod_le, Real.deriv_arcsin_aux, Real.exp_approx_end', unitInterval.subtype_Iic_eq_Icc, AnalyticOnNhd.sigmoid, seminormFromConst_bddBelow, Real.rpow_le_rpow_of_exponent_ge_of_imp, Complex.tendsto_log_nhdsWithin_im_nonneg_of_re_neg_of_im_zero, fourier_add', RCLike.continuous_im, IsLocalMin.fderiv_eq_zero, Nat.not_irrational, EuclideanGeometry.Sphere.angle_eq_pi_div_two_iff_mem_sphere_of_isDiameter, ProperCone.hyperplane_separation, lp.norm_eq_ciSup, Module.Basis.map_addHaar, Circle.exp_zsmul, MeasureTheory.Measure.setIntegral_toReal_rnDeriv_eq_withDensity, Real.log_inv, IsLocalMin.lineDeriv_eq_zero, MeasureTheory.tilted_eq_withDensity_nnreal, contDiff_norm_rpow, ProbabilityTheory.IsCondKernelCDF.lintegral, Real.tan_add_nat_mul_pi, spectralNorm_zero_lt, Complex.div_intCast_im, Real.sinh_le_sinh, ContinuousLinearMap.coe_complexOfReal, exists_contDiff_tsupport_subset, MeasureTheory.Integrable.fourier_smul, EReal.toReal_pos, LiouvilleWith.nat_add_iff, Asymptotics.isBigO_nat_atTop_induction_of_eventually_pos, unitInterval.eq_closedBall, Similar.exists_pos_pairwise_dist_eq, InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq', BoxIntegral.unitPartition.tag_apply, IsPrimitiveRoot.arg, ContinuousMap.HomotopyWith.apply_zero, intervalIntegral.continuousOn_primitive_interval', ContDiffBump.nonneg', AddGroupNorm.lt_def, Complex.frontier_setOf_le_re_and_im_le, Real.differentiableAt_qaryEntropy, ArchimedeanClass.le_stdPart_of_le, StieltjesFunction.length_Ioc, MeasureTheory.Measure.setIntegral_comp_smul_of_pos, Complex.norm_log_one_add_half_le_self, MeasureTheory.ae_le_of_forall_setIntegral_le, NNReal.hasSum_coe, ProbabilityTheory.indepFun_iff_integral_comp_mul, Quaternion.hasSum_expSeries_of_imaginary, coe_normGroupSeminorm, Complex.isBigO_comp_ofReal_nhds, ENNReal.toReal_strict_mono, ContinuousMultilinearMap.opNorm_le_iff, Measurable.exp, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_aestronglyMeasurable, MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound, Real.tendsto_sin_pi_div_two, variationOnFromTo.eq_neg_swap, LinearMap.IsSymmetric.re_trace_eq_sum_eigenvalues, hasMellin_cpow_Ioc, intervalIntegral.integral_comp_mul_add, PadicInt.norm_le_one, StrongDual.mem_polar_iff, exists_smooth_forall_mem_convex_of_local, DifferentiableAt.exp, Submodule.Quotient.norm_mk_le, Affine.Simplex.exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter, Real.Angle.cos_sub_pi_div_two, EisensteinSeries.eisensteinSeries_SIF_MDifferentiable, tsum_sq_fourierCoeff, Set.Countable.exists_pos_forall_sum_le, Convex.hasFDerivWithinAt_curveIntegral_segment_of_hasFDerivWithinAt_symmetric, BoundedContinuousFunction.charMonoidHom_apply, RCLike.normSq_add, MeasureTheory.Martingale.eq_condExp_of_tendsto_eLpNorm, Real.arccos_zero, intervalIntegral.integral_pos, Real.rpow_inv_lt_iff_of_pos, Complex.integral_boundary_rect_of_differentiableOn_real, Polynomial.Chebyshev.isExtrOn_T_real, Affine.Simplex.touchpoint_mem_affineSpan_simplex, GroupSeminorm.coe_add, RCLike.div_re, Complex.HadamardThreeLines.sSupNormIm_scale_right, Real.sqrtTwoAddSeries_monotone_left, aemeasurable_derivWithin_Ici, Submodule.isPathConnected, Orientation.inner_smul_rotation_pi_div_two_smul_left, integral_sin_pow, NumberField.mixedEmbedding.fundamentalCone.zero_mem_compactSet, ComputeAsymptotics.MultiseriesExpansion.Multiseries.notMem_nil, mem_closedBall_zero_iff, MeasureTheory.stoppedAbove_le, 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, PhragmenLindelof.eqOn_horizontal_strip, SchwartzMap.coe_apply, MeasureTheory.Measure.addHaar_ball, real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_pos_mul, MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_integral_norm, 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, norm_image_sub_le_of_norm_deriv_right_le_segment, MeasureTheory.eLpNorm_sub_le_of_dist_bdd, Real.sqrt_lt, AntitoneOn.integral_le_sum, summable_indicator_mod_iff_summable_indicator_mod, integral_gaussian_Ioi, NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply, MeasureTheory.condExp_bot', ContinuousAlternatingMap.unit_le_opNorm, Polynomial.Chebyshev.coeff_le_of_forall_abs_le_one, HasDerivAt.lhopital_zero_atTop, setIntegral_re_add_im, PhragmenLindelof.eq_zero_on_quadrant_I, Function.locallyFinsuppWithin.one_isLittleO_logCounting_single, RCLike.geometric_hahn_banach_compact_closed, SchwartzMap.smulLeftCLM_ofReal, Orientation.oangle_smul_right_of_pos, Real.arctan_add_eq_sub_pi, Circle.exp_eq_one, norm_iteratedFDeriv_smul_le, image_norm_le_of_norm_deriv_right_le_deriv_boundary, Complex.ofReal_tsum, HolderWith.dist_le, Real.cosh_eq, realPart_smul, MeasureTheory.ComplexMeasure.equivSignedMeasureₗ_apply, Metric.Sum.mem_uniformity_iff_glueDist, Real.iSup_nonneg_of_nonnegHomClass, StieltjesFunction.measure_Iic, MeasureTheory.lpNorm_smul_measure_of_ne_top, MeasureTheory.measureReal_add_diff, intervalIntegral.integral_Iic_add_Ioi, isLocalMax_of_deriv, PiCountable.dist_eq_tsum, AkraBazziRecurrence.growsPolynomially_one_sub_smoothingFn, abs_real_inner_div_norm_mul_norm_eq_one_iff, HasFDerivAt.hasFDerivAt_norm_smul_pos, ContDiffBump.tendsto_support_normed_smallSets, spectralValue_eq_zero_iff, Orientation.oangle_map_complex, Polynomial.supNorm_eq_iSup, MeasureTheory.exists_eq_setAverage, NNReal.div_rpow, Complex.integral_boundary_rect_eq_zero_of_continuousOn_of_differentiableOn, ContinuousLinearMap.sSup_unitClosedBall_eq_norm, mem_tangentConeAt_iff_exists_seq_norm_tendsto_atTop, Real.strictMonoOn_sin, integrable_exp_neg_mul_sq, ContinuousLinearEquiv.coord_norm, Real.cauchy_mul, fderiv_norm_rpow, Height.mulHeight₁_zero, SlashInvariantForm.slash_action_eqn', ENNReal.rpow_eq_pow, projIcc_eq_zero, MeasureTheory.lpNorm_one', Valuation.norm_pos_iff_valuation_pos, ProbabilityTheory.instIsGaussianProdProdOfSecondCountableTopologyEither, Real.tendsto_toNNReal_atTop, unitInterval.half_le_symm_iff, BoundedContinuousFunction.map_bounded', Complex.norm_eq_sqrt_sq_add_sq, instLocallyConvexSpaceRealOfPolynormableSpace, intervalIntegral.integral_hasDerivAt_left, UpperHalfPlane.cosh_dist', IsExtrFilter.hasLineDerivAt_eq_zero, PartitionOfUnity.mem_fintsupport_iff, HasStrictFDerivAt.cosh, NNReal.inner_le_Lp_mul_Lq_tsum, 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, Real.hasStrictDerivAt_const_rpow, ExistsContDiffBumpBase.w_nonneg, MeasureTheory.FiniteMeasure.continuous_integral_continuousMap, Real.hasSum_pow_div_log_of_abs_lt_one, HasStrictDerivAt.cos, disjoint_interior_extremePoints, RealRMK.range_cut_partition, MeasureTheory.integral_finset, Affine.Simplex.circumsphere_reindex, intervalIntegral.integral_deriv_eq_sub_uIoo, CStarAlgebra.norm_mem_spectrum_of_nonneg, Complex.neg_ofReal_mem_slitPlane, Metric.unitBall.instIsCancelMulZero, ContinuousMap.Homotopy.refl_apply, InnerProductGeometry.cos_angle_sub_mul_norm_of_inner_eq_zero, ProbabilityTheory.integrable_rpow_of_integrable_exp_mul, Real.enorm_eq_ofReal, ContinuousLinearMap.norm_adjoint_comp_self, ContinuousMap.HomotopyWith.cast_apply, summable_norm_sum_mul_antidiagonal_of_summable_norm, Real.tanh_sq_lt_one, unitary.norm_argSelfAdjoint_le_pi, Real.rpowIntegrand₀₁_le_rpow_sub_one, AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_le_nat, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWith, Real.rpow_lt_rpow_iff, QuotientGroup.norm_eq_groupSeminorm, ContDiffBump.tsupport_normed_eq, Real.eq_one_of_pos_of_logb_eq_zero, Orientation.inner_smul_rotation_pi_div_two_smul_right, spectralNorm_zero, RCLike.geometric_hahn_banach_point_closed, GaussianFourier.verticalIntegral_norm_le, summable_norm_pow_mul_geometric_of_norm_lt_one, unitInterval.eq_one_or_eq_zero_of_le_mul, dist_le_Ico_sum_of_dist_le, Asymptotics.IsLittleO.sum_range, MeasureTheory.integral_bilinear_hasDerivAt_eq_sub, Real.cos_arctan_pos, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_restrict_densityProcess_limitProcess, ContinuousAt.integral_sub_linear_isLittleO_ae, CircleIntegrable.out, NNReal.rpow_inv_natCast_pow, Besicovitch.exists_disjoint_closedBall_covering_ae_aux, RCLike.intervalIntegral_ofReal, Set.OrdConnected.image_hasDerivWithinAt, AddCircle.closedBall_ae_eq_ball, PadicInt.mem_nonunits, Real.le_inv_mul_exp, PadicInt.complete, Irrational.eventually_forall_le_dist_cast_rat_of_den_le, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_image_preimage_expMapBasis, IntervalIntegrable.ae_hasDerivAt_integral, SchwartzMap.integrable_pow_mul, ProbabilityTheory.covariance_const_add_right, Quaternion.instNormOneClassReal, Complex.borelCaratheodory, Complex.le_def, Orientation.cos_oangle_sub_left_of_oangle_eq_pi_div_two, Cardinal.mk_Ico_real, ZLattice.tsumNormRPowBound_pos, Convex.closure_subset_image_homothety_interior_of_one_lt, MeasureTheory.memLp_of_bounded, LipschitzWith.mapsTo_closedBall, Real.Icc_mem_vitaliFamily_at_right, ContinuousMultilinearMap.norm_map_cons_le, KuratowskiEmbedding.exists_isometric_embedding, Complex.div_natCast, ContinuousMultilinearMap.norm_smulRight, IsometricContinuousFunctionalCalculus.isGreatest_norm_spectrum, Real.rpow_mul, BumpCovering.toPOUFun_eq_mul_prod, Real.analyticOnNhd_sinh, MeasureTheory.integrableOn_Ioi_of_intervalIntegral_norm_tendsto, antitoneOn_of_deriv_nonpos, ConcaveOn.le_map_set_average, Complex.ofReal_comp_neg, Real.zpow_arith_mean_le_arith_mean_zpow, instSMulCommClass_sphere_closedBall_ball, curveIntegral_def', Real.expPartialHomeomorph_source, ModularGroup.det_coe, NumberField.FinitePlace.instNonarchimedeanHomClassReal, MeasureTheory.SignedMeasure.null_of_totalVariation_zero, NormedField.exists_norm_lt, AkraBazziRecurrence.continuous_sumCoeffsExp, Real.Angle.toReal_le_pi, MeasureTheory.rnDeriv_tilted_right, 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, Real.hasDerivAt_fourierIntegral, ProbabilityTheory.IndepFun.exp_mul, IntervalIntegrable.smul, CStarAlgebra.isBasis_nonneg_sections, EuclideanSpace.measurableEquiv_toEquiv, mulIndicator_cthickening_eventually_eq_mulIndicator_closure, MeasureTheory.Measure.toSphere_eq_zero_iff_finrank, fourier_add_half_inv_index, 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, Affine.Simplex.Equilateral.angle_eq_pi_div_three, MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono, EuclideanGeometry.dist_sq_add_dist_sq_eq_two_mul_dist_midpoint_sq_add_half_dist_sq, StrictMonoOn.exists_slope_lt_deriv, EuclideanGeometry.cospherical_iff_exists_mem_of_finiteDimensional, fourierCoeffOn_of_hasDerivAt, NonarchAddGroupSeminorm.coe_le_coe, Hyperreal.tendsto_ofSeq, ContinuousAlternatingMap.bound, EuclideanGeometry.inner_pos_of_dist_lt_radius, EuclideanGeometry.existsUnique_dist_eq_of_insert, ProbabilityTheory.mgf_pos, gauge_add_le, Affine.Simplex.circumradius_reindex, lipschitzWith_iff_norm_inv_mul_le, AnalyticOn.re_ofReal, MeasureTheory.Submartingale.memLp_limitProcess, Real.Angle.two_nsmul_neg_pi_div_two, UpperHalfPlane.IsZeroAtImInfty.slash, Metric.Sigma.dist_triangle, isCompact_cantorSet, IsLocalMax.norm_add_self, NumberField.InfinitePlace.one_le_of_lt_one, AffineIndependent.existsUnique_dist_eq, MeasureTheory.JordanDecomposition.real_smul_negPart_nonneg, Real.cosh_sq_sub_sinh_sq, continuousOn_taylorWithinEval, CFC.negPart_smul, Path.extend_of_le_zero, NormedSpace.polar_closedBall, ArithmeticFunction.vonMangoldt_mul_zeta, NumberField.mixedEmbedding.fundamentalCone.smul_mem_iff_mem, MeasureTheory.Measure.IicSnd_ac_fst, MeasureTheory.eLpNorm_enorm_rpow, Submodule.norm_orthogonalProjection, Seminorm.coe_iSup_eq, unitInterval.sigmoid_pos, IsBoundedBilinearMap.bound, Real.Lp_add_le_hasSum_of_nonneg, EisensteinSeries.E_qExpansion_coeff_zero, Asymptotics.isBigO_iff_eventually, Real.volume_uIoc, prod_vanishing_of_summable_norm, ClosedSubmodule.symplComp_sup, Polynomial.norm_root_le_one_of_mahlerMeasure_eq_one, RingSeminorm.apply_one, EReal.nhds_coe_coe, MeasureTheory.integral_one_sub_of_ae_eq_zero_or_one, Asymptotics.IsBigOWith.bound, ContinuousMapZero.toNNReal_smul, Hyperreal.coe_mul, intervalIntegral.integral_interval_add_Ioi, intervalIntegral.integral_eq_integral_of_support_subset, Real.continuousAt_log, integrable_mulExpNegMulSq_comp, SmoothBumpFunction.support_subset_source, integrable_cexp_quadratic, MeasureTheory.Measure.toSignedMeasure_restrict_eq_restrict_toSignedMeasure, CircleDeg1Lift.translationNumber_pow, AffineSubspace.signedInfDist_apply_self, Metric.isBounded_iff_exists_ge, ProbabilityTheory.gaussianReal_div_const, Complex.image_exp_Ioc_eq_sphere, Bornology.IsBounded.exists_pos_norm_le, CFC.log_algebraMap, ContinuousLinearMap.opNorm_lsmul, MeasureTheory.setIntegral_nonneg_of_ae, Real.ringEquivCauchy_apply, expNegInvGlue.zero, deriv_pos_right_of_sign_deriv, CuspFormClass.exp_decay_atImInfty, EuclideanGeometry.Sphere.IsIntTangent.dist_center, norm_le_insert, Real.posLog_nonneg, Complex.measurable_ofReal, Real.mul_iSup_of_nonpos, Real.arcosh_eq_zero_iff, approxOrderOf.image_pow_subset, KuratowskiEmbedding.embeddingOfSubset_coe, integral_sin_sq_mul_cos_sq, ProbabilityTheory.covarianceBilinDual_of_not_memLp, HurwitzZeta.completedHurwitzZetaEven_residue_zero, CircleIntegrable.abs, NumberField.mixedEmbedding.fundamentalCone.mem_integerSet, Real.le_log_of_rpow_le, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self_of_isProbabilityMeasure, fderivWithin_arctan, TemperedDistribution.smulLeftCLM_smul, TFAE_exists_lt_isLittleO_pow, norm_inf_le_add, Seminorm.continuous_of_continuousAt_zero, integral_mul_rpow_one_add_sq, irrational_intCast_add_iff, MeasureTheory.MemLp.integrable_enorm_rpow, Real.summable_Lr_of_Lp_Lq_of_nonneg, isScalarTower_closedBall_closedBall_ball, Real.sqrt_mul', Metric.infDist_eq_iInf, MeasureTheory.measureReal_biUnion_eq_sum_powerset, unitInterval.symm_involutive, Real.isSquare_iff, Cardinal.Real.Ioo_countable_iff, StrictMonoOn.exists_deriv_lt_slope, EuclideanSpace.euclideanHausdorffMeasure_eq_volume, 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, ContinuousMultilinearMap.opNorm_le_bound, 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, ProbabilityTheory.continuous_mgf, BoxIntegral.hasIntegral_iff, Int.tendsto_coe_cofinite, integral_bilinear_hasFDerivAt_right_eq_neg_left_of_integrable, 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, Real.rpow_of_add_eq, MeasureTheory.integrable_withDensity_iff, summable_geometric_of_lt_one, ConvexBody.coe_add, exists_tsupport_one_of_isOpen_isClosed, EuclideanGeometry.inversion_eq_center', NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace, instIsConvexMetricSpace, ContinuousMultilinearMap.norm_def, NNReal.coe_tsum, NormedSpace.double_dual_bound, thickening_ball, Real.mk_neg, ProbabilityTheory.condVar_ae_eq_condExp_sq_sub_sq_condExp, curveIntegralFun_trans_of_lt_half, fourierCoeffOn.const_smul, NumberField.mixedEmbedding.det_fderivPolarCoordRealSymm, Real.log_nonpos_iff, Asymptotics.IsBigO.norm_right, spectralAlgNorm_isPowMul, Affine.Simplex.inradius_pos, abs_integral_sub_setIntegral_mulExpNegMulSq_comp_lt, NNReal.coe_list_sum, PeriodPair.indep, Real.exp_bound_div_one_sub_of_interval', norm_sub_pow_two, UpperHalfPlane.tanh_half_dist, HasSum.rexp, AddCircle.pathConnectedSpace, MulRingNorm.apply_one, MeasureTheory.MemLp.enorm_rpow_div, Real.fourierInv_eq, intervalIntegral.sub_le_integral_of_hasDeriv_right_of_le_Ico, CFC.isUnit_nnrpow_iff, LSeries.norm_term_le, Module.Basis.opNorm_le, Real.continuousOn_rpowIntegrand₀₁, ProbabilityTheory.beta_pos, Archimedean.embedReal_one, ContMDiff.codRestrict_sphere, Real.differentiable_rpow_const, ProbabilityTheory.integrable_exp_mul_of_mem_Icc, AEMeasurable.sqrt, isConformalMap_complex_linear, unitInterval.volume_uIoc, Real.Angle.toReal_coe_eq_self_add_two_pi_iff, Real.tsum_eq_tsum_fourierIntegral, Real.zero_at_infty_vector_fourierIntegral, Real.sSup_of_not_bddAbove, ModularForm.coe_translate, Real.map_toNNReal_atTop, Real.rpow_add_intCast, ENNReal.fun_eq_funMulInvSnorm_mul_eLpNorm, MeasureTheory.integral_Icc_deriv_smul_of_deriv_nonpos, ProperCone.innerDual_iUnion, ContDiffBump.le_one, lipschitzWith_max, RCLike.conj_eq_re_sub_im, dist_le_of_le_geometric_of_tendsto, SchwartzMap.smulLeftCLM_apply, MeasureTheory.Integrable.norm, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self, NumberField.mixedEmbedding.fundamentalCone.expMap_sum, Real.uniformContinuous_mul, norm_injOn_ray_left, IsExtrOn.hasLineDerivAt_eq_zero, SzemerediRegularity.card_biUnion_star_le_m_add_one_card_star_mul, MeasureTheory.ofReal_average, SchwartzMap.tsum_eq_tsum_fourierIntegral, MeasureTheory.integrableOn_Ioi_comp_mul_right_iff, MeasureTheory.SignedMeasure.of_diff_eq_zero_of_symmDiff_eq_zero_positive, Complex.monotone_ofReal, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, Orientation.kahler_rightAngleRotation_right, NNReal.rpow_add_of_nonneg, Real.expPartialHomeomorph_target, Real.smoothTransition.monotone, NNReal.rpow_self_rpow_inv, Polynomial.mul_star_dvd_of_aeval_eq_zero_im_ne_zero, InnerProductSpace.Core.re_inner_smul_ofReal_smul_self, Real.Angle.sin_antiperiodic, Polynomial.Chebyshev.node_eq_one, AddCircle.norm_eq', ContinuousLinearMap.norm_snd, ProbabilityTheory.cdf_paretoMeasure_eq_lintegral, WithSeminorms.continuous_iff_continuous_comp, ProbabilityTheory.integrable_pow_of_integrable_exp_mul, Chebyshev.intervalIntegrable_one_div_log_sq, ENNReal.strictMono_rpow_of_pos, WeakDual.seminormFamily_apply, ENNReal.add_rpow_le_two_rpow_mul_rpow_add_rpow, Real.lt_logb_iff_rpow_lt_of_base_lt_one, NumberField.Units.finrank_mul_regulator_eq_det, Path.range_subpath_of_le, IsApproximateAddSubgroup.card_add_self_le, NormedAddGroupHom.Equalizer.norm_lift_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, NumberField.rootDiscr_rat, CFC.monotoneOn_cfcₙ_rpowIntegrand₀₁, UpperHalfPlane.neg_smul, Quaternion.linearIsometryEquivTuple_apply, norm_fderiv_le_of_lip', map_sub_le_max, EuclideanGeometry.Sphere.orthRadius_parallel_orthRadius_iff, MeasureTheory.isAddHaarMeasure_euclideanHausdorffMeasure, Complex.norm_cpow_le, MeasureTheory.integral_Iic_mul_deriv_eq_deriv_mul, Stirling.stirlingSeq_pow_four_div_stirlingSeq_pow_two_eq, Real.analyticWithinAt_cosh, MeasureTheory.lpNorm_const, Real.artanh_injOn, NumberField.InfinitePlace.prod_eq_abs_norm, ContinuousLinearMap.rayleighQuotient_neg_apply, MeasureTheory.intervalIntegrable_charFun, InnerProductGeometry.inner_eq_cos_angle_of_norm_eq_one, Real.strictMonoOn_tan, MeasureTheory.Lp.dense_hasCompactSupport_contDiff, Real.volume_Ioi, Polynomial.tendsto_div_exp_atTop, integral_Iic_inv_one_add_sq, Complex.arg_eq_nhds_of_re_neg_of_im_neg, IsRiemannianManifold.out, Real.rpow_rpow_inv, Real.pow_lt_of_lt_log, SmoothPartitionOfUnity.toPartitionOfUnity_toFun, isIntegral_two_mul_cos_rat_mul_pi, fderiv_cosh, ConvexOn.isMinOn_of_leftDeriv_eq_zero, PiTensorProduct.injectiveSeminorm_tprod_le, Real.lt_toNNReal_iff_coe_lt, CFC.rpow_zero, NNReal.rpow_one, Height.mulHeight_eval_le', Complex.isAbsoluteValueNorm, ExistsContDiffBumpBase.u_nonneg, IsOpen.affineSpan_eq_top, ENNReal.tendsto_toReal_iff, HurwitzZeta.isBigO_atTop_cosKernel_sub, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_integral_of_monotone, Monotone.cauchySeq_alternating_series_of_tendsto_zero, ProbabilityTheory.integrable_rpow_of_mem_interior_integrableExpSet, ContinuousOn.rexp, Real.log_pos_of_lt_neg_one, EuclideanGeometry.inner_vsub_vsub_of_mem_sphere_of_mem_sphere, Real.arccos_nonneg, 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, Convex.image_hasDerivWithinAt, one_add_mul_self_lt_rpow_one_add, Seminorm.mem_closedBall, rothNumberNat_le_ruzsaSzemerediNumberNat', ContinuousLinearMap.norm_holderL_le, fourier_add, SmoothPartitionOfUnity.contMDiff_smul, Asymptotics.IsBigOWith.right_le_add_of_lt_one, Real.borel_eq_generateFrom_Iic_rat, Real.rpow_lt_rpow_of_exponent_gt, ProbabilityTheory.condIndepFun_iff, gaugeSeminorm_lt_one_of_isOpen, tendsto_smoothingFun_of_eq_zero, ENNReal.le_rpow_self_of_one_le, cantorSet_eq_union_halves, Path.Homotopy.symm₂_apply, Real.compact_inner_le_weight_mul_Lp_of_nonneg, isLittleO_pow_const_const_pow_of_one_lt, PolynormableSpace.withSeminorms, Affine.Triangle.sSameSide_affineSpan_pair_excenter_singleton_point, unitInterval.add_pos, MeasureTheory.charFun_eq_integral_innerProbChar, NNReal.Lr_rpow_le_Lp_mul_Lq, Complex.re_nsmul, Topology.CWComplex.mapsTo, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, Metric.nhds_basis_closedBall_inv_nat_succ, LinearMap.polar_mem_iff, interval_average_eq, MeasureTheory.integral_mul_deriv_eq_deriv_mul, Asymptotics.IsBigOWith.sub, RightDerivMeasurableAux.B_mem_nhdsGT, Complex.isLittleO_ofReal_right, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsum, NonarchAddGroupSeminorm.add_le_max', Real.cos_eq_neg_one_iff, Real.abs_cos_eq_one_iff, ContractingWith.dist_fixedPoint_fixedPoint_of_dist_le', IsApproximateAddSubgroup.nsmul_inter_nsmul_covByVAdd_sq_inter_sq, gaugeSeminormFamily_ball, norm_sub_norm_le_norm_inv_mul, Complex.edist_of_im_eq, NumberField.HeightOneSpectrum.toNNReal_valued_eq_adicAbv, ValueDistribution.characteristic_top_mul_eventually_le, Real.volume_Ioo, IsLocalMax.hasDerivAt_eq_zero, HolderOnWith.ediam_image_le, ProbabilityTheory.HasGaussianLaw.eval, 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, Real.toNNReal_rpow_of_nonneg, BoxIntegral.norm_integral_le_of_norm_le, instNonemptySeedRatReal, UpperHalfPlane.σ_eventuallyEq, Asymptotics.IsBigOWith.const_mul_left, HolderOnWith.edist_le_of_le, SchwartzMap.instFourierInvSMul, Hyperreal.coe_le_coe, NumberField.mulHeight₁_eq, Seminorm.comp_smul_apply, differentiableWithinAt_complex_iff_differentiableWithinAt_real, IsExtrFilter.lineDeriv_eq_zero, Differentiable.rpow_const, Real.sin_sub_two_pi, TemperedDistribution.derivCLM_apply_apply, EReal.exists_between_coe_real, gauge_lt_eq, Real.cos_sub, HurwitzZeta.hasSum_int_completedCosZeta, NormedAddGroupHom.norm_def, NNReal.rpow_left_surjective, Real.aemeasurable_of_aemeasurable_exp, Real.Wallis.W_succ, Complex.Gamma_def, integral_cos_sq, TorusIntegrable.function_integrable, EReal.coe_ennreal_ofReal, NumberField.mixedEmbedding.volume_eq_two_pi_pow_mul_integral, EuclideanGeometry.two_zsmul_oangle_orthogonalProjection_self, ENNReal.toReal_div, has_unit_speed_naturalParameterization, MeasureTheory.L1.setToL1'_eq_setToL1SCLM, ProbabilityTheory.mgf_smul_measure, intervalIntegral.derivWithin_integral_left, lipschitzWith_iff_norm_neg_add_le, Metric.isBounded_iff_subset_closedBall, ContinuousAlternatingMap.norm_compContinuousLinearMap_le, NNReal.exists, integral_re, HasStrictFDerivAt.sinh, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne_eq_image, Real.le_logb_iff_rpow_le_of_base_lt_one, Real.negMulLog_zero, Stirling.tendsto_stirlingSeq_sqrt_pi, RCLike.tendsto_ofReal_atBot_cobounded, MeasureTheory.isTightMeasureSet_range_iff_tendsto_limsup_measure_norm_gt, ENNReal.ofReal_min, circleIntegrable_posLog_norm_meromorphicOn_of_nonneg, ContinuousMap.exists_mem_subalgebra_near_continuous_of_separatesPoints, ProbabilityTheory.HasSubgaussianMGF.sum_of_hasCondSubgaussianMGF, MeasureTheory.Supermartingale.smul_nonneg, norm_zpow_le_mul_norm, Real.arcsin_eq_arctan, NormedSpace.norm_normalize, abs_signedDist_le_dist, DirichletCharacter.LFunction_isBigO_horizontal, Complex.frontier_setOf_lt_re, EuclideanGeometry.Sphere.instNonemptySubtypeMemAffineSubspaceRealOrthRadius, EuclideanGeometry.tan_oangle_left_of_oangle_eq_pi_div_two, 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', MeasureTheory.Measure.addHaarScalarFactor_eq_integral_div_of_continuous_nonneg_pos, HurwitzZeta.LSeriesHasSum_sin, ruzsaSzemerediNumberNat_asymptotic_lower_bound, SlashInvariantFormClass.petersson_smul, spectrum_realPart', Metric.continuousOn_iff, hasDerivWithinAt_Ici_of_tendsto_deriv, NNReal.rpow_of_add_eq, NumberField.InfinitePlace.map_natCast, ModularGroup.three_lt_four_mul_im_sq_of_mem_fdo, NumberField.Units.sum_mult_mul_log, Real.cos_eq_sqrt_one_sub_sin_sq, Real.hasStrictFDerivAt_rpow_of_neg, InformationTheory.kraft_mcmillan_inequality, ENNReal.rpow_lt_top_of_nonneg, CFC.norm_mul_mul_star_self_of_nonneg, Rat.isEmbedding_coe_real, Real.qaryEntropy_pos, intervalIntegral.FTCFilter.pure_le, Real.arccos_le_arccos, intervalIntegral.deriv_integral_of_tendsto_ae_left, Real.tendsto_log_nhdsNE_zero, norm_div_pos_iff, Complex.isometryOfOrthonormal_symm_apply, Real.hasStrictDerivAt_rpow_const, closedBall_sub_closedBall, ContinuousMap.Homotopy.extend_one, Complex.arg_mul_cos_add_sin_mul_I_sub, ContDiffPointwiseHolderAt.zero_exponent_iff, ENNReal.ofReal_lt_one, Real.arcsin_le_iff_le_sin, Real.isLUB_sSup, MeasureTheory.weightedSMul_smul_measure, unitInterval.tendsto_sigmoid_atBot, MeasureTheory.integrable_count_iff, UpperHalfPlane.σ_mul_comm, norm_le_zero_iff', Real.integral_rpowIntegrand₀₁_eq_rpow_mul_const, RCLike.normSq_apply, IsAntichain.volume_eq_zero, Real.isGLB_sInf, LipschitzWith.uniformly_bounded, MeasureTheory.exists_le_average, intervalIntegral.integral_hasFDerivAt, ProperCone.innerDual_toSubmodule, NNReal.coe_zpow, irrational_intCast_div_iff, Real.tanh_arsinh, Real.lt_rpow_of_log_lt, 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, MeasureTheory.Submartingale.exists_ae_trim_tendsto_of_bdd, InnerProductSpace.HarmonicAt.comp_CLM, Metric.diam_one, Metric.hausdorffDist_le_of_infDist, Orientation.inner_rightAngleRotation_self, Complex.intCast_im, Metric.cauchySeq_iff', NormedGroup.uniformity_basis_dist, Real.exp_one_gt_two, ValueDistribution.proximity_coe, HasDerivAt.lhopital_zero_atTop_on_Ioi, IsApproximateAddSubgroup.addSubgroup, Besicovitch.SatelliteConfig.exists_normalized, smul_closedBall, ModularForm.coe_trace, Metric.Snowflaking.image_toSnowflaking_ball, Real.cos_pi_div_three, integrable_mul_cexp_neg_mul_sq, MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound, MeasureTheory.setIntegral_le_nonneg, MeasureTheory.integral_toReal_rnDeriv_mul, RCLike.ofRealCLM_coe, NumberField.InfiniteAdeleRing.ringEquiv_mixedSpace_apply, ProbabilityTheory.instIsGaussianMapHSub_1, Real.tanh_zero, Valued.integer.norm_coe_unit, ENNReal.ofReal_mul', ProbabilityTheory.HasCondSubgaussianMGF.integrable_exp_mul, Complex.frontier_setOf_le_im, Complex.GammaIntegral_convergent, MeasureTheory.hausdorffMeasure_homothety_preimage, TestFunction.lineDerivCLM_apply_of_gt, zero_lt_one_add_norm_sq', MeasureTheory.SimpleFunc.setToSimpleFunc_smul_real, AmpleSet.of_one_lt_codim, WithSeminorms.isVonNBounded_iff_seminorm_bounded, DifferentiableAt.arctan, HurwitzZeta.sinZeta_eq, Real.one_lt_rpow, InnerProductSpace.HarmonicOnNhd.exists_analyticOnNhd_ball_re_eq, Real.Icc_eq_closedBall, InnerProductSpace.Core.normSq_eq_zero, EuclideanGeometry.Sphere.IsTangent.radius_le_dist_center, ball_sub_ball, norm_sub_mul_le, Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius, ProbabilityTheory.IndepFun.charFun_map_fun_add_eq_mul, InnerProductSpace.laplacian_CLE_comp_left, MeasureTheory.tendsto_iff_forall_lipschitz_integral_tendsto, seminormFromBounded_bddAbove_range, HasStrictDerivAt.complexToReal_fderiv, intervalIntegral.fderiv_integral, EuclideanGeometry.Sphere.isIntTangent_self_iff, Real.le_sin_mul, GroupSeminorm.add_apply, Real.cos_zero, intervalIntegral.integral_unitInterval_deriv_eq_sub, Polynomial.norm_coeff_le_choose_mul_mahlerMeasure, ProbabilityTheory.gaussianReal_apply_eq_integral, MeasureTheory.tendsto_limUnder_of_hasDerivAt_of_integrableOn_Ioi, EuclideanGeometry.affineIndependent_iff_of_two_zsmul_oangle_eq, eventually_norm_trivializationAt_lt, integral_withDensity_eq_integral_smul₀, NNReal.toReal_liminf, Real.rpowIntegrand₀₁_apply_mul', Asymptotics.IsEquivalent.rpow, hasCompactSupport_norm_iff, NormedAddGroupHom.opNorm_zero, PadicInt.norm_natCast_zmodRepr_eq_iff, ENNReal.young_inequality, Complex.ofReal_nnqsmul, ModularGroup.coe_fdo, ConvexOn.exists_affine_le_of_lt, ProbabilityTheory.IsGaussian.charFunDual_eq', norm_lt_iff_of_nonempty_compactlySupported, BoxIntegral.Prepartition.eventually_splitMany_inf_eq_filter, mulIndicator_thickening_eventually_eq_mulIndicator_closure, Real.tan_sub, convex_halfSpace_re_gt, Real.sum_sqrt_mul_sqrt_le, 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, Height.mulHeight_eval_ge', NormedSpace.toLocallyConvexSpace', NumberField.mixedEmbedding.pos_of_notMem_negAt_plusPart, Real.HolderTriple.inv_pos', lp.norm_mono, isConnected_setOf_sameRay, Real.strictMonoOn_rpow_Ici_of_exponent_pos, 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, IsClosed.upperClosure_pi, ProbabilityTheory.covariance_zero_left, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, NonarchAddGroupSeminorm.coe_sSup_apply', ContinuousAt.cfc_nnreal, Filter.Tendsto.nnrpow, Real.limsSup_of_not_isBounded, Real.logb_neg_iff, Path.coe_reparam, MulRingSeminorm.ext_iff, MeasureTheory.integrableOn_Ioi_comp_rpow_iff, Metric.unitClosedBall.coe_zero, CompareReals.compare_uc, SmoothBumpFunction.nhdsWithin_range_basis, RealRMK.le_rieszMeasure_tsupport_subset, Finset.small_nsmul_of_small_tripling, Real.rexp_tsum_eq_tprod, Complex.one_re, AffineSubspace.signedInfDist_apply_of_mem, Submodule.Quotient.norm_mk_lt, Real.isLittleO_pow_log_id_atTop, Real.holderConjugate_one_div, ContinuousLinearMap.bound, ProbabilityTheory.analyticOnNhd_complexMGF, MeasureTheory.eLpNorm_le_eLpNorm_fderiv, 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, ODE.continuousOn_comp, Asymptotics.IsBigO.pow_of_le_right, Real.rpow_right_inj, Real.multipliable_of_summable_log', NumberField.mixedEmbedding.convexBodyLT'_neg_mem, Orientation.norm_div_cos_oangle_sub_right_of_oangle_eq_pi_div_two, EuclideanGeometry.dist_inversion_center, Real.probChar_apply, StrongDual.polar_singleton, AEMeasurable.coe_nnreal_real, intervalIntegral.integral_mul_deriv_eq_deriv_mul_of_hasDerivWithinAt, spectralValueTerms_of_lt_natDegree, Real.Angle.toReal_eq_pi_div_two_iff, NNReal.list_prod_map_rpow, Real.hasDerivAt_Gamma_nat, Real.exists_isLUB, ordinaryHypergeometricSeries_norm_div_succ_norm, EuclideanGeometry.cos_eq_one_iff_angle_eq_zero, Complex.abs_cpow_inv_two_im, MeasureTheory.L1.SimpleFunc.setToL1SCLM_nonneg, Path.coe_mk', Orientation.oangle_smul_right_self_of_nonneg, Path.truncate_one_one, Disjoint.exists_thickenings, Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitary, HasStrictFDerivAt.inner, Real.logb_neg_eq_logb, TopologicalGroup.IsSES.integrate_mono, NumberField.Units.regulator_eq_det', Complex.ofReal_pow, Height.AdmissibleAbsValues.product_formula, UpperHalfPlane.im_pnat_div_pos, ContDiffWithinAt.sin, ContDiffMapSupportedIn.iteratedFDerivLM_apply_of_gt, EuclideanGeometry.sin_pos_of_not_collinear, Polynomial.finite_mahlerMeasure_le, ContinuousMap.HomotopyRel.pi_apply, Cardinal.not_countable_real, Diffeology.DSmooth.contDiff, Real.map_exp_atTop, MeasureTheory.lintegral_deriv_eq_volume_image_of_monotoneOn, dist_le_of_le_geometric_two_of_tendsto₀, MeasureTheory.ContinuousMap.inner_toLp, AEMeasurable.cos, PiLp.nnnorm_toLp_const, Metric.nhdsWithin_basis_ball, ConvexOn.apply_rnDeriv_ae_le_integral, re_inner_le_norm, differentiableAt_abs, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat_rat, dist_norm_norm_le_norm_inv_mul, InnerProductGeometry.continuousAt_angle, IsLowerSet.null_frontier, le_gauge_of_subset_closedBall, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul', ENNReal.toReal_le_add, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, tendsto_const_div_pow, Asymptotics.isLittleO_pow_sub_sub, intervalIntegral.norm_integral_le_abs_of_norm_le, ConvexOn.real_sSup_of_nat_affine_eq, Nat.Prime.irrational_sqrt, Complex.norm_le_sqrt_two_mul_max, MeasureTheory.integrable_fun_norm_addHaar, integral_bilinear_fderiv_right_eq_neg_left_of_integrable, Polynomial.Chebyshev.abs_eval_T_real_le_one_iff, ProbabilityTheory.analyticAt_iteratedDeriv_mgf, skewAdjoint.I_smul_neg_I, NumberField.mixedEmbedding.polarCoordReal_target, MeasureTheory.integral_norm_eq_pos_sub_neg, Real.continuousAt_arctan, unitInterval.two_mul_sub_one_mem_iff, Real.posLog_sum, hasSum_zeta_nat, ProbabilityTheory.isGaussian_stdGaussian, 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, Orientation.oangle_add_left_eq_arccos_of_oangle_eq_pi_div_two, ProbabilityTheory.IsRatCondKernelCDF.integrable, Real.arcosh_surjOn, Orientation.inner_rev_eq_zero_of_oangle_eq_pi_div_two, Real.cos_add_int_mul_pi, MeasureTheory.sum_measureReal_le_measureReal_univ, Ideal.Quotient.norm_mk_le, Complex.coe_basisOneI, NNReal.mul_rpow, Real.logb_nonneg_iff, UpperHalfPlane.instContinuousSMulSL2R, Real.finset_prod_rpow, Affine.Simplex.height_reindex, ProbabilityTheory.charFun_gaussianReal, Cardinal.mk_Ioc_real, exists_eq_interval_average, Real.doublingGamma_one, exists_smooth_zero_one_nhds_of_isClosed, HasFDerivAt.cosh, measurable_infDist, CFC.abs_smul, ValueDistribution.characteristic_sum_top_eventuallyLE, ZLattice.sum_piFinset_Icc_rpow_le, derivWithin_sinh, 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.sin_le, 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, DifferentiableOn.norm, Diffeology.IsPlot.dSmooth_comp, Affine.Simplex.inradius_map, Complex.map_isometryOfOrthonormal, IsApproximateSubgroup.one_le, integral_exp_Iic_zero, exists_hasDerivWithinAt_eq_of_ge_of_le, Real.fib_succ_sub_goldenConj_mul_fib, IsUltrametricDist.isNonarchimedean_nnnorm, MeasureTheory.tilted_apply_eq_ofReal_integral', ValueDistribution.logCounting_coe, AnalyticOnNhd.log, SmoothBumpFunction.eventuallyEq_one, OpenPartialHomeomorph.unitBallBall_symm_apply, Real.tan_arcsin, AddChar.zmod_intCast, quasispectrum.instCompactSpaceNNReal, TemperedDistribution.fourierTransformInv_apply, HasDerivAt.sin, 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, tendsto_integral_comp_smul_smul_of_integrable', Real.tanh_injective, NormedDivisionRing.norm_le_one_of_discrete, Real.arcsin_eq_neg_pi_div_two, Real.cosh_add, IsMaxOn.hasLineDerivWithinAt_eq_zero, MeasureTheory.eval_integral_piLp, ContDiffOn.norm, Polynomial.gaussNorm_nonneg, 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, Real.diam_Ioc, SpectrumRestricts.lt_nnreal_iff, MeasureTheory.exists_upperSemicontinuous_lt_integral_gt, EuclideanGeometry.Sphere.secondInter_eq_lineMap, RCLike.mul_re_ax, MeasureTheory.mul_upcrossingsBefore_le, sum_mul_eq_sub_integral_mul₀, measurable_derivWithin_Ici, IsIntegralCurveAt.comp_add, Real.sin_sub_int_mul_two_pi, HasDerivWithinAt.exp, intervalIntegral.continuous_primitive, ProbabilityTheory.integrable_cauchyPDFReal, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, hasFDerivWithinAt_iff_tendsto, instSMulCommClass_sphere_sphere_closedBall, UpperHalfPlane.contMDiff_smul, Complex.measurableEquivRealProd_symm_apply, dist_le_pi_dist, Complex.isHomeomorphicTrivialFiberBundle_im, MeasureTheory.integral_llr_tilted_right, 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, HurwitzZeta.hasSum_int_completedSinZeta, ProbabilityTheory.IndepFun.charFun_map_add_eq_mul, NNReal.rpow_le_rpow_iff, Matrix.IsHermitian.mulVec_eigenvectorBasis, ContinuousMultilinearMap.le_opNorm_mul_pow_of_le, 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, Height.mulHeight_fun_mul_eq, NumberField.InfinitePlace.LiesOver.isometry_algebraMap, EuclideanGeometry.inversion_zero_radius, ContinuousMap.uniform_continuity, ProbabilityTheory.truncation_nonneg, dist_inf_sup_pi, ContDiffBump.rIn_pos, Quaternion.hasSum_coe, CircleDeg1Lift.map_map_zero_le, Real.fourierInv_eq', UniformFun.dist_def, Continuous.arsinh, Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div', tendsto_log_mul_rpow_nhdsGT_zero, UpperHalfPlane.tendsto_comap_im_ofComplex, signedDist_apply_linear, EuclideanGeometry.Sphere.secondInter_map, Asymptotics.isBigOWith_inv, 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, Polynomial.negOnePow_mul_eval_lt_zero_of_lt_roots_of_leadingCoeff_nonpos, MeasureTheory.Measure.toSignedMeasure_zero, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, ProbabilityTheory.integrable_poissonMeasure_iff, Complex.cos_ofReal_im, Bundle.RiemannianMetric.continuousAt, Real.rpow_inv_le_iff_of_pos, StrictConcaveOn.leftDeriv_lt_slope, dist_add_dist_of_mem_segment, ContDiff.real_of_complex, AkraBazziRecurrence.injective_sumCoeffsExp, LinearMap.IsSymmetric.toMatrix_eigenvectorBasis, MeasureTheory.charFun_zero, integral_re_add_im, IsUltrametricDist.norm_prod_le_of_forall_le_of_nonneg, continuous_stereoInvFun, parallelepiped_orthonormalBasis_one_dim, HurwitzZeta.hasSum_nat_hurwitzZetaOdd_of_mem_Icc, Real.fourierIntegral_deriv, MeasureTheory.measureReal_eq_zero_iff, EuclideanGeometry.Sphere.isDiameter_iff_left_mem_and_midpoint_eq_center, SmoothBumpFunction.support_updateRIn, Real.pi_rpow_zero, closure_halfSpace, PadicInt.coe_add, Real.exp_neg, ContinuousMap.Homotopy.extend_apply_of_le_zero, norm_sub_mul_self_real, NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completion, Real.arccos_of_one_le, hasSum_iff_tendsto_nat_of_nonneg, StrongDual.mem_polar_singleton, CFC.negPart_smul_of_nonneg, Metric.uniformity_basis_dist_le_pow, Chebyshev.psi_mono, NumberField.dedekindZeta_residue_pos, MeasureTheory.tendsto_integral_norm_approxOn_sub, tendsto_norm_comp_cofinite_atTop_of_isClosedEmbedding, image_le_of_liminf_slope_right_lt_deriv_boundary', 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, Real.sign_of_neg, 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, MeasureTheory.Integrable.hasSum_intervalIntegral_comp_add_int, ZLattice.covolume.tendsto_card_div_pow'', tsum_of_norm_bounded, Complex.norm_exp_I_mul_ofReal, Real.hasDerivAt_sinh, VectorFourier.norm_fourierIntegral_le_integral_norm, Besicovitch.goodδ_lt_one, AbsoluteValue.Completion.extensionEmbedding_dist_eq_of_comp, SchwartzMap.norm_fourier_apply_le_toLp_one, Complex.nnnorm_real, MeasureTheory.StronglyAdapted.norm, LiouvilleNumber.remainder_lt, Polynomial.toAddCircle_C_eq_smul_fourier_zero, EuclideanGeometry.Sphere.angle_eq_pi_div_two_iff_mem_sphere_ofDiameter, MeasureTheory.condExpL1CLM_smul, Orientation.inner_rev_eq_zero_of_oangle_eq_neg_pi_div_two, Real.deriv_log_comp_eq_logDeriv, MeasureTheory.DominatedFinMeasAdditive.of_measure_le_smul, real_inner_smul_self_right, Manifold.exists_lt_of_riemannianEDist_lt, MeasureTheory.integral_abs_condExp_le, MeasureTheory.MemLp.eLpNorm_indicator_le', Matrix.l2_opNorm_mul, memℓp_gen_iff', NumberField.mixedEmbedding.fundamentalCone.expMapBasis_source, dist_smul_add_one_sub_smul_le, Subalgebra.SeparatesPoints.rclike_to_real, Polynomial.gaussNorm_mul_le, Complex.norm_fderiv_le_div_of_mapsTo_ball, Subgroup.widthInfty_mem_periods, InnerProductGeometry.sin_angle_add, InnerProductGeometry.angle_add_eq_arcsin_of_inner_eq_zero, StrictConvexOn.ae_eq_const_or_map_average_lt, norm_innerSL_le, SeminormFamily.basisSets_iff, MeasureTheory.eLpNorm'_norm_rpow, Complex.isCauSeq_exp, MeasureTheory.norm_charFun_le, MeasureTheory.rnDeriv_tilted_left_self, polynomialFunctions_closure_eq_top, Real.Angle.cos_antiperiodic, VectorFourier.hasFDerivAt_fourierChar_smul, Hyperreal.IsSt.neg, integrable_cexp_quadratic', Metric.thickening_cthickening_subset, LipschitzWith.norm_compLp_le, OrthonormalBasis.measurePreserving_measurableEquiv, BoxIntegral.Box.coe_splitUpper, Orientation.rotation_pi, Real.exists_isGLB, SeminormedAddGroup.disjoint_nhds, Real.cosh_neg, Real.cos_sub_pi_div_two, strictConcaveOn_cos_Icc, EuclideanGeometry.angle_lt_pi_of_not_collinear, 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, HasFDerivWithinAt.cos, tendsto_mulIndicator_cthickening_mulIndicator_closure, Real.mul_iInf_of_nonpos, ENNReal.limsup_toReal_eq, Real.ofNat_le_toNNReal, ContinuousWithinAt.cfc_nnreal, ContinuousWithinAt.rpow, ArithmeticFunction.vonMangoldt.residueClass_apply_zero, MeasureTheory.measurable_charFun, Quaternion.continuous_imK, Urysohns.CU.lim_of_notMem_U, IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus, MeasureTheory.measure_unitBall_eq_integral_div_gamma, CStarAlgebra.exists_sum_four_unitary, norm_sum_le, Chebyshev.theta_eq_primeCounting_mul_log_sub_integral, integral_cos_sq_sub_sin_sq, range_norm, Metric.uniformContinuous_iff, NNReal.image_coe_Icc, ValueDistribution.logCounting_monotoneOn, ProbabilityTheory.variance_tilted_mul, Real.exists_extension_norm_eq, Subadditive.apply_mul_add_le, Seminorm.convex_closedBall, UpperHalfPlane.toSL2R_apply, 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, MeasureTheory.le_integral_rnDeriv_of_ac, NumberField.mixedEmbedding.fundamentalCone.measurableSet_paramSet, PadicInt.unitCoeff_coe, ProbabilityTheory.iIndepFun.cgf_sum₀, HolderOnWith.hausdorffMeasure_image_le, ENNReal.ofReal_natCast, RCLike.ofReal_inv, EuclideanGeometry.Sphere.instHasOrthogonalProjectionRealDirectionOrthRadius, AEMeasurable.ennreal_toReal, Polynomial.Chebyshev.intervalIntegrable_sqrt_one_sub_sq_inv, Metric.exists_closedBall_inter_eq_singleton_of_discrete, InnerProductGeometry.sin_angle_add_mul_norm_of_inner_eq_zero, ContDiffMapSupportedIn.structureMapLM_zero_apply, SchwartzMap.differentiableAt, nnnorm_cfcₙ_nnreal_le, Complex.frontier_reProdIm, ZetaAsymptotics.term_of_lt, 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, gauge_closedBall, 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, exists_dist_le_le, Metric.Snowflaking.image_ofSnowflaking_emetricBall, Complex.norm_cpow_eq_rpow_re_of_pos, ENNReal.ofReal_pow, isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt, Real.Gamma_neg_nat_eq_zero, MeasureTheory.Measure.haar.addPrehaar_sup_le, AddCircle.homeomorphCircle'_apply, Real.injOn_cos, EuclideanGeometry.OrthocentricSystem.exists_circumradius_eq, Real.log_div_self_rpow_antitoneOn, schnirelmannDensity_setOf_mod_eq_one, Real.continuous_arccos, Real.volume_pi_closedBall, DifferentiableWithinAt.sinh, Real.nndist_eq', Seminorm.continuous_of_forall, IsSelfAdjoint.le_algebraMap_norm_self, DifferentiableOn.arsinh, Real.rpow_inv_rpow, 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, ConvexOn.exists_affine_le_of_lt_real, SmoothPartitionOfUnity.nonneg', Complex.norm_mul, Complex.conjCAE_toAlgEquiv, apply_le_nnnorm_cfcₙ_nnreal, UpperHalfPlane.isometry_pos_mul, Set.Subsingleton.infsep_zero, MeasureTheory.eLpNorm'_const, Real.dist_mulExpNegMulSq_le_dist, taylor_mean_remainder_lagrange, tendsto_nhds_unique_dist, Real.rpow_neg, ProbabilityTheory.covarianceBilinDual_of_not_memLp', Complex.re_sum, Complex.borelCaratheodory_zero, MeasureTheory.SimpleFunc.integral_eq_lintegral', Real.HolderConjugate.sub_one_pos, tendsto_measure_thickening_of_isClosed, UnconditionalSchauderBasis.exists_norm_proj_le, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left', intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le', Affine.Triangle.orthocenter_vsub_circumcenter_eq_sum_vsub, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_le_one, Function.hasTemperateGrowth_one_add_norm_sq_rpow, UpperHalfPlane.toSL2R_smul_I, Orientation.two_zsmul_oangle_smul_smul_self, IsMIntegralCurveAt.comp_add, instIsAddHaarMeasureUnitAddCircleVolume, Polynomial.Chebyshev.sumZeroes_smul, ENNReal.rpow_lt_rpow_of_exponent_gt, intervalIntegral.norm_integral_min_max, Real.sin_eq_one_iff, SchwartzMap.fourier_convolution, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_continuousOn, ContDiffWithinAt.norm, Complex.log_inv_eq_integral, OnePoint.isZeroAt_iff, NumberField.mixedEmbedding.fundamentalCone.expMap_pos, ProbabilityTheory.measure_le_le_exp_cgf, intervalIntegral.integral_deriv_smul_comp'', ValueDistribution.abs_characteristic_sub_characteristic_shift_le, SmoothPartitionOfUnity.IsSubordinate.contMDiff_finsum_smul, norm_lineDeriv_le_of_lip', Real.tan_pi, RCLike.hasSum_im, Orientation.rotation_symm_apply, ContDiffBumpBase.eq_one, Real.arcosh_lt_arcosh, ZMod.LFunction_dft, ContinuousMap.exists_extension_forall_mem_of_isClosedEmbedding, HurwitzZeta.hasSum_nat_cosKernel₀, AbsolutelyContinuousOnInterval.integral_mul_deriv_eq_deriv_mul, Real.rpow_add_intCast', tendsto_iff_dist_tendsto_zero, Real.mem_closure_iff, Asymptotics.IsLittleO.abs_right, ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior, Real.tendsto_logb_nhdsGT_zero, 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, VectorFourier.integrable_fourierPowSMulRight, Affine.Simplex.altitudeFoot_mem_affineSpan_faceOpposite, InnerProductGeometry.inner_eq_zero_iff_angle_eq_pi_div_two, instSMulCommClass_closedBall_closedBall_closedBall, continuous_norm, Valued.toNormedField.norm_lt_one_iff, uniformity_basis_dist_pow_of_lt_one, ProbabilityTheory.poissonPMFRealSum, MeasureTheory.Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_addGroup, AddCircle.homeomorphCircle_apply, intervalIntegral.inv_mul_integral_comp_div_add, HurwitzZeta.hasSum_int_completedHurwitzZetaEven, ProbabilityTheory.integrable_gaussianPDFReal, Topology.CWComplex.continuousOn_symm, ae_not_liouvilleWith, Real.fib_succ_sub_goldenRatio_mul_fib, EuclideanGeometry.mapsTo_inversion_affineSubspace_of_mem, DifferentiableWithinAt.exp, 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, Real.holderConjugate_iff_eq_conjExponent, rpow_one_add_le_one_add_mul_self, 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, tendsto_norm_neg_add_self, CFC.rpow_neg_mul_rpow, PiNat.dist_self, OrthonormalBasis.abs_det_adjustToOrientation, Submodule.connectedComponentIn_eq_self_of_one_lt_codim, CircleDeg1Lift.lt_translationNumber_of_forall_add_lt, ENNReal.toReal_smul, Real.sqrt_lt_sqrt, AlternatingMap.mkContinuousLinear_norm_le_max, norm_le_of_mem_closedBall', Real.sSup_neg, ModularGroup.coeHom_apply, ContinuousLinearMap.dist_le_opNorm, DifferentiableWithinAt.rpow, ExistsContDiffBumpBase.y_le_one, Real.self_le_rpow_of_one_le, ProbabilityTheory.poissonPMFReal_nonneg, Real.tsum_eq_tsum_fourierIntegral_of_rpow_decay, Real.hasProd_of_hasSum_log, Circle.exp_sub_two_pi, EuclideanSpace.edist_eq, ValueDistribution.logCounting_isBigO_one_iff_analyticOnNhd, IsCompact.uniform_oscillationWithin, Differentiable.rpow, MeasureTheory.isProbabilityMeasure_iff_real, Orientation.volumeForm_comp_linearIsometryEquiv, RCLike.isCauSeq_re, Monotone.stieltjesFunction_eq, AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_ge_nat, Complex.ofReal_inv, ContDiffAt.exp, Real.ofDigits_const_last_eq_one', ProbabilityTheory.Kernel.HasSubgaussianMGF.aestronglyMeasurable, EuclideanGeometry.inversion_eq_lineMap, Continuous.arcsin, HasLineDerivAt.le_of_lipschitz, intervalIntegral.intervalIntegrable_one_div, Path.Homotopy.refl_apply, Real.logb_rpow, Seminorm.ball_zero_eq, PadicInt.coe_intCast, Real.exp_sum, Complex.frontier_setOf_im_le, Complex.integral_cpow_mul_exp_neg_mul_Ioi, Collinear.sbtw_of_dist_eq_of_dist_lt, InnerProductGeometry.IsConformalMap.preserves_angle, AkraBazziRecurrence.GrowsPolynomially.inv, Subgroup.strictPeriods_eq_zmultiples_strictWidthInfty, Metric.dist_lt_add_of_nonempty_ball_inter_closedBall, Orientation.norm_div_tan_oangle_sub_right_of_oangle_eq_pi_div_two, PadicInt.norm_natCast_p_sub_one, Complex.range_exp_mul_I, LinearMap.polar_mem, SimpleGraph.triangleRemovalBound_nonpos, RCLike.I_im', complexOfReal_derivWithin, StrictConvexSpace.of_norm_combo_lt_one, 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, ContinuousAt.rexp, Complex.norm_sub_one_sq_eq_of_norm_one, CFC.real_exp_eq_normedSpace_exp, CFC.norm_sqrt, LipschitzOnWith.ae_differentiableWithinAt, norm_fderiv_norm_id_rpow, Real.sin_mem_Icc, InnerProductGeometry.angle_eq_angle_add_add_angle_add_of_mem_span, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_integrable_exp_mul, Real.sqrt_eq_one, dist_pi_le_iff', Complex.range_im, swap_dist, NumberField.Units.basisOfIsMaxRank_fundSystem, Real.Lr_rpow_le_Lp_mul_Lq_of_nonneg, Subgroup.strictWidthInfty_SL2Z, deriv.lhopital_zero_atTop_on_Ioi, Metric.hausdorffDist_nonneg, Complex.mem_reProdIm, Function.Periodic.tendsto_atTop_intervalIntegral_of_pos, norm_nonneg, CircleDeg1Lift.translationNumber_eq_int_iff, CFC.continuousOn_rpow, Complex.dist_of_re_eq, ContinuousLinearMap.norm_holder_apply_apply_le, HasDerivWithinAt.log, NNReal.strictConcaveOn_rpow, ProbabilityTheory.variance_fun_add, Metric.diam_le_of_forall_dist_le, image_le_of_liminf_slope_right_lt_deriv_boundary, ClosedSubmodule.involutive_mulI, ClosedSubmodule.symplComp_inf, Orientation.tan_oangle_add_right_of_oangle_eq_pi_div_two, Real.continuous_arsinh, Real.qaryEntropy_one, NumberField.mixedEmbedding.fundamentalCone.linearIndependent_completeFamily, IsSelfAdjoint.imaginaryPart, MeasureTheory.lpNorm_of_not_memLp, RCLike.re_eq_self_of_le, intervalIntegral.integral_deriv_smul_comp, intervalIntegral.norm_integral_le_integral_norm_uIoc, Circle.argPartialEquiv_symm_apply, Real.analyticOnNhd_arcosh, Complex.isUniformEmbedding_equivRealProd, ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat, HurwitzZeta.oddKernel_undef, 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, SlashInvariantFormClass.slash_action_eq, SeminormedRing.toRingSeminorm_apply, MeasureTheory.lpNorm_exponent_zero, Real.exists_lt_of_strictMono, Affine.Simplex.signedInfDist_apply_of_ne, Chebyshev.theta_le_psi, Submodule.norm_subtypeL_le, CircleDeg1Lift.translate_pow, Real.cos_le_cos_of_nonneg_of_le_pi, ProbabilityTheory.continuousOn_mgf, Metric.eventually_isCompact_closedBall, Padic.padicNormE.image, integral_cos_mul_complex, WithLp.prod_norm_eq_of_L2, sum_mul_eq_sub_sub_integral_mul, LipschitzWith.const_max, Real.cos_sq_arctan, BumpCovering.exists_isSubordinate_hasCompactSupport_of_locallyFinite_t2space, IsUltrametricDist.isPowMul_invariantExtension, exists_contMDiffMap_one_nhds_of_subset_interior, ContDiffWithinAt.log, NNReal.le_rpow_inv_iff_of_pos, dist_sq_lineMap_of_inner_eq_zero, ModularForm.summable_eta_q, mul_mem_ball_iff_norm, Seminorm.coeFnAddMonoidHom_injective, Real.isLUB_of_tendsto_monotoneOn_bddAbove_nat_Ici, Complex.norm_eq_one_of_pow_eq_one, BoundedContinuousFunction.norm_ofNormedAddCommGroup_le, MeasureTheory.setIntegral_nonpos_of_ae_restrict, MeasureTheory.upcrossingsBefore_pos_eq, unitInterval.symm_bijective, Polynomial.fourierCoeff_toAddCircle, signedDist_left_lineMap, ContinuousLinearMap.bound_of_antilipschitz, Path.uniformContinuous_extend, ENNReal.trichotomy₂, ENNReal.top_rpow_of_neg, Affine.Simplex.direction_altitude, Complex.hasSum_iff, Real.deriv_mul_log_zero, ProbabilityTheory.Fernique.tendsto_normThreshold_atTop, AddGroupSeminorm.lt_def, ProbabilityTheory.Kernel.integral_withDensity, DifferentiableWithinAt.inner, 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, Real.rpow_le_rpow_of_exponent_le_or_ge, CovBySMul.of_subset, AbsolutelyContinuousOnInterval.continuousOn, SmoothPartitionOfUnity.sum_le_one, ENNReal.rpow_arith_mean_le_arith_mean2_rpow, Path.symm_range, unitInterval.sigmoid_lt_one, Complex.UnitDisc.exists, EReal.exists_rat_btwn_of_lt, CStarRing.norm_one, norm_mul_le_of_le, ContDiffBump.zero_of_le_dist, Metric.diam_union, NNReal.Lp_add_le_tsum, ArithmeticFunction.vonMangoldt.eqOn_LFunctionResidueClassAux, Real.rpowIntegrand₀₁_one_ge_rpow_sub_two, SlashInvariantForm.slash_action_eqn, CurveIntegrable.intervalIntegrable_curveIntegralFun_trans_right, intervalIntegral.integral_comp_mul_deriv'', LocallyBoundedVariationOn.ae_differentiableWithinAt_of_mem_real, NumberField.mixedEmbedding.norm_unit, MeasureTheory.exp_llr, MeasureTheory.Measure.setIntegral_toReal_rnDeriv, MonotoneOn.nnnorm_cfcₙ, Real.volume_preserving_transvectionStruct, seminormFromConst_seq_def, VectorFourier.fourierIntegral_fderiv, EuclideanGeometry.inner_vsub_center_vsub_pos, TemperedDistribution.lineDeriv_eq_fourierMultiplierCLM, range_cfc_nnreal_subset, MeasureTheory.ProbabilityMeasure.tendsto_iff_tendsto_charFun, Real.Wallis.W_pos, Function.Periodic.intervalIntegral_add_zsmul_eq, AnalyticWithinAt.log, 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, seminormFromConst_seq_zero, 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, norm_image_sub_le_of_norm_deriv_le_segment', 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, qExpansion_coeff_isBigO_of_norm_isBigO, Metric.uniformCauchySeqOn_iff, Hyperreal.stdPart_epsilon, Real.cot_inv_eq_tan, IsMaxFilter.norm_add_self, NNReal.image_coe_uIoo, PartitionOfUnity.continuous_smul, ModularFormClass.qExpansion_coeff_eq_intervalIntegral, UnitAddCircle.integral_preimage, ModularGroup.SL_neg_smul, NumberField.mixedEmbedding.fundamentalCone.expMap_single_source, ProbabilityTheory.covariance_sub_const_left, gaugeRescale_smul, Real.tanh_surjOn, intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right, padicNorm_two_harmonic, integral_one_div_of_neg, Real.sinh_nonpos_iff, Polynomial.Chebyshev.roots_U_real_nodup, OpenPartialHomeomorph.unitBallBall_apply, MeasureTheory.integral_Ioi_of_hasDerivAt_of_nonneg', EuclideanGeometry.dist_orthogonalProjection_line_eq_iff_two_zsmul_oangle_eq, Affine.Simplex.circumcenter_eq_centroid, Real.fourierIntegralInv_eq, Convex.thickening, 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, HasDerivAt.lhopital_zero_nhdsLT, 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', ContDiffBump.convolution_tendsto_right_of_continuous, ConcaveOn.slope_le_deriv, Affine.Simplex.excenter_reindex, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_top, GroupSeminorm.mul_bddBelow_range_add, measurableSet_of_differentiableWithinAt_Ici, Complex.approx_Gamma_integral_tendsto_Gamma_integral, MeasureTheory.measureReal_diff_le_iff_le_add, NumberField.mixedEmbedding.fundamentalCone.normLeOne_eq_preimage, ConvexOn.slope_le_of_hasDerivWithinAt_Iio, 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, IsLocalHomeomorph.exists_lift_nhds, 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, Chebyshev.eventually_primeCounting_le, intervalIntegral.integral_lt_integral_of_ae_le_of_measure_setOf_lt_ne_zero, AbsoluteValue.isEquiv_iff_isHomeomorph, Orthonormal.sum_inner_products_le, eventually_norm_mfderiv_extChartAt_lt, ProbabilityTheory.HasGaussianLaw.sum, Padic.norm_int_le_pow_iff_dvd, lipschitzWith_min, Real.exp_add, Complex.ofReal_def, Real.cos_pi, ContMDiffWithinAt.inner_bundle, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq, EuclideanGeometry.cos_oangle_right_of_oangle_eq_pi_div_two, MeasureTheory.Integrable.integral_eq_integral_Ioc_meas_le, Complex.smul_im, Complex.IsExpCmpFilter.isTheta_cpow_exp_re_mul_log, Summable.mul_norm, ProbabilityTheory.variance_smul, Real.contDiffOn_arcsin, PartitionOfUnity.sum_finsupport', IsMIntegralCurve.periodic_of_eq, Affine.Simplex.ninePointCircle_center, smoothingFun_one_le, MeasureTheory.JordanDecomposition.real_smul_def, TestFunction.injective_toBoundedContinuousFunctionCLM, ConvexOn.sSup_affine_eq, Real.cos_pos_of_le_one, EuclideanGeometry.dist_orthogonalProjection_line_eq_of_two_zsmul_oangle_eq, boundary_Icc, Real.Gamma_three_div_two_lt_one, properSpace_iff_isProperMap_dist, Real.BohrMollerup.tendsto_logGammaSeq_of_le_one, eq_midpoint_of_dist_eq_half, SchwartzMap.smooth, Hyperreal.st_neg, tendsto_norm_sub_self_nhdsGE, ProbabilityTheory.covariance_const_right, MultilinearMap.mkContinuous_norm_le', ProbabilityTheory.Kernel.measurable_rnDerivAux_right, Real.tan_sub_int_mul_pi, Real.contDiffAt_arccos_iff, HasProd.norm, MeasureTheory.charFun_prod, ProbabilityTheory.mgf_undef, Polynomial.card_roots_toFinset_le_derivative, MeasureTheory.integral_smul_measure, deriv_sqrt_mul_log', mem_unitary_iff_isStarNormal_and_realPart_sq_add_imaginaryPart_sq_eq_one, spectrum.subset_circle_of_unitary, Real.instNontrivial, isAddFundamentalDomain_Ioc', Real.strictConcaveOn_negMulLog, MeasureTheory.L1.setToL1'_apply_coeToLp, Asymptotics.IsBigOWith.abs_left, Padic.norm_p_zpow, UpperHalfPlane.c_mul_im_sq_le_normSq_denom, EuclideanGeometry.inner_vsub_vsub_of_dist_eq_of_dist_eq, CircleDeg1Lift.le_translationNumber_of_add_nat_le, ProbabilityTheory.covariance_eval_multivariateGaussian, SchwartzMap.denseRange_toLpCLM, isMIntegralCurve_comp_mul_ne_zero, ConformalAt.const_smul, GenLoop.uncurry_apply, Orientation.linearIsometryEquiv_comp_rightAngleRotation', ContDiffPointwiseHolderAt.fst, LinearIsometry.re_apply_eq_re, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_eq_one_iff, Real.sinh_artanh, ProbabilityTheory.Kernel.rnDeriv_def, ContinuousMap.dist_le_iff_of_nonempty, SchwartzMap.toLp_fourier_eq, Real.range_sigmoid, ProbabilityTheory.mgf_sum_measure, Polynomial.Chebyshev.leadingCoeff_eq_iff_of_forall_abs_le_one, Real.differentiableAt_binEntropy_iff_ne_zero_one, MeasureTheory.tendsto_integral_meas_thickening_le, Height.logHeight_fun_prod_eq, EisensteinSeries.vec_add_const_isTheta, summable_mul_of_bigO_atTop', LinearMap.IsSymmetric.coe_re_inner_apply_self, MeasureTheory.measureReal_add_measureReal_compl, UpperHalfPlane.coe_im_pos, MeasureTheory.lpNorm_const', Real.sigmoid_strictMono, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, Chebyshev.psi_le_const_mul_self, CFC.nnnorm_nnrpow, SchwartzMap.integrable_pow_mul_iteratedFDeriv, FormalMultilinearSeries.radius_eq_liminf, ContinuousLinearMap.norm_precompL_le, norm_add_sq_eq_norm_sq_add_norm_sq_real, 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, ConcaveOn.antitoneOn_deriv, MeasureTheory.tendsto_limUnder_of_hasDerivAt_of_integrableOn_Iic, isConformalMap_iff_is_complex_or_conj_linear, Real.sin_pos_of_pos_of_le_one, CircleDeg1Lift.dist_map_zero_lt_of_semiconjBy, ContinuousLinearEquiv.contDiffPointwiseHolderAt_left_comp, Real.tendsto_one_add_div_rpow_exp, ProbabilityTheory.integral_poissonMeasure', Function.Periodic.intervalIntegral_add_eq, NNReal.coe_eq_one, ae_eq_const_or_norm_integral_lt_of_norm_le_const, Metric.unitBall.coe_zero, CFC.rpow_eq_rpow_prod, tendsto_log_mul_self_nhdsLT_zero, Real.rpow_add_one', MeasureTheory.L1.setToL1_const, AbsolutelyContinuousOnInterval.smul, RCLike.span_one_I, Hyperreal.stdPart_map, GenLoop.fromLoop_coe, Real.cos_int_mul_pi, Metric.Snowflaking.preimage_ofSnowflaking_closedEBall, AffineSubspace.euclideanHausdorffMeasure_coe_image, OrthogonalFamily.summable_iff_norm_sq_summable, Complex.HadamardThreeLines.scale_bound_right, ContinuousLinearMap.norm_map_removeNth_le, Real.tanh_neg, CFC.rpow_mul_rpow_neg, BoundedContinuousFunction.tendsto_integral_of_forall_limsup_integral_le_integral, Real.rpow_lt_self_of_lt_one, Real.mk_le, Polynomial.Chebyshev.roots_T_real_nodup, Filter.Tendsto.ennrpow_const, PhragmenLindelof.eq_zero_on_quadrant_III, Behrend.exists_large_sphere_aux, hasContDiffBump_of_innerProductSpace, isLocalMin_of_deriv_Ioo, Real.exists_measure_rpow_eq_integral, summable_partition, 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, Real.fourierIntegral_continuousMultilinearMap_apply', ENNReal.ofReal_le_natCast, Real.sinc_le_inv_abs, instSMulCommClass_sphere_sphere_ball, Metric.uniformSpace_eq_bot, Real.BohrMollerup.ge_logGammaSeq, volume_regionBetween_eq_lintegral, 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, exists_forall_closed_ball_dist_add_le_two_mul_sub, Measurable.carg, Real.abs_log_mul_self_lt, MeasureTheory.norm_condExpIndL1Fin_le, BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg, Seminorm.uniformContinuous_of_forall', Real.isLittleO_pow_logb_id_atTop, IsLocalExtr.hasFDerivAt_eq_zero, ContinuousMultilinearMap.norm_image_sub_le', InnerProductGeometry.sin_angle_mul_norm_mul_norm, ValueDistribution.proximity_top, IsIntegralCurveOn.continuousWithinAt, 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, isLocalMin_of_deriv, Metric.infDist_nonneg, NNReal.dist_gm_am_le, CircleDeg1Lift.map_add_one, RCLike.geometric_hahn_banach_closed_compact, BoundedContinuousFunction.dist_lt_iff_of_compact, Mathlib.Meta.NormNum.isNat_rpow_pos, StieltjesFunction.right_continuous, Polynomial.mahlerMeasure_le_sum_norm_coeff, Real.fourier_eq', Real.smoothTransition.pos_denom, unitInterval.sigmoid_le, Real.differentiable_fourier, NNReal.coe_list_prod, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt₀, MeasureTheory.charFunDual_eq_prod_iff', Real.binEntropy_nonpos_of_one_le, EisensteinSeries.summand_bound, UpperHalfPlane.hasStrictFDerivAt_smul, MeasureTheory.Measure.toSphere.instIsOpenPosMeasure, ProbabilityTheory.integrable_comp_iff, dist_smul_pair, MeasureTheory.lpMeasToLpTrimLie_symm_toLp, ProbabilityTheory.IsAEKolmogorovProcess.q_pos, norm_norm', IsCoveringMap.eq_liftPath_iff, UpperHalfPlane.mdifferentiable_iff, UnitAddTorus.coe_symm_measurableEquivPiIoc_apply, InnerProductSpace.laplacianWithin_CLE_comp_left, EReal.nhdsWithin_bot, Real.fourierIntegral_iteratedFDeriv, MeasureTheory.integral_Iic_deriv_mul_eq_sub, Subgroup.IsArithmetic.discreteTopology, Real.ringEquivCauchy_symm_apply_cauchy, ModularFormClass.exp_decay_sub_atImInfty', Stirling.second_wallis_limit, Complex.neg_re_eq_norm, MeasureTheory.lintegral_comp_eq_lintegral_meas_lt_mul, closure_lowerClosure_comm_pi, Real.HolderTriple.inv_sub_inv_eq_inv, UpperHalfPlane.smulAux'_im, UpperHalfPlane.det_smulFDeriv, Submodule.orthogonalProjection_norm_le, NormedRing.toRingNorm_apply, Complex.HadamardThreeLines.norm_le_interp_of_mem_verticalClosedStrip₀₁', Orientation.oangle_sub_right_eq_arctan_of_oangle_eq_pi_div_two, integral_sin_pow_antitone, Complex.arg_neg_eq_arg_sub_pi_iff, Matrix.PosDef.posDef_sqrt, MeasureTheory.Integrable.summable_integral, MeasureTheory.StronglyMeasurable.norm_approxBounded_le, Function.HasTemperateGrowth.isBigO_uniform, InnerProductSpace.volume_ball_of_dim_even, MeasureTheory.Measure.haar.addPrehaar_self, integrable_cexp_neg_mul_sq, dist_vadd_vadd_le, intervalIntegrable_log_sin, integral_pow_abs_sub_uIoc, Valued.toNormedField.one_le_norm_iff, Seminorm.zero_apply, WithSeminorms.hasBasis_ball, Differentiable.cos, norm_cfcₙ_le_iff, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunctionAux_nonneg, Real.circleAverage_nonneg_of_nonneg, AbsoluteValue.Completion.extensionEmbedding_of_comp_coe, DiffeologicalSpace.CorePlotsOn.isPlotOn_univ, exists_contMDiffMap_forall_mem_convex_of_local_const, ProbabilityTheory.variance_const_mul, ArchimedeanClass.stdPart_inv, EuclideanSpace.volume_closedBall, tendsto_exp_mul_div_rpow_atTop, Orientation.rightAngleRotation_neg_orientation, NumberField.mixedEmbedding.integral_comp_polarCoordReal_symm, unitInterval.qRight_one_right, Orientation.rotationAux_apply, Metric.Snowflaking.preimage_toSnowflaking_emetricBall, NonarchAddGroupNorm.toNonarchAddGroupSeminorm_eq_coe, intervalIntegrable_inv_iff, NormedField.exists_lt_norm_lt, 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, exists_forall_closed_ball_dist_add_le_two_sub, SchwartzMap.fourierMultiplierCLM_smul, PiNat.dist_le_one, LipschitzOnWith.norm_inv_mul_le_of_le, Real.inv_logb, Real.sign_intCast, Real.Lr_rpow_le_Lp_mul_Lq, Real.contDiffAt_rpow_of_ne, Asymptotics.IsBigO.of_abs_right, AddGroupSeminorm.inf_apply, MeasureTheory.Lp.norm_le_mul_norm_of_ae_le_mul, Real.tan_zero, ConcaveOn.le_slope_of_hasDerivAt, Metric.Snowflaking.dist_toSnowflaking_toSnowflaking, Real.hasStrictDerivAt_exp, MeasureTheory.map_withDensity_abs_det_fderiv_eq_addHaar, ContinuousAt.arsinh, CFC.norm_nnrpow, Quaternion.continuous_normSq, Real.sin_half_eq_sqrt, intervalIntegral.integral_nonneg_of_forall, Real.sin_eq_sqrt_one_sub_cos_sq, fourierCoeffOn_of_hasDeriv_right, 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, limsup_mul_le, NNReal.Lr_le_Lp_mul_Lq_tsum, Asymptotics.IsLittleO.def, 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, Complex.conjLIE_toCLE, congruent_iff_pairwise_dist_eq, InformationTheory.deriv_klFun, ProbabilityTheory.covariance_const_sub_right, gronwallBound_mono, HolderWith.interpolate, one_add_rpow_hasFPowerSeriesOnBall_zero, CFC.conjugate_rpow_neg_one_half, Orientation.cos_oangle_add_left_mul_norm_of_oangle_eq_pi_div_two, AnalyticOnNhd.im_ofReal, MeasureTheory.L1.setToL1_lipschitz, WithLp.prod_edist_eq_add, MeasureTheory.setIntegral_toReal_rnDeriv_mul, NormedAddGroup.nhds_basis_norm_lt, NNReal.coe_sub_of_lt, MeasureTheory.measureReal_inter_add_diff, boundary_product, MeasureTheory.integral_exp_pos, ArithmeticFunction.zeta_mul_vonMangoldt, Manifold.exists_lt_locally_constant_of_riemannianEDist_lt, MeasureTheory.norm_condExpL2_le_one, HasCompactSupport.convolution_integrand_bound_right, differentiable_sigmoid, Complex.re_nonneg_iff_nonneg, isBigO_norm_restrict_cocompact, NNReal.bddAbove_coe, Real.rpow_def, CircleDeg1Lift.commute_sub_nat, ProbabilityTheory.tendsto_cdf_atBot, RightDerivMeasurableAux.mem_A_of_differentiable, 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, ENNReal.lintegral_Lp_mul_le_Lq_mul_Lr, norm_add_lt_of_not_sameRay, Orientation.cos_oangle_eq_inner_div_norm_mul_norm, NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, Metric.diam_cthickening_le, BumpCovering.coe_single, Real.mk_pos, Affine.Simplex.incenter_notMem_affineSpan_faceOpposite, Affine.Simplex.touchpoint_empty_mem_interior_faceOpposite, SlashInvariantForm.vAdd_apply_of_mem_strictPeriods, HasDerivAt.lhopital_zero_atBot, Complex.imLm_coe, MeasureTheory.summable_measure_toReal, GromovHausdorff.eq_toGHSpace_iff, MeasureTheory.setToFun_eq, Complex.normSq_ofReal_sub_I_mul_sqrt_one_sub, 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, Real.sin_le_mul, ENNReal.ofReal_mono, DifferentiableAt.abs_of_pos, MeasureTheory.condExpL2_comp_continuousLinearMap, one_add_mul_self_le_rpow_one_add, MeasureTheory.integral_of_hasDerivAt_of_tendsto, Real.HolderTriple.nonneg, inner_im_symm, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, ProbabilityTheory.cgf_undef, ConvexOn.real_sSup_affine_eq, SchwartzMap.laplacian_apply, Polynomial.supNorm_eq_zero_iff, dist_le_of_trajectories_ODE_of_mem, Measurable.norm, Complex.arg_eq_pi_iff, Real.toNNReal_lt_toNNReal_iff', Real.posLog_mul, NumberField.Units.regOfFamily_eq_zero, FormalMultilinearSeries.ofScalars_norm_eq_mul, AddGroupNorm.toAddGroupSeminorm_eq_coe, HasDerivAt.clog_real, 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, intervalIntegral.integral_deriv_smul_deriv_comp', Commute.cfcₙ_real, Real.range_cos_infinite, Tactic.NormNum.isNat_realSqrt_of_isRat_negOfNat, Real.one_div_sub_sq_hasFPowerSeriesOnBall_zero, Complex.arg_cos_add_sin_mul_I_eq_toIocMod, Real.sinhOrderIso_symm_apply, Real.iSup_nonneg, Complex.div_natCast_re, Complex.continuousAt_ofReal_cpow_const, Real.summable_exp_nat_mul_iff, StrictConvexSpace.of_norm_add, EuclideanSpace.coe_measurableEquiv_symm, NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlace, ContinuousMap.Homotopy.congr_arg, Real.norm_nnratCast, MeasureTheory.lintegral_coe_eq_integral, AEMeasurable.dist, lp.toNorm_coe, real_inner_self_pos, Real.rpowIntegrand₀₁_eqOn_mul_rpowIntegrand₀₁_one, Real.tendsto_logb_nhdsNE_zero, 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, LipschitzOnWith.of_le_add_mul, Circle.argEquiv_apply_coe, MeasureTheory.memLp_re_im_iff, ContinuousMapZero.toNNReal_apply, SzemerediRegularity.eps_pow_five_pos, EisensteinSeries.tsum_symmetricIco_tsum_eq_S_act, Set.Nontrivial.le_infsep_iff, HasFDerivAt.rpow, norm_mul_le', sameRay_iff_norm_smul_eq, Cardinal.mk_Ioi_real, HolderWith.nndist_le, disjoint_closedBall_ball_iff, NumberField.sum_archAbsVal_eq, gaugeSeminorm_toFun, LiouvilleWith.add_nat_iff, irrational_natCast_div_iff, Complex.UnitDisc.instIsScalarTower_closedBall_closedBall, Metric.uniformContinuous_infDist_pt, Metric.isOpen_singleton_iff, InformationTheory.toReal_klDiv_smul_left, continuous_circleMap_inv, Complex.re_nnratCast, Distribution.IsVanishingOn.lineDerivOp, ProbabilityTheory.truncation_zero, ProbabilityTheory.integral_tilted_mul_self, CompactlySupportedContinuousMap.nnrealPart_neg_eq_zero_of_nonneg, Real.round_pi_eq_three, ArchimedeanClass.stdPart_nonpos, Real.cos_two_mul', deriv.lhopital_zero_nhdsNE, LSeries_eq_mul_integral', Orientation.norm_div_cos_oangle_sub_left_of_oangle_eq_pi_div_two, Real.log_nonneg_iff, integrableOn_Ioi_deriv_norm_ofReal_cpow, Filter.Tendsto.arsinh, irrational_sqrt_two, ContDiffMapSupportedIn.structureMapLM_apply, Complex.normSq_eq_zero, CircleDeg1Lift.translationNumber_mono, Mathlib.Meta.Positivity.sinh_pos_of_pos, UniformSpace.Completion.uniformity_dist', AffineSubspace.right_mem_perpBisector, Path.extend_trans_of_half_le, ContinuousLinearMap.circleAverage_comp_comm, AnalyticOn.log, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangentAt, ProbabilityTheory.stronglyMeasurable_condVar, MeasureTheory.toReal_rnDeriv_tilted_right, ENNReal.one_le_rpow, Complex.isLittleO_ofReal_left, RCLike.normSq_sub, Real.rpow_natCast, Real.zero_rpow_nonneg, SimpleGraph.triangle_counting, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two, Real.norm_eq_abs, Real.inner_le_Lp_mul_Lq_of_nonneg, Real.fromBinary_continuous, Real.log_le_sub_one_of_pos, integrable_of_le_of_pow_mul_le, DifferentiableAt.abs_of_neg, Metric.tendsto_dist_right_atTop_iff, Subgroup.IsArithmetic.conj, Real.exists_int_int_abs_mul_sub_le, NNReal.young_inequality_real, Real.iSup_prod_eq_prod_iSup_of_nonnegHomClass, 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, AbsolutelyContinuousOnInterval.intervalIntegrable_deriv, ProbabilityTheory.cdf_gammaMeasure_eq_integral, SlashInvariantForm.coe_norm, Real.sin_eq_two_mul_tan_half_div_one_add_tan_half_sq, derivWithin.lhopital_zero_nhdsWithin_convex, MeasureTheory.integral_comap_eq_mulEquivHaarChar_smul, Real.Angle.tan_zero, Complex.ofReal_mul, MeasureTheory.toReal_rnDeriv_map, fourier_gaussian_pi, le_iff_norm_sqrt_mul_rpow, ContDiffBump.contDiffWithinAt, Real.sqrt_ne_zero', Mathlib.Meta.NormNum.nnreal_rpow_isRat_eq_inv_nnreal_rpow, Complex.sin_arg, UpperHalfPlane.σ_denom, exists_seq_norm_le_one_le_norm_sub', Function.Periodic.tendsto_atTop_intervalIntegral_of_pos', ContDiff.arsinh, 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, Real.one_sub_inv_le_log_of_pos, NumberField.mixedEmbedding.fundamentalCone.injective_expMap, ProbabilityTheory.instIsProbabilityMeasure_cauchyMeasure, Filter.Tendsto.arcsin_nhdsLE, norm_sub_le_norm_sub_add_norm_sub, Path.refl_extend, LipschitzWith.norm_compLp_sub_le, summable_prod_of_nonneg, ProbabilityTheory.HasSubgaussianMGF_sum_of_HasCondSubgaussianMGF, EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_left, tendsto_apply_add_mul_sq_div_sub, Real.tan_pos_of_pos_of_lt_pi_div_two, Complex.det_conjLIE, not_differentiableAt_abs_zero, ProbabilityTheory.covariance_map, Real.arcsin_lt_arcsin, MeasureTheory.llr_smul_left, Hyperreal.st_add, second_derivative_symmetric_of_eventually_of_real, MonotoneOn.ae_differentiableWithinAt, interior_euclideanQuadrant, hasDerivWithinAt_iff_tendsto, norm_sub_pos_iff, MeasureTheory.volume_sum_rpow_lt_one, antilipschitzWith_iff_exists_mul_le_norm, Complex.exp_im, Height.mulHeight₁_one, Polynomial.Chebyshev.C_two_mul_real_cos, intervalIntegral.intervalIntegrable_log', ball_sub_closedBall, NumberField.house.basis_repr_norm_le_const_mul_house, Complex.dist_conj_self, Unitary.path_apply, 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', IsCoercive.isClosed_range, NonarchAddGroupNormClass.toAddGroupNormClass, BoxIntegral.Box.mem_univ_Ioc, RCLike.realLinearIsometryEquiv_apply, Metric.thickening_thickening_subset, cantorSequence_get_succ, isLocalMax_of_deriv_Ioo, TemperedDistribution.laplacianCLM_apply, Real.strictConcaveOn_qaryEntropy, Metric.Sigma.isOpen_iff, EuclideanGeometry.Sphere.secondInter_eq_self_iff, derivWithin.log, isBigO_rpow_zero_log_smul, unitary.two_mul_one_sub_cos_norm_argSelfAdjoint, Hyperreal.coe_sub, Real.iInf_nonpos, Seminorm.finset_sup_apply_le, 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, spectralNorm_unique_of_finiteDimensional_normal, MeasureTheory.count_real_singleton, Polynomial.derivRootWeight_nonneg, ValueDistribution.proximity_sub_proximity_inv_eq_circleAverage, MeasureTheory.SignedMeasure.toJordanDecomposition_smul, InnerProductSpace.HarmonicContOnCl.contDiffAt, MeasureTheory.llr_smul_nnreal_right, continuousAt_gaussian_integral, ProperCone.innerDual_innerDual, LinearMap.bound_of_ball_bound, UniformSpace.Completion.dist_self, Real.eq_Gamma_of_log_convex, Real.arsinh_le_arsinh, UpperHalfPlane.vadd_im, Orientation.rightAngleRotation_map_complex, ProbabilityTheory.mgf_pos_iff, intervalIntegral.integral_deriv_of_contDiffOn_Icc, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, curveIntegralFun_def, HurwitzZeta.hurwitzZetaEven_neg, Circle.exp_nsmul, ConvexOn.rightDeriv_eq_sInf_slope_of_mem_interior, Complex.div_ratCast, Real.cosh_artanh, ProbabilityTheory.tilted_mul_apply_cgf', BarrelledSpace.continuous_of_lowerSemicontinuous, Mathlib.Meta.NormNum.isInt_rpow_neg, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_lt_one_iff, Seminorm.continuousAt_zero, ContinuousLinearMap.norm_smulRightL_apply, BoundedContinuousFunction.dist_le_two_norm', Complex.im_tsum, Metric.exists_real_pos_lt_infEDist_of_notMem_closure, MeasureTheory.Measure.haar.addPrehaar_empty, Orientation.areaForm_rightAngleRotation_left, Metric.Snowflaking.image_toSnowflaking_emetricBall, Real.tanh_bijOn, isPosSemidef_inner, torusIntegral_succAbove, AbsoluteValue.IsEquiv.log_div_log_eq_log_div_log, ZLattice.covolume_div_covolume_eq_relIndex', coeFn_fourierLp, Metric.nhds_basis_ball_pow, MeasureTheory.SignedMeasure.toJordanDecomposition_spec, Differentiable.norm, Real.deriv_fourier, CStarAlgebra.exists_sum_four_nonneg, contDiff_sigmoid, Path.truncate_range, CircleDeg1Lift.tendsto_translationNumber_of_dist_bounded_aux, HasFDerivWithinAt.sin, Real.cos_two_mul_eq_one_sub, cfcₙ_complex_eq_real, Real.pi_gt_d6, RCLike.tendsto_ofReal_atTop_cobounded, ConvexBody.coe_zero, SchwartzMap.smulLeftCLM_smul, ProbabilityTheory.iIndepFun.mgf_sum, Int.preimage_closedBall, Real.rpow_natCast_mul, HasDerivAt.le_of_lipschitzOn, Metric.Snowflaking.ediam_image_toSnowflaking, 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, ContDiffWithinAt.sqrt, EuclideanGeometry.dist_set_eq_iff_dist_orthogonalProjection_eq, ContinuousLinearMap.opNorm_le_bound₂, Quaternion.exp_coe, HasStrictFDerivAt.exp, 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, Real.hasSum_log_sub_log_of_abs_lt_one, NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal, Matrix.IsHermitian.instContinuousFunctionalCalculus, Metric.isBounded_range_iff, HolderWith.comp, AbsolutelyContinuousOnInterval.fun_mul, lipschitzOnWith_iff_norm_sub_le, DifferentiableAt.dist, MeasureTheory.measurable_embeddingReal, MeasureTheory.StronglyMeasurable.tendsto_approxBounded_of_norm_le, GaussianInt.normSq_div_sub_div_lt_one, image_le_of_deriv_right_lt_deriv_boundary', IccLeftChart_extend_bot_mem_frontier, fderiv_norm_sq_apply, LipschitzWith.ae_differentiableAt_real, RCLike.imCLM_apply, fderiv_sin, ODE.FunSpace.lipschitzWith, SmoothBumpFunction.nonempty_support, MeasureTheory.eLpNorm'_enorm_rpow, CFC.nnrpow_map_prod, MeasureTheory.eLpNorm_le_of_ae_bound, Real.norm_ofNat, NNReal.inner_le_Lp_mul_Lq, BoxIntegral.Integrable.dist_integralSum_sum_integral_le_of_memBaseSet_of_iUnion_eq, GroupSeminorm.sup_apply, RightDerivMeasurableAux.le_of_mem_A, Real.tan_eq_zero_iff', NNReal.coe_single, LinearMap.IsSymmetric.sort_roots_charpoly_eq_eigenvalues, GroupSeminorm.coe_lt_coe, Complex.cos_arg, mul_pow_le_nat_floor_pow, dist_convexCombination_right_le, 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, Real.lt_rpow_iff_log_lt, EuclideanGeometry.Sphere.finrank_orthRadius, CircleDeg1Lift.translationNumber_zpow, AffineSubspace.isConnected_setOf_sSameSide, norm_mul₃_le', MeasureTheory.probReal_compl_eq_one_sub, NumberField.mixedEmbedding.logMap_mul, AkraBazziRecurrence.growsPolynomially_zpow, NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasis, ConcaveOn.locallyLipschitzOn_iff_continuousOn, NNRat.instContinuousSMulRatReal, convexOn_rpow, EulerSine.integral_cos_mul_cos_pow_even, measurable_coe_nnreal_real_iff, LocallyLipschitz.min, AlternatingMap.mkContinuous_norm_le', ConvexOn.univ_sSup_of_nat_affine_eq, ENNReal.rpow_add_rpow_le_add, cfc_setIntegral, Asymptotics.IsLittleO.norm_right, InnerProductGeometry.inner_eq_mul_norm_iff_angle_eq_zero, TopologicalAddGroup.IsSES.integrate_apply, Quaternion.norm_toLp_equivTuple, ContDiffAt.sqrt, MeasureTheory.integral_comp_mul_deriv_Ioi, Icc_isBoundaryPoint_top, aestronglyMeasurable_withDensity_iff, integral_sin_pow_even, ConvexOn.slope_le_leftDeriv_of_mem_interior, InnerProductGeometry.ConformalAt.preserves_angle, InformationTheory.mul_klFun_le_toReal_klDiv, ContinuousAlternatingMap.ratio_le_opNorm, Real.arcsin_projIcc, ContinuousMultilinearMap.norm_mkPiAlgebraFin, Affine.Simplex.points_vsub_eulerPoint, NNReal.rpow_inv_lt_iff_of_neg, bernoulliFun_eval_half, Orientation.oangle_add_right_eq_arccos_of_oangle_eq_pi_div_two, MeasureTheory.condExp_mul_of_stronglyMeasurable_left, InnerProductGeometry.angle_smul_left_of_pos, QuotientGroup.norm_mk_le_norm, Real.summable_one_div_int_add_rpow, Polynomial.card_mahlerMeasure_le_prod, Real.natCast_le_toNNReal, ProbabilityTheory.ofReal_cdf, MeasureTheory.norm_setToFun_le, UpperHalfPlane.modular_T_smul, IsMaxFilter.norm_add_sameRay, Real.rpow_zero_pos, domain_mvt, MeasureTheory.Measure.euclideanHausdorffMeasure_def, Real.logb_pos_iff, MeasureTheory.integral_toReal, MulAlgebraNorm.smul', MeasureTheory.integrable_of_intervalIntegral_norm_bounded, LipschitzWith.of_le_add_mul', uniqueDiffOn_Ici, MeasureTheory.Lp.toTemperedDistribution_smul_eq, Quaternion.exp_eq, ContDiffAt.contDiffBump, UpperHalfPlane.IsBoundedAtImInfty.slash, Real.Angle.two_nsmul_toReal_eq_two_mul, Metric.ball_eq_ball', isClosedMap_dist, SchwartzMap.laplacian_eq_fourierMultiplierCLM, IsCoveringMap.liftHomotopy_lifts, MulAlgebraNorm.extends_norm, Metric.diam_univ_of_noncompact, EulerProduct.norm_tsum_smoothNumbers_sub_tsum_lt, RCLike.inner_eq_wInner_one, Real.isLittleO_one_exp_comp, Complex.norm_natCast_cpow_of_re_ne_zero, Memℓp.norm, Orientation.measure_orthonormalBasis, RCLike.geometric_hahn_banach_open_open, Real.cos_bound, CompactlySupportedContinuousMap.exists_add_nnrealPart_add_eq, Affine.Simplex.ExcenterExists.sSameSide_excenter_point_iff, EMetric.exists_real_pos_lt_infEdist_of_notMem_closure, MeasureTheory.ProgMeasurable.norm, ENNReal.rpow_rpow_inv_eq_iff, trapezoidal_integral_eq, LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div, Real.Angle.sign_coe_neg_pi_div_two, Real.exp_1_approx_succ_eq, MeasureTheory.integral_mul_const, Real.cos_abs, GaussianInt.intCast_complex_norm, RCLike.lipschitzWith_im, EuclideanGeometry.angle_rev_eq_pi_div_two_of_oangle_eq_neg_pi_div_two, Real.continuous_mulExpNegMulSq, MeasureTheory.Measure.integral_comp_div, intervalIntegral.integral_const, ProbabilityTheory.iIndepFun.hasGaussianLaw_fun_sub, Real.tendsto_atTop_csInf_of_antitoneOn_bddBelow_nat_Ici, fderiv_norm_sq, ContinuousLinearMap.opNorm_le_of_lipschitz, EReal.coe_lt_coe_iff, Seminorm.smul_le_smul, Complex.nonempty_linearEquiv_real, variationOnFromTo.self, AlternatingMap.norm_map_coord_zero, MeasureTheory.addEquivAddHaarChar_smul_integral_map, MeasureTheory.Measure.toSphere_apply_univ', Real.pi_lt_d4, Complex.continuous_im, LightProfinite.isClosedEmbedding_natUnionInftyEmbedding, GaussianInt.intCast_re, exists_eq_const_mul_setIntegral_of_ae_nonneg, Real.lt_sInf_add_pos, AEMeasurable.cosh, hasConstantSpeedOnWith_iff_variationOnFromTo_eq, Complex.coe_reAddGroupHom, Real.summable_mul_of_Lp_Lq_of_nonneg, Complex.ofReal_choose, Real.sqrt_prod, 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, HasStrictDerivAt.sqrt, seminormFromConst_seq_nonneg, Complex.equivRealProdCLM_apply, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_sub_smoothingFn, EReal.mem_nhds_top_iff, Function.HasTemperateGrowth.isBigO, HurwitzZeta.isBigO_atTop_sinKernel, real_inner_mem_Icc_of_norm_eq_one, SpectrumRestricts.nnreal_add, NNReal.rpow_sub_intCast', NumberField.mixedEmbedding.volume_eq_two_pow_mul_volume_plusPart, Asymptotics.isBigO_iff', Circle.argPartialEquiv_apply, ProbabilityTheory.cauchyMeasure_zero_scale, mulLeft_bound, LiouvilleNumber.remainder_lt', WeakFEPair.hf_top, ValueDistribution.characteristic_mul_top_eventuallyLE, PiLp.dist_eq_sum, MeasureTheory.charFun_eq_integral_probChar, Behrend.exp_four_lt, SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent, ConvexOn.continuousOn, AddGroupSeminorm.coe_sup, Real.logb_nonneg, NumberField.mixedEmbedding.convexBodySum_mem, MeasureTheory.lpNorm_fun_abs, poissonKernel_def, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', unitInterval.toNNReal_one, ContDiffOn.dist, Real.integrableOn_rpowIntegrand₀₁_Ici, EuclideanGeometry.angle_eq_pi_iff_sbtw, niven, Seminorm.sSup_apply, Real.smul_iInf_of_nonneg, MeasureTheory.condExpL1_eq, hasSum_L_function_mod_four_eval_three, MDifferentiable.inner_bundle, norm_deriv_le_of_lip', MeasureTheory.L1.SimpleFunc.coe_posPart, norm_cfc_lt, 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, deriv_cosh, 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, AkraBazziRecurrence.GrowsPolynomially.rpow, Real.enorm_ofReal_of_nonneg, surjective_stereographic, Real.sinh_bijective, Set.Icc.convexCombo_le, MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_rclike_tendsto, fourierIntegral_gaussian_pi', Complex.tendsto_tsum_powerSeries_nhdsWithin_lt, MeasureTheory.tilted_apply', Real.hasDerivWithinAt_arcsin_Iic, ContinuousLinearMap.toSesqForm_apply_norm_le, ProbabilityTheory.lintegral_cauchyPDF_eq_one, Function.Periodic.exp_decay_sub_of_bounded_at_inf, hasDerivAt_abs_pos, Real.sin_int_mul_pi, unitInterval.symm_symmMeasurableEquiv, MeasureTheory.measureReal_diff_lt_of_lt_add, Real.norm_of_nonneg, PiLp.edist_eq_of_L2, NumberField.mixedEmbedding.fundamentalCone.expMap_single_target, Real.sqrt_eq_zero, Real.dist_left_le_of_mem_uIcc, 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, Chebyshev.theta_pos, UpperHalfPlane.vadd_left_injective, NumberField.IsCMField.regOfFamily_realFunSystem, Orientation.oangle_smul_left_of_pos, Mathlib.Meta.NormNum.IsInt.nnreal_rpow_eq_inv_nnreal_pow, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le', 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, MeasureTheory.exists_notMem_null_average_le, ProbabilityTheory.variance_sum, continuous_sigmoid, Real.le_rpow_of_log_le, NNReal.coe_sub, MeasureTheory.eLpNorm_indicator_const, IsMIntegralCurveAt.eventually_hasDerivAt, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, norm_image_sub_le_of_norm_deriv_le_segment_01, Real.arctan_lt_arctan_iff, hasFDerivAt_stereoInvFunAux_comp_coe, SimpleGraph.lapMatrix_mulVec_eq_zero_iff_forall_adj, LipschitzWith.integral_lineDeriv_mul_eq, 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, image_le_of_deriv_right_lt_deriv_boundary, Affine.Triangle.dist_point_centroid, hasSum_geometric_of_lt_one, HurwitzZeta.hurwitzZetaEven_eq, ENNReal.coe_lt_ofReal, integral_im, integral_gaussian_complex_Ioi, cfc_integral', MeasureTheory.snd_integral_withLp, Complex.norm_cderiv_lt, ODE.picard_apply, summable_geometric_two_encode, balanced_iff_neg_mem, Real.log_doublingGamma_eq, AnalyticOnNhd.eq_re_add_const_mul_I_of_re_eq_const, MeasureTheory.condExpL2_indicator_nonneg, Seminorm.continuous_of_le, tendsto_norm_cocompact_atTop, Affine.Triangle.orthocenter_reindex, Path.eqOn_extend_segment, HasCompactSupport.hasFDerivAt_convolution_left, Complex.HadamardThreeLines.norm_mul_invInterpStrip_le_one_of_mem_verticalClosedStrip, PadicInt.coe_pow, NumberField.mixedEmbedding.convexBodyLT'_convex, ProbabilityTheory.charFunDual_stdGaussian, Real.geom_mean_le_arith_mean2_weighted, Real.tan_eq_sin_div_cos, geometric_hahn_banach_of_nonempty_interior, Real.iteratedDerivWithin_sin_Ioo, Affine.Simplex.circumradius_map, AkraBazziRecurrence.max_bi_le, MeasureTheory.charFun_map_add_const, MeasureTheory.MemLp.eLpNorm_indicator_norm_ge_le, 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, HurwitzKernelBounds.isBigO_atTop_F_int_zero_sub, MeasureTheory.integrable_rnDeriv_mul_log_iff, seminormFromConstRingNormOfField_def, PartitionOfUnity.sum_finsupport, Topology.RelCWComplex.map_zero_mem_closedCell, Real.two_mul_sin_mul_cos, TemperedDistribution.smulLeftCLM_apply_apply, Height.mulHeight_linearMap_apply_le, MeasureTheory.hasFiniteIntegral_count_iff, integrableAtFilter_rpow_atTop_iff, CircleDeg1Lift.semiconjBy_iff_semiconj, schnirelmannDensity_finset, isBigO_pow_pow_of_le_left, CFC.rpow_eq_cfc_real, Complex.not_lt_iff, MeasureTheory.eLpNorm'_exponent_zero, SimpleGraph.binomialRandom_one, expNegInvGlue.zero_of_nonpos, summable_jacobiTheta₂_term_iff, Delone.DeloneSet.exists_dist_le_coveringRadius, Complex.UnitDisc.sq_norm_lt_one, AddCircle.ergodic_zsmul_add, Real.BohrMollerup.tendsto_log_gamma, deriv_sqrt, MeasureTheory.integrable_sum_dirac_iff, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc, Euclidean.exists_pos_lt_subset_ball, GroupSeminormClass.toSeminormedCommGroup_norm_eq, RCLike.im_le_norm, HurwitzKernelBounds.summable_f_int, hasSum_mellin_pi_mul_sq, MeasureTheory.SimpleFunc.map_setToSimpleFunc, 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, ContinuousLinearMap.opNorm_le_of_re_inner_le, Metric.closure_eq_iInter_thickening, ProbabilityTheory.integral_preCDF_fst, fderiv_inner_apply, SmoothBumpCovering.toSmoothPartitionOfUnity_zero_of_zero, 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, MeasureTheory.Integrable.uniformIntegrable_condExp, AffineIsometryEquiv.pointReflection_midpoint_right, MeasureTheory.Measure.addHaar_closedBall', Real.ofDigits_digits_sum_eq, Height.mulHeight_one, Matrix.IsHermitian.im_star_dotProduct_mulVec_self, Asymptotics.IsBigOWith.sup', GenLoop.instContinuousEvalConst, uniformConvexOn_zero, MeasureTheory.measureReal_nnreal_smul_apply, Function.Periodic.exp_decay_of_zero_at_inf, Real.lt_pow_iff_log_lt, NumberField.mixedEmbedding.norm_apply, deriv2_sqrt_mul_log, Real.ofCauchy_inf, Real.rpow_le_rpow_of_exponent_le, SmoothPartitionOfUnity.contMDiff_sum, CompletelyRegularSpace.completely_regular_isOpen, ClosedSubmodule.mulI_orthogonal_eq_symplComp, mellin_comp_mul_left, ConvexOn.lipschitzOnWith_of_abs_le, IsUltrametricDist.norm_zpow_le, EuclideanGeometry.Sphere.infDist_eq_radius_iff_isTangent, Real.hasStrictDerivAt_log_of_pos, MeasureTheory.Measure.zero_le_toSignedMeasure, ENNReal.ofReal_ne_zero_iff, Real.rpowIntegrand₀₁_eqOn_pow_div, ContinuousMultilinearMap.norm_ofSubsingleton_id, Affine.Simplex.altitude_def, lintegral_Iic_eq_lintegral_Iio_add_Icc, DeltaGeneratedSpace.continuous_iff, Real.rpow_neg_ofNat, Hyperreal.isSt_ofSeq_iff_tendsto, unitInterval.volume_Iio, ValueDistribution.logCounting_mul_zero_le, sum_trapezoidal_integral_adjacent_intervals, Diffeology.dSmooth_iff, Complex.cpow_ofReal, RCLike.normSq_conj, Real.volume_interval, Subadditive.lim_le_div, ZSpan.fundamentalDomain_ae_parallelepiped, Real.sinhHomeomorph_apply, ContinuousMap.dist_eq_iSup, contMDiffOn_projIcc, Real.Angle.eq_iff_abs_toReal_eq_of_sign_eq, Complex.equivRealProd_apply_le, Real.diam_Icc, MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left', ContDiff.cosh, MeasureTheory.SignedMeasure.im_toComplexMeasure, Complex.im_ofNat, Asymptotics.IsBigO.add_add, NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces, EuclideanGeometry.angle_eq_pi_sub_angle_div_two_of_oangle_eq_of_sOppSide, DiffeologicalSpace.isOpen_iff_preimages_plots, ContDiffBump.integral_pos, AkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T, ContDiffBump.continuous_normed, Height.logHeight_comp_le, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, ProbabilityTheory.setLIntegral_toKernel_Iic, Real.log_injOn_pos, InnerProductGeometry.angle_eq_angle_add_add_angle_add, NNReal.summable_rpow, Mathlib.Meta.Positivity.sinh_nonneg_of_nonneg, Complex.lim_re, EisensteinSeries.div_max_sq_ge_one, ProbabilityTheory.covariance_fun_sum_left', Complex.rotation, MeasureTheory.pdf.hasFiniteIntegral_mul, Real.coe_sinOrderIso_apply, ProbabilityTheory.IsCondKernelCDF.toKernel_apply, Metric.exists_contMDiffMap_forall_closedEBall_subset, BoxIntegral.unitPartition.tag_mem_smul_span, signedDist_vadd_vadd, RCLike.complexLinearIsometryEquiv_apply, circleIntegrable_log_norm_meromorphicOn_of_nonneg, 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, Continuous.cfcₙ_nnreal', gronwallBound_ε0, NormedAddGroupHom.norm_id, HasDerivWithinAt.limsup_slope_le, ProbabilityTheory.instIsProbabilityMeasurecdf, ClosedSubmodule.mulI_orthogonal, Real.rpow_lt_of_lt_log, Real.one_lt_rpow_iff, Complex.one_im, Quaternion.nnnorm_coe, le_re_herglotzRieszKernel, Stirling.tendsto_self_div_two_mul_self_add_one, GroupNormClass.toNormedCommGroup_norm_eq, Real.sin_eq_zero_iff_of_lt_of_lt, SmoothBumpFunction.image_eq_inter_preimage_of_subset_support, PiLp.norm_eq_card, BoundedContinuousFunction.probCharDual_apply, DifferentiableWithinAt.cos, Real.deriv2_negMulLog, intervalIntegral.inv_smul_integral_comp_add_div, ContDiffOn.sinh, Memℓp.bddAbove, HolderOnWith.dist_le_of_le, ArchimedeanClass.stdPart_eq_sSup, Real.Wallis.le_W, Mathlib.Meta.Positivity.log_pos_of_isNegNat, 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, isIntegralCurveAt_comp_add, AkraBazziRecurrence.eventually_one_add_smoothingFn_nonneg, Nonneg.instIsometricContinuousFunctionalCalculus, MeasureTheory.Measure.integrable_pow_neg_integrablePower, Asymptotics.isBigO_abs_right, CircleDeg1Lift.map_lt_of_translationNumber_lt_int, hasFDerivAt_integral_of_dominated_loc_of_lip, Rat.uniformContinuous_coe_real, Real.sin_pi_div_four, Real.le_coe_toNNReal, ProbabilityTheory.IsGaussian.map_rotation_eq_self_of_forall_strongDual_eq_zero, RCLike.inv_re, RCLike.ofReal_ratCast, GromovHausdorff.HD_below_aux1, EuclideanGeometry.Sphere.self_mem_orthRadius, Real.Angle.toReal_zero, intervalIntegral.norm_integral_le_of_norm_le, Set.Icc.convexCombo_zero, ENNReal.rpow_sum_le_const_mul_sum_rpow, ZLattice.abs_repr_le, unitInterval.prod_mem, AkraBazziRecurrence.eventually_one_add_smoothingFn_pos, HasFDerivWithinAt.cosh, norm_jacobiTheta₂_term_fderiv_le, SlashInvariantForm.T_zpow_width_invariant, MeasureTheory.taylorWithinEval_charFun_zero, LinearMap.singularValues_eq_zero_iff_le_finrank_range, CFC.isUnit_sqrt_iff, Affine.Simplex.insphere_reindex, norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zero, EisensteinSeries.isBoundedAtImInfty_eisensteinSeriesSIF, ProbabilityTheory.IndepFun.mgf_add', ContinuousLinearEquiv.norm_pos, MeasureTheory.integral_sum_dirac, SeparationQuotient.liftNormedAddGroupHom_norm_le, Cardinal.summable_cantor_function, Affine.Simplex.excenterExists_restrict, real_inner_I_smul_self, kuratowskiEmbedding.isometry, Matrix.PosDef.re_dotProduct_pos, Seminorm.closedBall_smul_closedBall, isStarNormal_iff_commute_realPart_imaginaryPart, Complex.normSq_one, Real.binEntropy_eq_zero, ProbabilityTheory.IsAEKolmogorovProcess.p_pos, Real.natCast_lt_toNNReal, ComputeAsymptotics.MultiseriesExpansion.Multiseries.head_cons, PeriodPair.instIsZLatticeRealComplexLattice, pi_norm_const_le, MeasureTheory.Measure.toSphere_eq_zero_iff, Real.ediam_Ico, mellin_comp_mul_right, Real.zero_rpow_le_one, Asymptotics.isLittleO_abs_left, Real.sqrt_le_sqrt_iff', NumberField.Units.regOfFamily_pos, ZLattice.covolume_eq_det, Int.norm_cast_real, Real.isPiSystem_Ioo_rat, Real.posLog_add, GaussianFourier.integral_rexp_neg_mul_sq_norm, irrational_intCast_mul_iff, ENNReal.toReal_eq_one_iff, lp.tsum_mul_le_mul_norm, Real.sin_arctan_lt_zero, NumberField.mixedEmbedding.normAtPlace_real, Complex.exp_bound_sq, ContinuousMap.HomotopyRel.eq_snd, convexOn_norm, bernsteinApproximation.apply, EisensteinSeries.linear_inv_isBigO_right, ampleSet_univ, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero_of_measurable, Behrend.exists_large_sphere, IsMIntegralCurveOn.comp_add, MeasureTheory.SignedMeasure.rnDeriv_add, Real.tendsto_Icc_vitaliFamily_right, HurwitzZeta.hasSum_int_evenKernel₀, Real.tan_add_pi, tendsto_iff_norm_sub_tendsto_zero, integrableOn_rpow_mul_exp_neg_mul_rpow, MeasureTheory.Lp.continuous_posPart, RCLike.map_to_real, SmoothBumpFunction.closedBall_subset, MeasureTheory.Measure.integrable_toReal_rnDeriv, Real.rpow_lt_rpow_left_iff_of_base_lt_one, BoundedContinuousFunction.char_apply, 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, NNReal.concaveOn_rpow, Valued.integer.norm_irreducible_pos, MeasureTheory.Measure.addHaar_real_closedBall, WithLp.prod_antilipschitzWith_ofLp, Real.Angle.sin_sub_pi, ContinuousMap.Homotopy.curry_zero, Metric.sphere.instIsTopologicalGroup, AbsolutelyContinuousOnInterval.hasBasis_totalLengthFilter, MeasureTheory.integral_sum_dirac_eq_tsum, ContDiffOn.arsinh, 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, HasStrictFDerivAt.rpow_const, intervalIntegral.differentiableOn_integral_of_continuous, Hyperreal.tendsto_atTop_iff, RCLike.norm_nnqsmul, ContinuousAlternatingMap.le_opNorm_mul_prod_of_le, Complex.tendsto_exp_comap_re_atBot_nhdsNE, differentiable_circleMap, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge, UpperHalfPlane.mdifferentiable_smul, HolderWith.nndist_le_of_le, ProbabilityTheory.condVar_congr_ae, Real.eq_rpow_inv, HurwitzZeta.evenKernel_undef, Complex.dist_eq_re_im, Archimedean.ratLt'_bddAbove, ENNReal.truncateToReal_nonneg, Complex.conjCAE_toLinearMap, Function.locallyFinsuppWithin.toClosedBall_eval_within, 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, EReal.lt_iff_exists_real_btwn, NormedSpace.Core.norm_eq_zero_iff, integrableOn_exp_mul_complex_Ioi, Asymptotics.isBigOWith_pure, Real.smoothTransition.contDiff, Real.binEntropy_strictMonoOn, Real.Angle.coe_neg, LiouvilleWith.nat_mul_iff, Seminorm.uniformity_eq_of_hasBasis, summable_indicator_mod_iff, image_le_of_liminf_slope_right_le_deriv_boundary, Complex.angle_exp_exp, MeasureTheory.average_eq, Metric.isUniformEmbedding_iff', MeasureTheory.integral_bilinear_hasDerivAt_right_eq_neg_left_of_integrable, ProbabilityTheory.gaussianReal_absolutelyContinuous, AkraBazziRecurrence.isLittleO_self_div_log_id, curveIntegralFun_zero, Real.mul_iSup_of_nonneg, MeasureTheory.Integrable.im, WithLp.dist_fst_le, Affine.Simplex.sSameSide_point_incenter, NumberField.mixedEmbedding.fundamentalCone.intNorm_idealSetEquiv_apply, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, tendsto_rpow_atBot_of_base_gt_one, Real.instTietzeExtension, ProbabilityTheory.indepFun_iff_charFunDual_prod, not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter_aux, Metric.mk_uniformity_basis, le_iff_norm_sqrt_mul_sqrt_inv, MeasureTheory.integral_image_eq_integral_deriv_smul_of_monotoneOn, 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, NormedGroup.nhds_basis_norm_lt, 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, Real.log_neg_iff, 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', LSeries.norm_term_le_of_re_le_re, norm_fst_le, MeasureTheory.Measure.integral_comp_inv_mul_right, MultilinearMap.norm_map_coord_zero, Real.multipliable_of_summable_log, Function.Periodic.tendsto_atBot_intervalIntegral_of_pos, MeasureTheory.BorelCantelli.process_difference_le, RCLike.ofReal_lt_ofReal, strictConvexOn_of_deriv2_pos, Besicovitch.SatelliteConfig.exists_normalized_aux3, BoundedContinuousFunction.integrable_of_nnreal, controlled_prod_of_mem_closure, cfcₙ_integral', ContDiffMapSupportedIn.iteratedFDerivLM_apply_of_le, unitary.continuousOn_argSelfAdjoint, intervalIntegral.integral_nonneg, AffineSubspace.isPreconnected_setOf_sSameSide, Rat.AbsoluteValue.le_pow_log, GromovHausdorff.HD_candidatesBDist_le, Metric.exists_dist_lt_of_hausdorffDist_lt', Complex.rectangle_eq_convexHull, 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, Height.max_mulHeightBound_zero_one_eq_one, IsApproximateAddSubgroup.of_small_tripling, GroupSeminorm.mul_le', IsLocalMinOn.fderivWithin_eq_zero, Real.sSup_nonneg', ProbabilityTheory.integral_tilted_mul_eq_cgf, RCLike.geometric_hahn_banach_open_point, 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, rpow_mul_exp_neg_mul_rpow_isLittleO_exp_neg, SmoothBumpFunction.ball_inter_range_eq_ball_inter_target, Real.Lp_add_le_tsum_of_nonneg', InnerProductGeometry.norm_div_cos_angle_add_of_inner_eq_zero, Real.geom_mean_le_arith_mean_weighted, ConcaveOn.lipschitzOnWith_of_abs_le, Affine.Triangle.dist_orthogonalProjectionSpan_faceOpposite_eq_iff_two_zsmul_oangle_eq, MeasureTheory.SignedMeasure.rnDeriv_sub, MeasureTheory.Measure.addHaar_smul, squeeze_zero', GenLoop.apply_inl_apply_inr_eq_of_mem_boundary_sum, Real.ofDigits_le_one, cfc_imaginaryPart, Quaternion.norm_star, MeasureTheory.hasSum_integral_sum_dirac, mem_closedBall_iff_norm_inv_mul_le', Real.arctan_add_eq_add_pi, Asymptotics.IsBigOWith.const_mul_right, Complex.reCLM_apply, Metric.dist_mem_uniformity, AlgHom.norm_apply_le_self_mul_norm_one, Real.rpow_lt_one_iff', PartitionOfUnity.mem_finsupport, Real.hasDerivAt_negMulLog, NNReal.coe_sInf, Real.arccos_injOn, Diffeology.dSmooth_iff_contDiff, Cardinal.cantorFunction_le, 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, EuclideanGeometry.exists_circumradius_eq_of_cospherical, MeasureTheory.exists_continuous_eLpNorm_sub_le_of_closed, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero, Real.instIsStrictOrderedRing, MeasureTheory.Martingale.ae_not_tendsto_atTop_atBot, LinearMap.IsSymmetric.eigenvectorBasis_def, IsCoercive.antilipschitz, Complex.conjLIE_symm, EuclideanGeometry.angle_eq_angle_div_two_of_oangle_eq_of_sSameSide, LinearMap.card_support_singularValues, 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, StrictConvexOn.slope_lt_of_hasDerivAt, 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, CStarAlgebra.norm_sub_mul_self_le_of_inr, AkraBazziRecurrence.strictAntiOn_smoothingFn, MeasureTheory.Measure.addHaar_image_homothety, Unitary.two_mul_one_sub_cos_norm_argSelfAdjoint, RCLike.ofReal_lt_zero, measurable_dist, MeasureTheory.setIntegral_const, IsCoveringMap.liftPath_trans, Real.rpow_lt_rpow_of_exponent_lt, ContDiffBump.rOut_pos, IsUltrametricDist.norm_nsmul_le, norm_combo_lt_of_ne, ProbabilityTheory.integrable_rpow_mul_exp_of_mem_interior_integrableExpSet, InnerProductSpace.HarmonicContOnCl.differentiableAt, 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, ProbabilityTheory.covariance_fun_sum_fun_sum, ModularGroup.coe_truncatedFundamentalDomain, IsMaxOn.norm_add_sameRay, MeasureTheory.Integrable.comp_div, Affine.Simplex.inner_vsub_vsub_altitudeFoot_eq_height_sq, AkraBazziRecurrence.asympBound_pos, UpperHalfPlane.continuous_re, Zsqrtd.toReal_injective bridge: BoxIntegral.hasIntegralIndicatorConst, MeasureTheory.SimpleFunc.hasBoxIntegral, MeasureTheory.IntegrableOn.hasBoxIntegral, MeasureTheory.SimpleFunc.box_integral_eq_integral

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