abs 📖 | CompOp | 969 mathmath: max_sub_min_eq_abs', EuclideanGeometry.Sphere.mul_dist_eq_abs_power, MeasureTheory.Measure.integral_comp_inv_smul, HurwitzZeta.hasSum_int_hurwitzZetaOdd, Real.Angle.abs_toReal_neg_coe_eq_self_iff, Int.emod_lt_abs, abs_sub_abs_le_abs_add, abs_le_abs_of_nonpos, Real.Angle.sign_two_zsmul_eq_sign_iff, Real.Angle.neg_coe_abs_toReal_of_sign_nonpos, abs_lt_of_sq_lt_sq, norm_torusIntegral_le_of_norm_le_const, HasStrictFDerivAt.abs_of_pos, CauSeq.lt_irrefl, Int.abs_le_sqrt, EuclideanGeometry.abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq, MeasureTheory.Measure.addHaar_image_continuousLinearMap, Summable.abs, Real.abs_sinc_le_one, sign_mul_self, Int.negOnePow_abs, Set.abs_sub_right_of_mem_uIcc, Real.smul_map_volume_mul_right, ContinuousMap.abs_mem_subalgebra_closure, Matrix.abs_det_reindex, ZSpan.volume_real_fundamentalDomain, NumberField.mixedEmbedding.convexBodyLT'_mem, HurwitzZeta.hasSum_int_hurwitzZetaEven, Complex.norm_polarCoord_symm, MeasureTheory.Measure.integral_comp_mul_right, Function.locallyFinsuppWithin.toClosedBall_support_subset_closedBall, Finset.abs_sum_of_nonneg', MeasureTheory.integral_image_eq_integral_abs_det_fderiv_smul, abs_sub_round, abs_add_eq_add_abs_iff, Asymptotics.IsBigOWith.abs_right, Asymptotics.isBigO_abs_abs, ModularForm.mul_slash, deriv_abs, Complex.norm_le_abs_re_add_abs_im, CauSeq.sup_inf_distrib_right, Real.abs_cos_le_one, abs_neg, isLittleO_exp_neg_mul_sq_cocompact, Real.young_inequality, norm_jacobiTheta₂_term_fderiv_ge, ArchimedeanOrder.le_def, one_le_pow_mul_abs_eval_div, range_circleMap, Real.ofCauchy_sup, Asymptotics.IsBigO.abs_left, Int.cast_abs, NNRat.abs_coe, ZLattice.covolume_eq_det_inv, abs_dvd, Matrix.abs_det_submatrix_equiv_equiv, abs_eq_iff_mul_self_eq, Real.Angle.eq_iff_sign_eq_and_abs_toReal_eq, Chebyshev.abs_psi_sub_theta_le_sqrt_mul_log, differentiableWithinAt_abs_pos, abs_le_max_abs_abs, abs_smul, NumberField.dedekindZeta_residue_def, Zsqrtd.abs_norm, Asymptotics.isLittleO_abs_abs, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, two_nsmul_sup_eq_add_add_abs_sub, abs_le_of_sq_le_sq, Complex.angle_exp_one, RootPairing.Base.cartanMatrix_map_abs, Real.log_abs, norm_abs_sub_abs, NumberField.mixedEmbedding.norm_eq_norm, Real.cosh_abs, IsCoprime.abs_right_iff, UpperHalfPlane.im_smul_eq_div_normSq, TopologicalSpace.Opens.CompleteCopy.dist_eq, NumberField.Units.regOfFamily_eq_det, Rat.coe_nnabs, le_abs_self, EisensteinSeries.abs_le_right_of_norm, nhds_basis_abs_sub_lt, Real.summable_one_div_nat_add_rpow, NumberField.FinitePlace.prod_eq_inv_abs_norm, Real.abs_tanh_lt_one, AbsoluteValue.abs_abv_sub_le_abv_sub, Int.abs_sub_lt_of_lt_lt, CauSeq.sup_idem, PNat.dist_eq, Pi.abs_def, RCLike.abs_im_div_norm_le_one, ModularForm.prod_slash, NumberField.abs_discr_ge', FractionalIdeal.absNorm_eq', NumberField.abs_discr_ge, setOf_liouvilleWith_subset_aux, differentiableWithinAt_abs, add_abs_eq_two_nsmul_posPart, ProbabilityTheory.integrable_pow_abs_of_integrable_exp_mul, hasStrictDerivAt_abs_pos, min_abs_abs_le_abs_min, hasDerivWithinAt_abs_pos, Rat.dist_eq, abs_dvd_abs, Asymptotics.IsLittleO.abs_left, MeasureTheory.integrableOn_image_iff_integrableOn_abs_det_fderiv_smul, MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_image, Real.smul_map_diagonal_volume_pi, abs_ite, ArchimedeanClass.mk_le_mk, deriv_abs_neg, Real.Angle.abs_toReal_eq_pi_div_two_iff, ModularForm.prod_slash_sum_weights, DifferentiableWithinAt.abs_of_pos, EuclideanGeometry.dist_eq_abs_sub_dist_of_angle_eq_zero, Pi.abs_apply, Real.Angle.abs_toReal_le_pi, MeasureTheory.Measure.addHaar_preimage_smul, Real.abs_sinh, RCLike.abs_re_le_norm, CauSeq.const_lt, Asymptotics.isBigO_abs_left, neg_abs_le_neg, Nat.abs_cast, tendsto_zero_iff_abs_tendsto_zero, Real.Angle.abs_cos_eq_abs_sin_of_two_zsmul_add_two_zsmul_eq_pi, MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_det_fderiv_mul, Polynomial.abs_div_tendsto_atTop_of_degree_gt, Orientation.abs_volumeForm_apply_of_orthonormal, HahnSeries.support_abs, Real.ofCauchy_zero, abs_of_neg, Even.zpow_abs, CauSeq.inf_comm, RCLike.norm_ofReal, NumberField.Units.dirichletUnitTheorem.seq_next, abs_lt_norm_sub_of_not_sameRay, image_circleMap_Ioc, apply_abs_le_mul_of_one_le, Real.cauSeq_converges, apply_abs_le_mul_of_one_le', abs_fst_of_mem_pi_polarCoord_target, Affine.Simplex.abs_inner_vsub_altitudeFoot_div_lt_one, HasStrictFDerivAt.abs, NumberField.FinitePlace.prod_eq_inv_abs_norm_int, AbsoluteValue.exists_partition_int, Real.Angle.sign_two_nsmul_eq_neg_sign_iff, Real.ofCauchy_mul, HahnSeries.abs_lt_abs_of_orderTop_ofLex, NumberField.house_intCast, RCLike.abs_re_div_norm_le_one, NumberField.Units.dirichletUnitTheorem.logEmbedding_component_le, EuclideanGeometry.Sphere.dist_div_sin_oangle_div_two_eq_radius, abs_pos_of_pos, mabs_zpow, abs_eq_max_neg, Hyperreal.infinite_abs_iff, Polynomial.abs_div_tendsto_atBot_atTop_of_degree_gt, GenContFract.abs_sub_convergents_le', abs_sub_le, Real.infinite_rat_abs_sub_lt_one_div_den_sq_of_irrational, Real.log_two_near_10, Real.coe_toNNReal_le, Differentiable.abs, abs_le, abs_real_inner_le_norm, nhds_basis_zero_abs_lt, MeasureTheory.Measure.integral_comp_inv_mul_left, nhds_eq_iInf_abs_sub, ModularGroup.tendsto_abs_re_smul, CauSeq.not_limZero_of_pos, Polynomial.abs_div_tendsto_atTop_atTop_of_degree_gt, Real.isTheta_exp_comp_one, Real.cauchy_sub, SameRay.norm_sub, Real.volume_preimage_mul_left, Real.summable_abs_int_rpow, ProbabilityTheory.integrable_rpow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, Real.mk_one, abs_nnqsmul, hasDerivAt_abs_neg, ProbabilityTheory.integrable_exp_mul_abs, CauSeq.coe_sup, IsAbsoluteValue.abs_isAbsoluteValue, norm_circleMap_zero, Real.sqrt_sq_eq_abs, Ideal.span_singleton_abs, Real.map_matrix_volume_pi_eq_smul_volume_pi, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff', hasDerivWithinAt_abs, Rat.num_abs_eq_abs_num, abs_sub, Asymptotics.IsLittleO.abs_abs, Mathlib.Meta.NormNum.isNNRat_abs_neg, abs_inv, Rel.abs_edgeDensity_sub_edgeDensity_le_two_mul, abs_sub_sup_add_abs_sub_inf, Finset.abs_sum_of_nonneg, intervalIntegral.abs_intervalIntegral_eq, Filter.Tendsto.abs, abs_sub_lt_of_nonneg_of_lt, CauSeq.mul_pos, Real.ofCauchy_nnratCast, Hyperreal.isSt_iff_abs_sub_lt_delta, Real.smul_map_volume_mul_left, abs_max_sub_max_le_abs, Complex.abs_re_eq_norm, Real.Angle.cos_nonneg_iff_abs_toReal_le_pi_div_two, sq_le_sq, Real.Angle.abs_toReal_neg, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_of_norm_le, ZSpan.measureReal_fundamentalDomain, Finset.abs_sum_le_sum_abs, apply_abs_le_add_of_nonneg, MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar, abs_pow_eq_one, ProbabilityTheory.abs_truncation_le_bound, ArchimedeanClass.mk_lt_mk, abs_neg_one_pow, neg_abs_le, abs_eq, NumberField.Units.regulator_eq_det, ConvexOn.isBoundedUnder_abs, Polynomial.abs_tendsto_atTop_iff, abs_add_eq_two_nsmul_posPart, Real.lt_cauchy, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux1, Complex.dist_self_conj, ProbabilityTheory.integrable_rpow_abs_mul_exp_of_mem_interior_integrableExpSet, HasFDerivWithinAt.abs_of_neg, CauSeq.add_pos, eqOn_abs_add_one_of_isMIntegralCurveOn_Ioo, Real.exists_rat_abs_sub_lt_and_lt_of_irrational, abs_pos_of_neg, Rat.finite_rat_abs_sub_lt_one_div_den_sq, sign_mul_abs, Real.abs_le_sqrt, Affine.Simplex.abs_inner_vsub_altitudeFoot_lt_mul, norm_cauchyPowerSeries_le, abs_dist_sub_le, Int.cast_natAbs, abs_mul, Real.Angle.coe_abs_toReal_of_sign_nonneg, MeasureTheory.Measure.addHaar_preimage_continuousLinearMap, abs_one_div, eventually_abs_sub_lt, Complex.abs_arg_le_pi, AddCircle.norm_coe_mul, HurwitzZeta.hasSum_nat_hurwitzZetaEven, NumberField.Units.finrank_mul_regOfFamily_eq_det, Equiv.Perm.sign_abs, Real.instIsCompleteAbs, abs_sub_le_iff, abs_div, MeasureTheory.volume_sum_rpow_lt, Asymptotics.isBigOWith_abs_left, hasDerivAt_abs_rpow, abs_sub_round_div_natCast_eq, ZSpan.volume_fundamentalDomain, Polynomial.abs_tendsto_atTop, abs_dist_sub_le_dist_mul_mul, AddCircle.norm_half_period_eq, NumberField.det_basisOfFractionalIdeal_eq_absNorm, ZSpan.measure_fundamentalDomain, Real.logb_abs_base, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image, Complex.abs_im_le_norm, MeasureTheory.Measure.integral_comp_smul, max_zero_add_max_neg_zero_eq_abs_self, MeasureTheory.AEEqFun.coeFn_abs, HasFDerivAt.abs_of_pos, Int.one_le_abs, Real.abs_cos_int_mul_pi, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv_aux1, Real.ofCauchy_sub, abs_sub_lt_iff, HasFDerivAt.abs, Real.mk_lt, NumberField.Units.norm, Real.abs_iteratedDeriv_cos_le_one, AbsoluteValue.abs_apply, ProbabilityTheory.integrable_pow_abs_mul_exp_of_mem_interior_integrableExpSet, HasStrictFDerivAt.abs_of_neg, HasFDerivWithinAt.abs, Int.dist_eq', EuclideanGeometry.Sphere.dist_div_sin_oangle_eq_two_mul_radius, ProbabilityTheory.integrable_rpow_abs_mul_exp_of_integrable_exp_mul, Int.abs_le_sqrt_iff_sq_le, MeasureTheory.aemeasurable_ofReal_abs_det_fderivWithin, abs_sq, abs_lt_iff_mul_self_lt, Complex.abs_im_eq_norm, Orientation.abs_volumeForm_apply_of_pairwise_orthogonal, DifferentiableWithinAt.abs, NumberField.mixedEmbedding.convexBodySumFun_smul, Nat.cast_natAbs, Real.abs_mulExpNegMulSq_comp_le_norm, contDiffOn_abs, Real.coe_nnabs, dist_integral_mulExpNegMulSq_comp_le, ProbabilityTheory.integrable_exp_abs_mul_abs_add, Real.exp_one_near_20, MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_det_fderiv_mul, Polynomial.abs_tendsto_atBot_iff, MeasureTheory.volume_sum_rpow_le, MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_deriv_mul', uniform_continuous_npow_on_bounded, HahnSeries.order_abs, MeasureTheory.integral_image_eq_integral_abs_deriv_smul, FixedDetMatrices.reps_entries_le_m', NumberField.abs_discr_gt_two, sup_eq_half_smul_add_add_abs_sub', intervalIntegral.abs_integral_mono_interval, HurwitzZeta.hasSum_int_cosZeta, norm_abs_zsmul, Complex.isCauSeq_norm_exp, ContDiffOn.abs, Real.rpow_sum_le_const_mul_sum_rpow, Real.exists_nat_abs_mul_sub_round_le, HasProd.abs, Continuous.abs, sup_eq_half_smul_add_add_abs_sub, self_dvd_abs, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, Real.exp_abs_le, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, round_le, abs_sub_round_eq_min, Nat.dist_eq, RCLike.abs_wInner_le, norm_zpow_abs, GenContFract.of_convergence_epsilon, exists_polynomial_near_of_continuousOn, NumberField.mixedEmbedding.covolume_idealLattice, add_abs_nonneg, tendsto_abs_nhdsNE_zero, SimpleGraph.nonuniformWitnesses_spec, lt_abs, exists_abs_lt, ZMod.intCast_abs_mod_two, Real.mk_mul, Complex.angle_eq_abs_arg, Function.locallyFinsuppWithin.toClosedBall_divisor, BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg, le_abs, EuclideanGeometry.Sphere.abs_oangle_center_left_toReal_lt_pi_div_two, Int.norm_eq_abs, MeasureTheory.lintegral_image_eq_lintegral_abs_det_fderiv_mul, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv_aux2, abs_mul_sign, integral_comp_abs, ContinuousMap.abs_apply, MeasureTheory.Measure.addHaar_parallelepiped, Set.abs_projIcc_sub_projIcc, abs_by_cases, IsCoprime.abs_right, MeasureTheory.integral_target_eq_integral_abs_det_fderiv_smul, Real.posLog_eq_zero_iff, Filter.tendsto_abs_atBot_atTop, UpperHalfPlane.im_smul, Real.cauchy_inv, Int.abs_fract, Filter.comap_abs_atTop, Real.abs_sin_sub_sin_le, Real.rpow_logb_eq_abs, Real.Angle.abs_cos_eq_abs_sin_of_two_nsmul_add_two_nsmul_eq_pi, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, Real.abs_rpow_of_nonneg, Real.cauchy_nnratCast, ModularGroup.exists_row_one_eq_and_min_re, abs_max_sub_max_le_max, Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius, ValueDistribution.characteristic_sub_characteristic_inv_le, ArchimedeanClass.mk_abs, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, ArchimedeanClass.mk_le_mk_iff_lt, EuclideanGeometry.dist_eq_abs_sub_dist_iff_angle_eq_zero, Real.mk_add, Hyperreal.infinitePos_abs_iff_infinite_abs, tendsto_rpow_abs_mul_exp_neg_mul_sq_cocompact, abs_norm', ProbabilityTheory.meas_ge_le_variance_div_sq, differentiableAt_abs_neg, real_inner_self_abs, Int.abs_le_one_iff, AddSubgroup.relIndex_eq_abs_det, abs_mul_self, deriv_abs_zero, hasStrictDerivAt_abs, one_le_sq_iff_one_le_abs, RCLike.abs_im_le_norm, norm_intCast_abs, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_lt', Set.mem_Icc_iff_abs_le, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, HasFDerivAt.abs_of_neg, ContinuousLinearMap.rayleighQuotient_le_norm, abs_norm_sub_norm_le, Nat.abs_sub_ceil_le, NumberField.Ideal.tendsto_norm_le_div_atTop₀, min_abs_abs_le_abs_max, abs_sub_abs_le_abs_sub, SimpleGraph.not_isUniform_iff, MeasureTheory.lpNorm_abs, Rat.uniformContinuous_abs, deriv_abs_pos, Real.abs_sin_half, DifferentiableOn.abs, Real.abs_sin_eq_sqrt_one_sub_cos_sq, EuclideanGeometry.Sphere.abs_oangle_center_right_toReal_lt_pi_div_two, AkraBazziRecurrence.GrowsPolynomially.abs, associated_abs_left_iff, Birkhoff_inequalities, Real.abs_rpow_le_abs_rpow, MeasureTheory.Measure.integral_comp_mul_left, MeasureTheory.Integrable.abs, Asymptotics.isBigOWith_abs_abs, isLittleO_abs_log_rpow_rpow_nhdsGT_zero, Liouville.frequently_exists_num, Complex.norm_ratCast, nnnorm_intCast_abs, Real.ofCauchy_natCast, max_sub_min_eq_abs, Complex.abs_im_lt_norm, MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_deriv_mul, Affine.Simplex.inradius_eq_abs_inv_sum, FractionalIdeal.absNorm_eq, MeasureTheory.setIntegral_abs_condExp_le, nnnorm_zpow_abs, NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_le, Int.natAbs_abs, Multipliable.abs, MeasurableEmbedding.gaussianReal_comap_apply, alternating_series_error_bound, Real.Angle.sign_two_nsmul_eq_sign_iff, Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder, Real.enorm_eq_ofReal_abs, zpow_abs_eq_one, NumberField.mixedEmbedding.norm_smul, circleMap_preimage_codiscrete, Complex.abs_arg_inv, MeasureTheory.integral_comp_rpow_Ioi, Real.posLog_abs, InnerProductGeometry.mul_norm_eq_abs_sub_sq_norm, abs_nonpos_iff, abs_real_inner_div_norm_mul_norm_le_one, MeasureTheory.Measure.addHaar_image_linearMap, intervalIntegral.abs_integral_le_integral_abs, self_mul_sign, CauSeq.le_sup_left, Real.cauchy_natCast, abs_choice, Nat.abs_sub_floor_le, differentiableWithinAt_abs_neg, Complex.abs_arg_le_pi_div_two_iff, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, FractionalIdeal.absNorm_span_singleton, LiouvilleWith.frequently_lt_rpow_neg, Real.ofCauchy_ratCast, Asymptotics.IsBigOWith.abs_abs, Prime.abs, sq_lt_one_iff_abs_lt_one, hasStrictDerivAt_abs_neg, RCLike.isCauSeq_norm, DifferentiableWithinAt.abs_of_neg, Real.abs_cos_sub_cos_le, AddCircle.norm_coe_eq_abs_iff, ZLattice.covolume_eq_det_mul_measureReal, Int.abs_negOnePow, abs_cases, Int.isUnit_iff_abs_eq, RCLike.isCauSeq_im, NumberField.mixedEmbedding.covolume_integerLattice, Real.nnnorm_abs, MeasureTheory.integrableOn_image_iff_integrableOn_abs_deriv_smul, CauSeq.const_le, Int.abs_sign_of_ne_zero, summable_abs_iff, Int.sign_eq_abs_ediv, MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_deriv_mul, abs_pos, abs_unit_intCast, abs_signedDist_eq_dist_iff_vsub_mem_span, cexp_neg_quadratic_isLittleO_abs_rpow_cocompact, abs_sub_map_le_div, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le, abs_sup_sub_sup_le_abs, map_abs, ProbabilityTheory.integrable_exp_mul_abs_add, Filter.Germ.const_abs, Rat.den_abs_eq_den, Real.Angle.sign_two_zsmul_eq_neg_sign_iff, not_sameRay_iff_abs_lt_norm_sub, Orientation.abs_areaForm_le, ZLattice.exists_forall_abs_repr_le_norm, sq_lt_sq, MeasureTheory.Measure.addHaar_image_continuousLinearEquiv, ContinuousOn.abs, Real.tendsto_abs_tan_of_cos_eq_zero, Real.Angle.abs_cos_eq_of_two_zsmul_eq, BoundedContinuousFunction.coe_abs, Real.sin_div_le_inv_abs, ProbabilityTheory.integrable_exp_abs_mul_abs, CauSeq.sup_comm, NumberField.finite_of_discr_bdd, Real.Angle.abs_toReal_add_abs_toReal_eq_pi_of_two_zsmul_add_eq_zero_of_sign_eq, Real.Lp_add_le, Real.ofCauchy_intCast, abs_nsmul, Real.exists_rat_abs_sub_le_and_den_le, Real.abs_sin_lt_abs, MeasureTheory.measureReal_abs_gt_le_integral_charFun, EuclideanGeometry.mul_dist_eq_abs_sub_sq_dist, Real.cosh_lt_cosh, NumberField.Units.abs_det_eq_abs_det, Real.abs_circleAverage_le_circleAverage_abs, Polynomial.isBoundedUnder_abs_atBot_iff, abs_mem_iff, HasFDerivWithinAt.abs_of_pos, Liouville.exists_pos_real_of_irrational_root, ArchimedeanClass.mk_le_mk_iff_ratCast, Real.volume_real_interval, Complex.abs_im_div_norm_le_one, Real.ofCauchy_div, abs_zero, ProbabilityTheory.integrable_rpow_abs_of_integrable_exp_mul, Mathlib.Meta.NormNum.isNNRat_abs_nonneg, ConcaveOn.isBoundedUnder_abs, ProbabilityTheory.gaussianPDFReal_inv_mul, Real.abs_log_mul_self_rpow_lt, Rat.cast_abs, Complex.abs_re_le_norm, Real.map_linearMap_volume_pi_eq_smul_volume_pi, Int.dist_eq, CauSeq.inf_le_right, mellin_comp_rpow, sq_eq_sq_iff_abs_eq_abs, Real.abs_mulExpNegMulSq_one_le_one, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, abs_of_nonpos, norm_abs_eq_norm, abs_pow_sub_pow_le, ContDiffWithinAt.abs, IsCoprime.abs_left_iff, Real.dist_eq, Orientation.abs_areaForm_of_orthogonal, one_lt_sq_iff_one_lt_abs, UnitAddCircle.norm_eq, Set.Icc.abs_sub_addNSMul_le, IsCoprime.abs_left, Rel.abs_edgeDensity_sub_edgeDensity_le_two_mul_sub_sq, Module.Basis.abs_det_adjustToOrientation, EuclideanGeometry.abs_oangle_left_toReal_lt_pi_div_two_of_dist_eq, Real.sqrt_mul_self_eq_abs, MeasureTheory.Measure.map_addHaar_smul, comap_abs_nhds_zero, CauSeq.exists_lt, LiouvilleWith.exists_pos, Int.emod_abs, Rat.abs_def, ArchimedeanClass.mk_eq_mk, Real.cauchy_neg, intervalIntegral.norm_integral_le_of_norm_le_const_ae, differentiableAt_abs_pos, NNReal.abs_eq, ProbabilityTheory.integrable_rpow_abs_of_mem_interior_integrableExpSet, Int.abs_eq_normalize, ArithmeticFunction.abs_moebius_eq_one_of_squarefree, Real.isTheta_exp_comp_exp_comp, abs_add', Measurable.abs, CFC.abs_intCast, abs_neg_one_zpow, ArchimedeanClass.mk_le_mk_iff_denselyOrdered, Real.mk_const, Set.abs_sub_le_of_uIcc_subset_uIcc, Complex.abs_arg_lt_pi_div_two_iff, Real.Angle.abs_toReal_coe_eq_self_iff, NumberField.exists_ideal_in_class_of_norm_le, ZLattice.abs_repr_lt_of_norm_lt, circleIntegrable_sub_zpow_iff, Real.dist_0_eq_abs, Int.sign_mul_self_eq_abs, Real.cosh_le_cosh, abs_eq_zero, abs_dist, Affine.Simplex.exradius_eq_abs_inv_sum, Rel.abs_edgeDensity_sub_edgeDensity_le_one_sub_mul, NumberField.Ideal.tendsto_norm_le_div_atTop, hasDerivAt_abs, Real.cauchy_intCast, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt', ProbabilityTheory.integrable_pow_abs_of_mem_interior_integrableExpSet, Real.abs_cos_eq_sqrt_one_sub_sin_sq, Real.mk_zero, Asymptotics.isLittleO_abs_right, Nat.abs_floor_sub_le, Real.cauchy_add, MeasureTheory.Measure.addHaar_preimage_linearMap, abs_eq_neg_self, associated_abs_right_iff, Real.ofCauchy_add, abs_sub_nonpos, CauSeq.le_total, sameRay_iff_norm_sub, Real.uniformContinuous_abs, Mathlib.Meta.Positivity.abs_pos_of_ne_zero, abs_sub_map_le_sub, Finset.abs_expect_le, Real.volume_uIoo, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv, MeasureTheory.Measure.addHaar_preimage_continuousLinearEquiv, abs_sub_sq, Hyperreal.infinite_iff_abs_lt_abs, Orientation.volumeForm_robust', Polynomial.isBoundedUnder_abs_atTop_iff, Multipliable.abs_tprod, Set.abs_sub_left_of_mem_uIcc, InnerProductGeometry.norm_sub_eq_abs_sub_norm_iff_angle_eq_zero, EuclideanGeometry.angle_eq_abs_oangle_toReal, Complex.lim_im, Real.ofCauchy_inv, ExistsContDiffBumpBase.w_def, abs_le_abs_of_nonneg, MeasureTheory.Measure.setIntegral_comp_smul, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, Real.cauchy_zero, circleAverage_log_norm_factorizedRational, Real.toNNReal_abs, neg_le_abs, EuclideanGeometry.abs_oangle_toReal_lt_pi_div_two_of_angle_eq_pi_div_two, Real.ofCauchy_neg, MeasureTheory.restrict_map_withDensity_abs_det_fderiv_eq_addHaar, ModularGroup.abs_c_le_one, ProbabilityTheory.rpow_abs_le_mul_max_exp, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, Int.abs_sign_of_nonzero, CauSeq.le_sup_right, sub_abs_eq_neg_two_nsmul_negPart, ModularGroup.abs_two_mul_re_lt_one_of_mem_fdo, Complex.norm_sub_eq_iff, Real.abs_sin_eq_one_iff, Orientation.angle_eq_abs_oangle_toReal, Real.Angle.cos_pos_iff_abs_toReal_lt_pi_div_two, circleIntegral.norm_integral_le_of_norm_le_const', abs_abs_sub_abs_le_abs_sub, abs_dist_sub_le_dist_add_add, SimpleGraph.nonuniformWitness_spec, Rat.infinitePlace_apply, Int.sign_eq_ediv_abs', Real.abs_iteratedDeriv_sin_le_one, ProbabilityTheory.integrable_pow_abs_mul_cexp_of_re_mem_interior_integrableExpSet, abs_lt, MeasureTheory.abs_integral_le_integral_abs, isMIntegralCurve_abs_add_one_of_isMIntegralCurveOn_Ioo, Real.mk_inf, DifferentiableAt.abs, ArchimedeanOrder.lt_def, IntervalIntegrable.abs, pow_abs, Int.abs_one_sub_fract, abs_max_le_max_abs_abs, NumberField.abs_discr_ge_of_isTotallyComplex, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff, Real.Angle.cos_neg_iff_pi_div_two_lt_abs_toReal, ProbabilityTheory.rpow_abs_le_mul_exp_abs, EReal.abs_def, Complex.isCauSeq_im, Polynomial.abs_tendsto_atBot, ProbabilityTheory.integrable_pow_abs_mul_exp_of_integrable_exp_mul, Real.logb_abs, MeasureTheory.lintegral_image_eq_lintegral_abs_deriv_mul, dvd_abs, abs_of_nonneg, ContDiff.abs, abs_mul_abs_self, intervalIntegral.norm_integral_le_of_norm_le_const, abs_sub_le_max_sub, two_nsmul_inf_eq_add_sub_abs_sub, ProbabilityTheory.abs_truncation_le_abs_self, Int.abs_le_floor_nnreal_iff, MeasureTheory.aemeasurable_toNNReal_abs_det_fderivWithin, ContinuousWithinAt.abs, EisensteinSeries.abs_le_left_of_norm, posPart_add_negPart, Real.mk_eq, RootPairing.GeckConstruction.lie_e_lie_f_apply, AddCircle.norm_le_half_period, NumberField.mixedEmbedding.normAtPlace_smul, Complex.abs_re_lt_norm, Real.ofCauchy_one, intervalIntegral.abs_integral_eq_abs_integral_uIoc, Real.inner_le_Lp_mul_Lq, ProbabilityTheory.meas_ge_le_evariance_div_sq, Real.map_volume_mul_right, ZMod.abs_valMinAbs_eq_abs_valMinAbs, norm_intCast_eq_abs_mul_norm_one, MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_deriv_mul', Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, NumberField.isUnit_iff_norm, Int.modEq_abs, ModularForm.prod_fintype_slash, abs_abs, circleIntegrable_sub_inv_iff, FractionalIdeal.abs_det_basis_change, Rat.AbsoluteValue.real_eq_abs, ProbabilityTheory.rpow_abs_le_mul_max_exp_of_pos, Real.mk_sup, Int.abs_sub_lt_one_of_floor_eq_floor, abs_sub_comm, Real.tendsto_abs_logb_atTop, MeasureTheory.Measure.addHaar_preimage_linearEquiv, Complex.angle_one_left, InnerProductGeometry.norm_sub_eq_abs_sub_norm_of_angle_eq_zero, abs_real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, HurwitzZeta.hasSum_int_sinZeta, abs_norm_sub_norm_le', inf_eq_half_smul_add_sub_abs_sub, abs_dite, IsAbsoluteValue.abs_abv_sub_le_abv_sub, sq_le_one_iff_abs_le_one, Polynomial.abs_isBoundedUnder_iff, Int.abs_ediv_le_abs, Rat.sqrt_eq, hasDerivWithinAt_abs_neg, Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_abs, contDiffWithinAt_abs, Real.abs_sin_le_abs, ProbabilityTheory.strong_law_aux1, Hyperreal.coe_abs, ContinuousLinearMap.bddAbove_rayleighQuotient, Asymptotics.IsBigO.abs_abs, even_abs, Complex.angle_one_right, Complex.IsExpCmpFilter.abs_im_pow_eventuallyLE_exp_re, MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_image₀, ModularForm.slash_def, Complex.lim_norm, Real.abs_sin_le_one, FractionalIdeal.absNorm_div_norm_eq_absNorm_div_norm, ContinuousAt.abs, HahnSeries.orderTop_abs, abs_dvd_self, inf_eq_half_smul_add_sub_abs_sub', Int.abs_lt_one_iff, MeasureTheory.Lp.coeFn_abs, Filter.isBoundedUnder_le_abs, Int.le_abs_of_dvd, ZLattice.normBound_spec, Real.tendsto_abs_tan_atTop, Real.enorm_abs, SchwartzMap.le_seminorm', NumberField.mixedEmbedding.norm_real, AlternatingMap.measure_parallelepiped, Real.abs_mulExpNegMulSq_le, IsCoprime.abs_abs_iff, intervalIntegral.norm_integral_le_abs_integral_norm, AddCircle.norm_eq, NumberField.abs_discr_rpow_ge_of_isTotallyComplex, Nat.abs_ofNat, Orientation.abs_oangle_sub_left_toReal_lt_pi_div_two, AddSubgroup.isLeast_of_closure_iff_eq_abs, nnnorm_abs_zsmul, Real.exp_one_near_10, summable_pow_mul_jacobiTheta₂_term_bound, Real.Angle.abs_cos_eq_of_two_nsmul_eq, Real.Angle.abs_toReal_add_abs_toReal_eq_pi_of_two_nsmul_add_eq_zero_of_sign_eq, Complex.isCauSeq_norm, ENNReal.abs_toReal, apply_abs_le_add_of_nonneg', abs_of_pos, Complex.IsExpCmpFilter.tendsto_abs_re, Real.cauchy_one, sq_abs, Asymptotics.IsBigO.abs_right, Int.ediv_emod_unique'', differentiableOn_abs, Real.abs_ofDigits_sub_ofDigits_le, Real.circleAverage_abs_radius, ContDiffAt.abs, AEMeasurable.abs, EReal.coe_abs, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux2, CauSeq.lt_total, NNReal.dist_eq, Hyperreal.abs_omega, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, Real.Angle.abs_sin_eq_of_two_zsmul_eq, abs_add_le, abs_norm, Associated.abs_right, Subgroup.HasDetPlusMinusOne.abs_det, abs_add_three, Real.cauchy_ratCast, Real.Angle.abs_toReal_add_eq_two_pi_sub_abs_toReal_add_abs_toReal, Asymptotics.isBigOWith_abs_right, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, Real.abs_rpow_le_exp_log_mul, gauge_smul_left, UpperHalfPlane.mem_verticalStrip_iff, NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop, Real.half_mul_log_add_log_abs, MeasurableEquiv.gaussianReal_map_symm_apply, sup_sub_inf_eq_abs_sub, abs_one, zmultiples_abs, Metric.isBounded_of_abs_le, abs_sub_le_of_le_of_le, ArithmeticFunction.abs_moebius_le_one, NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply, abs_real_inner_div_norm_mul_norm_eq_one_iff, CauSeq.exists_gt, Real.cauchy_mul, Real.Angle.abs_sin_eq_of_two_nsmul_eq, GaussianFourier.verticalIntegral_norm_le, Hyperreal.abs_lt_real_iff_infinitesimal, Multiset.abs_sum_le_sum_abs, abs_le_one_iff_mul_self_le_one, odd_abs, Real.volume_uIoc, Real.ringEquivCauchy_apply, CircleIntegrable.abs, TFAE_exists_lt_isLittleO_pow, ProbabilityTheory.gaussianPDFReal_mul, Real.mk_neg, abs_integral_sub_setIntegral_mulExpNegMulSq_comp_lt, abs_sub_pos, CauSeq.trichotomy, AddCircle.norm_eq', NumberField.Units.finrank_mul_regulator_eq_det, NumberField.InfinitePlace.prod_eq_abs_norm, Real.abs_cos_eq_one_iff, continuous_abs, abs_min_sub_min_le_max, HurwitzZeta.hasSum_int_completedCosZeta, abs_signedDist_le_dist, Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius, abs_eq_abs, abs_abs_sub_abs_le, MeasureTheory.integrableOn_Ioi_comp_rpow_iff, RootPairing.Base.abs_cartanMatrix_apply, Complex.abs_cpow_inv_two_im, NumberField.Units.regulator_eq_det', differentiableAt_abs, intervalIntegral.norm_integral_le_abs_of_norm_le, Complex.norm_le_sqrt_two_mul_max, Polynomial.Chebyshev.abs_eval_T_real_le_one_iff, Set.abs_indicator_symmDiff, abs_eq_self, Filter.tendsto_abs_atTop_atTop, abs_zsmul, HurwitzZeta.hasSum_int_completedSinZeta, abs_min_le_max_abs_abs, Hyperreal.infinitePos_abs_iff_infinite, abs_nonneg, NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completion, MeasureTheory.integral_abs_condExp_le, Complex.norm_intCast, abs_sub_eq_two_nsmul_negPart, CauSeq.sup_inf_distrib_left, abs_zpow, abs_le', tendsto_pow_atTop_nhds_zero_iff, ValueDistribution.abs_characteristic_sub_characteristic_shift_le, Real.mem_closure_iff, Asymptotics.IsLittleO.abs_right, CauSeq.inf_idem, HurwitzZeta.hasSum_int_completedHurwitzZetaEven, OrthonormalBasis.abs_det_adjustToOrientation, RCLike.isCauSeq_re, Real.log_of_ne_zero, Nat.abs_ceil_sub_le, abs_sub_le_of_nonneg_of_le, Real.exp_log_eq_abs, NumberField.Units.regOfFamily_eq_det', Asymptotics.IsBigOWith.abs_left, abs_le_abs, Real.mk_le, Real.sinc_le_inv_abs, AddCircle.norm_eq_of_zero, Real.abs_log_mul_self_lt, Real.volume_preimage_mul_right, Real.ringEquivCauchy_symm_apply_cauchy, UpperHalfPlane.smulAux'_im, integral_pow_abs_sub_uIoc, Mathlib.Meta.NormNum.isNat_abs_neg, Even.pow_abs, abs_zsmul_eq_zero, MeasureTheory.map_withDensity_abs_det_fderiv_eq_addHaar, Complex.isCauSeq_re, Real.isCauSeq_iff_lift, ODE.FunSpace.dist_iterate_next_apply_le, DifferentiableAt.abs_of_pos, abs_le_iff_mul_self_le, Finset.abs_prod, circleMap_mem_sphere', Int.sign_mul_abs, measurable_abs, Metric.isBounded_of_abs_lt, Real.norm_eq_abs, DifferentiableAt.abs_of_neg, Real.exists_int_int_abs_mul_sub_le, exists_rat_near, CauSeq.const_pos, not_differentiableAt_abs_zero, MeasureTheory.volume_sum_rpow_lt_one, Complex.dist_conj_self, abs_inf_sub_inf_le_abs, le_abs', IsCoprime.abs_abs, Filter.Germ.abs_def, Asymptotics.superpolynomialDecay_iff_abs_tendsto_zero, Real.summable_one_div_int_add_rpow, abs_pow, Real.cos_abs, MeasureTheory.Measure.integral_comp_div, CauSeq.coe_inf, HasCompactSupport.abs, MeasureTheory.lpNorm_fun_abs, Orientation.abs_oangle_sub_right_toReal_lt_pi_div_two, Polynomial.Chebyshev.abs_eval_T_real_eq_one_iff, hasDerivAt_abs_pos, GenContFract.abs_sub_convs_le, RootPairing.GeckConstruction.e_lie_u, Real.infinite_rat_abs_sub_lt_one_div_den_sq_iff_irrational, Polynomial.abs_leadingCoeff_eq_one_of_mahlerMeasure_eq_one, Subgroup.hasDetPlusMinusOne_iff_abs_det, Int.abs_natCast, Complex.abs_re_div_norm_le_one, Int.abs_eq_natAbs, CauSeq.inf_le_left, Rat.abs_def', contDiffAt_abs, Real.ofCauchy_inf, Real.volume_interval, Real.Angle.eq_iff_abs_toReal_eq_of_sign_eq, ContinuousMap.coe_abs, Associated.abs_left, Complex.lim_re, HahnSeries.leadingCoeff_abs, negPart_add_posPart, Asymptotics.isBigO_abs_right, ZLattice.abs_repr_le, norm_jacobiTheta₂_term_fderiv_le, Asymptotics.isLittleO_abs_left, ZLattice.covolume_eq_det, NumberField.mixedEmbedding.normAtPlace_real, PowerSeries.IsRestricted.isRestricted_iff_abs, ModularForm.slash_apply, Mathlib.Meta.NormNum.isNat_abs_nonneg, Complex.angle_exp_exp, LinearOrderedAddCommGroup.tendsto_nhds, Int.natCast_natAbs, Real.abs_exp, Complex.lim_eq_lim_im_add_lim_re, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, MeasureTheory.Measure.integral_comp_inv_mul_right, MeasureTheory.BorelCantelli.process_difference_le, MeasureTheory.Measure.addHaar_smul, abs_two, ArithmeticFunction.abs_moebius, MeasureTheory.MemLp.abs, Orientation.abs_volumeForm_apply_le, UpperHalfPlane.petersson_slash, Real.map_volume_mul_left, MeasureTheory.Measure.addHaar_image_homothety, ModularGroup.coe_truncatedFundamentalDomain
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